A Recurrent Neural Network Model of Velocity Storage in the Vestibulo-Ocular Reflex
Authors: Thomas J. Anastasio
Published in: Advances in Neural Information Processing Systems 3  (NIPS 1990) (Main Conference Track), 1990

Abstract: A three-layered neural  network model was used to  explore  the  organization of  the  vestibulo-ocular  reflex  (VOR).  The  dynamic  model  was  trained  using  recurrent back-propagation to produce compensatory, long duration eye muscle  motoneuron  outputs  in  response  to  short  duration  vestibular  afferent  head  velocity  inputs.  The  network  learned  to  produce  this  response  prolongation,  known  as  velocity  storage,  by  developing  complex,  lateral  inhibitory  interac(cid:173) tions among the interneurons.  These had the low baseline, long time constant,  rectified  and  skewed  responses  that  are  characteristic  of  real  VOR  inter(cid:173) neurons.  The  model  suggests  that  all  of these  features  are  interrelated  and  result from lateral inhibition. 
1 SIGNAL PROCESSING IN THE VOR  The  VOR  stabilizes  the  visual  image  by  producing  eye  rotations  that  are  nearly  equal  and  opposite  to  head  rotations  (Wilson  and  Melvill  Jones  1979).  The  VOR  utilizes  head  rotational  velocity  signals,  which  originate  in  the  semicircular canal  receptors of  the  inner  ear,  to  control  contractions  of the  extraocular  muscles.  The  reflex  is  coor(cid:173) dinated by brainstem interneurons in the vestibular nuclei (VN),  that relay  signals from  canal afferent sensory neurons to eye muscle motoneurons. 
32 
A Recurrent Neural Network Model of Velocity Storage 
33 
The  VN  intemeurons,  however,  do  more  than just relay  signals.  Among  other func(cid:173) tions,  the  VN neurons process  the  canal afferent signals,  stretching out their time con(cid:173) stants by about four times before transmitting this signal to the motoneurons.  This time  constant  prolongation,  which  is  one  of the  clearest  examples  of signal  processing  in  motor neurophysiology,  has  been  termed velocity  storage  (Raphan  et  al.  1979).  The  neural mechanisms underlying velocity storage, however,  remain unidentified. 
The  VOR is bilaterally  symmetric  (Wilson  and  Melvill Jones  1979).  The semicircular  canals  operate  in  push-pull  pairs,  and  the  extraocular  muscles  are  arranged  in  agonist/antagonist  pairs.  The  VN  are  also  arranged  bilaterally  and  interact  via  in(cid:173) hibitory commissural connections.  The commissures are necessary  for velocity storage,  which is eliminated by cutting the commissures in monkeys (Blair and Gavin  1981). 
When  the  overall  V OR  fails  to  compensate  for  head  rotations,  the visual  image is not  stabilized but moves across the  retina at a velocity  that  is  equal  to  the  amount of VOR  error.  This  'retinal slip'  signal is transmitted back to the  VN,  and is known to  modify  VOR  operation  (Wilson  and  Melvill  Jones  1979).  Thus  the  VOR  can  be  modeled  beautifully as  a  three-layered neural network,  complete with  recurrent connections and  error signal back-propagation at the VN level.  By  modeling  the  VOR  as  a neural  net(cid:173) work,  insight can be gained into the global organization of this reflex. 
Figure  1:  Architecture  of  the  Horizontal  VOR  Neural  Network  Model.  lhc and  rhc,  left and  right  horizontal  canal  afferents;  Ivn  and  rvn,  left  and  right VN  neurons;  lr  and  mr,  lateral  and  medial  rectus  motoneurons  of the left eye.  This  and  all  subsequent  figures  are  redrawn  from  Anastasio  (1991),  with permission.