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Wiley Encyclopedia of Electrical and Electronics Engineering Biomedical NMR Standard Article Z.-P. Liang1 and E. M. Haacke2 1University of Illinois at Urbana-Champaign, Urbana, IL 2Washington University, St. Louis, MO Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4701 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (432K)

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Abstract The sections in this article are Signal Generation and Characteristics Signal Localization Image Contrast Mechanisms Application Examples Conclusion About Wiley InterScience | About Wiley | Privacy | Terms & Conditions Copyright © 1999-2008John Wiley & Sons, Inc. All Rights Reserved.

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412

BIOMEDICAL NMR

independently by Edward Purcell’s group at Harvard (1) and Felix Bloch’s group at Stanford (2) in 1946. The fundamental MRI concept was proposed by Paul Lauterbur in 1973 (3). Since then, MRI has developed into a premier tool for biomedical imaging (4). Like many other tomographic imaging techniques (5), MRI can produce images of internal structures of an object. However, MRI is significantly different from other techniques in terms of the principles of signal generation, spatial encoding, and image contrast manipulation. This article provides an introductory description of these principles as well as some illustrative applications. For easy reference, the following is a partial list of symbols used in this article: B0 B1 Gx, Gy, Gz Br Gss 웆0 웆rf 웆1 i, j, k M Mx, My, Mz Mxy ⬅ Mx ⫹ iMy Mxy(0), Mz(0) Mz0 웂, 웂– ⫽ 웂/2앟 h, ប ⫽ h/2앟 kB I J ␮ T1 T2, T*2 , T** 2 Ns N앖, N앗 T E ⫽ 2␶ TR TI ␶p 움 S(t) ␳( ⭈ ) k, kx, ky, kz Ts Tpe

Static magnetic field Radio-frequency (RF) field Magnetic field gradients along the x, y, and z directions Receiver sensitivity Slice-select gradient Larmor frequency corresponding to the B0 field Excitation frequency of the RF field Frequency of nuclear precession about the B1 field Unit direction vectors of the x, y, and z axes Bulk magnetization vector Components of M Transverse component of M (in complex notation) Post-excitation value for Mxy and Mz Thermal equilibrium value of M Gyromagnetic ratio Planck’s constant Boltzmann’s constant Spin quantum number Angular momentum Magnetic moment vector Longitudinal relaxation time constant Transverse relaxation time constants Total number of spins in a sample Number of spins pointing up and down, respectively Echo time Repetition time in a multiple pulse sequence Inversion time Time duration of an RF pulse Flip angle Measured time signal Spin density function Spatial frequency variables Absolute temperature of a spin system Phase encoding interval

SIGNAL GENERATION AND CHARACTERISTICS

BIOMEDICAL NMR Magnetic resonance imaging (MRI) is a tomographic imaging technique based on the well-known nuclear magnetic resonance (NMR) phenomenon first observed in bulk materials

Generating magnetic resonance (MR) signals from a sample is the first step of the imaging process. This section discusses some of the fundamental physical concepts underlying MR signal generation.

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.

BIOMEDICAL NMR

Bulk Magnetization

413

B0

It is well known that atoms consist of a nucleus surrounded by one or more orbiting electrons. The nucleus is composed of one or more positively charged protons and sometimes some neutral particles called neutrons. Protons, neutrons, electrons, and other particles possess an intrinsic angular momentum J, known as spin. In the atomic nucleus, the spins of a pair of protons or neutrons often cancel each other out. As a result, only atomic nuclei with an odd number of protons and/or an odd number of neutrons have a net spin, known as nuclear spin (6). Since nuclei are charged particles, those with a nonzero nuclear spin produces a magnetic moment ␮ which is related to J by (6,7) µ = γJ

(1)

where 웂 is a physical constant called the gyromagnetic ratio. The gyromagnetic ratio is nucleus-dependent. For hydrogen, 웂 ⫽ 2.675 ⫻ 108 rad s⫺1 T⫺1 or 웂– ⫽ 웂/2앟 ⫽ 42.58 MHz/T. The nucleus of the hydrogen atom is the simplest in nature, consisting of just one proton and no neutron. Because hydrogen is the most common element found in the human body, proton MRI is widely used. A sample has a large number of nuclear spins. The collective magnetism of a sample is represented by a bulk magnetization vector M defined as

M=

Ns


µn

(2)

n=1

Figure 1. Distribution of nuclear magnetic moments in the presence of the B0 field for a spin-
 system.

µz = ±γ ~/2

(5)

which corresponds to two spin states: pointing up (parallel) or pointing down (anti-parallel), as illustrated in Fig. 1. The transverse component 애xy, however, points in a random direction. Second, 애 precesses about the B0 field, as described by the following equation of motion: µ dµ = γ µ × B0 dt

(6)

where Ns is the total number of spins. To further characterize M, it is necessary to know the behavior of ␮. Based on the quantum-mechanical model, the magnitude of ␮, often denoted as 애, is given by

The precessional frequency, known as the natural resonant frequency of a spin system, is given by the well-known Larmor equation:

√ µ = γ ~ I(I + 1)

ω0 = γ B0

(3)

where ប is Planck’s constant h (6.6 ⫻ 10⫺34 J ⭈ s) divided by 2앟 and I is the nuclear spin quantum number. The spin quantum number takes integer, half-integer, or zero values such that I ⫽ 0, 1/2, 1, 3/2, 5/2, . . .. For 1H, 13C, 19F, and 31P nuclei, I ⫽ 1/2, and such a spin system is called a spin-
 system. A nucleus is NMR-active only if I ⬆ 0. While the magnitude of ␮ is certain, its direction is randomized under the thermal equilibrium condition due to thermal random motion. Therefore, M ⫽ 0 in the absence of an external magnetic field. To activate nuclear magnetism from a sample, we need to place the sample in a strong external magnetic field, often referred to as the B0 field, which is produced by the main magnet in an MRI system. The behavior of ␮ in the presence of B0 is summarized as follows. First, the orientation of ␮ is quantized along the direction of the external field while its orthogonal component still points to a random direction (6,7). To see this more clearly, consider a spin-
 system and assume that B0 points along the z direction such that B 0 = B 0k

(4)

where k is the unit direction vector of the z axis. The z component of ␮ will take one of two possible values. That is,

(7)

Clearly, given a spin system, its resonant frequency is determined by the magnetic field that it experiences. A group of spins with the same resonant frequency is called an isochromat. Third, the population difference among different spin states is governed by the Boltzman distribution (6,7). Specifically, for a spin-
 system, we have N↑ = exp N↓


E  kB Ts

(8)

where N앖 and N앗 denote the number of spins pointing up and down, respectively, such that Ns ⫽ N앖 ⫹ N앗, ⌬E ⫽ 웂បB0 is the energy difference between the two spin states (E앗 ⫺ E앖), kB is the Boltzmann constant (1.38 ⫻ 10⫺23 J/K), and Ts is the absolute temperature of the spin system. Noting that M = (N↑ − N↓ )µz k

(9)

and replacing the exponential function in Eq. (8) by its firstorder approximation yields M=

γ 2 ~2 B0 Ns k 4kB Ts

(10)

414

BIOMEDICAL NMR

Two points are evident from the above equations. First, M points along the direction of the applied magnetic field. Second, the magnitude of M is directly proportional to the external magnetic field strength and the total number of spins (Ns). The value of Ns is characteristic of a sample being imaged and cannot be changed in general. The only controllable parameters are B0 and Ts. Therefore, for a given spin system, one can increase the magnitude of M by increasing B0 or decreasing Ts. Since MRI experiments are often carried out in human subjects, one is limited to increasing the magnitude of the applied magnetic field for an increase in the bulk magnetization. The optimal field strength for imaging is applicationdependent. For most clinical MRI systems, B0 ranges from 0.2 T to 2 T. RF Excitation The presence of a bulk magnetization does not directly imply the generation of a measurable NMR signal. In fact, M is basically unmeasurable because M appears to be stationary in the laboratory reference frame when it lies parallel to the B0 field. The next step in MR signal generation is, therefore, to tip it away from the z axis so that the torque of the B0 field exerted on M will force it to precess about the B0 field; consequently, the precessing M will induce an electrical signal in a receiver coil. Tipping M is accomplished by exciting the spin system with a time-varying magnetic field, known as the B1 field. A simple, circularly polarizing B1 field is given, in complex notation, by B1 (t) = B1,x (t) + iB1,y (t) = B1 e−iωrf t ,

0 ≤ t ≤ τp

(11)

where 웆rf is the excitation frequency and ␶p is the time duration for which the B1 field is turned on. In practice, 웆rf is chosen according to the so-called on-resonance condition that 웆rf ⫽ 웆0, and ␶p is selected based on the desired frequency content of the B1 field. Because 웆rf is in the RF range and ␶p is on the order of microseconds to milliseconds, the excitation B1 field is commonly called an RF pulse. The excitation effect of an RF pulse is conveniently described in the rotating reference frame (x⬘, y⬘, z⬘) (8,9), in which the transverse plane is precessing in the same fashion as the B1 field. In this frame, the B1 field appears to be a static field pointing along the x⬘ axis while the B0 field ‘‘vanishes.’’ Consequently, M precesses about the x⬘ axis at the Larmor frequency 웆1 ⫽ 웂B1, as illustrated in Fig. 2. The tip z′

z

angle between M and the z axis at the end of the pulse is α = γ B1 τ p

If 움 ⫽ 90⬚, such a pulse is called a 90⬚ pulse. Similarly, we have 180⬚ pulses or arbitrary 움-degree pulses. Free Precession and Relaxation After a magnetized spin system is perturbed from the equilibrium state by an RF pulse, the spin system will return to this state provided that the B1 field is removed and sufficient time is given. This process is characterized by a precession of M about the B0 field, called free precession; a recovery of the longitudinal magnetization (Mz), called longitudinal relaxation; and the destruction of the transverse magnetization (Mxy), called transverse relaxation. Both relaxation processes are often ascribed to the existence of time-dependent microscopic magnetic fields surrounding a nucleus due to the random thermal motion present in a sample, but the exact mechanisms by which these relaxation events occur for an arbitrary spin system are far too diverse and complex to be properly covered here. The interested reader is referred to Ref. 7. Phenomenologically, free precession and the relaxation processes are described by the Bloch equation (8) M k Mxi + M y j (Mz − Mz0 )k dM = γM × B − − dt T2 T1

 Mxy (t) = Mxy (0)e−t/T2 e−iω 0 t Mz (t) = Mz0 (1 − e−t/T1 ) + Mz (0)e−t/T1

M y′

(14)

where Mz0 is the thermal equilibrium value of M, which can be calculated from Eq. (10). Note that with this model, the longitudinal component grows exponentially with time constant T1, while the transverse component precesses about the B0 field at the Larmor frequency and decays exponentially with time constant T2. The electrical signal introduced in a receiver coil by the precessing M according to Faraday’s law of induction is expressed by (9)

ω1

y′

(13)

Expressing the transverse magnetization as Mxy ⫽ Mx ⫹ iMy and the pulse condition as Mxy ⫽ Mxy(0), Mz ⫽ Mz(0), and B ⫽ B0k, the solution to the Bloch equation is given by

S(t) = −

M

(12)

d dt

 B c (rr ) · M (rr, t) drr

(15)

object

where Bc(r) describes the sensitivity of the receiver coil at different points in space. Because the time derivative of the longitudinal component Mz is much less than that of the transverse component Mxy, one often treats Mxy(t) as the measured signal with the omission of various weighting factors.

B1(t)

Signal Characteristics

B1 x′

x′ (a)

(b)

Figure 2. Precession of M in the presence of a rotating RF field as observed in (a) the rotating frame and (b) the laboratory frame.

The transient electrical signal observed from a spin system immediately after a pulse excitation is called a free induction decay (FID) signal. Ignoring various nonessential weighting factors, an FID signal generated by an 움-degree pulse can be expressed as

BIOMEDICAL NMR

z′

z′

y′

y′ s f

x′

90°

x′

t=0 (a)

t = τ– (b)

z′

z′ f y′

x′

x′

t = 2τ (c)

s

180° y′

t = τ+ (d)

Figure 3. Vector diagram illustrating the refocusing of isochromats in a spin-echo experiment.

 S(t) = sin α

∞ −∞

ρ(ω)e−t/T2 (ω) e−iωt dω,

t≥0

(16)

where ␳(웆) is known as the spectral density function such that M ⫽ 兰 ␳(웆) d웆. A characteristic of an FID signal is that it is a decaying signal, whose decay rate is strongly tied to the underlying spectral distribution. In the idealized case of a single spectral component, the FID signal bears a characteristic T2 decay. This is the case when both the sample and the external magnetic field to which the sample is exposed are perfectly homogeneous. When the magnetic field is inhomogeneous, the FID signal decays at a much faster rate, characterized by a new time constant T*2 . Specifically, if the field inhomogeneity lends itself to a Lorentzian distribution with fullwidth half-maximum ⌬B0, we have 1 1 = + γ B0 T2∗ T2

415

tively faster than the other, they progressively lose phase coherence as the free precession continues. After a time interval ␶, the two vectors fan out in the transverse plane by a phase angle (웆f ⫺ 웆s)␶ as shown in Fig. 3(b). At this point, the 180⬚ pulse is applied along the y⬘ axis, which flips the two vectors over to the other side of the transverse plane as shown in Fig. 3(c). As a consequence, the faster vector is now lagging behind the slower by the same phase angle with which it was leading the slower prior to the 180⬚ pulse. Since both vectors will continue to precess clockwise at angular frequencies 웆f and 웆s (assuming that the magnetic field inhomogeneity is time-invariant), the faster isochromat will ‘‘catch’’ the slower one after a time interval ␶, thus recreating a phase coherence between the two vectors at time t ⫽ 2␶ as shown in Fig. 3(d). Although Fig. 3 shows the situation with only two isochromats, the analysis can be extended to the general case. In fact, because of the existence of a large number of isochromats in a real sample, a total dephasing normally occurs by the time the 180⬚ pulse is applied. This means that the transverse magnetization Mxy completely vanishes and the FID signal disappears when the 180⬚ pulse is applied. After the 180⬚ pulse, Mxy grows gradually and reaches the maximum value at t ⫽ 2␶, which is often called the echo time TE. If we ignore the T2 relaxation, the mechanism responsible for the loss of the phase coherence among the isochromats during the free precession period before the 180⬚ is the same as that responsible for the recovery of the phase coherence after the pulse. Therefore, Mxy as a function of time possesses the following property: |Mxy (τ − t)| = |Mxy (τ + t)|,

0≤t ≤τ

(18)

In other words, 兩Mxy(t)兩 has a mirror symmetry about the time axis t ⫽ ␶. For t ⬎ ␶, Mxy(t) is a recalled transverse magnetization of which the rephasing part (␶ ⬍ t ⬍ 2␶) is responsible for one side of the echo signal and the subsequent dephasing part (t ⬎ 2␶) responsible for the other side of the echo. In practice, the echo suffers a T2 decay, as shown in Fig. 4, and

180° 90°

(17)

Another form of MR signal is known as echo. A distinct difference between an echo and an FID signal is that an echo is ‘‘two-sided,’’ with one side from the refocusing phase of a transverse magnetization and the other side from the dephasing phase. One type of echo signal, known as spin echo or RF echo, is generated by applying multiple RF pulses (10). A simple example is the two-pulse excitation scheme consisting of a 90⬚ pulse followed by a time delay ␶, then a 180⬚ pulse. Assume that the 90⬚ pulse is applied along the x⬘ axis and the 180⬚ is applied along the y⬘ axis and, further, that the sample has two isochromats with precessional frequencies 웆s (slow) and 웆f (fast) in the rotating frame. Ignoring any off-resonance effects, the 90⬚ pulse rotates both magnetization vectors onto the y⬘ axis, as shown in Fig. 3(a). After the pulse, these vectors precess about the z axis. Since one is precessing rela-

RF

τ

τ

e–t/T2 ∗

e–t/T2 Signal

Figure 4. Formation of a spin-echo signal by a 90⬚– ␶ –180⬚ sequence. Note that the FID signal quickly disappears as the spins dephase, and the echo signal formed after the 180⬚ pulse carries a T2 weighting.

416

BIOMEDICAL NMR

180°y

90°x RF

180°–y

τ

180°y



2τ ∗

ent x positions will acquire different phases in the rotating frame, which can be expressed as t

φ(x, t) = γ

−Gx x dτ = −γ Gx xt,

0≤t ≤τ

(19)

0

e–t/T2

e–t/T2 Signal

Figure 5. Formation of a train of spin echoes by multiple 180⬚ pulses. Note that the 90⬚ pulse is applied along the x⬘ axis and the subsequent refocusing 180⬚ pulses are applied alternatively along the ⫾y⬘ axis as the subscripts indicate.

consequently the echo amplitude carries a characteristic T2 weighting factor e⫺TE /T2. When a spin system is excited by a 90⬚ pulse followed by a sequence of 180⬚ pulses, a train of spin echoes will be generated, as shown in Fig. 5. Suppose that the 90⬚ pulse is applied at t ⫽ 0 and that the 180⬚ pulses are applied at (2n ⫺ 1)␶ for n ⫽ 1, 2, . . ., N. There will be a train of N echoes formed at t ⫽ 2n␶, and the echo amplitudes are weighted by e⫺2n␶ /T2. Specifically, if we assume that the 90⬚ pulse is applied along the x⬘ axis and the subsequent refocusing 180⬚ pulses are applied alternatively along the ⫾y⬘ axis (11), the resulting signal is known as the Carr–Purcell–Meiboom–Gill (CPMG) echo train. The phase shifts between the pulses are used in this pulse sequence to reduce the effect of practical imperfections in RF pulses. Another form of echo signal frequently used in MRI is generated using time-varying gradient magnetic fields. Such an echo is called a gradient echo to distinguish it from a spin echo. The key concept underlying gradient-echo formation is that a gradient field can dephase and rephase the transverse magnetization in a controlled fashion so that one or multiple echo signals can be created. For simplicity, consider the pulse sequence in Fig. 6 in which a negative x gradient is turned on after the application of an 움-degree RF pulse. It is easy to show that spins in differ-

Clearly, the loss of spin phase coherence becomes progressively greater as time elapses after the excitation pulse. The resulting signal decay is sometimes characterized by a new time constant T** 2 . After a time ␶ ⬎ 3T** 2 , the signal decays effectively to zero; but at this point, if a positive gradient of the same strength is applied, the transverse magnetization components will gradually rephase, resulting in a regrowth of the signal. Specifically, the spin phase function is now given by

 φ(x, t) = −γ Gx xτ + γ

t τ

Gx x dt

= −γ Gx xτ + γ Gx x(t − τ ),

(20) τ ≤ t ≤ 2τ

It is evident that the phase dispersal introduced by the negative gradient is gradually reduced over time after the positive gradient is turned on at t ⫽ ␶. After a time ␶, the spin phase ␾ is zero for any x value, which means that all the spins have rephased and an echo signal is formed. Note that it is not necessary to set the magnitude of the refocusing gradient to be identical to that of the dephasing gradient. If a different refocusing gradient is used, the echo time will be changed accordingly. Another point worth noting is that, in contrast to spin-echo signals, gradient-echo signals carry a characteristic T*2 decay because the phase dispersal term due to main field inhomogeneities cannot be refocused by gradient reversal. SIGNAL LOCALIZATION An important concept in MR signal localization is the use of magnetic field gradients. Consider the simple case that a linear gradient field is introduced along the x direction. The overall field become B(x) = B0 (x) + Gx x

(21)

and the Larmor frequency as a function of position becomes

α

ω(x) = ω0 (x) + γ Gx x

RF

(22)

This simple relationship is the basis of MR signal localization.

Gradient

Slice Selection ∗

e–t/T2 ∗∗

e–t/T2 Signal

Figure 6. Formation of a gradient echo. Note that after the 움-degree pulse, a negative gradient is turned on to dephase the spins, which is followed by a positive gradient to rephase the spins, thus generating an echo signal.

Slice selection is accomplished through the use of a shaped RF pulse and a slice-select gradient. To make an RF pulse spatially selective, it is necessary to make the spin resonant frequency position dependent or, most desirably, linearly varying along the slice-select direction. An obvious way to accomplish this is to augment the homogeneous B0 field with a linear gradient field. For example, if a gradient is applied in the z direction with an amplitude Gz, a slice of thickness ⌬z centered about the origin will have frequencies ranging from ⫺웂– Gz⌬z/2 ⫹ 웆0 to 웂– Gz⌬z/2 ⫹ 웆0. Consequently, an RF pulse with the finite frequency bandwidth ⌬웆 ⫽ 웂– Gz⌬z centered about 웆0 will just excite spins within this slice.

BIOMEDICAL NMR

z

pendent on its spatial origin. The physical principle used to realize this is rather simple. Consider first an idealized onedimensional object with spin density distribution ␳(x). If the magnetic field that the object sees after an excitation pulse is the homogeneous B0 field plus another linear gradient field (Gxx), the Larmor frequency at position x is given in Eq. (22). Correspondingly, the signal generated locally from spins in an infinitesimal interval dx at point x, with the omission of the transverse relaxation effect, can be written as

s

∆s

θ

s0

dS(x, t) ∝ ρ(x) dxe−iγ (B 0 +G x x)t

y

φ

Figure 7. Parameters for characterizing a slice of arbitrary orientation.

One approach to design such a pulse is to extend the simple RF pulse in Eq. (11) to have a more general amplitude function such that B1 (t) = Be1 (t)e−iωrf t

(23)

A popular example is the sinc pulse in which 웆rf ⫽ 웆0, and 0 ≤ t ≤ τp

(24)

More sophisticated pulses can be found in Ref. 12 and references therein. To select a slice in an arbitrary direction and location as shown in Fig. 7, we need to turn on gradients in all three directions. Specifically, representing the slice-select gradient as G ss = (Gx , Gy , Gz )

(25)

the required gradient along each spatial direction is

Gx = Gss sin θ cos φ Gy = Gss sin θ sin φ

(26)

Gz = Gss cos θ Correspondingly, the excitation frequency (웆rf) and bandwidth (⌬웆) for the RF pulse are ωrf = ω0 + γ Gss s0 ω = γ Gss s

(28)

where the constant of proportionality is dependent on the flip angle, B0, and so on. For notational convenience, we shall neglect this scaling constant and rewrite Eq. (28) as

x

Be1 (t) = A sinc[ω(t − τ p /2)],

417

(27)

It is clear that one can position the selected slice at will by adjusting the relative values of Gx, Gy, Gz, and the RF pulse. Frequency-Encoding and Phase-Encoding After a signal is generated from a region of interest, spatial information has to be encoded into the signal during the free precession period for image formation. Since an MR signal is in the form of a complex exponential, we have essentially two ways to encode spatial information: frequency-encoding and phase-encoding. Frequency encoding, as the name implies, makes the oscillating frequency of an MR signal linearly de-

dS(x, t) = ρ(x) dxe−iγ (B 0 +G x x)t

(29)

The signal in Eq. (29) is said to be frequency-encoded since its oscillating frequency 웆(x) ⫽ 웂(B0 ⫹ Gxx) is linearly related to the spatial location. For the same reason, Gx is called a frequency-encoding gradient. The total signal received from the entire object in the presence of this gradient is   ∞ S(t) = dS(x, t) = ρ(x)e−iγ (B 0 +G x x)t dx object −∞ (30)  ∞ ρ(x)e−iγ G x xt dxe−iω 0 t = −∞

After demodulation (i.e., removal of the carrier signal e⫺i웆0t), we have  ∞ S(t) = ρ(x)e−iγ G x xt dx (31) −∞

Phase-encoding is done in a similar fashion. Specifically, if we turn on a gradient Gx only for a short interval Tpe after an RF pulse, the local signal under the influence of this gradient is  ρ(x)e−iγ (B 0 +G x x)t 0 ≤ t ≤ Tpe dS(x, t) = (32) ρ(x)e−iγ G x xT pe e−iγ B 0 t , t ≥ Tpe It is evident that during the interval 0 ⱕ t ⱕ Tpe, the local signal is frequency-encoded. As a result of this frequency-encoding, signals from different x positions accumulate different phase angles after a time interval Tpe. Therefore, if we use the first time interval as a preparatory period, the signal collected afterward will bear an initial phase angle φ(x) = −γ Gx xTpe

(33)

Since ␾(x) is linearly related to the signal location x, the signal is referred to as being phase-encoded, with Gx being the phase-encoding gradient and Tpe being the phase-encoding interval. A useful insight is gained using a k-space interpretation of frequency-encoded or phase-encoded signals (13). Specifically, for the frequency-encoded signal given in Eq. (31), a simple variable substitution kx = − γ Gx t

(34)

418

RF

BIOMEDICAL NMR

90°

180°

Gz

t t

Gy

t

Gx Signal

RF

ky

kx

t t TE/2

180°

Gz

t t

Gy

t

Gx

t

Signal

TE

90°

ky

kx

t TE/2 TE

(a)

(b)

(a)

Figure 8. (a) Representative 2-D Fourier imaging pulse sequence with hybrid phase and frequency-encodings and (b) its corresponding k-space sampling trajectories.

will yield the following Fourier transform relationship (14):  S(kx ) =

∞ −∞

ρ(x)e−i2π k x x dx

(35)

In the case of phase-encoding, the same equation is obtained with the following mapping relationship: kx = − γ Gx Tpe

(36)

(b)

Figure 9. (a) Representative pulse sequence with 2-D frequency-encoding and (b) its corresponding k-space sampling trajectories.

imaging scheme is commonly known as the phase-encoding method because different time signals are phase-encoded. Figure 9(a) shows another 2-D imaging scheme. In this scheme, each spin-echo signal is frequency-encoded by a pair of gradients: Gn,x ⫽ G cos ␾n and Gn,y ⫽ G sin ␾n. The resulting k-space signals are given by

 S(k cos φn , k sin φn ) =

∞ −∞



∞ −∞

ρ(x, y)e−i2π k(x cos φ n +y sin φ n ) dx dy (39)

Therefore, the role of frequency-encoding or phase encoding is to map a time signal to a k-space signal. What distinguishes frequency-encoding from phase-encoding are the values that k takes. In the former case, k is a continuous function of time; but in the latter case, k is varied by changing G [or Tpe, as was done in the earlier days (15)]. Multidimensional Imaging With the above localization principles, it is easy to understand how multidimensional MR imaging is done. Consider the excitation sequence shown in Fig. 8(a), which generates a set of spin-echo signals by repeatedly exciting the object with a pair of slice-selective 90⬚ and 180⬚ pulses (one period is shown in the figure). Each spin-echo signal is first phase-encoded with a variable Gy (16) and then frequency-encoded by Gx. It is easy to show that the imaging equation for this excitation scheme is in the form of a two-dimensional (2-D) Fourier transform (17):  S(kx , ky ) =



∞ −∞

∞ −∞

ρ(x, y)e−i2π (k x x+k y y) dx dy

(37)

where φn = arctan


G  n,y

(40)

Gn,x

Therefore, each spin-echo signal is mapped to a line which runs through the origin of k space. By appropriately changing the relative strengths of the frequency-encoding gradients, one can effectively cover k space with a set of such time signals, as shown in Fig. 9(b). This 2-D frequency-encoding method is sometimes referred to as a projection-reconstruction imaging method because each data line corresponds to a projection of the underlying object according to the wellknown projection-slice theorem. To demonstrate the flexibility with data acquisition in MRI, Figs. 10(a) and 11(a) show two fast imaging sequences (18). The first is known as the echo-planar imaging (EPI) sequence (19), which acquires multiple raster lines per excitation using a fast switching gradient to form a number of gradient echoes. The second sequence samples k space in a spiral fashion through the use of time-varying gradients (20,21).

where



kx = − γ Gx t ky = − γ Gy Tpe

(38)

90°

180°

kx

RF CSS

For this excitation scheme, ky is a constant during the life span of each spin-echo signal. Therefore, each signal is mapped to a horizontal line parallel to the kx axis. For different signals, ky is changed so that each line assumes different locations along the ky axis. As a result, rectilinear sampling of k space, as shown in Fig. 8(b), is achieved with this hybrid phase and frequency-encoding scheme. In the literature, this

Gy

kx

Gx Figure 10. (a) Representative echo-planar imaging sequence and (b) its k-space sampling trajectory.

BIOMEDICAL NMR

The above concepts can be extended to three-dimensional (3-D) imaging. In practice, 3-D imaging can be performed in two different modes: multislice 2-D imaging or true 3-D imaging. Although true 3-D imaging differs from multislice 2-D imaging in terms of imaging time and signal-to-noise ratio (22), the fundamental concepts for signal generation and spatial information encoding are the same. Specifically, in the former case, slice-selective pulses are used for signal generation followed by 2-D spatial information encodings. In the latter case, nonselective pulses are used to activate signal from a 3-D volume followed by spatial information encoding along all three spatial directions. Image Reconstruction Image reconstruction in MRI is based on two basic computational algorithms: the Fourier reconstruction algorithm and the filtered backprojection reconstruction algorithm. If k space is sampled rectilinearly, the Fourier reconstruction algorithm is used. Otherwise, filtered backprojection reconstruction is used if k space is sampled radially. For other types of k-space coverage, data interpolation is often first performed to convert the data to one of the above two types, followed by Fourier or backprojection reconstruction. Fourier Reconstruction. Because the Fourier transform is separable, multidimensional Fourier reconstruction is implemented as cascaded 1D processing. The basic Fourier reconstruction formula is

ρ(x) = k

Figure 12. Illustration of the truncation artifact with Fourier reconstruction. Both images were reconstructed with 256 samples along the horizontal direction but along the vertical direction with (a) 256 samples and (b) 64 samples.

In addition, ␳(x) suffers from a characteristic Gibbs ringing artifact when sharp edges are present in the object (23). This artifact manifests itself as spurious ringing around sharp edges and propagates through the entire image, as illustrated in Fig. 12. Filtered Backprojection Reconstruction. The filtered backprojection algorithm consists of two major steps (24–26). The first step filters and Fourier transforms the k-space data along the radial direction. The second step backprojects the filtered projections obtained from the first step. In the 2-D case, the first step is described by 

N/2−1


S(nk)ei2π nkx

P(r, φ) =

(41)

k < 1/Wx

x =

1 Nk

(43)



π

ρ(x, y) =

P(x cos φ + y sin φ, φ) dφ

(45)

Note that the backprojection operator, as its name implies, assigns the value of any point in P(r, ␾) to the pixels on a line defined by r ⫽ x cos ␾ ⫹ y sin ␾. This operation is the opposite of the projection operation. Similar to Eqs. (44) and (45), the 3-D backprojection reconstruction algorithm is described by the following two equations:  P(r, θ, φ) =

RF GSS

(44)

0

ky

α°

|k|S p (k, φ)e−i2π kr dk

where Sp(k, ␾) represents the k-space data in polar form such that Sp(k, ␾) ⬅ S(k cos ␾, k sin ␾), and P(r, ␾) is a filtered projection of the underlying object function ␳(x, y) at an angle ␾ relative to the x axis. The subsequent step is to backproject P(r, ␾) to yield the desired image ␳(x, y):

(42)

where Wx is the object width along the x direction. The image function ␳(x) obtained from Eq. (41) will not be identical to the true image function desired because the Fourier series is truncated to N terms. As a result, the spatial resolution of ␳(x) is limited to

∞ −∞

n=−N/2

where N is the total number of data points measured and ⌬k is the sampling interval. To avoid the aliasing artifact, ⌬k must satisfy the well-known Nyquist criterion, which states that

419

∞ −∞

k2 S p (k, θ, φ)e−i2π kr dk

(46)

and

Gy

kx



2π



π

ρ(x, y, z) = 0

Gx

P(x sin θ cos φ + y sin θ sin φ

0

(47)

+ z cos θ, θ, φ) sin θ dθdφ (a)

(b)

Figure 11. (a) Representative spiral imaging sequence and (b) its kspace sampling trajectory.

In practical implementation, the above equations are discretized. In addition, to minimize noise amplification by the high-pass filters 兩k兩 or k2, other more practical filter functions

420

BIOMEDICAL NMR

90° 180°

before the nth pulse is given by

90° 180°

Mz(n) (90◦ −) = Mz0 (1 − e−TR /T1 ) + Mz(n−1) (90◦ +)e−TR /T1 ,

(48)

where n ⬎ 1. For this excitation sequence, it is usually assumed that Mz(n) (90◦ +) = 0,

n≥1

(49)

which is known as the saturation condition. Equation (48) can then be written as TE

TR

TE

TR

Mz(n) (90◦ −) = Mz0 (1 − e−TR /T1 ),

Figure 13. Representative saturation-recovery spin-echo sequence.

are also often used. The 3-D filtered backprojection algorithm can be implemented in a two-stage fashion. At each stage, 2-D filtered backprojection is performed. Detailed discussion can be found in Refs. 27 and 28. IMAGE CONTRAST MECHANISMS

(50)

which means that the spin system reaches a ‘‘steady state’’ by the time the second 90⬚ pulse is applied. For this reason, the first 90⬚ pulse is sometimes called the preparatory pulse and the corresponding signal is often discarded. From Eq. (50), we obtain (n) Mxy (90◦ +) = Mz0 (1 − e−TR /T1 ),

n>1

(51)

and the amplitude of the spin-echo signal becomes

Image contrast is an important imaging parameter. Good image contrast is useful not only for a clear definition of anatomical structures but also for differentiation between normal and diseased tissues. The MR image pixel value is, in general, dependent on a host of intrinsic parameters including the nuclear spin density ␳, the spin-lattice relaxation time T1, the spin–spin relaxation time T2, molecular motions (such as diffusion and perfusion), susceptibility effects, and chemical shift differences. The imaging effects of these parameters can be suppressed or enhanced in a specific experiment by another set of operator-selectable imaging parameters, such as repetition time (TR), echo time (TE), flip angle (움), and so on. If the data acquisition parameters are chosen such that the T1 effect is dominant, the resulting image is said to carry a T1 contrast or T1 weighting. Similarly, we have spin density contrast or T2 contrast. To see this, we consider the saturation-recovery spin-echo sequence consisting of a string of equally spaced 90⬚– ␶ –180⬚ pulses as illustrated in Fig. 13. The time interval between two successive 90⬚ pulses is called the repetition time (TR). Based on the relaxation behavior described in Eq. (14), the longitudinal magnetization after the (n⫺1)th pulse but just

180°

Figure 14. Representative inversion-recovery spin-echo sequence.

n≥2

90°

TI

Aecho = Mz0 (1 − 2e−(TR −TE /2)/T1 + e−TR /T1 )e−TE /T2

In practice, TE Ⰶ TR and the above expression can be simplified to Aecho = Mz0 (1 − e−TR /T1 )e−TE /T2

(53)

The signal expression in Eq. (53) indicates that the image intensity of this excitation sequence carries simultaneously a T1 weighting, a T2 weighting, and a spin-density weighting. However, one can selectively emphasize one of these weightings by properly choosing the sequence parameter TR and TE. For instance, if a short TE is used, the term exp(⫺TE /T2) approaches 1 and the T2-weighting factor can then be ignored. Similarly, if a long TR is used, the T1-weighting factor will drop out. The above discussion can be extended to the inversion-recovery spin-echo sequence shown in Fig. 14. Correspondingly to Eq. (53), one can derive for the inversion-recovery sequence that Aecho = Mz0 (1 − 2e−TI /T1 + e−TR /T1 )e−TE /T2

180°

180°

90°

180°

TI TR

(52)

TE

(54)

BIOMEDICAL NMR

421

Figure 16. Transaxial head images obtained from the same physical location as in Fig. 15. Two different echo times were used: TE ⫽ 20 ms in (a) and TE ⫽ 80 ms in (b), with the same TR ⫽ 2000 ms. Image (a) is heavily proton-density-weighted, while image (b) is T2-weighted.

suming that TR Ⰷ T2 such that Mxy(TR) ⫽ 0, one can shown that the echo amplitude, after dynamic equilibrium is reached, is given by

Figure 15. Transaxial head images as a function of TR: (a) TR ⫽ 250 ms, (b) TR ⫽ 500 ms, (c) TR ⫽ 1000 ms, and (d) TR ⫽ 2000 ms. The shorter TR images are heavily T1-weighted, while the long TR image is more proton-density-weighted. Note that the contrast between the white matter and gray matter reverses from the shortest to the longest TR.

which indicates that this sequence can generate T1-weighted, T2-weighted, and spin-density-weighted contrast as does the saturation-recovery spin-echo sequence. In contrast to the saturation-recovery sequence, we now have two sequence parameters, TI and TR, to adjust for optimal T1 contrast. Specifically, by properly choosing the inversion time interval, one can force some tissue components to take on negative or even zero intensities. For example, if TI is set to the value TI = [ln 2 − ln(1 + e−TR /T1 )]T1

Aecho =

∗ Mz0 (1 − e−TR /T1 ) sin αe−TE /T2 1 − cos αe−TR /T1

Equation (57) clearly shows that the image intensity from this gradient-echo sequence carries both T1 and T*2 weightings. The T*2 -weighting factor is characteristic of a gradient-echo sequence, and it is controllable by adjusting the echo time TE. This is similar to the way in which the T2 contrast is adjusted in a spin-echo imaging sequence. However, in contrast to that in a spin-echo sequence, the T1 contrast in the gradient-echo sequence is dependent on both the flip angle 움 and the repetition time TR. Specifically, when 움 is small, cos 움 앒 1 and consequently the T1-weighting factor is eliminated. As the flip angle is increased for a given TR, the T1-weighting factor becomes more significant. To further illustrate this concept, a set of brain images acquired with differ-

(55)

then

α ° Pulse

1 − 2e

−TI /T1

+e

−TR /T1

=0

α ° Pulse

(56)

and the corresponding tissue component will be nulled. This is known as the signal-nulling effect. To illustrate the concept of tissue contrast as a function of data acquisition parameters, two sets of axial head images, acquired using a saturation-recovery spin-echo sequence with different T1 and T2-weightings, are shown in Figs. 15 and 16. The imaging parameteres were field of view (FOV): FOVx ⫽ 256 mm and FOVy ⫽ 192 mm, and number of encodings: Nx ⫽ 256 and Ny ⫽ 192. One can appreciate the image appearance changes due to different acquisition parameters. As a final example, we consider the contrast behavior of a basic gradient-echo imaging sequence shown in Fig. 17. As-

(57)

TE

TE TR

Figure 17. Generic gradient-echo imaging sequence.

422

BIOMEDICAL NMR

Figure 19. One slice from a 128-slice 3-D TOF acquisition is shown in (a). The image in (b) was created by performing a maximum intensity projection (MIP) operation through 64 slices, which picks out the peak signal along any ray in the viewing direction. As can be seen, the arterial blood is clearly visible for the major vessels in the brain. The imaging parameters used were TR ⫽ 35 ms, TE ⫽ 6 ms, flip angle 움 ⫽ 25⬚, and a resolution of 0.28 ⫻ 0.28 ⫻ 1 mm3. (Images courtesy of Ramesh Venkatesan.) Figure 18. Brain images acquired using a gradient-echo sequence (TR ⫽ 25 ms, TE ⫽ 4.75 ms) with different flip angles: (a) 움 ⫽ 2⬚, (b) 움 ⫽ 5⬚, (c) 움 ⫽ 10⬚, (d) 움 ⫽ 20⬚, (e) 움 ⫽ 40⬚, and (f) 움 ⫽ 60⬚. Note that at small flip angles the images show the characteristics of proton density weighting, whereas at larger flip angles the T1 weighting becomes dominant. Each of these images is acquired from a 3D data set with Nx ⫽ 512, Ny ⫽ 512, Nz ⫽ 80, FOVx ⫽ 256 mm, FOVy ⫽ 256 mm, and FOVz ⫽ 160 mm. The image in (a) was obtained by averaging two slices to improve SNR. (Images courtesy of Ramesh Venkatesan.)

ent flip angles is shown in Fig. 18. As can be seen, at small flip angles the images show mainly the proton density distribution with cerebral spinal fluid having the highest intensity, followed by gray matter and white matter. At larger flip angles, the images become T1-weighted. APPLICATION EXAMPLES MR imaging is a very flexible technique. It has been used for both anatomical and functional imaging applications. This section gives the reader a sampling of some of these applications by looking at 3-D magnetic resonance angiography, cardiovascular imaging, and functional brain imaging.

sion in the previous sections. Imagine a thin slab of tissue which is excited and through which blood flows orthogonally to the imaging plane. If the distance the blood travels is greater than the slice thickness, then the blood that is present for a given RF pulse has never seen the previous pulse, and hence its signal is not saturated. For thicker slices, this analogy will not be completely true, but for 3-D imaging, the slices near the incoming edge of the excited slab will have the brightest blood and the slices on the far side will have the darkest blood. For fast-flowing blood in vessels like arteries, even slabs 5 cm thick still reveal blood brighter than the background tissue. The blood in the veins, on the other hand, has traveled through the region of interest as arterial blood and is usually naturally saturated. This TOF approach is demonstrated in Fig. 19(a), where blood is seen to be bright on a single image from a 3-D data set, and in Fig. 19(b), where the entire 3-D data set is projected onto a single viewing plane. TOF MRA is very dependent on the actual flow rate; and although it is very commonly used and often very good, it can lead to saturation of blood. The use of a T1 reducing contrast agent can eliminate this dependence on flow because T1 of all blood is dramatically reduced, making the signal bright on short TR, T1-weighted im-

MR Angiography The method of data acquisition described so far is for stationary spins. MR signals are known to be sensitive to flow. MR angiography (MRA) is a technique to exploit this property to image vascular structures and/or measure flow (29). Two distinct types of flow effects have been used for MRA: time-offlight effects (spin motion between RF pulses) and phase effects (spin motion in the presence of a gradient field), which are discussed next. Time-of-Flight MRA. Time-of-flight (TOF) MRA is a popular clinical method to image blood flow. This method uses the motion of the blood to enhance its signal. Consider the mechanism of how the signal is generated in an MRI experiment. The local spins being imaged experience multiple RF pulses, one for each phase encoding step. These pulses lead to a suppression of the signal, as can be understood from the discus-

Figure 20. Saturation of blood in TOF methods can still cause some ambiguities in the clinical interpretation of MRA data. For this reason, a contrast agent is often used to enhance the signal from the blood. A 3-D MIP over 64 slices in the same volume, as in Fig. 19, shows the enhancement of all vessels. A larger-than-usual flip angle (25⬚) was used because of the short TR the blood has inherited. (Images courtesy of Ramesh Venkatesan.)

BIOMEDICAL NMR

Figure 21. Phase contrast MRA images through the vessels in the thorax show how well background tissue is eliminated and the flow information in the vessels is illuminated at any given point in the cardiac cycle. The bright vessel is the aorta. Shown here are (a) the magnitude image and (b) the phase image. The data were acquired with a five-segment cardiac-gated data set using TR ⫽ 21.2 ms. This means that a flow image is available every 106 ms in the cardiac cycle. The imaging parameters were TE ⫽ 5 ms, 움 ⫽ 30⬚, FOVx ⫽ FOVy ⫽ 256 mm, Nx ⫽ 256, Ny ⫽ 128, and slice thickness ⌬z ⫽ 6 mm. (Images courtesy of Debiao Li.)

ages (see Fig. 20) and independent of its flow characteristics. For this reason, this new 3-D method is likely to prove the most reliable. Phase Contrast MRA. Phase contrast MRA is based on the phase change that the transverse magnetization of moving

423

spins experience relative to that of their stationary counterparts. To understand this effect, consider the phase accumulation of stationary spins and moving spins in the presence of a gradient Gx. It is easy to show that stationary spins at location x accumulate a phase ␾ ⫽ 웆t ⫽ 웂Gxxt, while spins moving at velocity v along the gradient direction will accumulate a bigger phase ␾ ⫽ 웂G(xt ⫹ vt2 /2). Hence, moving spins can be recognized on the basis of the extra phase shift that they accumulate. How much spins have dephased during the data acquisition window is dependent on the readout gradient as a function of time. For example, it is possible to design the gradient waveform such that its nth-order moments are zero at the peak of the echo signal. That is,  n t Gx (t) dt = 0, n = 0, 1, . . . (58) These are called flow-compensation conditions, and in practice we are usually concerned with the zeroth and first moments. Specifically, if the first moment is not zero, spins with various velocities across a vessel lumen dephase, and little or no signal from the blood appears in the image. For phase contrast MRA, two data sets are often acquired, one with and one without a flow-encoding gradients. Complex subtraction of the two data sets will then give an image of the vascular tissues ‘‘free’’ of the stationary background structures. An example of flow in the aorta and vena cava is shown in Fig. 21.

Figure 22. Cine imaging is a means to visualize cardiac motion during the cardiac cycle. In this figure, a series of four images is extracted from a total of 12 images acquired during the cardiac cycle with TR ⫽ 60 ms. A five-segment breath-hold method was used with cardiac gating. The imaging parameters were TE ⫽ 5 ms, 움 ⫽ 20⬚, FOVx ⫽ FOVy ⫽ 350 mm, Nx ⫽ 256, Ny ⫽ 128, and 8 mm slice thickness. (Images courtesy of Debiao Li.)

424

BIOMEDICAL NMR

Figure 23. Images of the coronary artery. (a) A 2-D data set of the left main coronary vessel. (b–d) Three adjacent slices from a 3-D data set. The imaging parameters for the 2-D experiment were TE ⫽ 6.2 ms, TR ⫽ 6.2 ms, FOVx ⫽ 300 mm, FOVy ⫽ 225 mm, Nx ⫽ 256, Ny ⫽ 110, and 4 mm slice thickness. The imaging parameters for the 3-D parameters were TE ⫽ 2.7 ms, TR ⫽ 8 ms, FOVx ⫽ 300 mm, FOVy ⫽ 225 mm, Nx ⫽ 256, Ny ⫽ 96, and 2 mm slice thickness. (Images courtesy of Jie Zheng.)

Cardiovascular Imaging MRI is becoming an important tool for studying cardiac function and diagnosing cardiovascular diseases (30). Using flowcompensated gradient-echo imaging sequences and cardiac gating, it is now possible to obtain dynamic images from a beating heart with high spatial and temporal resolution. These images are often viewed in cine format to visualize the global cardiac motion, thus the name cine imaging. An example of cine cardiac imaging is illustrated in Fig. 22, in which a series of four images from a cine set is shown. Fast imaging has also been extended along with the above mentioned MRA capabilities to create images of the coronary arteries using either fast 2-D breath-hold or fast 3-D imaging techniques. Figure 23(a) shows an example of a 2-D breathhold image of a section of the heart containing the left coronary artery. Figure 23(b–d) shows three slices from a 3-D data set showing the same vessel. One of the advantages of using a 3-D method is that a series of thin contiguous slices can be acquired. Another advantage is that when the region of interest is not exactly in plane, it is possible to reformat the data so that it appears as if it is in plane (this processing is referred to as multiplanar reconstruction). Functional Brain Imaging Functional MRI (fMRI) is a class of new techniques developed in the last few years to image MR signal changes related to neuronal activity (31). Since changes in neuronal activity are

accompanied by local changes in cerebral blood flow (CBF), blood volume (CBV), blood oxygenation, and metabolism, various pulse sequences have been developed to capture these physiological changes in MR signals to produce what are called functional maps of cognitive tasks (32). The original Science article (31) on fMRI showed functional maps acquired in the presence of a contrast agent. More recent methods exploit blood-oxygenation-level-dependent (BOLD) signal changes (33,34). It is known that venous blood has a different local magnetic field than arterial blood because it has a higher concentration of deoxyhemoglobin, which is paramagnetic. This difference can be captured in complex gradient-echo images whose phase is directly proportional to the local magnetic field. Figure 24 shows an example of fMRI with a simple mental task—that is, moving the fingers of the right hand. In this experiment, the region by the primary motor cortex in the left part of the brain responds by changing the local blood flow while not significantly increasing its consumption of oxygen. This decoupling of the local metabolism with flow leads to a reduced concentration of the venous deoxyhemoglobin (an increase in oxygen saturation) and, hence, a reduction of the local magnetic field. This results in a change in the signal intensity in the associated pixels in the motor cortex region. Furthermore, the reduced field will also cause the local T2 of blood to increase, and this also leads to a signal increase. Upon subtraction with the original resting-state image, the excited region can be visualized.

BIOMEDICAL NMR

425

6. C. P. Slichter, Principles of Magetic Resonance, 3rd ed., New York: Springer-Verlag, 1990. 7. A. Abragam, Principles of Nuclear Magnetism, Oxford, UK: Oxford Univ. Press, 1989. 8. W. S. Hinshaw and A. H. Lent, An introduction to NMR imaging: From the Bloch equation to the imaging equation, Proc. IEEE, 71: 338–350, 1983. 9. C.-N. Chen and D. I. Hoult, Biomedical Magnetic Resonance Technology, New York: Adam Hilger, 1989. 10. E. L. Hahn, Spin echoes, Phys. Rev., 80: 580–594, 1950. 11. S. Meiboom and D. Gill, Modified spin-echo method for measuring nuclear relaxation times, Rev.Sci. Instrum., 29: 669–691, 1958. 12. A. A. Maudsley and G. B. Matson, Selective excitation in MRI, in D. M. Grand and R. K. Harris (eds.), Encyclopedia of Nuclear Magnetic Resonance, Vol. 7. Chichester, England: Wiley, 1995, pp. 4210–4218. 13. D. B. Twieg, The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods, Med. Phys., 10: 610–621, 1983. 14. R. N. Bracewell, The Fourier Transform and Its Applications, New York: McGraw-Hill, 1978. 15. A. Kumar, D. Welti, and R. Ernst, NMR Fourier zeugmatography, J. Mag. Reson., 18: 69–83, 1975. Figure 24. Illustration of functional brain imaging with a motor task. A gradient-echo sequence with an echo time of 79 ms was used to collect data during resting state (no finger motion) and activated state (movement of the fingers of the right hand). Subtracting the former from the latter yields an activation region, which is shown as an overlay on one of the original anatomical images. As expected, the activation region sits in the area of the primary motor cortex. The imaging parameters were TR ⫽ 5 s, 움 ⫽ 90⬚, FOVx ⫽ FOVy ⫽ 206 mm, Nx ⫽ 256, Ny ⫽ 192, and 5 mm slice thickness. (Images courtesy of Karthik Kuppusamy.)

CONCLUSION Magnetic resonance imaging is a powerful imaging modality. It is capable of imaging the structure, metabolism, and function of a biological object. While an incredible array of methods and applications have been developed in the last two decades, the technology is still far from maturation. Technological developments will continue to improve the speed, efficiency, and accuracy of the imaging method. These technical improvements will further enhance the practical utility of the method for many important applications ranging from 3-D cardiac imaging to functional brain mapping. BIBLIOGRAPHY 1. E. M. Purcell, H. C. Torrey, and R. V. Pound, Resonance absorption by nuclear magnetic moments in a solid, Phys. Rev., 69: 37– 38, 1946. 2. F. Bloch, Nuclear induction, Phys. Rev., 70: 460–474, 1946. 3. P. C. Lauterbur, Image formation by induced local interactions: Examples employing nuclear magnetic resonance, Nature, 242: 190–191, 1973. 4. D. D. Stark and W. G. Bradley, Jr., Magnetic Resonance Imaging, Vols. 1 and 2, 2nd ed., St. Louis: Mosby–Year Book, 1992. 5. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging, New York: IEEE Press, 1988.

16. W. A. Edelstein et al., Spin warp NMR imaging and applications to human whole-body imaging, Phys. Med. Biol., 25: 751–756, 1980. 17. Z. H. Cho et al., Fourier transform nuclear magnetic resonance tomographic imaging, Proc. IEEE, 70: 1152–1173, 1982. 18. F. W. Wehrli, Fast-Scan Magnetic Resonance: Principles and Applications, New York: Raven Press, 1991. 19. P. Mansfield and P. G. Morris, NMR Imaging in Biomedicine, New York: Academic Press, 1982. 20. A. Macovski, Volumetric NMR imaging with time-varying gradients, Magn. Reson. Med., 2: 29–40, 1985. 21. A. B. Ahn, J. H. Kim, and Z. H. Cho, High speed spiral-scan echo planar NMRV imaging—I, IEEE Trans. Med. Imaging, MI-5: 1–6, 1986. 22. J. Carlson et al., Signal-to-noise ratio and section thickness in two-dimensional versus three-dimensional Fourier transform MR imaging, Radiology, 166: 266–270, 1988. 23. R. M. Henkelman and M. J. Bronskill, Artifacts in magnetic resonance imaging, Rev. Magn. Reson. Med., 2 (1): 1–126, 1987. 24. Z.-P. Liang et al., Constrained reconstruction methods in MR imaging, Rev. Magn. Reson. Med., 4: 67–185, 1992. 25. S. R. Deans, The Radon Transform and Some of Its Applications, New York: Wiley, 1983. 26. G. T. Herman, Image Reconstruction from Projection: The Fundamentals of Computerized Tomography, New York: Academic Press, 1980. 27. W. B. Hyslop, R. K. Woods, and P. C. Lauterbur, Four-dimensional spectra-spatial imaging using projection reconstruction, IEEE Trans. Med. Imaging, 14: 374–383, 1995. 28. Z.-P. Liang and D. C. Munson, Partial Radon transforms, IEEE Trans. Image Process., 6: 1467–1469, 1997. 29. E. J. Potchen et al., Magetic Resonance Angiography: Concepts and Applications, St. Louis: Mosby–Year Book, 1993. 30. E. M. Haacke, D. Li, and S. Kaushikkar, Cardiac MR imaging: Principles and techniques, Topics Magn. Reson. Imaging, 7: pp. 200–217, 1995. 31. J. W. Belliveau et al., Functional mapping of the human visual cortex by magnetic resonance imaging, Science, 254: 716–719, 1991.

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32. S.-G. Kim and K. Ugurbil, Functional magnetic resonance imaging of the human brain, J. Neurosci., 74: 229–243, 1997. 33. K. R. Thulborn et al., Oxygenation dependence of the transverse relaxation time of water protons in whole blood at high field, Biochim. Biophys. Acta, 714: 265–270, 1982. 34. S. Ogawa et al., Brain magnetic resonance imaging with contrast dependent on blood oxygenation, Proc. Natl. Acad. Sci. USA, 87: 9868–9872, 1990.

Z.-P. LIANG University of Illinois at UrbanaChampaign

E. M. HAACKE Washington University

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Wiley Encyclopedia of Electrical and Electronics Engineering Computerized Tomography Standard Article Ge Wang1 and Michael W. Vannier1 1University of Iowa, Iowa City, IA Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4702 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (751K)

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8

COMPUTERIZED TOMOGRAPHY

waves are generated by changes of orientation and magnitude of internal magnetic fields, which are produced by spinning nuclei in external magnetic fields. The radio signals are detected by an antenna to provide information on the Fourier transform of a cross section, which is directly related to line integrals of the nuclei density. In transmission electron microscopy, an electron beam penetrates a specimen over a limited angular range to collect projections. In ionospheric tomography, the total electron content is measured between an orbiting satellite and several ground stations. In geophysics, phase shifts of electromagnetic signals are detected for spatial reconstruction of the electrical conductivity and dielectric permittivity of the subsurface. In oceanography, acoustic transmission from a single source suspended from a ship to sonobuoys dropped from the air are recorded for mapping of ocean sound speed. In astronomy, the sun can be observed using an antenna with a parabolic section, and an integral signal is recorded over a thin strip of the radio emission distribution. By moving the antenna, the integrals are obtained over different strips for reconstruction of the ratio emission distribution. CT principles are also applied in optical tomography, diffraction tomography, and other areas. The CT literature is large and growing. Historically, three contributors are most important: Radon, Hounsfield, and Cormack. Reconstruction of a function from its projections was first formulated by Radon in 1917 (1). The first experimental X-ray CT scanner was fabricated and tested by Hounsfield in 1972 (2). An important contribution to mathematics of X-ray CT was made by Cormack (3,4). Hounsfield and Cormack shared the 1979 Nobel Prize for medicine. In this article, we introduce physical and mathematical principles of CT, describe practical reconstruction algorithms for various imaging geometries, and discuss image quality. We focus on X-ray CT, the most prominent example of CT, which has been greatly advanced over the past two decades, has benefited millions of patients, and still represents an important research area. CT in medical and industrial applications is now a worldwide major industry.

COMPUTERIZED TOMOGRAPHY Tomography refers to the synthesis of sectional images or slices from external measurements of a spatially varying function. Line integrals are the most common external measures, which are also known as projections. Availability of multiple projections at different orientations allows accurate recovery of the originating function. Because practical implementation of tomography typically requires large amounts of data and calculations, modern computing technologies are important. Computerized tomography (CT) is interdisciplinary, involving electrical and electronics engineering, mathematics, computer science, physics, mechanics, and biomedical sciences. CT applications are numerous and diverse. Due to its penetrating power and contrast mechanism, X-ray CT has found wide use in medical imaging, industrial nondestructive evaluation, airport screening, and microtomography. In nuclear medicine, a radiating source distribution inside a patient is observed as the intensity of singly (single photon emission computerized tomography, SPECT) or pairwise (positron emission tomography, PET) emitted photons detected outside the patient. If the attenuation of the body is neglected, measures are line integrals of the source distribution. In magnetic resonance imaging (MRI), radio-frequency electromagnetic

CT PRINCIPLES The principles of CT are conceptually simple. Physically, X rays can traverse a cross section of an object along straight lines, can be attenuated by the object, and can be detected outside it. During CT scanning, the cross section is probed with X rays from various directions, and attenuated signals are recorded and converted to projections of the linear attenuation coefficient distribution of the cross section. These X-ray shadows are directly related to the Fourier transform of the cross section, and they can be processed to reconstruct the cross section. Projection Measurement Let us consider the simplest case, a single block of homogeneous tissue and a monochromatic beam of X rays. The linear attenuation coefficient 애 is defined by Sa = Si exp [−µ
l]

(1)

where ⌬l is the length of the block, and Si and Sa are incident and attenuated intensities of the X ray, respectively. Let

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.

COMPUTERIZED TOMOGRAPHY

애(x, y) denote the sectional attenuation variation. For an infinitely thin beam of monochromatic X rays, the detected intensity of the X ray along a straight line L is expressed as
  Sa = Si exp − µ(x, y) dl (2)

9

gas atoms produces electron–ion pairs. These electron–ion pairs form a current between the anode and the cathode when a high voltage is applied. The intensity of this current is proportional to the intensity of the incoming radiation. In terms of the conversion efficiency, the scintillation detector is better.

L

as shown in Fig. 1. The line integral of 애(x,y) along L can be found as follows:   Si , 0 ≤ θ < π, −∞ < t < ∞ (3) dp (θ, t) = ln Sa where p denotes parallel-beam geometry and ␪ and t represent the projection angle and the detector position, respectively. Actually, ␪ and t are polar coordinates of the perpendicular vector from the center of object to the X ray. For a fixed ␪, dp(␪, t) is also referred to as a projection. Because incremental attenuations are summed along X rays in the projection process, and variations of 애(x,y) are superimposed along X rays, it is impossible to reconstruct 애(x,y) from a single projection. However, as we will see in the following section, 애(x,y) can be exactly reconstructed if all projections, dp (␪, t), are available. Note that if the X-ray intensity is low, statistical fluctuation must be taken into account. Technologies of X-ray sources, detectors, and collimators are critical to data acquisition. Currently, a diagnostic type X-ray tube is used as the radiation source of the medical CT scanners. The tube is operated with high-frequency power, a rotating anode disk, and a small focal spot down to 0.6 mm. The disk is usually made of a rhenium, tungsten, and molybdenum (RTM) alloy and can be rotated at a speed of up to 10,000 rotations per minute. Radiation from these X-ray tubes is polychromatic, and it is narrowed by appropriate filtration to have a more concentrated spectrum. Pre- and postpatient collimators restrict the filtered X-ray beam to the anatomy of interest. CT detectors convert attenuated X-ray signals into electrical signals. There are two types of detectors: scintillation detectors and xenon detectors. In the scintillation detector, scintillation crystals will produce light if they are exposed to ionizing radiation. The light is then transformed into an electric signal by a photomultiplier or a silicon photodiode (also called solid-state photodiode). In the xenon detector, a xenon gas ionization chamber is used to measure incoming radiation, where interaction of X-ray photons and

X-ray detector

y

Sa

t

L

µ (x, y)

θ

x Si X-ray tube

Figure 1. Line integrals of 애(x, y), the linear attenuation of an object, can be determined from Si and Sa, incident and attenuated intensities of the X ray along a path L.

Fourier Slice Theorem In tomography, various geometries are used to collect projection data, as detailed below. For simplicity, we introduce image reconstruction with the 2-D parallel-beam geometry. The 2-D Fourier transform of an image function i(x,y) is defined as  I(u, v) =

∞



−∞

∞

i(x, y)e− j2π (ux+vy) dx dy

(4)

−∞

Restricting I(u, v) to the line defined by v ⫽ 0, we have  I(u, 0) =



∞ −∞

∞

i(x, y)e− j2π ux dx dy

(5)

−∞

Because the phase is no longer dependent on y, the integral can be split into two parts:  I(u, 0) =

∞




−∞

∞

 i(x, y) dy e− j2π ux dx

(6)

−∞

The term in brackets is recognized as the projection along lines of constant x,  dp (0, x) =

∞

i(x, y) dy

(7)

dp (0, x)e− j2π ux dx

(8)

−∞

that is,  I(u, 0) =

∞ −∞

In other words, the Fourier transform of the vertical projection of an image is the horizontal radial profile of the 2-D Fourier transform of the image. This relationship can be generalized for any projection orientation. By the nature of the Fourier transform, if an image i(x,y) is rotated by an angle with respect to the x axis, the Fourier transform I(u,v) will be correspondingly rotated by the same angle with respect to the u axis. Therefore, the Fourier transform of a projection along the lines that make an angle ␪ ⫹ 90⬚ with respect to the x axis depicts the Fourier transform of the image along the radial line that makes an angle ␪. This relationship is illustrated in Fig. 2 and is referred to as the Fourier slice theorem; mathematically, Dp (θ, w) = I(w cos θ, w sin θ )

(9)

where Dp(␪, w) is the Fourier transform of dp(␪, t) with respect to t. In n dimensions, we define the Radon transform Rn of a 씮 function i(x) in the Schwartz space as the set of씮 its integrals over the (n⫺1)-dimensional hyperplanes. Let ␪ be a vector defined on the (n⫺1)-dimensional unit sphere, and let s be a real number:

10

COMPUTERIZED TOMOGRAPHY

dp(θ ,t)

Dp(θ,w) = I(wcos θ , wsin θ )

y

y t

θ

w

θ

x

i(x,y)

x

I(u,v)

Image space

Fourier space

(a)

(b)

Figure 2. Fourier slice theorem. (a) Fourier transform of a projection at an angle ␪ corresponds to (b) a radial profile at the same angle in the Fourier space.

Rn (θ , s) =

 x·θ =s

i(x) dx 씮

(10) 씮

Rn is an even function, that is, Rn(⫺␪ , ⫺s) ⫽ Rn(␪ , s). The generalized Fourier slice theorem (5) states that the Fourier 씮 씮 transform of Rn(␪ , s) with respect to s equals I(␪ , w). The Fourier slice theorem plays a fundamental role, because it relates Radon data to a radial profile in the Fourier space. In the ‘‘complete’’ case where all Radon data are available or derivable, the corresponding radial lines will cover the entire Fourier space. Then, the image can be reconstructed using the inverse Fourier transform. In practice, complete projection data are discretely sampled; and quantization error, nonlinearities, noise, and other nonidealities are present. There are many algorithms for image reconstruction from projections, and we will explain the most important ones below. Imaging Geometries The imaging geometry of CT is of fundamental importance in designing a CT scanner system and a reconstruction algorithm. Popular types of CT geometries are summarized in Fig. 3. The first generation scanner is characterized by an assembly of an X-ray source and a single detector [Fig. 3(a)]. For a given projection angle, a parallel-beam projection profile is collected while the assembly is translated along a straight line segment. The projection angle can be controlled by rotation of the assembly. The second generation scanner is also in a translation–rotation mode, but multiple detectors are employed that extend a small fan-beam angle [Fig. 3(b)]. The third-generation scanner utilizes many more detectors and has a much wider fan-beam angle so that X rays from an Xray source cover the entire cross section to be reconstructed [Fig. 3(c)]. Therefore, there is no need for translation of the source-detector assembly. In other words, the assembly works in a rotation fashion. In the fourth-generation design, detectors are distributed along a full circle, and only an X-ray source is orbited [Fig. 3(d)]. Fan-beam spiral/helical scanning is the standard medical CT mode. Spiral CT is implemented by simultaneous patient translation, gantry rotation, and data acquisition [Fig. 3(e)] (6–8). The slip-ring is a key component for spiral scanning, in which a brush slides along a ring as the x-ray source rotates so that electrical energy is continuously supplied. The maximum scanning time with the slip-ring technique is deter-

mined by the thermal limitation of the X-ray tube. Twin-beam spiral CT is based on helical scanning of two contiguous transaxial sections (9). Traditionally, volumetric image reconstruction is achieved by scanning a series of cross sections and by stacking these slices. In cone-beam geometry, instead of scanning an object with a planar beam of X rays, the entire object is illuminated with a point source, and the X-ray flux is measured on a detector plane behind the object [Fig. 3(f)]. The primary advantages of cone-beam geometry include reduced data acquisition time, improved image resolution, and optimized photon utilization. Two unique CT scanners deserve special mentions: the dynamic spatial reconstructor (DSR) (10) and the electron-beam CT scanner (11). Both can complete data acquisition in a fraction of a second and can enable cardiac imaging. In the SDR, 28 X-ray tubes are arranged in a semicircle in a circular gantry. Projections are formed on the fluorescent screen arc, scanned via multiple imaging chains, and reconstructed volumetrically. In the electron-beam scanner, conventional mechanical rotation of an X-ray source is replaced by electromagnetic steering of an electron-beam around one of four semicircular tungsten targets of 210⬚ and 90 cm in radius. Projections are measured by two stationary detector rings of 216⬚ and 67.5 cm in radius. Fig. 4 shows an Elscint twin-beam spiral CT scanner. Fig. 5 reveals an inside view of a Siemens spiral CT gantry. Fig. 6 is a transaxial slice of a human head reconstructed by a Picker spiral CT scanner. Fig. 7 contains a photo and a schematic drawing of the DSR. IMAGE RECONSTRUCTION There are two major classes of CT image reconstruction algorithms: filtered backprojection and iterative reconstruction. Filtered backprojection is the most popular, since it is accurate and amenable to fast implementation. Iterative reconstruction has significant potential for increased use in future, because it provides a solid framework for handling incomplete and noisy projection data. Filtered Backprojection The filtered backprojection algorithms are described for parallel-beam, fan-beam, and cone-beam cases in this section. Parallel-Beam Reconstruction. With the inverse Fourier transform, an image i(x, y) can be expressed as  ∞ ∞ i(x, y) = I(u, v)e j2π (ux+vy) du dv (11) −∞

−∞

Let u = w cos θ,

v = w sin θ

(12)

we have 

2π



∞

i(x, y) = 0

I(θ, w)e j2π (x cos θ +y sin θ )w w dw dθ

(13)

0

Because I(θ + π, w) = I(θ, −w)

(14)

COMPUTERIZED TOMOGRAPHY

we have 

π

i(x, y) =



∞

I(θ, w)|w|e j2π (x cos θ +y sin θ )w dw dθ

(15)

−∞

0

Using the Fourier slice theorem, we have



π

i(x, y) = 

0

= 0

π

 

∞

Note that f(t) does not exist in an ordinary sense, but Dp(␪,w) is essentially band-limited, and f(t) can be accurately evaluated within the maximum bandwidth of Dp(␪, w). Geometrically, this formula performs filtered backprojection for image reconstruction. Let us decompose the formula into two parts: 

π

i(x, y) =

Dp (θ, w)|w|e j2π (x cos θ +y sin θ )w dw dθ

∞ ∞

11

q(θ, x cos θ + y sin θ ) dθ

(18)

0

(16)

−∞

where

dp (θ, t) f (x cos θ + y sin θ − t) dt dθ

 q(θ, x cos θ + y sin θ ) =

where f(t) is the reconstruction filter:  f (t) =

∞ −∞

|w|e j2π wt dw

=

(17)

Detector

∞

−∞  ∞ −∞

dp (θ, t) f (x cos θ + y sin θ − t) dt (19)

Detectors

X-ray source

X-ray source

(a)

(b) Detector ring

Detector array

X-ray source

X-ray source (d)

(c) Helical locus

Dp (θ, w)|w|e j2π (x cos θ +y sin θ )w dw

z X-ray source

2-D Detector array

z

y X-ray source y

x x Detector array (e)

(f)

Figure 3. CT geometries. (a) First generation: one detector, translation and rotation of source and detector; (b) second generation: multiple detectors, translation and rotation of source and detectors; (c) third generation: one detector array, rotation of source and array; (d) fourth generation: one detector ring, source rotation; (e) spiral CT: simultaneous source rotation and patient translation, in either the third or fourth generation geometry; (f) cone-beam geometry: 2-D detector array.

12

COMPUTERIZED TOMOGRAPHY

Figure 4. Twin-beam spiral CT scanner CT-Twin. (Courtesy of Elscint, Inc.)

Clearly, q(␪, t) is a filtered version of dp(␪, t), which is the convolution of dp(␪, t) and f(t). Equivalently, q(␪, t) is the Hilbert transform of d⬘p(␪, t). i(x,y) is the sum of backprojected q(␪, t) along X rays. This backprojection process can be better appreciated by considering a projection at a fixed ␪. In this case the X ray through a point (x,y) in the field of view intersects the projection axis at t(x,y) ⫽ x cos ␪ ⫹ y sin ␪; and the filtered projection value q(␪, x cos ␪ ⫹ y sin ␪) contributes to reconstruction of i(x,y), after weighing with an appropriate angular increment. Note that the filtered projection at the angle ␪ will make the same contribution to reconstruction at all those points in the field of view that correspond to the same t, as shown in Fig. 8. In other words, each filtered projection is additively smeared back, or backprojected, over the field of view. Fan-Beam Reconstruction. In fan-beam reconstruction, an X-ray point source emanates a fan-beam that penetrates an

Figure 6. CT slice of a human head. (Courtesy of Picker International, Inc.)

object and enters a detector array. The source and the detector array are rotated about the object to collect sufficient fanbeam projections. Fan-beam data are often described in two formats, depending upon whether a projection is sampled at equiangular or equispatial intervals. Although the algorithms for these two types of fan-beam data differ, their derivations are essentially the same. Here we focus on equispatial fanbeam reconstruction. As shown in Fig. 9, equispatial fan-beam projections, df (웁, p), are generated when detectors are evenly spaced on a straight line facing the X-ray source and through the origin of the reconstruction system, where 웁 and p are the source rotation angle and the detector position, respectively. Note that a real projection can be readily scaled onto the corresponding line through the origin. Assume that an X-ray source scanning locus ␳(웁) satisfies the following three conditions: 1. ␳(웁) ⫽ ␳(웁 ⫹ 앟). 2. ␳⬘(웁) exists almost everywhere. 3. ␳2(웁) ⬎ ␳⬘(웁)pmin almost everywhere, pmin is the minimum value such that df (웁, p) ⫽ 0, 兩p兩 ⬎ pmin. The third condition is easily satisfied in practice, because ␳(웁) is generally larger than pmin and ␳⬘(웁) is not very large; in particular, a circular scanning locus meets all these conditions. With the Jacobi transform, parallel-beam data dp(␪, t) can be converted to fan-beam data df (웁, p) according to the following relationship: t = p cos γ

and θ = β + γ

where 웂 ⫽ tan⫺1[p/ ␳(웁)]. That is, Figure 5. Inside view of a CT gantry. (Courtesy of Siemens Medical Systems.)

pρ(β )

t=  ρ 2 (β ) + p2

and θ = β + tan

−1



p ρ(β )

 (20)

COMPUTERIZED TOMOGRAPHY

13

Figure 7. Dynamic spatial reconstructor (DSR). The DSR is the first system that allows near real-time tomographic imaging, and it has been applied in cardiac studies. (Courtesy of Dr. Ritman with Mayo Clinic.)

It can be verified that

Then, the parallel-beam reconstruction formula can be transformed into the fan-beam reconstruction formula (12):

  3  ρ − pρρ   dt dθ  =  2 d p dβ (ρ + p2 )3/2 

(21)




ρ3 pρρ  − 2 2 2 3/2 (ρ + p ) (ρ + p2 )3/2

1 2



2π 0

×f

If the third condition is satisfied, we obtain dt dθ =

i(x, y) =

 d p dβ

(22)

y



ρ 2 (β ) [ρ(β ) − s]2

(x,y)

θ

∞ −∞

ρ(β )  d f (β, p) ρ 2 (β ) + p2

 ρ(β )t − p d p dβ ρ(β ) − s

(23)

where t ⫽ x cos 웁 ⫹ y sin 웁 and s ⫽ ⫺x sin 웁 ⫹ y cos 웁. Note that the term involving ␳⬘ is equal to zero. Similar to

y

X-ray source

qp(θ ,t)



t

t

γ

(x,y)

x

t = xcos θ + ysin θ

ρ (β )

p

γ

β θ

β x

Figure 8. Backprojection of a filtered projection. After weighting with an angular increment, each filtered projection is additively smeared back to reconstruct an image. Figure 9. Geometry of equispatial fan-beam reconstruction.

14

COMPUTERIZED TOMOGRAPHY

z

z Helical locus

X-ray source

Helical locus

X-ray source

y

y

x

x

(a)

opposite directions, and thus reduces the angular range from 720⬚ to 360⬚ plus two fan-angles. Fig. 11 is a flowchart of the spiral CT process.

(b)

Figure 10. Spiral CT raw data interpolation. (a) Full-scan interpolation: An in-plane projection value is linearly interpolated from nearest raw data collected at the same orientation. (b) Half-scan interpolation: An in-plane projection value is linearly interpolated from nearest raw data collected at the opposite orientations.

the parallel-beam reconstruction formula, the fan-beam reconstruction formula can be interpreted as weighted filtered backprojection. If ␳ is a constant, the fan-beam formula agrees with the circular fan-beam formula (13). In spiral CT, planar projection sets are synthesized from raw projection data via interpolation. Among various interpolation methods, linear interpolation is usually preferred due to its efficiency and performance (8,14). Typical linear interpolation techniques include full-scan interpolation (FI) and half-scan interpolation (HI), as shown in Fig. 10. In the FI method, a set of planar projection data in a 360⬚ angular range is obtained via linearly interpolating neighboring raw projection data at the same orientation; hence the involved raw data span a 720⬚ angular range. The HI method utilizes redundancy of raw data, interpolates neighboring raw data at

Exact Cone-Beam Reconstruction. When a point X-ray source and a 2-D detector array are used, cone-beam image reconstruction is required. Kirillov developed a formula for reconstruction of a complex valued n-dimensional function from complex valued cone-beam projection data (15). A sufficient condition for exact reconstruction in the Schwarz space is that an unbounded source point locus intersects almost every hyperplane. Complex-valued cone-beam formulation cannot be directly used in practice. An inversion formula in the real space was developed under the condition that almost every hyperplane through a compact function support meets a source locus transversely (16). Important theoretical analyses on cone-beam reconstruction of a real-valued function were done by Smith (17) and Grangeat (18). Due to their fundamental work, we have the following sufficient condition for exact cone-beam reconstruction: If there exists at least a conebeam source point on any plane intersecting an object, exact cone-beam reconstruction can be achieved. Recall that if there exists at least a fan-beam source point on any straight line intersecting an object, exact fan-beam reconstruction can be achieved. Grangeat’s derivation of this sufficient condition has a clearer geometrical interpretation. Various exact conebeam reconstruction algorithms have been implemented according to Smith’s theory (19–21), Grangeat’s framework (22–25), and Tuy’s method (26), respectively. The Grangeat algorithm consists of two parts. In the first part, the radial derivative of planar integrals are computed, according to the relationship between the radial derivative of Radon data and the line integral of cone-beam data. The results are distributed on various spheres in the Radon space determined by a scanning locus. If the scanning locus is com-

Start

Set scan parameters (position, range; collimation, feed) Collect spiral raw data Preprocess spiral raw data

Ramp-filter planar data

Set interpolation parameters (interpolation option; reconstruction interval)

Backproject filtered data

Specify slice position

Figure 11. Flowchart of the spiral CT process.

Synthesize complete planar projection data

N

Done?

Y

2-D/3-D Analysis and visualization

End

COMPUTERIZED TOMOGRAPHY

Detector

15

Derivative of Radon space

Detector data From detector data to derivatives of Radon data

Source

Source

Data acquisition Interpolation to vertical planes 2-D reconstruction of horizontal planes

Reconstructed object

2-D reconstruction of vertical planes

Horizontal planes 2-D Radon data

Vertical planes 3--D Radon data

Figure 12. Exact cone-beam reconstruction. 3-D Radon data are derived from cone-beam data, interpolated on vertical planes, reconstructed into 2-D Radon data on horizontal planes, and reconstructed into an image volume. (Courtesy of Drs. Axelsson and Danielsson. Reprinted from Phys. Med. Biol., 39: 478, 1994, with permission.)

plete, the Radon space can be completely filled. In the second part, these Radon data are inverted. Although the direct filtered backprojection formula may be applied with the 3-D Radon data, the computational complexity is O(N5), where N is the size of a 3-D reconstruction grid and is proportional to the number of cone-beam projections. With the Marr method (27), the 3-D Radon inversion is decomposed into two steps, as shown in Fig. 12. First, 3-D Radon data are interpolated on vertical planes, and 2-D reconstruction is done for each vertical plane. As a result, 3-D Radon data are transformed into 2-D Radon data associated with the vertical planes. Data in the vertical planes are then grouped into data in horizontal planes, and 2-D reconstruction is performed for each horizontal plane. This method has a computational complexity of O(N4). Axelsson and Danielsson developed a direct Fourier method (24), which is a refined version of the Grangeat algorithm. Among existing algorithms, the Axelsson and Danielsson algorithm is computationally most efficient for a sufficiently large amount of data and has a complexity of O(N3 log N) (24). The reduction was made by adapting the linogram method (28). The linogram method requires that the projection profile sampling step and the projection angular increment vary appropriately, so that equidistant samples along concentric squares can be formed in the Fourier domain, and reconstruction accelerated. Exact filtered backprojection algorithms for cone-beam reconstruction were independently derived by Defrise and Clack (22) and by Kudo and Saito (23), which require that a scanning locus be complete, data redundancy weighting and nonstationary 2-D filtering be applied. Approximate Cone-Beam Reconstruction. Despite progress in exact cone-beam reconstruction, approximate cone-beam reconstruction remains important, especially in the cases of

incomplete scanning loci and partial detection coverage. Furthermore, approximate reconstruction is usually associated with higher computational efficiency and may produce less image noise and ringing. We focus on Feldkamp-type conebeam reconstruction, the main stream of approximate conebeam reconstruction. Let i(x, y, z) be an image with a cylindrical support. A scanning locus is described in a cylindrical coordinate system (␳(웁), h(웁), 웁), where 웁 is the source rotation angle around the z axis, without loss of generality 웁 僆 [0, 2앟), ␳(웁) describes the distance between the source and the z axis, and h(웁) is the distance from the source to the x–y plane. If the 3-D scanning locus is vertically projected onto the x–y plane, a 2-D scanning locus will be obtained. We assume that this 2-D scanning locus meets all the three fan-beam scanning conditions described earlier. An equispatial cone-beam projection is denoted as dc(웁, p, ␨), where the ␨ axis of the detection plate p-␨ is superimposed on the z axis, and the central normal of the detection plate is toward the x-ray source. In Fig. 13, we consider reconstruction of a point object 웃(x ⫺ x0, y ⫺ y0, z ⫺ z0) from its cone-beam data, which can be expressed as  2
2 ρ (β ) + p2 + ζ 2 ρ (β ) δ(p − p0 )δ(ζ − ζ0 ) dc,δ (β, p, ζ ) = σ 2 (β ) ρ(β ) (24) where ␴(웁) is the difference between ␳(웁) and the signed distance from the point object to the detection plate, and (p0, ␨0) are coordinates of the point object projected on the detection plate. Geometrically, the first factor scales the point object because of the divergence of the cone beam, and the second factor is due to the angle between the X ray through (x0, y0, z0) and the normal of the p-␨ plate. We note that in the plane z ⫽ z0, the equispatial fan-beam projection of the point object

16

COMPUTERIZED TOMOGRAPHY

and then perform fan-beam reconstruction. By doing so, we immediately obtain the generalized Feldkamp cone-beam reconstruction formula (29):

ζ Scanning locus

α

(x0, y0, z0) Imaginary source

σ (β )

dc(β ,p,ζ0)

z

h(β )

df( β,p)

Real source

p

ρ (β )

β

x

y Figure 13. Approximate cone-beam reconstruction. Cone-beam data are corrected to fan-beam data by multiplying cone-beam data with the cosine of the corresponding X-ray tilting angle. For a point object, the corrected fan-beam data are exact.

is




ρ 2 (β ) df,δ (β, p) = σ 2 (β )

 2 ρ (β ) + p2 δ(p − p0 )δ(0) ρ(β )

(25)

Comparing Eq. (24) with Eq. (25), we observe that the fanbeam projection df,웃(웁, p) of this point object can be exactly obtained by multiplying the corresponding horizontal profile dc,웃(웁, p, ␨0) of the cone-beam projection with the cosine of the X-ray tilting angle; mathematically,

 ρ 2 (β ) + p2

df,δ (β, p) =

dc,δ (β, p, ζ0 ) ρ 2 (β ) + p2 + ζ02

(26)

Clearly, applying the fan-beam reconstruction formula derived in the preceding subsection with corrected cone-beam data, exact reconstruction can be achieved in the plane z ⫽ z0. Generally speaking, i(x, y, z) is not a point object, but it can be viewed as a combination of many point objects. To reconstruct a point object at (x, y, z), we can correct cone-beam data in the same way to obtain approximate fan-beam data,

Figure 14. Cone-beam X-ray microtomography. (a) Conebeam projection. (b) Surface rendered view of a snail shell reconstructed using the generalized Feldkamp algorithm. (Courtesy of Dr. P. C. Cheng, S. J. Pan, A. Shih, and W. S. Liu with AMIL, SUNY/Buffalo.)



 ∞ ρ 2 (β ) ρ(β )  2 2 (ρ(β ) − s) ρ (β ) + p2 + ζ 2 0 −∞   ρ(β )t − p d p dβ × dc (β, p, ζ ) f ρ(β ) − s

1 i(x, y, z) = 2

2π

(27)

where t ⫽ x cos 웁 ⫹ y sin 웁, s ⫽ ⫺x sin 웁 ⫹ y cos 웁, and ␨ ⫽ ␳(웁)(z ⫺ h(웁))/[␳(웁) ⫺ s]. Fig. 14 shows a real cone-beam projection of a snail as well as a surface-rendered image reconstructed using the generalized Feldkamp algorithm with the X-ray cone-beam micro-CT system at the AMIL, SUNY/Buffalo. Because this formula is based on fan-beam reconstruction, it is also in a weighted filtered backprojection format. With a circular scanning locus, the generalized Feldkamp cone-beam formula is equivalent to the well-known Feldkamp formula (30). The generalized Feldkamp formula allows a wide class of scanning loci, reconstructs spherical, rod-shaped and planar specimens, and preserves all the exactness properties Feldkamp et al. established (30), including that the longitudinal integral of a reconstructed volumetric image is equal to that of the actual image. Interestingly, the generalized Feldkamp reconstruction can be similarly formulated in a rotated reconstruction system x⬘–y⬘–z⬘ after cone-beam data are corrected onto the new imaginary detector plane through the z⬘ axis. Suppose that the vertical projection of a 3-D scanning locus allows exact fan-beam reconstruction, it can be proven in the same way that the integral of a reconstructed volumetric image along the z⬘ axis is exact. Note that if the projected scanning locus does not satisfy the three fan-beam scanning conditions, Feldkamp-type reconstruction can still be performed using an appropriate fan-beam reconstruction formula (data rebinning may be involved). The exact longitudinal integral of a reconstructed volumetric image equals the 2-D parallel-beam projection along the direction of integration. Therefore, exact stereoimaging from incomplete cone-beam data is feasible. If a sufficient amount of exact 2-D parallel projection data is available, exact 3-D image reconstruction can be performed. Therefore, a sufficient condition for exact cone-beam reconstruction can be stated below: If for any projection direction a projected scanning locus

COMPUTERIZED TOMOGRAPHY

is complete for exact fan-beam reconstruction on a projected object support, the object can be exactly reconstructed. This stereoimaging based sufficient condition is equivalent to the traditional sufficient condition. If the stereoimaging-based sufficient condition is satisfied, for any projection direction the projected scanning locus is complete, and we have the family of all the planes parallel to the projection direction and containing at least one source position. That is, the traditional sufficient condition is also satisfied. If the stereoimaging-based sufficient condition is not satisfied, there is a projection direction along which the projected scanning locus is incomplete, a line can be found that intersects the projected object support but meets no projected source point, and this line represents a plane that intersects the object but contains no source point. That is, the traditional sufficient condition is violated. Iterative Reconstruction Available noniterative cone-beam algorithms require that projections should not be truncated along at least one direction. Therefore, satisfactory cone-beam reconstruction with these algorithms is impossible in cases where objects contain X-ray opaque components and/or are larger than the conebeam aperture defined by effective detection area and X-ray source position. Various iterative methods are known for years. Recently, Snyder et al. interpreted the expectation maximization (EM) formula for emission CT (31) in a deterministic sense, and established its properties on convergence and optimality (32). Using the notation of Snyder et al. (32), the linear, discrete, and nonnegative deblurring problem is formulated as inversion of 

h(y| x )c(x) = a(y)

(28)

X x∈X 씮

씮씮

where a(y) is an observed function, h(y兩x), a known blurring 씮 씮 씮 kernel, c(x) a function to be recovered, x 僆 X, y 僆 Y, and all the functions are nonnegative. The following iterative deblurring formula can be used: ck+1 (x) = ck (x)


1  h(y| x) a(y)   H0 (x) y∈YY | x )ck (x ) X h(y x ∈X

(29)

where H0(x) ⫽ 兺y僆Y h(y兩x), ck(x) and ck⫹1(x) are current and 씮 씮씮 씮 updated guesses of c(x). It was shown that 兺x僆X h(y兩x)c앝(x) fits 씮 a(y) nonnegatively, monotonically, and optimally in the sense of the I-divergence I(a储b) (32) 씮

씮

씮씮

씮

씮

씮

I(ab) =

 Y y∈Y

a(y) log

a(y)  − [a(y) − b(y)] b(y) y∈YY

(30)

Use of the I-divergence to define the optimality is justifiable (33,34). Briefly, among many discrepancy measures, the I-divergence and the Euclidean distance were shown to be appropriate choices in nonnegative and real spaces, respectively. In their work (32), Snyder et al. require a strictly positive 씮씮 kernel, h(y兩x) ⬎ 0. Recently, this constraint was relaxed to 씮씮 allow a nonnegative kernel, h(y兩x) ⱖ 0, under the following extended assumptions (35):

1. 2. 3. 4. 5. 6.

씮

17

씮

a(y) ⬎ 0 for all y, 씮 a(y) is summable, 씮 씮씮 H0(x) ⫽ 兺y僆Y h(y兩x) ⬎ 0, 씮 씮씮 H0(y) ⫽ 兺x僆X h(y兩x) ⬎ 0, 씮씮 씮 씮 h(y兩x) ⱖ 0 for all x, y, 씮씮 씮 씮 h(y兩x) is summable with respect to x and y. 씮

씮

Several comments on the extended assumptions are in order. 씮 First, a(y) ⬎ 0 may appear more restrictive than the original 씮 a(y) ⱖ 0, but it is not. Actually, a deblurring problem with 씮 씮 a(y) ⱖ 0 can be transformed to the one with a(y) ⬎ 0 by the 씮 씮 following preconditioning procedure: if a(y0) ⫽ 0, c(x) is set to 씮 씮 씮 씮 씮 씮 zero for all x 僆 X(y0), where X(y0), ⫽ 兵x 僆 X, h(y0兩x) ⬆ 0其, then 씮 씮 y0 and X(y0) can be removed from Y and X, respectively. This 씮 is consistent with what was done by Snyder et al.: if a(y) ⬅ 0, 씮 씮 씮 then c(x) ⬅ 0 (32). Also, H(x) ⬎ 0 means that c(x) is somehow 씮 씮 씮 measured at any specific x. If H(x0) ⫽ 0, c(x0) is totally unob씮 servable. Hence, x0 can be removed from X. On the other 씮 씮 hand, H(y) ⬎ 0 means that every a(y) carries a certain 씮 씮 amount of information about c(x). Actually, if H(y0) ⫽ 0, 씮 씮 씮 씮 h(y0兩x) ⫽ 0 for all x, and no information about c(x) can be de씮 씮 rived from a(y0) ⬅ 0. Therefore, y0 can be removed from Y. These preconditioning operations exclude uninformative situations. We showed that all the properties Snyder et al. established remain essentially valid under the extended assump씮씮 씮씮 tions [mainly, h(y兩x) ⱖ 0, instead of h(y兩x) ⬎ 0]. Although it is computationally expensive, the major advantages of the iterative approach include insensitivity to data noise and capability of reconstructing an optimal image in the case of incomplete data, where traditional Fourier-transformbased methods are subject to serious artifacts. With rapid evolution of computing technologies, iterative reconstruction will be more practical. Theoretically, a projection datum is the value of a linear integral along an X-ray path contained in an object. After discretization of detection and reconstruction systems, continuous projection can be approximated as values at a detection grid, each of which equals a sum of weighted values of those voxels that are in a neighborhood of the correponding X ray. Then, the generic iterative deblurring formula can be specialized for image reconstruction in parallel-beam, fan-beam, or cone-bean geometry. A flowchart of the iterative cone-beam reconstruction algorithm is given in Fig. 15. First, cone-beam projection data are measured given a cone-beam geometry and a scanning locus. Based on measured cone-beam data, a characteristic projection mask is formed to indicate whether or not a reading is significant for a combination of source and detector positions. For example, if there are X-ray opaque structures in an object, some detectors may receive little photons, and corresponding data are lost. To take beam divergence and data incompleteness into account, a relaxation function (the dis씮 crete version of H0(xp)) is generated from the projection mask, the cone-beam geometry, and the scanning locus. Also, a positive intermediate image volume is initialized. In each iteration, cone-beam projection data are estimated via ray-tracing based on the intermediate image volume. Discrepancies between measured and estimated projection data are computed as ratios for every significant combination of detector and source positions. Then, these ratios are backprojected over the 3-D image grid, multiplied with the intermediate image, and

18

COMPUTERIZED TOMOGRAPHY

in a unified way due to introduction of the projection mask. Consequently, the iterative X-ray CT algorithm is a powerful framework for metal artifact reduction and local region reconstruction from truncated data.

Start

Measure projection data

IMAGE QUALITY

Form projection mask

Initialize intermediate image

Generate relaxation factor

Estimate projection data

Update intermediate image

Divide measured with estimated data

Continue?

Image quality can be described in two categories: resolution and artifacts. Image resolution has three aspects: high-contrast resolution (spatial resolution) for distinguishing adjacent objects of high-contrast, low-contrast resolution (contrast resolution) for differentiating an object from its background which is similar to the object in gray-scale, and temporal resolution for resolving time-varying structures. Image noise imposes a grainy appearance due to random fluctuations of the X-ray photon flux, and it is a major factor in defining lowcontrast resolution. Image artifacts are structured or patterned interference over the field of view. Although the X-ray dosage delivered to the patient is an extremely important issue in medical CT and closely related to image quality, it is beyond the scope of this article. Interested readers are referred to Rothenberg and Pentlow (36) and McGhee and Humphreys (37). In discussion of image quality, we emphasize unique features of spinal CT, the standard mode of medical X-ray CT.

Y

N

End Figure 15. Flowchart of the EM-type iterative X-ray cone-beam CT algorithm with data incomplete due to either X-ray opaque structures or an insufficient cone-beam aperture.

divided by the relaxation factor to obtain an updated image. A priori knowledge, such as a known image support, can be enforced upon the updated image. Image quality and fitting errors may be estimated after each iteration. A numerically simulated example is presented in Fig. 16. Iterative deblurring has been used for PET and SPECT image reconstruction, where it is interpreted in a statistical sense for maximization of the likelihood. The iterative X-ray CT algorithm has two important features. First, this algorithm is interpreted in a deterministic sense, which minimizes the I-divergence of measured and fitted data instead of maximizing the likelihood of the solution. Actually, the likelihood in X-ray CT can be maximized using a more complicated iterative formula (31). Second, it handles data incompleteness

Resolution Spiral CT was introduced for faster volumetric scanning than conventional incremental CT. However, spiral CT produces inconsistent projection data for any transaxial plane, and it broadens the slice sensitivity profile (SSP) as compared with conventional CT. It appeared that temporal resolution of spiral CT was improved at the cost of degraded high- and lowcontrast resolution. However, as will be seen below, this is not necessarily the case. High-Contrast Resolution. Generally, high-contrast resolution in a scanning plane can be easily visualized using the multibar phantom, as shown in Fig. 17, which is an array of high-contrast bars being uniform in both the bar width and their separation. When the width and separation of the bars become smaller, the image contrast of the bars will decrease. The in-plane resolution is described by the modulation transfer function (MTF), which is the ratio between the image con-

Phantom

1cm

1cm

Figure 16. Numerical simulation of EMtype iterative X-ray cone-beam tomography with a cylindrical phantom from incomplete data due to an embedded X-ray opaque sphere. (a) Diagram of the phantom containing 7 disks (thickness not shown) and the opaque sphere, (b) middle sagittal slice, (c) reconstructed counterpart after 40 iterations.

X-ray opaque object (a)

(b)

(c)

COMPUTERIZED TOMOGRAPHY

Figure 17. High-contrast resolution is measured with the multibar phantom. The modulation transfer function is described by the ratio between the image contrast and the bar contrast as a function of the spatial frequency of the bars. (Courtesy of Picker International, Inc.)

trast and the object contrast as a function of the spatial frequency of the bars. Ideally, the MTF is defined in terms of sinusoidal functions, which are, however, difficult to fabricate. On the other hand, high-contrast resolution through the scanning plane is described in terms of the SSP, which can be computed as the derivative of an edge response in a plane orthogonal to the scanning plane. Several studies have shown that in-plane high-contrast resolution of spiral CT is quite similar to that of incremental CT (8,14). As far as through-plane high-contrast resolution is concerned, although spiral CT degrades the SSP, it allows retrospective reconstruction: Raw data are collected first, and any transaxial slice can be reconstructed afterward; in other words, the longitudinal sampling rate in spiral CT can be much higher. To compare through-plane high-contrast resolution, the SSPs and corresponding MTFs were derived for incremental CT and spiral CT with the HI method (38). The one-tenth-cutoff and mean-square-root measures were used to quantify the bandwidths of the MTFs. It was proven that for a given X-ray dose, spiral CT with overlapping reconstruction has a wider bandwidth and thus better longitudinal high-contrast resolution than incremental CT. It is recommended that 3–5 slices be reconstructed per slice thickness. Experiments also demonstrated merits of overlapping reconstruction in spiral CT (39). With state-of-the-art spiral CT scanners, volumetric images of sub-mm isotropic 3-D resolution can be obtained. Low-Contrast Resolution. Low-contrast resolution characterizes recognizability of a low-contrast object and is influenced by several factors, including the object size, contrast between object and background, image noise, and the system MTF. Image noise is primarily determined by the dose setting of the X-ray tube, the slice thickness, the reconstruction algorithm, the characteristics of the CT scanner, and the struc-

19

tures scanned in the field of view. As shown in Fig. 18, lowcontrast resolution can be measured with a multihole phantom. A good descriptor of low-contrast resolution is the CT value difference of those holes that are barely recognizable in the image. Conventional CT being the standard, spiral CT with the HI method increases image noise, while spiral CT with the FI method decreases image noise (8,14,40). On the other hand, the HI method degrades the SSP significantly less than the FI method (8,14). As a result, spiral CT could suffer from either poorer high-contrast resolution using the FI method or poorer low-contrast resolution using the HI method. Because both the HI and FI methods have their advantages and disadvantages, they can be combined for a balance. Specifically, from a spiral CT raw data set and at a given longitudinal position, two transaxial images can be reconstructed using the FI and HI methods, respectively. Then, the two images are averaged to produce a new image. Apparently, the averaging operation can be moved into the interpolation process for better efficiency, resulting a balanced interpolation method. The image noise, the one-tenth-cutoff, and the mean-squareroot measures of the longitudinal MTFs were derived for incremental CT and spiral CT using this balanced interpolation method and were experimentally verified (41). It was found that given an X-ray dose and a longitudinal bandwidth, spiral CT on average allows less image noise and better low-contrast resolution than incremental CT. Temporal Resolution. To capture rapidly varying structures, the speed of data acquisition is critical. The development of CT scanners was motivated, to a major degree, by the need for better temporal resolution. The primary indicator of temporal resolution is the period of data acquisition, although the temporal resolution also depends on the reconstruction algorithm. State-of-the-art spiral CT scanners collect projection data of 360⬚ in a second. Recently, CT fluoroscopy (CTF) has attracted increasing interest. In CTF, a patient is contin-

Figure 18. Low-contrast resolution is measured with a multi-hole phantom. (Courtesy of Picker International, Inc.)

20

COMPUTERIZED TOMOGRAPHY

CT value Corrected Uncorrected s

Homogeneous region

Shorter path

Longer path (a)

s

Shorter path (b)

(c)

Figure 19. Beam-hardening artifacts and correction. (a) Uncorrected ‘‘cupping’’ profile of a homogeneous phantom due to beam hardening, which causes a right shift in the effective energy of the X-ray beam over longer paths. (b) Image reconstructed at the petrous bones without beamhardening correction, in which an erroneous shadow is indicated by the arrow. (c) With beamhardening correction. (Courtesy of Dr. Jiang Hsieh at GE Medical Systems.)

uously scanned while an intervention is done such as a needle being inserted. Recently, Hsieh (42) quantified temporal resolution of CTF in terms of the time lag and the time delay. The time lag is the minimum time needed to reveal the actual movement of the biopsy needle, while the time delay is the minimum time for the needle to reach its real location in the CT image. The DSR and the electron-beam CT scanner reduce the scanning time by an order of magnitude to about onetenth second. Generally, the power of an X-ray source can be a limiting factor. The faster the scanning is, the less the dose delivered, and the more the image noise. A trade-off between temporal resolution and low-contrast resolution depends upon the intended application of CT images. Artifacts Substantial research has been done on causes, characteristics, and correction of image artifacts (43). We only discuss the most common artifacts: beam hardening artifacts, blurring artifacts, motion artifacts, metal artifacts, and stairstep artifacts. Beam-Hardening Artifacts. Conventional X-ray sources for medical CT are rotating anode tubes, which have polychromatic spectra. That is, X-ray photons emitted from a X-ray tube do not all have the same energy. The X-ray attenuation of an object depends on the photon energy. As an X-ray beam traverses an object, the higher energy portion of the X-ray spectrum increases, since lower energy photons are attenuated more. If this nonlinear beam-hardening effect is not compensated, a ‘‘cupping’’ in image gray-scale will be seen. The beam-hardening artifacts are more serious when high X-ray absorption structures are in the field of view. Means for suppressing beam-hardening artifacts include prefiltering X-rays, avoiding high X-ray absorbing regions if possible, and applying appropriate algorithms (44,45). Figure 19 illustrates beam-hardening artifacts and correction with a homogeneous

phantom and an image at the petrous bones, respectively. Scattered radiation-induced artifacts should also be mentioned, which lead to cupping, streaks, and CT number errors. It was shown that this type of artifact can be more significant than beam-hardening artifacts for large body parts, such as in the pelvis, and may be corrected to a substantial degree, assuming a constant scatter background (46). Blurring Artifacts. Blurring artifacts refer to a blurred appearance of discrete structures in a CT image, due mainly to sizes of an X-ray source and detectors. Another name for this type of artifact is partial volume averaging, since a reconstructed voxel value is approximately an average of attenuation distribution in a neighborhood of the center of that voxel. A common phenomenon is that sharp edges look blurred in an image, indicating a degraded system high-frequency response. The blurring artifacts are certainly undesirable when details are examined. For example, blurring in spiral CT images limits the in vivo study on the middle and inner ear for cochlear implantation. Digital deblurring is an established approach to undo image blurring retrospectively. There are various image deblurring algorithms available. It was demonstrated that the iterative maximum likelihood deblurring method produced a satisfactory deblurring effect in spiral CT (35,47). The spiral CT imaging process can be approximated as a 3-D linear spatially invariant system, and the 3-D system point spread function (PSF) modeled as a separable Gaussian function (35). Roughly speaking, in iterative deblurring of a reconstructed image, a previous guess is convolved with the system PSF, the reconstructed image is point by point divided by the convolved guess, the ratio image is convolved again with the PSF, and the convolved ratio image is point by point multiplied by the previous guess to update it. The reconstructed image can be used as an initial guess. This iterative deblurring method is a special case of the linear, discrete, and

COMPUTERIZED TOMOGRAPHY

21

Figure 20. Blurring artifacts and correction. (a) Spiral CT slice of the temporal bone. (b) Counterpart deblurred using the iterative maximum likelihood algorithm. (Original data courtesy of Dr. Gregory Esselman with Washington University.)

nonnegative deblurring formula described earlier, and can be regularized for suppression of deblurring artifacts, which are primarily image noise and edge ringing (35). Figure 20 shows a spiral CT slice of temporal bone and the counterpart iteratively deblurred. Motion Artifacts. Motion artifacts are produced in a CT image if an object is not static but assumed so in the reconstruction process. In medical CT, anatomical structures move periodically due to respiration or cardiac pulsation. Severely injured patients or children frequently move during scanning. Fig. 21 demonstrates that respiratory motion artifacts can be significant with incremental CT and can be eliminated by spiral CT single breath-hold scanning. Crawford et al. (48) developed a pixel-specific filtered backprojection algorithm for motion artifact reduction. In their algorithm, in-plane motion is corrected by pixel-specific reconstruction in the coordinate system associated with the in-plane motion. Metal Artifacts. Metal artifacts are typically pronounced dark and bright streaks around a metal part in an image reconstructed via filtered backprojection, as shown in Fig. 22. Because of the higher atomic number, the metal attenuates X-rays in the diagnostic energy range much more than soft tissues and bone. As a result, almost no photons penetrate the metal, and corresponding line integrals are lost. As men-

tioned earlier, metal artifacts can be optimally suppressed via iterative deblurring in the sense of the I-divergence (49). Stairstep Artifacts. Stairstep artifacts are well known in conventional CT, and have special features in spiral CT (50). They are associated with inclined surfaces in reformatted longitudinal slices, as shown in Fig. 23. In spiral CT, the stairstep artifacts were due to not only large reconstruction interval but also asymmetric spiral CT interpolation. Even if the reconstruction interval is sufficiently small, the stairstep artifacts will appear as long as the object cross section varies longitudinally. In this case, the height of the stairsteps depends on the pattern of asymmetry in the transverse image, which is mainly determined by the interpolation method and the structures in the field of view. For minimal stairstep artifacts, both detector collimation and table increment should be minimized, which should be less than the longitudinal dimension of features of interest if it is possible. DISCUSSION AND FURTHER READINGS Although X-ray CT has been intensively studied for years, further developments are anticipated. Most important, spiral CT remains an active area. Spiral CT involves more parameters and raw data processing than conventional CT. Optimi-

Figure 21. Respiratory motion artifacts. (a) Artifacts in multiplanar reformation with incremental CT (85 s), as indicated by arrows, and (b) eliminated with single breath-hold spiral CT scanning (12 s). (Courtesy of Dr. James Brink, Yale University.)

22

COMPUTERIZED TOMOGRAPHY

Figure 22. Metal artifacts caused by a prosthesis. (Courtesy of Dr. Douglas Robertson, Washington University.)

zation of imaging protocols and image quality needs major additional efforts (51). Multislice spiral CT is emerging for faster scanning and wider coverage. Cone-beam spiral CT seems a promising mode in medical imaging, industrial inspection, airport screening, and other applications. It is desirable and possible that an exact cone-beam spiral CT algorithm could be designed that takes longitudinally truncated cone-beam data and can be efficiently implemented. The wavelet approach has a significant potential for radiation reduction and multiresolution reconstruction. Olson and DeStefano (52) observed that space-frequency localized wavelet bases can be used in sampling the Radon transform and performing local region reconstruction. Zhao et al. (53) established an upper error bound in L2-norm between the Radon transform and its wavelet approximation, and obtained an estimate of the accuracy of a local image reconstructed from localized Radon data at multiple levels. The current results can be extended to fan-beam and cone-beam geometry. Iterative reconstruction methods will play a substantial role for better image quality and less radiation dose. In addition to the iterative algorithm described above, a statisticalmodel-based iterative algorithm was developed for X-ray CT (31). In this case, X-ray CT with low photon counts is viewed as an estimation problem, and it is solved in the maximum likelihood (ML) sense (31). ART-type iterative algorithms are also valuable (54). Theoretical and practical issues with itera-

tive CT algorithms include regularization and acceleration (55–57). Progress in hardware will broaden horizons of CT applications. During the past decade, X-ray tubes were greatly enhanced. The availability of highly brillant and collimated synchrotron radiation (SR) pushed spatial resolution into the micron domain. Using the energy tunability of SR, elemental composition of materials can be studied in 3-D. Various area detectors accelerated data acquisition. Techniques of X-ray sources, detectors, and other relevant hardware will be further developed. In particular, computing technologies are in rapid development. All of these will be directly translated into better CT peformance and suggest more CT applications. With dramatic refinement in CT resolution, volumetric image analyses and visualization are altering clinical practice. For example, Gastrointestinal (GI) tract examination with X-ray CT is currently performed by slice-based visual inspection despite the volumetric nature of the anatomical components, tumors, and lesions. Recently, spiral CT virtual colonoscopy is being actively pursued for colon cancer screening, in which a convoluted large intestine in a spiral CT image volume is interactively explored in a ‘‘fly-through’’ fashion, and may be explicitly mapped onto an elongated planar display. Spiral CT angiography is another example. Among further readings, introductory descriptions of CT principles can be found in Russ (58) and Parker (59), various applications and practical algorithms with detailed derivations can be found in Herman (60,61) and Kak and Slaney (13), and a rigorous mathematical treatment in Natterer (5). A history of radiological tomography can be found in Webb (62). Articles on CT are published in many journals, such as SIAM Journal on Applied Mathematics, SIAM Journal on Optimization, Proceedings of IEEE, IEEE Transactions on Image Processing, IEEE Transactions on Signal Processing, IEEE Transactions on Information Theory, IEEE Transactions on Medical Imaging, IEEE Transactions on Nuclear Science, Medical Physics, Physics in Medicine and Biology, Journal of the Optical Society of America, Optical Engineering, Applied Optics, Journal of Scanning Microscopy, Journal of Computer Assisted Tomography, and Radiology.

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43. J. Hsieh, Image artifacts, causes, and correction, In L. W. Goldman and J. B. Fowlkes (eds.), Medical CT and Ultrasound: Current Technology and Applications. Madison, WI: Advanced Medical Publishing, 1995.

22. M. Defrise and R. Clack, A cone-beam reconstruction algorithm using shift-variant filtering and cone-beam backprojection, IEEE Trans. Med. Imaging, 13: 186–195, 1994.

44. P. M. Joseph and C. Ruth, A method for simultaneous correction of spectrum hardening artifacts in ct images containing both bone and iodine. Med. Phys., 24: 1629–1634, 1997.

23. H. Kudo and T. Saito, Derivation and implementation of a conebeam reconstruction algorithm for nonplanar orbits, IEEE Trans. Med. Imaging, 13: 196–211, 1994.

45. P. M. Joseph and R. D. Spital, A method for correcting bone induced artifacts in computed tomography scanners. Med. Phys., 2: 100–108, 1978.

24. C. Axelsson and P. E. Danielsson, Three-dimensional reconstruction from cone-beam data in O(n3 log n) time, Phys. Med. Biol., 39: 477–491, 1994.

46. P. M. Joseph and R. D. Spital, The effects of scatter in x-ray computed tomography. Med. Phys., 9: 464–472, 1982.

25. H. Hu, An improved cone-beam reconstruction algorithm for the circular orbit, J. Scanning Microsc., 18: 572–581, 1996. 26. G. L. Zeng, R. Clack, and G. T. Gullberg, Implementation of Tuy’s cone-beam inversion formula, Phys. Med. Biol., 39: 493–507, 1994.

47. G. Wang, M. W. Skinner, and M. W. Vannier, Temporal bone volumetric image deblurring in spiral CT, Acad. Radiol., 2: 888– 895, 1995. 48. C. R. Crawford, K. F. King, C. J. Ritchie, and J. D. Godwin, Respiratory compensation in projection imaging using a magnification and displacement model, IEEE Trans. Med. Imaging, 15: 327–332, 1996.

27. R. B. Marr, C. Chen, and P. C. Lauterbur, On two approaches to 3D reconstruction in NMR zeugmatography. In G. T. Herman and F. Natterer (eds.), Mathematical Aspects of Computerized Tomography, Berlin: Springer-Verlag, 1981.

49. G. Wang, D. L. Snyder, J. A. O’Sullivan, and M. W. Vannier, Iterative deblurring for CT metal artifact reduction, IEEE Trans. Med. Imaging, 15: 657–664, 1996.

28. P. R. Edholm and G. T. Herman, Linograms in image reconstruction from projections, IEEE Trans. Med. Imaging, 6: 301–307, 1987.

50. G. Wang and M. W. Vannier, Stair-step artifacts in three-dimensional helical CT—An experimental study, Radiology, 191: 79– 83, 1994.

24

COMPUTER NETWORKS

51. G. Wang and M. W. Vannier, Optimal pitch in spiral computed tomography, Med. Phys., 24: 1635–1639, 1997. 52. T. Olson and J. DeStefano, Wavelet localization of the Radon transform, IEEE Trans. Signal Process., 42: 2055–2067, 1994. 53. S. Y. Zhao, G. Welland, and G. Wang, Wavelet sampling and localization schemes for the Radon transform in two dimensions, SIAM J. Appl. Math., 1997, in press. 54. Y. Censor and G. T. Herman, On some optimization techniques in image reconstruction from projections, Appl. Numer. Math., 3: 365–391, 1987. 55. G. L. Herman and L. B. Meyer, Algebraic reconstruction techniques can be made computationally efficient, IEEE Trans. Med. Imaging, 12: 600–609, 1993. 56. J. A. Browne, J. M. Boone, and T. J. Holmes, Maximum-likelihood X-ray computed tomography. Appl. Opt., 34: 5199–5209, 1995. 57. S. H. Manglos, G. M. Gagne, A. Krol, F. D. Thomas, and R. Narayanaswamy, Transmission maximum-likelihood reconstruction with ordered subsets for cone beam CT, Phys. Med. Biol., 40: 1225–1241, 1995. 58. J. C. Russ, The Image Processing Handbook. Boca Raton, FL: CRC Press, 1995. 59. J. A. Parker, Image Reconstruction in Radiology. Boca Raton, FL: CRC Press, 1990. 60. G. T. Herman, Image Reconstruction from Projections—The Fundamentals of Computerized Tomography. New York: Academic Press, 1980. 61. G. T. Herman, Image Reconstruction from Projections—Implementation and Applications. New York: Springer-Verlag, 1979. 62. S. Webb, From the Watching of Shadows. New York: Adam Hilger, 1990.

GE WANG MICHAEL W. VANNIER University of Iowa

COMPUTERIZED TRANSACTION INTERCHANGE. See ELECTRONIC DATA INTERCHANGE. COMPUTER KEYBOARDS. See KEYBOARDS. COMPUTER MEMORY HIERARCHY. See MEMORY ARCHITECTURE.

COMPUTER MOTION ANALYSIS. See MOTION ANALYSIS BY COMPUTER.

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Wiley Encyclopedia of Electrical and Electronics Engineering Diagnostic Imaging Standard Article Thomas F. Budinger1 1University of California at Berkeley, Berkeley, CA Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4711 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (492K)

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Abstract The sections in this article are X Ray X-Ray CT Ultrasound Magnetic Resonance Imaging Radionuclide Emission Imaging (Nuclear Medicine Imaging) Endoscopy Interventional Radiology Diagnostic Radiological Imaging Brain Chest (Lung) Radiology Breast Cancer

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246

DIAGNOSTIC IMAGING

DIAGNOSTIC IMAGING Radiology is divided into diagnostic radiology, interventional radiology, and radiotherapy. Diagnostic radiology encompasses not only X-ray imaging but all modes of noninvasive human imaging, which are listed in Table 1. Of these, the principal methods used since 1970 are planar X-ray methods (e.g., fluoroscopy, angiography, gastrointestinal contrast series, urography, myelography), X-ray computed tomography (CT), ultrasound (US), techniques of positron emission tomography [positron emission tomography (PET) and single photon emission computed tomography (SPECT)], nuclear magnetic resonance methods of magnetic resonance imaging (MRI), magnetic resonance angiography (MRA), and magnetic resonance spectroscopy (MRS) also known as chemical shift imaging. Currently 70% of all the conventional radiological procedures use X rays. About 60% of the initial diagnostic procedures are X-ray based with only 8% nuclear medicine emission, 3% ultrasound, and 3% MRI. Advances in imaging speed, resolution, and data processing are rapidly changing the relative importance of these modalities particularly in areas such as MRI, fast X-ray CT, ultrasound, and emission tomography. These main methods are described in general terms below with more technical details presented in (1,2) and elsewhere in this encyclopedia. Following a description of these methods, major medical applications are highlighted for all of the major organ systems along with selected radiologic images (Fig. 1). X RAY Presently the most widely used imaging modality is the X-ray transmission intensity projection, most commonly known as ‘‘the X ray.’’ The difference between the X ray, a simple 2dimensional projection image, and the X-ray computed tomograph, ‘‘the CT,’’ is that the latter is the result of mathemati-

Table 1. Diagnostic Imaging Methods Summary Method (1) X-ray (contrast, X-ray CT, electron beam CT, spiral CT) (2) Ultrasound (US) Doppler Ultrasound (3) Emission Tomography (PET, SPECT) (4) Magnetic Resonance Imaging (MRI), Spectroscopy (MRS), Angiography (MRA) (5) Electrical Source Imaging (ESI) (6) Magnetic Source Imaging (MSI); Magnetoencephalographya (MEG) (7) Electrical Impedance Tomography (EIT) (8) Optical Imaging (Spectroscopy) a

Information Electron density Atomic composition Vascular lumens Acoustic impedance mismatches, Motion Radionuclide concentration (metabolism, receptor densities) Spin density, relaxation, diffusion, Chemical composition Brain and heart current sources Brain current sources

Electrical conductivity Attenuation, scattering, molecular status

Same as ESI.

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.

DIAGNOSTIC IMAGING

Brain

situation of constant attenuation along z. The attenuation coefficient of lung, water, tissue, and bone differ. Thus the intensity arriving at the film is more generally

Figs. 9, 10

Neck

Fig. 19

I(x, y) = I0 e−

Lung Fig. 11, 14 Heart Breast

Fig. 12, 13

Kidney

Fig. 16

Knee

Figs. 17, 18

Figure 1. This, a guide to the second half of this article, gives selected imaging results to demonstrate applications of the major diagnostic methods.

cally reconstructing an image of a slice through the body from multiple X-ray transmission projection images taken at multiple angles (usually equal) around the body. X rays are generated by the interaction of accelerated electrons with a target material such as tungsten. The electrons are produced by a heated cathode and accelerated by applying a voltage of about 100 keV between the cathode and a tungsten or molybdenum anode contained in a vacuum container called the X-ray tube or X-ray gun. The electron beam colliding with the anode releases X rays characteristic of the target materials. K-shell X rays from tungsten are about 70 keV and these as well as other X rays or photons are emitted from the X-ray tube placed one or more meters from the patient. The X-ray radiograph is usually a film, not unlike a photographic negative, which is darkened due to the interaction of the photons with the silver halide granules of the film. To enhance efficiency, a screen containing a phosphor is juxtaposed with the film. The electrons which interact with the phosphor release thousands of photons in the visible wavelength. The image reflects the number or intensity of photons reaching the film, and as is the case for a conventional negative, the greater the intensity, the darker the X ray. The intensity of photons transmitted through the body is modulated by the processes of Compton scattering and photoelectric absorption in tissue which are dependent on electron density and tissue elemental composition, respectively. These modulation processes are lumped into a simple attenuation coefficient. The intensity (or number) of photons arriving at a particular position, (x, y), on the X-ray film is given as I(x, y) = I0 e−µz

247

(1)

where I(x, y) is the photon intensity at position (x, y), I0 is the intensity from the X-ray tube, 애 is the attenuation coefficient (units of length⫺1), and z is the path length through the patient to the image position x, y. This equation applies to a



µ(x,y,z)z i

(2)

where we divided the path z into intervals ⌬zi. Here we assume parallel X-ray paths and no magnification; otherwise the image coordinates would be different from the object coordinates. The contrast or intensity difference between a lung tumor region and the surrounding normal tissue, as recorded on a conventional projection X ray, is related to the difference in number of photons projected through the tumor and through the parallel paths surrounding the tumor. This difference in number of photons would be about 23% for a 3-cm tumor, but the contrast visualized will depend on the image detector (e.g., silver halide film, solid state detector). Recall the fact that as the number of photons decreases the less the exposure of the X-ray film and the ‘‘whiter’’ the image in that region. X-ray imaging is mainly an anatomical procedure. The absorption of X rays due to differences in elemental composition has an important effect for imaging bone or calcium deposits because this absorption process is proportional to the atomic number. To provide image contrast between the blood vasculature and surrounding tissue, a dense fluid with elements of high atomic number (e.g., iodine, barium) can be injected or swallowed during the X-ray exposures. The movement through the body vasculature of a ‘‘contrast agent’’ such as an iodinated compound can be visualized by acquiring a sequence of X rays. The iodine or barium agent absorbs photons more than blood and tissue because the density is higher and the elements iodine and barium have a high atomic number giving rise to more photoelectric absorption. X-RAY CT X-ray transmission computed tomography (X-ray CT) gives anatomical information of the tissues mainly based on the density and elemental composition in specific regions as derived by manipulation of the projections of X rays through the body at multiple angles. It is useful to examine the log of the ratio of incoming intensity to the exiting intensity to parameterize these projections P(x, y) = ln


I0 = µ(x, y, zi )zi I(x, y) i∈ray x,y

(3)

Note the logarithm of the intensity ratio which we designate a projection P(x, y) is simply the line integral of attenuation coefficients along the path orthogonal to x, y if the ⌬zi’s approach zero. Thus for each angle:  P(x,y) =

Detector

µ(x, y, z) dz

(4)

Source

This summation is called a ray sum and the projection position is called a bin. The usefulness of this manipulation is that we can work with projections in a linear fashion to reconstruct the 3-dimensional distribution of linear attenuation coefficients and thus create an X-ray computed tomograph using linear operations discussed below. The denser the

248

DIAGNOSTIC IMAGING

First-generation CT

Fourth-generation CT

In spiral CT slip-ring technology provides continuous 360⬚ rotation of the X-ray gantry for up to 40 s (4). Because the table continuously moves the patient through the gantry during scanning, the projection data are collected along a continuous spiral path instead of as parallel transaxial slices in conventional X-ray CT. The simultaneous table movement and continuous gantry rotation (gantry rotation period is 1 s) without an interscan delay allow data to be collected very rapidly. When using intravenously administered iodinated contrast, images of the abdomen can be captured when the contrast is in the arterial or venous phase of the circulation. A typical high resolution (ⱕ3 mm collimation) spiral examination of the abdominal aorta can be performed in 30 s covering 9 to 18 cm of volume. A conventional CT scan may take several minutes to cover the same column and therefore cannot precisely image during the arterial contrast phase. This mode has brought X-ray CT applications to lung and abdominal scanning including data acquisition for virtual bronchoscopy and virtual colonoscopy. Electron Beam Computed Tomography (EBCT)

Electron beam CT

Spiral CT

Figure 2. X-ray computed tomography has evolved to rapid scanning systems over the last 25 years. Electron beam techniques can scan a few transverse sections without distortion from heart motion, and spiral X-ray CT can cover the abdomen with 2 breath-holds at 1 s per each transverse section.

electrons, the more the X-ray beams are scattered or attenuated. In addition, the absorption of X rays due to the photoelectric effect has important effects. Indeed the reason there are small differences between gray from white matter in the brain in CT images is that the H, C, N, O, P content for gray and white matter differ slightly resulting in about 3% changes between gray and white matter. The 3-D reconstruction in X-ray CT is the composite of a stack of 2-D transverse planes. A single 2-D transverse plane or tomograph consists of pixels whose values are proportional to the attenuation coefficients (i.e., scattering from electron density and photoelectric absorption). Individual solid state detectors are used for X-ray CT wherein the photon intensity is recorded as current generated in the detector for a given time interval. To perform the reconstruction, many one-dimensional projections are acquired from multiple angles. The idea is shown as the ‘‘1st generation CT’’ in Fig. 2. From these multiple projections the map or image of the anatomy in a particular slice is mathematically reconstructed using a computer, thus the word CAT for computer assisted tomography. The main method of reconstruction involves Fourier transformation of each projection, application of a ramp filter, inverse Fourier transformation, and back projection. This process is equivalent to back projection of each projection after each has been convolved with a kernel which is the Fourier transform of a ramp in spatial frequency space, thus the terminology ‘‘convolution method’’ (3). The contemporary trend for X-ray CT is to acquire finer resolution at high speed. These innovations have application to moving organs wherein data can be collected during 10 s to 16 s of breath holding.

Another mode of fast X-ray scanning with or without contrast injection employs an accelerated electron beam that strikes an anode target consisting of a large arc of tungsten encircling about 225 degrees transaxial to the patient (Fig. 2). The purpose is to avoid motion blurring from heart motion and to achieve an image sampling fidelity sufficient to evaluate the flow of contrast through the vascular and extracellular spaces mainly for heart, lung, aorta, kidney, and sometimes brain studies. EBCT applications are mainly for evaluation of coronary calcium and usually involve acquisition of 40 contiguous 3-mm thick sections extending from the right pulmonary artery to the heart apex. Each section is timed for acquisition during late diastole using ECG triggering and breath holding to minimize heart motion effects. Digital X-Ray Systems and Digital Radiology Though the present standard detector is X-ray film wherein the efficiency is enhanced by a phosphor which converts X rays to light photons for subsequent film exposure, there is a major technological development to deploy flat-panel imaging systems using solid-state detectors for direct electronic readout to supplant the screen-film based systems. This is part of the conversion of diagnostic imaging centers to an all digital electronic-based imaging and information communication center. All of the radiological imaging methods with the exception of the most commonly used X ray are digitally based. It is estimated that approximately 70,000 radiographic units in the United States will be retrofitted by digital detectors in the next few years. The present number of mammography units in the United States is approximately 11,000 and there is currently a major effort to create a digital system capable of providing a resolution at least as good as 50 애m (10 line pairs per mm) which is one-half as good as the contemporary screen film analog mammography systems. The benefits anticipated for digital mammography systems are great if the systems can meet the design criteria including resolution, image acquisition time, and heat loading of the X-ray tube (5). The technologies now being evaluated range from miniature 200 애m or less pixel-based, direct X-ray electronic detectors.

DIAGNOSTIC IMAGING

A proposed mode uses complementary metal oxide semiconductor (CMOS) electronics coated with selenium for real-time readout of electrons generated by the X rays striking the detector. Another mode uses cesium iodide scintillators coupled to silicon photodiodes or amorphous silicon solid state twodimensional arrays to allow direct electronic readout into computer systems. These are developments which go beyond the charged coupled devices (CCDs) which have been limited to wafers (12-cm diameter) which are too small for general radiographic replacement without elaborate methods to expand the field of view using optical systems and multiple wafers. A new concept in X-ray imaging embodied in the digital detector is known as reverse geometry imaging which matches a large X-ray source to a small solid state detector. The X rays are created using an electron beam which scans a 2-dimensional anode through magnetic deflection. A cone of X rays are focused onto a small solid state detector which records the attenuation through each patient position. The ideal detector for this application is cadmium zinc telluride (CZT) which is too expensive to make into panels for large field of view digital radiography. The concept of reverse geometry overcomes the size limitations and though designed for fluoroscopy, this innovation has other applications including breast mammography. Digital radiology systems facilitate image enhancement, calibration, distortion removal, and communications including storage, dissemination, consultation, and teleradiology.

ULTRASOUND Ultrasound, as currently practiced in medicine, is a real-time tomographic imaging modality. Not only does it produce realtime tomograms of the position of reflecting surfaces (internal organs and structures), but it can be used to produce realtime images of tissue and blood motion due to the Doppler effect. Ultrasound uses longitudinal compression waves generated by the voltage-induced oscillations of a piezoelectric crystal which is typically a ceramic disk consisting of lead zirconium titinate (PZT). The oscillations are at frequencies of 0.5 MHz to 20 MHz. The ultrasound is a coherent pressure wave which is reflected from surfaces of varying acoustic impedances, Z (Z ⫽ tissue density ⫻ velocity of sound in tissue). Loss of ultrasound energy dissipated as heat is at about 2 dB per cm for 2 MHz. This dissipation is due to loss of coherence. The ultrasound scatters from surfaces and this scattering is proportional to frequency. The attenuation amounts to 1 dB per cm tissue depth for each MHz. Thus at 3 MHz the loss at 2 cm of tissue penetration is 6 dB or a halving of the signal strength. Thus for imaging the heart in children 5 MHz can be used but for imaging an adult abdomen frequencies are usually 1 MHz. The major uses of ultrasound are in the examination of the carotid arteries, heart value function, heart wall motion, gall bladder, and examination of the pregnant abdomen including the anatomy of the fetus. The technique is to sonicate tissues with a transducer coupled by Vaseline to the skin surface over the area of study (e.g., carotid arteries, heart, gall bladder, uterus in pregnant women). The location of surfaces within tissues is determined

249

Ultrasound

(a)

(b)

(c)

(d)

Figure 3. Modes of ultrasound imaging which allow direct 2-D evaluation by mechanical scanning (a) or electronic scanning at frequencies between 1 to 5 MHz (b–d). Catheter-tip transducers are also available for vascular wall studies using 10 to 20 MHz frequencies.

by measuring the time interval between the production of an ultrasonic pulse and the detection of its echo resulting from the pulse reflected from those surfaces. By measuring the time interval between the transmitted and detected pulse, we can calculate the distance between the transmitter and the object. d=

1 t·c 2

(5)

where c is the speed of sound in tissue, ca. 1450 m ⭈ s⫺1. The ultrasound pulses are both produced and detected by the piezoelectric crystal or transducer. The reflected ultrasound imposes a distortion on the crystal, which in turn produces an oscillating voltage in the crystal. The same crystal is used for both transmission and reception. Types of ultrasound instruments are shown in Fig. 3. In addition to imaging (discussed under organs below), ultrasound is being used for monitoring therapy methods such as hyperthermia, cryosurgery, drug injections, and as a guide during biopsies and catheter placements. Tissue acoustic impedance changes with temperature, the material being injected, and the metal or plastic surfaces of the catheters. Doppler Ultrasound If a structure is stationary, the frequency of the reflected wave will be identical to that of the impinging wave. A moving structure will cause a backscattered signal to be frequency shifted higher or lower (⫾⌬f) depending on the structure’s velocity toward or away from the sound generator or transducer. The Doppler equation is f =

− f 0 v cos θ −2 f 0 v cos θ ≈ c+v c

(6)

250

DIAGNOSTIC IMAGING

Doppler imaging

Blood cells Figure 4. A major use of ultrasound is evaluation of blood flow in particular in the carotid arteries of the neck. The frequency changes associated with moving blood cells can give speed and direction of moving blood cells toward or away from the transducer.

where f 0 is the transmission frequency, (v) is the velocity of the moving cells, (c) the velocity of sound, and ␪ the angle between the transducer axis and the flow axis. For example, when an impinging sound pulse passes through a blood vessel, scattering and reflection occurs from the moving red cells (Fig. 4). In this process, small amounts of sound energy are absorbed by each red cell, then reradiated in all directions. If the cell is moving with respect to the source, the backscattered energy returning to the source will be shifted in frequency, with the magnitude and direction proportional to the velocity of the respective blood cell. Thus, if we use ultrasound to image the cross-sectional area of the blood vessel, the volume of blood flow can be calculated from the area of the vessel and the average velocities of the blood cells. The frequency shift data are color coded (e.g., carotid arteries in red and veins in blue) to form 2-D images. Image positional data are provided by the range (distance) of the signal whose frequency shift gives the speed at that range. Obstructions to blood flow are readily evaluated by this method using hand-held scanning devices. Power Doppler is a relatively new method of imaging the partial volume of moving blood. The sum of the square power of all frequency shifts gives information about the number of moving surfaces independent of direction. A local increase in vascularity as seen in breast cancer and lymph node metastases will give a relatively high power doppler signal. MAGNETIC RESONANCE IMAGING Magnetic resonance imaging (MRI) has evolved into one of the most powerful noninvasive techniques in diagnostic imaging and biomedical research. MRI uses the principles of a well-known analytical method of chemistry, physics, and molecular structural biology. However, this basic method has been slightly modified by applying relatively small spatial magnetic field gradients of varying amplitudes and directions to achieve spatial information of the density and characteristics of nuclei with magnetic spins. MRI is primarily used as a technique for producing anatomical images, but as described below, MRI also gives information on the physical–chemical state of tissues, flow, diffusion, and motion information. Magnetic resonance spectroscopy (MRS) gives chemical composition information. Most elements have at least one reasonably abundant isotope whose nucleus is magnetic. In biological materials, the magnetic nuclei of 1H, 13C, 23Na, 31P, and 39K are all abundant.

The hydrogen nucleus (a single proton) is abundant in the body due to the high water content of nonbony tissues. When the body is immersed in a static magnetic field, slightly more protons become aligned with the magnetic field than against the static field (Fig. 5). At 1 T (10,000 gauss) and 25 ⬚C the difference between these aligned populations of about one proton in a million produces a net magnetization. The net magnetization precesses around the static field at a frequency, ω = 2πv = γ B

(7)

where 웆 is frequency, 웂 is the gyromagnetic ratio particular to each nuclear species, and B is the field. A rapidly alternating magnetic field at the resonant frequency 웆, applied by a coil near the subject or specimen in the static magnetic field, changes the orientation of the net magnetization relative to the direction of the static magnetic field. These changes are accompanied by the absorption of energy (from the alternating magnetic field) by nuclei which undergo the transition between energy states. When the alternating field is turned off, the nuclei return to the equilibrium state, emitting energy at the same frequency as was previously absorbed. The nuclei of different elements, and even of different isotopes of the same element, have very different resonance frequencies. For a field of 1 T (10,000 gauss), the resonance frequency of protons is 42 MHz and that of phosphorus is 17 MHz. Thus, the magnetic nuclei in the body, when placed in a static magnetic field, can be thought of as tuned receivers and transmitters of RF energy. The governing relation is Eq. (7). Unlike its X-ray counterparts, MRI is not a transmission technique. Rather, similar to PET and SPECT, the material imaged is in itself the signal source (i.e., the polarized nuclear spins). The motion of the macroscopic nuclear spin magnetization, M is conveniently described in terms of the phenomenological Bloch equation: Mxy dM Mz − M0 = γM × B − − dt T2 T1

(8)

where M0 is the equilibrium magnetization, and T1 and T2 are relaxation times. T1 is the characteristic relaxation time for longitudinal magnetization to align with the magnetic field: following a perturbation such as an RF pulse or a change in

Normal (randomly arranged) magnetic nuclei

Magnetic nuclei polarized by immersion in a magnetic field

Figure 5. Magnetic resonance imaging is based on detection of the net magnetism of nuclei which have magnetic spin such as the hydrogen nuclei (protons) of tissue water. The detection is facilitated by RF pulses which stimulate signals from the oriented nuclei.

DIAGNOSTIC IMAGING

magnetic field, the longitudinal magnetization typically returns to its equilibrium value, M0, with a time constant T1. T2 is the characteristic time for decay of coherent magnetization in the transverse plane: the transverse magnetization decays exponentially with time constant T2 to its equilibrium value, Mxy ⫽ 0. For proton MRI, both relaxation times are determined by interaction of water with macromolecules in tissues. The dependence of image contrast on these parameters is appreciated by the equation components of the signal from a typical spin echo experiment: S(t) = f (v)ρ(1 − exp(−TR/T1 )) exp(−TE/T2 )






B x x

(10)

It can be seen that the frequency for any nuclei at position x will be ω + ω(x)

(11)

The received signal for all the nuclei in the space being imaged will be the linear superposition of the respective frequencies with amplitudes and individual signal decay characteristics (i.e., T1 and T2) determined by the local tissue biophysics at each spatial position. Three-dimensional information is gleaned by varying gradients in the x, y, z directions. The Fourier transform of this complex signal gives directly the image projections of intensities of nuclear magnetization. Reconstruction is implemented by back projection of these projections with appropriate filtering as is done in X-ray CT. An alternate reconstruction strategy involves use of phase alterations to encode information related to spatial positions of the nuclei. The RF coils used to excite the nuclei usually are quadrature coils which surround the head or body, but small (e.g., 6 to 10 cm) flat coils placed on the surface of the head or body are also used. Besides being the essential element for spatial encoding, the gradient-coil subsystem of the MRI scanner is responsible for the encoding of specialized contrast such as flow information, diffusion information, and modulation of magnetization for spatial tagging. Magnet types in current use are of the superconducting, resistive, and permanent magnet designs ranging in strength

Open Design < 0.5 T

1996 Design

Magnet designs

(9)

where f(v) is a flow function, ␳ is the density of 1H (protons), TR the pulse sequence time interval, and TE the time to detect the echo from a 180⬚ pulse applied TE/2 after the 90⬚ RF pulse. Tissues have T1 values which vary from 600 ms to 3000 ms (cerebral spinal fluid) and T2 values of 20 ms to 40 ms, except tumors whose values can be greater than 60 ms. The time needed to acquire MR images was thought to be prohibitive for functional studies such as done with X-ray angiography; however, when it was discovered that flip angles less than 90⬚ for the RF pulse could be used for MRI with acceptable signal to noise ratios and tissue contrast, a major horizon for contemporary studies was discovered (6). Now single slices can be obtained in less than 40 ms. The principal components of the MRI machine are the magnet, radio frequency (RF) coils, and the gradient coils. The gradient coils are used to acquire spatial information. Note that if Eq. (7) is modified by superposing a spatial gradient ⌬B/⌬x on the large static field, there will be a frequency shift in accord with ω + ω(x) = γ B +

1.5 T– 8 T Design

251

Figure 6. Magnets used for human imaging use superconducting wire in liquid helium systems or permanent magnet elements arranged around the subject for fields of about 0.3 T. Technological advances have allowed open designs for fields up to 1.5 T using superconductor wire.

from 0.06 to 4 T and have evolved from 2-m-long cylinders to more open designs for patient access and acceptability (Fig. 6). The majority of MR systems use superconducting magnets which provide fields of 1.5 T. Most currently produced magnets are based on niobium–titanium (NbTi) alloys, which are remarkably reliable, but require a liquid helium cryogenic system to keep the conductors at approximately 4.2 K (⫺268.8⬚C). MRI Contrast Agents MRI contrast agents are used to demonstrate perfusion and vasculature of organs. The usual contrast agents are watersoluble chelates of gadolinium. The chelates distribute in the vasculature and interstitial spaces much like the iodine contrast agents used for X-ray CT. Gadolinium causes an increase in the relaxation rates of the tissue water, thus, a decrease in T1 and T2. Presence of the gadolinium results in a signal enhancement on the images produced by pulse sequences which are designed to give higher signal for tissues with short T1 [e.g., short TR in Eq. (9)]. Manganese complexed to a chelate accumulates intracellularly in some tissues and also causes T1 shortening which leads to signal enhancement. Other types of contrast agents used by MRI are colloidal iron oxides (e.g., magnetite) coated with dextran which cause a MRI signal decrease in the region of their accumulation or a transient signal decrease as they perfuse through tissue due to the increase T2 relaxivity [short T2 times cf. Eq. (9)] of local tissue protons. Magnetic Resonance Spectroscopy (MRS) The nuclei constituting compounds in the human body have a resonance frequency governed by Eq. (7) relative to the imposed magnetic field. A nucleus of hydrogen will be in a slightly different magnetic field than the imposed magnetic field from the magnetic resonance magnet because adjacent spinning nuclei generate a small local field that shifts the frequency a few parts per million. Thus the protons of lactate are shifted in frequency by a few hundred hertz from the resonance frequency of water protons of 64 MHz at 1.5 T. This shift is known as the chemical shift and the resulting magnetic resonance spectrum gives specific information about the concentration of compounds in tissue noninvasively. Thus by

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manipulating the MRI gradients, selected regions can be sampled to determine the concentrations of tissue constituents containing hydrogen-1, carbon-13, phosphorus-31, and other NMR nuclei. As the spectra change with disease states, MRS has an important role in diagnoses of diseases, particularly brain cancer, prostate cancer, epilepsy, and brain trauma. The sensitivity of MRS is very low, thus only tissue constituents with concentrations in the millimolar range are evaluated in selected volumes usually greater than 0.2 mL (6 ⫻ 6 ⫻ 6 mm) for proton spectroscopy and greater than 1 mL for phosphorus spectroscopy. The sensitivity increases with field strength and MRS imaging, though feasible for low-resolution imaging of protons for maps of choline-containing compounds, N-acetylaspartate, lactate, and lipids.

tion followed by an over-compensation of blood rich in oxygen to the activated region of the brain. Thus there is initially an increase in oxygen extraction, local blood volume possibly first of the capillary bed and then a compensatory increase in the regional flow of oxygenated blood leading to less local magnetic field distortion and thus a positive signal when the before activation image is subtracted from the activation image. The positive BOLD signal, though not precisely positioned at the area of activation due to the overflow phenomenon, is used in clinical medicine to aid in epilepsy and tumor surgery by showing the neurosurgeon which vital areas of the brain to avoid in the surgical procedure. Magnetoencephalography is also used for this purpose and the combination of fMRI and MEG can give improved functional brain activity maps.

Functional Magnetic Resonance Imaging (fMRI)

RADIONUCLIDE EMISSION IMAGING (NUCLEAR MEDICINE IMAGING)

Though 25 years ago nuclear medicine methods demonstrated flow changes associated with mental activity in humans, it was not until the less invasive (i.e., no radioactivity) methods of MRI showed a magnetic resonance signal associated with stimulation of the brain that the medical scientists embraced fMRI as a method for mapping brain function. Methods that reflect brain activity currently use the fact that in response to a stimulus (e.g., light flash, sound, touch, physical movement), there is an increase in local blood volume and blood flow in order to supply that region of the brain with oxygen and nutrients. The local blood flow in areas of 5 mm or more around the part of the brain being stimulated is in response to an increase in metabolism and electrical activity. Radioactive tracers have shown this functional response and MRI measurements can also show flow changes using injected contrast material such as Gd-EDTA or Gd-albumin or other methods of detecting flow (see above). However, the principal method now employed by fMRI relies on an intrinsic change in the local magnetic field associated with a change in the partial volume of oxygenated hemoglobin (diamagnetic) and deoxygenated hemoglobin (paramagnetic). The process is known as the BOLD (blood oxygen level dependent) effect. The presence of paramagnetism from deoxyhemoglobin in capillaries, arterioles, and venules causes a magnetic field gradient across the imaging pixel sufficient to lower the MR signal. The positive BOLD signal is due to the effective decrease in paramagnetism and associated magnetic gradients over ranges less than 1 mm due to an increase in the partial volume of diamagnetism associated with more oxyhemoglobin in the region of activation. The fMRI is a map of the result of subtraction of the MRI before the activation from the MRI obtained by fast imaging methods performed during the activation. The more paramagnetism or deoxyhemoglobin the lower the signal and when one subtracts the MRI image taken before the activation from that taken after the activation the region of activation will appear relatively darker (a negative BOLD signal). The almost universal findings from studies done at 1.5 T show a positive BOLD signal (e.g., a 2% change), and until recently, this was thought to represent an in-flow of diamagnetic oxyhemoglobin because the brain was not extracting metabolic oxygen; however, using fields of 4 T it has been shown that the positive BOLD signal is preceded by a negative BOLD signal which corresponds to an initial decrease in blood oxygen (more paramagnetism) within 0.5 s of the activa-

Nuclear medicine imaging, also known by the terms emission imaging, radio-isotope imaging, scintigraphy (i.e., making pictures of the scintillations from crystals), is the technique of making images of the distribution of radioactive compounds. The two major elements of this method are the type of radiopharmaceutical which is injected into the patient and the type of scanner or camera (e.g., Anger camera, PET, SPECT) used for detection of gamma radiations from the radioactive isotope in the injected compound (Fig. 7). The particular diagnostic application relies on the fact that radiopharmaceuticals go to different organs in varying amounts depending on the disease state and the type of radiopharmaceutical. An example of this technique is the use of radioactive iodine to map the metabolic activity of the human thyroid gland in the neck. As about 25% of the ingested or injected iodine accumulates in the thyroid within 24 h as part of the process of making thyroid hormone, it is possible to detect trace amounts of radioactive iodine by use of nuclear detectors, and to make images of the thyroid. These are not anatomic images but are images reflecting the spatial distribution of metabolic activity. The majority of contemporary nuclear medicine studies are for brain blood flow, heart flow with and without induced stress by exercise or a pharmacologic agent, bone tumor scanning, thyroid scanning, and cancer detection. Specialized studies such as the detection of internal bleeding by injection of the patient’s red blood cells after labeling with Tc-99m and a host of other applications are enabled by use of specific tracers. The radiation dose to the patient is about equivalent to that from background radiation of one year (i.e., 0.1 cGy) with a maximum to any organ equivalent to a back X-ray examination (i.e., 1 cGy). Table 2 lists a few of the commonly used agents and their applications. Positron Emission Tomography (PET) Whereas most radioactive isotopes decay by release of a gamma ray and electrons, some decay by the release of a positron. A positron is similar to an electron but has a positive charge. PET imaging begins with the injection of a biological molecule that carries with it a positron-emitting isotope (for example, 11C, 13N, 15O, or 18F). Within minutes, the isotope accumulates in an area of the body for which the molecule has an affinity. As an example, glucose labeled with 11C (half-life, 20 min), or a glucose analog labeled with 18F (half-life, 1.8 h),

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Gamma Camera

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Photomultiplier tubes Scintillation crystal NaI (T1) Lead sheet with holes Detected gamma rays

Spect Pet

accumulates in the brain, where glucose is used as the primary source of energy. The radioactive nuclei then decay by positron emission. The emitted positron collides with a free electron usually within 1 mm from the point of emission. The interaction of the two subatomic particles results in a conversion of matter to energy in the form of two gamma rays, each with an energy of 511 keV (note: E ⫽ mc2 ⫽ 511 keV for the mass of each particle). These high-energy gamma rays emerge from the collision point in opposite directions (180⬚ ⫾ 0.25⬚), and are detected by an array of detectors which surround the patient (Fig. 8). When the two photons are recorded simultaneously by a pair of detectors, the nuclear decay that gave rise to them must have occurred somewhere along the line connecting the

Table 2. Selected Radionuclides and Associated Imaging Targets Radioactive Compound 123,131,122a

Iodine Iodine compounds

Tl, 13NH3a, 62Cu a Tc Pyrophosphate DTPA HMPAO Peptides Sestamibi Sulfur collide 111 In compounds 67 Ga 18 a F 18 a F —deoxyglucose —neuroreceptor ligands 15 a O —H2O —O2 201

Organ Thyroid Tumors Brain neuroreceptors Heart muscle

99m

a

⫽ positron emitters

Bone Kidney Brain White blood cells and platelets Heart Liver Tumors Tumors Bone Brain, heart, tumor Brain neuroreceptors Brain blood flow Brain, heart, tumor

Figure 7. The three commonly used instruments for imaging radionuclides (nuclear medicine imaging). Relative sensitivity is determined by the area of detector material to which a source is exposed. For conventional gamma camera imaging the sensitivity is related to the solid angle (d21 /4앟r2) provided by the detector or proportional the resolution divided by the distance squared between the radiation and the detector. For PET the sensitivity is related to area (not resolution) of detector material divided by 4앟r2.

detectors. If one of the photons is scattered then the line of coincidence will be incorrect. After 500,000 or more annihilation events are detected, the distribution of the positron emitting tracer is calculated by tomographic reconstruction procedures. PET usually reconstructs a two-dimensional image. Three-dimensional reconstructions can also be done using 2-D projections from multiple angles (7). The sensitivity of PET to detect nanomolar concentrations of tracers distinguishes this modality and its applications from those of MRI and MRS. MRI has exquisite resolution for anatomic studies and for flow or angiographic studies. In addition, magnetic resonance spectroscopy (MRS) has the unique attribute of evaluating chemical composition of tissue but in the millimolar range rather than the nanomolar range. Since the nanomolar range is the concentration range of most receptor proteins in the body, positron emission tomography is ideal for this type of imaging. Single-Photon Computed Tomography (SPECT) SPECT, like PET, acquires information on the spatial distribution of radionuclides injected into the patient. As in X-ray CT, SPECT imaging involves the rotation of a photon detector array around the body to acquire data from multiple angles. Because the emission sources (injected radionuclides) are inside the body cavity, the reconstruction tomography task is far more difficult than for X-ray CT, where the source position and strength (outside the body) are known at all times. In Xray CT the attenuation is measured, not the source strength. In PET and SPECT the reconstruction problem requires determination of the source position and strength (concentration) which is a much more difficult problem than simply determining the attenuation coefficient distribution. To compensate for the attenuation experienced by emitted photons from injected tracers in the body, contemporary SPECT machines use mathematical reconstruction algorithms more complex than those needed for X-ray CT (8). SPECT sensitivity is inferior to PET thus the attainable resolution of SPECT is limited due to a statistical limitation

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Positron annihilation photons 180° ± 0.25°

e+

Figure 8. The PET isotopes usually have more protons than neutrons and when a proton becomes a neutron the positron (positive electron) is released which encounters an electron. Positron and electron pair masses annihilate creating two photons that disperse at 180⬚ to be detected by PET sensors.

11

–1 mm

C nucleus

associated with acceptable amounts of injected radionuclides. Radionuclides used for SPECT imaging emit a single photon (e.g., 140 keV for 99mTc, 160 keV for 123I) but the positron emitters (e.g., 11C, 13N, 15O, 18F) result in two 511 keV photons for PET detection. Because only a single photon is emitted from the radionuclides used for SPECT, a special lens known as a collimator is used to acquire the image data from multiple views around the body. The use of a collimator results in a significant decrease in detection efficiency as compared with PET. In PET, collimation is achieved naturally by the fact that a pair of detected photons (gamma rays) can be traced to a line after being produced. In PET, there might be as many as 500 detectors that could ‘‘see’’ a PET isotope at any one time where as in SPECT, there may be only 1, 2, or 3 collimators; thus, only 1, 2, or 3 detectors are available to each resolution volume in the subject. The statistics needed for reliable images and practical radioactive dose limitations limit the useful resolution of SPECT. The resulting useful resolution (about 7 mm) for SPECT is inferior to PET resolutions of about 4 mm for contemporary commercial systems and 2 mm for current research instruments. Although SPECT imaging resolution is not that of PET, the ready availability of SPECT radiopharmaceuticals, particularly for the brain and head, and the practical and economic aspects of SPECT instrumentation make this mode of emission tomography attractive for clinical studies of the brain, heart, bone, and tumors (i.e., tumor metastases). ENDOSCOPY Endoscopy (i.e., visualization of the lumen of human conduits such as blood vessels and intestines) ranks among the most important advances in imaging over the last few decades. Unlike ultrasound, X-ray CT, and MRI, however, endoscopy has not in general been embraced by radiologists, being largely performed by other specialists and often viewed as competitive with well-established radiologic techniques.

The modern endoscope is a complex instrument requiring considerable precision in its construction. The shafts are circular in cross section with diameters dependent on the function of the instrument. Upper gastrointestinal instruments vary in diameter from 8 to 13 mm, side viewing duodenoscopes are 10 to 13 mm, and colonoscopes can be 15 mm in diameter. There are two principal forms of the endoscope: the fiberoptic endoscope and the video endoscope. In the former the shaft carries a fiberoptic–optic bundle to transmit light, and a second fiberoptic–optic bundle (the viewing bundle) transmits an image to a lens system in the eyepiece of the endoscope. The fibers in this bundle retain their spatial relationship to each other throughout their length in order to transmit the image. Video endoscopes are now becoming the preferred type. The viewing bundle is replaced by a high-resolution video ‘‘chip’’ at the tip of the endoscope. The image is displayed on a color monitor which is more comfortable for the endoscopist, facilitates image storage and manipulation, and aids training by dynamic image access by multiple viewers. The shaft of both types of endoscopes accommodates a ‘‘working channel’’ (up to 4.2 mm in the largest side-viewing duodenoscopes) for the passage of accessories such as biopsy forceps, baskets, balloons, snares, and stents. INTERVENTIONAL RADIOLOGY For many years a wide range of diagnostic and therapeutic procedures have been performed by fluoroscopic-aided catheter or device insertion. Currently, ultrasound, X-ray CT, and MRI are used in addition to fluoroscopy to guide the placement of probes with minimal disruption of tissue. The procedures include drainage of fluid from the pericardium, lungs, and abdomen; minimally invasive neurosurgical treatment of arteriovenous malformation of cerebral vessels; treatment of vertebral disk pathology; guided placement of radiation sources; and image controlled freezing or hyperthermia treat-

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ment of cancer. The percutaneous approach to surgical treatment depends on contemporary advances in 3-D imaging methodologies and new methods of visualization including virtual reality. Three technological advances that have enabled interventional radiology to replace many surgical methods include the 3-D capabilities of MRI, microfabrication methods for developing miniature surgical tools, and image manipulation and visualization methods. DIAGNOSTIC RADIOLOGICAL IMAGING Below the applications of the main methods of diagnostic imaging in human health care are presented under the categories of the body most commonly studied: brain, chest and lung, heart, abdomen, liver, kidneys, female reproductive organs, breast, prostate, and the skeletal system. Some illustrative images are presented as catalogued by Fig. 1. Medical background material and patient-based radiological procedures are found in (9). BRAIN Two of the most widely used imaging modalities in the study of the brain, cranial nerves, and spine are X-ray CT and MRI. As X-ray CT is well suited to imaging of bone, calcifications, and hemorrhage, it is still a mainstay of imaging in the emergency room particularly in the evaluation of head and face trauma and in suspected subarachnoid hemorrhage of the brain. With the advent of X-ray CT and MRI, the uses of plain film X rays and injection of air for demarcating the ventricles (i.e., pneumoencephalography) have disappeared. Though ultrasound study of the infant brain is possible because of less attenuation from the infant’s underdeveloped skull bone, even applications of ultrasound have been supplanted by X-ray CT and MRI in infants. Cerebrovascular Diseases (Hemorrhage and Stroke) A major application of X-ray CT in the emergency room is the evaluation of subarachnoid hemorrhage which is associated with trauma to the head but also occurs spontaneously. Of the spontaneous types 75% occur from the rupture of an arterial aneurysm and 25% occur due to leakage from an arteriovenous malformation. X-ray CT is the diagnostic mode which gives an increased signal from blood in the cerebral spinal fluid spaces. Intracerebral hemorrhage which can occur in hypertension is also best evaluated by X-ray CT which has wellknown temporal changes in signal intensity with time after the episode. Stroke is the result of a disruption of the nutrient blood flow to part of the brain and is a major cause of brain malfunction, particularly in the elderly. A transient stroke known as the transient ischemic attack lasts for 24 h or less, the stroke in evolution causes a progressive neurological defect, and the completed stroke is one in which the neurological defect appears fixed with no or very slow return to some function. MRI if available is the procedure of choice at the onset of symptoms using diffusion-weighted imaging methods. Later due to the cytogenic and then extracellular edema MRI and even X-ray CT can pinpoint the tissues involved. Frequently, the usual MRI study will not reveal the stroke terri-

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tory until 8 h after the event but the pathology can be detected by diffusion weighted imaging within 15 min of the event. Use of fast imaging methods such as echo-planar MRI will, with a MRI contrast agent, show decrease in regional blood flow. PET and SPECT techniques can in principle detect a stoppage in flow to regions of the brain at the time of the event because these techniques measure tissue blood flow directly by following the distribution of a flow tracer. The lack of day and night availability of a flow tracer for PET has limited its application to stroke. As PET and SPECT have a major importance in determination of vascular reactivity of compromised regions of the brain they are useful in the staging of patient treatment after the acute phase. Brain Angiography The use of contrast X-ray studies in evaluation of the brain vascular system (i.e., cerebral angiography) has to some extent been replaced by magnetic resonance angiography (MRA) though digital subtraction angiography still provides higher resolution images of the vascular tree when very high resolution is diagnostically important. MRA need not require any contrast medium injection as the method uses intrinsic properties of magnetic resonance of moving protons to attain contrast between flowing blood and stationary protons. The phase-sensitive technique uses a bipolar flow encoding gradient to cause a phase shift for a moving proton but a zero phase shift or canceled phase shift for a stationary spins. By reversing the polarity of the flow encoding gradient on alternate acquisitions and subtracting the data from these acquisitions the movement of the protons provides the signal. The time-of-flight method relies on magnetization of spins flowing into an excited volume wherein the stationary spins have been saturated; thus the unsaturated flowing blood will have a detectably higher signal compared with the surrounding previously saturated parenchyma. In addition, recently developed intravascular contrast agents such as a gadolinium– albumin complex have been used with MRI to improve definition of the cerebral vascular system. Brain Tumors The prevalence of primary brain tumors in the population is lower than most tumors and other diseases (about 2% of autopsies) yet the importance in diagnosis is vital to health care decisions particularly for metastatic tumors, which constitute 20% of brain tumor diagnoses. The majority of primary tumors are glioblastoma multiforme (25%) and the prognosis for these tumors is poor; however, therapy guided by presurgical and postsurgical MRI does aid in prolonging life with good quality for a few years. The prognosis for meningioma, pituitary adenoma, and acoustic neuroma, which together constitute 32% of brain tumors is very good if detected early, and both MRI and CT have played a major role in the presurgical planning for treatment. Tumors are usually hyperintense on T2 weighted MRI with a large region of vasogenic edema surrounding the main tumor site (Fig. 9). Though MRI studies provide a wealth of data in brain tumor detection, X-ray CT can in some cases (e.g., meningioma) be as valuable. MRI sequences designed to show blood volume have been useful in defining tumor locations and response to therapy.

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PET and SPECT have played a major role in the postsurgical followup of treated tumors. PET imaging following glioblastoma surgery for example can distinguish recurrent tumor from radiation necrosis (Fig. 9); however, recently use of magnetic resonance spectroscopy (MRS) has shown that in areas of recurrent tumor there is an elevated choline signal representative of an increase in one or more of the cholinecontaining compounds in a tumor. Brain Neurodegeneration (Alzheimer’s Disease and Multiple Sclerosis) The most common form of neurodegeneration is Alzheimer’s disease. As this disease is associated with the atrophy of the hippocampus and the parietal lobe during the early course of the disease, X-ray CT and now more recently MRI have been used to demonstrate the extent of loss of brain mass. Unfortunately, the atrophy of Alzheimer’s disease is not dissimilar to that found in normal aging as shown in Fig. 10. PET patterns of a decrease in the parietal lobe glucose metabolism are very characteristic of Alzheimer’s disease as is a decrease in blood flow as revealed by either PET or SPECT. The quantification of changes in glucose metabolism do correlate with the progression of the disease and can be used to monitor any efficacy of proposed therapies. Huntington’s and Parkinson’s diseases are generally detected by neurological examination but in these two diseases of neurodegeneration of parts of the brain, the X-ray CT and MRI patterns usually appear normal. However, the metabolic data of PET give specific and diagnostic patterns of decreases of glucose metabolism of the caudate nucleus in Huntington’s patients and decrease in the dopamine neurochemical system in the central gray matter of Parkinson’s patients.

Figure 10. MRI using the 3-D method of gradient recall shows brain atrophy during normal aging of an 86-year-old athlete (lower left) compared with that of a 77-year-old patient with Alzheimer’s disease (lower right). The atrophied areas look like two seahorses facing each other on either side of the central brain stem. These seahorselike structures are the hippocampi and are responsible for some memory functions.

Demyelinating Disorders (Multiple Sclerosis) MRI is the method of choice in the diagnosis of multiple sclerosis which appears as diffuse lesions of the white matter in the brain of the middle-aged adult. The areas of increased water content are associated with demyelination in regions usually surrounding the ventricles but lesions are found also

in the spinal cord and optic nerve. The other demyelinating diseases such as the congenital leukodystrophies have the common characteristic of increased water content of regions of the cerebral white matter. CHEST (LUNG) RADIOLOGY

MRI

PET

Figure 9. Comparison between MRI spin echo and PET glucose metabolism of a brain tumor. MRI shows increased water and longer T2 relaxation in and around (edema) the tumor. PET shows increase in glucose metabolism typical of brain tumors. Detection of probable islands of tumors outside the bright spot (arrow) depends on the resolution of the PET scanner.

The major uses of radiological imaging methods has been in the diagnosis of diseases of the chest or thorax. The major conditions for which radiologic imaging is essential is detection and evaluation of pneumonia (bacterial, fungal or viral), cancer, pulmonary embolism, and chest trauma. Pneumonia (infective consolidation of the lung) is detected as increased density by the standard X-ray radiograph but the specific diagnosis is not usually made (e.g., 30% to 50% of pneumonias have no causative diagnosis). The most commonly identified organism is Strep. pneumoniae (30%) followed by Hemophilius influenzae, Legionella, Chlamydia, and Mycoplasma pneumonias. Viral pneumonias are uncommon in adults but do predispose to bacterial pneumonias. The standard radiograph usually shows blotchy densities in localized areas sometimes involving both lungs. Tuberculosis is a bacterial infection with an insignificant incidence until the early 1990s when an increase in incidence occurred related to HIV infections. Densities around the central thorax (i.e., paratracheal and tracheobronchial adenopa-

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thy), effusions and patchy and multifocal opacities in the apicoposterior segment of an upper lobe or the apical segment of a lower lobe are common X-ray patterns in tuberculosis. Lung Cancer Lung cancer is usually classified into squamous cell carcinoma, adenocarcinoma, and undifferentiated carcinomas which are further divided into small (oat)-cell and large-cell types. Squamous cell carcinoma and adenocarcinoma are found most often. The peak incidence age group is 50 to 60 years old. Once a tumor is suspected, three modalities of imaging are brought to bear: X-ray CT, MRI, and PET (or SPECT). The plain X ray does show patterns which help distinguish bronchioloalveolar carcinoma from the other cell types, and the pattern of size, localization, and numbers of opacities can dictate treatment. Most patients still require an invasive procedure to distinguish a benign from a malignant lesion. Bronchoscopy, percutaneous needle biopsy, thoroscopy, and open lung biopsy have associated risks and do not always provide a definitive answer. A solitary pulmonary mass or nodule is the single most common presenting sign of bronchial cancer in 40% to 60% of lung cancers. But the majority of diagnosed solitary nodules are not malignant and even the malignant solitary nodules less than 20 mm in diameter can be successfully removed with a 5-year survival of 50%. X-ray CT, MRI, and PET can assist in a major way in staging these patients as these modalities allow evaluation of whether there is disease in the mediastinum in which case surgical resection would not be done as there is extended disease. Unfortunately most lesions remain undiagnosed and patients usually proceed to biopsy or surgery, which frequently reveals benign processes. In a recent study of radiographically indeterminate thoracoscopically resected solitary pulmonary nodules, 52% were benign (10). Thus, indeterminate lesions remain a dilemma with significant cost and morbidity. FDG PET imaging of thoracic neoplasms has been successful in distinguishing benign from malignant focal pulmonary abnormalities (11), in staging treatment for known malignancies, and in following patients after treatment for neoplasm (Fig. 11). Once the diagnosis of malignancy has been established, radiographic staging is usually performed using various modalities such as radionuclide bone scanning thoracic X-ray CT and, if available, 18FDG PET. The overall sensitivity and specificity of X-ray CT in detecting intrathoracic lymph node me-

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tastases in most series is only about 60%. FDG PET appears to be more sensitive although less specific for malignancy. Surgically proven metastases to hilar and mediastinal lymph nodes as small as 5 mm in diameter have demonstrated increased FDG uptake. After radiotherapy, residual abnormalities noted on chest radiographs can be differentiated as recurrent neoplasm or fibrosis using PET scanning (12). Pulmonary Embolism Blood clots in the lung circulation represent one of the most serious threats to life in both seriously ill patients, healthy patients in the postsurgical period, and in healthy patients (e.g., travelers in sedentary positions, leg fracture and sprained ankle cases in adults and youths). Postmortem studies have shown that up to 65% of hospitalized patients have emboli lodged in their pulmonary arteries (13) though only 1% have the clinical diagnosis. No single diagnostic test can be regarded as completely reliable in confirming or excluding the diagnosis of pulmonary embolism. In 90% of the cases blood clots arise from thrombosis of the deep veins in the legs. Blood stagnation is the major predisposing cause with only 15% or less of the pulmonary embolism patients having some blood clotting disorder. Radiological imaging techniques are used in to detect deep vein thrombosis and also to detect the existence of pulmonary embolism by direct radiographic examination of the lungs. Actual detection efforts commence when a patient has some signs of leg thrombosis (e.g., leg pain, swelling). It is important to verify if deep vein thrombosis exists as half of these patients may have had silent pulmonary embolism and a diagnosis leading to therapy (i.e., anticoagulation) is imperative. A second situation is the patient who presents symptoms of pulmonary embolism (e.g., coughing up blood). The deep veins of the legs and possibly pelvis are involved and thrombosis can be detected by injection of X-ray contrast material or a radioactive tracer into the peripheral veins (e.g., foot) and subsequent X ray or radionuclide imaging can detect blockage. But these techniques are imperfect as there are problems in venous access, incomplete filling, and discomfort to the patient. Indeed the patient can have thrombosis induced by the procedure. Of all the methods explored, magnetic resonance angiography seems now to have the potential for detection of deep vein thrombosis (14). Spiral X-ray CT has shown a 90% sensitivity and similar specificity for detection of pulmonary emboli relative to the gold standard of pulmonary angiography (15). More clots are detected with spiral X-ray CT that with pulmonary angiography. Though now considered to be a potential solution to the accurate, noninvasive diagnosis of pulmonary embolism, spiral X-ray CT shows great variability in detecting subsegmental emboli which have a frequency of 6%. This limitation is shared with the gold standard, however. BREAST CANCER

Figure 11. Metabolic response of metastatic prostate cancer to Suramin therapy measured by 18F-fluorodeoxyglucose (18FDG) positron emission tomography (PET). Note also the normal uptake of 18FDG in the left heart muscle whose brightness depends on the nutritional status of the patient (courtesy of C. Hoh, UCLA).

The incidence of breast cancer has been rising at 3% per year over the last 13 years to a prevalence level of about 0.1% of women in the United States. Since the mid-1980s when X-ray mammography became a readily available screening procedure, 44% of adult American women have had at least one procedure. The mortality rate of breast tumors remains high,

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Figure 12. High resolution digitized mammogram which shows microcalcification which could represent breast tumor but confirmation requires a biopsy (courtesy of D. Gur, University of Pittsburgh).

however, at a rate of 25 per 100,000 per year. There are approximately 11,000 dedicated mammography units in the United States. The consensus is that better methods of verification of suspicious lesions detected on X-ray mammography are needed (only 1 in 4 are biopsy positive). In addition, a method is needed to evaluate (screen) patients with radiographically dense breasts. Even the most advanced methods of digital image processing of high resolution mammograms fail to give specific diagnosis in a large fraction of cases (Fig. 12). Early breast cancers are often identified by planar X-ray mammography. The cost of this examination is low, the spatial resolution high (⬍100 애m). X-ray mammography is an effective screening technique for detection of cancerous growth in early stages. However, the complexity and heterogeneity of tissue within normal breasts makes unambiguous identification of malignant tumors difficult, as benign tumors and other breast structures can be similar in appearance to cancerous lesions. As a result, a large fraction (50% to 75%) of the suspicious structures identified in mammograms are noncancerous (16) and, thus, further diagnosis is necessary before determining that the patient should be treated for cancer. This further diagnosis is often obtained by biopsy. The biopsy can determine whether the structure is cancerous, and if so, can also determine the type of cancer and so suggest a course of treatment. The biopsy is time consuming for the physician, often uncomfortable for the patient, can increase the patient’s radiation exposure and, unless done by a cytopathologist at the bedside, takes several days before the results of a full assay for tumor type are available. Should the tumor prove to be cancerous, it is desirable to know before performing surgery whether the cancer has

spread to the axillary nodes, as this affects the treatment selection and prognosis (60% to 90% of patients without nodal involvement have no further breast cancers detected in their lifetimes) (16). Nodal involvement is difficult to determine before surgery from an X-ray CT or MRI scan. Nodes can be enlarged for a variety of benign reasons and small tumors difficult to observe by contemporary radiologic imaging methods. Contrast enhanced MRI has demonstrated a high sensitivity to detection of small (⬍1 cm) lesions in the breast; however, the specificity is less than 40%. The specificity improves slightly when dynamic techniques are used to measure the rate of contrast agent uptake during the initial minutes after contrast injection (17), but this specificity increase comes at the expense of spatial resolution or full imaging coverage of the breast. The axillary nodes are poorly evaluated with MRI mainly because of the inability to separate involved and uninvolved nodes based on contrast enhancement, as contrast enhancement occurs for both normal and pathological nodes. Doppler-ultrasound using color to encode velocity or blood volume (power) is another method of evaluating X-ray mammographically detected suspicious lesions before biopsy (18). This method is noninvasive and inexpensive, but it requires a skilled operator and is not envisioned as a screening method. Doppler-ultrasound imaging has been successful in showing which of the suspicious lesions are cancerous and has value in determining lymph node involvement (19) in preliminary detection studies, particularly in those with contrast agents (20). Positron emission tomography (PET) and the tracer F-18fluorodeoxyglucose (18FDG) can provide excellent sensitivity for malignant breast tumors and axillary node involvement. Because of the expense and limited availability of PET, single photon methods (SPECT, Gamma camera imaging, scintimammography) can play a major role in the differential diagnosis of suspicious X-ray mammography lesions. The specificity of the radiopharmaceutical 99mTc-sestamibi for axillary node involvement with breast cancer ranges from 42% to 88%. This specificity, though better than X-ray mammography, could be increased by an improved detector system. It is believed that the 8% to 20% of tumors that are not revealed by 99m Tc-sestamibi and those below 1.5 cm in diameter could be detected if the limitations of contemporary gamma cameras are overcome. Contemporary scintimammography and SPECT studies use large field of view gamma cameras which use a scintillator block coupled to a bulky array of photomultiplier tubes. By nature of their large size, these instruments are inadequate in most clinical situations because imaging of small organs such as the breast is usually awkward due to the fact that close access to the breast and axillae is prevented by the camera housing imaging system (Fig. 13). Solid state cameras have the potential to overcome these limitations.

HEART There are multiple methods used for examination of the human heart: ultrasound, X-ray coronary angiography, magnetic resonance imaging (MRI), magnetic resonance angiography (MRA), and nuclear medicine imaging methods (PET and SPECT). Ultrasound is used in the cardiologist’s office for

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Conventional gamma camera breast imaging

Figure 13. A major problem in breast imaging with conventional gamma cameras is to get close to the probable cancer site. Compact solid state imaging systems currently being designed for the breast can overcome this problem.

evaluation of valvular function using the M-mode method wherein motion of the valves is recorded as reflected signal distance versus the temporal sequence of the cardiac cycles. Using the 2-D imaging mode, the surface of much of the heart muscle can be imaged on-line, thus abnormalities in the synchronous motion of the contracting and expanding heart can be visualized by the cardiologist and changes of the heart muscle thickening during infusion of mild pharmacological stress can give evidence of the health of the heart. Ultrasound contrast agents using microbubbles have been introduced recently to aid in imaging the heart chambers and flow dynamics. Magnetic resonance imaging can also image the motion of the walls of the heart during each heart beat and though currently more cumbersome to operate, MRI has more complete coverage of the heart than ultrasound particularly on obese patients or patients with large breasts. MRI can also show fine detail of wall motion by specifically showing the muscle motion. A grid of saturated image pixels is placed over the heart slice using a saturating RF pulse sequence. The heart is then imaged during the cardiac cycle and the saturated pixels move with the pixel elements thus allowing determination of muscle motion and calculation of strain. Alternatively, the motion of each pixel can be deducted by phase changes associated with motion and the trajectories of muscle displacements. Nuclear medicine methods are employed in the evaluation of ischemic heart disease. The most common test is evaluation of the difference in perfusion between rest and stress induced by treadmill exercise or a pharmacological agent. In the absence of flow from an obstructed coronary artery, no tracer will reach part of the heart muscle fed by that artery and a hole will appear on the image. Frequently, when there is some but diminished flow to part of the heart, this difference between normal and low flow can be amplified by stressing the heart which increases the flow to normal tissue by as much as fourfold without any significant increase in flow to the compromised tissue. The difference between rest images and stress images is used to diagnose viable from infarcted tissue. As emission methods do allow specific chemical and metabolic processes to be detected, PET has been used to show glucose uptake (see heart uptake in Fig. 11), fatty acid metabolism, and neurochemical status of the heart. It has been discovered that the viable but jeopardized (low coronary flow)

regions of the heart accumulate an analogue of glucose labeled with 18F and this fact has been used to show that patients with a seeming absence of flow by perfusion methods but an accumulation of FDG do have some viable tissue and are candidates for revascularization surgery. Coronary Angiography The major use of X-ray imaging of the heart other than the routine chest X ray is coronary catheterization performed for the detection of coronary atherosclerosis. The procedure involves inserting a catheter in the femoral artery of the groin and feeding this catheter into the opening to the left and right coronary arteries which are at the aorta near the base of the heart. Contrast material having a high concentration of iodine is injected selectively into each coronary artery. Separate catheters are usually used for each coronary and the procedure is carried out by the cardiologist or radiologist in a hospital setting. This procedure, though considered the gold standard for definitive diagnosis of coronary athersosclerosis, is uncomfortable and costly, thus alternative methods for evaluation of the heart have been sought. MR angiography with or without use of MR contrast material is used to show the lumen of vessels just as is done with X-ray arteriography but presently with less resolution. In theory it is possible to image the coronary artery down to about 0.5 mm using intravascular contrast material and fast imaging methods and this modality could replace the commonly performed coronary catheterization (Fig. 14). Coronary Artery Calcification Detection Calcification of the coronary arteries increases with age in the asymptomatic population, but the quantity of coronary artery calcification is high in patients with clinically symptomatic coronary artery disease. Calcification is detected by intracoronary ultrasound and noninvasively by fast CT or electron beam CT (EBCT) wherein 100 ms duration scan times and EKG gating minimize motion blurring, which have hindered fluoroscopic and conventional CT for detection and quantification of calcium deposits. The fact that 8% of the asymptomatic subjects have calcium quantities above the 75th percentile for age and sex has led to the recommendation that older patients with risk factors (e.g., high cholesterol) for a coronary event have an EBCT (21).

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Left coronary artery Right coronary artery

Figure 14. Coronary angiography using invasive catheters is expected to be replaced by noninvasive MRI using spiral imaging methods and intravascular contrast material. This is a cartoon of the coronary arterial tree.

Right marginal

Circumflex

Anterior descending

Posterior descending

GASTROINTESTINAL Liver Two major radiological applications of ultrasound have been detection of primary and secondary cancer of the liver and gallstones in the gallbladder. The principal radiological diagnostic problem in the evaluation of the liver is the detection of cancer metastases from cancers elsewhere in the body and the differentiation of solid tumor masses from cysts, abscesses, and hemangiomas. Liver imaging is also valuable in evaluation of cirrhosis and fatty infiltration. X-ray CT with contrast agents, ultrasound, radionuclide methods, MRI, and most recently spiral X-ray CT have been compared in their accuracy to detect and differentiate liver lesions (22). The accuracy of US and CT is generally believed to be about 60% to 80%. A major problem of liver imaging in the past has been blurring and artifacts from normal liver motion during the tomographic scan. Motion, until recently, has rendered MRI less valuable than ultrasound or X-ray CT. But since 1994 methods of compensation for motion and faster imaging strategies of MRI and spiral X-ray CT have resulted in significant improvement in diagnoses. X-ray CT is the most widely used cross-sectional method for liver tumor evaluation in the United States. However, with the introduction of different MRI contrast agents which have specificity for normal parenchymal Kupfer cells, extracellular space or blood pool, the diagnostic potential of MRI might compete with spiral X-ray CT and possibly avoid needle biopsy frequently required to make the diagnosis of liver masses. MRI is the best technique for evaluating fatty infiltration and both MRI and ultrasound are effective in evaluating liver vasculature.

evaluation of tumor therapy. PET was found to be superior to pelvis X-ray CT in detecting local disease recurrence (23). The accuracy for local disease recurrence was 95% for PET and 65% for pelvis CT. No significant difference was found for the accuracy in detecting lesions in the liver, 98% for PET and 93% for CT or US. PET whole body scanning detects dissemination of colorectal tumors (24). GENITAL AND URINARY Fetus and Pregnancy Ultrasound using either an abdominal probe or a transvaginal probe is used to confirm the presence of intrauterine pregnancy at 4 to 5 weeks of gestation, the heart beat at 6 weeks, and subsequently the normal or abnormal development as well as the gestational age by the length of the embryo/fetus. Abdominal sonography has a vital role in deciding whether amniocentesis should be performed for genetic purposes and for detection of lung maturity. The electronic control of data from modern ultrasound transducers (Fig. 3) allows three-dimensional data extraction such that the face and other surfaces of the fetus can be visualized in utero (Fig. 15). Other uses of ultrasound relative to pregnancy are evaluation of causes of infertility, facilitation of embryo transfer, and investigation of causes of abdominal pain and masses, because X-ray methods are not used due to concern of exposing the fetus to ionizing radiation. MRI procedures are not in widespread accepted use at least in the first 2 trimesters though there is no known reason not to take advantage of MRI diagnostic capabilities throughout pregnancy. Female Reproductive Organ Cancer

Colorectal Tumors Colorectal tumors are usually suspected from symptoms of pain and bleeding with confirmation by conventional barium enema and colonoscopy. Since 1990, spiral X-ray CT (see above) has been utilized for the study of the abdomen and pelvis because the rapid coverage avoids motion artifacts from respiratory-based organ motion. Spiral X-ray CT data from the air-filled colon has been used effectively and is the basis for virtual colonoscopy. A major diagnostic problem is the

Ultrasound of the female pelvis is routinely used to depict the normal pelvic anatomy and to demonstrate both physiological and pathological changes of the ovaries, uterus, and cervix. Whereas ultrasound at 3.5 to 5 MHz provides diagnostic information of clinically suspected disease, X-ray CT and MRI are used to provide accurate localization for both biopsy and radiotherapy. Carcinoma of the uterine cervix is the second most common malignancy in women and accounts for two-thirds of ma-

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Kidney The major diseases for which radiological procedures are needed include, kidney injury, kidney artery stenosis (e.g., atherosclerosis), kidney failure, kidney carcinoma, and kidney transplant rejection. X-ray CT, ultrasound, radionuclide procedures, and MRI all have a role in the diagnosis of kidney disease. X-ray CT is the procedure of choice in evaluation of the patient with suspected kidney trauma. Use of spiral Xray CT with breadth holding and contrast agents provides a comprehensive evaluation for many situations; however, equivalent and in some cases supplemental information can be gleaned from use of fast MRI methods with injected contrast material (e.g., Gd-DTPA) as shown by the comparison in Fig. 16. Ultrasound methods provide a convenient approach to determination of dilation of the collection system in order to determine the presence of obstruction which can be caused by obstruction of an ureter or even benign prostatic hypertrophy. Figure 15. Three-dimensional ultrasound image of the face and hands of a normal fetus in the mother’s uterus (courtesy of Aloka Co. Ltd.).

lignant tumors found in the female genital tract. Neither ultrasound nor X-ray CT are clinically useful in the diagnosis of early disease, but X-ray CT can show local spread in more advanced disease. MRI is now established as a highly accurate method of demonstrating invasive cervical carcinoma but in early disease MRI underestimates superficial cervical carcinoma. These modalities are also of limited effectiveness in detection of carcinoma of the uterus which is one-third as common as cervical carcinoma. X-ray CT for uterine cancer requires use of intravenous contrast which enters the normal myometrium better than into the cancer. A common benign but clinically important condition of the uterus is fibroids which are usually accurately detected by ultrasound. Both ultrasound and X-ray CT are used in the definition of ovarian tumors and cysts but the differentiation is frequently difficult. The accuracy of MRI in distinguishing benign from malignant ovarian cancers remains controversial. Overall imaging techniques currently have a limited supportive role in the initial assessment of ovarian cancer but MRI appears to be superior in depicting local tumor infiltration of the bladder, pelvic fat, and other tissues including metastases to the liver and local invasion of the myometrium. Although MRI is superior to X-ray CT, X-ray CT is currently preferred for the assessment of the entire abdominoperitoneal cavity as it is more widely available, less expensive, and is a method with which there is a vast experience.

Prostate The two major diseases of the prostate gland are benign prostatic hypertrophy and prostate cancer. Prostatitis is an acute or chronic bacterial infection diagnosed and treated medically. Prostate cancer is the second commonest cause of cancer death in American men over age 55. It is the commonest human cancer found at autopsy in 30% of men at age 50 and in 90% at age 90 but usually as a latent disease. The best techniques for early diagnosis are measurement of prostatic serum antigen (PSA) and the rectal exam. The radiological procedures are transrectal ultrasound (TRUS) and transrectal MRI. Though neither technique can definitively separate prostatitis from carcinoma in all cases, both techniques can help define the likelihood of cancer and TRUS as well as Xray CT are used to guide biopsy needles to confirm cancer and metastases. Both techniques help define whether the cancer has invaded the capsule or tissues outside the prostate and therefore aid in the therapeutic choices. When cancers are confined to the prostate gland they are curable by surgical removal of the prostate gland. X-ray CT is not now used for routine tumor staging but is useful in advanced cancer when lymph nodes are enlarged. PET and SPECT are not useful in defining the primary disease because radionuclide accumulation in the bladder interferes with imaging the adjacent prostate. The prostate tumor metastases have low avidity for static accumulation of fluorodeoxyglucose (FDG) in bone but soft tissue metastases are detected by PET (Fig. 11). Recently, MRS (magnetic resonance spectroscopy) superposed on MRI has been effective in detection of prostatic tumors and in evaluation of therapy us-

Figure 16. Fast MRI with contrast material (left—courtesy of GE Medical Systems) reveals major vessels as well as kidney function through visualization of the ureter because the contrast material is excreted into the ureters by the kidney. Xray CT (right—courtesy of Siemens Medical Systems) using contrast material shows vessels and the presence of severe atherosclerosis revealed by multiple large calcium deposits in the aorta.

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ing an image of the ratio of choline containing compounds to citrate obtained from spatial maps of spectral information or chemical shift imaging. The normal prostate shows a high concentration of citrate on proton MRS and tumors have a relatively high signal from the trimethyl groups of cholinecontaining compounds. SKELETAL SYSTEM Joint Disease The three main categories of joint disease are injury, rheumatoid arthritis, and osteoarthritis. The important tissues of the joint are the synovial membrane, which is like a sleeve around the joint; the cartilage material on the surfaces of the articulating bones, which provides a low coefficient of friction surface allowing smooth joint motion; and the ligaments and tendons, which attach the articulating surfaces or are attached to these surfaces. Athletic injuries to shoulders and knees are common injuries which require diagnostic methods of X-ray CT and MRI. MRI has provided a major advance in the diagnostic imaging of the shoulder (rotator cuff) and knee (meniscus, cartilage) injuries (Fig. 17). Meniscal MRI, however, has a unique role. In many circumstances it substitutes for other techniques that are either less accurate (physical examination); largely operator dependent, mildly invasive and expensive (i.e., arthrography and diagnostic arthroscopy). MRI of the knee menisci is one of the most efficient uses of this technology. Although MRI certainly has a role in evaluating muscle, tendon, and ligament pathology in the knee, clinical assessment determines therapy. Rheumatoid arthritis is a systemic disease and at the joint level major pathophysiological mechanisms include immune, inflammatory, and healing or remodeling reactions. This disease starts as an inflammatory reaction of the synovium from an unknown cause. This reaction attracts white blood cells with a resulting swelling, edema, and soft tissue laxivity, thus weakening the joint and causing dysjunction between opposing bones. The nutrient supply to the cartilage is from nonvascular diffusion into and out of the synovium; thus, processes which influence the function of the synovium will

inevitably affect functioning of cartilage which depends on a balance between collagen, protein polysaccharide matrix, water, and ions for its health. Uncontrolled inflammatory responses of the white cells break down collagen and components of the cartilage with eventual destruction of the cartilage, a narrowing of the joint space and destruction of the adjacent surfaces of the bone of the joint. There also occurs a loss of bone early in the disease due to the inflammatory reaction which causes increased local destruction of the bone. The pattern of rheumatoid arthritis is also associated with some general disorders such as systemic lupus erythematosis, ankylosing spondylitis, scleroderma, and juvenile chronic polyarthritis but there is a high prevalence of rheumatoid arthritis of the extremities with no known etiology. The radiological pattern of rheumatoid arthritis is that of progressive changes in the joint tissue symmetry, bone alignments, and patterns of swelling which can be chronic or intermittent. Osteopenia (local regions of loss of bone mineralization) inevitably occur in spite of the treatment. These patterns are readily observed by plane X-ray examination of the hands and other joint spaces. MRI now can give exquisite details of synovium and cartilage changes (Fig. 17) particularly using sequences such as magnetization transfer. Osterarthritis is the most common joint disease and is characterized by noninflammatory cartilage loss accompanied by new bone formation. Joint trauma and joints undergoing repeated stress [knees and ankles of athletes (Fig. 17) and laborers] are probably the major causes of what is known as secondary osteoarthritis. The primary osteoarthritis currently of unknown etiology is believed to be the result of an intrinsic abnormality of cartilage leading to its degeneration. Both types have the radiological pattern of joint space narrowing and sclerosis of the opposing surfaces of subchondral bone. Deviations and subluxations between articulating bones develop slowly particularly in the fingers and knees. The abnormal bone growth in the fingers is often noted in the elderly as joint prominences known as Heberden’s nodes. The radiological pattern of narrowed joint spaces is easily visualized by the standard X-ray, but MRI can give much more detail of the pathology. Figure 18 shows a comparison of spiral X-ray CT and high resolution MRI of the knee, tibia and patella. Vertebral Spine Diseases

Figure 17. Different types of information provided by X-ray CT and high resolution MRI of the human knee (right—courtesy of S. Majumdar, University of California, San Francisco). The difference in magnetic susceptibility between trabeculae of bone and marrow allows high resolution and high contrast imaging.

Degenerative disk disease is the most common pathology of the vertebrae and may occur anywhere in the spine but is most dominant in the lower cervical and lower lumbar spine. It is characterized by disk-space narrowing, sclerosis of the vertebral body endplates, generation of osteophytes (bone spurs). The basis for much of lumbar spine disease is from the disk cartilage degeneration due to abnormal physical stressrelated biomechanical factors but also narrowing of the spinal column (spinal stenosis) by abnormal bone growth during aging plays an important role in progressive low back spinal cord symptoms. Abnormally high or sustained loading on the human disk cartilage results in water absorption from the nucleus pulposa by adjacent vertebrae, osmotic pressure change in the cartilage, stress on the collagen fibers of the disk annulus, bulging of the disk, and subsequent encroachment of disk material on the nerve roots. Congenital or acquired narrowing of the spinal canal (spinal stenosis) through abnor-

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to distinguish general tissue types has been valuable in differentiating benign from malignant tumors. Radionuclide imaging is used to evaluate metastases of nonbone tumors (e.g., lung, prostate, and breast) to bone. For this purpose conventional gamma camera planar imaging (scintigraphy) is one of the most often performed nuclear medicine procedure after injection of 99mTc-phosphate complex (e.g., pyrophosphate, diphosphate salt). The 99mTccomplex is readily available at all hospitals with a gamma camera and after injection 50% of these bone seeking radiotracers is deposited in the body skeleton as a technetium–calcium–phosphate complex one hour after injection. Whole body planar images are obtained. The amount of local uptake reflects the metabolic state independent of the amount of bone mineralization. The increase in blood flow accompanying the presence of increased metabolism is the major cause for increased uptake in tumors and areas of rapid bone turnover (e.g., osteoarthritis). Figure 18. MRI of joints can demonstrate defects in cartilage, ligaments, and bone with greater specificity than possible by other methods including arthroscopy. This image shows a lateral meniscus tear and cyst of the knee (courtesy of D. Rubin, University of Pittsburgh).

mal bone growth is frequently associated with disk disease. Spurs of the bony process of the joints of Luschka in the cervical spine result frequently in neurological compressive symptoms. Comprehensive evaluation of debilitating symptoms of spinal column and nerve root compression is now provided by MRI examination of the cervical and lumbar regions (Fig. 19). Bone Tumors Bone tumors and tumorlike lesions are most commonly detected by conventional radiography. MRI and X-ray CT are used to determine the extent of the tumor. MRI’s capability

Osteoporosis Osteoporosis is the most common metabolic bone disorder beginning in the fifth or sixth decade in women and the sixth or seventh decade in men. The loss of bone mineral is 3% to 10% per decade. The prevalence of osteoporosis in the aged is high and usually evades routine diagnosis because as much as 60% of bone mineral loss will occur before the osteopenia is detected on conventional X-ray examination. Postmenopausal osteoporosis is identified by a fracture pattern involving vertebral bodies and frequently the wrist (distal radius). Senile osteoporosis presents by fractures involving the hip and vertebrae. There is bone loss of both trabeculae and cortex but in the main the loss is of secondary trabeculae. Fractures in the elderly following minimal trauma as well as back pain frequently lead to diagnostic examination of bone density quantitation using two energy bands of photons either from a dual gamma ray emitting radionuclide such as gadolinium153 or a single X-ray source operated with filters or different energies to provide two energy bands such that the differential absorption between calcium and the elements of soft tissue can be measured. The bone density is interpreted as a percentage change from a normal or from that expected for a given age. Recent advances in MRI high resolution imaging show promise of providing architectural information of trabecular bone undergoing changes as shown by a comparison between high resolution X-ray CT and high resolution MRI of the knee (Fig. 18). Vascular System

Figure 19. MRI of sagittal view through the cervical spine shows a disk defect which is impinging on the spinal cord. MRI of the spine is also the optimum diagnostic imaging method for low back pain.

Radiological methods of imaging the arteries and veins of the body generally have used injection of iodinated contrast material followed by rapid imaging using plane X-ray film or digital subtraction methods. These methods involved inserting catheters in arteries and though precise in diagnostic specificity, they have some morbidity. Yet they remain the major methods for identification of atherosclerosis in brain, carotid, coronary, renal, aorta, and leg arteries. There are three methods of visualizing these arteries using MRI. The phase-sensitive technique uses a bipolar flow encoding gradient to cause a phase shift for a moving proton but a zero phase shift or canceled phase shift for a stationary spin. By reversing the polarity of the flow encoding gradient on alternate acquisitions and subtracting these acquisitions the movement of the

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protons provides the signal. The time-of flight method relies on magnetization of spins into an excited volume wherein the spins have been saturated thus the unsaturated flowing blood will have a detectably higher signal compared to the surrounding previously saturated parenchyma. A third method which will replace much of the conventional X-ray angiography uses injected contrast material which unlike previously used MRA contrast material stays in the blood pool (intravascular contrast). This material is gadolinium complexed to albumin which does not diffuse into tissues due to the large molecular size of albumin. The new contrast material overcomes limitations of the past related to temporal changes of contrast material which diffuses through the extracellular space. Image acquisition from moving organs and an imaging time not dependent on the rapidly changing concentration of the injected bolus allows high-resolution angiography. This method has promise to visualize most of the important elements of the arterial blood pool including the coronary arteries down to less than 1 mm before year 2000 (see Fig. 14). Flow quantitation particularly in the carotid arteries has been provided by Doppler ultrasound techniques which are in widespread use and when combined with ultrasound imaging the method is known as duplex scanning. Doppler images in color denoting direction (red for artery and blue for venous) with intensity related to speed are superposed on the gray level 2-D image which for the carotid shows the vessel and surrounding soft tissues. A new technique known as Power Doppler superposes the intensity of the Doppler signal rather than direction and speed thus this image represents the volume of moving red cells. This technique has been applied with success to a number of problems including detection of malignant lymph nodes from breast cancer and evaluation of kidney disease. Picture Archiving and Communication System (PACS) A major component of diagnostic radiology is the digital databased image storage, transfer, and processing systems embodied in software and hardware of PACS (picture archiving and communications system). PACS, developed many years ago for archiving and digitally transferring conventional radiographs after digitization, has established the methodologies and formats needed for the management of digital data acquired by contemporary radiologic imaging devices (e.g., MRI, PET, SPECT, US) (25). The very high bandwidth data currently being handled by PACS includes cardiac angiography image sequence involving 512 ⫻ 512 images taken at 30 frames per second. For transmission and display, optical fiber-based networks based on asynchronous transfer mode (ATM) are used. Workstations for review of these data can handle a complete or full injection sequence in ‘‘loop RAM (random access memory)’’ using the 512 ⫻ 512 format interpolated to 1024 ⫻ 1024 while displaying at 30 frames per second. A common standard for image transfer, storage, and retrieval is the DICOM (digital imaging and communications in medicine) standard. Standards for interfacing image data acquired by different modalities (PACS) with radiology information systems (RIS) and hospital information systems (HIS) will allow integration of patient images with the radiologist’s interpretation, clinical data, and demographic information for

ready access by authorized health-care personnel. These capabilities enable a new dimension in teleconferencing and local workstation-based image processing for 3-D visualization, segmentation, and contrast enhancement. This technology not only enables rapid access to patient information but expedites consultation, education, and research. ACKNOWLEDGMENTS This work was supported by the Office of Health and Environmental Research of the U.S. Department of Energy under contract DE-AC03-76SF00098 and National Heart, Lung, and Blood Institute. Dr. Kathleen Brennan assisted in the manuscript. BIBLIOGRAPHY 1. E. Krestel (ed.), Imaging Systems for Medical Diagnostics, Berlin and Munich: Siemens, 1990. 2. J. D. Bronzino (ed.), The Biomedical Engineering Handbook, Boca Raton: CRC Press, IEEE Press, 1995. 3. T. F. Budinger et al. (ed.), Mathematics and Physics of Emerging Biomedical Imaging, Washington, DC: National Academy Press, 1996. 4. W. A. Kalender et al., Spiral volumetric CT with single-breathhold technique, continuous transport, and continuous scanner rotation, Radiol., 176 (1): 181–3, 1990. 5. S. A. Feig and M. J. Yaffe, Digital mammography, computeraided diagnosis, and telemammography, Radiol. Clinics North Amer., 33 (6): 1205–30, 1995. 6. A. Haase et al., FLASH imaging. Rapid NMR imaging using low flip-angle pulses, J. Magn. Resonance, 67: 258, 1996. 7. S. R. Cherry and M. E. Phelps, Positron Emission Tomography: Methods and instrumentation, in M. P. Sandler et al. (eds.), Diagnostic Nuclear Medicine, Baltimore: Williams & Wilkins, 1995, pp. 121–138. 8. T. F. Budinger, Single Photon Emission Computed Tomography, in M. P. Sandler et al. (eds.), Diagnostic Nuclear Medicine, Baltimore: Williams & Wilkins, 1995, pp. 121–138. 9. J. B. Wyngaarden and L. H. Smith Jr. (eds.), Textbook of Medicines, Philadelphia: Saunders, 1988. 10. M. J. Mack et al., Thoracoscopy for the diagnosis of the indeterminate solitary pulmonary nodule, Ann. Thoracic Surg., 56 (4): 825–30, discussion 830–2, 1993. 11. E. F. J. Patz and P. C. Goodman, Positron emission tomography imaging of the thorax, Radiol. Clinics North Amer., 32 (4): 811– 23, 1994. 12. E. E. Kim et al., Differentiation of residual or recurrent tumors from post-treatment changes with F-18 FDG PET, Radiographics, 12: 269–279, 1992. 13. D. G. Freiman, J. Suyemoto, and S. Wessler, Frequency of thromboembolism in man, New England J. Med., 272: 1278–1280, 1965. 14. C. E. Spritzer et al., Detection of deep venous thrombosis by magnetic resonance imaging, Chest, 104 (1): 54–60, 1993. 15. M. Remy-Jardin et al., Diagnosis of pulmonary embolism with spiral CT: Comparison with pulmonary angiography and scintigraphy, Radiol., 200 (3): 699–706, 1996. 16. Institute of Medicine (ed.), Strategies for Managing the Breast Cancer Research Program, Washington, DC: National Academy of Sciences Institute of Medicine, 1993. 17. S. H. Heywang et al., Dynamische kontrastmittelunteruschungen mit FLASH bei kernspintomographie der mamma, Digitale Bildiagn, 8: 7–13, 1988.

DIAMOND-BASED SEMICONDUCTING DEVICES 18. R. P. Kedar et al., Automated quantification of color Doppler signals: A preliminary study in breast tumors. Radiol., 197: 39–43, 1995. 19. C. I. Perre, V. C. M. Koot, and P. de Hooge, Colour Doppler ultrasonography in the diagnosis of axillary lymph node metastases in breast cancer, The Breast, 5: 10–12, 1996. 20. R. P. Kedar et al., Microbubble contrast agent for color Doppler US: Effect on breast masses. Work in progress, Radiol., 3 679– 686, 1996. 21. R. B. Kaufmann et al., Quantity of coronary artery calcium detected by electron beam computed tomography in asymptomatic subjects and angiographically studied patients. Mayo Clinic Proc., 70: 223–232, 1995. 22. R. E. Larson et al., Hypervascular malignant liver lesions: Comparison of various MR imaging pulse sequences and dynamic CT, Radiol., 192 (2): 393–9, 1994. 23. C. Schiepers et al., Contribution of PET in the diagnosis of recurrent colorectal cancer: Comparison with conventional imaging, Eur. J. Surg. Oncol., 21 (5): 517–522, 1995. 24. G. Beets et al., Clinical value of whole-body positron emission tomography with [18F]fluorodeoxyglucose in recurrent colorectal cancer, Brit. J. Surg., 81 (11): 1666–1670, 1994. 25. H. K. Huang, PACS: Basic Principles and Applications. New York: Wiley, 1998.

THOMAS F. BUDINGER University of California at Berkeley

DIAGNOSTICS, PROGRAM. See PROGRAM DIAGNOSTICS.

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Wiley Encyclopedia of Electrical and Electronics Engineering Magnetic Source Imaging Standard Article M. S. Hämäläinen1 and J. T. Nenonen1 1Helsinki University of Technology, Otakaari, Finland Copyright © 1999 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4707 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (432K)

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Abstract The sections in this article are MEG and MCG Studies Instrumentation Generation of Bioelectromagnetic Fields Source Modeling Integration with Other Imaging Modalities Applications Other Applications Discussion About Wiley InterScience | About Wiley | Privacy | Terms & Conditions Copyright © 1999-2008John Wiley & Sons, Inc. All Rights Reserved.

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MAGNETIC SOURCE IMAGING

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magnetocardiogram and the magnetoencephalogram, various biomagnetic fields arising from the body have been studied since then. Biomagnetic measurements offer information that is very difficult to obtain with other imaging methods (4–8). MEG and MCG are generated by the electric currents in neurons or myocardial cells, and therefore the measurements provide direct real-time functional information about the brain or the heart, respectively. The time scale of the detectable signals ranges from fractions of a millisecond to several seconds or even longer periods. The biomagnetic measurements are totally noninvasive and the body is not exposed to radiation or high magnetic fields. Mapping of biomagnetic signals at several locations simultaneously is easy and fast to perform with multichannel systems. The metabolic processes associated with the neural or myocardial activity can be studied with positron emission tomography (PET), but the imaging times are several minutes, and the spatial resolution is about 5 mm. Better spatial resolution is obtained from functional magnetic resonance imaging. Estimation of bioelectric current sources in the body from biomagnetic measurements is often called magnetic source imaging (MSI). To relate the functional information provided by MSI to the underlying individual anatomy, other imaging methods are employed, such as magnetic resonance imaging (MRI), computer tomography (CT), and X ray. In this article, we focus on MEG and MCG, followed by a brief discussion of other fields of biomagnetism. Furthermore, instead of a comprehensive review of MEG and MCG applications we provide a few illustrative examples of recent MSI studies.

MEG AND MCG STUDIES

MAGNETIC SOURCE IMAGING More than 200 years ago, it was discovered that biological processes are accompanied by electrical currents. Since then, measurements of bioelectric signals have become widespread procedures of great importance in both biophysical research and medical applications in clinical use. These studies include, for example, measurements of electric potential differences arising from human heart [the electrocardiogram (ECG)], brain [the electroencephalogram (EEG)], and other organs. The same bioelectric activity that generates electrical potentials also generates weak magnetic fields. Because these biomagnetic fields measured outside the body are extremely low in magnitude (앑10 fT to 100 pT), it was not until 1963 that the first successful detection of the magnetic field arising from human heart was performed (1). This was the beginning of magnetocardiography (MCG). Magnetoencephalography (MEG) was introduced in 1968 when magnetic signals due to the spontaneous 움-rhythm in the brain were detected (2). However, it was only after the development of ultrasensitive superconducting quantum interference device (SQUID) detectors in the beginning of the the 1970s (3) that easier detection of biomagnetic signals became possible. In addition to the

During recent years, MEG and MCG have attained increasing interest. The ability of these methods to locate current sources combined with precise timing of events is valuable both in basic research and in clinical studies. One common type of an MEG experiment is to record the magnetic field associated with a sensory stimulus or a movement. Since these fields are usually masked by the ongoing background activity, signal averaging is routinely employed to reveal the interesting signal component. Recordings of neuromagnetic fields have provided a wealth of new information about the organization of primary cortical areas (9). Sensor arrays covering the whole head have made studies of complicated phenomena involving simultaneous or sequential processing in multiple cortical regions feasible. Because MEG is a unique tool to study information processing in healthy humans, several language-related studies have recently been conducted (10–12). It is also possible to record the ongoing rhythmic spontaneous brain activity in real time and follow its changes under different conditions (13,14). In addition to the well-known 10 Hz 움-rhythm originating in the vision-related cortical areas, similar spontaneous signals occur, for example, in the somatosensory system. MEG measurements have provided new information about both the generation sites of these rhythmic activities and their functional significance (15). Both evoked responses and spontaneous activity recordings can be utilized in clinical studies (16). For example, the locations of the somatosensory and motor cortices deduced

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.

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from evoked MEG signals can be superimposed on threedimensional surface reconstructions of the brain, computed from MRI data. The resulting individual functional map can be a valuable aid in planning neurosurgical operations. Encouraging results have also been obtained in locating epileptic foci in candidates for epileptic surgery. High-resolution MCG recordings have been applied both in basic cardiac research and in clinical studies. In the first MCG studies in the 1970s and 1980s, only single-channel devices were available, which limited the use of MCG to subjects and patients with normal sinus rhythm. Introduction of multichannel recording systems in the 1990s made the technique more suitable for routine clinical studies and for analysis of beat-to-beat variations. Currently, MCG is being used at some hospitals to test and further develop its clinical use. Multichannel MCG studies are particularly promising in two clinically important problems: (1) in locating noninvasively abnormal cardiac activity critical for the arousal of lifethreatening arrhythmias and (2) in evaluating the risk of such arrhythmias in different cardiac pathologies, especially after myocardial infarction. Successful MCG results have been reported, for example, in locating abnormal ventricular preexcitation sites associated with the Wolff–Parkinson– White syndrome, the origin of ventricular extrasystolic beats, and the origin of focal atrial tachycardias (17–21). Furthermore, MCG localization accuracy has been tested with artificial sources, such as a pacing catheter in the heart (20,22). The localization accuracy reported so far, ranging from about 5 mm to 25 mm, is sufficient to provide valuable information for preablative evaluation of the patients. In addition to localization studies, MCG has been applied to retrospective identification of patients prone to malignant arrhythmias with about 90% sensitivity and specificity (23).

active compensation. The inside floor area is usually 3 m by 4 m, and the height around 2.5 m. In addition, the sensitivity of the SQUID measuring system to external magnetic noise can be greatly reduced by the proper design of the flux transformer, a device normally used for bringing the magnetic signal to the SQUID. For example, an axial first-order gradiometer consists of a pickup (lower) coil and a compensation coil with identical effective area and connected in series but wound in opposition [see Fig. 1(a)]. This system of coils is insensitive to a spatially uniform background field, but it responds to inhomogeneities. Therefore, a source near the lower coil, which will cause a much greater field in the pickup loop than in the more remote compensation coil, will thus produce a net output. Most biomagnetic measurements have been performed with axial gradiometers. However, the off-diagonal planar configuration of Fig. 1(b) has some advantages over axial coils: The double-D construction (30) is compact in size, and it can be fabricated easily with thin-film techniques. The locating accuracies of planar and axial gradiometer arrays are essentially the same for superficial sources (31–33). The spatial sensitivity pattern, lead field, of off-diagonal gradiometers is narrower and shallower than that of axial gradiometers. These sensors thus collect their signals from a more restricted area near the sources of interest, and there is less overlap between lead fields of adjacent sensors in a multichannel array.

INSTRUMENTATION Detection of Neuromagnetic Fields The detector that offers the best sensitivity for the measurement of these tiny fields is the SQUID (24,25), which is a superconducting ring, interrupted by one or two Josephson junctions (26). These weak links limit the flow of the supercurrent, which is characterized by the maximum critical current Ic that can be sustained without loss of superconductivity. Direct-current (dc) SQUIDs, with two junctions, are preferred because the noise level is lower in them than in radio-frequency (RF) SQUIDs (27–29). The magnetic signals from the body are extremely weak compared with ambient magnetic field variations (5) Thus, rejection of outside disturbances is of utmost importance. Significant magnetic noise is caused, for example, by fluctuations in the earth’s geomagnetic field, by moving vehicles and elevators, and by the omnipresent powerline fields. For rejection of external disturbances, biomagnetic measurements are usually performed in a magnetically shielded room. To make such an enclosure, four different methods exist: Ferromagnetic shielding, eddy-current shielding, active compensation, and the recently introduced high-Tc superconducting shielding. Many experimental rooms have been built for biomagnetic measurements utilizing combinations of these techniques (34–36). Commercially available rooms utilized in biomagnetic measurements usually employ two layers of aluminum and ferromagnetic shielding, possibly combined with

∂ B z/ ∂ z (a)

∂ B z/ ∂ z

(b) Figure 1. Left: Coil configurations for (a) an axial and (b) a planar gradiometer. Right: The corresponding sensitivity patterns, lead fields (see section entitled ‘‘Distributed Source Models.’’). The plots show the lead fields on a spherical surface. The gradiometer coil is located above the center of each pattern. The direction and size of the arrows indicate the magnitude and direction of the lead field at the center of the arrow.

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Nevertheless, distant sources can often be detected more easily with axial gradiometer or magnetometer sensors. Therefore, many experimental and commercial systems include these coil configurations, possibly in combination with planar gradiometers.

Living cells sustain a potential difference between intraand extracellular media. In a static situation, most cells are, as seen externally, electrically and magnetically silent. Excitable cells can produce electric surface potentials and external magnetic fields, which can be detected from outside.

Multichannel Magnetometers

The Quasi-Static Approximation

The first biomagnetic measurements were performed with single-channel instruments. However, reliable localization of current sources requires mapping in several locations, and this is time-consuming with only one channel. Besides, unique spatial features present in, for example, brain rhythms cannot be studied. Fortunately, during the past 15 years, multichannel SQUID systems for biomagnetic measurements have been developed to provide reliable commercial products. A detailed account of this development can be found in Ref. 5. A state-of-the-art multichannel MEG system comprises more than 100 channels in a helmet-shaped array to record the magnetic field distribution across the brain simultaneously. The latest MCG systems contain 60 to 80 detectors in a flat or slightly curved array to cover an area about 30 cm in diameter over the subject’s chest or back. The dewar containing the sensors is attached to a gantry, which allows easy positioning of the dewar above the subject’s head or chest. The position of the dewar with respect to the subject’s head or torso is typically determined by measuring the magnetic field arising from an ac current fed into small marker coils attached to the skin (37,38) and by calculating their locations with respect to the sensor array. The locations of the marker coils with respect to an anatomical frame of reference are determined before the biomagnetic measurement by a three-dimensional digitizer. As an example of an MEG installation we describe the Neuromag-122 system (Neuromag Ltd., Helsinki, Finland) (33). This device employs planar first-order two-gradiometer units to measure the two off-diagonal derivatives, ⭸Bz /⭸x and ⭸Bz /⭸y, of Bz, the field component normal to the dewar bottom at 61 locations. The thin-film pickup coils are deposited on 28 ⫻ 28 mm2 silicon chips; they are connected to 122 dc SQUIDs attached to the coil chip. The separation between two double-sensor units is about 43 mm. The system is depicted in Fig. 2. The MCG system from the same company shown in Fig. 2 comprises 67 channels arranged on a slightly curved surface with diameter about 30 cm. The magnetic-field component (Bz) perpendicular to the sensor array surface is sensed by seven large-coil axial gradiometers and 30 two-channel planar gradiometer units identical to those described in the previous paragraph.

The total electric current density in the body, J, is time-dependent, and the electric field (E) and the magnetic field (B) produced by J can be found from Maxwell’s equations. However, the variations in time are relatively slow (below 1 kHz) (8,39), which allows treatment of the sources and the fields in a quasi-static approximation. This means that inductive, capacitive, and displacement effects can be neglected. In the quasi-static approximation Maxwell’s equations thus read:

GENERATION OF BIOELECTROMAGNETIC FIELDS Cellular Sources To interpret the measured signals, one has to understand how electric and magnetic fields are generated by biological tissue. In this article, we consider biomagnetic signals generated by the electric currents in excitable tissue. These magnetic fields are linked to bioelectric potentials, and it is useful to consider both the magnetic field and the electric potential together.

∇ · E = ρ/ 0

(1)

∇ ×E = 0

(2)

∇ ·B = 0

(3)

∇ × B = µ0 J

(4)

where 애0 and ⑀0 are the magnetic permeability and electric permittivity of the vacuum, respectively. Primary Current It is useful to divide the total current density in the body, J(r), into two components. The passive volume or return current is proportional to the conductivity ␴(r) and the electric field E: E (rr ) J v (rr ) = σ (rr )E

(5)

Jv is the result of the macroscopic electric field on charge carriers in the conducting medium. Everything else is the primary current Jp: E (rr ) J (rr ) = J p (rr ) + σ (rr )E

(6)

This definition would be meaningless without reference to the length scale. Here ␴(r) is the macroscopic conductivity; cellular-level details are left without explicit attention. The division in Eq. (6) is illustrative in that neural or cardiac activity gives rise to primary current mainly inside or in the vicinity of a cell, whereas the volume current flows passively everywhere in the medium. It should be emphasized that Jp is to be considered the driving ‘‘battery’’ in the macroscopic conductor; although the conversion of chemical gradients to current is due to diffusion, the primary current is largely determined by the cellularlevel details of conductivity. In particular, the membranes, being good electrical insulators, guide the flow of both intracellular and extracellular currents. If the events are considered on a cellular level, it is customary to speak about the impressed rather than primary current (39). Neurons Signals propagate in the brain along nerve fibers called axons as a series of action potentials. During an action potential, the primary current can be approximated by a pair of current

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Figure 2. Left: The Neuromag-122TM MEG system. Right: The 67-channel MCG system. (Photographs courtesy of Neuromag, Ltd.)

dipoles corresponding to a local depolarization of the cell membrane, followed by repolarization. This source moves along the axon as the activation propagates. Although the model is a simplified one, the experimental magnetic findings are in reasonable agreement with this concept (40,41). The axons connect to other neurons through synapses. In a synapse, transmittter molecules are released to the synaptic cleft and attach to the receptors on the postsynaptic cells. As a result, the ionic permeabilities of the postsynaptic membrane are modified and a postsynaptic potential is generated. The postsynaptic current can be adequately described by a single-current dipole. The dipolar field produced by the postsynaptic current flow falls off with distance more slowly than the quadrupolar field associated with the action potentials. Furthermore, the postsynaptic currents last tens of milliseconds, whereas the duration of a typical action potential is only about 1 ms. On this basis, it is believed that that the electromagnetic signals observed outside and on the surface of the head are largely due to the synaptic current flow. The two principal groups of neurons on the surface layer of the brain, the cortex, are the pyramidal and the stellate cells. The former are relatively large; their apical dendrites from above reach out parallel to each other, so that they tend to be perpendicular to the cortical surface. Since neurons guide the current flow, the resultant direction of the electrical current flowing in the dendrites is also perpendicular to the cortical sheet of gray matter.

Myocardium In heart tissue, there are three main types of cells: pacemaker cells in the sinus and atrioventricular nodes, cells specialized for rapid conduction of the excitation along the bundle of His and Purkinje network, and, finally, muscle cells that perform mechanical work. Cardiac muscle consists of a large number of individual cells, each about 15 애m in diameter and 100 애m long. The intracellular spaces of adjacent muscle cells are interconnected, which makes the three-dimensional structure very complex. An action potential in myocardial cells lasts 300 ms to 400 ms, which is over 100 times longer than a typical neural action potential. Provided that we observe a single myocardial cell at some distance from the membrane, the depolarization and repolarization can be modeled, respectively, by an equivalent depolarization and repolarization dipole. Ventricular depolarization or repolarization propagates as about 1 mm thick wavefronts in the heart. A commonly used model to describe such propagating fronts is a uniform double layer (39). It consists of dipoles with equivalent strengths (assuming a constant dipole density), oriented perpendicular to the wavefront. The model is more suitable than a single current dipole in characterizing an excitation taking place simultaneously in a spatially large region, but it cannot account for possible holes in the wavefront (e.g., necrotic tissue). In addition, the classical concept of a uniform double layer is not valid if the anisotropic nature of myocardial tissue is to be included.

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Calculation of the Bioelectromagnetic Fields In the quasi-static approximation, the electric potential ␾ obeys Poisson’s equation: ∇ · (σ ∇φ) = ∇ · J p

(7)

while the magnetic field due to the total current density, J, is obtained from the Ampe`re–Laplace law: B (rr ) =

µo 4π


V

J (rr  ) × R dv R3

(8)

where the integration is performed over a volume V containing all active sources, r⬘ 僆 V, R ⫽ r ⫺ r⬘. It can be shown that the volume currents in an infinite homogeneous volume conductor give no contribution to the electric potential or the magnetic field, which are solely due to the primary currents, Jp (42). Next, we assume that the body consists of homogeneous subvolumes v⬘k, k ⫽ 1, 2, . . ., M, bounded by the surfaces Sk. The electrical conductivity within v⬘k is constant, ␴k. Usually, the body is surrounded by air, and thus the conductivity outside the body surface is zero. In this case, the surface potential, ␾S, can be obtained from an integral equation (43)

(σl + σl )φS (rr ) = 2σn φ∞ (rr ) +


M 1  R Sk · 3 (σk − σk ) φS dS 2π k=1 R Sk (9)

where ␴n is the conductivity at the source location, ␴k⬘ is the conductivity inside and ␴k⬙ is the conductivity outside the surface Sk, and dSk is the surface element vector perpendicular to the boundary. The term ␾앝 denotes the electric potential in an infinite homogeneous medium (in the absence of the boundaries Sk), and the surface integral accounts for the contribution of the counductivity change on the boundary Sk. The external magnetic field is then evaluated by substituting the total current density, J, into Eq. (8). It can be shown (44) that the result can be transformed to the form

B (rr ) = B ∞ (rr ) +


M µo  R (σk − σk ) φS dS k × 3 4π k=1 R S

(10)

k

where the term B앝 is the magnetic field in the absence of the boundaries, Sk. Again, the surface integral accounts for the contribution of the counductivity change on the boundary Sk. Analytic Solutions. Analytic solutions of Eqs. (9) and (10) exist only in a few simple symmetric geometries. If we approximate the head or the torso by a layered spherically symmetric conductor, it is possible to derive a simple analytic expression for the magnetic field of a current dipole (41): B (rr ) =

Q × r Q · r )∇F (rr, r Q ) Q × r Q − (Q µ0 FQ 4π F (rr, r Q )2

(11)

where rQ is the location of the current dipole, Q is the dipole moment vector, F(r, rQ) ⫽ a(ra ⫹ r2 ⫺ rQ ⭈ r), and ⵜF(r, rQ) ⫽ (r⫺1a2 ⫹ a⫺1a ⭈ r ⫹ 2a ⫹ 2r)r ⫺ (a ⫹ 2r ⫹ a⫺1a ⭈ r)rQ, with a ⫽ (r ⫺ rQ), a ⫽ 兩a兩, and r ⫽ 兩r兩.

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An important feature of the sphere model is that the result is independent of the conductivities and thicknesses of the layers; it is sufficient to know the center of symmetry. The calculation of the electric potential is more complicated: The results can be expressed only as a series expansion of Legendre polynomials, and full conductivity data are required (45). Furthermore, radial currents do not produce any magnetic field outside a spherically symmetric conductor. Thus MEG is, to a great extent, selectively sensitive to tangential sources, and EEG data are required to recover all components of the current distribution. The obvious advantage of a simple forward model is that a fast analytical solution is available. It has also been shown (46) that a sphere model fitted to the local curvature of the skull’s inner surface (4) provides accurate enough estimates for many practical purposes. However, when the source areas are located deep within the brain or in the frontal lobes, it is necessary to use more accurate approaches. In the first MCG localization studies the body was approximated as a homogeneous semi-infinite space, which can be regarded as a generalization of a spherical model with the radius extended to infinity (47,48). However, later computer studies have shown that the semi-infinite approximation is oversimplified, and a more accurate description of the thorax shape is needed in the inverse studies (21,49). A slightly more accurate description of the thorax geometry can be obtained by using cylindrical or spheroidal models. However, the analytical expressions for arbitrary dipolar sources become substantially more complex than in the spherical case (50), and only a few studies to apply spheroids have been reported. Numerical Approaches. When a realistic geometry of the head or the thorax is taken into account, numerical techniques are needed to solve the Maxwell equations. When applying the boundary-element method (BEM), electric potential and magnetic field are calculated from the (quasi-static) integral equations [Eqs. (9) and (10)], which can be discretized to linear matrix equations (46,49,51). In most BEM applications to the bioelectromagnetic forward problem, the surfaces are tessellated with triangular elements, assuming either constant or linear variation for the electric potential on each triangle. However, the accuracy of the magnetic-field computation may suffer if a dipole source is located near a triangulated surface. The accuracy can be improved, for example, by applying Galerkin residual weighting instead of the standard collocation method and by approximating the surfaces with curved elements instead of plane triangles (52). Realistically shaped geometries of each subject are usually extracted from MRI data. The regions of interest (e.g., the heart, the lungs, and the thorax; or the brain, the skull, and the scalp) need to be segmented from the data first (see section entitled MRI). The volumes or the surfaces are then discretized for numerical calculations. The segmentation and tessellation problems are still tedious and nontrivial (53). The relatively low conductivity of the skull greatly facilitates the modeling of MEG data. In fact, a highly accurate model for MEG is obtained by considering only one homogeneous compartment bounded by the skull’s inner surface (46). With suitable image processing techniques it is possible to

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isolate this surface from high-contrast MRI data with little or no user intervention. The boundary-element model is more complex for EEG, because three compartments need to be considered: the scalp, the skull, and the brain. While the surface of the head can be easily extracted from the MRI data, it is difficult to construct a reliable algorithm to automatically isolate the scalp-skull boundary. In addition, special techniques are required to circumvent the numerical problems introduced by the high conductivity contrast due to the low-conductivity skull. It is also possible to employ the finite-element method (FEM) or the finite-difference method (FDM) in the solution of the forward problem. The solution is then based on the discretization of Eq. (7). In this case, any three-dimensional conductivity distribution and even anisotropic conductivity can be incorporated (54). However, the solution is more time-consuming than with the BEM, and therefore the FEM or FDM has not been used in routine source modeling algorithms which require repeated calculation of the magnetic field from different source distributions. SOURCE MODELING The Inverse Problem The goal of the bioelectric (EEG, ECG) and biomagnetic (MEG, MCG) inverse problems is to estimate the primary source current density underlying the electromagnetic signals measured outside or on the surface of the body. Unfortunately, the primary current distribution cannot be recovered uniquely, even if the electric potential and the magnetic field were known precisely everywhere at the surface and outside the body (55). However, it is often possible to use additional anatomical and physiological information to constrain the problem and facilitate the solution. One can also replace the actual current sources by equivalent generators that are characterized by a few parameters. The values of the parameters can then be uniquely determined from the measured data by a least-squares fit. The solution of the forward problem is a prerequisite for dealing with the inverse problem requiring repeated solution of the forward problem. The Current Dipole Model. The simplest physiologically sound model for the neural or myocardial current distribution comprises one or several point sources, current dipoles. In the simplest case the field distribution, measured at one time instant, is modeled by that produced by one current dipole. The best-fitting equivalent current dipole (ECD) can be found by using standard least-squares optimization methods such as the Levenberg–Marquardt algorithm (56). In the time-varying dipole model, introduced by Scherg and von Cramon (57,58), an epoch of data is modeled with a set of dipoles whose orientations and locations are fixed but whose amplitudes vary with time. Each dipole corresponds to a small patch of cerebral cortex or other structures activated simultaneously or in a sequence. The precise details of the current distribution within each patch cannot be revealed by the measurements, which are performed at a distance in excess of 3 cm from the sources. As a result of the modeling, one obtains the locations of the sources and the orientation of the dipole component tangential to the inner surface of the overlying skull. In addition,

traces of the evolution of the source strengths are obtained. Again, the optimal source parameters are found by matching the measured data collected over a period of time with those predicted by the model using the least-squares criterion. From a mathematical point of view, finding the best-fitting parameters for the time-varying multidipole model is a challenging task. Because the measured fields depend nonlinearly on the dipole position, the standard least-squares minimization routines may not yield the globally optimal estimates. Therefore, global optimization algorithms (59) and special fitting strategies (60), taking into account the physiological characteristics of particular experiments, have been suggested. For each candidate set of dipole positions and orientations it is, however, straightforward to calculate the optimal source amplitude waveforms using linear least-squares optimization methods (61). In cardiac studies, an ECD is applicable for approximating the location and strength of the net primary current density confined in a small volume of tissue. Myocardial depolarization initiated at a single site spreads at a velocity of about 0.4 mm/ms to 0.8 mm/ms, and the ECD can be thought to be moving along the ‘‘center of mass’’ of the excitation. In practice, localization based on a single ECD is meaningful only during the first 10 ms to 20 ms of excitation. Because both nonlinear fits for spatial coordinates and linear fits for dipole moment parameters need to be searched at every time instant, the use of even two ECDs becomes very complicated in cardiac studies. Alternatively, cardiac excitation can be modeled with a set of spatially fixed stationary or rotating dipoles, but attempts to define the time courses of the dipole magnitudes usually result in physiologically unacceptable results. The Current Multipole Expansion. It is often convenient to present the electric potential and the magnetic field as multipole expansions. In the current multipole expansion the field due to the primary current, B앝 in Eq. (10), is expressed as a Taylor series (62). Thus, more complex source current configurations can be described as higher-order multipole moments, such as quadrupole moments. Different source models can be built by combining dipole and quadrupole moments. A current dipole is actually the lowest-order term in a general current multipole expansion (62); higher-order terms, such as quadrupoles and octupoles, can be used to account for more complex primary current configurations (48). Distributed Source Models. Another approach often taken in source modeling is to relax the assumptions on the sources and use various estimation techniques to yield a distributed image of the sources. These methods include, for example, the minimum-norm estimates (63), magnetic-field tomography (MFT) (64), and low-resolution electromagnetic tomography (LORETA) (65). The source images can provide reasonable estimates of complex source configurations without having to resort to complicated multidipole fitting strategies. However, one must keep in mind that even if the actual source is pointlike, its image is typically blurred, extending a few centimeters in each linear dimension. Therefore, the size of the ‘‘blobs’’ in the source images does not directly relate to the actual dimen-

MAGNETIC SOURCE IMAGING

sions of the source but rather reflects an intrinsic limitation of the imaging method. The basic concept relevant to all distributed source estimation methods is the lead field. The signal bk detected by the kth sensor in the sensor array is a linear functional of the primary current distribution Jp and can be expressed as
bk = L k (rr ) · J p (r) dv (12) G

where the integration extends over the source region G, which can be a curve, a surface, or a volume. The functions Lk are often called lead fields, which can be readily obtained by solving the forward problem for dipole sources. The minimum-norm estimate (63) is the current distribution that has the smallest norm and is compatible with the measured data. Here, the norm is defined by
J 2 = J J(rr )2 dv (13) G

The minimum-norm estimate J* can be expressed as a N weighted sum of the lead fields, J* ⫽ 兺k⫽1 wkLk. The weighting coefficients are found by fitting the data, computed from the minimum-norm estimate with those actually measured. Since the lead fields in a large array are almost linearly dependent, regularization techniques are needed to produce stable estimates. Another type of a distributed source model was developed for reconstructing the sequence of ventricular depolarization by van Oosterom et al. (66). Their model is based on a uniform double layer of constant strength. Lead fields for MCG and ECG sensors are evaluated at each node on the endo- and epicardial surfaces of the heart. These transfer functions are weighted by the Heaviside time step function to define the onset of excitation at each surface node. Physiological constraints and regularization are then applied to limit the number of solutions. Regularization and Constraints The bioelectromagnetic forward problem can be written as b ⫽ Lx ⫹ e, where vector x represents the unknown (linear and nonlinear) source parameters, vector b consists of the measured (MEG/EEG or MCG/ECG) signals, vector e contains the contribution of measurement noise, and matrix L is effectively the transfer (lead field) function between the sources and the measurement sensors. Even small contributions of the noise e make the solution for x very ill-posed. Therefore, regularization techniques are needed to stabilize the solution (67). In bioelectromagnetic studies dealing with source distributions, the most frequently applied techniques include the truncated-eigenvalue singular value decomposition (63) and the L-curve method (67). Another new approach is based on Wiener filtering and orthogonalized lead fields (68). In addition, spatial weighting can be applied to improve the solutions (21,69). Futher improvements are achieved by applying more than one constraint at the same time (70). One can also make explicitly the additional assumption that the activated areas have a small spatial extent. For example, the MFT algorithm obtains the solution as a result of an iteration in which the probability weighting is based on

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the previous current estimate (64). According to the authors, this procedure produces more focal images than the traditional minimum-norm solutions. Another possibility is to use a MUSIC-type probability weighting (61) combined with cortical constraints to focus the image (71). An approach that incorporates the desire to procure focal source images is to use the L1 norm, that is, the sum of the absolute values of the current over the source space, as the criterion to select the best current distribution among those compatible with the measurement (72–74). In contrast to the traditional L2-norm cost function [see Eq. (13)], the L1-norm criterion yields estimates focused to a few small areas within the source space. The most powerful way to constrain the bioelectromagnetic inverse problem is to apply anatomical and functional a priori information. For example, accurate reconstruction of the cortex surface or myocardial tissue from MRI data limits the spatial extent and orientation of the sources (75). Solutions can also be made more robust by requiring temporal smoothness. Invasively recorded signals such as intraoperative potential recordings from the cortex or from the heart can also be very valuable in developing proper physiological and temporal constraints for distributed sources. The Relation between Bioelectric and Biomagnetic Signals Both bioelectric and biomagnetic fields are generated by the same activity. As a consequence, there must be a correlation both in the temporal waveforms and in the spatial maps of the measured signals. Therefore, it is evident that bioelectric and biomagnetic measurements reveal partly redundant information. However, neither one can be used to uniquely reproduce the other; there are current configurations that produce either electric or magnetic field, but not both. A practical example of a magnetically silent source is a radial dipole in a spherically symmetric conductor. On the other hand, solenoidal currents do not produce any electric potential. This may become important, for example, in cardiac exercise studies (76). Therefore, a combination of magnetic and electric recordings seems appealing to obtain more complete information about the current distributions. Still, few attempts to combine electric and magnetic data have been reported (21,58,77,78). In the previous considerations it was assumed that the volume conductor is homogeneous or piecewise homogeneous. However, many biological tissues are organized directionally, and the electrical conductivity depends on the direction of the fibers. For example, the conductivity in myocardial fibers is about three times higher in the main fiber direction than across the fibers. Colli-Franzone et al. (79) showed that a classical uniform dipole layer, as representing the myocardial wavefront, should be revised to take into account the anisotropic nature of the tissue. They were able to explain experimentally measured potential distributions with an oblique dipole layer, where the dipoles may also have tangential components in addition to the normal component. Wikswo (80) studied isolated animal preparations and employed microSQUIDs and microelectrodes to measure magnetic and electric fields during and after applying a current stimulus. According to their results, the magnetic field is more sensitive to the underlying anisotropy than the electric potential. With such combined electric and magnetic re-

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cordings, it is at least in principle possible to determine the intra- and extracellular conductivity values. The anisotropic properties of the heart are especially evident near the ventricular apex, where the spiral arrangements of the myocardial fibers can be observed on the epicardial surface. It has been argued that this kind of vortex geometry leads to electrically silent components in magnetic field. However, van Oosterom et al. (66) arrived at the conclusion that the anisotropy does not play a significant role in the ECG or MCG during the normal ventricular depolarization. On the other hand, the findings of Brockmeier et al. (76) in pharmacological MCG stress testing indicate that the anisotropy may cause larger repolarization changes in multichannel MCG signals than in the simultaneously recorded ECG maps. The tissue is directionally oriented also in the brain. For example, the conductivity of the white matter in the direction of the fibers may be 10 times higher than the conductivity across the fibers. In the cerebral cortex, the corresponding factor is about two. In general, the anisotropy influences the body surface potentials and magnetic fields. However, in the sphere model a difference between the radial and the two tangential conductivities does not affect the magnetic field, while the influence on the electric potential is still substantial.

INTEGRATION WITH OTHER IMAGING MODALITIES Fast high-field MRI devices provide precise anatomical data. Besides reconstruction of accurately shaped volume-conductor models, anatomic MRI data on the heart and the brain are necessary to combine the inverse solutions with the anatomy in a clinically useful presentation. Examples of source displays of both MRI slices and three-dimensional surface reconstructions are shown in the section entitled ‘‘Applications.’’ Segmentation of the structures of interest from image data is presently the most time-consuming part in constructing individualized boundary element models. In the medical imaging field, accurate extraction of anatomic structures from image data sequences is still an open problem. In practice, manual extraction of the objects of interest—for example, from MRI slices—is often considered the most reliable technique. Recently, automated region-based and boundary-based segmentation and triangulation methods have been developed, for example, for extracting the lungs, heart, and thorax, or the brain and skull. In region-based methods, some features based on the intensity of the images are used to merge voxels. The boundary-based methods, in turn, rely on an intensity gradient detection. Both methods have limitations, but the utilization of prior geometrical knowledge, such as triangulated surfaces generated from data on other subjects, provides useful additional information. For example, a deformable pyramid model can then provide automatic segmentation and triangulation of the anatomic objects (53,81). MRI is still fairly expensive, especially for large patient populations. Thus, methods are being developed to use other imaging methods for reconstructing individualized triangulated surfaces. In cardiac studies, two orthogonal thorax Xray projections, or ultrasound images of the heart combined with three-dimensional (3D) digitization of the thorax surface, can be utilized to acquire patient-specific geometry models.

In principle, CT images could be used instead of MRI to construct a boundary-element model of the head. The skull is particularly easy to isolate from these data. However, the classification of soft tissues is often easier from MR images and the radiation load imposed by a CT scan is generally considered too high for healthy subjects. To present the MEG/MCG inverse solutions accurately on the individual anatomy, special care needs to be taken with regard to combining the different coordinate frames. Prior to biomagnetic recordings, one has to fix some marker points, for example, with a 3-D digitization system. During MRI or X-ray imaging, specific markers clearly visible and identifiable, such as vitamin pills or tubes filled with MgCl solution, are attached on the reference points. Three or more markers are usually required to achieve sufficient accuracy in the data fusion. Functional MRI perfusion studies of ischemic or infarcted heart are particularly valuable in developing physiological constraints and in validating the MCG/ECG localization results of ischemia or arrhythmogenic tissue. In brain studies, new possibilities are opened by combining the millimeterlevel spatial resolution of functional MRI and the millisecondscale temporal resolution of MEG and EEG. Weighting of minimum-norm solutions by functional MRI voxel information has been applied, for example, in visual stimulation studies (82). However, it must be taken into account that fMRI and biomagnetic measurements are not always detecting common activity. Very clear changes of electric and magnetic signals can be easily missed by fMRI if they occur rarely or are very transient thus producing relatively small average changes in the metabolic level. Furethermore, all experimental setups cannot be easily used in both biomagnetic and fMRI studies. It may thus be necessary to often compare the final results of the analysis of each modality rather than aiming at a combination during the source reconstruction. It is also possible to utilize positron emission tomography (PET) studies in combination with the electromagnetic methods. However, PET imposes a radiation load on the subject, and therefore the possibilities to perform multiple studies on a given subject are limited. Furthermore, PET is available only in a few centers, whereas MRI systems capable of functional imaging are generally available in modern hospitals. APPLICATIONS Brain Studies Auditory Evoked Fields. Fig. 3 shows the results of a typical auditory evoked-response study performed with a whole-head MEG instrument (83). The responses were elicited by 50 ms tones delivered every 4 s to the subject’s right ear. The data were averaged over about 100 repetitions with the stimulus onset as a trigger. The signals were modeled with two current dipoles in a spherically symmetric conductor. The optimal locations, orientations, and time courses of the dipoles were determined with a least-squares search. Fig. 3 shows the averaged data, the distribution of the magnetic field component normal to the measurement surface at the peak signal value, the time courses of the source amplitudes, and the locations of the sources superimposed on a 3-D surface rendering computed

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Figure 3. Left: Auditory evoked magnetic fields recorded with a 122-channel magnetometer (33) to 50 ms, 1 kHz tones presented to the subject’s right ear once every 4 s. The head is viewed from above, and the helmet surface has been projected onto a plane; the nose points up. Right, above: The pattern of the field component normal to the helmet surface, Bz, shows the peak of the response. White indicates magnetic flux into and gray out of the head. The locations of the sensor units are indicated with squares. The positions and orientations of the two current dipoles modeling the data are projected to the helmet surface. Middle: Time dependence of the dipole strengths, indicating the time behavior of the active area in the left (LH) and right (RH) hemispheres. Q denotes the dipole moment; goodness-of-fit (g) indicates how well the model agrees with the measurement. Right, below: The locations of the dipoles projected on an MRI surface rendering, viewed from above. To show the supratemporal surface, frontal lobes have been removed from the images. (Modified from Ref. 83.)

from the subject’s MRI data. The locations of the sources agree nicely with the known site of the auditory cortex on the supratemporal plane. Furthermore, the time courses of the source amplitudes show that the source in the left hemisphere, opposite to the stimulus, is stronger and peaks about 20 ms earlier than the source on the right. Characterization of Cortical Rhythms and their Reactivity. Since the advent of EEG, the rhythmic oscillations of various cortical areas have been described and also utilized in clinical diagnosis, but their functional significance has remained unclear. With the whole-scalp neuromagnetometers, studies of cortical rhythms have become feasible. Because these rhythms do not repeat themselves, it is mandatory to record them simultaneously over the whole scalp. The neuromagnetic brain rhythms in healthy adults have been recently characterized in (84) and their reactivity has been quantified during different situations. An efficient way to reveal task-related changes in the level of different frequency components is to filter the signal to the frequency passbands of interest, rectify it, and finally average the rectified signal with respect to the event of interest, like the onset of a voluntary movement (85).

Such an analysis has unraveled new features—for example, of the well-known mu rhythm, which is seen in the EEG records over the somatomotor cortices of an immobile subject. The comb shape of the mu rhythm already indicates the coexistence of two or three frequency components, strongest around 10 Hz and 20 Hz. The sources of the magnetic mu rhythm components cluster over the hand somatomotor cortex, with slightly more anterior dominance for the 20 Hz than for the 10 Hz cluster (see Fig. 4) (85). This difference suggests that the 20 Hz rhythm receives a major contribution from the precentral motor cortex, whereas the 10 Hz component seems mainly postcentral (somatosensory) in origin. Further support for the functional segregation of these rhythms comes from their different reactivity to movements (15). The level of the 10 Hz rhythm starts to dampen 2 s before a voluntary movement and then returns back within 1 s after the movement. Suppression of the 20 Hz rhythm starts later and is relatively smaller, and the ‘‘rebound’’ after the movement is earlier and stronger than in the 10 Hz band. Locating Epileptic Foci. Many patients with drug-resistant epilepsy suffer from seizures triggered by a small defective brain area. In preoperative evaluation of these patients, it is

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behind the right-sided spikes by about 20 ms and probably reflected transfer of the discharges through corpus callosum from the primary to the secondary focus. Identification of secondary epileptogenesis is important for presurgical evaluation of patients because the secondary foci may with time become independent, and removal of the primary focus would then no longer be efficient in preventing the seizures. Cardiac Studies

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Figure 4. Reactivity of spontaneous activity over the somatomotor hand region in association with voluntary right index finger movements. The time dependencies of the 10 Hz and 20 Hz activities are indicated by the two traces showing the temporal spectral evolution (84) of the signal recorded over the left somatomotor hand area. The locations of sources corresponding to 10 Hz and 20 Hz activity are indicated on the 3 D surface rendition of the subject’s magnetic resonance images. The site of the source for electrical stimulation of the median nerve at the wrist is shown by the black dot.

important to know whether their epileptic discharges are focal and how many brain areas are involved, what is the relative timing between the foci, and how close they are to functionally irretrievable locations such as the motor and speech areas. MEG recordings have been able to answer some of these questions (86,87). The patients cannot be studied with MEG during major seizures, owing to movement artifacts, but in many cases the foci can be identified from interictal discharges occurring during the periods between the seizures. As an example of a recording during an actual seizure Fig. 5 depicts MES signals from a patient who suffered from convulsions in the left side of his face (88). He was able to trigger the seizure by touching the left-side lower gum with his tongue. The recordings show clear epileptic spikes which appear only in the right hemisphere at first, but later start to emerge in the corresponding areas of the left hemisphere as well. After the 14 s seizure, the epileptic discharges ended abruptly. Figure 5 also depicts locations of the spike ECDs, superimposed on the patient’s MRI surface rendering. The sources are clustered along the anterior side of the central sulcus, extending 1 cm to 3 cm lateral to the SI hand area, as determined by somatosensory median-nerve evoked responses. The sources of the epileptic spikes thus agree with the face representation area in the precentral primary motor cortex and are in accord with the patient’s clinical symptoms. Spikes generated by the focus in the left hemisphere lagged

Ventricular Preexcitation. Ventricular preexcitation associated with the Wolff–Parkinson–White (WPW) syndrome is caused by an accessory pathway between the atria and the ventricles, which may lead to supraventricular tachycardias and life-threatening arrhythmias refractory to drug therapy. Intervention therapy, such as catheter ablation, is then needed, but a necessary condition for successful elimination of the premature conduction is the reliable localization of the accessory pathway. Catheter ablation techniques have significantly decreased the need for cardiac surgery, but simultaneously increased the need for accurate noninvasive localization techniques. Noninvasively obtained prior knowledge of the site of the accessory pathway can improve the result and shorten the time needed in invasive catheter mapping, and thus diminish patient discomfort and surgical risk. In addition, shortening the time needed in invasive catheterization also reduces radiation exposure due to fluoroscopy monitoring of catheter positions. Several MCG studies have been reported on localizing the ventricular preexcitation site in patients with the WPW syndrome (17,20,89,90). The reported accuracy of MCG localiza-

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AEF Figure 5. Epileptic discharges after voluntary triggering (88). The trace on the top illustrates MEG activity from the right hemisphere during the whole 14 s seizure. In the middle and lower parts of the figure, selected periods (a, b, c) are expanded and signals generated by the corresponding area in the left hemisphere are shown for comparison. Lower right corner: Locations of ECDs for ictal and interictal spikes (white cluster), and for auditory (AEF) and somatosensory (SEF) evoked fields, superimposed on the patient’s MRI surface rendering. The course of the Rolandic and Sylvian fissures are indicated by the white dashed lines. (Adapted from Ref. 88.)

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tions ranges from 5 mm to 25 mm, which is sufficient to be useful in preablative or presurgical consideration of the patients. Ventricular Tachycardia. Generally, malignant ventricular tachycardia (VT) is much more difficult to locate for ablation treatment than the ventricular preexcitation. It is estimated that the lesion produced by the application of RF current is about 6 mm in diameter and about 3 mm in depth. Currently, clinical practice for precise localization introduces several catheters through arteries and veins into the ventricles for invasive recordings of cardiac activation sequences. This procedure can be very time-consuming, and noninvasively obtained information could shorten the procedure from several hours even to less than 1 hour. VT patients include postmyocardial infarction patients, patients with different cardiomyopathies, and patients with monomorphic VT. MCG studies reported so far have attempted to locate the origin of ventricular extrasystoles or arrhythmias that have occurred spontaneously during the MCG recording (17,19,20). The results have been compared to the results of successful catheter ablations, presented over X-ray and magnetic resonance images when available. In such comparisons the average MCG locations were found to be within 2 cm from the invasively determined sites. Examples of such studies are displayed in Fig. 6. These results were obtained with an individualized boundary-element torso model; an example is displayed in Fig. 7(a). Cardiac Evoked Fields. Artificial dipole sources inserted in the heart with catheters (e.g., during routine electrophysiological studies) have been tested to verify the MCG localization accuracy (17,20,22). For example, Fenici et al. (22) studied five patients in whom a nonmagnetic pacing catheter (16) was used to stimulate the heart during MCG recordings. In general, the MCG localization results at the peak of 2 ms catheter stimuli and at the onset of paced myocardial depolarization were within 5 mm from each other. Because these are two physically different sources, the study provided further support for the good localization accuracy of the MCG method. In another recent study (91), simultaneous MCG and ECG mapping recordings were performed during pacing in 10 patients. The localizations were compared to catheter positions documented on fluoroscopic X-ray images. MCG results were, on the average, within 5 mm from the documented catheter position, while the ECG showed somewhat worse accuracy. Reconstruction of Distributed Sources. For comparison of MCG and ECG mapping results, simultaneously recorded MCG and ECG data were applied in reconstructing ventricular depolarization isochrones on the endo- and epicardial surfaces of the heart of a healthy normal subject (92). The results showed almost identical isochrones from both magnetic and electric data. An example of the MCG isochrone reconstructions is shown in Fig. 6(d). The minimum-norm estimates (MNE) have been applied in estimating the primary current distributions underlying measured MCG signals. An intrinsic problem associated with MNE is that it has a poor depth resolution of the sources without proper regularization and physiological constraints.

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Various regularization and depth weighting methods have shown promising results (21,69). Recently, depth-weighted MNE reconstruction has been applied in MCG data recorded in patients with chronical myocardial ischemia (18,93). Clinical validation for the results was provided by SPECT imaging. In general, the site of smallest current density, i.e., the missing depolarization component, was in good agreement with the SPECT result.

OTHER APPLICATIONS Until now, magnetic source imaging studies have been focused in the brain or the heart. However, other applications are being developed as well. Studies of compound action fields (CAF) from peripheral nerves require a very high sensitivity, because the signal amplitudes are below 10 fT (94–97). In addition, signal averaging of hundreds of stimulated sequences may be required to find the CAF waveforms. Analysis of the waveforms demonstrates the quadrupolar nature of neural activity, provided that the observations are performed at a distance from the depolarized segment (96). Multipole analysis has been applied to model the depolarization process; dipole terms reveal the location and intensity of the source, while octupolar terms are related to its longitudinal extension along the nerve fibers. In addition to studying propagation of the nerve impulses, multichannel measurements can reveal abnormalities such as proximal conduction blocks in the spinal nervous system (97). High sensitivity and specific signal processing are also needed to detect low-frequency (0.05–0.15 Hz) magnetic signals from gastrointestinal system (98,99). Distinguishing between gastric and small bowel signals may provide a new tool to study abnormalities in the gastrointestinal system (98). Multichannel recordings allow feasible and continuous monitoring of magnetically marked capsules within the gastrointestinal tract with a temporal resolution on the order of milliseconds and a spatial resolution within a range of millimeters (99).

DISCUSSION Modeling Despite the inevitable ambiguities in source analysis, very useful information has been obtained by using relatively simple models. For example, the localization of functional landmarks in the brain using the current dipole model and a spherically symmetric conductor in the forward calculations has already been developed to the extent of being a reliable clinical tool (16). The results of these studies have also been often verified in direct intraoperative recordings. The focal source analysis methods are sometimes criticized for being too extreme simplifications of the actual current distributions, which renders them rather useless in the study of complicated functions performed by the human brain. This intuitively appealing opinion is not well backed up by experimental data. Rather, recent fMRI data may be taken to indicate that the significant changes in metabolic activity associated even with complicated cognitive tasks might well be relatively focal.

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Reconstruction methods to deal with source distributions are under development, but there are still difficulties in interpretation of the results obtained from measured data. Implementation of available physiological information and constraints is probably needed to obain a reasonable correlation with actual physiological events in the source regions. If the assumptions of the source model are not compatible with the characteristics of the actual electrophysiological sources, misleading estimates may ensue. As discussed in the section entitled ‘‘Distributed Source Models,’’ the distributed source model may produce a distributed estimate even for a focal source. Only very recently have there been attempts to reliably estimate the actual extent of the current source using

Bayesian parameter estimation (100) in conjunction with reasonable physiological and anatomical constraints. Invasively recorded cardiac signals, such as potentials measured during electrophysiological studies on epi- and endocardial surfaces, provide the golden standard for validation of the MCG/ECG inverse solutions. Even though patient populations studied by MCG before or during invasive catheterization are still relatively small, the localization studies of various cardiac arrhythmias have shown encouraging results. Multichannel systems and accurate combination of the results with cardiac anatomy have improved the accuracy to the order of 5 mm to 10 mm, which is sufficient to aid in planning the curative therapy of arrhythmia patients. Further valida-

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(b) (d) Figure 6. (a) MCG curves recorded from a patient suffering from ventricular tachycardia (VT). The seven axial gradiometers show (1) a normal sinus-rhythm beat and (2) an arrhythmogenic ventricular extrasystole (VES). (b) Isocontours of the magnetic-field component perpendicular to the sensor array (see Fig. 2). The field values were interpolated from the measured data with the minimum-norm estimation (68). Solid and dashed lines here indicate, respectively, magnetic flux toward or out of the chest. The step between adjacent contours is 1 pT. (c) MCG localization results obtained with a single moving ECD. (d) Ventricular activation sequence reconstructed from the VES by the method reported in Ref. 92.

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Figure 7. (a) An example of a boundaryelement torso model constructed from MRI data. The surfaces of the body, the lungs, and the heart are tessellated into triangulated networks. The total number of triangles here is about 1500. (b) An example of MCG localization of tachycardias. The patient was suffering from continuous atrial tachycardia with the heart rate of over 140 beats per minute. ECD localization was performed from 67-channel MCG data at the onset of the P-wave, and the ECD locations were superimposed on the MRI data. Catheter ablation performed later at the location pinpointed by the MCG result terminated all arrhythmias.

tion for the MCG localization accuracy has been obtained by locating artificial dipole sources, such as pacing catheters inserted into the heart during electrophysiological studies. Future Trends The arrhythmogenic substrate is not manifested in all normal sinus rhythm recordings, and interventions may be needed during MCG to stimulate controlled arrhythmias to locate them. Thus, MCG should be available in a catheterization laboratory, but the demand of magnetical shielding and liquid helium is, in practice, limiting the use of MCG mapping in guiding invasive arrhythmia localization. For this purpose, compact-size higher-order magnetometer arrays operated without external shielding would be required. MCG mapping under exercise is a promising tool for noninvasive characterization and localization of myocardial ischemia (76). Improved source modeling and localization methods are under test, especially in patients with coronary artery disease (93). Despite over 20 years of MCG and MEG research, common standards of measurement techniques, data processing, and presentation are still lacking. Suggestions for such standards are emerging, but it is clear that there is and will be large differences between sensors and their arrangement in multichannel magnetometers. Fortunately, tools such as MNE (63,68) have been developed to interpolate signal morphologies and isocontour maps that are directly comparable to studies performed in other centers. The field of magnetic source imaging may expand during the next few years with the implementation of low-noise highTc SQUID arrays that can be operated at the temperature of liquid nitrogen (101–103). The higher noise level of the highTc SQUIDs is, particularly in MEG studies, partly compensated by the smaller distance between the sensors and the body. At present, however, the low-Tc SQUIDs are easier to produce and thus cheaper than the high-Tc ones. The future of MEG, with commercial whole-head instruments now available, looks promising. The capability to monitor activity of several cortical regions simultaneously in real time provides a unique window to study the neural basis of human cognitive functions. Important information can be obtained both from evoked responses and from spontaneous ongoing activity.

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63. M. S. Ha¨ma¨la¨inen and R. J. Ilmoniemi, Interpreting magnetic fields of the brain: Minimum-norm estimates, Med. Biol. Eng. Comput., 32: 35–42, 1994. 64. A. A. Ioannides, J. P. R. Bolton, and C. J. S. Clarke, Continuous probabilistic solutions to the biomagnetic inverse problem, Inverse Problems, 6: 523–542, 1990. 65. R. D. Pascual-Marqui, C. M. Michel, and D. Lehmann, Low resolution electromagnetic tomography: A new method for localizing electrical activity in the brain, Int. J. Physchopsysiol., 18: 49– 65, 1994. 66. A. van Oosterom et al., The magnetocardiogram as derived from electrocardiographic data, Circ. Res., 67: 1503–1509, 1990. 67. P. Hansen, Numerical tools for analysis and solution of fredholm integral equations of the first kind, Inverse Problems, 8: 849– 872, 1992. 68. J. Numminen et al., Transformation of multichannel magnetocardiographic signals to standard grid form, IEEE Trans. Biomed. Eng., 42: 72–77, 1995. 69. K. Pesola et al., Comparison of regularization methods when applied to epicardial minimum norm estimates, Biomed. Tech., 42 (Suppl. 1): 273–276, 1997. 70. R. MacLeod and D. Brooks, Recent progress in inverse problems in electrocardiography, IEEE Eng. Med. Biol., 17: 73–83, 1998. 71. A. M. Dale and M. I. Sereno, Improved localization of cortical activity by combining EEG and MEG with MRI cortical surface reconstruction: A linear approach, J. Cog. Neurosci., 5: 162– 176, 1993. 72. K. Matsuura and Y. Okabe, Selective minimum-norm solution of the biomagnetic inverse problem, IEEE Trans. Biomed. Eng., 42: 608–615, 1995.

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M. S. HA¨MA¨LA¨INEN J. T. NENONEN Helsinki University of Technology

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Wiley Encyclopedia of Electrical and Electronics Engineering Medical Image Processing Standard Article J. Alison Noble1 1University of Oxford Copyright © 1999 by John Wiley & Sons, Inc. DOI: 10.1002/047134608X.W4703 Article Online Posting Date: December 27, 1999 Abstract | Full Text: HTML PDF (266K)

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Abstract The sections in this article are Data Processing Image Understanding, Analysis, and Interpretation Some Applications Further Reading Keywords: medical visualization; 3-D reconstruction; image feature enhancement and segmentation; image registration; medical shape analysis; quantifying dynamics; image-guided applications About Wiley InterScience | About Wiley | Privacy | Terms & Conditions Copyright © 1999-2008John Wiley & Sons, Inc. All Rights Reserved.

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J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering c 1999 John Wiley & Sons, Inc. Copyright


MEDICAL IMAGE PROCESSING Medical image processing is a broad and general term used to refer to the application of image processing and analysis techniques to medical data [X rays, computer tomography (CT), nuclear medicine, and ultrasound] for visualization or quantification purposes, or both. It is a relatively new field that is evolving in response to the increasing widespread availability of good medical image acquisition systems. Clinicians can now “see inside” the human body. Medical image processing deals with making measurements on these (usually digital) pictures and interpreting the measurements in a clinically meaningful way. Medical image processing now plays a regular part in diagnosis and treatment in many areas of medicine, including breast cancer, cardiac disease, diseases of the brain, and orthopedics, and for automating tasks such as image-guided surgery and surgery planning. Early work in this area mainly involved the direct application to medical data of two-dimensional (2-D) image-processing algorithms developed for analyzing 2-D static visual images. The limitations of this approach were soon realized, as noise and signal properties of medical images can be quite different from those of visual images. As a result, research is moving towards developing approaches that make use of knowledge of anatomical geometry and physical properties of tissues to interpret medical imagery. Another recent trend is the increased use of three-dimensional (3-D, volumetric) images and image sequences in the medical domain. This presents new challenges in terms of visualization needs and processing speed. This article is divided into three main sections. The following section consers specific aspects of data processing that are relevant to processing medical images for visualization and display, reconstructing an object from multiple image slices, and medical image enhancement and segmentation. The section after considers the tasks of interpreting and analyzing medical images. Medical image registration (bringing two data sets into spatial alignment), medical shape representations and analysis, and medical image tracking and analysis are discussed. Some medical image application areas are outlined in the final section.

Data Processing Visualization and Display. Image processing is the focus of this entry. However, one of the most important roles it plays is to preprocess data so that information of interest can be visualized in a clinical meaningful way. This is particularly important for 3-D and 3-D + time data. Here we restrict the discussion to visualizing volumetric data. For an illustration of medical visualization in practice, see, for example, 1. One of the simplest ways to visualize a 3-D data set is using planar reformatting. This involves treating the scan data as a volume and mathematically defining a cutting plane through the volume. The intensity of the voxels traversing this plane is mapped as pixels into a 2-D image (the slice plane or cross-sectional image). This technique is particularly useful for visualizing anatomy in directions that are more intuitive than those provided by the data acquisition process. Another method of visualizing 3-D data is using a technique known as maximum-intensity projection (MIP), which has proved especially popular for visualizing magnetic resonance angiography (MRA) data (2). An example is shown in Fig. 1. (3). The main idea is to create an “X-ray” 1

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Fig. 1. (a) a maximum-intensity projection (MIP) and (b) a surface rendering of an MRA volume of a brain aneurysm (3). Note how the surface visualization gives a better indication of three-dimensionality by the use of shading.

projection image of the 3-D data set, that is, to project a ray from a point source (usually positioned at infinity so that parallel projection geometry is assumed) through the volume. The maximum intensity of all voxels encountered in this traversal is displayed in the resulting 2-D image. MIP images are typically generated from a number of viewing angles about a rotary axis, and the resulting image sequence displayed as a movie. The key advantage of this method is its computational simplicity. Its key disadvantage is the loss of 3-D information in the projection process; also, because only the maximum intensity is retained, in some cases low-intensity structures are not seen. Variants of the standard projection technique have been proposed to deal with this, including depth-sensitive MIP and multifeature-extraction ray tracing (3,4). The two main techniques used for visualizing medical data in three dimensions are surface rendering and volume rendering (5,6). These methods use spatial information about objects in three dimensions, shadowing, and perspective to create a 3-D impression of the data volume (a displayable), which is projected on a 2-D screen. In surface rendering a surface is first extracted from a data set, typically using an intensity threshold operation (isovalue selection), reconstructed as a mathematical model, and then rendered using standard computer graphics techniques such as raycasting (7). One of the classic methods of reconstruction, called the marching cubes algorithm, converts the thresholded data set into polygonal surface patches (8). Much of the original information content of the image volume is thus lost, leaving a clear representation of the surface in question. This makes surface rendering especially useful for displaying anatomical data such as CT images of bone. The main advantages of surface rendering include the relatively rapid speed of rendering and reduced storage requirements once the surface has been determined. The disadvantages include that for some data types (e.g., ultrasound data) it may prove difficult to segment a good surface, and this approach can handle small features incorrectly (9,10). In volume rendering, shading and perspective are determined by spatial position and the relative intensity difference in the original data. This is an important difference between surface and volume rendering. In the former case you effectively create a mathematical model of the surface in terms of geometric primitives such as points, lines, and polygons and render the object assuming that it is opaque (no light is transmitted through it). The interior of the object is not described. Volume rendering assumes the object is transparent. It produces an image without generating an intermediate geometric description. Clearly, from the medical visualization perspective this is more powerful, because you can look inside an object and visually inspect different tissue regions. Thus it is typically used for displaying soft tissue structures such as cerebral tumors or other soft tissue lesions. However, introducing transparency makes basic ray-casting (a fundamental step

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in all rendering techniques) computationally impractical unless some sort of acceleration method is used to improve performance. This is because the entire 3-D data set must be used for each new viewpoint. This has limited the practical application of volume rendering until quite recently. The surface and volume rendering techniques described above all aim to give the appearance of threedimensionality in a planar image (a 2-D display device). True 3-D display or stereo rendering can be achieved by exploiting binocular parallax (11). There are a variety of ways to do this, including generating lenticular photographic prints, using a polarized filter projection system (as used in 3-D movie presentations), and using liquid-crystal shutter glasses or virtual reality (VR) heads-up displays (as used for viewing computer-generated images or video games) (5). The basic idea is to generate two images of a scene taken from slightly different viewpoints and to use special optical processing, equipment, or glasses to create a stereoscopic effect, similar to the way in which the human visual system perceives 3-D information. This can be particularly useful to determine the relative depth of close objects in a scene (e.g., vascular structures) and for visualizing textured or translucent objects, such as tumors, which do not have regular shapes or clearly defined boundaries and which are not readily seen in 2-D slice visualization (12). The advantages of using true 3-D display over using surface or volume rendering in medical applications are strongly dependent on the application and are much debated. For instance, head displays have the advantage of being portable and interactive, but are inconvenient for a surgeon to use in an operating room. For diagnostic needs, clearly, bulkiness is not an issue, but then you might prefer a method that could be readily used for documentation (such as lenticular photographic prints). Limiting factors in the end are cost and image quality. Reconstruction. Here we define the term reconstruction to mean postprocessing of two or more 2-D images acquired from a medical imaging system to generate a 3-D representation of an object or volume in space. Thus we do not consider, for example, how to construct a magnetic resonance image from its k -space representation, or a computed tomography image from radiographs (X-ray projections). See the separate entries on individual medical imaging modalities for discussions on these methods. With this definition, reconstruction methods can be classified as volumetric-based versus sparse-viewbased, or alternatively intensity-based versus feature-based. We consider the former classification. Volumetric methods involve using a dense set of 2-D scans to reconstruct an object volume. The simplest example of this type of approach involves interpolating between a series of parallel cross-sectional MR or X-ray CT scans. A common variant of this idea is called spatial compounding. It involves mapping into a volume the intensities of pixels in a 2-D slice that is located at a known position and orientation in 3-D space. When two (or more) 2-D slices intersect at a voxel location, the intensity is taken as the average intensity of the two values. Spatial compounding is used in 3-D freehand ultrasound imaging, where a number of 2-D B scans (ultrasonic reflection images) are acquired in rapid succession (a sweep), possibly from different look directions (acquisition angles), and processed to give a visualisation of 3-D anatomy (13,14). By imaging from a variety of look directions the effects of noise (speckle) and imaging artifacts can be significantly reduced. However, spatial compounding requires very accurate slice registration, which has proved difficult to achieve with ultrasound data because localizing image features accurately in noisy ultrasound data is difficult. This has limited the clinical application of 3-D freehand ultrasound to date. It may prove that recent advances in multimodality image registration (see “Registration and Matching” in the next section) will provide a solution to this problem in the near future (15). Sparse-view methods differ from volumetric methods in that they use a small number of 2-D images to reconstruct a 3-D object or scene and the images are typically acquired at a large angular separation. This is the classical stereo vision setup, and many of the methods used in sparse view medical object reconstruction have been borrowed from the computer vision and photogrammetric literature. Sparse view reconstruction has proved especially popular in 3-D reconstruction of coronary arteries from X-ray images (angiograms). In these applications it is typically possible to only acquire four to eight views, so that classical X-ray reconstruction methods based on, for example, filtered backprojection cannot be employed. In the conventional biplane

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angiographic imaging system set-up, two images are simultaneously acquired at 90◦ to each other; the center points of vessels or bifurcations (junctions) are extracted in both views, either manually or using semiautomatic methods; these features are matched between views; and then triangulation is used to find the location of the vessels in three dimensions. Having reconstructed the essential global geometric structure, it is possible to estimate the size and the shape of blood vessels from X-ray intensities and assumptions about vessel shape (15,16,17). This approach has not proved so successful for cerebral vessel reconstruction, due to the increased complexity of and variability in the cerebral vasculature branching pattern, which makes establishing correspondences difficult. Although there has been some progress in this area using model-based techniques that employ a 3-D preoperatively acquired model of vessel structure to guide correspondence matching (18), the general problem of 3-D reconstruction from a few projection angiograms using geometric methods remains unsolved. Finally, there has been some recent work investigating variants of the iterative algebraic reconstruction technique (ART) (19) to reconstruct cerebral vessels and pathologies such as aneurysms and arteriovenious malformations from few-view data (20,21). Classical ART and its multiplicative equivalent (MART) do not work well on limited-view data, because the optimization problem is underconstrained. To overcome this, regularization can be used to favor a smooth reconstruction result. This approach has produced promising results and may find application in interventional neuroradiology procedures and for angiographic examinations performed prior to radiotherapy. In this case, full volumetric CT reconstruction is not feasible, due to acquisition-time constraints or limitations of equipment that cannot rotate at the high speeds required for 3-D acquisition. Image Enhancement and Segmentation. Much effort in medical image processing is dedicated to enhancing the visibility of structures of interest in an image (such as tumors or vessels) and reducing imaging noise and the effects of imaging artifacts, as a preprocessing step prior to image measurement and interpretation. The process of producing an image where features of interest are more clearly visible is called image enhancement. Although general- purpose image-processing filters such as Gaussian and median filtering can improve image appearance, the danger is that the application of such methods can make lesions less easy to locate or, worse still, remove them. Thus the most successful approaches to image enhancement are methods that aim to model the physics of image formation or make use of prior knowledge about object properties such as shape. Thus image enhancement is very much a modality- and application-dependent task. Here we highlight some examples in different domains. By modeling the mammographic imaging process Highnam et al. (22), show that it is possible to transform a mammographic X-ray image into an image (representation) of breast tissue where principal degradation effects and “uninteresting” structure have been removed. Orkisz et al. (23) developed a matched-filter algorithm for enhancing small vessels in magnetic resonance angiographic images based on anisotropic diffusion (see below), which favors improving the contrast of line-like features. To correct for intrascan intensity inhomogeneities due to RF coils in MR scans, the bias field, Wells et al. (24), developed an adaptive algorithm that classifies pixels according to their most probable tissue type. This approach assumes a parametrized model for the intensities in the image data (in this case they used a Gaussian mixture model) and uses the expectation maximization (EM) algorithm (25), to estimate the model parameters (see below for further discussion of the EM algorithm and its application in segmentation). Related ideas have been used, for example, to fit intensity models to multispectral MR images (26), and MRA data (27) so as to identify tissue regions. The general goal in medical image segmentation is to partition a raw 2-D or 3-D image into regions corresponding to anatomically meaningful structures as a precursor to geometric reasoning or interpretation. For example this might involve identifying vessels in a MRA, classifying tissue in brain MR images, or detecting and characterizing lesions in breast X-ray images. This task differs from image enhancement in that in image enhancement the output is another image. In image segmentation the output is a set of image features (regions, edges, corners), which may subsequently be grouped, prior to being used as input to a measurement or visualization. The segmentation approach adopted is clearly application-dependent and may involve modeling and extracting static or dynamic edges or textured regions, or using local matched filters (e.g., wavelets).

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Many of the algorithms in the literature are adaptations of algorithms developed for analyzing visual images. Straightforward methods borrowed from the 2-D image-processing literature—such as thresholding, mathematical morphological operators, or Canny edge detection—can be defined in three dimensions (28), and can be applied to segment sufficiently clean low-textured CT and MRI data. However, these approaches do not always work well on highly textured and noisy data such as ultrasound and brain MR images. This is because in these cases boundaries are not necessarily well modeled by a straight (1-D) step edge [Canny’s model (29)], and the assumption that object regions are associated with image regions of constant intensity corrupted with additive noise is not valid. To overcome these difficulties a number of generic, model-driven medical image segmentation methods have evolved. We mention three of the key types of algorithm here. These all make use of geometric models or models of image physics to help guide image segmentation. Two of these model-based approaches make use of a combination of geometric and intensity knowledge rather than local intensity information only; they are based on deformable models (30), and anisotropic diffusion (31), and make use of a combination of geometric and intensity knowledge. A third, EM segmentation (24), is a statistical approach that has its foundations in statistical stochastic theory. Deformable model segmentation combines a priori knowledge of the shape of a geometric structure (typically represented parametrically as a 2-D contour spline or a 3-D surface) with constraints derived from the image in an energy minimization functional, which can be accomplished iteratively using numerical algorithms based on, for example, finite element methods. For instance, in two dimensions, the energy functional E(x, y) of a deformable contour model could be represented by

Here, S(x, y) is the internal energy characterizing the deformation of the contour, and P(x, y) is a scalar potential derived from image measurements. For example, the contour will be attracted to intensity edges in an image I(x, y) if P(x, y) = c|grad I(x, y)|, where c is a weighting factor. Numerous applications of deformablemodel-based segmentation have appeared in the medical image analysis literature for automatically or semiautomatically segmenting. 2-D and 3-D anatomical structures (see the extensive review in see the extensive review in Ref. 32). This approach does, however, require a good initialization, and the user is usually left to decide when the process has converged. The traditional approach does not take into consideration changes in topology, which are particularly important for vessel segmentation, but there has been some recent research aimed at extending the deformable model concept to accommodate this need, as in Ref. 33. A variant of the general idea is a dynamic deformable model that replaces Eq. (1) by a functional that describes the shape and motion of an object. This allows the quantification of shape evolution (deformation) over time. See the subsection “Intrepretation” below on motion and tracking. Anisotropic diffusion was introduced by Perona and Malik as a method for performing edge-preserving smoothing prior to edge detection (31). This is a particularly attractive feature in medical applications because of their low signal-to-noise ratio and weak edges. The original idea was to smooth homogeneous regions while preserving the boundaries according to the anisotropic diffusion equation

Here It represents the image, and c(x, y, t) is a conductance function that is monotonic in the image gradient. The conductance function defines the manner in which diffusion occurs across an edge. For example, one might penalize smoothing at edges with a high gradient (which are assumed significant) but allow smoothing at edges with a low gradient (assumed spurious). Various authors have investigated different forms of the conductance function to incorporate knowledge of expected geometric structure or image physics. For instance, Steen and Olstad (34), integrated anisotropic diffusion with an ultrasound signal model, Gerig et al. applied

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Fig. 2. Example of anisotropic diffusion: (a) original image; (b) classic Perona–Malik anisotropic diffusion; (c) knowledgebased anisotropic diffusion (37).

the approach to multichannel MR data (35), Krissian et al. constrained smoothing of 3-D vascular images according to an analysis of local differential structure (36), and Sanchez-Ortiz et al. defined the conductance function as a product of a function of the image gradient and a (cylindrical) shape function to segment cardiac cine MR images (37) (see Fig. 2). The EM algorithm provides a method for estimating the distribution parameters of a data set given an appropriate model for the distribution by maximizing the likelihood of the distribution. Having estimated the parameters, each data point can subsequently be labeled as belonging to the class for which the conditional probability of belonging to the class is maximized. This approach has been successfully applied to identify cerebral tissues from MR image data with (24), and without (26,38) bias field correction, and to segment vascular structures (27). An attraction of the method is that classification is fully automatic and that different models for the intensity distributions can be readily introduced to accommodate statistical variations in the data. Finally, due to the wide variety of image types and image quality, it is frequently not possible to automatically segment an image. Thus there is a role for interactive tools for image segmentation where a manually placed approximate contour is adjusted using an iterative minimization process to find an optimal boundary. Snakes or active contour algorithms and live-wire segmentation (39), are examples of this type of approach.

Image Understanding, Analysis, and Interpretation Although one use of medical image processing is to provide better visualization, its prime use is for quantification, that is, to provide clinical meaningful measurements to improve diagnosis and treatment. Much of the work in this area involves the application of geometric methods to solve general computer vision problems such as registration and matching, shape analysis, and motion and tracking. In some cases this has led to the development of new concepts and new techniques that go beyond the boundaries of computer vision (e.g., in the areas of medical image registration and, increasingly, medical motion analysis). Registration and Matching. Medical image analysis frequently involves integrating information from multiple modalities. For example, in radiotherapy treatment, it is useful to be able to register a MR scan (which gives better delineation of tumor tissue) with a CT scan (which is needed to estimate radiation dosage). It is also frequently desired to integrate anatomical and functional modalities. Registration of time sequences of images of the same modality is also important, to monitor treatment and disease progression for example. The process of bringing the modalities into spatial alignment is referred to as registration. This is one of the most successful areas where medical image processing has been applied in clinical practice to date. Most work has focused on the 2-D–3-D and 3-D–3-D rigid registration of two images (no time involved).

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Fig. 3. Example of 3-D–2-D feature-based registration: (a) 3-D skeleton of a 3-D MRA segmentation scan like Fig. 1(b); (b) initial approximate alignment (white dots) of projected 3-D skeleton model (black dots) on 2-D X-ray view; (c) best-fit 3-D–2-D registration of projected model to image data (45).

For recent surveys of registration methods the reader is referred to Refs. 40 and 41. In Ref. 41, registration methods are classified according to nine criteria: dimensionality; nature of registration basis (extrinsic or intrinsic); nature of transformation (rigid, affine, projective, or curved); domain of transformation; degree of interaction; optimization procedure; modalities involved; subject (intrasubject, intersubject, or image-to-atlas); object type (part of the body). We will briefly consider the second criterion to highlight some of the popular state-of-the-art methods. Extrinsic registration involves placing markers (fiducial objects) on a patient that are designed to be readily visible and detectable in each modality. Correspondence between the data sets is established manually or automatically, and the parameters of the transformation determined using for example linear or nonlinear least-squares fitting. A commonly used fiducial object utilized in neurosurgery is a stereotactic frame that is screwed rigidly to a patient’s skull (42). Noninvasive markers glued to the skin are also popular. This type of approach is relatively simple and fast to use, but is often restricted to rigid transformations (translations and rotations)—clearly, the markers cannot move between acquisitions. Intrinsic methods utilize image content and can be divided into two types: feature-based and voxel-based. Feature-based registration (43,44,45) utilizes salient feature points (landmarks), contours, or surfaces derived via some segmentation process as features for matching (see Fig. 3). These features might for example be anatomically significant points located interactively by a user, or automatically localized points of extrema in curvature or object surface points. Optimization algorithms are then used to optimize measures such as the average distance ( L2 norm) between each landmark and its closest counterpart (the Procrustean metric) or the iterated minimal landmark distance. Optimization of the latter using the iterative closest point (ICP) algorithm and its variants has proved especially popular(43,46,47), gradient measures (49), or mutual information (50, 51,52) (see also Ref. 53). These methods are being actively researched at the current time. They tend to be computationally expensive but are automatic and, with the increased speed of computers, are now usable in clinical practice for applications such as rigid or affine 3-D–3-D registration of head images. However, they have not yet been successfully applied to time-constrained tasks such as intraoperative 2-D–3-D registration. Most of the methods currently in clinical use perform rigid-model registration. However, there is also great interest in using deformable models to deform one image elastically to another. This type of approach finds application in intrasubject matching or atlas registration as well as for tracking objects, such as heart chambers, over time. Typically a template is constructed from one image and is then deformed to fit a segmented structure in the second using an interative process. The demon algorithm (54), and the ICP algorithm (43), have been used for this purpose. The success of the approach depends on the choice of deformation model (elasticity constraint) and auracy of the segmentation process. Registration algorithms using nonpoint features such as

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special curves and special points on those curves are also being investigated (55,56). The motivation is that richer feature descriptors enable the quality of match to be defined more robustly, which should lead to more powerful methods of registering medical images. However, the need to extract reproducible geometric features for multimodality registration, and reliable features in noisy data has limited the practical use of this approach to date.

Interpretation. Shape Representations and Analysis. The representation of

2-D and 3-D shape and expected shape across a population is a very important problem in medical image analysis. For instance, many medical objects do not have any identifying characteristics (such as color or texture) other than shape. Shape parameters (such as area, eccentricity, axes of symmetry) and their variances can provide a natural way to describe properties of an anatomical object for detection or classification purposes. Further, the definition of a parametrized model of shape enables model-based (so-called top-down) segmentation and registration methods to be employed, which are more robust to image measurement error than pure image-based (so-called bottom-up) techniques. Most work in medical shape analysis deals with the statistical analysis of landmarks, that is, sets of specially selected points (57,58). A prime reason for this is that the statistical analysis of point sets is well understood and that measures such as the Euclidean distance metric between two points and the covariance of a point set can be defined. Higher-level shape primitives, such as boundary points (points with direction normals), curves, medial loci (points on loci of symmetry), and surfaces, appear less frequently in the literature. These provide more powerful features for registration and matching. However, the statistical analysis of nonpoint primitives is still being developed (59), and they are typically more difficult to extract from image data. A popular method to describe a medical object is as an eigenshape model (60,61,62). An eigenshape model is a statistical shape model that represents the variability of a set of examples (the training set) in a compact and statistically robust way. The model is constructed by representing each example in the training set as a vector in a high-dimensional vector space and performing principal component analysis (PCA) upon the resulting set of vectors (63). PCA determines the modes of variation of the data as the eigenvectors of the data set with largest eigenvalues. If the variability is well represented by a few modes, then the dimensionality of the data can be reduced. Typically three to eight modes capture 95% of the total variability. When the eigenshape model is constructed from a set of closely spaced points along the boundary of an object, it is sometimes called a point distribution model (PDM) (62). PDM s and the related concept of an active shape model (ASM) which combines a model of shape and gray-level appearance, have been successfully applied to a variety of medical problems, for instance, to locate structures in noisy images (64), to learn normal and abnormal left-ventricle “average”-shape models (65), and to detect abnormal instances of 2-D biological shapes (62). One key issue in eigenspace analysis is how to select suitable corresponding features on the training-set examples. In most cases this is done by hand, which requires expert knowledge of the objects being analyzed and is time-consuming, and the problem of how to do this in three dimensions is unsolved. Further, the individual modes do not typically describe shape variation in a clinically meaningful way. However, in spite of these limitations, eigenshape decomposition remains one of the most powerful and convenient ways to simplify the description and shape analysis of medical objects. Another way to describe shape is in terms of medial (skeletal) primitives. Here the essential idea is to summarize a shape by the loci of points that lie medially between its boundaries and their distance to the boundary. The work has been largely restricted to two dimensions and has focused on extracting skeletons from objects rather than the applications of the representation. Pizer et al. develop a related medial representation of shape, called the core, that is extracted directly from image intensities rather an (already extracted) object boundary. Cores can be defined in three dimensions and, unlike classical skeletonization, are insensitive to small image disturbances (66,67). A skeleton or core characterizes shape in terms of constituent parts. An alternative view is to characterize a shape via a sequence of transformations (or deformations) from a simple shape. Koenderink’s theory on

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Fig. 4. 2-D echocardiogram model-based tracking: (a) tracking using a simple (affine) motion model; (b) tracking using a motion model learnt from some training data. The latter enables the actual motion to be followed more accurately; this is most clearly seen by comparing frames 4 to 6 in (a) and (b) (75).

dynamic shape (68), and Kimia’s reaction–diffusion-space theory (69) fall into this category, but neither has yet been shown to be usable for computational image analysis. Finally, there is a whole subfield of applied statistics, called morphometrics that deals with multivariate analysis of shape (70,71). In this approach the emphasis is on analyzing landmark sets (point sets), which are sets of anatomically significant features located on the object of interest. It is assumed that these have been identified in each image instance of the object by some mean (usually manual selection). The key idea is to define a distance (the Procrustes distance), or metric, that is a least-squares formula used to describe the distance between a pair of shapes. This then enables measures such as an average shape to be defined and classical linear multivariate analysis to be performed to test group differences and the like. Bookstein suggested using a thin-plate spline to warp one average shape onto another as a way to visualize shape differences as patterns in the deformation grid. Such techniques are being used, for example, in studies of schizophrenia to understand whether the shape characteristics of a schizophrenic’s brain, as measured from MR brain scans, differ statistically from those of a normal human brain. Motion and Tracking. There has been considerable interest in developing tracking and deformation analysis methods for nonrigid objects, motivated primarily by the need to develop techniques for assessing the dynamical behavior of a heart, and in particular the left ventricle. Much effort has been undertaken to automate the tracking and analysis of heart chamber movement from 2-D echocardiographic image sequences using, for example, methods based on optic-flow computation (72) or snakes (73,74). Heart movement can be complex, and ultrasound measurements are noisy, with the net result that a classical snake can wander from the object of interest. To increase tracking robustness, Cootes et al. propose to constrain the allowable contour deformation to lie within the bounds of a shape model learnt from a large training set (62). Jacob et al. develop a Kalman-filter-based tracker whose system model is a motion model whose parameters have been learnt from observing normal heart motion (75) (see Fig. 4).

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Fig. 5. Wireframe model showing the trajectories of selected points on the left ventricle endocardial and epicardial walls. The model was derived by best-fitting a 4-D (3-D + T) heart model to tagged MR volume data (79).

Two-dimensional ultrasound analysis has the advantages that is relatively cheap and can be performed rapidly and is the most widely accepted method of cardiac image analysis in clinical practice today. It is however limited in that slice analysis does not enable 3-D motion to be characterized—the socalled throughplan problem—with the result that ultrasound scan view directions have to be carefully chosen. With the recent advances in 3-D cardiac imaging technology [especially nuclear-medicine SPECT or positron emission tomography (PET) imaging, tagged-MR imaging, and 3-D ultrasound], 3-D heart image analysis may soon become a reality. To date, the focus in 3-D cardiac image analysis has been in two areas: 3-D heart reconstruction and tracking, and shape modeling (76,77,78,79). Two general approaches to tracking have evolved. The first approach, suitable for MR, SPECT or PET data, performs a segmentation and surface fit on each volume frame and then computes the motion field between model fits in pairs of successive frames (76,77). The second approach, used in tagged-MR image analysis, finds features (usually manually extracted points) in each frame, establishes the frame-to-frame correspondence of features, and then fits some model to the features (78,80). The first approach involves extensive volume processing and is too slow for practical use. The principal difficulty in the second approach is reliable feature detection. The end goal of left ventricle tracking is to provide intuitive parameters that describe characteristic normal and abnormal heart chamber motions, but how model parameters correlate to clinical conditions is still an active area of research. The superquadric model of Ref. 78, which describes basic heart motion in terms of a contraction, elevation, and twist, and the 4-D polar transformation of Ref. 79, which adapts this to incorporate parameters describing regularity and periodicity (Fig. 5), are perhaps the most developed methods at the current time.

Some Applications Image processing is now utilized in many areas of medicine to help improve diagnosis and treatments, and a complete list of applications falls outside the scope of this review. Here we highlight a few of the areas: •

Atlas Matching. This is a special case of registration where a brain image acquired from a patient is compared with an “average” or statistical brain image, or template, obtained from imaging of many subjects. Any statistically significance different local or global shape change is attributed to abnormal growth or development. The key issue is how to develop an average representation of neuroanatomy that captures the normal variability and structural and functional differences of the brain observed across a healthy

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population; methods based on deformable templates (81,82) and probabilistic techniques (83,84) have been applied to solve this problem. Brain atlases are used to help understand pathological states such as Alzheimer’s disease as well as to guide neurosurgical procedures. Orthopedic and Craniofacial Surgery. Image processing is increasingly being used in the planning and execution of orthopedic surgery, for example, to register real-time intraoperative fluoroscopy images with 3-D preoperative CT images in spine surgery or to guide a robot in hip replacement surgery (85). Here, imaging is used in presurgical planning and to provide in vivo measurements to improve the accuracy and precision of surgical execution. Similar needs have led to the application of 3-D imaging in craniofacial surgical reconstruction (86). 3-D CT-based modeling and visualization can be used to develop a very precise 3-D computer model of a custom implant, typically using a mirror image of the normal side of the face as the template for the prosthesis. During the execution of surgery, the preoperative model can be registered to the patient’s skull (using a number of optical beacons placed on the bone-fragments to act as landmarks) and be used to guide cutting and bone-fragment repositioning. Medical image processing is also starting to be used for orthopedic surgery simulation and in related clinical areas (87,88). Neurosurgery. Neurosurgery provided one of the earliest application domains for 3-D medical imaging in clinical practice and remains one of the dominant successful areas of application of 3-D medical image processing. One of the basic requirements in neurosurgical operations is to be able to register a preoperative 3-D image (typically a CT and/or MR scan) to a patient as they are seen during surgery in order to guide a surgeon to the target of interest. Thus the main problem is one of 3-D-to-2-D (MR or CT to video image) registration. Conventional stereotaxy, in which a rigid frame is attached to the patient’s skull before preoperative scanning and left in place for surgery to provide a common frame of reference, was used in early work. It was cumbersome and found to be suitable only for a small of operations in practice. The general trend has been to move to frameless registration which does not use an attached frame or landmarks, but relies on techniques borrowed from visual image object recognition to register a preoperative 3-D model to real-time video images (89,90). For instance, Grimson et al. at MIT and Brigham and Women’s Hospital, Boston, have developed a system that performed a 3-D-to-3-D surface registration between a preoperative MR (or CT) scan and a laser range scan of the patient’s skull in the operating room, and then determined the relationship between a video camera and the patient by matching video images of known points on the table to the actual 3-D laser data of the same features. The registered 3-D model is then transformed into the frame of reference of the video image, so that the surgeon sees the model superimposed on the video image (89). Colchester et al. at Guy’s Hospital, London, have independently developed a similar system, VISLAN. This system initially performs a registration to the skin surface, but has the capability to update this initial registration in the event of patient movement using a point-based method that uses markers affixed to the skull at the beginning of surgery (90). Variants of both systems are now used regularly in clinical practice. More recent research includes work aimed at increasing the accuracy of the guidance process by using multiple video images (91), and the development of registration methods that relax the rigid-body assumption to enable tissue deformations (such as brain swelling) to be accommodated (92,93) in order to maintain the registration during a surgical procedure. Mammography. Mammographic image processing primarily deals with processing X-ray images of a breast (X-ray mammograms) to diagnose breast cancer. One of the earliest reports on mammographic image processing by 94. Since this time therhas been much research in this area, motivated by the need to support the growing size of national screening programs (25 million woman are screened annually in the EC at a cost of approximately US $3 billion a year) and the desire to introduce computer-assisted methods to reduce the cost and improve the accuracy of diagnosis. Mammographic image processing represents a tough challenge to image processing because the images typically have a low signal-to-noise ratio, in the 5 dB to 6 dB range, and many of the abnormalities that one wants to detect, such as microcalcifications, appear as quite subtle and irregular changes in intensity. Highnam and Brady provide an excellent upto-date review on the field (95). Research has addressed issues such as understanding noise properties

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Fig. 6.

•

X-ray mammogram (a) before and (b) after physics-based enhancement (95).

of images (96), image enhancement (22), developing mammographic feature extraction methods (97), and quantification (98). Some work has also been done to match two X-ray views of the same breast to try to infer 3-D information (such as the volume extent of a suspected mass, and more precise locations of microcalcifications) that cannot be inferred from a single X-ray view (99). Finding reliable features turns out to be the limiting factor here that has prevented the successful application of this idea to date. Highnam and Brady (95) argue that successful mammographic image processing has to be firmly based on a physics-based approach that takes into consideration how the image is formed. In their approach they go through an image enhancement step to construct what they called an hint image which is a measure of breast tissue (rather than intensity) at each image location, from a conventional X-ray image. All further image measurement and interpretation are based on the hint image. (see Fig. 6.) Today, most of the successful algorithms that are used in clinical practice are individual techniques designed to assist a radiographer in diagnosis. However, the ultimate goal is to develop fully automatic procedures that could, at a minimum, reduce the large volume of mammograms viewed by a radiographer to a small number of “suspect” cases. Fully automatic microcalcification detection and classification schemes and quantification are active subjects of current research (100,101,102,103). The idea of embedding information provided by image processing into an AI-based clinical decision-making system to aid trained radiographers in the interpretation of mammograms is another interesting area under investigation (104). Cardiology. Most medical image-processing research in cardiac analysis has focused on the problem of tracking left-ventricle boundary motion to provide global heart function measurements such as the ejection

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fraction (ratio of minimum volume to maximum volume) as outlined in the preceding section. As noted there, 2-D echocardiograpy is the most widely used cardiac imaging technique in clinical partice. Commercial echo systems have a relatively limited image-processing capability, consisting perhaps of acoustic boundary detection, simple linear or area measurement, and intensity profiling tools. Automated image analysis systems are still at the laboratory stage of development (75,105,106). Recent advances in ultrasonic imaging technology such as second-harmonic imaging, and the use of contrast agents, together with the introduction of digital and 3-D ultrasound technology, have created renewed interest in this area. 3-D SPECT imaging is used routinely to provide 3-D density maps of blood perfusion. Image processing is used to register stress and rest images and to quantify the extent of diseased tissue (myocardial infarction) (107,108,109). Techniques for measuring 3-D heart motion based on tagged MR are also being actively developed. However, tagged-MR and nuclear-medicine cardiac imaging are currently only available in large research laboratories.

Further Reading For further information about current research in medical image processing refer to the leading journals in the field, such as Medical Image Analysis (Oxford University Press) and the IEEE Transactions on Medical Imaging, or to specialized journals on medical imaging modalities, the appropriate clinical fields, or computer vision and image processing journals. The journals referenced below should provide a good starting point.

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74. V. Chalana, et al. A multiple active contour model for cardiac boundary detection in echocardiographic sequences, IEEE Trans. Med. Imaging, 15: 290–298, 1996. 75. G. Jacob, et al. Evaluating a robust contour tracker on echocardiographic sequences, Med. Image Anal., 3 (1): 63–76, 1999. 76. P. Shi, et al. A unified framework to assess myocardial function from 4D images, Proc. Int. Conf. Comput. Vision, Virtual Reality, Robot. Med., pp. 327–337, 1995. 77. E. Bardinet, L. Cohen, N. Ayache, Superquadrics and free-form deformations: A global model to fit and track 3D medical data, Proc. Int. Conf. Comput. Vision, Virtual Reality, Robot. Med., pp. 319–326, 1995. 78. J. Park, D. Metaxas, L. Axel, Analysis of left ventricle wall motion based on volumetric deformable models and MRI-SPAMM, Med. Image Anal., 1 (1): 53–71, 1996. 79. J. Declerck, J. Feldmar, N. Ayache, Definition of a 4D continuous planispheric transformation for the tracking and the analysis of LV motion, Med. Image Anal., 4 (1): 1–17, 1998. 80. T. S. Denney J. L. Prince, 3D displacement field reconstruction from planar tagged cardiac MR images, IEEE Workshop Biomed. Image Anal., pp. 51–60, 1994. 81. A. C. Evans, et al. Warping of a computerized 3D atlas to match brain image volumes for quantitative neuroanatomical and functional analysis, in Medical Imaging III, SPIE, 1991, pp. 264–274. 82. G. E. Christensen, S. C. Joshi, M. I. Miller, Volumetric transformation of brain anatomy, IEEE Trans. Med. Imaging, 16: 864–877, 1997. 83. A. C. Evans, et al. An MRI-based probabilistic atlas of neuroanatomy, in S.D. Shorvon et al. (eds.), Magnetic Resonance Scanning and Epilepsy, New York: Plenum, 1994, pp. 263–274. 84. P. M. Thompson, A. W. Toga, A surface-based technique for warping 3-dimensional images of the brain, IEEE Trans. Med. Imaging, 15: 1–16, 1996. 85. R. H. Taylor, et al. An image-directed robotic system for precise orthopaedic surgery, IEEE Trans. Robot. Autom. 10: 261–275, 1994. 86. C. B. Cutting, F. L. Bookstein, R. H. Taylor, Applications of simulation, morphometrics, and robotics in craniofacial surgery, in R. H. Taylor et al., (eds.), Computer-Integrated Surgery, Cambridge, MA: MIT Press, 1996, pp. 641–662. 87. S. Gibson, et al. Simulating arthroscopic knee surgery using volumetric object representations, real-time rendering and haptic feedback, Proc. Comput. Vision, Virtual Reality Robot. Med. Conf., Berlin: Springer-Verlag, 1997. 88. S. Cotin, H. Delingette, N. Ayache, Real-time non-linear elastic deformations of soft tissues for surgery simulation, IEEE Trans. Vis. Comput. Graphics, 5 (1): 62–73, 1999. 89. W. E. L. Grimson, et al. An automatic registration method for frameless stereotaxy, image guided surgery, and enhanced reality visualization, IEEE Trans. Med. Imaging, 15: 129–140, 1996. 90. A. C. Colchester, et al. Development and preliminary evaluation of VISLAN, a surgical planning and guidance system using intra-operative video imaging, Med. Image Anal., 1 (1): 73–90, 1996. 91. M. J. Clarkson, et al. Registration of multiple video images to pre-operative data for image-guided surgery, Proc. Med. Image Understanding Anal. 98, Leeds, UK, pp. 73–76, 1998. 92. P. J. Edwards, D. L. G. Hill, D. J. Hawkes, Image guided interventions using a three component tissue deformation model, Proc. Med. Image Understanding Anal. Conf., Oxford, UK, pp. 33–36, 1997. 93. E. Grimson, et al. Clinical experience with a high precision image-guided neurosurgery system, Proc. Med. Image Computing and Computer-Assisted Interventions, Lect. Notes in Comput. Sci., 1496 Springer-Verlag, 1998, pp. 63–73. 94. F. Winsberg, et al. Detection of radiographic abnormalities in mammograms by means of optical scanning and computer analysis, Radiology, 89: 211–215, 1967. 95. R. H. Highnam, J. M. Brady, Mammographic Image Processing, Kluwer Ser.—Med. Imaging, Boston: Kluwer Academic Publishers, 1999. 96. R. M. Nishikawa, M. J. Yaffe, Signal-to-noise properties of mammographic film–screen systems, Med. Phys., 12: 32–39, 1985. 97. T. C. Parr, et al. Model-based classification of linear structures in digital mammograms, 3rd Int. Workshop on Digital Mammography Int. Congr. Ser, Excerpta Med., 1119: 1996. 98. J. H. Richter, E. Claridge, Extraction of quantitative blur measures for circumscribed lesions in mammograms, Med. Inf. 16: 229–240, 1991. 99. W. Spiesberger, Mammogram inspection by computer, IEEE Trans. Biomed. Eng. 26: 213–219, 1979.

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100. N. Karssemeijer, Adaptive noise equalization and recognition of microcalcification clusters in mammograms, Int. J. Pattern Recognition Artif. Intell., 7: 1357–376, 1993. 101. D. H. Davies, D. R. Dance, Automatic computer detection of clustered calcifications in digital mammograms, Phys. Med. Biol., 35: 1111–1118, 1990. 102. T. Ema, et al. Image feature analysis and computer-aided diagnosis in mammography: Reduction of false-positive clustered microcalcifications using local edge-gradient analysis, Med. Phys., 22: 161–169, 1995. 103. R. M. Nishikawa, et al. Computer-aided detection of clustered microcalcifications on digital mammograms, Med. Biol. Eng. Comput. 33: 174–178, 1995. 104. P. M. Taylor, J. Fox, A. Todd-Pokropek, A model for integrating image processing into decision aids for diagnostic radiology, Artif. Intell. Med., 9: 205–225, 1997. 105. V. Chalana, Y. Kim, A methodology for evaluation of boundary detection algorithms on medical images, IEEE Trans. Med. Imaging, 16: 642–652, 1997. 106. P. J. Slomka, et al. Automated alignment and sizing of myocardial stress and rest scans to three-dimensional normal templates using an image registration algorithm, J. Nucl. Med., 36: 1115–1122, 1995. 107. A. Giachetti, On-line analysis of echocardiographic image sequences, Med. Image Anal., 2 (3): 261–284, 1998. 108. R. Mullick, N. F. Ezquerra, Automatic determination of LV orientation from SPECT data, IEEE Trans. Med. Imaging, 14: 88–99, 1995. 109. J. Declerck, et al. Automatic registration and alignment on a template of cardiac stress and rest reoriented SPECT images, IEEE Trans. Med. Imaging, 16: 727–737, 1997.

J. ALISON NOBLE University of Oxford

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Wiley Encyclopedia of Electrical and Electronics Engineering Radionuclide Imaging Standard Article Mark T. Madsen1 1University of Iowa, Iowa City, IA Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved. DOI: 10.1002/047134608X.W4704.pub2 Article Online Posting Date: July 13, 2007 Abstract | Full Text: HTML PDF (744K)

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Abstract The sections in this article are Introduction Radioactive Decay Counting Statistics Ray Interactions with the Matter Scintillators Emission Tomography Image Quality Applications Summary Keywords: radionuclide; PET; SPECT; radiopharmaceutical; decay; scintillator About Wiley InterScience | About Wiley | Privacy | Terms & Conditions

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RADIONUCLIDE IMAGING

INTRODUCTION Radionuclide imaging is performed in nuclear medicine clinics and positron emission tomography (PET) centers. In both cases, radionuclides are used to label interesting compounds (radiopharmaceuticals) that are injected into patients. The distribution and kinetics of these radiotracers reveal the physiology of tissues and organs and thereby provide diagnostic information. Radionuclides are nearly ideal as tracers. Although they can be readily detected outside the body, the total mass of the radionuclides administered for diagnostic studies is typically in the nanogram range. Thus, the toxic and perturbing effects of the radionuclides are minimal. Radiotracers used in conventional nuclear medicine studies are imaged with a scintillation camera. The scintillation camera is used for imaging conventional planar (2-D) studies and single photon emission computed tomography studies (SPECT). PET systems image the annihilation radiation resulting from positron emitting radionuclides using coincidence detection. This article will review the principles of these radionuclide imaging systems. It will begin with a brief summary of radioactive decay and the interactions of γ rays with materials. Radiation detection and imaging devices will be discussed next. The factors that degrade radionuclide images will be reviewed along with techniques to improve image quality. The article will be concluded with a discussion of clinical nuclear medicine and PET applications of radionuclide imaging along with pre-clinical small animal imaging systems. RADIOACTIVE DECAY Energy Units In atomic and nuclear physics, energy is typically expressed in units of electron volts. One electron volt is equal to the kinetic energy of an electron accelerated through a 1-volt potential. Visible light has photon energy of 2–3 eV. The energy of γ rays is much higher and is usually given in terms of keV (1 keV = 1000 eV) or MeV (1 MeV = 1,000,000 eV). The masses of atomic and nuclear particles are also commonly expressed in units of MeV calculated from the Einstein equation (E = mc2 ). Nuclear Nomenclature Radioactive decay has a nuclear origin. Although the nucleus occupies a very small fraction of the volume of an atom, it has virtually all the mass. The nucleus consists of A nucleons (Z protons and N neutrons), held together by the strong force. Different nuclear species are referred to as nuclides and they are represented by A X, where X is the chemical symbol associated with the nuclide. Nuclides with the same Z and different N are called isotopes, whereas those with the same N are called isotones. Nuclides with the same A are called isobars. Nucleons have discrete energy levels, and when a nucleon is in an excited state, it returns to the ground state with the emission of a

high energy photon called a γ ray. Some nuclides such as 16 O never change their nuclear identity and are said to be stable. Others, such as 14 C, spontaneously change into another nuclide with the emission of energetic particles. These nuclides are called radioactive. Three primary types of radioactive emissions exist: α particles, β particles, and γ radiation. α particles are helium nuclei that are emitted through a quantum mechanical tunneling process, and as no α emitters are used in radionuclide imaging, they will not be discussed further. β particles are high energy electrons or positrons that are created as part of an isobaric decay process in which one nucleon is transformed into its counterpart. There are three modes of β decay, β−, β+, and EC (EC); these modes will be discussed in more detail below. α and β particles have short ranges in tissue (< 0.1 millimeters for α and < 10 millimeters for β). Thus, they deliver a radiation dose to the patient without yielding useful information. γ rays, however, are very penetrating and can be detected externally. Radionuclides that emit γ rays without emitting any charged particles are especially attractive as imaging tracers because they deliver a low radiation dose to the body. Table 1 has a list of γ emitting radionuclides along with their physical properties. γ rays, as noted above, are high energy, monoenergetic photons resulting from the transition of a nucleon from an excited state to a lower energy level. This process is called an isomeric transition (IT). In some nuclides, only one transition occurs from the excited state to the ground state and only a single γ ray is emitted. In other nuclides, intermediate states exist, so more than 1 γ ray may be emitted. Quite often (not always) α or β emission will leave the daughter nuclide in an excited state so that γ radiation frequently accompanies the other decay modes. In most cases, the emission of the γ ray is virtually instantaneous (< 10−24 sec). For some nuclides, the excited state persists for seconds, hours, or even days. These states are called isomeric or metastable states and they are denoted with an “m” following the atomic mass number. Technetium-99m (99m Tc) is an extremely important example of a metastable radionuclide in radionuclide imaging.

β Decay β decay is a manifestation of the weak force in which nucleon exchange occurs. Either a proton is changed into a neutron or a neutron is changed into proton. The atomic mass remains constant and the atomic number changes by either +1 or −1. β− decay occurs in unstable nuclides that have a relative abundance of neutrons. With β− decay, a neutron is changed into a proton and the Z of the daughter nuclide is increased by 1. During the process of β− decay, an energetic electron is created and emitted along with a massless, neutral particle, the anti-neutrino. β− radionuclides are produced from neutron activation of stable nuclides or are separated from fission byproducts in a nuclear reactor. As a result of the β particle, β− emitters are not preferred for imaging studies, but are sometimes used because no suitable alternatives exist. 133 Xe and 131 I are examples of β− emitters that are used for imaging.

J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright © 2007 John Wiley & Sons, Inc.

2

Radionuclide Imaging Table 1. Radionuclides Commonly Used in Medical Imaging Radionuclide 99m Tc 81m Kr 133 Xe 131 I 111 In 67 Ga 123 I 201 TI 15 O 13 N 11 C 18 F 82 Rb

Decay Mode IT IT ββEC EC EC EC β+ β+ β+ β+ β+

Production Method 99 Mo Generator 81 Rb Generator Fission Byproduct Fission Byproduct 111 Cd( p, n)111 In 68 Zn( p, 2n)67 Ga 124 Te( p, 5n)123 I 201 Hg(d, 2n)201 TI 14 N(d, n)15 O 16 O( p, α)13 N 10 B(d, n)11 C 18 O( p, n)18 F 82 Sr Generator

Half Life 6 hr 13 sec 5.3 dy 8 dy 67 hr 78 hr 13 hr 73 hr 122 sec 10 min 20 min 110 min 75 sec

Principal Photon Emissions (keV) 140 190 30, 80 364 172, 247 93, 185, 296 159 60–80 (X rays), 167 511 511 511 511 511

Table 2. Scintillation Properties of NaI(TI), BGO, LSO, and GSO Properties Effective Z Density µ (cm−1 ) @ 511 keV Max Emission λ (nm) Relative light output Decay time (nsec) Refractive index

NaI(TI) 50 3.67 0.33 410 1 230 1.85

BGO 74 7.13 0.91 480 0.1 300 2.15

LSO 66 7.4 0.833 420 0.75 40 1.82

GSO 60 6.71 0.684 430 0.35 60 1.85

Table 3. Nuclear Medicine and PET Diagnostic Studies Radiopharmaceutical 99m Tc Medronate (MDP), Oxidronate (HDP) 99m Tc Sestamibi, Tetrofosmin 99m Tc Pentetate (DTPA) 99m Tc Mirtiatide (MAG3) 99m Tc Macroaggregated Albumin (MAA) 99m Tc Red Blood Cells 99m Tc Exametazine (HMPAO), Bicisate (ECD) 99m Tc Desofenin (DISIDA), Lidofenin (HIDA), Mebrofenin 99m Tc Arcitumomab (CEA Scan) 133 Xe 131 I Metaiodobenzylguanidine (MIBG) 131 I Sodium Iodide 67 Ga Citrate 111 In Oxine 111 In Capromab Pendetide (ProstaScint) 111 In Pentetreotide (OctreoScan) 201 TI Thallous Chloride 123 I Sodium Iodide 15 O Water 13 N Ammonia 11 C Acetate 11 C Methionine 18 F Fluoro-2-deoxyglucose (FDG) 18 F Fluro-Labeled Thymidine (FLT) 82 Rb

Application Bone scans Myocardial perfusion, breast cancer Renal function (GFR) Renal function (Flow) Lung perfusion Cardiac wall motion, LV Ejection fraction Brain perfusion Hepatobilliary function Colon cancer Lung ventilation, cerebral blood flow Neuroendocrine tumors Thyroid cancer Infection, tumor localization Leukocyte & platelet labeling (Infection) Prostate cancer Neuroendocrine cancer Myocardial perfusion Thyroid cancer Regional cerebral blood flow Myocardial perfusion Myocardial function Tumor localization Tumor localization, myocardial viability seizure localization Tumor proliferation Myocardial perfusion

The other two modes of β decay, β+ and EC decay, occur for nuclides with an abundance of protons. In both of these modes, a proton is changed into a neutron and the Z of the daughter nuclide is decreased by 1. In EC, an inner shell orbital electron is captured in the nucleus and is used in the conversion of a proton into a neutron. During

this process, a neutrino is created, but no charged particles are emitted, and this feature makes them attractive as imaging agents. There will be characteristic X rays and Auger electrons emitted as the electron vacancy is filled, and sometimes the characteristic X rays are collected along with the γ rays to form images. EC radionuclides are pro-

Radionuclide Imaging

duced in charged particle accelerators such as a cyclotron (1). 201 TI, 123 I, 111 In, and 67 Ga are examples of commonly used EC radionuclides. β+ decay results in the emission of a positron as a proton is changed into a neutron. A positron is the anti-particle of the electron having the same mass and other quantum properties of the electron, but has a positive charge. The energetic positron dissipates its energy within a few millimeters and captures an electron. Within a very short time, the positron and electron mutually annihilate each other, yielding two co-linear 511-keV photons. The coincidence detection of these two photons provides the basis of PET imaging. Charged particle accelerators, typically cyclotrons, produce positron emitters (1, 2). Some of the positron emitters that are useful for medical imaging, such as 11 C, 13 N, and 15 O, have short half lives that require an on-site accelerator. Fluorine-18 (18 F) with a 110-minute half life can be shipped over short distances and is commercially available. Radioactivity Radioactivity is a measure of the number of decays per second in a sample and is defined by the equation A = λN

(1)

where A is the activity (decays per second), N is the number of radioactive atoms, and λ is the decay constant (defined below). The former unit of radioactive decay was the Curie, 3.7 × 1010 decays per second, while the SI unit for radioactive decay is the becquerel (Bq), 1 decay/second. Typically, 1 to 30 mCi (∼40 MBq to 1000 MBq) are administered for diagnostic imaging studies depending on the radionuclide. Although radioactive decay occurs at random, the probability of decay over a fixed time interval (the decay constant, λ) is constant and unique for every radionuclide. The decay of a radioactive source is an exponential function: A(t) = A0 exp(−λt)

(2)

N(t) = N0 exp(−λt)

(3)

where A0 is the initial quantity of activity, No is the initial number of radioactive atoms, and A(t) and N(t) are the quantities at some later time t. Because the fractional decrease over any fixed time interval remains constant, one can use the half-life (T1/2 ) to characterize the decay behavior. The half-life is the time interval in which the activity (or number of radioactive atoms) decreases by a factor of two. The relationship between the half-life and the decay constant is: T1/2 = ln(2)/λ = 0.693/λ

(4)

The half lives for radionuclides used in radionuclide imaging range from seconds (e.g., 81m KrT1/2 = 13 s) to days (131 IT1/2 = 8 days). COUNTING STATISTICS The emission and detection of γ rays is governed by Poisson statistics. As a result, the uncertainty (standard deviation)

3

of a measurement with N counts is N1/2 . If precision is defined as 100% × N1/2 /N, then it is obvious that precision improves (gets smaller) as N increases (Fig. 1). Subtle details in images are often lost in the statistical fluctuations (image noise). Therefore, it is desirable to acquire as many detected events as possible to maintain good image quality. As the detection efficiency for γ rays in imaging systems is low, this requirement often presents a problem because limitations exist both on the amount of radioactivity that can be administered to a patient and on the study duration. Arithmetic operations on radionuclide images propagate the individual uncertainties into the result. For example, when images are subtracted, areas where the result is close to zero will be especially noisy. Image noise is also a major limiting factor in SPECT and PET imaging, as the reconstruction algorithm both amplifies and spatially correlates the image noise. γ RAY INTERACTIONS WITH THE MATTER The intensity of a γ-ray beam decreases as it traverses through a material because of interactions between the γ rays and the electrons in the material. This process is referred to as attenuation. Attenuation is an exponential process described by I(x) = I0 exp(−µx)

(5)

where I0 is the initial photon intensity, I(x) is the photon intensity after traveling a distance x through the material, and µ is the linear attenuation coefficient of the material. Over the range of γ-ray energies used in radionuclide imaging, the two primary interactions that contribute to the attenuation coefficient are photoelectric absorption and Compton scattering. Photoelectric absorption refers to the total absorption of the γ ray by an inner shell atomic electron. The inner shell electron is ejected from the atom with an energy equal to the γ-ray energy—the binding energy of the electron. Photoelectric absorption can only occur with electrons whose binding energy is less than the γ-ray energy. The cross section for photoelectric absorption (τ) is proportional to the media density, the cube of the atomic number and is inverse the proportional to the cube of the γ-ray energy (τ α ρZ3 /Eγ 3 ). As a result of the low effective Z of body tissues (Zeff = 7.6), photoelectric absorption is not the dominant interaction. However, it is the primary interaction in high Z detecting materials such as sodium iodide, bismuth germanate, and shielding material such as lead, which is advantageous, because the signal generated by photoelectric absorption is proportional to the total γ-ray energy. Compton scattering occurs when the incoming γ ray interacts with a loosely bound outer shell electron. A portion of the γ-ray energy is imparted to the electron and the remaining energy is left with the scattered photon. The amount of energy lost in the scattering event depends on the angle between the incident γ ray and scattered photon. The cross section for Compton scattering (σ) depends on the electron density of the media and is (approximately) inversely proportional to the γ-ray energy (σ ∼ ρe /Eγ ). Compton scattering is the dominant interaction in body tissues,

4

Radionuclide Imaging

Figure 1. Image noise. The detection and emission of radiation is governed by Poisson statistics. As a result, the precision of a count measurement improves as the number of detected counts increase. Figure 1(a) shows a series of four images of a circular defect with a 5% defect. Each succeeding image to the right has a factor of two increase in the count density. Note that as the count density increases, the relative level of the noise decreases and the defect becomes more perceptible. Figure 1(b) illustrates how statistical errors propagate with arithmetic operations. The resulting subtracted image has a mean near zero with a standard deviation that is larger than either of the original images. The graph below the images shows a count profile through the image labeled B along with a profile through the result of the subtraction.

and it contributes significantly to the attenuation of 511keV photons in the shielding and detecting materials.

SCINTILLATORS The efficient detection of γ rays requires detectors with high density, high atomic number, and a large sensitive volume. Scintillators are the most common type of detector used in radionuclide imaging (3). Scintillators emit a flash of visible light photons when they absorb γ rays. The brightness of the scintillation is directly proportional to the absorbed energy of the detected event. Although a large number of scintillators are used in medical applications, the most common in single photon imaging is sodium iodide activated with thalium (NaI(Tl)), whereas the scintillators used in PET imaging include bismuth germanate (BGO), gadolinium oxyorthosilicate (GSO), and lutetium oxyorthosilicate (LSO). Table 2 lists the physical properties of these detectors. Although it is expected that scintillators will remain the preferred detectors in PET, applications exist within conventional radionuclide imaging where semiconductor detectors are making inroads. Both cadmium telluride-and cadmium zinc telluride-based γ imaging systems are currently available for imaging low energy γ-ray emitters such as 99m Tc (4).

Electronics All scintillation detectors (individual detectors and imaging devices) use similar electronics as shown in Fig. 2. In discrete detectors, the scintillation is converted to an electronic pulse by a photomultiplier tube, although solid-state devices such as avalanche photodiodes are beginning to replace these devices (5). The pulse is further amplified and shaped and is sampled by a pulse height analyzer. The pulse height analyzer identifies pulses of a pre-selected amplitude range corresponding to the desired γ-ray energy. Pulses falling within this range trigger a standard signal that is counted by a scaler or other counting device. All other pulses are ignored. As the pulse height maintains its proportional relationship with the energy absorbed in the scintillator, the pulse height analyzer can be calibrated in keV units. Intrinsic efficiency The intrinsic efficiency of a detector (denoted by ε) is determined by its thickness (x) and its linear attenuation coefficient (µ): ε = 1 − exp(−µx)

(6)

The intrinsic efficiency is high (i.e., close to 1) when the product µx is large, which requires that µ or x or both are large. Increasing the detector thickness adversely affects spatial resolution from parallax errors, so it is preferable to have a large µ. Detector materials with high density

Radionuclide Imaging

5

Figure 2. Scintillation detector electronics. The components in scintillation detectors are similar. The detector is optically coupled to a photomultiplier tube that converts the scintillation into an electronic pulse. The visible light generates photoelectrons at the photocathode. These electrons are accelerated to a terminal post called a dynode with sufficient energy (usually about 100 eV) to free four to five new electrons, which continues through a succession of dynodes to achieve an overall signal gain of >1,000,000. The output of the photomultiplier tube gets a power boost from the pre-amplifier and is transmitted to the main amplifier where the signal is shaped and amplified. At this point, it is sent to the pulse height analyzer. If the pulse amplitude lies between the upper and lower thresholds (energy window), a logic pulse is generated indicating a good event. The scale counts and records the number of good events.

and high atomic number are especially important for coincidence detection of the 511-keV annihilation radiation. As both photons have to be detected to register a valid coincidence event, the coincidence detection efficiency is ε2 . Energy Resolution As γ rays are monoenergetic, a detector with perfect energy resolution would generate pulses with the same amplitude for each γ ray that was totally absorbed. The energy spectrum for such a device would be a delta function. Scintillation detectors do not have perfect energy resolution because of statistical fluctuations in the number of electrons liberated at the photocathode of the photomultiplier tube. The noise level associated with these electrons is decreased as the brightness of the scintillation increases. As a result, the efficient conversion of absorbed γ-ray energy into visible light is an important feature. Both NaI(Tl) and LSO have high light outputs, while BGO is an order of magnitude lower. In addition, their refractive index is better matched to the glass face of the photocathode. Energy resolution is quantified from the width of the energy peak measured in keV at the half maximum level (full-width-athalf maximum, FWHM): Energy Resolution = 100% × FWHM(keV)/Eγ(keV) (7) Good energy resolution is important for rejecting scattered radiation, a major factor in reducing image contrast. If a γ ray is Compton scattered within the patient, it necessarily loses energy. When the energy resolution is good, a narrow energy window can be set on the photopeak restricting the number of scattered photons. With poor energy resolution, a broad window has to be used to maintain sensitivity, and more scattered radiation is included in the acquired image data. The energy resolution of NaI(Tl) is sufficient to permit the simultaneous acquisition information from γ rays of different energy, which is accomplished by selecting individual energy windows on multiple pulse height analyzers for each of the desired γ rays. In the single isotope mode,

the information from all of the selected energy windows is summed and stored as one image. Studies using radionuclides with multiple γ-ray emissions like 111 In (172, 247 keV) or 67 Ga (93, 185, 300 keV) are examples. In the multiple isotope mode, separate images are generated for each selected energy window, which yields spatially registered images with unique information. One application of dual isotope imaging is 99m Tc MDP bone scanning in conjunction with 111 In white cell labeling for localizing sites of infection. In PET imaging, this type of acquisition has been used to simultaneously collect a coincidence emission study and a single photon transmission study with 137 Cs(Eγ = 662 keV) for attenuation correction. Temporal Resolution It is important to realize that every event detected by a radionuclide imaging device is analyzed individually. As the conversion of γ-ray energy into an electronic pulse is not instantaneous, the detection process requires a finite amount of time. If an additional event occurs before the system has finished processing the previous one, pulse information is compromised and the events cannot be properly interpreted. The length of time it takes to process an event is often called the dead time, because the system appears to be insensitive during this time. The primary limiting factor in scintillation detectors is the length of time the scintillation persists. Both NaI(Tl) and BGO are relatively slow scintillators, whereas LSO and GSO are 6–7 times faster. Fast scintillators have an additional benefit for PET because they allow a narrower coincidence time window thus reducing the level of accidental coincidences. They also provide the potential for time-of-flight PET imaging discussed below. Few single photon studies exist that are limited by the count rate capability of NaI(Tl) because of the very low count sensitivity of the collimator. However, the ability to handle high count rates is crucial for PET systems, where the unshielded detectors often achieve singles counting rates in the range where count rate losses are apparent

6

Radionuclide Imaging

(6).

tion.

Scintillation Camera

SPECT Systems

Conventional nuclear medicine images are acquired on scintillation cameras (also referred to as Anger or γ cameras). The detector of the scintillation camera is a large (∼50 × 40 cm), thin (9 mm) NaI(Tl) crystal (Fig. 3). The location of a γ-ray interaction is determined by the positionweighted average of the electronic pulses generated by the photomultiplier tubes in the vicinity of the absorption. Photomultiplier tubes are arranged in a close-packed array covering the entire sensitive area of the crystal. In addition to estimating the position of the scintillation event, the photomultiplier tube signals are also combined to estimate the energy absorbed in the interaction. The energy signal is used to discriminate against scattered radiation and is also used to normalize the position signals so that the size of the image does not depend on the γ-ray energy. As the sampling and response of the photomultiplier tubes to individual scintillations is not uniform, additional corrections are made for position-dependent shifts in the energy signal (referred to as Z or energy correction) and in the determination of the event location (referred to as L or spatial linearity correction). Thus, when a γ ray is absorbed, the scintillation camera must determine the position and energy of the event, determine if the energy signal falls within a selected pulse height analyzer window, and apply spatial linearity correction. At this point, the location corresponding to the event within a pre-selected image matrix is incremented. A scintillation camera image is generated from the accumulation of these events. γ rays cannot be focused because of their high photon energy. Therefore, a collimator must be used to project the distribution of radioactivity within the patient onto the sodium iodide crystal. A collimator is a multi-hole lead device that selectively absorbs all γ rays except those that traverse the holes, which severely restricts the number of emitted γ rays that can be detected. Less than 0.05% of the γ rays that hit the front surface of the collimator are transmitted through to the crystal. Most collimators have a parallel hole design, although diverging, converging (cone beam), and fan beam geometries are available. As the design parameters that favor good spatial resolution (small hole size and extended length) adversely affect the collimator sensitivity, collimators are optimized for the type of imaging required. The energy of the γ rays being imaged is also a factor in the design of a collimator, as high energy photons require thicker septa between the holes. Thus, medium energy collimators (designed for Eγ > 200 keV) and high energy collimators (designed for Eγ > 350 keV) have lower sensitivity and poorer spatial resolution than those designed for the 140-keV γ rays from 99m Tc.

A SPECT system consists of one or more scintillation cameras mounted to a gantry that can revolve about a fixed axis in space, the axis of rotation (Fig. 4) (7). As projection views must be acquired from 360 degrees about the patient, additional scintillation cameras increase the sensitivity. The most common configuration available today is the dual detector system, which not only yields better SPECT sensitivity, it also allows the simultaneous acquisition of anterior and posterior views for conventional planar imaging. In the dual detector SPECT systems, each scintillation camera has the ability to move independently in the radial direction as the heads revolve about the patient, which allows body contouring and improves the overall spatial resolution of the study. SPECT systems are usually operated in a step-and-shoot mode. That is, the camera rotates over an angular increment and then remains motionless as it acquires a projection view. Alternatively, it is possible to acquire SPECT studies in a continuous rotation mode. In this mode, information is acquired into a pre-selected number of frames during the time the camera is a rotating continuously about the patient, each frame representing data acquired over a small, fixed angle of rotation. Typically, 60–120 projection views are acquired over 360 degrees, which helps to partially compensate for attenuation. One exception is the myocardial perfusion study. As the heart is not centrally located in the thorax, most clinics acquire only the 180 degrees in which the heart is attenuated by the least amount of tissue. Although it causes some distortion, it yields tomographic images with higher contrast than those for which projections were acquired over the full revolution. To obtain accurate reconstructed images, corrections must be made for attenuation. An accurate correction for attenuation requires an estimate of the regional attenuation coefficients (attenuation map). Many SPECT systems use the Chang method, which presumes that the body is a uniform, unit density elliptical cylinder. A correction matrix is generated of the average attenuation factors for each point in the transverse plane. This correction matrix is then applied to the reconstructed image. Although this method works reasonably well in the abdomen and head, it is not effective in the thorax where most of the assumptions are invalid. SPECT systems can be equipped with a radionuclide transmission system that directly measures the attenuation map of the patient. An iterative reconstruction algorithm incorporates this information resulting in an accurate attenuation correction (8, 9). More recently, CT systems have been combined with SPECT systems to provide high quality anatomic information and even more accurate attenuation correction (10). Pictures of SPECT CT systems along with a clinical image are shown in Fig. 5.

EMISSION TOMOGRAPHY Two kinds of emission tomographic imaging systems exist: single photon emission computed tomography (SPECT) and positron emission tomography (PET). SPECT systems use scintillation cameras to collect (attenuated) projection information, whereas PET systems use coincidence detec-

PET Systems Coincidence detection is used to detect the 511-keV photons resulting from positron annihilation (Fig. 6). As these photons are co-linear, one can determine the line along which the source is located from the simultaneous detec-

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Figure 3. Scintillation camera. The scintillation camera uses one large, thin NaI(Tl) crystal as the sensitive element. γ or X rays from the internally distributed source are projected onto the NaI(Tl) crystal by the collimator, the image forming aperture of the scintillation camera. The scintillation resulting from γ-ray absorptions are sampled by photomultiplier tubes arranged in a close-packed array over the entire crystal surface. Location information is obtained from a position-weighted sum of the photomultiplier tube signals in the immediate vicinity of the interaction and energy information is obtained from the unweighted sum. The energy signal is used to normalize the position signals and to discriminate against scattered radiation. An event that meets the energy criteria is corrected for spatial linearity and uniformity, and it is registered by incrementing the pixel in a digital image corresponding to the event location on the crystal.

Figure 4. SPECT system. A SPECT system uses scintillation cameras to collect projection data. The scintillation cameras rotate about the patient collecting 60–120 views over a 360-degree rotation.

tion in opposing detectors. For a coincidence event to be registered, it must be detected by both detectors. Thus, if the detection efficiency for absorbing one of the annihilation photons is 0.30, then the coincidence efficiency is 0.3 × 0.3 = 0.09, which illustrates why high detection efficiency is critical. The time that it takes the detector to register an event is also very important. The decay time of the scintillation limits the ability of the system to accurately determine the timing of the associated electronic pulse. The coincidence time window used in PET imaging systems is on the order of 10 nanoseconds. It is inevitable that the coincidence detectors will sometimes detect two unrelated events within the time window. These events are referred to as accidental or random coincidences. The random coincidence rate, CR , depends on the size of the coincidence time window ( t) and on the

magnitude of the count rates at the two detectors (C1 , C2 ). CR = 2 × C1 × C2 × t

(8)

As random coincidences present unwanted background, it is important to keep this rate as low as possible. One way of accomplishing this feat is to restrict or shield against sources that are outside the coincidence field of view of the two detectors. A PET imaging system consists of a large number of individual coincidence detectors (or multiple scintillation cameras) in coincidence (2, 7). The coincidence lines of response generate (attenuated) projection information without the need for collimation. As a result, the efficiency for detecting the 511-keV annihilation radiation is significantly higher than the efficiency for detecting low energy γ rays using collimators. Most dedicated PET systems use many individual detectors grouped in rings. Each detec-

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Figure 5. Commercial SPECT CT systems. These systems combine a CT system for anatomical information with a SPECT system. The devices shown are the GE Infinia Hawkeye, Philips Precedence, and Siemens Symbia. The lower right image shows an example of an 111 In Pentetreotide study in a patient with carcinoid along with co-registered CT images.

Figure 6. PET imaging system. PET imaging systems rely on the coincidence detection of the positron annihilation radiation. Opposed detectors register events that occur during a 10-nanosecond timing window. Although some PET tomographs use scintillation camera technology, most are made of a large number of individual coincidence detectors. For both designs, the lines of response are determined by the coincidence rays. Designs using individual detectors are arranged in rings. Multiple rings are stacked together to increase the axial field of view. PET cameras can be operated in the 2-D mode where only coincidence events in the plane of the ring or its adjacent neighbors are considered, or in the 3-D mode where are all coincidence paths are used.

tor forms a potential coincidence pair with the detectors on the opposite side of the ring, which provides sufficient sampling for generating tomographic images. The acquired PET studies need several corrections, including corrections for the random coincidences, scatter, and attenuation. The random coincidence rate can be estimated using equation (9) if the individual count rates at each of the detectors are known. Scattered radiation cannot be totally eliminated by energy discrimination. Thus, estimates of scatter and a means for eliminating it are necessary. Corrections for attenuation require an estimate of

the attenuation map for each reconstructed slice, which is typically measured on the PET system with the acquisition of a transmission study. It should be noted that the correction for attenuation in PET studies is large with maximum correction factors often greater than 100. Pet imaging systems may be operated in the 2-D or 3-D modes. In the 2-D mode, the axial angle for coincidences is restricted to direct planes and the adjacent cross planes with lead shields, which reduces count sensitivity, but also reduces the magnitude of the scatter and random coincidence correction. The 3-D mode allows coincidence events

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to be recorded over the entire axial field of view, which provides higher sensitivity and continuous axial sampling but with a significantly higher scatter fraction. 3-D PET also requires a 3-D reconstruction algorithm, which is computationally intensive and time-consuming. A more efficient approach re-bins the acquired data into appropriate 2-D data sets where conventional reconstruction algorithms can be applied (11, 12). Recent developments in PET imaging include PET/CT hybrid imaging systems, the rebirth of time-of-flight PET, and small animal PET systems. Combined PET and CT imaging systems were introduced in 2000 and were rapidly embraced by the medical imaging community to the point that, within 2 years, they dominated the market. These devices consist of a high performance PET tomograph coupled to a high performance CT system sharing a common imaging table. Patients first get a helical CT study and then a PET study of the selected body region. The information from the CT scan is used to generate the attenuation correction factors required for the PET study and also provides high resolution anatomical images that are readily co-registered to the functional PET images (Fig. 7). These capabilities are particularly advantageous for oncology studies and account for the incredibly rapid growth of these devices in the medical community (13–15). With conventional PET systems, the timing of coincident events is not precise enough to provide source localization. Light travels about 30 cm per nanosecond, and a time window of even several nanoseconds is too coarse to provide useful information. In the mid 1980s there was a PET tomograph based on barium fluorite (BaF2 ) detectors that had very fast timing and could operate in the timeof-flight mode. However, the detection efficiency of BaF2 was very poor and this device could not complete with conventional PET tomographs. Recently, a commercial timeof-flight PET system based on LYSO detectors has become available (13). This system has the capability of determining the source location to within several centimeters based on the time differential between the detection of the annihilation photons at two detectors. When this information is employed in the reconstruction algorithm, it improves the signal-to-noise-ratio, especially in large patients. This improvement in image quality can be used to reduce imaging time.

tion can still be applied, but unless corrections are made, there will be artifacts. Although the detection mechanisms used by SPECT and PET are different, the steps for generating tomographic images are similar. Projections of the radioactivity distribution within the patient are acquired from a large number of views. These projections are organized by projection angle (sinogram) and, after the appropriate filter is applied, a computer algorithm is used to reconstruct the tomographic images. Two general reconstruction approaches exist: filtered backprojection and iterative reconstruction. With filtered backprojection, the projections are first modified by a windowed ramp filter and then backprojected at the angle at which they were acquired. Filtered backprojection has the advantage of being fast and easy to implement, but it cannot easily incorporate complex corrections. The other approach to image reconstruction uses iterative algorithms (16). Iterative algorithms for image reconstruction were introduced in the 1970s with the introduction of X-ray computed tomography. These algorithms were extensions of general approaches to solving linear systems with sparse matrices. Figure 8 illustrates the method. An initial guess (usually a constant field) is used as the first estimate of the desired distribution. Projections are calculated from this distribution and arithmetically compared with the corresponding measured projections. This comparison may be a subtraction forming the basis for the algebraic techniques or a division that is characteristic of maximum likelihood algorithms. The result of this operation is backprojected to generate a correction image that is multiplied into the estimated distribution to complete the first iteration. This process is continued until the stopping criteria are met. Iterative algorithms are more time consuming than filtered backprojection, but they have several important advantages as follows:

Reconstruction

These important advantages coupled with the increasing computational capabilities of computer systems now make iterative algorithms an attractive alternative.

Conventional nuclear medicine images are acquired with a scintillation camera positioned over the organ of interest. The resulting image is a 2-D attenuated projection of the 3-D distribution of radioactivity, and as a result, these images frequently suffer from low contrast. With the advent of computerized tomography in the mid-1970s, it became apparent that the same algorithms could be extended to emission imaging. Tomographic images of the internal distribution of a radiopharmaceutical can be reconstructed if a complete set of true projections is acquired. True projections are obtained from the line integrals of the radioactive distribution along a set of view angles. As a result of attenuation within the body, it is not possible to directly measure projection data. The techniques of tomographic reconstruc-

1. They eliminate the radial streak artifacts, which accompany filtered backprojection. 2. They can effectively model and thereby correct for physical degradations of the imaging process such as scatter, attenuation, and spatial resolution. 3. They yield superior results in situations where a wide range of activities is present or where limited angle data is available.

IMAGE QUALITY The ability to detect information in an image depends significantly on the signal-to-noise ratio (k). In the model developed by Rose, an estimate of the signal-to-noise ratio for white noise is given by: k2 = n C2 d 2

(9) 2

where n is the image count density (counts/cm ), C is the contrast between an area of interest and the surrounding region, and d is the linear dimension of the area. Although

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Figure 7. Commercial PET CT systems. These systems combine a fully functional CT scanner with a PET tomograph. The devices shown are the Siemens Biograph, Philips Gemini, and GE Discovery. The lower right image shows an example of the fused PET 18 F FDG and CT image data of a patient with lingual tonsilar carcinoma.

Figure 8. Iterative reconstruction. In iterative techniques, the calculated projections from the current estimate of the reconstructed image are arithmetically (difference or ratio) compared with the measured projection set. The result is backprojected and used to update the estimated reconstruction, which continues until the stopping criteria are reached. Maximum likelihood algorithms with rapid convergence such as the ordered subset approach are the most commonly used techniques. The images below show a comparison of an image reconstructed with filtered backprojection (left) and an ordered subset algorithm (8 subsets, 6 iterations). The iterative approach eliminates streak artifacts and yields a more accurate image in the vicinity of intense concentrations of activity.

this model is not strictly accurate for complicated image scenes or for cases where the noise is correlated as in tomography, it illustrates the importance of contrast and count density on detection. Although contrast primarily depends on the in vivo distribution of the radiotracer, the performance of the imaging system is an important factor especially for objects that are smaller than two × the FWHM associated with the system spatial resolution.

Spatial Resolution The finite spatial resolution of radionuclide imaging reduces contrast, especially for small objects. Spatial resolution is characterized by the point or line spread response function (PSF or LSF). Although the entire response curve is needed to fully characterize the spatial resolution, often only the full-width-at-half-maximum is reported. The system spatial resolution depends on multiple components

Radionuclide Imaging

including the intrinsic resolution of the detectors, the geometric resolution, and any spatial filtering. To the extent that each of these components have Gaussian response curves, the system FWHM (Rsys) is estimated from Rsys = (




1/2

Ri )

(10)

where Ri is the FWHM associated with each component. In SPECT imaging, the spatial resolution components are the intrinsic spatial resolution of the scintillation camera (typically 3.5 mm), the geometric resolution of the collimator (∼8–15 mm depending on the source distance), and the kernel width of the windowed reconstruction filter (∼5–15 mm depending on the count density). As the spatial resolution of the collimator depends on the sourceto-collimator distance, it is important to maintain close proximity of the collimator to the patient whenever possible. All SPECT systems have body contouring capability for this reason. In addition to the contribution from the reconstruction filter, four physical factors exist that limit the spatial resolution of PET systems: the size of the detector elements, the non-colinearity of the annihilation radiation, the positron range, and the detector parallax. Annihilation photons are co-linear only if the annihilation takes place with the positron and electron at rest. As thermal motion of the particles exists, about a 0.25◦ statistical deviation exists from true co-linearity. This deviation restricts the spatial resolution and becomes a larger problem as the coincidence detectors are separated at larger distances. Annihilation always takes place outside the nucleus after the positron has dissipated its energy. For low energy positrons such as emitted by 18 F, the reduction in spatial resolution from this effect is relatively small (