{"title": "Information Processing to Create Eye Movements", "book": "Advances in Neural Information Processing Systems", "page_first": 351, "page_last": 355, "abstract": null, "full_text": "Information Processing  to  Create Eye Movements \n\nDavid A.  Robinson \n\nDepartments of Ophthalmology \nand Biomedical Engineering \nThe Johns Hopkins University \n\nSchool of Medicine \nBaltimore,  MD 21205 \n\nABSTRACT \n\nBecause  eye  muscles  never  cocontract  and  do  not deal  with  external \nloads,  one can write an equation that relates  motoneuron firing rate to \neye  position and  velocity  - a  very  uncommon  situation  in  the  CNS. \nThe semicircular canals  transduce head velocity in a linear manner by \nusing  a  high  background  discharge  rate,  imparting  linearity  to  the \npremotor  circuits  that  generate  eye  movements.  This  has  allowed \ndeducing  some  of the  signal  processing  involved,  including  a  neural \nnetwork that integrates.  These  ideas  are  often  summarized  by block \ndiagrams.  Unfortunately,  they  are  of little  value  in  describing  the \nbehavior  of single  neurons  - a  fmding  supported  by  neural  network \nmodels. \n\n1  INTRODUCTION \nThe neural networks in our studies are quite simple.  They differ from other applications \nin that they  attempt  to  model  real  neural  subdivisions of the oculomotor system which \nhave  been  extensively  studied  with  microelectrodes.  Thus,  we  can  ask  the  extent  to \nwhich neural networks succeed in describing the behavior of hidden units that is already \nknown.  A  major  benefit  of using  neural  networks  in  the  oculomotor  system  is  to \nillustrate  clearly  the  shortcomings  of block  diagram  models  which  tell  one  very  little \nabout  what  one  may  expect  if one  pokes  a  microelectrode  inside  one  of its  boxes. \nConversely, single unit behavior is so loosely coupled to system behavior that,  although \nthe  simplicity of the oculomotor system allows  the  relationships to be understood,  one \nfears  that, in a more complicated system,  the behavior of single (hidden)  units will give \n\n351 \n\n\f352 \n\nRobinson \n\nlittle information about what a system is trying to do, never mind how. \n\n2  SIMPLIFICA TIONS  IN OCUWMOTOR CONTROL \nBecause it is impossible to cocontract our eye muscles and because their viscoelastic load \nnever varies,  it is possible to write an equation that uniquely relates  the discharge rates \nof their motoneurons and the position of the load (eye position).  This cannot be done in \nthe case of,  for example, limb muscles.  Moreover, this system is well-approximated by \na first-order,  linear differential equation.  Linearity comes about from  the design of the \nsemicircular canals,  the origin of the vestibulo-ocular reflex (VOR).  This reflex creates \neye  movements  that compensate  for  head  movements  to  stabilize the  eyes  in space  for \nclear  vision.  The  canals  primarily  transduce  head  velocity,  neurally  encoded  into  the \ndischarge  rates  of  its  afferents.  These  rates  modulate  above  and  below  a  high \nbackground  rate  (typically  100 spikes/sec)  that keeps  them well  away  from  cutoff and \nprovides a wide linear range.  The core of this reflex is only three neurons long and the \ncanals impose their properties - linear modulation around a high background rate - onto \nall down-stream neurons including the motoneurons. \n\nIn addition  to  linearity,  the  functions  of the  various  oculomotor subsystems  are  clear. \nThere is no messy stretch reflex,  the muscle  fibers are straight and parallel, and there is \nonly  one  \"joint.\"  All  these  features  combine  to  help  us  understand  the  premotor \norganization of oculomotor signals in the  caudal  pons,  a system that has enjoyed  much \nblock-diagram modelling and now,  neural  network modelling. \n\n3  DISTRIBUTION OF OCULOMOTOR SIGNAlS \nThe  first  application  of neural  networks  to  the  oculomotor  system  was  a  study  of \nAnastasio and Robinson (1989).  The problem addressed concerned  the convergence of \ndiverse  oculomotor  signals  in  the  caudal  pons.  There  are  three  major  oculomotor \nsubsystems:  the VOR;  the saccadic system that causes the eyes to jump rapidly from one \ntarget to another;  and the  smooth pursuit system that allows the eyes  to  track a moving \ntarget.  Each  appears  in  the  caudal  pons  as  a  veloci.ty  command.  The canals,  via the \nvestibular nuclei, provide an eye-velocity command, Ev,  for compensatory vestibular eye \n'Povements.  Burst neurons  in  the  nearby pontine reticular formation  provide a signal, \nEat  for the desired eye velocity for a saccade.  Purkinje cells in the cerebellum carry an \neye-velocity signal, Ep'  for pursuit eye movements.  Thus, three eye-velocity commands \nconverge in the region of the motoneurons. \n\nWhen one records  from cells in this region one fmds a discharge rate R of: \n\n. \nR.=.. Ro  + rp  Ep  + rvEv  + r.E. \n\n. \n\n. \n\n(1) \n\nwhere  Ro  is  the  high  background  rate  previously  described  and  rp,  rv  and  r.  are \ncoefficients that can assume any values, in a seemingly random way,  for anyone neuron \n(e.g. Tomlinson and Robinson,  1984).  Now a block-diagram model need show only the \nthree  velocity  commands  converging  on  the  motoneurons  and  would  not  suggest  the \nexistence of neurons  carrying complicated  signals like that of Equ.  (1).  On  the  other \nhand, such behavior has a nice,  messy,  biological flavor.  Somehow, it wOl;lld ~m oqd \nif such signals did not exist.  What is clearly happening is that the signals Ep,  Ev  and E. \n\n\fInformation Processing  to Create Eye Movements \n\n353 \n\nare being distributed over the intemeurons and then  reassembled  in the correct amount \non  the  motoneurons.  This  is  just a  simple,  specific  example  of distributed  parallel \nprocessing in the nervous system. \n\nA  neural  network  model  is  merely  an  explicit statement of such  a  distribution.  Initial \nrandomization of the synaptic weights followed by error-driven learning creates hidden \nunits that conform to Equ.  (1).  We concluded that a neural network model was entirely \nappropriate for this neural system.  This exercise also brought home, although in a simple \nway,  the  obvious,  but  often  overlooked,  message  that  block-diagram  models  can  be \nmisleading about how their conceptual  functions are realized  by  neurons. \n\nWe next examined distribution of the spatial properties of the intemeurons of the VOR \n(Anastasio and Robinson,  1990).  We used only the vertical VOR to keep things simple. \nThe inputs were  the primary afferents of the four vertical semicircular canals  that sense \nhead  rotations  in  all  combinations of pitch  and  roll.  The  output  layer  was  the  four \nmotoneurons of the vertical  recti and oblique muscles  that move  the eye vertically and \nin cyclotorsion.  The model was trained to perform compensatory eye movements in all \ncombinations of pitch and roll. \n\nThe  sensitivity  axis  is  that  axis  around  which  rotation  of the  head  or  eye  produces \nmaximum  modulation  in  discharge  rate.  The  sensitivity  axis  of  a  canal  unit  is \nperpendicular  to  the  plane  in which  the canal  lies.  That of a  motoneuron  is  that axis \naround which its muscle will rotate the eye.  What were the sensitivity axes of the hidden \nunits? \n\nA  block  diagram  of the  spatial  manipulations  of the  VOR  consists  of matrices.  The \ngeometry of the canals can be described by a  3 x 3 matrix that converts a head-velocity \nvector into  its  neurally  encoded  representation on canal  nerves.  The geometry  of the \nmuscles  can  be  described  as  another  matrix  that  converts  the  neurally-encoded \nmotoneuron vector into a physical eye-rotation vector.  The brain-stem matrix describes \nIn  this \nhow  the  canal  neurons  must  project  to  the  motoneurons  (Robinson,  1982). \nscheme,  intemeurons would have only fixed sensitivity axes laying somewhere between \nIn our  model,  however,  sensitivity axes  are \nthat  of a  canal  unit  and  a  motoneuron. \ndistributed in the network; those of the hidden units point in a variety of directions.  This \nhas also been confirmed by  microelectrode recordings (Fukushima et al.,  1990).  Thus, \nspatial  aspects  of transformations,  just  like  temporal  aspects,  are  distributed  over  the \nintemeurons. \n\nAgain,  block-diagrams, in this case  in the  form of a matrix,  are  misleading about what \none will  find  with a  microelectrode.  Again,  recording  from  single units  tells one little \nabout what  a  network  is  trying  to  do.  There  is  much  talk  in  motor physiology about \ncoordinate  systems  and  transformations  from  one  to  another.  The  question  is  asked \n\"What coordinate system is this neuron working in?\"  In this example, individual hidden \nunits  do  not  behave  as  if they  belonged  to  any  coordinate  system  and  this  raises  the \nproblem of whether this is really a meaningful question. \n\n4  THE NEURAL INTEGRA TOR \nMuscles are largely position actuators;  against a  constant load,  position is  proportional \n\n\f354 \n\nRobinson \n\nto  innervation.  The  motoneurons  of  the  extraocular  muscles  also  need  a  signal \nproportional to desired eye position as well as velocity.  Since eye-movement commands \nenter the caudal pons as eye-velocity commands. the necessary  eye-position command is \nobtained  by  integrating  the  velocity  signals  (see  Robinson.  1989.  for  a  review).  The \nlocation of the neural network has been discovered in the caudal pons and it is intriguing \nto speculate how it might work.  Hardwired networks. based on positive feedback.  have \nbeen  proposed  utilizing  lateral  inhibition  (Cannon  et  a1..  1983)  and  more  recently  a \nlearning  neural  network  (dynamic)  has  been  proposed  for  the  VOR  (Arnold  and \nRobinson.  1991).  The  hidden units  are  freely  connected.  the  input is from  two  canal \nunits in push-pull. the output is two motoneurons also in push-pull. which operate on the \nplant  transfer  function.  lI(sTc  +  1).  (Tc  is  the  plant  time  constant).  to  create  an  eye \nposition which should be the time integral of the input head velocity.  The error is retinal \nimage slip (the difference between actual  and  ideal  eye velocity).  Its ems  value over a \ntrial  interval  is  used  to change  synaptic  weights  in  a steepest  descent  method until  the \nerror  is  negligible.  To  compensate  the  plant  lag.  the  network  must  produce  a \ncombination output of eye velocity plus its integral.  eye position. and these two signals. \nwith various weights. are seen on all hidden units which.  thus.  look remarkably like the \nintegrator neurons  that we record  from. \n\nThis exercise  raises  several  issues.  The block-diagram model  of this network is a box \nmarked  lis in parallel with the direct velocity feedforward  path given the gain Tc.  The \nparallel combination is  (sTc  + 1)/s.  The zero cancels  the pole of the plant leaving  lis. \nso  that  eye  position is  the  perfect  integral  of head  velocity.  While  such  a  diagram  is \nconceptually very useful  in diagnosing disorders (Zee and Robinson.  1979).  it contains \nno  hint  of how  neurons  might  effect  integration  and  so  is  useless  in  this  regard. \nMoreover. Galiana and Outerbridge (1984) have pointed out. although in a more complex \ncontext.  that a  direct  feedforward  path of gain T c with a positive feedback  path around \nit containing a model of the plant. produces exactly the same transfer function.  Should \nwe worry about which  is  correct  - feedforward  or feedback?  Perhaps  we  should.  but \nnote that the neural network model of the integrator just described contains both feedback \nand feedforward  pathways and relies on positive feedback.  There is a suspicion that the \nlatter network may subsume both block diagrams making questions about which is correct \nirrelevant.  One thing is certain. at this level of organization. so close to the neuron level. \nblock-diagrams.  while  having  conceptual  value.  are  not  only  useless  but  can  be \nmisleading if one is interested in describing real  neural  networks. \n\nFinally.  how  does  one  test  a  model  network  such  as  that  proposed  for  the  neural \nintegrator?  It involves the  microcircuitry  with which  small  sets of circumscribed cells \ntalk to  each  other and process  signals.  The technology is  not yet  available  to allow us \nto answer  this question.  I know of no  real.  successful  examples.  This.  I believe.  is a \ntrue roadblock in neurophysiology.  If we cannot solve it. we must forever be content to \ndescribe  what cell groups do but not how they do it. \n\nAcknowledgements \nThis research  is supported by Grant 5 R37 EYOO598  from  the National Eye Institute of \nthe National Institutes of Health. \n\n\fInformation Processing to Create Eye Movements \n\n355 \n\nReferences \nT.J.  Anastasio  &  D.A.  Robinson.  (l989)  The  distributed  representation  of vestibulo(cid:173)\nocular signals by brain-stem neurons.  Bioi.  Cybern.,  61:79-88. \n\nT.J.  Anastasio &  D.A. Robinson.  (l990) Distributed parallel processing in the vertical \nvestibulo-ocular reflex:  Learning networks  compared  to  tensor theory.  Bioi.  Cybern., \n63:161-167. \n\nD.B. Arnold &  D.A. Robinson. (1991) A learning network model of the neural integrator \nof the oculomotor system.  Bioi.  Cybern.,  64:447-454. \n\nS.C.  Cannon,  D.A. Robinson &  S.  Shamma.  (1983) A proposed neural network for the \nintegrator of the oculomotor system.  Bioi.  Cybern.,  49: 127-136. \n\nK.  Fukushima, S.I.  Perlmutter, J.F.  Baker &  B.W.  Peterson.  (1990)  Spatial properties \nof second-order vestibulo-ocular relay neurons in the alert cat.  Exp.  Brain Res., 81:462-\n478. \n\nH.L.  Galiana &  J.S.  Outerbridge.  (1984)  A bilateral model  for  central neural pathways \nin vestibuloocular reflex. J.  Neurophysiol.,  51:210-241. \n\nD.A. Robinson.  (1982) The use of matrices in analyzing the three-dimensional behavior \nof the vestibulo-ocular reflex.  Bioi.  Cybern.,  46:53-66. \n\nD.A. Robinson.  (1989) Integrating with neurons.  Ann.  Rev.  Neurosci.,  12:33-45. \n\nR.D.  Tomlinson  &  D.A.  Robinson.  (1984)  Signals  in  vestibular  nucleus  mediating \nvertical eye movements in the monkey.  J.  Neurophysiol.,  51: 1121-1136. \n\nD.S.  Zee &  D.A. Robinson. (l979) Clinical applications of oculomotor models.  In H.S. \nThompson  (ed.),  Topics  in Neuro-Ophthalmology,  266-285.  Baltimore,  MD:  Williams \n&  Wilkins. \n\n\f", "award": [], "sourceid": 464, "authors": [{"given_name": "David", "family_name": "Robinson", "institution": null}]}