{"title": "An Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex", "book": "Advances in Neural Information Processing Systems", "page_first": 742, "page_last": 749, "abstract": null, "full_text": "742 \n\nDeWeerth and Mead \n\nAn Analog  VLSI Model  of Adaptation \n\nin the  Vestibulo-Ocular  Reflex \n\nStephen P.  DeWeerth and  Carver A.  Mead \n\nCalifornia Institute of Technology \n\nPasadena, CA 91125 \n\nABSTRACT \n\nThe vestibulo-ocular reflex (VOR)  is  the primary mechanism that \ncontrols the compensatory eye movements that stabilize retinal im(cid:173)\nages during rapid head motion.  The primary pathways of this sys(cid:173)\ntem are feed-forward,  with inputs from  the semicircular canals and \noutputs  to  the  oculomotor system.  Since  visual  feedback  is  not \nused  directly  in  the  VOR  computation,  the  system  must  exploit \nmotor learning to perform correctly.  Lisberger(1988) has proposed \na  model for  adapting the  VOR gain  using  image-slip  information \nfrom  the  retina.  We  have  designed  and  tested  analog  very  large(cid:173)\nscale integrated (VLSI) circuitry that implements a  simplified ver(cid:173)\nsion of Lisberger's adaptive VOR model. \n\nINTRODUCTION \n\n1 \nA characteristic commonly found in biological systems is  their ability to adapt their \nfunction  based  on  their  inputs.  The  combination  of the  need  for  precision  and \nthe variability inherent in  the environment necessitates such learning in  organisms. \nSensorimotor systems present obvious  examples of behaviors  that  require learning \nto function  correctly.  Simple actions such  as  walking,  jumping, or throwing a  ball \nare not  performed correctly the first  time they are attempted; rather, they require \nmotor learning throughout many iterations of the action. \n\nWhen creating artificial systems that must execute tasks accurately in  uncontrolled \nenvironments, designers can exploit  adaptive techniques to improve system perfor(cid:173)\nmance.  With this in mind, it is  possible for  the system designer to take inspiration \nfrom systems already present in biology.  In particular, sensorimotor systems, due to \n\n\fAn Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex \n\n743 \n\ntheir direct interfaces with the environment, can gather an immediate indication of \nthe correctness of an action,  and hence can learn without supervision.  The salient \ncharacteristics of the environment are extracted by the adapting system and do  not \nneed to  be specified in  a  user-defined training set. \n\n2  THE VESTIBULa-OCULAR REFLEX \nThe  vestibulo-ocular  reflex  (VOR)  is  an  example  of  a  sensorimotor  system  that \nrequires  adaptation  to  function  correctly.  The  desired  response  of this  system  is \na  gain  of -1.0 from  head  movements to eye  movements  (relative  to  the head),  so \nthat,  as  the  head  moves,  the  eyes  remain  fixed  relative  to  the surroundings.  Due \nto the feed-forward  nature of the primary VOR pathways, some form  of adaptation \nmust be present to calibrate the gain of the response in infants and to maintain this \ncalibration during growth,  disease,  and aging  (Robinson, 1976). \n\nLisberger (1988) demonstrated variable gain of the VOR by fitting magnifying spec(cid:173)\ntacles onto a  monkey.  The monkey moved about freely,  allowing the VOR to learn \nthe  new  relationship  between  head  and  eye  movements.  The  monkey  was  then \nplaced  on  a  turntable,  and  its  eye  velocity  was  measured  while  head  motion  was \ngenerated.  The eye-velocity  response to  head motion for  three different  lens  mag(cid:173)\nnifications is  shown  in  Figure  1. \n\n------G = -1.05 \n\nG = -1.57 \n\n30 deg/sec I \n\nG =  -0.32 \n\n~_v_el_o_cl_'t_y ______ _ \n\n150  msec \n\nFigure 1:  VOR data from Lisberger (1988).  A monkey was fitted with magnifying \nspectacles and allowed to learn the gain needed for an accurate VOR. The monkey's \nhead was  then  moved  at a  controlled velocity,  and the  eye  velocity  was  measured. \nThree experiments were  performed with  spectacle magnifications of 0.25,  1.0,  and \n2.0.  The corresponding eye  velocities  showed  VOR gains  G  of -0.32,  -1.05,  and \n-1.57. \n\nLisberger  has  proposed  a  simple  model  for  this  adaptation  that  uses  retinal-slip \ninformation from  the visual  system, along with  the head-motion information from \nthe  vestibular  system,  to  adapt  the  gain  of the  forward  pathways  in  the  VOR. \n\n\f744 \n\nDeWeerth and Mead \n\nFigure  2  is  a  schematic diagram of the  pathways  subserving  the  VOR.  There are \ntwo  parallel  VOR pathways from  the vestibular system to the  motor neurons that \ncontrol eye  movements  (Snyder,  1988).  One pathway consists of vestibular inputs, \nVOR interneurons, and motor neurons.  This pathway has been shown to exhibit an \nunmodified gain of approximately -0.3.  The second pathway consists of vestibular \ninputs,  floccular  target  neurons  (FTN),  and  motor  neurons.  This  pathway  is  the \nsite of the proposed gain  adaptation. \n\nFlocculus \n\n-I-\n\nPC \n\n() \n\nC) \n\nretinal \nslip \n\nI eye  movement \n\nVestibular \nInputs \n\n\"-\n< \nFTN \n\n---\u00ab0 \n\nVOR interneuron \n\n, \n\n' \n\n'.' \n\nfeedback  D \n\n',' \n: \n\n(0 \n\nT \nMotor neuron \n\nFigure  2:  A  schematic  diagram  of the  VOR  (Lisberger,  1988).  Two  pathways \nexist connecting the vestibular neurons to the motor neurons driving the eye  mus(cid:173)\ncles.  The  unmodified  pathway connects via the  VOR inter neurons.  The modified \n~athway (the  proposed  site  of gain  adaptation)  connects  via  the  floccular  target \nneurons (FTN). Outputs from the Purkinje cells  (PC) in the flocculus  mediate gain \nadaptation at the FTN s. \n\nLisberger's hypothesis is  that feedback from the visual system through the flocculus \nis  used  to  facilitate  the  adaptation  of the  gain  of  the  FTNs.  Image  slip  on  the \nretina indicates that the total VOR gain is  not adjusted correctly.  The relationship \nbetween the head motion and the image slip on  the retina determines the direction \nin which the gain  must be changed.  For example, if the head is  turning to the right \nand  the  retinal image slip  is  to  the right,  the eyes  are turning too slowly  and the \ngain should be increased.  The direction of the gain change can be considered to be \nthe sign  of the product of head motion and retinal image slip. \n\n3  THE ANALOG  VLSI IMPLEMENTATION \nWe  implemented  a  simplified  version  of  Lisberger's  VOR  model  using  primarily \nsubthreshold analog very large-scale integrated (VLSI) circuitry (Mead, 1989).  We \ninterpreted  the  Lisberger  data to  suggest  that  the  gain  of the  modified  pathway \n\n\fAn Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex \n\n745 \n\nvaries from  zero to some fixed  upper limit.  This assumption gives  a  minimum VOR \ngain equal to the gain of the unmodified pathway, and a  maximum VOR gain equal \nto  the sum of the  unmodified  pathway  gain  and  the  maximum  modified  pathway \ngain.  We  designed  circuitry for  the  unmodified  pathway  to  give  an  overshoot  re(cid:173)\nsponse to a  step function similar to that seen in  Figure 1. \n\nneuron  circuits \nPI \nP2 \n\nFigure  3:  An  analog  VLSI  sensorimotor framework.  Each  input  circuit  consists \nof a  bias  transistor  and  a  differential  pair.  The  voltage  Vb  sets  a  fixed  current \nib  through  the  bias  transistor.  This  current is  partitioned into  currents  i l  and  i2 \naccording to the differential voltage VI  - V2 ,  and these currents are summed onto a \npair of global wires.  The global currents are  used  as  inputs to two  neuron circuits \nthat convert  the currents into pulse trains PI  and P2 \u2022 \n\nThe VOR model was designed within the sensorimotor framework shown in Figure 3 \n(DeWeerth,  1987).  The framework  consists of a  number of input  circuits  and  two \noutput circuits.  Each input circuit consists of a bias transistor and a differential pair. \nThe gain  of the circuit  is  set  by  a  fixed  current  through the  bias  transistor.  This \ncurrent is  partitioned according to  the  differential input  voltage  into  two  currents \nthat pass through the differential-pair transistors.  The equations for  these currents \nare \n\nThe  two  currents  are  summed onto  a  pair  of global  wires.  Each  of these  global \ncurrents is  input to a neuron circuit (Mead, 1989) that converts the current linearly \ninto  the  duty  cycle  of a  pulse  train.  The  pulse  trains can  be  used  to  drive  a  pair \nof antagonistic actuators that  can  bidirectionally  control the  motion of a  physical \nplant.  We  implement a  system  (such  as  the VOR)  within  this  framework  by aug(cid:173)\nmenting the differential pairs with circuitry that computes the function  needed for \nthe particular application. \n\n\f746 \n\nDeWeerth and Mead \n\n~~----~--------~--------------~r\u00ad\nr-\n~ \n\nFigure 4:  The VLSI implementation of the unmodified pathway.  The left differen(cid:173)\ntial pair is  used to convert proportionally the differential voltage representing head \nvelocity (Vhead - 'Vref)  into output currents.  The right differential pair is  used in con(cid:173)\njunction with  a  first-order section  to give  output currents related to the derivative \nof the head velocity.  The gains of the two  differential  pairs are set  by  the voltages \nVp  and Vo. \n\nThe  unmodified  pathway  is  implemented  in  the  framework  using  two  differential \npairs (Figure 4).  One of these circuits proportionally converts the head motion into \noutput currents.  This  circuit generates a  step in eye  velocity when  presented with \na  step in  head velocity.  The  other differential  pair is  combined  with  a  first-order \nsection  to  generate output  currents  related  to  the  derivative  of  the  head  motion. \nThis  circuit generates a  broad impulse in  eye  velocity  when  presented with  a  step \nin  head  velocity.  By  setting  the  gains  of  the  proportional and  derivative  circuits \ncorrectly,  we  can  make  the overall  response of this  pathway similar to that of the \nunmodified  pathway  seen  when  Lisberger's  monkey  was  presented with  a  step  in \nhead velocity. \n\nWe implement the modified pathway within the framework using a single differential(cid:173)\npair circuit  that generates output currents  proportional to the  head velocity  (Fig(cid:173)\nure  5).  The system adapts the gain of this  pathway  by integrating an error signal \nwith  respect  to  time.  The  error signal  is  a  current,  which  the  circuitry computes \nby  multiplying  the  retinal image slip  and  the  head  velocity.  This  error current  is \nintegrated onto a  capacitor,  and the voltage  on  the capacitor is  then  converted to \na  current that sets the gain  of the modified pathway. \n\n4  EXPERIMENTAL METHOD  AND  RESULTS \nTo  test  our VOR circuitry,  we  designed  a  simple  electrical  model of the head  and \neye  (Figure 6).  The head motion is  represented by a  voltage that is  supplied by a \nfunction  generator.  The oculomotor plant  (the eye  and corresponding muscles)  is \nmodeled by an RC circuit that integrates output pulses from the VOR circuitry into \na voltage that represents eye velocity in head coordinates. We model the magnifying \n\n\fAn  Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex \n\n747 \n\n~~------------------------------~~r-\n~ \n\nr-\n\nhead \n\nslip \n\nFigure  5:  The VLSI implementation of the modified  pathway.  A  differential  pair \nis  used to convert  proportionally the differential voltage representing head velocity \n(Vhead  - v;.er)  into  output currents.  Adaptive  circuitry capacitively integrates the \nproduct  of head  velocity  and  retinal  image  slip  as  a  voltage  Vg \u2022  This  voltage  is \nconverted to a  current ig  that sets the gain  of the differential  pair.  The voltage VA \nsets the maximum gain of this  pathway. \n\n>---+ \nslip \nVhead--\n\nFigure  6:  A  simple  model  of the  oculomotor  plant.  An  RC  circuit  (bottom) \nintegrates pulse trains PI  and P2  into a  voltage \u00a5eye  that encodes eye velocity.  The \nmagnifying spectacles are modeled by an operational amplifier circuit  (top), which \nhas a magnification m = R2/ R I .  The retinal image slip is encoded by the difference \nbetween  the  output voltage  of this  circuit  and  the voltage  Vhead  that encodes the \nhead velocity. \n\n\f748 \n\nDeWeerth and Mead \n\nspectacles using an operational amplifier circuit that multiplies  the eye  velocity by \na  gain before the velocity is  used to compute the slip information.  We compute the \nimage slip  by subtracting the head velocity from  the magnified eye  velocity. \n\nG = -1.45 \n\nG = -0.32 \n\nFigure  7:  Experimental data from  the VOR circuitry.  The system was  allowed  to \nadapt  to spectacle  magnifications of 0.25,  1.0,  and  2.0.  After adaptation,  the eye \nvelocities  showed corresponding VOR gains of -0.32,  -0.92, and -1.45. \n\nWe  performed an experiment to generate data to compare to the data measured by \nLisberger (Figure 1).  A head-velocity step was supplied by a function generator and \nwas used as input to the VOR circuitry.  The VOR outputs were then converted to an \neye velocity by the model of the oculomotor plant.  The proportional, derivative, and \nmaximum adaptive gains were set to give a system response similar to that observed \nin  the  monkey.  The  system  was  allowed  to adapt over a  number of presentations \nof the input  for  each  spectacle magnification.  The  resulting eye  velocity  data are \ndisplayed  in  Figure 7. \n\n5  CONCLUSIONS AND  FUTURE WORK \nIn  this  paper,  we  have  presented an analog  VLSI  implementation of a  model of a \nbiological  sensorimotor system.  The system performs unsupervised learning using \nsignals  generated as  the  system  interacts  with  its  environment.  This  model  can \nbe  compared to  traditional adaptive control schemes  (Astrom,  1987)  for  perform(cid:173)\ning  similar  tasks.  In  the  future,  we  hope  to  extend  the  model  presented  here  to \nincorporate more of the information known  about the VOR. \n\nWe are currently designing and testing chips that use ultraviolet storage techniques \nfor gain adaptation.  These chips will allow us  to achieve adaptive time constants of \nthe same order as  those found in  biological systems  (minutes to hours). \n\nWe  are also combining our chips with  a  mechanical model of the head and eyes  to \ngive  more accurate environmental feedback.  We  can  acquire  true image-slip  data \nusing a  vision  chip  (Tanner,  1986)  that computes global field  motion. \n\n\fAn Analog VLSI Model of Adaptation in the Vestibulo-Ocular Reflex \n\n749 \n\nAcknowledgments \n\n\\Ve  thank Steven Lisberger for his suggestions for improving our implementation of \nthe VOR model.  \\Ve would also like to thank Massimo Sivilotti, Michelle Mahowald, \nMichael Emerling, Nanette Boden, Richard Lyon, and Tobias Delbriick for their help \nduring the writing of this paper. \n\nReferences \n\nK.J.  Astrom,  Adaptive  feedback  control.  Proceedings  of the  IEEE,  75:2:185-217, \n1987. \n\nS.P.  DeWeerth,  An Analog  VLSI Framework  for  Motor  Control.  M.S.  Thesis,  De(cid:173)\npartment of Computer Science,  California Institute of Technology,  Pasadena,  CA, \n1987. \n\nS.G.  Lisberger, The neural basis for  learning simple motor skills.  Science,  242:728-\n735,  1988. \nC.A. Mead, Analog VLSI and Neural Systems.  Addison-Wesley, Reading, MA, \n1989. \nD.A.  Robinson,  Adaptive gain control of vestibulo-ocular reflex by  the cerebellum. \n1.  Neurophysiology,  39:954-969, 1976. \nL.H.  Snyder and W.M.  King,  Vertical vestibuloocular reflex in cat:  asymmetry and \nadaptation.  1.  Neurophysiology,  59:279-298, 1988. \nJ.E.  Tanner.  Integrated  Optical  Motion  Detection.  Ph.D.  Thesis,  Department  of \nComputer Science,  California Institute of Technology,  S223:TR:86,  Pasadena, CA, \n1986. \n\n\f", "award": [], "sourceid": 258, "authors": [{"given_name": "Stephen", "family_name": "DeWeerth", "institution": null}, {"given_name": "Carver", "family_name": "Mead", "institution": null}]}