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n i (r s , r d )/ O x (r s , r,)] exp . Here, x (r s , r,.) represents the excitation fluence detected at a fixed reference position, r,, in response to excitation from the source position, r s . Even though the excitation fluence, ^Trs, r,), is updated during the iteration, the Jacobian matrix can be directly calculated from Eq. (36), and
the change in <J> x (r s , rr) is small compared to that in <J> m (r s , r r ). As the source term of the emission diffusion equation is modified after each iteration [Eq. (22)], changes in the emission fluence are greater than that of the excitation fluence. The same consequence can be inferred from the integral equation [Eq. (36)]. Moreover, the phase of the emission fluence is greater than that of the excitation fluence and the normalized fluence, mAI>x, maintains a high phase contrast. Owing to noise and the ill condition of the Jacobian matrix and for inverting the systems of equations, updating can be accomplished using Newton's method  with Marquardt-Levenburg parameters A:
(37) Using excitation referencing at a single reference point, Lee and SevickMuraca  reconstructed an 8 X 4 X 8 cm3 phantom containing a 1 X 1 X 1 cm3 target with 100-fold greater ICG concentration, by using 8 excitation sources, twenty four detection fibers for collecting excitation light, and two reference detection fibers (one on either side of the reflectance and transillumination measurements) for collecting excitation light. Figure 28a is the original map containing two-dimensional slices of the three-dimentional geometry that demark the heterogeneity placement, while Fig. 28b is the three-dimensional reconstructed image. The results in Fig. 28 represent reconstructions based on emission FDPM measurements relative to excitation FDPM measurements at a fixed reference position: Ntziachristos and Weissleder  successfully reconstructed two fluorescent targets in a 2.5-cm diameter, 2.5-cm-long cylindrical vessel containing ICG and Cy5.5, and using CW emission measurements referenced to excitation measurements at each of the 36 detector fibers as a result of point excitation at 24 source fibers. The high density of measurements for reconstruction of the small simulated tissue volume is troublesome for validity of the diffusion equation used in the forward solver, but is similar to that demonstrated by Yang and coworkers  who reconstructed ICG and DTTCI in similarly sized phantoms and mice, presumably from absolute FDPM measurements at the emission wavelength alone. It is noteworthy that the studies of the reconstruction presented above assumed that the absorption and scattering properties were known a priori. However, using differential approaches coupled with Bayesian reconstruction approaches (see below), Eppstein and coworkers  demonstrated the insensitivity of reconstructions to changes in endogenous optical properties. Using a synthetic 256-cm3 volume containing 0.125-cm3 targets with 10:1 contrast in absorption owing to fluorophore and surrounded on four
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FIGURE 28 The reconstruction of piaxf using the excitation wave as a reference using the integral approach and Marquardt-Levenburg reconstruction. The image was required after 27 iterations with regularization parameters for AC ratio (ACR), AAC = 1.0, and for relative phase shift (RPS), A,, = 0.02 (a) optical property maps of true juaxf distribution (b) and reconstructed /uaxf distribution. Peak values of /uaxf reached 0.1205 cm 1 (c) Iteration vs. SSE.
sides with 68 sources and 408 detection fibers, Eppstein showed that when the absorption cross-section at the excitation wavelength, /zaxi, varied as much as 90% and was unmodeled while the scattering coefficient, ;ttsxl, varied 10% or less and was also unmodeled, the impact on the reconstruction was minimal or negligible. Similar results have recently been shown by Roy and Sevick-Muraca [ 109] who show unmodeled variations in all endogenous optical properties by as much as 50%, which did not impact reconstructions when emission FDPM measurements were individually self-referenced to excitation FDPM measurements, as was done with the CW measurements of Ntziachristos and Weissleder . While it appears promising that fluorescence-enhanced optical tomography can be accomplished without much a priori information regarding the endogenous optical properties, these results are nonetheless on synthetic studies and need to be conducted on actual tissues of substantive and clinically relevant volumes for validation. 5.3
Differential Formulation of the Inverse Problem
A second approach of the full inverse imaging problem may be the differential formulation, but in reality, this time it is rewritten for measurement Z(r d > r s ), whether absolute, or relative to a reference measurement at the emission or excitation wavelength, or self-referenced relative to the excitation wavelength at each detector position, rd. We term this approach the differential formulation because a small change in the predicted measurements is directly expressed in terms of a small change in the optical properties, AX, using a Jacobian matrix, J, d(AZj)/3Xj. Considering the number of detectors to be M; then the error function is defined as the sum of square of errors between the measured and calculated values at detector i = 1..M:
F(X) = We refer to each f; as a residual and the gradients of the error function with respect to the property, X: VF(X) = 2JTf(X) |-
V2F(X) = 2 JTJ + 2 L
fi(X)V 2 f,(X)
Consider the Taylor's expansion of function F around a small perturbation of optical properties, AX: F(X + AX) = F(X) + VF(X)-AX + - AX r - V 2 F(X)- A(X)
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which can be expressed as: F(X + AX) = F(X) + 2JTf(X) • AX JTJ +
+ 2 • AX
f,(X)V 2 f,(X) ' AX
and the function to be minimized, <J>(AX), can be explicitly written: 4>(AX) = F(X + AX) - F(X) = 2JTf(X) • AX + 2- AX T J T J +
For first order Newton's methods, the term 2-AXT[E!l1 f i (X)V 2 f i (X)j • AX is neglected and the Gauss-Newton Method becomes one of minimizing, VO(AX) => 0 = JTJ • AX + J T f(X)
JTJ AX = -J T f(X)
The Levenberg-Marquardt method of optimization becomes [JTJ + A I ] - A X = -J T f(X)
The gradient based truncated Newton's method is based on retaining the second-order terms such that Eq. (43) becomes : VO>(AX) => 0 = J T f(X) +
JTJ + L
fi(X)V 2 f,(X) • AX i= l
or, alternatively, VO(AX) => 0 = VF(X) + V2F(X) • AX
Typically, the first order Newton's methods are employed with the exception of the work by Roy . In Newton's methods, it is assumed that A = J • AX and the solution is found using one of the several optimization approaches. The Jacobian can be computed either directly from the stiffness matrices of the finite element formulation or, simply but more computationally time consuming, from backward, forward, or central differencing approaches that compute the differences in the values of Z(r d , r s ) with small differences in the parameter to be updated, X(r s ). The Gauss-Newton and the Levenberg-Marquardt algorithms performed poorly in a large residual problem. Since the inverse is highly nonlinear and ill conditioned due to the error in measurement data, the residual at the solution will be large. It seems reasonable, therefore, to consider the truncated Newton method.
For the truncated Newton's method, the additional computational cost of computing the Hessian [associated with V2F(X)] is assisted by reverse automatic differentiation [89,110]. Using synthetic data, Roy has shown the feasibility for using the technique for three-dimensional reconstruction of lifetime, T, and absorption coefficient ^iaxf changes in frustrum and slab geometries from synthetic data containing noise that mimics experimental data .
Regularization and Other Approaches for Parameter Updating
In both the integral and differential formulations of the inverse problem, the tissue to be imaged must be mathematically discretized into a series of nodes or volume elements (voxels) in order to solve these inverse problems. The unknowns of the inverse problems then comprise the optical properties at each node or voxel. The final image resolution is naturally related to the density nodes or voxels. However, the dimensionality of the imaging problem is directly related to the number of nodes and can easily exceed 10,000 unknowns for a three-dimensional image. In a problem of this scale, the calculation of Jacobian matrices and matrix inversions involved in updating the optical property map are computationally intensive and contribute to the long computing times required to reconstruct the image. The instability arises because the measurement noise in the data or errors associated with the validity of the diffusion approximation can result in large errors in the reconstructed image. One of the greatest challenges associated with fluorescence-enhanced tomography is the propagation of error. In comparison with absorption imaging based on measurements of excitation light, fluorescence measurements have a reduced signal level and SNR. Lee and Sevick-Muraca  measured the SNR for single-pixel excitation and emission frequency domain measurements at 100 MHz to be 55 and 35 dB, respectively. In addition to the reduced signal, the noise floor of emission measurements can be expected to be elevated when excitation light leakage constitutes an increased proportion of the detected signal. Consequently, for emission tomography measurements, excitation light leakage is crucial and interference filters that attenuate excitation light four orders of magnitude (i.e., filters of optical density 4) may be clearly insufficient. Excitation light leakage will be a significant problem when emission measurements are conducted in tissue regions in which the target is absent and fluorescent contrast agents are not activated. Unfortunately, this type of error is not present in synthetic studies and is undoubtedly underestimated in the vast proportion of tomographic investigations to date.
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Regularization is a mathematical tool used to stabilize the solution of the inverse problem and to make it more tolerant to measurement error. Regularization approaches will play an important role in the development of suitable algorithms for actual clinical screening. For example, when discretized the differential and integral general formulations result in a set of linear Newton's equations generally denoted by AY = Z, where Y are the unknown optical properties and Z are the measurements. This system is commonly solved in the least-squares sense where the object function Q = ||AY — Z||2 + A Y 2 is minimized, where A is called the regular!zation parameter. Minimization of this function results in Y = (A1 A + AI) 'ATZ. The regularization parameter is generally chosen either arbitrarily or by a Levenberg-Marquardt algorithm so that the object function is minimized . Thus, the choice of regularization parameter is through a priori information and adds another degree of freedom to the inverse problem solution. While this section is not meant to be a mathematical treatise of inverse algorithm and regularization approaches, we nonetheless point out that in a recent work by Pogue and coworkers , a physically based rationale for empirically choosing a spatially varying regularization parameter is presented to improve image reconstruction. Bayesian Regularization. Eppstein and coworkers [87,88,91,108] use actual measurement error statistics to govern the choice of varying regularization parameters in their Kalman filter implementation to optical tomography. In their work, they developed novel Bayesian reconstruction technique, called APPRIZE (Automatic Progressive Parameter-Reducing Inverse Zonation and Estimation), specifically for groundwater problems and adapted them to fluorescence-enhanced optical tomography [104-106]. Unique components of the APPRIZE method are an approximate extended Kalman filter (AEKF), which employs measurement error and parameter uncertainty to regularize the inversion and compensate for spatial variability in SNR, and a unique approach to stabilize and accelerate convergence called data-driven zonation (DDZ). Using the notation [AX, f(X)] as described in Sec. 5.3, here the Newton's solution is formulated as : AX = [[JT(Q + R) 'J + P;X'] ' • JT(Q + R ) - ' l - f ( X )
where Q is the system noise covariance which describes the inherent model mismatch between the forward model (the diffusion equation) and the actual physics of the problem; R is the covariance of the measurement error that is actually acquired in the measurement set; and Pxx is the recursively updated error covariance of the parameters, X, being estimated from the measurement error, f(X). The use of this spatially and dynamically variant co-
variance matrix results in the minimization of the variance of the estimated parameters taking into account the measurement and system error. The novel Bayesian minimal variance reconstruction algorithm compensates for the spatial variability in signal to noise ratio that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging. Figure 29 illustrates the image reconstruction of 256-cm3 tissue-mimicking phantoms containing none (case 3), one (case 1), or two (case 2)
FIGURE 29 Image reconstruction with APPRIZE, a) The initial homogeneous estimate discretized onto the 9 x 1 7 x 1 7 grid used for the initial inversion iteration, and shown with the true locations of the 3 heterogeneities and the 50 detectors (small dots), b) Case 1: The reconstructed absorption due to the middle fluorescing heterogeneity, interpolated onto the 17 x 33 x 33 grid used for prediction, and shown with the locations of the 4 sources used (open circles), c) Case 2: The reconstructed absorption due to the top and bottom fluorescing heterogeneities shown with the locations of the 8 sources used (open circles), d) Case 3: The reconstructed absorption of a homogeneous phantom shown with the locations of the 4 sources used (open circles). Although the phantoms and reconstructions were actually 8 cm in the vertical dimension, only the center 4 vertical cm is shown here. (From Ref. 91.)
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1-cm3 heterogeneities with 50- to 100-fold greater concentration of ICG dye over background levels. The spatial parameter estimate of absorption owing to the dye was reconstructed from only 160 to 296 surface reference measurements of emission light at 830 nm (as described in Sec. 5.2.2) in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emission wavelengths is shown to be highly variable. Another important feature of the Bayesian APPRIZE algorithm is the use of DZZ. With DDZ, spatially adjacent voxels with similarly updated estimates are identified through cluster analysis and merged into larger stochastic parameter "zones" via random field union . Thus, as the iterative process proceeds, the number of unknown parameters, X, decreases dramatically, and the size, shape, value, and covariance of the different "parameter zones" are simultaneously determined in a data-driven fashion. Other approaches to reduce the dimensionality of the problems involve concurrent NIR optical imaging with MRI [10,114,115] and ultrasonography  to compartmentalize tissue volumes and to reduce the number of parameters to be recovered in the optical image reconstruction. 5.4.2
Simply Bounded Constrained Optimization
Imposing restrictions on the ill-posed problem can transform it to a wellposed problem as discussed above. Regularization is one method to reduce the ill posedness of the problem . In the optical tomography problem, its solution, i.e., the optical properties of tissue, must satisfy certain constraints, and imposing these conditions in itself can regularize or stabilize the problem. Imposing these constraints explicitly restricts the solution sets and can restore uniqueness. Provencher and Vogel  have suggested two techniques: (1) prior
FIGURE 30 Three-dimensional reconstruction from simply bound truncated Newton's method. Actual distribution of fluorophore absorption coefficient of background tissue variability of endogenous (50%) and exogenous (500%) properties, (b) Reconstructed fluorophore absorption coefficient of background tissue variability of endogenous (50%) and exogenous (500%) properties using relative measurement of the emission fluence with respect to the excitation fluence at the same detector point, s = 0.0001. (c) Reconstructed fluorophore absorption coefficient of background tissue variability of endogenous (50%) and exogenous (500%) properties using relative measurement of the emission fluence with respect to the excitation fluence at the same detector point. (From Ref. 109.)
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knowledge and (2) parsimony for well posedness of the problem. The first condition requires that all prior physical knowledge about the solution be included in the model. The second condition protects against the introduction of nonphysical phenomena. Tikhonov and Arsenin  also suggested that, to obtain a unique and stable solution from the data, supplementary information should be used so that the inverse problem becomes well posed. The basic principle of using a priori knowledge of the properties of the inverse problem is to restrict the space of possible solutions so that the data uniquely determine a stable solution. In his work, Roy showed that the constrained optimization technique, which places simple bounds on a physical parameter to be estimated, may be more appropriate for solving the fluorescence-enhanced optical tomography problem . Specifically, a range of fluorescent optical properties is physically defined for the problem and the recovered parameter, X, must always be positive. Specifically, he demonstrated use of the bounding parameter, £, not only as a means to regularize and accelerate convergence but as a means to set the level of optical property contrast that is to be reconstructed using referenced emission measurements . Here the possible values of parameter estimates are stated to lie between upper and lower bounds. In the first pass of the iterative solution, the optical property map is recovered and parameter estimates that lie within the upper and lower bounds plus and minus a small bounding parameter, s, are recovered and held constant for the next iteration. In this manner, the number of unknowns decrease with iteration. Indeed, the value of the bounding parameter can be used to set the resolution and the performance of the tomographic image. For example, if the bounding parameter is large, then the tomographic image will "filter" out artifacts not associated with the target, whereas if the bounding parameter is small, then the tomographic image may sensitively capture artifacts and heterogeneity that is not necessarily associated with the target. Figure 30 illustrates the reconstruction using the simply bounded truncated Newton's method, which shows that as the bounding parameter is increased, the recovered image becomes less sensitive to the background "noise." 6.
SUMMARY: THE CHALLENGES FOR NIR FLUORESCENCE-ENHANCED IMAGING AND TOMOGRAPHY
In the earlier sections, an overview of the status of fluorescence-enhanced optical imaging was presented. The opportunity to develop an emissionbased tomographic imaging modality similar to that provided by nuclear imaging but without the use of radionucleotides is offered by NIR fluorescent agents. Yet the added challenge for NIR fluorescence-enhanced im-
aging over nuclear imaging is that, unlike nuclear techniques, an activating or excitation signal must first be delivered to the contrast agent before there is registration of the emission signal from the tissue. Preliminary data from animals (Table 1) and phantoms (not presented herein) suggest that penetration depth and sensitivity may very well be comparable to those of nuclear techniques. A side-by-side comparison of NIR fluorescence-enhanced imaging with nuclear imaging is needed before the comparative performance can be ascertained. Another opportunity for optical imaging is the potential for tomographic reconstruction and additional diagnostic information based on the fluorescence decay kinetics of smartly designed probes. Tomography of large tissue-simulating volume has been demonstrated from experimental data as well as synthetic data as reviewed herein (Table 2), albeit with the somewhat inconvenient point source and point detector geometries. The single point source and detector geometry is a throw-back to NIR optical tomography from endogenous contrast studies and may not be the appropriate geometry for fluorescence-enhanced optical imaging, especially when transillumination through large tissues is required. Nonetheless, the tomographic algorithms as reviewed in Sec. 5, are already established for these systems. The challenge for the future is to develop tomographic algorithms for illumination and detection that are clinically feasible and adaptable for hybrid, nuclear imaging. Although the area of NIR fluorescence-enhanced optical imaging is less than a decade old, the developments are apt to continue for the coming decade, hopefully resulting in an adjuvant tomographic imaging modality for nuclear imaging. ACKNOWLEDGMENTS The review is supported in part by the National Institutes of Health grants R01 CA67176 and R01CA88082 (P. I. Eppstein, University of Vermont) and the Texas Advanced Technology Research Program. REFERENCES 1.
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R Roy, EM Sevick-Muraca. A numerical study of gradient-based nonlinear optimization methods for contrast-enhanced optical tomography. Opt Exp 9(l):49-65, 2001. 95. V Ntziachristos, R Weissleder. Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation. Opt Lett 26(12):893-895, 2001. 96. J Lee, EM Sevick-Muraca. 3-D fluorescence enhanced optical tomography using references frequency-domain photon migration measurements at emission and excitation measurements. J Opt Soc Am A 19:759-771, 2002. 97. EM Sevick-Muraca, DY Paithankar. Fluorescence imaging system and measurement. U.S. patent #5.865,754, issued 2/2/99. 98. JM Schmitt, A Knuttel, JR Knutson. Interference of diffusive light waves. J Opt Soc Amer A 9:1832-1843, 1992. 99. DY Paithankar, A Chen, EM Sevick-Muraca. Fluorescence yield and lifetime imaging in tissues and other scattering media. Proc Soc Photo-Opt lustrum Eng 2679:162-175. 1996. 100. B Pogue, T McBride, J Prewitt. U Osterberg, K Paulsen. Spatially varying regulari/ation improves diffuse optical tomography. Appl Opt 38:2950-2961. 1999. 101. MJ Holboke, AG Yodh. Parallel three-dimensional diffuse optical tomography. Biomedical Topical Meetings, OS A, Miami Beach, FL, 2000, pp 177-179. 102. M Xu, M Lax, RR Alfano. Time-resolved fourier diffuse optical tomography. Biomedical Topical Meetings, OSA, Miami Beach, FL, 2000, pp 345-347. 103. SR Arridge, JC Hebden. M Schweiger, FEW Schmidt, ME Fry, EMC Hillman, H Dehghani, DT Delpy. A method for three-dimensional time-resolved optical tomography. Int J Imaging Sys Technol 11:2-11, 2000. 104. MJ Eppstein, DE Dougherty. Optimal 3-D traveltime tomography. Geophysics 63:1053-1061. 1998. 105. MJ Eppstein, DE Dougherty. Efficient three-dimensional data inversion: soil characterization and moisture monitoring from cross-well ground penetrating radar at a Vermont test site. Wat Resources Res 34:1889-1900. 1998. 106. MJ Eppstein. DE Dougherty. Three-dimensional stochastic tomography with upscaling. U.S. patent application 09/110,506, (9 July 1998). 107. TJ Yorkey, JG Webster, WJ Tompkins. Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans Biomed Eng BME-34, 843— 852, 1987. 108. MJ Eppstein, DE Dougherty, DJ Hawrysz, EM Sevick-Muraca. Three-dimensional Bayesian optical image reconstruction with domain decomposition. IEEE Trans Med Imaging 20(3): 147-163, 2000. R Roy. A Godavarty, EM Sevick-Muraca. Fluorescence-enhanced, optical tomography using referenced measurements of heterogeneous media. IEEE Trans Med Imaging (in press). R Roy. EM Sevick-Muraca. Truncated Newton's optimization scheme for absorption and fluorescence optical tomography: part I theory and formulation. Opt Exp 4:353-371, 1999. J Lee. EM Sevick-Muraca. Fluorescence-enhanced absorption imaging using
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15 Fluorescence in Photodynamic Therapy Dosimetry Brian C. Wilson Ontario Cancer Institute, University of Toronto, and Photonics Research Ontario, Toronto, Ontario, Canada Robert A. Weersink Photonics Research Ontario, Toronto, Ontario, Canada Lothar Lilge University of Toronto and Photonics Research Ontario, Toronto, Ontario, Canada
Photodynamic therapy (PDT) is a technique for treating a variety of malignant and nonmalignant conditions based on the use of light-activated drugs (photosensitizers). Typically, the photosensitizer is administered either systemically (intravenously or orally) or topically to the tissue to be treated. After allowing time for uptake of the photosensitizer to the target tissues or tissue structures, light of an appropriate wavelength to activate the drug is applied. This results in the photoproduction of one or more cytotoxic agents, leading to the intended cellular and tissue effects. For most photosensitizers used or under investigation clinically, it is likely that the main photophysical pathway is production of singlet oxygen, 'O2. Singlet oxygen is an excited form of oxygen that is highly reactive with biomolecules, leading typically 529
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to oxidative damage. The Jablonski energy diagram for this so-called type II process is shown in Fig. 1. The absorption of a photon by the groundstate photosensitizer activates the molecule to the excited singlet state. This short-lived state (typically nanoseconds) may de-excite to the ground state either nonradiatively or by fluorescence emission, or may undergo a change of spin to the triplet state. This is relatively long lived, since decay to the ground state is a quantum mechanically forbidden transition. Energy exchange with ground-state oxygen is, however, an allowed transition, since 3 O2 is also a triplet state, and this excites the oxygen to 'O2. (Note that type I processes are those in which the reactive species are generated directly from the photosensitizer-excited singlet or triplet state and may or may not be oxygen dependent. They also lead to photosensitizer fluorescence from the singlet state.) Most of the current photosensitizers have some fluorescence emission. (The in vivo measurement of nonfluorescent drugs is discussed briefly later.) For the PDT efficiency to be as high as possible, a high triplet state quantum yield is desirable, which competes with the fluorescence quantum yield. However, using the fluorescence emission to monitor the photosensitizer does not require a high yield (e.g., a few percent), so that in practice a high triplet-state yield can be selected. Figure 2 shows the absorption and fluorescence emission spectra of some common PDT drugs. Note that the fluorescence excitation spectrum is generally very similar to the absorption spectrum, but that these may both change in biological media compared to the spectra in simple solutions, due to substrate (e.g., protein) binding. Shifts in the absorption peaks by several nanometers are common.
BIOLOGICAL »-"-• ^
FIGURE 1 Jablonski diagram for type II photodynamic reactions. The vertical axis indicates the energy for the distinct electronic states of the photosensitizer and oxygen molecules.
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FIGURE 2 (a) Absorption and fluorescence emission spectra of some common PDT photosensitizers. (b) Corresponding excitation-emission matrices.
Most PDT photosensitizers have spectra across the visible range, often with a strong Soret band in the UV-A/blue region. In order to obtain maximal light penetration in tissue for treating larger lesions (such as solid tumors), many newer PDT drugs have strong absorption bands in the far-red (650700 nm) and near-infrared (700-850 nm), and correspondingly their fluorescence is also at these long wavelengths. Figure 3 summarizes the classes of disease for which PDT is being investigated as a possible therapeutic method. Several of these treatments have regulatory approvals and are entering routine clinical practice. The potential applications are wide, reflecting the facts that (1) PDT can be applied to many body sites through the use of fiberoptic light delivery, as summarized schematically in Fig. 4, and (2) with different photosensitizers the mechanisms of action are varied, and include direct cell kill (by necrosis
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and/or apoptosis), vascular destruction, and immune stimulation or suppression. The photosensitizer fluorescence may be utilized in a number of ways, including: 1. 2. 3.
Lesion detection in vivo Lesion localization in vivo for therapy guidance, both PDT and surgical Quantification of the concentration of the photosensitizer in the target and other tissues in vivo for the purposes of a. Determining the drug pharmacokinetics in order to select the optimum time for light activation, or
Photodynamic Therapy Dosimetry In Vivo
treatment light • solid tumors • dyslasias • papillomas • rheumatoid arthritis • age-related macular degeneration • cosmesis • psoriasis • endometrial ablation • localized infection • prophylaxis of arterial restenosis
• extracorporeal photophoresis • blood purging: HIV, hepatitis B, protozoa • bone marrow purging photosensitizer
Potential clinical applications of PDT.
Individualizing the light delivery to produce the required biological response ("dosimetry") Measurement of the photosensitizer photobleaching during PDT light activation, in order to estimate the effective PDT "dose" delivered Photosensitizer quantification in tissue samples (e.g., biopsies) ex vivo Determining the microdistribution of photosensitizer in tissues (ex vivo) or cells (in vitro) by fluorescence microscopy
Tissue autofluorescence may be used in addition or as an alternative to photosensitizer fluorescence for purposes 1, 2, and 4, or as a monitor of tissue response to treatment. Fluorescence imaging of other "contrast agents" may be of value for PDT in particular sites, such as the use of fluorescein angiography in PDT of age-related macular degeneration, a dis-
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Whole Surface Intracavitory
FIGURE 4 Light irradiation methods for PDT, showing the wide variety of target geometries.
ease that leads to blindness due to growth of abnormal blood vessels in the choroid layer of the eye near the macula, which is the area of central acute vision. In this case, as illustrated in Fig. 5, fluorescein angiography is used both before treatment to show the area of choroidal neovasculature so as to target the treatment light and after treatment to evaluate the area and completeness of vascular closure. In this chapter, the emphasis will be on topics 2-6, since lesion detection and localization for treatment guidance are dealt with elsewhere, in the general context of fluorescence "contrast agents." It is worth noting, however, that many of the in vivo fluorescence-based methods and instruments that have been developed over the past 20 years have been strongly
Photodynamic Therapy Dosimetry
FIGURE 5 Fluorescein angiograms before and after PDT for age-related macular degeneration, showing closure of the area of abnormal neovasculature.
associated with the corresponding development of PDT as a treatment modality, since they provide complementary "search and destroy" capabilities. Thus, for example, autofluorescence bronchoscopy (Chapter 11) grew from the original endoscopic spectroscopy and imaging work with the photosensitizer hematoporphyrin derivative (HPD) and was originally aimed at localizing tumors in the lung for PDT treatment. (Interestingly, HPD itself was developed from hematoporphyrin in an attempt to improve its fluorescence properties and was only subsequently discovered to be an effective PDT drug.) Studies were performed with successively decreasing doses of HPD in order to reduce the associated skin photosensitization, and in the case of early bronchial cancer/dysplasia it was found that the detection accuracy was greatest with zero dose, i.e., using only the autofluorescence. However, fluorescence of HPD continues for the other objectives listed above, and many developments in fluorescence spectroscopy and imaging in vivo continue to be tightly linked to improving and monitoring PDT treatments, although they are also developing independently. In addition to PDT applications exploiting the photosensitizer fluorescence, fluorescence-based optical fiber probes are being developed for light fluence monitoring in tissue. In these, a small point-like volume of specific fluorophore is incorporated into an optical fiber and placed on or within the tissue. The PDT treatment light then excites the fluorescence, a fixed fraction of which is transmitted along the fiber and detected. Probes incorporating several different fluorophores at different positions along the fiber allow
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multipoint measurements to be made simultaneously by spectral deconvolution. The concept can also be extended to tissue oxygen measurements using phosphorescence lifetime measurements. This technology and its applications will be discussed at the end of the chapter. 2. 2.1
PHOTOSENSITIZER QUANTIFICATION IN VIVO Relative Measurements
Figure 6 shows a simplified schematic diagram of noninvasive measurement of photosensitzer fluorescence in vivo. The excitation light from a light source (laser, or filtered lamp or light-emitting diode) at wavelength Aex is delivered to the tissue surface by an optical fiber (or fiber bundle). Then one or more collection fibers pick up some fraction of the light remitted through the tissue surface; this comprises elastically scattered light (diffuse reflectance), photosensitizer fluorescence (at wavelength A cm ), tissue autofluorescence, and inelastic (Raman) scattered light. Typically, the order of magnitude of total photons remitted for each of these components, relative to the incident light, is around 10 ', 10~ 4 , 10 \ and 10 7, respectively, a small fraction of which is collected by the detector fibers. The elastic scattering is removed by optical filtering, typically, placing a long-pass filter (>Aex) between the output end of the collection fibers and the photodetector. The Raman signal is usually negligible, whereas the photosensitizer fluorescence is observed superimposed on the tissue autofluorescence background. Figure 7 shows such fluorescence spectra, for different administered doses of a specific agent, in this case the prodrug aminolevulinic acid (ALA), m
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Photodynamic Therapy Dosimetry
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FIGURE 7 In vivo fluorescence spectra in Barrett's and normal human esophagus, at different times post ALA administration and for different ALA doses. Individual spectra represent measurements at different points on the tissue and are normalized to the autofluorescence background at 500 nm. (See color insert.)
which induces increased biosynthesis of heme, the penultimate step of which is the fluorescent photosenisitizer protoporphyrin IX (PpIX). These data illustrate a number of points. First, the fluorescence intensity is highly variable from patient to patient and even point to point in the same patient for a given drug level and time point. This type of variability has been reported for other photosensitizers and is, of course, a major reason why quantitative measurements are required. Second, the drug fluorescence spectrum is known and can be easily identified on the autofluorescence background, at least for higher levels of drug; however, at low levels, the added drug spectrum may not be easily seen, especially if the autofluorescence itself is highly variable (which is certainly the case for diseased tissue, and indeed is the basis of autofluorescence-based diagnostics). Third, the increase in the PpIX fluorescence with ALA dose and the dependence on time after administration can be observed, at least in the average spectra of each tissue type. In order to obtain a quantitative estimate of the PpIX concentration, a fit may be made to the autofluorescence background: in the simplest case, by a linear interpolation between points just outside the main PpIX fluores-
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cence peak, as illustrated in Fig. 8a, or by a polynomial fit, taking the (local) shape of the background into account (Fig. 8b). The residual photosensitizer signal, PSF*, is then proportional to the (average) tissue concentration, C ps . If all factors other than C—namely, the excitation light, excitation and detection geometry, fluorescence quantum yield, and tissue optical absorption and scattering coefficients at Aex and A ox —remain constant, then the FSF* values yield the relative drug concentrations. The assumption of these factors remaining constant usually holds best in following the photosensitizer pharmacokinetics in a given location in an individual patient. Even in this idealized case, however, complications arise. For example, photosensitizer aggregation/disaggregation depends in many cases on the local microenvironment (pH, polarity, etc.) and this alters the fluorescence yield. The yield can also change when the photosensitizer binds
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solution to that in an optically turbid medium. PLS is one of a number of multivariant statistical techniques that are used widely in spectroscopic analysis, and here is considered as a "black box" calibration technique. It requires simulated or measured training data sets (here, fluorescence spectra) for a range of known C values. This set must encompass the range of possible variations in the spectra and expected photosensitizer concentrations. These two methods were compared in phantoms, where the prediction error was —5% for PLS and — 1 8 % for the KM model. To achieve this low prediction error in PLS, the input data set consisted of the combination of fluorescence spectra collected at two excitation wavelengths. The limitation of PLS is that building of an adequate training set requires an extensive set of measurements that encompasses all possible C values across the range of tissue types. This must be repeated for each photosensitizer. Furthermore, a wide spectral measurement range must be used to provide an adequate spectral "signature" in the tissues. Applying it to layered tissues or inhomoge-
Photodynamic Therapy Dosimetry
neous drug distributions may also present problems. Finally, although it can be very accurate, it provides no physical insight, so that it is difficult to assess what would be the effect of altering any of the measurement conditions. 2.4
To avoid the need for tissue-dependent calibration, assumptions can be made about the fluorescence escape function and excitation fluence distribution, based on a priori knowledge of the tissue optical properties. One approach is to collapse the escape function into 1-D by employing a broad-beam excitation with point collection and assume a single exponential dependence on depth. Another simplification is to assume that the optical properties at Aex and Aem are the same. Thus, Potter and Mang  postulated that the fluorescence signal was proportional to C*§2, where 8 is the penetration depth of light in the tissue at Aex = 630 nm. Separate measurements of 8 using diffuse reflectance were required using a second optical fiber probe. This was tested in vivo in an animal model with Photofrin. However, correcting the fluorescence signal by 82 still resulted in errors in the prediction of C. Profio et al.  used similar approximations but derived a relationship between the ratio of the fluorescence signal and the quantity (1 — y)/(l + y), where y is the diffuse reflectance. At Acx = 633 nm in tissue-simulating phantoms containing Photofrin, the prediction error for C was —20%, for a range of background absorption coefficients tissue/Ji
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