Nerve, Brain and Memory Models, Volume 2 (Progress in Brain Research)

PROGRESS IN BRAIN RESEARCH

ADVISORY BOARD W. Bargmann

E. De Robertis J. C. Eccles J. D. French

H. Hyden J. Ariens Kappers S. A. Sarkisov

Kiel Buenos Aires Canberra Los Angeles

Goteborg Amsterdam Moscow

J. P. SchadC

Amsterdam

T. Tokizane

Tokyo

H. Waelsch

New York

N. Wiener J. Z. Young

Cambridge (U.S.A.) London

PROGRESS IN BRAIN RESEARCH VOLUME 2

NERVE, B R A I N AND MEMORY MODELS EDITED BY

N. W I E N E R Massachusetts Instifute of Technology, Cambridge, Mass. (U.S.A.) AND

J. P. S C H A D B Central Institufe for Brain Research, Amsterdam (The Ne fherlanak)

ELSEVIER P U B L I S H I N G C O M P A N Y AMSTERDAM

/

LONDON

1963

/

N E W YORK

S OL E D I S T R I B U T O R S F O R T H E U N I T E D S T A T E S A N D C A N A D A AMERICAN ELSEVIER PUBLISHING COMPANY, INC.

52

VANDERBILT AVENUE, N E W YORK

17,

N.Y.

S OL E D I S T R I B U T O R S F O R G R E A T B R I T A I N E L S E VI E R P U B L I S H I N G C O M P A N Y L I M I T E D 12B, R I P P L E S I D E COMMERCIAL ESTATE R I P P L E R OAD, B A R K I N G , ESSEX

This volume contains a series of’lectures delivered during a symposium on CYBERNETICS OF THE N E R V O U S SYSTEM

which was held as part of the Second International Meeting of Medical Cybernetics at the Royal Academy of Sciences at Amsterdam f r o m 16-18 April, 1962 The organization of the Symposium was partly supported by grants from The Netherlands Government Philips (Eindhoven, The Netherlands) I. B. M . (Amsterdam, The Netherlands) Electrologica (The Hague, The Netherlands)

L I B R A R Y OF CONGRESS CATALOG C A R D NUMBER

WITH

96

ILLUSTRATIONS A N D

63-17304

1 TABLE

A L L RIGHTS RESERVED T H I S B OOK O R A N Y P A R T T H E R E O F MAY N O T BE R E P R O D U C E D I N A N Y F O RM, I N C L U D I N G P H O T O S T A T I C O R M I C R O F I L M FORM, W I T H O U T WRITTEN PERMISSION FROM THE PUBLISHERS

List of Contributors

W. R. ASHBY,University of Illinois, Urbana, Ill. (U.S.A.). V. BRAITENBERG, Centro di Cibernetica del Consiglio Naziouale delle Ricerche, Istituto di Fisica Teorica, Universita di Napoli (Italy). J. CLARK,Burden Neurological Institute, Bristol (Great Britain).

J. D. COWAN,Massachusetts Institute of Technology, Cambridge (U.S.A.). Institut fur Nachrichtenverarbeitung und Nachrichtenubertragung der H. FRANK, Technischen Hochschule Karlsruhe, Karlsruhe (Deutschland). F. H. GEORGE, Department of Psychology, University of Bristol, Bristol (Great Britain).

E. HUANT,9 Avcnue Niel, Paris (France). P. L. LATOUR,Institute for Perception Physiology, Soesterberg (The Netherlands). P. MULLER,Institut fur Nachrichtenverarbeitung und Nachrichtenubertragung der Technischen Hochschule Karlsruhe, Karlsruhe (Deutschland). A. V. NAPALKOV, Moscow State University, Moscow (U.S.S.R.).

P. NAYRAC,Clinique Neurologique et Psychiatrique de I’Universitt de Lille, Lille (France). A. NIGRO,Via Garibaldi, Messina (Italy). G. PASK,System Research Ltd., Richmond, Surrey (Great Britain). N. RASHEVSKY, Committee on Mathematical Biology, University of Chicago, Chicago, Ill. (U.S.A.). J. L. SAUVAN, 43, Boulevard Albert-ler, Antibes (France).

J. P. S C H A DCentral ~, Institute for Brain Research, Amsterdam (The Netherlands). N. STANOULOV, U1.k. Peitchinovitch, Sofia (Bulgaria). M. TEN HOOPEN,Institute of Medical Physics TNO, National Health Research Council, Utrecht (The Netherlands). A. A. VERVEEN, Central Institute for Brain Research, Amsterdam (The Netherlands). H. VON FOERSTER, University of Illinois, Urbana, 111. (U.S.A.). C. C. WALKER,University of Illinois, Urbana, Ill. (U.S.A.). 0. D. WELLS,Artorga Research Group, Beaulieu, Hants (Great Britain).

N. WIENER,Massachusetts Institute of Technology, Cambridge, Mass. (U.S.A.).

J. ZEMAN,Philosophical Institute, Czechoslovak Academy of Sciences, Prague (Czechoslovakia). G. W. ZOPF,JR., University of Illinois, Urbana, Ill. (U.S.A.).

1

Introduction to Neurocybernetics N . WIENER

AND

J. P. S C H A D E

Massachusetts Institute of Technology, Cambridge, Mass. (U.S.A.) and Netherlands Central Institute for Brain Research, Amsterdam (The Netherlands)

Cybernetics is the study of communication and control in machines and living organisms. Biocybernetics is that part of cybernetics in which living organisms are emphasized. In biocybernetics there are two fields which we must distinguish between, even though this distinction can not be made perfectly sharp. These fields are: neurocybernetics and medical cybernetics. The former is concerned with the pathways of action via sense-organs, neurons and effectors because of the fact that cybernetics is primarily concerned with the construction of theories and models. The symbols and hardware in neurocybernetics resemble more closely the elements of the nervous system and the sense-organs. Medical cybernetics is where homeostasis or the maintenance of the internal constant environment is the main consideration. There is no sharp distinction between these two fields, because changes in the level of equilibrium of our internal factors are unquestionably associated with changes in our external reactions. For example, our external reactions are dependent on chemical messengers such as the hormones, which belong to our internal environment. Even the more precise transfer of messages which takes place by nervous transmission has important chemical and even possibly hormonal factors. The propagation of an action potential along the course of a nerve is an electrochemical process, and the transmission of a message across a synapse is probably the same process but much more complicated. In both cases, changes in the general chemistry will effect the communication of nerves and we can not make an absolute sharp separation between these two fields of biocybernetics. However, one cannot take a complicated subject like biocybernetics and hope to treat it as a whole. It must be broken up into parts. In other words, analysis necessarily has an element of falsification. It is impossible to make any great progress without the division of biocybernetics into neurocybernetics, and what we have called medical Cybernetics. Our tool for the study of a complicated system is the measurement of certain quantities associated with the system and the study of their mathematical relations. The older views of physics thought that it was possible to give a complete account of all the quantitative relations in a total system. The modern view is that some of these relations can not be completely described and can only be given in a statistical form, which tells us not what always happens but, withn a certain precision, what usually happens. It is immaterial which of these two views is taken in the study of biocybernetics

2

N. W I E N E R A N D J. P.

SCHADB

because a complete account of all the quantities is far beyond our powers. The complexity of the brain is enormous, and all that we can measure is a minor part of what happens. The rest must be estimated on a statistical basis or not at all. Thus the mathematics of the nervous system and of cybernetics must be statistical. Not only should it be statistical but it must be essentially non-linear. In a linear system, when we add inputs we add outputs. When we multiply an input by a constant, we multiply an output with that constant. Linear systems seem to be very common. In the swing of a pendulum we have a system which we can consider linear for small angles. Since strictly linear systems are almost non-existent, it is instructive to consider nearly linear systems. Now the distinction between the nearly linear system and the truly linear system is vital. In a strictly linear system, no two modes of oscillation can interact in any degree and a general balance between the modes of oscillation is impossible. In a nearly linear system there can be a transfer of energy from one mode to another. There are certain states of the system where very slow changes will produce an equilibrium. This is closely connected with the theory of adiabatic invariance of Ehrenfest. A clock is an interesting highly non-linear system. We often think of the grandfather clock only in terms of the pendulum, but it also includes the weights, the train of gears moving and the pointers. Here we have a direct current input and a direct current load; the pendulum is the machine that regulates the time. There must be a flow of energy between the input and the output, but a flow of energy between a part of zero frequency and the hands of the pendulum involves non-linearity. Nonlinearity of this general type occurs in cybernetic phenomena, and we must be very careful not to suppose that because a system is nearly linear it is linear truly. In the nervous system with thresholds, limitations of amplitude and one-direction conduction, we have all the forms of non-linearity which you find in electrical systems with amplitude limiters, rectifiers and switches. The mathematics for the nervous system and for cybernetics must be a non-linear statistical theory. Memory involves the storage of information, conditioning involves long time effects. These, like the sort of adiabatic invariance which Ehrenfest considers, involve long time intervals and are highly non-linear. If we attempt to make an electrical apparatus in which memory and conditioning play a role, we do not attempt to make all the memories and conditionings of one type. We have a large repertory of methods, some for short term memories and some for long term memories but are not confined to any one way of doing this task. This multiplicity of methods is probably the reason why we have found it so difficult to make any real headway as to the mechanism of the actual memory and conditioning of the nervous system. Caianiello (1960) at Napleihas presented a theory of the nerve net which is both statistical and non-linear. There is no question that a great amount of work is being done in these directions, and it seems that this will be one of the most fruitful techniques of cybernetics in the near future. Cybernetics is not only the study of control and communication in man and machine, but also between man and machine. There has been a certain attitude against this relation, to be found particularly in some engineering circles which

INTRODUCTION

3

involves the comparison of human performance with machine performance, to the disadvantage of humans. In a comparative study of human performance and machine performance, it must be realized that the human being does some things much better than the machine and some things worse. The human system is not as precise nor as quick as a computing machine. On the other hand, the computing machine tends to go to pieces unless all details of its programming are strictly determined. The human being has a great capacity for achieving results while working with imperfect programming. We can do a tremendous amount with vague ideas, but to most existing machines vague ideas are of absolutely no use. Precision and speed are valued by some engineers much more than the sum of all human qualities. This preference of machine over man displays a fundamental contempt for man and dislike for human values. However, the relation between the machine and man should not be conceived in terms of competition. The proper relation between man and machine is not that of competition, but in the development of systems utilizing both human and mechanical abilities. An important future machine is the learning machine which can modify its programming by its own success or failure. Such machines already exist, for the playing of checkers for example, and can exist for many other purposes. These machines modify their programming by virtue of their success, and in order to engineer this one must know what success means. In a machine for playing a game, success means winning the game according to certain rules. Although the other player is part of the conditioning system, the judgement of success is very objective. If, however, you want to make a translating machine, success consists in the actual intelligibility of the translation to a reader. In the success determination of the translation machine a human element must be utilized. It is conceivable to give a purely mathematical account of this, but it won’t be easy. The nervous system is unbelievably complex, particularly if we examine a great mass such as the cerebral cortex. There are various ways of analysing the fine structure of the nervous system, ways which are largely incompatible with one another in detail and yet must be put together to give a complete picture. If we are to see the individual neuron in clarity, one of the best ways is the Golgi staining process. But this method stains only a few neurons out of the total mass, and still the question is whether the selection is at random or not. It gives us, however, a good opportunity to study the organization of the dendritic plexus. The classical Nissl methods stain cell bodies of neurons and glial cells but do not reveal anything but very short pieces of dendrites and axons. The electron microscopist cuts the sections so thin that he has only small scraps of neurons and pieces of processes so that the relationships in which he is interested are lost. Staining techniques such as the silver methods can be employed in much thicker sections, the disadvantage being that a bewildering mass of closely interwoven fibre is presented which makes analysis of the connections impossible. A number of these difficulties can be overcome by using combinations of histological methods such as the Nissl and the Golgi technique, the electron microscopic and Golgi technique. In general we are left with the extraordinary difficult task of putting together pieces

4

N. W I E N E R A N D J. P. S C H A D B

of evidence obtained in various ways. This explains partly why our knowledge of the relationship between neural structure and function is rather obscure. Neurophysiology can analyse only by partial destroying. If a micro-electrode is put in the nervous system we may get locally detailed results, but we have also produced a small trauma. The inability to study the nervous system without producing a trauma is analogous to the inability in quantum theory to study a physical phenomenon without producing a disturbance in the phenomenon. This observation is not an innocent and detached act. In discussing neurophysiology and neuroanatomy an essential point comes into focus : the difference between long myelinated fibres and the short unmyelinated axons. The long fibres tend to conduct an impulse in an all-or-none way as a series of spikes. The spike if it occurs has a constant shape. On the other hand, a spike may fall out or not appear at all at the end of the fibre in the teledendron. This is taken by many to be the normal mode of behaviour in the nervous system, including the short fibres as well. Here the complicated effects of one neuron with its neighbouring neurons are left out, but the old classical view of the spike is taken. In order that this chain of reactions assumes a permanent form a certain headway, both in time and in distance, is needed. Is it possible that enough headway exists in the short fibres? Moreover, the short fibres are not uniform in cross-section and the velocity is subject to changes. Frankly, there is much doubt whether the all-or-none principle applies at all to the very short fibres of the cortex. I have said that the neurophysiologist and neuroanatomist must produce trauma and destruction in order to see. However, their particular type of destruction is one which is relevant to their problems. There are other types of analysis which are necessary for the cyberneticist: analysis of behaviour. In this there is also destruction, as a matter of fact it is quite literally destruction. Animals can be wrecked completely by their conditioning. There is also the intellectual destruction of the treatment of the conditioned reflex as a whole in itself, without the consideration of the entire animal’s past. Here is a falsification necessary for analysis in another form. It can’t be said which way is right or wrong. The methods of behaviourists, neuroanatomists and physiologists must be united in order to approximate the large scale of cybernetic views. These many modes of analysis make the training for the cyberneticist very complicated. He needs the talent of a neurophysiologist, neuroanatomist, mathematician, physicist, behaviourist and sensory psychologist. One thing of importance is that you can not hope to get people of these different disciplines to produce cybernetic work merely because they are brought together. They must understand language, methods and thoughts of the others. This volume contains the proceedings of the Symposium on Cybernetics of the Nervous System held at the Royal Dutch Academy of Sciences in April 1962. We have tried to organize a multidisciplinary symposium around three main subjects : nerve, brain and memory models. The multidisciplinary character was emphasized by inviting neurologists, psychiatrists, biologists, engineers, mathematicians and physicists to cover some of the many intriguing problems and theories in this field of

INTRODUCTION

5

bionics. Although not every aspect of bionics is covered, we were very fortunate to have such an outstanding group of scientists together. Ten Hoopen and Verveen describe experiments on isolated nodes of Ranvier. A comparison with studies on models was made to elucidate the phenomenon on fluctuation in excitability. This is the property of a neural element to respond to a non-random input with a certain probability. This phenomenon was considered to result from a form of biological noise. The results from animal experiments and model studies showed a very close resemblance. In both it was found that the relation between probability of response and stimulus intensity approximates the Gaussian distribution function. In his paper on the engineering approach to the problem of biological integration, Cowan from McCulloch’s laboratory at the Massachusetts Institute of Technology, discusses the necessity of using many-valued logics and/or information theory where noisy units and noisy connections are given. He demonstrates that redundant computers exhibiting arbitrarily low frequencies of error could be constructed so that they are not completely redundant but process a finite fraction of information. A very interesting result was that such a computer need not be precisely connected and that a certain bounded fraction of errors in connection might be tolerated. These results may lead to an interesting application to the construction of mathematical models of cortical structure. The sequential behavior of a set of idealized neurons is the subject of Latour’s paper. He investigated nerve nets with mathematical methods similar to those in the theory of linear sequential networks. By assuming that this approach could also be valid to describe cortical events he explains in a simple way the periodicities found in reaction time experiments. George’s paper is a wonderful example of a lucid account on the comparison of finite automata and the nervous system. His lecture is primarily concerned with the logical net type representing a sort of idealized or conceptual nervous system. He describes the extent to which these automata can be made to fit the facts discovered by neurophysiologists and neuroanatomists. Also a number of general suggestions is made to try to bring the conceptual nervous system more into line with the existing empirical facts. A different approach was employed by Nigro who gives a scheme of the cerebIal cortex mainly based on the data of Bykov’s school. He gives a theoretical interpretation of the mechanism of conditioned reflexes whose action is made possible by evoking a pattern that is already well established in the brain structures. Napalkov represented the cybernetic group of the Moscow State University. In his paper he describes an analysis of some complex forms of brain activity on the basis of a study of the information processes. Besides his theoretical studies he also deals with the cybernetic explanation of pathologic phenomena such as hypertension. An interesting feature of neurocybernetics is that work is being done at so many different levels. This is particularly true of Zeman who, in his paper, is mainly concerned with linking together the symbols in the contents of a language, informational machine language translations and the process of registration, elaboration and

6

N. W I E N E R A N D J. P.

SCHADB

transmission of information in the brain. This whole process of what he calls ‘brain writing’ is, as he assumes, closely connected with the creation of ‘brain fields’, where temporary phenomena are transformed into symbols, similarly as in the pictures of visible speech or in Chladni’s sound images. He assumes then that every brain field is connected with a certain excitation energy and a certain informational content which manifests itself as a specific semantic spectrum. A mathematical model is drawn up to connect the results of brain physiology with mathematics and linguistics. Steinbuchs active group at the Institut fur Nachrichtenverarbeitung und Nachrichteniibertragung at the University of Karlsruhe was represented by Frank and Miiller. Information psychology and telecommunication were tied together by Frank using conceptual and perceptual models. His ideas are nicely illustrated by the learning matrix for pattern recognition processes. A description is given of a device which works invariantly to translation, affined transformation and skewness. Muller is particularly discussing the characteristics and patterns of learning matrices. A learning phase and a knowing phase can be distinguished in the learning matrix. These two phases operate consecutively; when the learning phase is completed, the knowing phase starts during which the previously learned characteristics of the particular pattern presented to the matrix are indicated by a maximum detection device. The construction and some applications are discussed showing its simple use in many respects. The following two papers are concerned with the input relations and homeostasis of sense-organs. Zopf discusses more from the physiological and anatomical point of view the cybernetic significance of: (a) the innervation of the accessory motor apparatus of the sensory systems, and (b) the efferent fibres ending on or near the receptor cells. The first class may play a role in attenuating or normalizing the intensity dimension of the stimulus which of course is an interesting hypothesis. The second class, the actual existence has always bothered the neuroanatomists, was discussed in a relation to stimulus configurations. The utility of this efferent sensory control lies mainly in the direction of exploiting stimulus constraints (input redundancy). Huant approaches the problem of sensory information more from the psychiatric point of view and draws a close correlation between the interaction of sensory information with information already obtained in the brain on the one hand and the a-rhythms of the electroencephalogram on the other hand. It seems likely from many other investigations that this relationship is not at all very clear. The elucidation of a few of the many intriguing problems existing in the basic mechanism of memory and thinking should be one of the main goals of neurocybernetics. The papers of Sauvan and Stanoulov are concerned with the construction of models explaining some of the parameters of human memory and thinking. The research of Braitenberg combines classical neurohistology with the logic of nerve nets. He proposes a method for the functional analysis of the structures of grey substances in the brain. The approach is comparative, using techniques such as the Golgi staining method and a quantitative assessment of myelin. His method has already proved to be useful in an analysis of the cerebellar cortex. He was able to

INTRODUCTION

7

describe the structure of the molecular layer of the cerebellum into a functional scheme representing a clock that will translate distance into time intervals and vice versa. Cybernetic models of learning and cognition in evolutionary systems and brains are extensively discussed by Pask. In his review he gives a beautiful survey of the models and the conception of learning. His model illuminates among many other properties the role of ‘distributed’ or ‘non-localised’ functions and it possesses an interesting asymmetry which seems to account for some of the peculiar discontinuities in behavior associated with ‘attention’ and ‘insight’. The following five papers cover some of the neurologic and psychiatric implications of cybernetic models. Nayrac gives a survey of his ideas on the problems of non-linearity in clinical and experimental neurology. Adapted machines and their possible use in psychiatry are discussed by Clark. He suggests the use of an adapted machine in the form of a game taught to the patients by a Pask teaching machine as a possible source of objective diagnostic measurements in psychiatric patients. The paper of Ross Ashby and coworker is concerned with the relevance of the essential instability of systems that use threshold. Rashevsky’s lecture bridges mathematical biology, homeostasis and kinetics of the endocrine system and some psychiatric aspects. Wells does not believe in the dominant role played by the nervous system in many respects. The thesis of his paper is that the nervous system develops late in evolution and that the central nervous system was not essential until rapid organism-initiated movement led to refinement of ‘distance receptors’. One of his main points is that most of the essential organisation to be studied was developed prior even to the autonomic system, way down in the evolutionary scale. He puts forward an interesting hypothesis that ‘this organisation involves a mapping of the set of chromcjsomes onto the total organismand the mapping of the set of surviving organisms into the set of chromosomes’.

8

Nerve-Model Experiments on Fluctuation in Excitability M. T E N H O O P E N

AND

A. A. VERVEEN

Institute of Medical Physics T N O , National Health Research Council, Utrecht and Central Institute for Brain Research, Amsterdam (The Netherlands)

INTRODUCTION

A nerve fibre stimulated with identical electrical rectangular pulses of about-threshold intensity responds with an action potential in a fraction of all trials. This phenomenon, the fluctuation in excitability, viz. the property that in the threshold region the fibre responds to a non-random, fixed, input with a certain probability, reveals the existence of a noise factor in excitation. This is an endogenous property of the fibre, as can be concluded from the mutual independency in reacting of fibres in a two-fibre preparation upon application of the same stimulus (Pecher, 1939). It was shown (Verveen, 1960, 1961) that upon low frequency stimulation (once per 2 sec) with identical stimuli : (1) the successive reactions have each time the same probability of occurrence, independent of the preceding reactions; (2) the relation between the probability of response and stimulus intensity approximates the Gaussian distribution function ; (3) both parameters of this function, the threshold (the mean) and the spread (the standard deviation) are dependent on the stimulus duration : the (50 %) stimulation threshold is related to the stimulus duration according to the strength-duration characteristic; the coefficient of variation, the quotient of spread and threshold, called the relative spread (RS), proves to be independent of the stimulus parameters and about equal for short (0.25 msec) and long (2.5 msec) pulses; (4) the fluctuation in excitability is also present during the recovery period, during a sub-rheobasic current and after the application of strychnine and urethane; only the parameters of the probability-intensity relation undergo a change; (5) the RS, the measure of the width of the threshold range relative to the value of the threshold, is related to the fibre diameter: the smaller the fibre, the larger the RS (Verveen, 1962). MODEL E X P E R I M E N T S

One of the possible sources of threshold fluctuation (cf. Frishkopf and Rosenblith, 1958) might be given by local statistical variations of the membrane potential due to

F L U C T U A T I O N IN E X C I T A B I L I T Y

9

thermal agitation noise (Pecher, 1939; Fatt and Katz, 1952). In this case the RS might be a measure of the effective membrane noise potential relative to the threshold membrane potential (Verveen, 1962). As long as we are not able to study the proper biological noise directly, in the above mentioned case for instance as slight disturbances of the resting membrane potential (Brock et al., 1952), additional information may be obtained in an indirect way, assuming that a voltage noise is responsible for the phenomenon. To this end mode1 experiments were carried out with a twofold intention. First to gain an understanding of the influence of noise on a triggerable device. Second to develop methods allowing a more effective study of the processes occurring in the nerve fibre. Work is also in progress on a mathematical model. The central problem is related to the axis-crossing problem, a topic well-known in the field of information and detection theory. For the case in question the difficulty arises in the form of a timedependent function. In earlier studies on the theoretical interpretation of threshold measurements in the presence of noise of excitable tissue only the amplitude distribution (mostly assumed as Gaussian) of the random function and not the rate of change (the frequency spectrum) of the variable seems to have been at stake (Rashevsky, 1948; Hagiwara, 1954). Recently Viernstein and Grossman (1960) paid attention to the necessity to involve this aspect of the process in computations. For reasons of simplicity we desired to start with a simple analogue device, general impression at this stage of the study being more valuable than numerical solutions on complex models. More intricate problems, for instance in connection with the local potential andits fluctuation (Del Castillo and Stark, 1952) are not yet considered either. This communication is, therefore, not a presentation of a rounded off investigation. We are just gaining some understanding of the behaviour of a triggerable device in the presence of noise. Harmon's electronic neuron model (Harmon, 1959) provided the triggerable device. The stimulus, delivered by a Tektronix pulse generator, was fed into it via a network transforming the stimulus in the same way as it apparently occurs in an arbitrary functionally isolated single frog node of Ranvier (A-fibre, situated in intact sciatic frog nerve), one of the neural elements investigated in the previously mentioned experiments. This transformation is deduced from the time course of excitability after applying a non-effective constant stimulus of long duration and from the strengthduration relation. The excitability cycle after the application of a constant stimulus at t = 0 is of the form: f(r)

= exp

(- r / t l )

- exp

(- r / n ) with

TI

> "2.

For a rectangular stimulus of finite duration T, starting at t forming function can be written as: f(t)forO f ( t )- f ( t References p. ZOjZl

< t < T,

- T )for

t > T.

= 0,

this stimulus-trans-

10

M. T E N H O O P E N A N D A. A. V E R V E E N

The resulting excitability cycle and strength-duration relation of this model are comparable to those of the frog node studied in the situations mentioned above. The rest of the model consists essentially of a monostable multivibrator. As soon as the voltage at the input reaches a critical value a pulse is given off. On the internal threshold of the device noise of a verifiable quality is superimposed. The noise is initiated in the model via a suitable network and a band-pass filter (Krohn-Hite; max. 20-20,000 c/s; slope 24 db/octave) by a white noise generator (Peekel; 20-20,000 c/s). In the experiments reported hereafter band-limited white noise of an adjustable intensity and frequency spectrum was used. No recovery period was involved in these experiments, though another version of the model with a supra- and a second subnormal phase in the relative refractory period is ready for further investigation. Intentionally the duration of the recovery period was made much shorter in the model than it is in the fibre, thereby allowing to test the model with higher frequencies (intervals between the stimuli 160 msec). The lengthy recovery period of the nerve fibre requires a stimulation frequency not higher than once per 2 sec. Otherwise cumulative effects will complicate the interpretation of the experimental results. RESULTS

The first series of observations on the model were limited to noise with a frequency spectrum of 20-1000 cjs. It followed that the behaviour of the model, on the whole, is about equal to that of the nerve fibre: (I) the existence of a threshold region (Fig. 1); (2) the relation between probability of response and stimulus intensity, with given stimulus duration, can be approximated by a Gaussian distribution function ; (3) both parameters, the threshold and the spread, depend on stimulus duration (Fig. 2). As Nerve fibre

I

......

I I

I

II

I I

I

I

I

I

I I

I

Model

.. .... .

.......

98

L

LL

L

L

l h

J

L

100 102 stimulus intensify

Fig. 1. The relation between probability of response and stimulus intensity, in percentage of the threshold. Stimulus given every 2 sec.

11

FLUCTUATION IN EXCITABILITY

mentioned earlier for the nerve fibre the RS is the same for short and long pulses. For the model this is the case under certain conditions of the noise characteristics only. This property will be discussed later; ( 4 ) the relation between probability of response and stimulus duration - for intensities which are different but fixed each Nerve fibre

Model

10G

i!

5c

C

12.0

lo(

126

13.0

13.5

14.0

145

-v

€52

-E2 5( a,

c, c a, Q

1

29,O

Slimulus duration

.'

25msec 0.25msec

29.5

30.0

Stimulus duration

30.5

31.0

31.5

-v

32.0

'o o'20msec lOmsec

Fig. 2. The relation between probability of response and stimulus intensity for two stimulus durations (A, B) and the same relations after standardization of the threshold (C).

time -has the same properties (Fig. 3): the curves are asymmetrical to the right and steeper at higher intensities. At rheobasic stimulus intensities a percentage of 100 is never reached. It appeared, therefore, that the agreement between the model experiments and our physiological experiments is satisfactory. The question, however, is whether the model can be used as a tool allowing a more effective study of the processes occurring in the nerve fibre. Together with the fluctuation in excitability a variation is seen in the time interval References p . 20121

12

M. TEN H O O P E N A N D A. A. V E R V E E N

between the initiation of the stimulus and the passage of the eventual action potential in the part of the nerve fibre below the recording electrodes. This fluctuation in response time occurs at the point of stimulation as a variation in latency. It is indeA

B

Nerve fibre

Model 193 144 111

101

0

msec

05

10

15

20

25 30 m sec

Fig. 3. Duration-probability curves. Stimulus intensity in percentage of the rheobase.

pendent of the site of the recording electrodes on the nerve fibre (Blair and Erlanger, 1933) and probably due to the different instances of time at which the process of Nerve fibre

70-

Model

A1

60-

50. 4 0.

30.

,’;I:

40

4

lC2

, k 1 6

10

O O

rn sec

Fig. 4. Latency-distributionhistograms. Stimulus intensity in percentage of rheobase: A1 : 110.0; B1: 100.3; C1: 99.7; A2: 103.0; B2: 100.8; C2: 99.8. Numbers beside histograms indicate the percentages of response. Stimulus durations in all cases 10 msec. For the nerve fibre the latency includes the time of conduction over a length of 12 cm (frog A-fibre).

FLUCTUATION I N EXCITABILITY

13

excitation, initiated by the stimulus, triggers the nerve, because of its fluctuating excitability (Erlanger and Gasser, 1937). The same phenomenon is present in the model. An orientating investigation of the latency distributions in the model upon stimulation with a pulse of long duration (10 msec) revealed the following characteristics (Fig. 4). At higher stimulus intensities the mean latency between stimulus and response is shorter and the dispersion is smaller. The histograms are asymmetrical to the right, in particular at low intensities of the stimulus. Investigation of a frog nerve fibre (also with 10 msec duration pulses) showed that the characteristics predicted by the model are present (Fig. 4). It will be noted that these latency distributions bear a close resemblance to the interval distributions studied by Buller et al. (1953) and by Hagiwara (1954) for the muscle spindle, by Grossman and Viernstein (196 1) for slowly adapting, spontaneously discharging neurons of the cochlear nucleus and by Amassian et al. (1961) for the spontaneous activity of neurons in the reticular formation of the midbrain. It is probable that this phenomenon allows a closer investigation of the noise

Fig. 5. Probit transformation of a Gaussian distribution function (Finney, 1952). References p . 20121

14

M. TEN H O O P E N A N D A. A. VERVEEN

characteristics. As yet no model studies were made on the relations between different modes of noise and the latency distributions. By way of convenience the probability intensity function was chosen as a means to study the influences exerted by different modes of noise and to compare the behaviour of the model to that of the nerve fibre in this respect. In particular the RS is a surveyable measure. The procedure used is the probit analysis (Finney, 1952). This analysis is applied to each set of data covering the relation between probability of response and stimulus intensity. The method is based on a transformation of the Gaussian distribution function in such a way that the function is made linear. The manner in which percentages are converted into probits is illustrated in Fig. 5.

{

20-2000

:m

[ 1 -[ i

20-500

20-200

m-wo

1 -;---;/ -1

1 26 Probit

hblse spwtrum

__

24 22 20

18

A

16 14 steps

__

7, B

/.

,

,

,

,

,

,i

C

Fig. 6 . Probability-intensity relations after the probit transformation. Stimulus durations: 0.2 mscc (A), 1.0 msec (B) and 10 msec (C). The value of one step is 1 of the threshold stimulus intensity. The band width of the noise frequency spectrum is indicated on the left in cps. Stimulus transforming function: 1 - exp (- t i t ) with t 0.5 msec. Standard noise intensity (for explanation see text). ~

15

FLUCTUATION I N EXCITABILITY

In this transformation the inverse of the standard deviation appears as the slope of the transformed function. Owing to the technique used, viz. plotting the intensity on the abscissa in units of the threshold, the reciprocal of the slope is not an estimate of the standard deviation but of the coefficient of variation, the RS. Each set of data was obtained in the following way. The stimulus intensity is adjusted to such a value that upon stimulation the model reacts with a probability of about 50%. This value is then an estimate of the threshold. Hereafter, the stimulus intensity is varied in steps, each step being equal to a given percentage (1 %) of the

F-71i-i 200-200

{ j.--+-

3 0 2 8 2 6 2 4 2 2 2 0 18 16 steps

14

/ .

9502882624222018

Steps

I

Fig. 7. Probability-intensity relations after the probit transformation. Stimulus durations: 0.2 rnsec (A), 1.0 rnsec (B) and 10 msec (C). The value of one step is 1 % of the threshold stimulus intensity. The band width of the noise frequency spectrum is indicate4 on the left in cps. Stimulus transforming function: 1 -exp (- t i t ) with t = 0.5 msec. Noise intensity 5 db below (Al, B1, C1) and 5 db above (A2, B2, C2) standard intensity.

threshold value. The threshold range is scanned in this way, while a certain number (100) of stimuli is given at each step; the total number of reactions per step is noted and converted into percentages and probits. After this transformation the estimates for threshold and RS were determined graphically. The estimates obtained for the RS were not corrected for the shift in the (50%) stimulation threshold following a change of the noise level or the frequency spectrum. This omission does not alter the estimates of the RS significantly (less than 10%). The results of the measurements concerning the intensity-probability relations for different noise intensities and noise frequency spectra are presented in Figs. 6, 7 and 8. Figs. 9 and 11 give a graphical summary of the estimates of the RS, while Fig. 10 gives an example of the degree of reproducibility of the measurements. Several values References p . ZO/Z/

16

M. TEN H O O P E N A N D A. A. V E R V E E N

Steps

Steps

Fig. 8. Probability-intensity relations after the probit transformation. Stimulus durations : 0.2 msec (A), 1.0 msec (B) and 10 msec (C). The value of one step is 1 ”/, of the threshold stimulus intensity. The band width of the noise frequency spectrum is indicated on the left in cps. Stimulus transforming function: exp (- ?/TI)- exp (- t / t z ) with T I = 6.7 msec and T Z = 0.5 msec. Noise intensity 5 db below (At, B1, C t ) and 5 db above (A3, B3, C3) standard intensity (A2, B2, C2).

of the upper limit of the noise frequency band width were examined. For ease of survey only the results for 20,000,2,000 and 200 cps are reproduced in Figs. 9 and I 1. Three intensities of the noise were used: a so-called standard intensity and two other intensities 5 db above and below the first respectively. The root mean square (r.m.s.) value of the noise amplitude relative to the internal threshold is about 0.005 in the case of the standard intensity and for a frequency-band of 20-2,000 cps. The r.m.s. values for the other intensities and for the same frequency band are then 77