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A study of macroelectrode signals in the cat's optic tract Aube, Paul 1970

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A STUDY OF MACROELECTRODE SIGNALS IN THE CAT'S OPTIC TRACT by PAUL AUBE' B.A.Sc, Laval U n i v e r s i t y , 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard Research Supervisor Members of the Committee Head of the Department (Acting) Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA October, 1970 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e at t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Depar tment o f The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date ABSTRACT The s i g n a l c o l l e c t e d by a macroelectrode inserted i n the cat's o p t i c t r a c t i s made up of a slow component and f a s t v a r i a t i o n s (spike d i s -charge) . The mean amplitude of the peaks of the fa s t v a r i a t i o n s appears to be corr e l a t e d with the slow component. The spike discharge i s studied by an amplitude dis c r i m i n a t o r ; the e f f e c t of f i l t e r i n g and overlapping are discussed, and i t i s seen that the mean counting value (weighted mean) obtained from the amplitude discriminator i s a representation of the number of f i r i n g s occurring i n the neighbourhood of the macroelectrode. The curves obtained f o r the weighted mean show a high degree of. s i m i l a r i t y with the slow component. The r e l a t i o n s h i p between the slow com-ponent and the weighted mean i s calculated i n the form of a tr a n s f e r function. This t r a n s f e r function appears to be the same f o r a wide range of stimulus conditions. These findings suggest that d e n d r i t i c a c t i v i t y has l i t t l e to do with generation of op t i c t r a c t p o t e n t i a l s . I t also i n d i c a t e s that the nerve f i r i n g must be associated i n the op t i c t r a c t with a prompt p o s i t i v e over-shoot allowing b u i l d i n g up of p o s i t i v e macropotentials. ( i i ) TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS i v ACKNOWLEDGEMENT v I. INTRODUCTION 1 I I . ELECTRICAL ACTIVITY IN NERVE CELLS 2 I I I . THE ORIGIN OF THE SLOW WAVE 3 IV. DESCRIPTION OF EXPERIMENTS 5 V. SLOW WAVE AND SPIKE DISCHARGE 7: VI. INFORMATION GIVEN BY THE AMPLITUDE DISCRIMINATOR • 11 (a) Superposition of the A c t i v i t y of Many Nerve Fibres 11 (b) E f f e c t of F i l t e r i n g 13 (c) E f f e c t of Overlaps 13 VII. WEIGHTED MEAN 17 VIII. RELATIONSHIP BETWEEN THE SLOW WAVE AND THE WEIGHTED MEAN 22 IX. CONCLUSIONS 28 APPENDIX A. DESCRIPTION OF THE AMPLITUDE DISCRIMINATOR 29 APPENDIX B. LIST OF EXPERIMENTS.. 30 APPENDIX C. CHARACTERISTICS OF THE AMPLIFIER 31 REFERENCES 34 ( i i i ) LIST OF ILLUSTRATIONS Figure Page 1 Action P o t e n t i a l and Post-synaptic P o t e n t i a l s . . . 2 2 Schematics of Mammalian V i s u a l System 5 3 Signal Recorded from OT (cat #007) 8 4 Spike Discharge from OT (cat #007) , 8 5 Output of Amplitude Discriminator 9 6 Amplitude D i s t r i b u t i o n Curves Obtained with the Ampli-tude Discriminator 10 7 Spike Discharge from OT (cat #C35) 11 8 Spike Discharge from OT (cat #C35) 14 9 Spike Discharge from OT with a Reduction i n the Amp-l i f i e r Bandwidth (cat //C35) 14 10 Possi b l e Cases of Overlaps • 16 11 Slow Wave and Weighted Mean (cats #003 and #007) 19 12 Slow Wave and Weighted Mean (cat #007) 20 13 Slow Wave and Weighted Mean (cats #013, #009 and #003).. 21 14 Transfer Function Relating the Slow Wave to the Weighted Mean (cat #013) 25 15 Transfer Function Relating the Slow Wave to the Weighted Mean (cats #007 and #003) 26 16 Transfer Function Relating the Slow Wave to the Weighted Mean (cats #A3 and #009) . .' 27 A . l Operation of the Amplitude Discriminator 29 A.2 E f f e c t of the Lower Cut-off Frequency of the Amplifier.. 33 (iv) ACKNOWLEDGEMENT I am thankful to those who contributed to this t h e s i s . Dr. J. S. MacDonald supervised t h i s work. Professor F. K. Bowers read the th e s i s . Dr. K. Uenoyama gave encouragement and help. Miss Veronica Komczynski typed the manuscript. Mr. Rick Corman provided t e c h n i c a l assistance. Mr. Herb Black did the photographic work. Fellow graduate students proofread the thes i s . The National Research Council provided f i n a n c i a l support. (v) 1 1. INTRODUCTION Much of the knowledge we have about the nervous system has been gained through electrophysiology. In t h i s , the contribution of microelectrode studies has been enormous. However, microelectrodes give information at most on a few f i b r e s . Compared to the thousands of nerve f i b r e s encountered i n any area of the c e n t r a l nervous system, t h i s i s a r e l a t i v e l y poor sampling s i z e . The goal of t h i s work was to get information on nerve f i r i n g s by means of macroelectrodes (0.5 mm i n diameter). I t was thought that the macroelectrode, because of i t s larger s i z e , would give a b e t t e r p i c t u r e of the a c t i v i t y of a population of nerve f i b r e s . The experiments were confined to the cat's v i s u a l system, mainly to the o p t i c t r a c t . The s i g n a l c o l l e c t e d by the macroelectrode consists of a slow-varying component on top of which ride f a s t v a r i a t i o n s . These f a s t v a r i a t i o n s are b e l i e v e d to be caused by nerve f i r i n g s , the v a r i a b i l i t y of t h e i r amp-l i t u d e s being explained by t h e i r r e l a t i v e distance from the recording e l e c -trode, the s i z e of the nerve f i b r e and the degree of overlapping. An attempt was made to decompose the waveform into sets of pulse t r a i n s of various amplitudes, phases and r e p e t i t i o n rates. Such an i t e r a t i v e technique had been successful i n the case of the locust v e n t r a l cord (13). However, the large number of f i b r e s i n f l u e n c i n g the electrode as w e l l as the high degree of overlapping forced us to abandon t h i s approach. More a t t e n t i o n was given to a deeper understanding of the various processes involved. 2 I I . ELECTRICAL ACTIVITY IN NERVE CELLS Nerve impulse generation and transmission induce various e l e c t -r i c a l p o t e n t i a l s , the most commonly studied being the action p o t e n t i a l and the post-synaptic p o t e n t i a l s . p o t e n t i a l s (usually a negative a f t e r - p o t e n t i a l followed by a longer p o s i t i v e a f t e r - p o t e n t i a l , sometimes followed by a second negative a f t e r - p o t e n t i a l ) . A f t e r - p o t e n t i a l s r e f l e c t changes i n membrane conductance following the spike; the negative and p o s i t i v e a f t e r - p o t e n t i a l s are re s p e c t i v e l y a r e p o l a r i z a t i o n and h y p e r p o l a r i z a t i o n of the membrane. Unlike the spike, they are s e n s i t i v e to metabolic changes (8). by release of a chemical transmitter at the synapse. They can be of two types: e x c i t a t o r y (EPSP) or i n h i b i t o r y (IPSP). with increasing distance from the synapse. The spike and the a f t e r - p o t e n t i a l s on the other hand are axonal and of the all-or-none type. The action p o t e n t i a l i s composed of the spike and the a f t e r -Post-synaptic p o t e n t i a l s (PSP's) are produced i n the dendrites The PSP's are l o c a l graded responses and t h e i r amplitude decreases EPSP Spike 5 w s . — -negative a f t e r - p o t e n t i a l p o s i t i v e a f t e r - p o t e n t i a l Figure 1. Action p o t e n t i a l ( l e f t ) and post-synaptic p o t e n t i a l s . Upwards d i r e c t i o n i s negative. 3 I I I . THE ORIGIN OF THE SLOW WAVE The terms "macropotentials" or "slow p o t e n t i a l s " represent the e l e c t r i c a l a c t i v i t y recorded by macroelectrodes from nervous tissues (see Figure 3). If t h i s a c t i v i t y i s induced by a r e p e t i t i v e stimulus and i s time-locked to i t the terms "evoked p o t e n t i a l s " or "evoked responses" are used. Macropotentials and evoked responses are employed for i n v e s t i g a t i n g c onnectivity between various regions of the nervous system as well as for monitoring c e r t a i n psychophysiological v a r i a b l e s . However the absence of agreement on t h e i r o r i g i n , therefore on t h e i r f u n c t i o n a l meaning has s e r i o u s l y impaired t h e i r e f fectiveness as a research t o o l . Although attempts were made to bypass this d i f f i c u l t y by the use of s t a t i s t i c a l techniques such as mu l t i v a r i a t e procedures (3,4), considerable e f f o r t has been spent i n recent years explaining the o r i g i n of macropotentials. Pharmacological studies l e d many to a t t r i b u t e the o r i g i n of macro-po t e n t i a l s to d e n t r i t i c a c t i v i t y (PSP's); Freeman (7), for instance, came up with a model explaining the various peaks of the evoked response by al t e r n a t i n g sequences of EPSP's and IPSP's. To some extent, there e x i s t s c o v a r i a t i o n between the average slow p o t e n t i a l waveform and the post-stimulus histogram (the p r o b a b i l i t y that a c e l l w i l l f i r e at a given time a f t e r the onset of the stimulus)(3,7). Such c o r r e l a t i o n i s p a r t i c u l a r l y noticeable i n the op t i c t r a c t (5). Verzeano (11), Laufer (9) and Calma (10) observed unit f i r i n g s that kept a constant' time r e l a t i o n s h i p with the slow wave. This appeared to them as an i n d i c a t i o n that a f t e r - p o t e n t i a l s play an important role i n the production of the slow wave; depending on the region of the cortex, the slow wave would be due to after-potentials alone or to the combined influences of PSP's and a f t e r - p o t e n t i a l s : 4 " I f the o s c i l l a t i o n s i n the o p t i c nerve and optic t r a c t were due, simply, to the e l e c t r o t o n i c spread of the r e t i n a l p o s t -synaptic potentials,the amplitude of such o s c i l l a t i o n s should become progressively smaller at increasing distances from the r e t i n a , along the o p t i c nerve and o p t i c t r a c t , according to a rate of decay imposed by the space constant of the axones. The experimental findings show that t h i s i s not the case... This suggests that the o s c i l l a t i o n s i n the optic nerve and o p t i c t r a c t are summations of slow o s c i l l a t o r y axonal a f t e r - p o t e n t i a l s whose amplitude i s independent of the distance from the r e t i n a . Further-more, i f o s c i l l a t i o n s i n the o p t i c nerve and o p t i c t r a c t were due to e l e c t r o t o n i c spread of r e t i n a l postsynaptic p o t e n t i a l s , some o s c i l l a t i o n s i n the o p t i c t r a c t should not be accompanied by axonal a c t i o n p o t e n t i a l s , since synaptic a c t i v i t y does not neces-s a r i l y r e s u l t i n neuronal discharge. The tracings... show that t h i s i s not the case but that, on the contrary, every o s c i l l a t i o n i n the o p t i c t r a c t i s accompanied by axonal spike p o t e n t i a l s and remains i n constant phase r e l a t i o n s with them. This, again, sug-gests that the o s c i l l a t i o n s i n the o p t i c t r a c t develop i n the axones i n r e l a t i o n with axonal post-spike a c t i v i t y . " (Laufer and Verzeano (9), p. 225) 5 IV. DESCRIPTION OF EXPERIMENTS Data recorded over a two-year period by Dr. K. Uenoyama were studied. The methods used are described i n more d e t a i l elsewhere (14). Two macroelectrodes were inse r t e d i n the br a i n of an anaesthetized cat: one i n the o p t i c t r a c t (OT) , the other i n the l a t e r a l geniculate nucleus (LGN). A solder electrode was placed on the v i s u a l cortex. The signals were recorded on an 8-tract PI recorder together with the electroretinogram (ERG). Also recorded on separate channels, was the high-passed version of the macroelectrode s i g n a l (spike discharge). -The stimulus consisted usually of a b r i e f f l a s h once a second; l e s s often i t was of the square wave type. To improve the si g n a l - t o - n o i s e r a t i o , a Fabri-tek average response computer was used to average a preset number of waveforms. Figure 2 shows the p o s i t i o n of the macroelectrodes with respect to the cat's v i s u a l system. c OJ Figure 2, r.c h a g Primary v i s u a l cortex V i s u a l I V i s u a l II V i s u a l I I I l a t e r a l geniculate nucleus Schematics of mammalian v i s u a l system (From Science Journal, May 1967). Arrows superimposed on o r i g i n a l drawing i n d i c a t e p o s i t i o n of electrodes, r . c : rods and cones, h. : h o r i z o n t a l c e l l , b.: b i -polar c e l l s , a. : amacrine c e l l , g. : ganglion c e l l s 6 In the o p t i c t r a c t (OT) , the a c t i v i t y recorded i s mostly from the axones, while the cortex i s usually entangled with multiple d e n d r i t i c l a y e r s . As f o r the l a t e r a l geniculate nucleus (LGN), i t d i f f e r s according to Hubel (2) from most other structures i n the c e n t r a l nervous system by i t s r e l a t i v e s i m p l i c i t y : i t i s a mere one-synapse way s t a t i o n . The o p t i c t r a c t i s made of many bundles of nerve f i b r e s , plus connective and n u t r i t i v e tissues (6). I t s 120,000 nerve f i b r e s are my-e l i n a t e d and of 3 or 4 d i f f e r e n t v e l o c i t y and s i z e groups (12). The macro-electrode i s 0.5 mm i n diameter and i s placed i n the same plane as the course of the f i b r e s . 7 V. SLOW WAVE AND SPIKE DISCHARGE A l i g h t stimulus induces i n the o p t i c t r a c t p o t e n t i a l v a r i a t i o n s which are characterized by a sequence of maxima and minima whose amplitude and latency depend on the type of stimulus. (Latency i s the time delay between the stimulus and the evoked response). The s i g n a l recorded by the macroelectrode consists of a slow component on top of which ride f a s t spike-l i k e v a r i a t i o n s (Figure 3). Usually an averaging process i s used to smooth out the fast v a r i a t i o n s and one studies the r e s u l t i n g slow wave seeking the influence of various parameters on the c h a r a c t e r i s t i c s of the slow wave (amplitude and latency of the peaks). This thesis i s concerned with the f a s t v a r i a t i o n s r i d i n g on top of the slow component. The macroelectrode s i g n a l was passed through a high-pass f i l t e r so that these f a s t v a r i a t i o n s could be studied without the bias of the slow component. The high-passed version of the macroelectrode s i g n a l appears i n fi g u r e 4 and w i l l be ref e r r e d to i n the res t of the thesis as the "spike discharge". Figures 3 and 4 were taken from the same experiment and at the same time scale to permit comparison of the two waveforms. One can see that the two are correlated: maximum amplitude i n the spike discharge corresponds to a p o s i t i v e peak i n the slow component, minimum amplitude i n the spike discharge to a negative peak i n the slow component. Note that according to conventions used i n neurophysiology, p o s i t i v i t y i s downwards i n figure 3. Because i t was r e a d i l y a v a i l a b l e , an amplitude discriminator was used to study the spike discharge. This amplitude discriminator gives a standard pulse (5 v o l t s , 36 ys wide) whenever the amplitude of the spike discharge l i e s between two set values: V and V . This i s i l l u s t r a t e d i n figure 5 F i g u r e 3. S i g n a l r e c o r d e d from OT ( c a t #007, i n t e n s i t y : 10 " u n i t ) . Time s c a l e :20 m s / d i v . P o s i t i v i t y i s downwards and a m p l i f i e r b a n d w i d t h . i s f r o m 5 to 1000 Hz (3 db p o i n t ) . F i g u r e 4. S p i k e d i s c h a r g e from OT ( c a t #007, i n t e n s i t y J l O u n i t ) . scale'20 m s / d i v . A m p l i f i e r bandwidth:500 Hz to 10 KHz. Time 9 spike discharge output from amplitude discriminator Figure 5. Output of amplitude d i s c r i m i n a t o r with l i m i t s set at and and described i n more d e t a i l s i n appendix A. At the same time, the F a b r i -tek computer provided a means of counting over many observations the number of pulses de l i v e r e d by the amplitude discriminator. Figure 6 shows such amplitude d i s t r i b u t i o n s obtained by this technique. Twelve windows were used and the boundary values are given at the extreme r i g h t . The bottom curve i s the corresponding average slow wave with p o s i t i v i t y downward. Here again, one notices that high amplitude peaks of the spike discharge are clustered around p o s i t i v e peaks of the slow wave. -1- w CAT #007 INTENSITY : 7 un/Y 5/2 AVERAGES attenuation 2 2 4 4 8 16 16 16 16 J L J l . window bounda ries (volts) 525- 5.75 4.75-5.25 4.25-4.75 3.75-4.25 3.25-3.75 2.75-3.25 2.25-2.75 1.75-2.25 1.25-1.75 0.75-1.25 * v ^ r * i . 0.25- 0.75 ^ y ^ w W l ^ A . r V W U ^ W ^ S y , Q.OO- Q.25 slow wave too ms. Figure 6. Amplitude d i s t r i b u t i o n curves obtained with the amplitude discriminator, together with the slow wave (bottom curve, where downward d i r e c t i o n i s p o s i t i v e ) VI. INFORMATION GIVEN BY THE AMPLITUDE DISCRIMINATOR The a m p l i t u d e d i s c r i m i n a t o r l o o k s a t the peaks o f t h e spike, d i s -c h a r g e . To i n t e r p r e t c o r r e c t l y the i n f o r m a t i o n g i v e n by the a m p l i t u d e d i s -c r i m i n a t o r , we w i l l c o n s i d e r the. e f f e c t o f s u p e r p o s i t i o n o f t h e a c t i v i t y o f many n e r v e f i b r e s , t h e e f f e c t o f f i l t e r i n g and t h e e f f e c t o f o v e r l a p p i n g o f a d j a c e n t peaks. a) S u p e r p o s i t i o n o f the a c t i v i t y o f many n e r v e f i b r e s The m a c r o e l e c t r o d e i s 500 u i n d i a m e t e r and i t i s e s t i m a t e d t h a t the number o f n e r v e f i b r e s l y i n g c l o s e s t to i t i s between 50 and 100. Added to t h a t i s the c o n t r i b u t i o n o f the a d j a c e n t l a y e r s . The peaks seen i n f i g u r e 7 can t h e n be e x p e c t e d t o r e s u l t from the. s u p e r p o s i t i o n o f many n e r v e f i r i n g s , each one w i t h an a m p l i t u d e i n v e r s e l y p r o p o r t i o n a l to t h e d i s t a n c e o f the f i b r e from t h e m a c r o e l e c t r o d e . F i g u r e 7. S p i k e d i s c h a r g e from OT ( c a t #C35, i n t e n s i t y : 4 u n i t s ) . Time scale :0. 5 ms/div. V e r t i c a l d e f l e c t i o n :5 i;V/div. Bandwidth: 600 Hz - 10 KHz. The binary code appearing i n t h e lower trace i d e n t i f i e s t h e r e c o r d . 12 A big peak can therefore be the r e s u l t of three things: 1. - a small number of f i b r e s close to the electrode and f i r i n g at the same time. Since they are close to the electrode, they w i l l have a r e l a t i v e l y large amplitude. 2. - many f i b r e s f i r i n g at the same time but at some distance from the electrode. Each f i r i n g w i l l be of small amplitude but since there are many of them, they w i l l add to a r e l a t i v e l y large amplitude. 3. - a combination of (1) and (2). Since there i s no reason f o r only those f i b r e s that are at a given distance from the electrode to f i r e , t h i s would be the general case. The macroelectrode was in s e r t e d i n the o p t i c t r a c t i n such a way that i t s surface was p a r a l l e l to the course of the nerve f i b r e s . Moreover, o p t i c t r a c t f i b r e s tend to group according to t h e i r s i z e (12,15): f i b r e s of d i f f e r e n t s i z e s group i n d i f f e r e n t areas of the t r a c t . We can imagine the f i b r e s i n -fluencing the electrode to be d i s t r i b u t e d on layers p a r a l l e l to the surface of the electrode. The f i b r e s of one layer would be of the same s i z e and at the same distance from the electrode, hence they would contribute to the recorded s i g n a l by the same amount. The hundreds of f i b r e s i n f l u e n c i n g the macroelectrode define a very small subgroup of the t o t a l 120,000 f i b r e s of the cat's o p t i c t r a c t . We assume that i n t h i s subgroup and with the stimulus conditions used, there are at one time as many f i b r e s f i r i n g on the f i r s t layer as there are on the second layer, and on the t h i r d and so on. Then a given peak w i l l be made of the same number of b i g spikes, medium spikes and small spikes. High amp-l i t u d e peaks w i l l be the r e s u l t of many f i r i n g s , medium ones of a medium number of f i r i n g s and small ones of few f i r i n g s . 1 J b) E f f e c t of f i l t e r i n g The spike discharge waveforms were often (see appendix C) analyzed with the upper cut-of f frequency of the f i l t e r lowered down to 4 KHz. To examine the e f f e c t of this bandwidth reduction, pictures were taken of the same record i n the period of maximum a c t i v i t y , some at f u l l bandwidth (600 Hz -10 KHz), others at reduced bandwidth (600 Hz-4 KHz). Two of those pictures appear i n figures 8 and 9. A comparison of figures 8 and 9 shows that l i t t l e information about r e l a t i v e peak amplitude i s l o s t by reducing the bandwidth. c) E f f e c t of overlaps As we have seen i n b) and c) the spike discharge i s a r e f l e c t i o n of the e l e c t r i c a l a c t i v i t y of the o p t i c t r a c t axones. I f a l l the f i b r e s were to f i r e synchronously and i f the nerve impulses would t r a v e l at the same speed along the axones, then the nerve f i r i n g s would be superimposed exactly i n time. A peak f i v e times bigger than another one would correspond exactly to f i v e times as many f i r i n g s . This i s not the case however and one has to expect some int e r f e r e n c e between impulses adjacent i n time. A given nerve impulse can occur on the t a i l of another nerve f i r i n g and i t s amplitude w i l l be increased or decreased: increased i f i t occurs on the p o s i t i v e part of the t a i l , decreased i f i t occurs on the negative part. Since the amplitude discriminator looks at the amplitude of the peaks, t h i s e f f e c t i s most important and we w i l l examine i t i n d e t a i l . Consider the various ways i n which two spikes can add together (as i l l u s t r a t e d i n figure 10): 1. They coincide i n time. The peak amplitude of the r e s u l t i n g spike i s then simply the sum of the peak amplitude of the two i n d i v i d u a l spikes 14 Figure 8. S p i k e d i s c h a r g e from OT ( c a t #C35, i n t e n s i t y : 4 u n i t s ) . Time scale:0.5 ms / d i v . V e r t i c a l d e f l e c t i o n : 5 u V / d i v . B a n d w i d t h : 600 Hz - 10 KHz. The b i n a r y code o f t h e l o w e r t r a c e i d e n t i f i e s the r e c o r d . Figure 9. Same r e c o r d as f i g u r e 8 e x c e p t t h a t the bandw i d t h has been reduced t o : 600 Hz - 4 KHz. and the amplitude d i s c r i m i n a t o r w i l l r e g i s t e r i t c o r r e c t l y . 2. They occur close enough i n time that only one peak i s seen, the other one being reduced to a shoulder. Then only one peak w i l l be seen by the amplitude discriminator and i t s amplitude w i l l be less than the actual sum of the two peak amplitudes. 3. They occur f a r enough apart that the peaks are d i s t i n c t , but one i s r i d i n g on top of the p o s i t i v e part of the t a i l of the other. The two peaks are registered by the amplitude discriminator but one with a greater amplitude than i t should have. 4. Two peaks are d i s t i n c t and p o s i t i v e but one i s r i d i n g on the negative t a i l of the other. The two peaks are registered but one with a smaller amplitude than i t should have. 5. Two peaks are d i s t i n c t . One i s r i d i n g on the negative t a i l of the other and i t s amplitude i s not b i g enough f o r i t to cross the zero l i n e . Since the amplitude discriminator considers only the p o s i t i v e part of the spike discharge, the negative peak w i l l not be registered at a l l . Because of th i s overlap, we cannot say that the amplitude of the peaks of the spike discharge i s proportional to the number of f i r i n g s . Most of the time, i n f a c t , i t underestimates the number of f i r i n g s . As a r e s u l t of t h i s , we would not expect an accurately l i n e a r r e l a t i o n s h i p between the slow wave and the amplitude of the spike discharge. Figure 10. Possible cases of overlaps, i ) , i i ) , i i i ) , i v ) and v) correspond to cases 1), 2), 3), 4) and 5) of text. 17 VII. WEIGHTED MEAN We have seen that the amplitude of the spike discharge gives a q u a l i t a t i v e representation of the number of f i r i n g s . The amplitude d i s -criminator could then be used to get an ensemble average of the amplitude of the spike discharge, which i n turn would be a r e f l e c t i o n of the ensemble average of the number of f i r i n g s . The amplitude discriminator was used i n the following manner. The upper and lower boundaries of the window were set to some values. The tape recorder was accelerated ten times and was run for a c e r t a i n number of observations (usually 512). The Fabri-tek computer counted the number of times a pulse was deli v e r e d by the amplitude discriminator i n each of 1024 time i n t e r v a l s . This amplitude d i s t r i b u t i o n was punched on paper tape and output on a pen recorder. The upper and lower boundaries of the window were then moved to a new set of values and the procedure was repeated u n t i l the waveform had been t o t a l l y covered. Usually twelve or t h i r t e e n windows were used to cover the whole waveform. An example of the curves obtained i s shown i n fi g u r e 6. The bottom trace i s the slow wave, the upper ones the curves obtained f o r the corresponding windows. To construct.the curve corresponding to the ensemble average of the amplitude of the spike discharge the amplitude d i s t r i b u t i o n curves were added together a f t e r each had been m u l t i p l i e d by a factor corresponding to the mean value of the boundaries of the corresponding window. For example, for the upper and lower boundaries of the window set at 5.25 and 4.75 v o l t s , the amplitude d i s t r i b u t i o n curve would be m u l t i p l i e d by 5; for the upper and lower boundaries set at 1.75 and 1.25, i t would be m u l t i p l i e d by 1.5. This i s i l l u s t r a t e d by the formula: N. = E A. V (1) l w iw w 18 where i s the ensemble average of the amplitude of the spike discharge. A. i s the value of the amplitude d i s t r i b u t i o n at time i n t e r v a l i 1W and f o r window w. V i s the weight associated with t h i s window w. This i s simply the w number corresponding to the mean of the two boundaries of the window. The N. curve obtained by t h i s formula i s re f e r r e d to as the weighted mean i n the rest of the the s i s . Data from 11 d i f f e r e n t experiments and from 5 d i f f e r e n t cats were analysed using the amplitude discriminator. The PDP-9 computer was used to c a l c u l a t e N. according to equation 1. The obtained curve and the slow I wave were then punched on paper tape. These paper tapes were taken-to the Computing Centre for p l o t t i n g and further processing. Some of these pl o t s are seen i n Figures 11, 12 and 13. The curves appear very s i m i l a r to the slow waves. This i s so over a wide range of stimulus conditions: blue and red s t i m u l i , ON and OFF responses, flashes of 1 and 10 Hertz, low and high i n t e n s i t i e s . To each major peak i n the slow wave corresponds a major peak i n the weighted mean. The r e l a t i v e amplitudes are also preserved. No time s h i f t can be observed for the f a s t - r i s i n g peaks. For the s l o w e r - r i s i n g peaks (as seen i n Figure 12) the weighted mean tends to lag behind the slow wave. This l a g can however be explained by the lower c u t - o f f point (5 Hertz) of the a m p l i f i c a t i o n system (see appendix C). 19 jiR P 1 n Tiff If w Hit Mill nit lifl (P flft f t m iffli Hill mm St i n T -I PI iii! ill! li i !!i i i i " ft liii 1 ; ii III! II! Ill li j jji-j iii! ; i ; Illi we MM: t?bc 4 UIBi i ' 1 ! i i 1 RV JWGI SM j l i ; i l l i I|!i ; | : Nil i ! i I I i i i l l ! I ! • ! 1 Illi 1 i-i 1"! l| i i 1 : 1 !• III i ii illi lillllil 1 ! i IN; l ! i - l ijij Nil II 111 ' ; I: illi •1 1 jii ! i :t | jii| Mi 1 •:i Hi: •II i l r ! i' :l:i i . i - i ! .;-! I-I-JI- Iii' M l ill Iii I i ! : i III; ii III M , . , . 1 M |!![ III!. Mi! j i l f J. 1 pi IF .::) -i 1 il-iy •ill .i i"! I" [" iiiji i I! Hi u i | l i h ill! i i i i 11 1 III II; i • I : • 1 • • 1 ! • 1 .: ! : i : I i 1 !.! '!' I I i - . ill : ::|. i.i:!: i-l li ji- • -f !• •i ,|:| . : j . ill iii T" '•ill i i i : Iii! ii- i !i Hi V I M'' M-|1 !"!•! 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Arrows show time correspondence between the two curves. ( P o s i t i v i t y i s upwards). a : cat //003, red stimulus, i n t e n s i t y : 16 units b : cat #007, white stimulus, i n t e n s i t y : 0.1 unit ho Figure 12. Cat #007: slow wave and weighted mean. Arrows show ° time correspondence, p o s i t i v i t y i s upwards, a, b, c: stimulus i n t e n s i t y at 10~3, 10~2 and 1 u n i t . Figure 13. Slow wave and weighted mean, arrows show time correspondence, p o s i t i v i t y upwards. a,b: cat #013, ON and OFF responses. M c: cat #009, stimulus i n t e n s i t y : 16 units M d: cat #003, blue stimulus, i n t e n s i t y : 16 u n i t s . 22' .VIII. RELATIONSHIP BETOEEN THE SLOW WAVE AND THE WEIGHTED MEAN We have seen i n chapter VI that the amplitude of the spike d i s -charge (or the weighted mean) i s a representation of the number of f i r i n g s occurring i n the neighbourhood of the macroelectrode. The high s i m i l a r i t y between the slow wave and the weighted mean indicates that this representation i s adequate. I t would be then of i n t e r e s t to f i n d the r e l a t i o n s h i p l i n k i n g the slow wave to the weighted mean for two reasons: 1. I f a unique r e l a t i o n s h i p i s found, the slow wave recorded by a macroelectrode could be regarded as a measure of the number of f i r i n g s i n the neighbourhood of the electrode. 2. This r e l a t i o n s h i p i n the form of a t r a n s f e r function would provide information on the frequency spectrum of the i n d i v i d u a l s i g n a l s which make up the macropotentials. A frequency response experiment would have been of great u t i l i t y . Such an approach demands,.however} a s i n u s o i d a l stimulus generator as w e l l as a great deal of experimentation. Rather, i t was decided to f i n d the transfer function r e l a t i n g the two curves, using standard programs of the Computing Centre. According to current procedures (16, 17, 18), the data were scaled to a zero mean and a cosine b e l l window was used. The transforms obtained were i r r e g u l a r even though a d e f i n i t e trend could be seen. To shorten the p l o t t i n g time, the data for frequencies higher than 64 Hertz were averaged over 2, 4, 8 and 16 points. Then two curves were drawn by hand through the points so that the majority of the points would l i e between them. This was done f o r both the slow wave and the weighted mean. 23 Two r a t i o s were taken: (1) the r a t i o of the higher curve (A) of the slow wave spectrogram to the lower curve (D) of the weighted mean spectrogram. (2 ) the r a t i o of the lower curve (B) of the slow wave spectrogram to the higher curve (C) of the weighted mean spectrogram. » « * ^ B "<«. \ Slow wave Weighted mean Slow wave -ml . L*' '\ D Weighted mean The two curves obtained were drawn on a t h i r d graph as the upper and lower l i m i t s of the desired t r a n s f e r function r e l a t i n g the slow wave to the weighted mean. A/D B/C Spectrogram of the Function Transfer As can be seen i n figures 14, 15 and 16, the trans f e r functions obtained from the 5 cats and the 11 experiments are s i m i l a r . They are more so for the same cat. The trans f e r functions reach a peak around 40 Hertz and drop at higher frequencies at a rate close to 6 db per octave. Some curves seem to drop at the lowest frequencies, but t h i s may be due to the a m p l i f i e r low-frequency cut-of f of 5 Hertz. 25 Figure 14. Cat #013, ON and OFF response. Amplitude of the tra n s f e r function r e l a t i n g the slow wave to the weighted mean. The two l i n e s describing each t r a n s f e r function define the e r r o r l i m i t s . The curves were normalized so that the maximum value would be 0 db. -II If- 2 ,4,8 (averaged) FREQUENCY (Hx} •i 1 1 1 1 1 1 1 1 1 1 4- l£ 6 4 256 loat Figure 15. Same as fi g u r e 14, but with cats #007 and #003 ; 27 28 IX. CONCLUSIONS Signals recorded by macroelectrode from the cat's o p t i c t r a c t were studied. I t appears that they can be decomposed into two components: a slow wave and fa s t v a r i a t i o n s (spike discharge). The amplitude of the spike discharge i s c l o s e l y correlated with the slow wave. This holds f o r a great v a r i e t y of stimulus conditions; a preliminary experiment (not reported here because of uncertain experimental conditions) seems to i n d i c a t e that t h i s i s also true f o r the l a t e r a l gen-i c u l a t e body. This suggests that, contrary to current views, the macropotentials depend p r i m a r i l y on nerve f i r i n g s and owe l i t t l e to d e n d r i t i c a c t i v i t y , at l e a s t i n the o p t i c t r a c t . This also gives some information about the shape of the nerve f i r i n g . The f a c t that a high number of nerve f i r i n g s corresponds to a p o s i t i v e peak of the slow wave, and a small number to a minimum i n the slow wave, implies that the nerve f i r i n g i n the o p t i c t r a c t i s associated with a p o s i t i v e overshoot following the nerve impulse. Because sharp peaks correspond i n the slow wave and the weighted mean with i n 4 or 5 ms, t h i s p o s i t i v e overshoot w i l l have to follow the nerve impulse within 4 or 5 ms. The existence of th i s b r i e f p o s i t i v e overshoot i s i n c o n t r a d i c t i o n with the commonly accepted shape for the action p o t e n t i a l i l l u s t r a t e d i n f i g u r e 1. This discrepancy may be due to the fac t that microelectrodes which are used to study s i n g l e unit f i r i n g s have a d i f f e r e n t impedance than macroelectrodes. Because i t was believed that the weighted mean was an adequate representation of the number of f i r i n g s , the r e l a t i o n s h i p between the slow wave and the weighted mean was sought. This r e l a t i o n s h i p would permit us to get information on the spike discharge d i r e c t l y from the slow wave. This r e l a t i o n s h i p was obtained i n the form of a transfer function and for the range of stimulus conditions used,appeared to be the same with i n the l i m i t s of uncertainty inherent to the technique. APPENDIX A DESCRIPTION OF THE AMPLITUDE DISCRIMINATOR The amplitude discriminator compares the input waveform with two set voltages, and and gives out a standard pulse (5 v o l t s , 36 us i n duration) whenever a peak occurs whose amplitude i s between and V£• and define the boundaries of the window. 2 ~ waveform analysed 5 v o l t s output of amplitude di s c r i m i n a t o r 36 us Figure A . l . Operation of the amplitude discriminator V2 and V^: upper and lower boundaries of, th?. window. peaks of the waveform analysed P 1 ' P 2 ' P 3 ' V I t can be noticed i n Figure A . l that the amplitude discriminator does not d e l i v e r a pulse f o r peaks p^ and p^,which are below the lower threshold,nor f o r peak P2,which i s above the upper threshold. Only p^ -generates an output and the pulse i s produced at the crossing of the waveform with the lower boundary of the window. 30 APPENDIX B LIST OF EXPERIMENTS Stimulus d e s c r i p t i o n -3 10 unit -3 10 unit 10 unit 1 0 - 1 unit 1 u n i t 2,4,8 uni ts (averaged) Length of record 500 ms 1 sec 500 ms 500 ms 500 ms 500 ms Cat #007 #007 #007 #007 #007 #007 Number of averages 512 310 512 512 512 384 Lowest win-dow used 0.0 0.0 0.0 0.0 0.25 v. 0.0 Upper cu t - o f f frequency of spike f i l t e r 10 KHz 4 KHz 10 KHz 10 KHz 10 KHz 10 KHz 16 units 16 units blue f i l t e r 16 units red f i l t e r 500 ms 500 ms 500 ms #009 #003 #003 1024 512 512 1.25 v. 0.0 0.0 4 KHz 4 KHz 4 KHz 10 4 unit 10 Hz repet-i t i o n rate 100 ms #A3 256 0.0 4 KHz ON response OFF response 500 ms 500 ms #013 #013 512 256 0.0 0.0 4 KHz 4 KHz APPENDIX C CHARACTERICS OF THE AMPLIFIER Time s h i f t vs. frequency Frequency (Hertz) Time s h i f t (ms) 1.0 302 1.5 168 2.0 108 2.5 82 3.0 62 3.5 51 4.0 42 4.5 34 5.0 28 6.0 20 Amplitude vs. frequency Frequency (Hertz) Amplitude (db) 0. 7'5 -18.5 1.0 -15.1 1.5 -11.4 2.0 - 9.1 2.5 - 7.3 3.0 - 6.0 4.0 - 4.3 5.0 - 3.0 6.0 - 2.3 8.0 - 1.4 10.0 - .9 20.0 - .1 50.0 0 The e f f e c t of the lower c u t - o f f frequency of the a m p l i f i c a t i o n system was simulated on the IBM 360. Since the slow wave was high-passed at 5 Hertz, we high-passed the weighted mean also at 5 Hertz. This was done by taking the convolution of the weighted mean by.the impulse response corresponding to the transfer function _ . The r e s u l t appears s + l/2TTf i n f i g u r e A.2. I t i s seen that the two curves now correspond more c l o s e l y i n time and i n amplitude. 33 Figure A.2. E f f e c t of the lower cut-off frequency of the a m p l i f i e r . The upper p i c t u r e shows the o r i g i n a l curves, the lower one displays the curves a f t e r the weighted mean had been high-passed at 5 Hertz. In both p i c t u r e s , the upper curve i s the slow wave and the lower one the weighted mean. REFERENCES 1. Ochs, Sidney, "Elements of Neurophysiology", New York, J . Wiley, 1965. 2. Hubel, D. H., "Integrative Processes i n Central V i s u a l Pathways of the Cat", Journal of the O p t i c a l Society of America, Vol. 53: 58-66, 1953. 3. John, E. R. , Ruchkin, D. S., and V i l l e g a s , J . , "Experimental Back-ground: Signal Analysis and Behavioral Correlates of Evoked P o t e n t i a l Configurations i n Cats", Ann. N. Y. Acad. S c i . , Vol. 112: 362-420, 1964. 4. Donchin, E., "A M u l t i v a r i a t e Approach to the Analysis of Average Evoked Potentials",. I.E.E.E. Trans. Bio-Medical Engineering, Vol. BME-13: 131-139, Ju l y 1966. 5. Steinberg, R. H., " O s c i l l a t o r y A c t i v i t y i n the Optic Tract of Cat and Li g h t Adaptation", J . Neurophysiol., Vol. 29: 139-156, 1966. 6. Polyak, S. L. , "The Vertebrate V i s u a l System", edited by H. Kliiver, (Chicago) U n i v e r s i t y of Chicago Press, 1957. 7. Freeman, W. J . , "Relations Between Unit A c t i v i t y and.Evoked P o t e n t i a l s i n Prepyriform Cortex of Cats", J . Neurophysiol., V o l . 31: 337-348, 1968. 8. Brazier, M.A.B., "The E l e c t r i c a l A c t i v i t y of the Nervous System", 3rd . ed., Baltimore, Williams and Wilkins, 1968. 9. Laufer, M., and Verzeano, M., "Periodic A c t i v i t y i n the V i s u a l System of the Cat", V i s i o n Res., Vol. 7: 215-227, 1967. 10. Verzeano, M. , and Calma, I., "Unit A c t i v i t y i n Spindle Bursts", J_. Neurophysiol., Vol. 17: 417-428, 1954. 11. Verzeano, M., "Sequential A c t i v i t y of Cerebral Neurons", Arch, i n t e r n a t . P h y s i o l . Biochim., V o l . 63: 458-476, 1955.. 12. Lennox, M. A., "Single Fiber Responses to E l e c t r i c a l Stimulation i n Cat's Optic Tract", J . Neurophysiol., Vol. 21: 62-69, 1958. 13. Keehn, D. G., "An I t e r a t i v e Spike Separation Technique", I.E.E.E. Trans. Bio-Medical Engineering, Vol. BME-13: 19-28, January 1966. 14. Uenoyama, K., McDonald, J . S., Drance, S. M., "The E f f e c t of I n t r a -ocular Pressure on V i s u a l E l e c t r i c a l Responses", Arch. Ophthal., Vol. 81: 722-729, 1969. 15. Bishop, G. H., and Clare, M. H., "Organization and D i s t r i b u t i o n of Fibers i n the Optic Tract of the Cat", J . Comp. Neurol., Vol. 103: . 269-304, 1955. 16. Bergland, G. D., "A Guided Tour of the Fast Fourier Transform", I.E.E.E. Spectrum, Vol. 6 , July, 1969; 41-52. 17. Richards, P. I., "Computing Re l i a b l e Power Spectra", I.E.E.E. Spectrum, Vol. 4:, January 1967;" 83-90.. 18. Bingham, C., Godfrey, M. D., and Tukey, J. W., "Modern Techniques of Power Spectrum Estimation", I.E.E.E. Trans. Audio and E l e c t r o -acoustics, V o l. AU-15: 56-66, June 1967. 19. Maffei, L. and R i z z o l a t t i , G., "Transfer Properties of the L a t e r a l Geniculate Body", J . Neurophysiol., Vol. 30: 333-340, 1967. 20. Hughes, G. W. and Maffei, L., "Retinal Ganglion C e l l Response to Sinuso i d a l Light Stimulation", J. Neurophysiol., Vol. 29: 333-352, 1966. 21. Poppele, R. E., and Maffei, L., "Frequency Analysis of the E l e c t r o r e t -inogram", J . Neurophysiol., V o l. 30: 982-992, 1967. 22. Maffei, L., and Poppele, R. E., "Frequency Analysis of the Late Receptor P o t e n t i a l " , J . Neurophysiol., V o l. 30: 993-999, 1967. 

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