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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 . S c , L a v a l 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 o f Electrical  We accept  this  Engineering  t h e s i s as conforming  required  to the  standard  Research S u p e r v i s o r Members o f the Committee  Head o f the Department (Acting) Members o f the Department of THE  Electrical  Engineering  UNIVERSITY OF BRITISH COLUMBIA October,  1970  In  presenting  this  an a d v a n c e d d e g r e e the L i b r a r y I  further  for  of  this  written  at  agree  for  financial  British  by  for  gain  Columbia  shall  the  requirements  Columbia, reference  copying  of  I agree and this  that  not  copying  or  for  that  study. thesis  t h e Head o f my D e p a r t m e n t  is understood  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  of  for extensive  p u r p o s e s may be g r a n t e d It  fulfilment of  available  permission.  Department  Date  freely  that permission  representatives. thesis  in p a r t i a l  the U n i v e r s i t y  s h a l l make i t  scholarly  by h i s  thesis  or  publication  be a l l o w e d w i t h o u t  my  ABSTRACT The s i g n a l c o l l e c t e d by a m a c r o e l e c t r o d e i n s e r t e d optic  t r a c t i s made up o f a slow component and f a s t v a r i a t i o n s  charge) .  (spike  The mean amplitude o f the peaks o f the f a s t v a r i a t i o n s  to be c o r r e l a t e d w i t h the slow component. by  i n the cat's dis-  appears  The s p i k e d i s c h a r g e i s s t u d i e d  an amplitude d i s c r i m i n a t o r ;  the e f f e c t o f f i l t e r i n g  and o v e r l a p p i n g a r e  d i s c u s s e d , and i t i s seen t h a t  the mean c o u n t i n g v a l u e  (weighted mean)  o b t a i n e d from t h e amplitude d i s c r i m i n a t o r of  f i r i n g s occurring  i s a representation  o f the number  i n the neighbourhood o f the m a c r o e l e c t r o d e .  The curves o b t a i n e d f o r the weighted mean show a h i g h degree o f . s i m i l a r i t y w i t h t h e 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 c a l c u l a t e d This  transfer  function  i n the form o f a t r a n s f e r  function.  appears to be the same f o r a wide range o f s t i m u l u s  conditions. These f i n d i n g s  suggest t h a t  with generation of optic  tract potentials.  f i r i n g must be a s s o c i a t e d shoot a l l o w i n g  building  d e n d r i t i c a c t i v i t y has l i t t l e  i n the o p t i c  I t also  indicates  that  t r a c t w i t h a prompt p o s i t i v e  up o f p o s i t i v e m a c r o p o t e n t i a l s .  (ii)  to do the nerve over-  TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS  iv  ACKNOWLEDGEMENT  v  I.  INTRODUCTION  1  ELECTRICAL ACTIVITY IN NERVE CELLS  2  THE ORIGIN OF THE SLOW WAVE  3  DESCRIPTION OF EXPERIMENTS  5  SLOW WAVE AND SPIKE DISCHARGE  7:  II. III. IV. V. VI.  VII. VIII. IX.  INFORMATION  GIVEN BY THE AMPLITUDE DISCRIMINATOR of the A c t i v i t y o f Many Nerve F i b r e s  •  11  (a)  Superposition  11  (b)  Effect of F i l t e r i n g  13  (c)  E f f e c t o f Overlaps  13  WEIGHTED MEAN  17  RELATIONSHIP BETWEEN THE SLOW WAVE AND THE WEIGHTED MEAN  22  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  (iii)  LIST OF ILLUSTRATIONS Figure  Page  1  A c t i o n P o t e n t i a l and P o s t - s y n a p t i c P o t e n t i a l s . . .  2  2  Schematics  5  3  S i g n a l Recorded  4  S p i k e D i s c h a r g e from OT ( c a t #007)  5  Output  6  Amplitude D i s t r i b u t i o n Curves Obtained w i t h the A m p l i tude D i s c r i m i n a t o r  10  7  S p i k e D i s c h a r g e from OT ( c a t #C35)  11  8  Spike D i s c h a r g e from OT ( c a t #C35)  14  9  S p i k e D i s c h a r g e from OT w i t h a R e d u c t i o n i n the Ampl i f i e r Bandwidth ( c a t //C35)  14  o f Mammalian V i s u a l System from OT ( c a t #007)  o f Amplitude  8 ,  Discriminator  8 9  10  P o s s i b l e Cases o f O v e r l a p s  11  Slow Wave and Weighted Mean ( c a t s #003 and #007)  19  12  Slow Wave and Weighted Mean ( c a t #007)  20  13  Slow Wave and Weighted Mean ( c a t s #013, #009 and #003)..  21  14  Transfer Function Relating Mean ( c a t #013)  the Slow Wave to the Weighted 25  Transfer Function Relating Mean ( c a t s #007 and #003)  the Slow Wave to the Weighted  Transfer Function Relating Mean ( c a t s #A3 and #009)  the Slow Wave to the Weighted . .'  A.l  O p e r a t i o n o f the Amplitude  Discriminator  A.2  E f f e c t o f the Lower C u t - o f f Frequency  15  16  • 16  26  (iv)  o f the A m p l i f i e r . .  27 29 33  ACKNOWLEDGEMENT I am t h a n k f u l to those who c o n t r i b u t e d to t h i s  thesis.  Dr. J . S. MacDonald s u p e r v i s e d t h i s work. P r o f e s s o r F. K. Bowers  read the t h e s i s .  Dr. K. Uenoyama gave encouragement and h e l p . M i s s V e r o n i c a Komczynski typed  the manuscript.  Mr. R i c k Corman p r o v i d e d t e c h n i c a l a s s i s t a n c e . Mr. Herb B l a c k d i d t h e p h o t o g r a p h i c work. F e l l o w graduate  s t u d e n t s p r o o f r e a d the t h e s i s .  The N a t i o n a l Research C o u n c i l p r o v i d e d f i n a n c i a l  (v)  support.  1  1.  INTRODUCTION  Much of the knowledge we gained  through e l e c t r o p h y s i o l o g y .  s t u d i e s has  been enormous.  most on a few i n any  fibres.  have about the nervous system has In t h i s ,  the c o n t r i b u t i o n of  However, m i c r o e l e c t r o d e s  been  microelectrode  give information  Compared to the thousands of nerve f i b r e s  at  encountered  a r e a 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  size. The  g o a l o f t h i s work was  means of m a c r o e l e c t r o d e s macroelectrode,  (0.5 mm  to get i n f o r m a t i o n on nerve f i r i n g s  i n diameter).  I t was  thought t h a t  by  the  because o f i t s l a r g e r s i z e , would g i v e a b e t t e r p i c t u r e o f  the a c t i v i t y o f a p o p u l a t i o n o f nerve f i b r e s .  The  experiments were  confined  to the c a t ' s v i s u a l system, m a i n l y to the o p t i c t r a c t . The varying  signal  component on  are b e l i e v e d to be l i t u d e s being  c o l l e c t e d by  the m a c r o e l e c t r o d e c o n s i s t s o f a slow-  top of which r i d e f a s t v a r i a t i o n s .  caused by n e r v e f i r i n g s ,  e x p l a i n e d by  attempt was  t r a i n s of various technique  had  the v a r i a b i l i t y o f t h e i r amp-  t h e i r r e l a t i v e d i s t a n c e from the r e c o r d i n g e l e c -  t r o d e , the s i z e of the nerve f i b r e and An  These f a s t v a r i a t i o n s  the degree of  overlapping.  made to decompose the waveform i n t o s e t s o f  amplitudes,  phases and  repetition rates.  Such an  been s u c c e s s f u l i n the case of the l o c u s t v e n t r a l c o r d  pulse iterative (13).  However, the l a r g e number o f f i b r e s i n f l u e n c i n g the e l e c t r o d e as w e l l as h i g h degree o f o v e r l a p p i n g  f o r c e d us  More a t t e n t i o n was processes  involved.  to abandon t h i s  the  approach.  g i v e n to a deeper u n d e r s t a n d i n g  o f the  various  2  II.  ELECTRICAL ACTIVITY IN NERVE CELLS  Nerve impulse g e n e r a t i o n and t r a n s m i s s i o n i n d u c e v a r i o u s r i c a l potentials,  the most commonly s t u d i e d  the p o s t - s y n a p t i c  potentials.  The potentials  elect-  b e i n g the a c t i o n p o t e n t i a l and  a c t i o n p o t e n t i a l i s composed o f t h e s p i k e and the a f t e r -  (usually  a n e g a t i v e a f t e r - p o t e n t i a l f o l l o w e d by a l o n g e r p o s i t i v e  a f t e r - p o t e n t i a l , sometimes f o l l o w e d by a second n e g a t i v e a f t e r - p o t e n t i a l ) . After-potentials  reflect  changes i n membrane conductance f o l l o w i n g  the  n e g a t i v e and p o s i t i v e a f t e r - p o t e n t i a l s  and  hyperpolarization  o f the membrane.  are r e s p e c t i v e l y  U n l i k e the s p i k e ,  the s p i k e ;  a repolarization  they a r e s e n s i t i v e  to m e t a b o l i c changes (8). Post-synaptic potentials by  release  of a chemical transmitter  types: e x c i t a t o r y The  a t the synapse.  (EPSP) o r i n h i b i t o r y  They can be o f two  (IPSP).  PSP's a r e l o c a l graded responses and t h e i r amplitude decreases  with increasing on  (PSP's) a r e produced i n t h e d e n d r i t e s  distance  from the synapse.  The s p i k e and the a f t e r - p o t e n t i a l s  the o t h e r hand a r e axonal and o f t h e a l l - o r - n o n e  type.  EPSP Spike 5 ws.  —  -  negative a f t e r - p o t e n t i a l positive  F i g u r e 1.  after-potential  A c t i o n p o t e n t i a l ( l e f t ) and p o s t - s y n a p t i c p o t e n t i a l s . d i r e c t i o n i s negative.  Upwards  3  III. The  THE ORIGIN OF THE SLOW WAVE  terms " m a c r o p o t e n t i a l s " o r "slow p o t e n t i a l s " r e p r e s e n t t h e  electrical activity  r e c o r d e d by m a c r o e l e c t r o d e s  from nervous t i s s u e s ( s e e  Figure 3).  I f 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 s t i m u l u s and i s  time-locked  to i t the terms "evoked p o t e n t i a l s " o r "evoked r e s p o n s e s " a r e  used. Macropotentials  and evoked responses  a r e employed f o r i n v e s t i g a t i n g  c o n n e c t i v i t y between v a r i o u s r e g i o n s o f t h e nervous system as w e l l as f o r monitoring  certain psychophysiological variables.  agreement on t h e i r o r i g i n , impaired  t h e r e f o r e 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  t h e i r e f f e c t i v e n e s s as a r e s e a r c h Although  of s t a t i s t i c a l  However the absence of  tool.  attempts were made to bypass t h i s d i f f i c u l t y by the use  techniques  such  as m u l t i v a r i a t e procedures  (3,4), c o n s i d e r a b l e  e f f o r t has been spent i n r e c e n t y e a r s e x p l a i n i n g the o r i g i n o f m a c r o p o t e n t i a l s . Pharmacological potentials up w i t h  s t u d i e s l e d many to a t t r i b u t e  to d e n t r i t i c a c t i v i t y  (PSP's);  the o r i g i n of macro-  Freeman ( 7 ) , f o r i n s t a n c e , came  a model e x p l a i n i n g the v a r i o u s peaks o f t h e evoked response by  a l t e r n a t i n g sequences o f EPSP's and IPSP's. To some e x t e n t , t h e r e 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 p o s t - s t i m u l u s h i s t o g r a m cell will  fire  a t a g i v e n time  (the p r o b a b i l i t y  that a  a f t e r t h e o n s e t o f the s t i m u l u s ) ( 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 n o t i c e a b l e i n the o p t i c t r a c t  (5).  Laufer  a constant' time  (9) and Calma (10) observed  r e l a t i o n s h i p with  the slow wave.  unit f i r i n g s  t h a t kept  Verzeano  (11),  T h i s 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 p l a y an important  r o l e i n the p r o d u c t i o n o f t h e slow  wave; depending on the r e g i o n o f the c o r t e x , the slow wave would be due to a f t e r - p o t e n t i a l s a l o n e o r to the combined i n f l u e n c e s o f PSP's and a f t e r - p o t e n t i a l s :  4  "If due,  the 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 s i m p l y , to t h e e l e c t r o t o n i c spread o f the r e t i n a l p o s t -  synaptic  potentials,the  become p r o g r e s s i v e l y  amplitude o f such o s c i l l a t i o n s s h o u l d  smaller at increasing  d i s t a n c e s from the  r e t i n a , a l o n g the o p t i c nerve and o p t i c t r a c t , a c c o r d i n g to a r a t e of decay imposed by the space c o n s t a n t o f the axones. experimental findings suggests t h a t are  show t h a t  t h i s i s not the c a s e . . .  The  This  the 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  summations o f 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  amplitude i s independent o f the d i s t a n c e  from the r e t i n a .  tract whose 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 s p r e a d o f r e t i n a l p o s t s y n a p t i c  potentials,  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 s h o u l d n o t be accompanied by axonal a c t i o n p o t e n t i a l s , sarily  since  synaptic  r e s u l t i n neuronal discharge.  t h i s i s n o t the case but t h a t , i n the o p t i c  activity  The t r a c i n g s . . .  on the c o n t r a r y ,  every  show  the o s c i l l a t i o n s i n the o p t i c  axones i n r e l a t i o n w i t h axonal p o s t - s p i k e  (Laufer  This,  that  oscillation  t r a c t i s accompanied by axonal s p i k e p o t e n t i a l s  remains i n c o n s t a n t phase r e l a t i o n s w i t h them. gests that  does not n e c e s -  and  a g a i n , sug-  t r a c t develop i n the activity."  and Verzeano  ( 9 ) , p. 225)  5  IV. Data r e c o r d e d studied.  DESCRIPTION OF EXPERIMENTS  over a two-year p e r i o d by Dr. K. Uenoyama were  The methods used a r e d e s c r i b e d i n more d e t a i l Two m a c r o e l e c t r o d e s  cat:  one i n the o p t i c t r a c t  (LGN).  were i n s e r t e d i n the b r a i n o f an a n a e s t h e t i z e d (OT) , the o t h e r i n the l a t e r a l  A s o l d e r e l e c t r o d e was p l a c e d on the v i s u a l c o r t e x .  were r e c o r d e d (ERG).  elsewhere ( 1 4 ) .  on an 8 - t r a c t PI r e c o r d e r  Also recorded  on s e p a r a t e  together with  channels,  geniculate  nucleus  The s i g n a l s  the e l e c t r o r e t i n o g r a m  was the h i g h - p a s s e d v e r s i o n of  the m a c r o e l e c t r o d e s i g n a l ( s p i k e d i s c h a r g e ) . The  stimulus  consisted usually of a b r i e f  l e s s o f t e n i t was o f the square wave type.  f l a s h once a second;  To improve the s i g n a l - t o - n o i s e  r a t i o , a F a b r i - t e k average response computer was used to average a p r e s e t number o f waveforms. F i g u r e 2 shows the p o s i t i o n o f t h e m a c r o e l e c t r o d e s to  the c a t ' s v i s u a l  with  respect  system.  r.c  c  h  OJ  a  Primary v i s u a l cortex Visual I Visual II Visual III  g  lateral F i g u r e 2,  geniculate  nucleus  Schematics o f mammalian v i s u a l system (From S c i e n c e J o u r n a l , 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 o f e l e c t r o d e s , r . c : rods and cones, h. : h o r i z o n t a l c e l l , b.: b i p o l a r c e l l s , a. : amacrine c e l l , g. : g a n g l i o n c e l l s  6  In the o p t i c  tract  (OT) , the a c t i v i t y  r e c o r d e d i s mostly from the  axones,  w h i l e the c o r t e x i s u s u a l l y e n t a n g l e d w i t h m u l t i p l e 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 g e n i c u l a t e n u c l e u s (LGN), i t d i f f e r s a c c o r d i n g to Hubel  (2)  from most o t h e r s t r u c t u r e s i n the c e n t r a l nervous system by i t s r e l a t i v e simplicity:  i t i s a mere one-synapse  The o p t i c  way  station.  t r a c t i s made of many bundles o f nerve f i b r e s ,  c o n n e c t i v e and n u t r i t i v e  tissues  (6).  I t s 120,000 nerve f i b r e s  e l i n a t e d and o f 3 o r 4 d i f f e r e n t v e l o c i t y and s i z e groups e l e c t r o d e i s 0.5 o f the  fibres.  mm  (12).  are  plus my-  The macro-  i n diameter and i s p l a c e d i n the same p l a n e as the c o u r s e  7  V.  SLOW WAVE AND SPIKE DISCHARGE  A l i g h t s t i m u l u s i n d u c e s i n the o p t i c  tract potential  variations  which a r e c h a r a c t e r i z e d by a sequence o f maxima and minima whose amplitude and l a t e n c y depend on the type o f s t i m u l u s . (Latency i s t h e time d e l a y between the s t i m u l u s and the evoked  response).  The s i g n a l r e c o r d e d by t h e  m a c r o e l e c t r o d e c o n s i s t s o f a slow component on top o f which r i d e f a s t like variations  (Figure 3).  spike-  U s u a l l y an a v e r a g i n g p r o c e s s i s used to smooth  out t h e f a s t v a r i a t i o n s and one s t u d i e s the i n f l u e n c e o f v a r i o u s parameters  the r e s u l t i n g slow wave s e e k i n g  on t h e c h a r a c t e r i s t i c s o f the slow wave  (amplitude and l a t e n c y o f t h e p e a k s ) . T h i s t h e s i s i s concerned w i t h the f a s t v a r i a t i o n s r i d i n g on top o f t h e slow component. high-pass  filter  The m a c r o e l e c t r o d e s i g n a l was passed  so t h a t these f a s t v a r i a t i o n s  b i a s o f the slow component. s i g n a l appears  through a  c o u l d be s t u d i e d w i t h o u t the  The h i g h - p a s s e d v e r s i o n o f the m a c r o e l e c t r o d e  i n f i g u r e 4 and w i l l be r e f e r r e d  to i n the r e s t o f t h e t h e s i s  as the " s p i k e d i s c h a r g e " . F i g u r e s 3 and 4 were taken from the same experiment same time s c a l e to p e r m i t comparison  o f t h e two waveforms.  and a t the  One can see that  the two a r e c o r r e l a t e d : maximum amplitude i n the s p i k e d i s c h a r g e corresponds to a p o s i t i v e peak i n the slow  component, minimum amplitude  d i s c h a r g e to a n e g a t i v e peak i n the slow  component.  c o n v e n t i o n s used i n n e u r o p h y s i o l o g y , p o s i t i v i t y Because i t was r e a d i l y a v a i l a b l e , an amplitude study  the s p i k e d i s c h a r g e .  pulse  (5 v o l t s ,  T h i s amplitude  i n the s p i k e  Note t h a t a c c o r d i n g to  i s downwards i n f i g u r e 3. d i s c r i m i n a t o r was used to  d i s c r i m i n a t o r gives a standard  36 y s wide) whenever t h e amplitude o f t h e s p i k e d i s c h a r g e  l i e s between two s e t v a l u e s : 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 f r o m OT ( c a t #007, i n t e n s i t y : 10 " u n i t ) . T i m e s c a l e :20 m s / d i v . P o s i t i v i t y i s downwards a n d 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 t o 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 f r o m OT ( c a t #007, i n t e n s i t y J l O unit). scale'20 m s / d i v . A m p l i f i e r bandwidth:500 Hz t o 1 0 KHz.  Time  9  spike discharge  output from amplitude d i s c r i m i n a t o r  F i g u r e 5.  Output o f amplitude  d i s c r i m i n a t o r with l i m i t s s e t at  and d e s c r i b e d i n more d e t a i l s i n appendix A.  At the same time,  and  the F a b r i -  tek computer p r o v i d e d a means o f c o u n t i n g over many o b s e r v a t i o n s the number o f p u l s e s d e l i v e r e d by the amplitude amplitude  d i s c r i m i n a t o r . F i g u r e 6 shows such  d i s t r i b u t i o n s o b t a i n e d by t h i s  technique.  Twelve windows were  used and the boundary v a l u e s are g i v e n at the extreme r i g h t . curve i s the c o r r e s p o n d i n g average  slow wave w i t h p o s i t i v i t y  a g a i n , one n o t i c e s t h a t h i g h amplitude  The bottom downward.  peaks o f the s p i k e d i s c h a r g e are  c l u s t e r e d around p o s i t i v e peaks o f the slow wave.  Here  -1-  CAT  #007  INTENSITY 5/2  :  7  w  un/Y  AVERAGES  window  attenuation  bounda ries (volts) 2  2  4  JL Jl.  525- 5.75 4.75-5.25 4.25-4.75  4  3.75-4.25 3.25-3.75 2.75-3.25 2.25-2.75 1.75-2.25  8 1.25-1.75  16  0.75-1.25  16  *v^r*i.  16  16  ^ y ^ w W l  slow  ^A.rVWU^W^Sy,  0.25- 0.75  Q.OO-  Q.25  wave  too ms.  F i g u r e 6.  Amplitude d i s t r i b u t i o n curves o b t a i n e d w i t h the amplitude d i s c r i m i n a t o r , t o g e t h e r w i t h 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.  The charge.  INFORMATION G I V E N BY THE AMPLITUDE DISCRIMINATOR  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,  To i n t e r p r e t  c r i m i n a t o r , we w i l l many n e r v e  fibres,  of adjacent a)  correctly  t h e i n f o r m a t i o n g i v e n by t h e a m p l i t u d e  the effect  of filtering  and t h e e f f e c t o f o v e r l a p p i n g  peaks.  The  o f many n e r v e  fibres  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  t h e number o f n e r v e  fibres  lying  closest  and i t i s e s t i m a t e d  t o i t i s b e t w e e n 50 a n d 1 0 0 .  to that 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 . f i g u r e 7 c a n t h e n be e x p e c t e d  of  Figure  7.  to result  from  that Added  The p e a k s s e e n i n  f r o m the. s u p e r p o s i t i o n o f many  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  the f i b r e  dis-  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  Superposition of the a c t i v i t y  firings,  dis-  proportional  nerve  to the d i s t a n c e  the macroelectrode.  S p i k e d i s c h a r g e f r o m OT ( c a t #C35, i n t e n s i t y : 4 u n i t s ) . T i m e s c a l e :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 b i n a r y code a p p e a r i n g i n t h e lower t r a c e ident if ies the record.  12  A b i g peak can t h e r e f o r e be the r e s u l t o f three  things:  1. - a s m a l l number o f f i b r e s c l o s e to the e l e c t r o d e and f i r i n g a t the same time.  Since  relatively 2. - many f i b r e s  they are c l o s e to the e l e c t r o d e ,  large  firing  electrode.  amplitude.  a t the same time b u t a t some d i s t a n c e  add to a r e l a t i v e l y  3. - a combination o f (1) and ( 2 ) . that are at a given  would be the g e n e r a l The  Since  there  distance  large  amplitude.  i s no reason f o r o n l y  from the e l e c t r o d e  those  to f i r e ,  this  case.  m a c r o e l e c t r o d e was i n s e r t e d i n the o p t i c t r a c t i n such a way t h a t i t s  s u r f a c e was p a r a l l e l fibres  tend  to the course o f t h e nerve f i b r e s .  to group a c c o r d i n g  s i z e s group i n d i f f e r e n t f l u e n c i n g the e l e c t r o d e o f the e l e c t r o d e .  recorded  to t h e i r s i z e  areas o f the t r a c t .  Moreover, o p t i c t r a c t  (12,15): f i b r e s of d i f f e r e n t We can imagine the f i b r e s i n -  to be d i s t r i b u t e d on l a y e r s p a r a l l e l  to the s u r f a c e  The f i b r e s o f one l a y e r would be o f the same s i z e and  a t the same d i s t a n c e  from the e l e c t r o d e , hence they would c o n t r i b u t e  to the  s i g n a l by the same amount. The  very  from the  Each f i r i n g w i l l be o f s m a l l amplitude b u t s i n c e t h e r e are  many o f them, they w i l l  fibres  they w i l l have a  hundreds o f f i b r e s  i n f l u e n c i n g the m a c r o e l e c t r o d e d e f i n e a  s m a l l subgroup o f the t o t a l 120,000 f i b r e s of the c a t ' s o p t i c  We assume t h a t i n t h i s subgroup and w i t h are a t one time as many f i b r e s  the s t i m u l u s  f i r i n g on the f i r s t  second l a y e r , and on the t h i r d and so on.  tract.  c o n d i t i o n s used,  l a y e r as there  there  are on the  Then a g i v e n peak w i l l be made o f  the same number o f b i g s p i k e s , medium s p i k e s  and s m a l l s p i k e s .  High amp-  l i t u d e peaks w i l l be the r e s u l t o f many f i r i n g s , medium ones o f a medium number o f f i r i n g s  and s m a l l ones o f few f i r i n g s .  1J  b)  E f f e c t of  filtering  The s p i k e d i s c h a r g e waveforms were o f t e n w i t h the upper  cut-off  frequency of the f i l t e r  (see appendix  lowered  C) a n a l y z e d  down to 4 KHz.  To  examine the e f f e c t o f t h i s bandwidth r e d u c t i o n , p i c t u r e s were taken o f the same r e c o r d i n the p e r i o d o f maximum a c t i v i t y ,  some a t f u l l bandwidth  10 KHz),  KHz). Two  appear  o t h e r s a t reduced bandwidth  i n f i g u r e s 8 and A comparison  about  c)  (600 Hz-4  (600 Hz  of those p i c t u r e s  9. o f f i g u r e s 8 and 9 shows that l i t t l e i n f o r m a t i o n  r e l a t i v e peak amplitude i s l o s t by r e d u c i n g the  bandwidth.  E f f e c t of overlaps As we have seen i n b) and c) the s p i k e d i s c h a r g e 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 o f 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 s y n c h r o n o u s l y and i f the nerve impulses would t r a v e l a t the same speed  a l o n g the axones, then the nerve f i r i n g s would be  e x a c t l y i n time.  A peak f i v e  times b i g g e r than another one would  exactly  to f i v e  times as many f i r i n g s .  one has  to expect some i n t e r f e r e n c e between impulses  g i v e n nerve impulse  superimposed correspond  T h i s i s not the case however and a d j a c e n t i n time.  can o c c u r on the t a i l o f another nerve f i r i n g  and i t s  amplitude w i l l be i n c r e a s e d o r d e c r e a s e d : i n c r e a s e d i f i t o c c u r s on p o s i t i v e p a r t o f the t a i l , the amplitude  d i s c r i m i n a t o r l o o k s at the amplitude o f the peaks,  1.  this  effect  examine i t i n d e t a i l .  C o n s i d e r the v a r i o u s ways i n which two i n figure  the  d e c r e a s e d i f i t o c c u r s on the n e g a t i v e p a r t . S i n c e  i s most i m p o r t a n t and we w i l l  illustrated  A  s p i k e s can add t o g e t h e r (as  10):  They c o i n c i d e i n time. then simply the sum  The peak amplitude o f the r e s u l t i n g s p i k e i s  o f the peak amplitude of the two  i n d i v i d u a l spikes  -  14  F i g u r e 8.  S p i k e d i s c h a r g e f r o m OT ( c a t #C35, i n t e n s i t y : 4 u n i t s ) . T i m e scale:0.5 ms/div. V e r t i c a l d e f l e c t i o n : 5 uV/div. Bandwidth: 600 Hz - 10 K H z . The b i n a r y c o d e 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  Same r e c o r d as f i g u r e 8 e x c e p t reduced t o : 600 Hz - 4 KHz.  9.  that  the bandwidth  has been  and 2.  the amplitude  discriminator w i l l  They o c c u r c l o s e enough i n time t h a t o n l y one peak i s seen, one b e i n g reduced the amplitude  to a s h o u l d e r .  They o c c u r f a r enough a p a r t t h a t the peaks are d i s t i n c t , b u t one i s  peaks a r e r e g i s t e r e d by the amplitude g r e a t e r amplitude  o f the o t h e r .  amplitude  The two  d i s c r i m i n a t o r b u t one w i t h a  and p o s i t i v e b u t one i s r i d i n g on the n e g a t i v e  The two peaks a r e r e g i s t e r e d b u t one w i t h a s m a l l e r  than i t s h o u l d have.  Two peaks a r e d i s t i n c t . o t h e r and i t s amplitude line.  o f the o t h e r .  than i t s h o u l d have.  Two peaks a r e d i s t i n c t tail  5.  than the  amplitudes.  r i d i n g on top o f the p o s i t i v e p a r t o f the t a i l  4.  the o t h e r  Then o n l y one peak w i l l be seen by  d i s c r i m i n a t o r and i t s amplitude w i l l be l e s s  a c t u a l sum o f the two peak 3.  register i t correctly.  One i s r i d i n g on the n e g a t i v e t a i l  o f the  i s n o t b i g enough f o r i t to c r o s s the zero  S i n c e the amplitude  d i s c r i m i n a t o r c o n s i d e r s o n l y the p o s i t i v e  p a r t o f the s p i k e d i s c h a r g e , the n e g a t i v e peak w i l l n o t be r e g i s t e r e d at  all. Because o f t h i s o v e r l a p , we cannot  say t h a t the amplitude  o f the  peaks o f the s p i k e d i s c h a r g e i s p r o p o r t i o n a l to the number o f f i r i n g s . of  the time, i n f a c t , i t u n d e r e s t i m a t e s  of  t h i s , we would not expect  slow wave and the amplitude  the number o f f i r i n g s .  Most  As a r e s u l t  an a c c u r a t e l y l i n e a r r e l a t i o n s h i p between the o f the s p i k e d i s c h a r g e .  F i g u r e 10.  P o s s i b l e cases o f o v e r l a p s , i ) ,i i ) , i i i ) , to cases 1 ) , 2 ) , 3), 4) and 5) o f t e x t .  i v ) and v)  correspond  17  VII.  WEIGHTED MEAN  We have seen t h a t the amplitude o f the s p i k e d i s c h a r g e g i v e s a q u a l i t a t i v e r e p r e s e n t a t i o n o f the number o f f i r i n g s . c r i m i n a t o r c o u l d then be used  The amplitude  dis-  to get an ensemble average o f the amplitude  o f the s p i k e d i s c h a r g e , which i n t u r n would be a r e f l e c t i o n o f the ensemble average  o f the number o f f i r i n g s . The  upper  amplitude d i s c r i m i n a t o r was used i n the f o l l o w i n g manner.  and lower b o u n d a r i e s o f the window were s e t to some v a l u e s .  r e c o r d e r was a c c e l e r a t e d observations  (usually  The  The tape  t e n times and was run f o r a c e r t a i n number o f  512).  The F a b r i - t e k computer counted  the number o f  times a p u l s e was d e l i v e r e d by the amplitude d i s c r i m i n a t o r i n each o f 1024 time i n t e r v a l s .  T h i s amplitude d i s t r i b u t i o n was punched on paper tape and  o u t p u t on a pen r e c o r d e r .  The upper  and lower b o u n d a r i e s  o f the window  were then moved to a new s e t o f v a l u e s and the procedure was r e p e a t e d the waveform had been t o t a l l y were used  covered.  until  U s u a l l y twelve o r t h i r t e e n windows  to cover the whole waveform. An example o f the curves o b t a i n e d i s shown i n f i g u r e 6.  The bottom  trace i s the slow wave, the upper ones the curves o b t a i n e d f o r t h e c o r r e s p o n d i n g windows.  To c o n s t r u c t . t h e curve c o r r e s p o n d i n g to the ensemble average o f  the amplitude o f the s p i k e d i s c h a r g e the amplitude  d i s t r i b u t i o n curves were  added t o g e t h e r a f t e r each had been m u l t i p l i e d by a f a c t o r c o r r e s p o n d i n g to the mean v a l u e o f the b o u n d a r i e s o f the c o r r e s p o n d i n g window. For example, f o r the upper at 5.25 and 4.75 v o l t s ,  and lower b o u n d a r i e s o f the window s e t  the amplitude d i s t r i b u t i o n  by 5; f o r the upper and lower b o u n d a r i e s m u l t i p l i e d by 1.5.  curve  would be m u l t i p l i e d  s e t a t 1.75 and 1.25, i t would be  T h i s i s i l l u s t r a t e d by the formula:  N. = l  E  w  A. V iw w  (1)  18  where  i s the ensemble average o f the amplitude o f the s p i k e A.  discharge.  i s the v a l u e o f 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 V  w  w.  i s the weight a s s o c i a t e d w i t h t h i s window w.  T h i s i s s i m p l y the  number c o r r e s p o n d i n g to the mean o f the two b o u n d a r i e s o f the window. The N. curve o b t a i n e d by t h i s in  the r e s t o f the  f o r m u l a i s r e f e r r e d to as the weighted mean  thesis.  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  a n a l y s e d u s i n g the amplitude d i s c r i m i n a t o r . to c a l c u l a t e N. a c c o r d i n g to e q u a t i o n 1. I  wave were then punched  on paper tape.  cats were  The PDP-9 computer was  used  The o b t a i n e d c u r v e and the slow  These paper tapes were taken-to the  Computing Centre f o r p l o t t i n g and f u r t h e r p r o c e s s i n g . Some o f t h e s e p l o t s curves appear v e r y s i m i l a r  are seen i n F i g u r e s 11, 12 and 13.  to the slow waves.  T h i s i s so o v e r a wide  of s t i m u l u s c o n d i t i o n s : b l u e and r e d s t i m u l i , ON o f 1 and 10 H e r t z , low and h i g h  The range  and OFF r e s p o n s e s , f l a s h e s  intensities.  To each major peak i n the slow wave corresponds a major peak i n the w e i g h t e d mean.  The r e l a t i v e amplitudes are a l s o p r e s e r v e d .  shift  can be observed f o r the f a s t - r i s i n g peaks.  peaks  (as seen i n F i g u r e 12)  wave.  No  F o r the s l o w e r - r i s i n g  the weighted mean tends to l a g b e h i n d the slow  T h i s l a g can however be e x p l a i n e d by the lower c u t - o f f p o i n t  o f the a m p l i f i c a t i o n system  time  (see appendix C ) .  (5 H e r t z )  19 -I PI ill! li i !!i i i i lifl (P flft m iffli Hillmm St ; i; 4 UIBi we t?bc j l i ; iii! illi MM: SM ;|: I|!i 1 RV JWGI Illi iii! Ill li III! i ' 1 ! i i I N ; Nil Nil i ! i I I i i i l l ! Illi 1 i-i l|i i 1 : III ijij II 111 i ii illi lillllil 1 ! il!i-l 1 !• :l:i i.i-i! •1 jii ! i I !•!1 ii 1 " ! .;-! I I J I ' ; I: • I I Iii I i ! : III; i : t | jii| Iii' M l i' Mi • : i Hi: ill III M ilr! illi 1 1 J. ui| M |!![ III!. j .::) -i1 ilpi .i , ., . 1 i"! I" [" iiiji i I! Hi l i h ill! i i i i 11 1 III II; 1 ilf IF iy •ill i• ••I : 1• .:! •1! :1iIMi! ,|:| . : j . : ::|. i.i:! jili !.!i :I I '!' 1 - . ill • i ill iii T" '•ill i i i : Iii! ii- i !i Hi i-l • -f !• ::. i i.l.i I M-| . •Mi: ii 1 i iii|i!i j; Itl -jiiji 11 j.! ii' i ii! i 1! V I M'' 1 !"!•! I Mi ii i: . i.'I -i. j i ! ' !!A jl:: til i- -ill P H Itlil i i i Mii l i i •i HI i!i i f •f\ I- •! " t j -i: -i-i • 1 - i:. i . j 1 i j !J i ::1 j- i ! i-l :li life jjl'l M 111- ' 31 |:-:| j i t II I" ii-l-i ill i !:.! III •|4: i~l• :- : -ji ---jy :fi:l-l :|::L :: : 11! t\liii IHA hi-l - ff 1 iii.i i: :i: : n:j: j : ffli: • k is :• 111 -I-I y '";; liliii - - ; 1: ± : :. -Hi • 1 'IT • '-S vi ;• i • ll ' 'j 'i p : i l ! 11 :i 11 -i iiiiiiy i : .-j; i | :. :.i ii:! Ii-Ii i '-! IF MJ ^ I".:: X it I'iil "i j-'tt" ft r 1 .-- i t : : * :jj i- ! :| :::) J" :i : ill !'!-'! .1:i i - : j . ; : | i i ! "iii Iii . 1 . 1-' 11 i • lit''..: •i i i : l : iH f\W' -li :! .!:[ .1! iii. ••1 I Ill ' • i i ! iiii H "i Eitl - "I1 Slil" i ' Jl' V: '1 j:|tj:. Li ;: |:h:It: :t .r :j:j: -1 • ill •: :p ii'iii: Iii! 1 1 l-H ill n TM • • -i:|: m I I I - ' 'ill -j: 1- HUM . -L ;l. ; | | l • •i-i!1•!! i INin Hi p-r f i it: i 1 1 JL. |-"i j"T ; I.l.i ; 1! !i i Sit :i:i: :::. : i i i y y :|-K: "i" ": X j.: :::j T: : :i: :::):: -i. : : . i ! . :i:::: -: :ttr; |f: :::::(:: .|.J. 1i i ii|ii •f-i-ii ! IN Hi i i i 'ifflJi Li.\. Si :,±: 1 p i l jl EM: i ;; ; r r : | : J j : :±j i!il y :l:i i p i i Till Iii S i ! - IIFl- -III -.i-i •ill | T-+R+ . . 1 if: -? N 4 ip » c 1ii illl i i f '#11 i #li m ift tm4 1 --1B :|:=  jiR Pn TiffIf  1ii  "  ft liii 1 ;  ft  w Hit Millnit  II!  j jji-j  inT  :  1  . j/  :  ;  ;  It  ••|  t  (  ' |-  [  •  !•  1  :  :  1  •  -  1  \- •  !  !#  :  :  :  '-' -!/  l i  :  kM  (!•!-]  !  :  ;  :  ; : ;  ISli  rm  y  ;  :  mi Nil N 1I'l ill J M II 1 filf ilflf miiiffl §H i I ' : lEpt :s Mi i l l •it ,,-., i Nil ill! 11:1 i i i : III! li i 1 m P I 1 111 ji _ \ 11 III ! l 1 j j . •!|iit II! 1 1 il i1 l1 l1 I1 Ii Mi l | l ! ill 1 ! ]111 i 1! II Iii i i i . i 1 1 j- j 1 11 |i i 111 | l s I i i ilil Hi! MM HI! Hi! i 1 u. _: i i i ! i Nil j N Ii ii v1 M i ! ill 1. II i ) i 1 li | iII! i .i i | 1 ii li! \i III! i i i i-i i i i ii ! i -i n i' - 1 11 i il: Nil iii' Wjrs t-ii || ii |li|  IIII ill:  |||  Ill  ill!  ! 1! ill  ml Hli Hi M i Hi!  i!;l  •  Ii  ii  f  li Illi iii!  III  {  ill)  :i i 11 N i T 7? ' 1' 1 : i 1: Iji! !-I i i Nil 1 y \\\\ ill! 11 \ I! ]: ' \ ! l/ i | Iiii IH ilf  : :;i  !  I  II  I f JO  p  ii r I j i l ' i Ti - — I • lii-i i il "i ii-i : - •j-ii-i i-i r  •U-U.•i j II  11 "111 i  il  1 i-l111"  i ;  Ill j  !|  1  .. • •ti •  11  II ii! j| I :||  Jii;  Ml  1  11 ;'  Hii  I'M  Illi  IN  :  H|!  HI! Nil M ! Iii!  11: i I: • li HH::l ;i| M i l li tIi lI.I ill HI III ii! l| i || :!.; I i !.;• i j • 11 Mi Mi i;i  Mi  i  1  liM  >N  III! j;  111 II • ill! iiii |j I ' li ii li i i j Hi | i 1 T!i 1 | i Hi n ; l! i. i1r f i-|: ii-iLI:j M-! li ':'! . L i " li i i ill! li N ill : i-i-j ii Hi 1•' ;It:: |:| -j. Hi' ! iii uli ;11i M i mIII;i IN: I j- ii ':} |:i r Mil IMi N i l l-i-lill! i IM ; i 1i-l 11 j -i-l ' : * ! 'J\ .r •li L MI Ml i-l li-ii Il' •! II- Mr !'ii •' i i n i l III i i •1 •ill Mil Nil MM jii i: :.i ill! i: i-l lii-l Nil 1. i i-i !:i.i 11 ! l liii I'-;!-!'-i i i 11 j i !'! \v I i. i- : 1Hi I •: 1 .ii. II iuj i-l t i 1 | 1 i l l i ill! ':! Iii! Mi Li-ii ! i-|:| I-" l ! i' i li iI- •i i ill iM M i I I I li ;.; i i l l ! INN N i l •f iiii iiii !- i I it I-I M : 11 i l l MM i MI i. » w sir mi -] ' i iii I|• ; if ^ i-l 1 i-ii *4 $1 & i i i 11i• i i:;: ill i I i Mil Ji i ,:i:i 1 illi Nil i 11 i ! I iiii I liii i'l. I Hi- |.l 1 i" Li i iiii i ii i i-fi ill! TTT. lil % iii ill1 jjil ilil liii •"li 11:11 iii! III! ii 1! !; j.j Hi i H i i ill" •ill iiii i'li i i-i iiii ilil Hi! il IIII ill! i i: j 1 1 : I hit i ; ; i i'l j ; • M i j I Hli i-i i Ipl III! lll-H iiii i-lii i-i! Iiii 1 I t : II j_ Iii J i 11- Ui;iii j i t i T ii iii-i-i'l. ;:1- l-.I•'ii! il : U M M i IHI :• i i 1 1 ili i-t iTTr lM£ 1 oJoj i-iIlil iiii l: 00 7f lio'i-l : I 10 io-iiiH •Mr3018 MM i HI HI* 1 ! iiiii l •; -.:. :: I" Tip ii { " jij:? 'ill Iii -V  '  [  1  Ijj  i;  :  1  ;  |  ;  1  ;  1  ;  1  :  u  :  F i g u r e 11.  1  1  :  Top and bottom curves show slow wave and weighted mean. Arrows show time correspondence between the two c u r v e s . ( P o s i t i v i t y i s upwards). a : c a t //003, r e d s t i m u l u s , i n t e n s i t y : 16 u n i t s b : c a t #007, w h i t e s t i m u l u s , i n t e n s i t y : 0.1 u n i t  ho  F i g u r e 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: s t i m u l u s i n t e n s i t y a t 10~3, 10~2 and 1 u n i t .  °  F i g u r e 13.  Slow wave and weighted mean, arrows show time correspondence, p o s i t i v i t y a,b: c a t #013, ON and OFF r e s p o n s e s . c: c a t #009, s t i m u l u s i n t e n s i t y : 16 u n i t s d: c a t #003, b l u e s t i m u l u s , i n t e n s i t y : 16 u n i t s .  upwards. M M  22'  .VIII.  RELATIONSHIP BETOEEN THE  We charge  ( o r the weighted  mean) i s a r e p r e s e n t a t i o n o f the number o f  between the slow wave and adequate.  o f the m a c r o e l e c t r o d e .  the weighted  I f a unique  mean  The h i g h  firings  similarity  mean i n d i c a t e s t h a t t h i s r e p r e s e n t a t i o n  I t would b e then o f i n t e r e s t  the slow wave to the weighted 1.  THE WEIGHTED MEAN  have seen i n c h a p t e r VI t h a t the amplitude of the s p i k e d i s -  o c c u r r i n g i n the neighbourhood  is  SLOW WAVE AND  f o r two  to f i n d  the r e l a t i o n s h i p  linking  reasons:  r e l a t i o n s h i p i s found,  the slow wave r e c o r d e d by  a m a c r o e l e c t r o d e c o u l d be regarded as a measure of the number o f f i r i n g s i n the neighbourhood 2.  o f the e l e c t r o d e .  T h i s r e l a t i o n s h i p i n the form o f a t r a n s f e r f u n c t i o n would  p r o v i d e i n f o r m a t i o n on the frequency spectrum which make up  o f the i n d i v i d u a l  signals  the m a c r o p o t e n t i a l s .  A frequency response experiment would have been o f g r e a t Such an approach  demands,.however a s i n u s o i d a l s t i m u l u s g e n e r a t o r as w e l l }  as a g r e a t d e a l o f e x p e r i m e n t a t i o n . transfer  function relating  Computing C e n t r e .  the two  Rather, i t was  d e c i d e d to f i n d  A c c o r d i n g to c u r r e n t procedures  (16, 17, 18), the d a t a used.  transforms o b t a i n e d were i r r e g u l a r even though  t r e n d c o u l d be seen.  To s h o r t e n the p l o t t i n g  a definite  time, the d a t a f o r f r e q u e n c i e s  h i g h e r than 64 H e r t z were averaged o v e r 2, 4, 8 and 16 p o i n t s . curves were drawn by hand through p o i n t s would l i e between them. the weighted  mean.  the  c u r v e s , u s i n g s t a n d a r d programs o f the  were s c a l e d to a zero mean and a c o s i n e b e l l window was The  utility.  Then  two  the p o i n t s so that the m a j o r i t y o f the  T h i s was  done f o r both the slow wave and  23  »  Two r a t i o s were taken: (1)  the r a t i o  B  *  ^  "<«. \  o f the h i g h e r curve (A) o f the  slow wave s p e c t r o g r a m to the lower curve (D) of  «  Slow wave  the weighted mean spectrogram.  Weighted mean (2)  the r a t i o o f the lower curve (B) o f the slow wave s p e c t r o g r a m to the h i g h e r curve (C) of  the weighted mean spectrogram.  Slow wave  -ml  .  L*' '\  D Weighted mean  The two curves o b t a i n e d were drawn on a t h i r d graph as the upper and lower l i m i t s o f the d e s i r e d t r a n s f e r f u n c t i o n r e l a t i n g  the slow wave to the  weighted mean.  A/D  B/C  Spectrogram o f the T r a n s f e r Function  As can be seen i n f i g u r e s 14, 15 and 16,  the t r a n s f e r  o b t a i n e d from the 5 c a t s and the 11 experiments are s i m i l a r . more so f o r the same c a t .  The  functions  They are  t r a n s f e r f u n c t i o n s r e a c h a peak around  40  H e r t z and drop a t h i g h e r f r e q u e n c i e s a t a r a t e c l o s e to 6 db p e r o c t a v e . Some curves seem to drop a t the lowest f r e q u e n c i e s , but t h i s may the a m p l i f i e r low-frequency c u t - o f f o f 5 H e r t z .  be due  to  25  F i g u r e 14.  Cat #013, ON and OFF response. Amplitude o f the t r a n s f e r f u n c t i o n r e l a t i n g the slow wave t o the weighted mean. The two l i n e s d e s c r i b i n g each t r a n s f e r f u n c t i o n d e f i n e the e r r o r l i m i t s . The curves were n o r m a l i z e d so t h a t the maximum v a l u e would be 0 db.  -II  1  •i  If-  1  4-  F i g u r e 15.  2,4,8  1  (averaged) FREQUENCY 1  l£  1  Same as f i g u r e and #003 ;  (Hx} 1  64  1  1  256  1  1  loat  14, b u t w i t h c a t s #007  27  28  IX. Signals recorded were s t u d i e d .  CONCLUSIONS  by m a c r o e l e c t r o d e from the c a t ' s o p t i c t r a c t  I t appears t h a t  they can be decomposed i n t o two components:  a slow wave and f a s t v a r i a t i o n s ( s p i k e The  amplitude o f the s p i k e d i s c h a r g e  the slow wave. preliminary  discharge).  This holds  experiment  i s c l o s e l y c o r r e l a t e d with  f o r a great v a r i e t y of stimulus  (not r e p o r t e d  conditions; a  here because o f u n c e r t a i n  experimental  c o n d i t i o n s ) seems t o i n d i c a t e t h a t t h i s i s a l s o t r u e f o r the l a t e r a l  gen-  i c u l a t e body. T h i s suggests t h a t , c o n t r a r y depend p r i m a r i l y on nerve f i r i n g s l e a s t i n the o p t i c t r a c t . of the nerve f i r i n g .  to c u r r e n t views, the m a c r o p o t e n t i a l 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  T h i s a l s o g i v e s some i n f o r m a t i o n  The f a c t  about the shape  t h a t a h i g h number o f nerve f i r i n g s  corresponds  to a p o s i t i v e peak o f the slow wave, and a s m a l l number to a minimum i n t h e slow wave, i m p l i e s with  t h a t the nerve f i r i n g  i n the o p t i c t r a c t  a p o s i t i v e o v e r s h o o t f o l l o w i n g t h e n e r v e impulse.  i s associated  Because sharp peaks  c o r r e s p o n d i n t h e slow wave and the w e i g h t e d mean w i t h i n 4 o r 5 ms,  this  p o s i t i v e o v e r s h o o t w i l l have to f o l l o w the nerve impulse w i t h i n 4 o r 5 ms. The  e x i s t e n c e o f t h i s b r i e f p o s i t i v e o v e r s h o o t i s i n c o n t r a d i c t i o n w i t h the  commonly a c c e p t e d This discrepancy  shape f o r the a c t i o n p o t e n t i a l i l l u s t r a t e d may be due to the f a c t t h a t m i c r o e l e c t r o d e s  i n f i g u r e 1. which a r e used  to study s i n g l e u n i t f i r i n g s have a d i f f e r e n t impedance than m a c r o e l e c t r o d e s . Because i t was b e l i e v e d t h a t the weighted mean was an adequate r e p r e s e n t a t i o n o f the number o f f i r i n g s , wave and the weighted mean was sought. to get i n f o r m a t i o n  T h i s r e l a t i o n s h i p would p e r m i t us  on the s p i k e d i s c h a r g e  r e l a t i o n s h i p was o b t a i n e d range o f s t i m u l u s  the r e l a t i o n s h i p between the slow  directly  from the slow wave.  This  i n the form o f a t r a n s f e r f u n c t i o n and f o r t h e  c o n d i t i o n s used,appeared to be the same w i t h i n the l i m i t s  of uncertainty inherent  t o the t e c h n i q u e .  APPENDIX A DESCRIPTION OF THE AMPLITUDE  The a m p l i t u d e set voltages,  DISCRIMINATOR  d i s c r i m i n a t o r compares the i n p u t waveform w i t h two  and  and g i v e s out a s t a n d a r d p u l s e (5 v o l t s ,  d u r a t i o n ) whenever a peak o c c u r s whose amplitude i s between and  36 us i n  and V £ •  d e f i n e the b o u n d a r i e s o f the window.  2 ~  waveform a n a l y s e d  5 volts output o f amplitude discriminator 36 us Figure A . l .  O p e r a t i o n o f the amplitude d i s c r i m i n a t o r V2 and V^: upper and lower b o u n d a r i e s of, th?. window. P  It  1' 2' 3'V P  P  peaks o f the waveform a n a l y s e d  can be n o t i c e d i n F i g u r e A . l that  the amplitude  discriminator  does n o t d e l i v e r a p u l s e f o r peaks p^ and p^,which a r e below the lower t h r e s h o l d , n o r f o r peak P2,which  i s above the upper t h r e s h o l d .  -generates an output and t h e p u l s e i s produced  Only p^  a t the c r o s s i n g of the  waveform w i t h the lower boundary o f the window.  30  APPENDIX B LIST OF EXPERIMENTS  Stimulus description -3 10  unit -3  Cat  Number o f averages  500 ms  #007  512  0.0  1 sec  #007  310  0.0  Length o f record  Lowest window used  Upper c u t - o f f frequency o f spike f i l t e r 10 KHz  4  KHz  10  unit  500 ms  #007  512  0.0  10 KHz  10  unit  500 ms  #007  512  0.0  10 KHz  unit  500 ms  #007  512  500 ms  #007  384  units  500 ms  #009  1024  16 u n i t s blue f i l t e r  500 ms  #003  512  500 ms  #003  10 unit 10 Hz repeti t i o n rate  100 ms  ON response OFF  10  - 1  1  unit  0.25 v . 0.0  10 KHz 10 KHz  2,4,8 u n i ts (averaged) 16  16 u n i t s red f i l t e r  1.25 v.  4 KHz  0.0  4 KHz  512  0.0  4 KHz  #A3  256  0.0  4 KHz  500 ms  #013  512  0.0  4  500 ms  #013  256  0.0  4  response  4  KHz  KHz  APPENDIX C CHARACTERICS OF THE AMPLIFIER  Time s h i f t v s . f r e q u e n c y  Frequency  Amplitude  (Hertz)  Time s h i f t  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  (ms)  v s . 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 o f the lower c u t - o f f frequency o f the a m p l i f i c a t i o n system was s i m u l a t e d on the IBM 360.  S i n c e the slow wave was h i g h - p a s s e d a t  5 H e r t z , we h i g h - p a s s e d the weighted mean a l s o a t 5 H e r t z . by t a k i n g the c o n v o l u t i o n o f the weighted c o r r e s p o n d i n g to the t r a n s f e r f u n c t i o n  T h i s was done  mean by.the impulse  _  .  response  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 t h a t the two curves now correspond more c l o s e l y  i n time and i n amplitude.  33  F i g u r e A.2.  E f f e c t o f the lower c u t - o f f frequency o f 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 c u r v e s , the lower one d i s p l a y s the curves a f t e r the weighted mean had been h i g h - p a s s e d a t 5 Hertz. I n b o t h 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 N e u r o p h y s i o l o g y " ,  New  York, J . W i l e y ,  1965.  2.  Hubel, D. 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