{"title": "Neural Control of Sensory Acquisition: The Vestibulo-Ocular Reflex", "book": "Advances in Neural Information Processing Systems", "page_first": 410, "page_last": 418, "abstract": null, "full_text": "410 \n\nNEURAL CONTROL OF SENSORY ACQUISITION: \n\nTHE VESTIBULO-OCULAR REFLEX. \n\nMichael G. Paulin,  Mark E. Nelson and James M. Bower \n\nDivision of Biology \n\nCalifornia Institute of Technology \n\nPasadena, CA 91125 \n\nABSTRACT \n\nWe present a new hypothesis that the cerebellum plays a key role in ac(cid:173)\ntively controlling the acquisition of sensory infonnation by the nervous \nsystem.  In this paper we explore this idea by examining the function of \na  simple  cerebellar-related  behavior,  the  vestibula-ocular  reflex  or \nVOR, in  which  eye movements  are generated to minimize image slip \non  the  retina  during  rapid  head  movements.  Considering  this  system \nfrom  the point of view of statistical estimation theory, our results  sug(cid:173)\ngest that the transfer function of the VOR, often regarded as a static or \nslowly  modifiable  feature  of the  system,  should  actually  be  continu(cid:173)\nously and rapidly changed during head movements. We further suggest \nthat these changes are under the direct control of the cerebellar cortex \nand propose experiments to test this hypothesis. \n\n1. INTRODUCTION \n\nA  major  thrust  of research  in  our laboratory  involves  exploring  the  way  in  which  the \nnervous system  actively controls the acquisition of infonnation about the outside world. \nThis  emphasis  is  founded  on  our  suspicion  that  the  principal  role  of the  cerebellum, \nthrough its influence on motor systems, is to monitor and optimize the quality of sensory \ninformation entering the brain.  To explore this question, we have undertaken an investi(cid:173)\ngation  of  the  simplest  example  of a  cerebellar-related  motor  activity  that  results  in \nimproved sensory inputs,  the vestibulo-ocular reflex  (VOR).  This reflex is  responsible \nfor  moving the eyes to  compensate for  rapid head  movements  to prevent retinal image \nslip which would otherwise significantly degrade visual acuity (Carpenter, 1977). \n\n2. VESTIBULO-OCULAR REFLEX (VOR) \n\nThe VOR relies on the vestibular apparatus  of the inner ear which is  an  inertial sensor \nthat detects  movements of the head.  Vestibular output caused by head movements  give \nrise  to  compensatory  eye  movements  through  an  anatomically  well  described  neural \npathway in the brain stem  (for a review see Ito,  1984).  Visual feedback also makes  an \nimportant contribution  to  compensatory  eye  movements  during  slow  head  movements, \n\n\fNeural Control of Sensory Acquisition \n\n411 \n\nbut during rapid  head movements  with  frequency  components  greater than  about  1Hz, \nthe vestibular component dominates (Carpenter, 1977). \n\nA  simple analysis of the image stabilization problem  indicates that during  head rotation \nin  a  single plane,  the  eyes  should  be made  to rotate  at equal  velocity  in  the  opposite \ndirection.  This  implies  that,  in  a  simple feedforward  control  model,  the VOR  transfer \nfunction should have unity gain and a 1800  phase shift.  This would assure stabilized reti(cid:173)\nnal images of distant objects.  It turns out, however, that actual measurements reveal the \nsituation is not this simple.  Furman, O'Leary and Wolfe (1982), for example, found that \nthe monkey VOR has approximately unity gain and 1800  phase shift only in a narrow fre(cid:173)\nquency band around 2Hz.  At 4Hz the gain is too high by a factor of about 30%  (fig.  1). \n\n1.2 \n\n~ \n-< \nC)  1.0 \n\n0.8 \n\nj \n\nI \nHf \n\n,...., \n~ 5 \n0 \n\n-\n\nI til f f1d1t H f~ff 1\\ \n\nlIJ \n(f) \n\n~O \nn.. \n\n2 \n\n3 \n\n4 \n\n5 \n\nFREQUENCY  (Hz) \n\n-5 \n\n2 \n\n3 \n\n4 \n\n5 \n\nFREQUENCY  (Hz) \n\nFigure  1:  Bode gain and phase plots for the  transfer function  of the \nhorizontal component of the VOR of the alert Rhesus monkey at high \nfrequencies (Data from Furman et al. (1982\u00bb. \n\nGiven the expectation of unity gain, one might be tempted to conclude from  the monkey \ndata that the VOR simply does not perform  well at high frequencies.  But 4Hz is  not a \nvery  high  frequency  for  head  movements,  and  perhaps  it  is  not  the  VOR  which  is \nperforming  poorly,  but  the  simplified  analysis  using  classical  control  theory. \nIn  this \npaper, we argue that the VOR uses a more sophisticated strategy and that the \"excessive\" \ngain in the system seen at higher frequencies actually improves VOR performance. \n\n3. OPTIMAL ESTIMATION \n\nIn order to  understand the discrepancy between the predictions of simple control theory \nmodels  and  measured  VOR  dynamics,  we believe it is  necessary  to  take  into account \nmore  of the  real  world  conditions  under  which \nthe  VOR  operates.  Examples  include \nnoisy head velocity measurements, conduction delays and multiple, possibly conflicting, \nmeasurements  of  head  velocity,  acceleration,  muscle  contractions,  etc.,  generated  by \ndifferent sensory modalities.  The mathematical framework that is appropriate for analyz-\n\n\f412 \n\nPaulin, Nelson and Bower \n\ning problems of this kind  is stochastic state-space dynamical systems theory (Davis and \nVinter,  1985).  This framework is an extension of classical linear dynamical systems the(cid:173)\nory that  accommodates multiple inputs and outputs, nonlinearities, time-varying dynam(cid:173)\nics, noise and delays.  One area of application of the state space theory has been in target \ntracking, where the basic principle involves using knowledge of the dynamics of a target \nto estimate its most probable trajectory given imprecise data.  The VOR can be viewed as \na target tracking  system  whose  target is  the \"world\",  which moves in head coordinates. \nWe have reexamined the VOR from this point of view. \n\nThe Basic VOR. \nTo  begin  our  analysis  of the  VOR  we  have  modeled  the  eye-head-neck  system  as  a \ndamped inverted pendulum with linear restoring forces (fig. 2) where the model system is \ndriven  by  random  (Gaussian  white)  torque.  Within  this  model,  we  want  to  predict the \ncorrect  compensatory  \"eye\"  movements  during  \"head\"  movements  to  stabilize  the \ndirection in which  the eye is  pointing.  Figure 2 shows  the amplitude spectrum  of head \nvelocity for this model.  In this case,  the parameters of the model result in a system that \nhas a natural resonance in the range of 1 to 2 Hz and attenuates higher frequencies. \n\n20 \n\n\u2022 \n\n\u2022  \u2022 \u2022 \u2022  S IS   z ,   s. u \u2022  '. \n1.0 \n\n0.1 \n\nFREQUENCY \n\n\u2022  \u2022\u2022 i.  I \n\nFigure 2:  Amplitude spectrum of model head velocity. \n\nWe provide noisy measurements of \"head\" velocity and then ask what transfer function, \nor filter,  will give the most accurate \"eye\" movement compensation?  This is an estima(cid:173)\ntion  problem  and,  for  Gaussian  measurement  error,  the  solution  was  discovered  by \nKalman  and  Bucy (1961).  The optimal fIlter  or estimator is  often  called  the  Kalman(cid:173)\nBucy filter.  The gain and phase plots of the  optimal filter for tracking movements of the \ninverted pendulum model are shown in figure 3.  It can be seen that the gain of the opti(cid:173)\nmal estimator for this  system peaks near the maximum in the  spectrum of  \"head-neck\" \nvelocity (fig. 2).  This is a general feature of optimal  filters.  Accordingly, to accurately \ncompensate for head movement in this system, the VOR would need to have  a frequency \ndependent gain. \n\n\fNeural Control of Sensory Acquisition \n\n413 \n\n-~ 20 -~  0 \n0 5 ~ -20 \n~ \n\n-bO \n0 \nSo \nj \n\n~ \ntI) \n\n~90 \n\n0.1 \n\n1.0 \n\n10.0 \n\n.0 \n\nFigure 3:  Bode gain plot (left) and phase plot (right) of an  optimal \nestimator for tracking the inverted pendulum using noisy data. \n\nTime Varying dynamics and the VOR \nSo far we have considered our model for VOR optimization only in the simple case of a \nconstant head-neck  velocity  power spectrum.  Under natural  conditions,  however,  this \nspectrum would be expected to change.  For example, when gait changes from walking to \nrunning,  corresponding  changes  in  the  VOR  transfer  function  would  be  necessary  to \nmaintain optimal performance.  To explore this, we added a second inverted pendulum to \nour model  to  simulate body  dynamics.  We  simulated changes  in  gait by  changing  the \nresonant frequency  of the  trunk.  Figure 4 compares  the  spectra of head-neck  velocity \nwith  two  different  trunk  parameters.  As  in  the  previous  example,  we  then  computed \ntransfer functions of the optimal filters for estimating head velocity from  noisy measure(cid:173)\nments  in  these  two  cases.  The  gain  and  phase  characteristics  of these  filters  are  also \nshown  in  Figure  5.  These  plots  demonstrate  that  significant  changes  in  the  transfer \nfunction of the VOR  would be necessary  to maintain visual  acuity in  our model system \nunder these different conditions.  Of course, in the real situation head-neck dynamics will \nchange rapidly  and  continuously  with  changes  in gait,  posture,  substrate,  etc.  requiring \nrapid continuous changes in VOR dynamics rather than the simple switch implied here. \n\nHEAD \n\n-~  20 \n-~ \n\u00a7 \n5 ~ \n\n~  -20 \n\n0  ....... ----~~-~ \n\n0.1 \n\n1.0 \nFREQUENCY \n\n10.0 \n\nFigure 4: Head velocity spectrum during \"walking\" (light) and \"running\" (heavy). \n\n\f414 \n\nPaulin, Nelson and Bower \n\n-\n.8 -\n\n1----\"\"'::3I~ \n\n~  0 \n~ \n\u00a7 \n5 \n~ -20 \n\n\u2022  \u2022 \u2022\u2022 , Ci. \n.1 \n\nD  \u2022 \u2022  \n\n1.0 \n\n10.0 \n\n.1 \n\n1.0 \n\n10.0 \n\nFigure 5:  Bode  gain  plots  (left)  and  phase plots  (right)  for  optimal  estimators  of \nhead angular velocity during \"walking\" (light) and \"running\" (heavy). \n\n4. SIGNIFICANCE TO THE REAL VOR \n\nOur results show that the optimal VOR transfer function requires a frequency dependent \ngain to accurately adjust to a wide range of head movements under real world conditions. \nThus,  the deviations from  unity gain  seen  in actual  measurements of the  VOR  may  not \nrepresent  poor,  but rather  optimal,  performance.  Our  modeling  similarly  suggests  that \nseveral other experimental results can be reinterpreted.  For example,  localized peaks or \nvalleys in the VOR gain function can be induced experimentally through prolonged sinu(cid:173)\nsoidal  oscillations  of subjects  wearing  magnifying  or reducing  lenses.  However, \nthis \n\"frequency selectivity\" is  not thought to occur naturally  and  has  been interpreted  to  im(cid:173)\nply the existence of frequency selective channels in the VOR control network (Lisberger, \nMiles and Optican, 1983).  In our view  there is no real distinction between this phenom(cid:173)\nenon and the \"excessive\" gain in normal monkey VOR;  in each case the VOR  optimizes \nits response for the particular task which it has to solve.  This is  testable.  If we are cor(cid:173)\nrect,  then frequency  selective gain changes will occur following prolonged narrow-band \nrotation in the light without wearing lenses.  In the classical framework there is no reason \nfor any gain changes to occur in this situation. \n\nAnother  phenomenon  which  has  been  observed  experimentally  and  that  the  current \nmodeling sheds new  light on is referred  to as  \"pattern storage\".  After single-frequency \nsinusoidal oscillation on a turntable in the light for several hours, rabbits will continue to \nproduce  oscillatory  eye  movements  when  the  lights  are  extinguished  and  the  turntable \nstops.  Trained rabbits also produce eye oscillations at the training frequency  when oscil(cid:173)\nlated in  the  dark  at a different frequency  (Collewijn,  1985).  In  this  case  the  sinusoidal \npattern seems to be \"stored\" in the nervous system.  However, the effect is naturally  ac(cid:173)\ncounted for  by  our optimal  estimator hypothesis  without relying on  an  explicit \"pattern \nstorage  mechanism\".  An  optimal  estimator  works  by  matching  its  dynamics  to  the \ndynamics of the signal generator, and in effect it tries to force an internal model to mimic \nthe signal generator by comparing actual and expected patterns of sensory inputs.  When \n\n\fNeural Control of Sensory Acquisition \n\n415 \n\nno  data is  available,  or the  data  is  thought  to  be very  unreliable,  an optimal  estimator \nrelies completely, or almost completely, on the model.  In cases where  the signal is  pat(cid:173)\nterned  the  estimator will  behave as  though  it had  memorized  the  pattern.  Thus,  if we \nhypothesize that the VOR is  an optimal estimator we do not need an  extra hypothesis to \nexplain pattern storage.  Again, our hypothesis is testable.  If we are correct,  then repeat(cid:173)\ning the pattern storage experiments using rotational velocity waveforms obtained by driv(cid:173)\ning a frequency-tuned oscillator with Gaussian white noise will produce identical dynam(cid:173)\nical effects  in  the VOR.  There is  no  sinusoidal  pattern in  the  stimulus, but we predict \nthat the rabbits  can  be  induced  to  generate  sinusoidal  eye  movements  in  the  dark after \nthis training. \n\nThe  modeling results shown  in  figures 4  and 5 represent an  extension of our ideas  into \nthe area of gait (or more generally \"context\") dependent changes in VOR which has not \nbeen considered very much in  VOR research.  In fact,  VOR experimental paradigms, in \ngeneral,  are  explicitly  set  up  to  produce  the  most  stable  VOR  dynamics  possible. \nAccordingly,  little  work  has  been  done  to  quantify \nthe  short  term  changes  in  VOR \ndynamics  that must occur in response to changes in effective head-neck dynamics.  Ex(cid:173)\nperiments  of this  type  would  be  valuable  and  are  no  more  difficult  technically  than \nexperiments which  have already been done.  For example,  training an animal on a turn(cid:173)\ntable  which  can  be  driven  randomly  with  two  distinct velocity  power spectra,  i.e.  two \n\"gaits\",  and  providing  the  animal  with  external  cues  to  indicate  the  gait  would,  we \npredict, result in  an animal that could use the cues to switch its VOR dynamics.  A  more \ndifficult but also  more compelling demonstration  would be to test VOR dynamics  with \nimpulsive head accelerations in different natural situations, using an unrestrained animal. \n\ns. SENSOR FUSION AND PREDICTION \n\nTo this point, we have discussed compensatory eye movements by treating the VOR as a \nsingle input, single output system.  This allowed us to concentrate on  a particular aspect \nof VOR control:  tracking a  time-varying dynamical system  (the  head) using noisy data. \nIn reality  there are a  number of other factors  which  make control of compensatory eye \nmovements  a  somewhat  more  complex  task  than  it appears  to  be  when  it is  modeled \nusing classical control theory.  For example, a variety of vestibular as well as non-vestib(cid:173)\nular  signals  (e.g.  visual,  proprioceptive) relating  to  head  movements  are  transmitted  to \nthe compensatory eye movement control network (Ito,  1984).  This gives rise to a \"sen(cid:173)\nsor fusion\" problem  where data from  different sources must be combined.  The optimal \nsolution  to  this problem for  a  multiple input - multiple output,  time-varying linear,  sto(cid:173)\nchastic system is also given by the Kalman-Bucy filter (Davis and Vinter,  1985).  Borah, \nYoung and Curry (1988) have demonstrated  that a  Kalman-Bucy filter model of visual(cid:173)\nvestibular  sensor  fusion  is  able  to  account  for  visual-vestibular  interactions  in  motion \nperception.  Oman  (1982)  has  also  developed  a  Kalman-Bucy  filter  model  of visual(cid:173)\nvestibular interactions.  Their results show that the optimal estimation approach is  useful \n\n\f416 \n\nPaulin, Nelson and Bower \n\nfor analyzing multivariate aspects of compensatory eye movement control, and comple(cid:173)\nment our analysis of dynamical aspects. \n\nAnother set of problems arises in the VOR because of small time delays in neural trans(cid:173)\nmission and muscle activation.  To optimize its response, the mammalian VOR needs to \nmake up for these delays by predicting head movements about  lOmsec in advance (ret). \nOnce  the  dynamics  of the  signal generator have  been identified, prediction can  be per(cid:173)\nformed  using  model-based estimation  (Davis and Vinter,  1985).  A neural analog of a \nTaylor  series  expansion  has  also  been  proposed  as  a  model  of prediction  in  the  VOR \n(pellionisz and LUnas,  1979), but  this  mec.hanism  is  extremely  sensitive to  noise in the \ndata and was abandoned as a practical technique for general signal prediction several de(cid:173)\ncades ago in  favor  of model-based techniques  (Wiener,  1948).  The later approach  may \nbe more  appropriate  for  analyzing  neural  mechanisms  of prediction  (Arbib  and  Amari, \n1985).  An elementary  description of optimal estimation theory for  target tracking,  and \nits possible relation to cerebellar function, is given by Paulin (1988). \n\n6. ROLE OF CEREBELLAR CORTEX IN VOR CONTROL \n\nTo this point we have presented a novel characterization of the problem of compensatory \neye  movement control  without considering  the physical circuitry  which  implements the \nbehavior.  However,  there are two parts to  the optimal estimation problem.  At each in(cid:173)\nstant it is necessary  to  (a)  filter the data using  the optimal  transfer function  to drive  the \ndesired response and  (b) determine  what transfer function  is  optimal at that instant and \nadjust the filtering network accordingly.  The first problem is  fairly  straightforward, and \nexisting  models  of  VOR  demonstrate  how  a  network  of  neurons  based  on  known \nbrains tern  circuitry can implement a particular transfer function (Cannon and Robinson, \n1985).  The second problem is more difficult because requires continuous monitoring of \nthe context in which head movements occur using a variety of sources of relevant data to \ntune the optimal filter for that context.  We speculate that the cerebellar cortex performs \nthis task. \n\n, \n\nFirst, the cortex of the vestibulo-cerebellum is  in a position to mflke the required compu-\ntation,  since  it  receives  detailed  information  from  multiple  sensory  modalities  that \nprovide information on the state of the motor system (Ito,  1985).  Second, the cerebellum \nprojects to  and appears to modulate the brain stem compensatory eye movement control \nnetwork (Mackay and Murphy,  1979).  We predict that the cerebellar cortex is  necessary \nto  produce  rapid,  context-dependent optimal  state  dependent changes  in  VOR  transfer \nfunction which we have discussed.  This speculation can be tested with turntable experi(cid:173)\nments  similar  to  those  described in  section  4 above  in  the  presence and absence  of the \ncerebellar cortex. \n\n\fNeural Control of Sensory Acquisition \n\n417 \n\n7. THE GENERAL FUNCTION OF CEREBELLAR CORTEX \n\nAccording  to our hypothesis,  the cerebellar cortex is required for  making optimal com(cid:173)\npensatory eye movements during head movements.  This is accomplished by continuous(cid:173)\nly modifying the dynamics of the  underlying control network in the brainstem, based on \ncurrent sensory information.  The function of the cerebellar cortex in  this case can then \nbe seen  in  a  larger context as  using  primary  sensory  information  (vestibular,  visual)  to \ncoordinate the use of a motor system (the extraoccular eye muscles) to position a sensory \narray  (the  retina)  to  optimize  the  quality  of sensory  information  available  to  the  brain. \nWe  believe  that this  is  the  role  played by  the  rest of the  cerebellum  for  other  sensory \nsystems.  Thus, we suspect that the hemispheres of the rat cerebellum, with their peri-oral \ntactile  input  (Bower et al.,  1983),  are  involved  in  controlling  the  optimal  use  of these \ntactile  surfaces  in  sensory  exploration  through  the  control  of  facial  musculature. \nSimilarly, the hemispheres of the primate cerebellum, which have hand and finger tactile \ninputs (Ito,  1984), may be involved in an analogous exploratory task in primates.  These \ntactile  sensory-motor systems  are difficult  to  analyze,  and  we  are  currently  studying  a \nfunctionally  analogous  but more  accessible  model  system,  the  electric  sense of weakly \nelectric fish (cf Rasnow et al., this volume). \n\n8.CONCLUSION \n\nOur  view  of  the  cerebellum  assigns  it  an  important  dynamic  role  which  contrasts \nmarkedly  with  the  more  limited  role  it  was  assumed  to  have  in  the  past as  a  learning \ndevice  (Marr,  1969;  Albus,  1971;  Robinson,  1976).  There  is  evidence  that cerebellar \ncortex has  some learning abilities (Ito,  1984), but it is recognized that cerebellar cortex \nhas  an  important dynamic  role  in  motor control.  However,  there  are  widely  differing \nopinions as to the nature of that role (Ito,  1985; Miles and Lisberger, 1981; Pellionisz and \nLlinas,  1979).  Our proposal,  that the  VOR  is  a  neural analog of an optimal estimator \nand  that  the  cerebellar  cortex  monitors  context and  sets  reflex  dynamics  accordingly, \nshould  not  be  interpreted  as  a  claim  that  the  nervous  system  actually  implements  the \ncomputations  which  are  involved  in  applied  optimal  estimation,  such  as  the  Kalman(cid:173)\nBucy  filter.  Understanding  the  neural  basis  of  cerebellar  function  will  require  the \ncombined power of a number of experimental,  theoretical and  modeling approaches  (cf \nWilson et al., this volume).  We believe that analyses of the kind presented here have an \nimportant role in characterizing behaviors controlled by the cerebellum. \n\nAcknowledgments \nThis  work  was  supported by the NIH (BNS  22205),  the NSF (EET-8700064),  and the \nJoseph Drown Foundation. \n\nReferences \nArbib M.A.  and  Amari S.  1985.  Sensori-moto Transformations in the Brain (with a cri(cid:173)\ntique of the tensor theory of the cerebellum). J. Theor. BioI.  112:123-155 \n\n\f418 \n\nPaulin, Nelson and Bower \n\nBorah  J.,  Young  L.R.  and  Curry,  R.E.  1988.  Optimal  Estimator  Model  for  Human  Spatial \nOrientation.  In: Proc. N.Y. Acad. Sci.  B. Cohen and V. Henn (eds.). In Press. \n\nBower  lM.  and  Woolston  D.C.  1983.  The  Vertical  Organization  of  Cerebellar  Cortex.  J. \nNemophysiol. 49: 745-766. \n\nCarpenter R.H.S.  1977.  Movements of the Eyes. Pion, London. \n\nDavis M.B.A. and Vinter R.B.  1985.  Stochastic Modelling and Control. 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MIT \nPress, Boston. \n\n\f", "award": [], "sourceid": 168, "authors": [{"given_name": "Michael", "family_name": "Paulin", "institution": null}, {"given_name": "Mark", "family_name": "Nelson", "institution": null}, {"given_name": "James", "family_name": "Bower", "institution": null}]}