{"title": "Neural Network Simulation of Somatosensory Representational Plasticity", "book": "Advances in Neural Information Processing Systems", "page_first": 52, "page_last": 59, "abstract": null, "full_text": "52 \n\nGrajski and Merzenich \n\nNeural  Network Simulation \n\nof \n\nSomatosensory Representational  Plasticity \n\nKamil A. Grajski \nFord Aerospace \n\nSan Jose,  CA 95161-9041 \nkamil@wd11.fac.ford.com \n\nMichael M. Merzenich \nColeman  Laboratories \n\nUC San Francisco \n\nSan Francisco, CA 94143 \n\nABSTRACT \n\nThe  brain  represents  the  skin  surface  as  a  topographic  map  in  the \nsomatosensory  cortex.  This  map  has  been  shown  experimentally  to \nbe  modifiable  in  a  use-dependent  fashion \nthroughout  life.  We \npresent  a  neural  network  simulation  of  the  competitive  dynamics \nunderlying  this  cortical  plasticity  by  detailed  analysis  of  receptive \nfield  properties  of  model  neurons  during  simulations  of  skin  co(cid:173)\nactivation, cortical  lesion,  digit amputation and nerve  section. \n\n1  INTRODUCTION \nPlasticity  of adult  somatosensory  cortical  maps  has  been  demonstrated  experimentally \nin  a  variety  of maps  and  species  (Kass,  et al.,  1983;  Wall,  1988).  This  report  focuses \non modelling  primary somatosensory cortical  plasticity in  the adult monkey. \nWe  model  the  long-term  consequences  of  four  specific  experiments,  taken  in  pairs. \nWith  the  first  pair,  behaviorally controlled  stimulation of restricted  skin  surfaces  (Jen(cid:173)\nkins,  et  al.,  1990)  and  induced  cortical  lesions  (Jenkins  and  Merzenich,  1987),  we \ndemonstrate  that  Hebbian-type  dynamics  is  sufficient  to  account  for  the  inverse  rela(cid:173)\ntionship  between  cortical  magnification  (area  of cortical  map  representing  a  unit  area \nof skin)  and  receptive  field  size  (skin  surface which  when  stimulated excites a  cortical \nunit)  (Sur, et al.,  1980;  Grajski  and  Merzenich,  1990).  These results  are obtained  with \nseveral  variations  of  the  basic  model.  We  conclude  that  relying  solely  on  cortical \nmagnification  and  receptive  field  size  will  not  disambiguate  the  contributions  of each \nof the  myriad  circuits  known  to  occur in  the  brain.  With  the  second pair,  digit ampu(cid:173)\ntation  (Merzenich,  et al.,  1984)  and  peripheral  nerve  cut  (without  regeneration)  (Mer(cid:173)\nzenich,  ct al.,  1983),  we  explore  the  role  of local  excitatory  connections  in  the  model \n\n\fNeural Network Simulation of Somatosensory Representational Plasticity \n\nS3 \n\ncortex  (Grajski,  submitted). \nPrevious  models  have  focused  on  the  self-organization  of topographic  maps  in  general \n(Willshaw  and  von  der  Malsburg,  1976;  Takeuchi  and  Amari,  1979;  Kohonen,  1982; \namong  others).  Ritter  and  Schulten  (1986)  specifically  addressed  somatosensory  plas(cid:173)\nticity  using  a variant  of Kohonen's self-organizing  mapping.  Recently,  Pearson,  et  al., \n(1987),  using  the  framework  of  the  Group  Selection  Hypothesis,  have  also  modelled \naspects  of nonnal and reorganized  somatosensory plasticity. \nElements  of the  present  study  have  been  published  elsewhere  (Grajski  and  Merzenich, \n1990). \n\n2  THE MODEL \n\n2.1  ARCIDTECTURE \nThe  network  consists  of three  heirarchically  organized  two-dimensional  layers  shown \nin  Figure  1A. \n\nCortical Layer \n\nSubcortical Layer \n\nSkin Layer \n.... \n\na.) \n\nb.) \n\nFigure 1:  Network architecture. \n\nThe  divergence  of projections  from  a  single  skin  site  to  subcortex  (SC)  and  its  subse(cid:173)\nquent  projection  to  cortex  (C)  is  shown at left:  Skin  (S)  to  SC,  5 x 5;  SC  to  C,  7 x 7. \nS  is  \"partitioned\"  into  three  15  x  5  \"digits\"  Left,  Center  and  Right.  The  standard  S \nstimulus  used  in  all  simulations  is  shown  lying  on  digit Left.  The  projection  from  C \nto  SC  E  and  I  cells  is  shown  at right.  Each  node  in  the  SC  and  C layers  contains  an \nexcitatory  (E)  and  inhibitory  cell  (I)  as  shown  in  Figure  lB.  In  C,  each  E  cell  forms \nexcitatory  connections  with  a  5 x  5 patch  of I  cells;  each  I  cell  fonns  inhibitory  con-\n\n\f54 \n\nGrajski and Merzenich \n\nnections  with  a  7  x  7 path  of E cells.  In  se,  these  connections  are  3  x  3  and  5  x  5, \nrespectively.  In  addition,  in  e only, E cells form  excitatory connections with a  5 by 5 \npatch  of E  cells.  The  spatial  relationship  of E  and  I  cell  projections  for  the  central \nnode is  shown at left (C  E  to  E  shown in  light gray, e I  to  E shown in  black). \n\n2.2  DYNAMICS \nThe  model  neuron  is  the  same  for  all  E  and  I  cells:  an  RC-time  constant  membrane \nwhich  is  depolarized and  (additively)  hyperpolarized by  linearly  weighted connections: \n\n'\"  , \n\nu,~,E  =  -'t  u~,E + ~v~C,Ew~,E:SC,E + ~v9,Ew~,E:C,E _  ~v9Jw~,E:CJ \n~ J \ni i i  \nU\u00b7~J  =  -A'  u~J + ~v9,Ew~J:C,E \n, \n\n~ J \n\n~ J \n\n-\"\"\" \n\n'J \n\n'J \n\n'J \n\n&J \n\n~ J \nj \n\nu,~C,E  =  -t  u~C,E + ~o~w~C,E:S + ~v9,Ew~C,E:C,E _  ~v~C,Ew~C,E:SCJ \n\n'\"  , \n\n~ J \ni i i  \n\n~ J \n\n~ J \n\n'J \n\n'J \n\n&J \n\nU\u00b7~CJ  - -t  u~CJ + ~v~C,Ew~CJ:SC,E + ~v9,Ew~CJ:C,E _  ~v~C,Ew~C,E:SCJ \n, \n\n~ J \ni i i  \n\n~ J \n\n~ J \n\n\"\" \n\n'J \n\n'J \n\n'J \n\n-\n\nut Y  - membrane  potential  for  unit  i  of type  Y on  layer  X; vt ,f - firing  rate  for  unit i \nof type  Y on  layer  X; of - skin  units  are  OFF (=0)  or  ON  (=1);  tIft  - membrane  time \nconstant  (with  respect  to  unit  time);  wrsr(x,y):preltY)  - connection  to  unit  i  of  post(cid:173)\nsynaptic  type  y  on  postsynaptic  layer  x from  units  of presynaptic  type  Y on  presynap(cid:173)\ntic  layer  X.  Each  summation  tenn  is  normalized  by  the  number  of incoming  connec(cid:173)\ntions  (corrected  for  planar  boundary  conditions)  contributing  to  the  term.  Each  unit \nconverts  membrane  potential  to  a  continuous-valued  output  value  Vi  via  a  sigmoidal \nfunction  representing an average firing  rate  @ = 4.0): \n\n1 \n\n1 \n2(l+tanh(~(ui-2 ))) \no \n\nui~\u00b702, \n\nui<0.02 \n\nSYNAPTIC PLASTICITY \n\n2.3 \nSynaptic  strength  is  modified  in  three  ways:  a.)  activity-dependent  change;  b.)  passive \ndecay;  and  c.)  normalization.  Activity-dependent and  passive  decay  tenns  are  as  fol(cid:173)\nlows: \n\nwii  - connection  from  cell  j  to  cell  i;  t.l}'11 =0.01 tIft =0.005  - time  constant  for  passive \nsynaptic  decay;  a.=O.05,  the  maximum  activity-dependent  step change;  Vi,Vi  - pre- and \npost-synaptic  output  values,  respectively.  Further modification  occurs  by a multiplica(cid:173)\ntive  normalization  performed  over  the  incoming  connections  for  each  cell.  The  nor(cid:173)\nmalization is such that the  summed total  strength of incoming connections  is R: \n\n\fNeural Network Simulation of Somatosensory Representational Plasticity \n\n5S \n\n1 \n-\n, \nN . \n\nl: \u00b7w\u00b7 \u00b7  =  R \n'J \n\n'1 \n\nNi  - number  of incoming  connections  for  cell  i;  Wij  - connection from  cell  j  to  cell  i; \nR  = 2.0  - the  total  resource available  to  cell  i for  redistribution  over its  incoming  con(cid:173)\nnections. \n\n2.4  MEASURING  CORTICAL  MAGNIFICATION,  RECEPTIVE  FIELD \n\nAREA \n\nCortical  magnification  is  measured  by  \"mapping\"  the  network,  e.g.,  noting  which  3x3 \nskin  patch  most  strongly  drives  each  cortical  E  cell.  The  number  of cortical  nodes \ndriven  maximally  by  the  same  skin  site  is  the  cortical  magnification  for  that  skin  site. \nReceptive  field  size  for  a  C  (SC)  layer  E  cell  is  estimated by  stimulating  all  possible \n3x3  skin patches  (169)  and  noting  the  peak response.  Receptive  field  size  is  defined as \nthe number of 3x3  skin patches which  drive  the  unit at ~50% of its peak response. \n\n3  SIMULATIONS \n\n3.1 \n\nFORMATION  OF  THE  TOPOGRAPHIC  MAP  ENTAILS  REFINEMENT \nOF SYNAPTIC PATTERNING \n\nThe  location  of  individual  connections  is  fixed  by  topographic  projection;  initial \nstrengths  are  drawn  from  a  Gaussian  distribution  (JJ.  =  2.0,  (12 = 0.2).  Standard-sized \nskin  patches  are  stimulated  in  random  sequence  with  no  double-digit  stimulation. \n(Mapping  includes  tests  for  double-digit receptive  fields.)  For each  patch,  the  network \nis  allowed  to reach  steady-state  while  the  plasticity rule  is  ON.  Synaptic  strengths  are \nthen  renonnalized.  Refinement  continues  until  two  conditions  are  met:  a.)  fewer  than \n5%  of all  E cells change  their receptive  field  location;  and b.) receptive  field  areas  (us(cid:173)\ning  the  50%  criterion)  change  by  no  more  than  \u00b11  unit  area  for  95%  of E  cells.  (See \nFigures 2 and 3 in  Merzenich  and Grajski,  1990; Grajski, submitted ). \n\n3.2  RESTRICTED  SKIN  STIMULATION  GIVES  INCREASED  MAGNIFICA-\n\nTION, DECREASED RECEPTIVE FIELD SIZE \n\nJenkins,  et aI.,  (1990)  describe  a  behavioral  experiment  which  leads  to  cortical  soma(cid:173)\ntotopic  reorganization.  Monkeys  are  trained  to  maintain  contact  with  a  rotating  disk \nsituated  such  that  only  the  tips  of one  or  two  of their  longest  digits  are  stimulated. \nMonkeys  are  required  to  maintain  this  contact  for  a  specified  period  of time  in  order \nto  receive  food  reward.  Comparison  of pre- and  post-stimulation  maps  (or  the  latter \nwith  maps  obtained  after  varying  periods  without disk  stimulation)  reveal  up  to  nearly \n3-fold  differences  in  cortical  magnification  and  reduction  in  receptive  field  size  for \nstimulated skin. \nWe  simulate  the  above  experiment  by  extending  the  refinement  process  described \nabove,  but  with  the  probability  of stimulating  a  restricted  skin  region  increased  5: 1. \n(See  Grajski  and  Merzenich  (1990),  Figure  4.)  Figure  2  illustrates  the  change  in  size \n(left)  and synaptic patterning  (right)  for a  single representative cortical  receptive  field. \n\n\f56 \n\nGrajski and Merzenich \n\nFigure 2:  Representative co-activation  induced receptive  field changes. \n\nIncoming Synaptic Strengths \n\nSkin to Subcortex \n\nSubcortex  to Cortex \n\nCortical RF \n\nPost Co(cid:173)\nActivation \n\nPre Co(cid:173)\nActivation \n\na.) \n\nb.) \n\nlow \n\nhigh \n\n3.3  AN  INDUCED,  FOCAL  CORTICAL  LESIONS  GIVES  DECREASED \n\nMAGNIFICATION, INCREASED RECEPTIVE FIELD SIZE \n\nThe  inverse  magnification  rule  predicts  that  a  decrease  in  cortical  magnification  is  ac(cid:173)\ncompanied  by  an  increase  in  receptive  field  areas.  Jenkins,  et  al.,  (l987)  confirmed \nthis  hypothesis  by  inducing  focal  cortical  lesions  in  the  representation  of  restricted \nhand  surfaces,  e.g.  a  single  digit.  Changes  included:  a.)  a re-emergence  of a represen(cid:173)\ntation  of the skin  fonnedy  represented  in  the  now  lesioned  zone in  the intact surround(cid:173)\ning  cortex;  b.)  the  new  representation  is  at  the  expense  of cortical  magnification  of \nskin  originally  represented  in  those  regions;  so  that c.)  large  regions  of the  map  con(cid:173)\ntain  neurons  with abnonnally large receptive  fields. \nWe  simulate  this  experiment by  eliminating  the  incoming  and outgoing connections of \nthe  cortical  layer  region  representing  the  middle  digit  The  refinement  process \ndescribed  above  is  continued  under  these  new  conditions  until  topographic  map  and \nreceptive  field  size  measures  converge.  The  re-emergence  of  representation  and \nchanges  in  distributions  of receptive  field  areas  are  shown  in  Grajski  and  Merzenich, \n(1990)  Figure  5.  Figure  3  below  illustrates  the  change  in  size  and  location  of  a \nrepresentative (sub)  cortical receptive  field. \n\n3.4  SEVERAL MODEL VARIANTS REPRODUCE THE INVERSE MAGNIFI-\n\nCATION RULE \n\nRepeating  the  above  simulations  using  networks  with  no  descending  projections  or us(cid:173)\ning  networks  with  no  descending  and  no  cortical  mutual  exciatation,  yields  largely \nnonnal  topography  and  co-activation  results.  Restricting  plasticity  to  excitatory  path(cid:173)\nways  alone  also  yields  qualitatively  similar results.  (Studies  with  a  two-layer  network \n\n\fNeural Network Simulation of Somatosensory Representational Plasticity \n\n57 \n\nyield  qualitatively  similar results.)  Thus,  the  refinement  and  co-activation  experiments \nalone  are  insufficient  to  discriminate  fundamental  differences  between  network  vari(cid:173)\nants. \n\nFigure 3:  Representative cortical  lesion induced receptive  field  changes. \n\nPre-Cortical Lesion  Post-Cortical Lesion \n\nCortical \nReceptive \nField \n\nSub-cortical \nReceptive \nField \n\n3.5  MUTUALLY  EXCITATORY  LOCAL  CORTICAL  CONNECTIONS  MAY \nBE CRITICAL FOR  SIMULATING  EFFECTS  OF DIGIT  AMPUTATION \nAND  NERVE SECTION \n\nThe  role  of lateral  excitation  in  the  cortical  layer  is  made  clearer through  simulations \nof nerve  section  and  digit  amputation  experiments  (Merzenich,  et  al.,  1983;  Merzen(cid:173)\nich,  et at. 1984;  see  also Wall,  1988).  The  feature  of interest  here  is  the cortical  dis(cid:173)\ntance  over  which  reorganization  is  observed.  Following  cessation  of peripheral  input \nfrom  digit  3,  for  example.  the  surrounding representations  (digits  2 and  4)  expand  into \nthe  now  silenced  zone.  Not  only  expansion  is  observed.  Neurons  in  the  surrounding \nrepresentations  up  to  several  l00's  of  microns  distant  from  the  silenced  zone  shift \ntheir receptive  fields.  The shift is  such  that  the  receptive  field  covers  skin  sites  closer \nto  the  silenced skin. \nThe  deafferentation  experiment is  simulated by  eliminating the  connection between  the \nskin  layer  CENTER  digit  (central  1/3)  and  SC  layers  and  then  proceeding  with \nrefinement  with  the  usual  convergence  checks.  Simulations  are  run  for  three  network \narchitectures.  The  \"full\"  model  is  that  described  above.  Two  other  models  strip  the \ndescending and both  descending and lateral excitatory connections, respectively. \nFigure 4 shows features  of reorganization:  the conversion  of initially silenced  zones, or \nrefinement  of initially  large,  low  amplitude  fields  to  normal-like  fields  (a-c).  Impor(cid:173)\ntantly,  the  receptive  field  farthest  away  from  the  initially  silenced  representation  (d) \nundergoes  a  shift  towards  the  deafferented  skin.  The  shift  is  comprised  of a  transla(cid:173)\ntion  in  the  receptive  field  peak  location  as  well  as an  increase  (below  the  50%  ampli(cid:173)\ntude  threshold.  but increases  range  25  - 200%)  in  the  regions surrounding the peak and \nfacing  the  silenced  cortical  zone  (shown  in  light  shading).  Only  the  \"full\"  model \nevolves  expanded and  shifted  representations.  These  results  are  preliminary  in  that no \nparameter adjustments  are made  in  the  other networks  to  coax  a result.  It may  simply \nbe  a  matter  of  not  enough  excitation  in  the  other  cases.  Nevertheless,  these  results \nshow  that local cortical excitation can contribute critical activity for reorganization. \n\n\f58 \n\nGrajski and Merzenich \n\nFigure 4:  Summary of immediate and long-term  post-amputation effects. \nPost-amputation \n\nPost-amputation \n\nNormal \n\nImmediate  Long-term \n\na\u00b7)LJDO \nb\u00b7)~[]EJ \n\nNormal \n\nImmediate  Long-term \n\nc\u00b7)O[]O \nd\u00b7)DD~ \n\n4  CONCLUSION \nWe  have  shown  that a.)  Hebbian-type  dynamics  is sufficient to  account  for  the  quanti(cid:173)\ntative  inverse  relationship  between  cortical  magnification  and  receptive  field  size;  and \nb.)  cortical  magnification  and  receptive  field  size  alone  are  insufficient  to  distinguish \nbetween model variants. \nAre  these  results  just  \"so  much  biological  detail?\"  No.  The  inverse  magnification(cid:173)\nreceptive  field  rule  applies  nearly  universally  in  (sub)cortical  topographic  maps;  it \nreflects  a  fundamental  principle  of brain  organization.  For  instance,  experiments  re(cid:173)\nvealing  the  operation  of mechanisms  possibly  similar  to  those  modelled  above  have \nbeen  observed in  the  visual system.  Wurtz,  et al.,  (1990)  have observed that following \nchemically  induced  focal  lesions  in  visual  area  MT,  surviving  neurons'  visual  recep(cid:173)\ntive  field  area  increased.  For  a  review  of use-dependent  receptive  field  plasticity  in \nthe auditory  system  see  Weinberger, et al.,  (1990). \nResearch  in  computational  neuroscience  has  long  drawn  on  principles  of topographic \norganization.  Recent  advances  include  those  by  Linsker  (1989),  providing  a  theoreti(cid:173)\ncal  (optimization)  framework  for  map  formation  and those  studies  linking  concepts  re(cid:173)\nlated  to  localized  receptive  fields  with  adaptive  nets  (Moody  and  Darken,  1989;  see \nBarron,  this  volume).  The  experimental  and  modelling  issues  discussed  here  offer  an \nopportunity  to  sustain  and further  enhance  the  synergy inherent in  this  area  of compu(cid:173)\ntational neuroscience. \n\nAcknowldegements \n\n4.0.1 \nThis  research  supported  by  NIH  grants  (to  MMM)  NSI0414  and  GM07449,  Hearing \nResearch  Inc.,  the  Coleman  Fund  and  the  San  Diego  Supercomputer  Center.  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On  the  stationary  state  of  Kohonen's  self(cid:173)\n\n\f", "award": [], "sourceid": 287, "authors": [{"given_name": "Kamil", "family_name": "Grajski", "institution": null}, {"given_name": "Michael", "family_name": "Merzenich", "institution": null}]}