{"title": "Instabilities in Eye Movement Control: A Model of Periodic Alternating Nystagmus", "book": "Advances in Neural Information Processing Systems", "page_first": 138, "page_last": 144, "abstract": "", "full_text": "Instabilities in Eye Movement Control: A Model \n\nof Periodic Alternating Nystagmus \n\nErnstR. Dow \n\nCenter for Biophysics and \nComputational Biology, \n\nBeckman Institute \n\nUniversity of Illinois at Urbana(cid:173)\nChampaign,Urbana, IL 61801. \n\nedow@uiuc.edu \n\nThomas J. Anastasio \n\nDepartment of Molecular and Integra(cid:173)\ntive Physiology, Center for Biophysics \n\nand Computational Biology, \n\nBeckman Institute \n\nUniversity of Illinois at Urbana(cid:173)\nChampaign, Urbana, IL 61801. \n\ntstasio@uiuc.edu \n\nAbstract \n\nNystagmus is  a pattern of eye movement characterized by  smooth rota(cid:173)\ntions  of the eye in one direction  and  rapid  rotations  in  the opposite di(cid:173)\nrection that reset eye position.  Periodic alternating nystagmus (PAN) is \na form  of uncontrollable  nystagmus  that  has  been  described  as  an  un(cid:173)\nstable but amplitude-limited oscillation.  PAN has been observed previ(cid:173)\nously  only  in  subjects  with  vestibulo-cerebellar damage.  We describe \nresults in  which  PAN can be produced  in normal  subjects by prolonged \nrotation in darkness.  We propose a new model  in  which the neural  cir(cid:173)\ncuits  that control eye movement are  inherently  unstable,  but  this  insta(cid:173)\nbility  is  kept  in  check  under  normal  circumstances  by  the  cerebellum. \nCircumstances  which  alter  this  cerebellar  restraint,  such  as  vestibulo(cid:173)\ncerebellar damage or plasticity  due  to  rotation  in  darkness,  can  lead  to \nPAN. \n\n1  INTRODUCTION \nVisual perception involves not only an operating visual  sensory system,  but also the abil(cid:173)\nity  to control  eye movements.  The oculomotor subsystems  provide eye movement con(cid:173)\ntrol.  For example, the vestibulo-ocular reflex  (VOR)  maintains retinal  image stability by \nmaking slow-phase eye rotations that counterbalance head rotations, making it possible to \nmove and  see at the same time (Wilson and Melvill Jones,  1979).  The VOR makes slow(cid:173)\nphase  eye  rotations  that  are  directed  opposite  to  head  rotations.  When  these  ongoing \nslow-phase  eye  rotations  are  interrupted  by  fast-phase  eye  rotations  that  reset  eye  posi(cid:173)\ntion,  the  resulting  eye  movement  pattern  is  called  nystagmus.  Periodic  alternating  nys-\n\n\fA Model of Periodic Alternating Nystagmus \n\n139 \n\ntagmus  (PAN)  is  a congenital  or  acquired  eye  movement  disorder  characterized  by  un(cid:173)\ncontrollable nystagmus that alternates direction roughly  sinusoidally with  a period of 200 \ns to  400 s (Baloh et al.,  1976; Leigh et al.,  1981; Furman et aI.,  1990).  Furman  and  col(cid:173)\nleagues  (1990) have determined that PAN  in  humans is  caused  by  lesions of parts of the \nvestibulo-cerebellum  known  as  the  nodulus  and  uvula  (NU).  Lesions  to  the  NU  cause \nPAN  in  the dark  (Waespe et aI.,  1985; Angelaki  and  Hess,  1995).  NU  lesions  also  pre(cid:173)\nvent  habituation  (Singleton,  1967;  Waespe  et  aI,  1985;  Torte  et  al.,  1994),  which  is  a \nsemi-permanent decrease in  the  gain  (eye  velocity /  head  velocity)  of the VOR response \nthat can  be brought about by  prolonged  low-frequency rotational  stimulation in  the  dark. \nVestibulo-cerebellectomy  in  habituated  goldfish  causes  VOR  dishabituation  (Dow  and \nAnastasio,  1996).  Temporary inactivation of the vestibulo-cerebellum in habituated gold(cid:173)\nfish  causes  temporary  dishabituation  and  can  result  in  a temporary  PAN  (Dow  and  An(cid:173)\nastasio,  in  press).  Stimulation  of  the  NU  temporarily  abolish  the  VOR  response \n(Fernandez and  Fredrickson,  1964).  Cerebellar influence on  the  VOR  may  be  mediated \nby connections between the NU and vestibular nucleus neurons,  which have been demon(cid:173)\nstrated in many species (Dow,  1936;  1938). \n\nWe  have  previously  shown  that  intact  goldfish  habituate  to  prolonged  low-frequency \n(0.01  Hz)  rotation  (Dow  and  Anastasio,  1996)  and  that  rotation  at  higher  frequencies \n(0.05-0.1  Hz)  causes  PAN  (Dow  and  Anastasio,  1997).  We also  proposed  a limit-cycle \nmodel  of PAN  in  which  habituation or PAN  result from  an  increase or decrease,  respec(cid:173)\ntively,  of the  inhibition  of the  vestibular  nuclei  by  the  NU.  This  model  suggested  that \nvelocity  storage,  which  functions  to  increase  low-frequency  VOR  gain  above  the  bio(cid:173)\nphysical  limits of the semicircular canals (Robinson,  1977;1981), is  mediated by a poten(cid:173)\ntially  unstable  low-frequency  resonance.  This  instability  is  normally  kept  in  check  by \nconstant suppression by the NU. \n\n2 METHODS \nPAN  was  studied  in  intact,  experimentally  naive,  comet  goldfish  (carassius  auratus). \nEach goldfish  was restrained horizontally underwater with  the head at  the center of a cy(cid:173)\nlindrical  tank.  Eye  movements  were  measured  using  the  magnetic  search  coil  technique \n(Robinson,  1963).  For technical  details  see  Dow  and  Anastasio  (1996).  The  tank  was \ncentered  on  a horizontal  rotating  platform.  Goldfish  were  rotated  continuously for  vari(cid:173)\nous durations  (30 min  to  2 h)  in  darkness  at  various single frequencies  (0.03  - 0.17  Hz). \nSome  data  have  been  previously  reported  (Dow  and  Anastasio,  1997).  All  stimuli  had \npeak rotational velocities of 60 degls.  Eye position and rotator (i.e.  head) velocity signals \nwere digitiZed for analysis.  Eye position data were digitally differentiated to compute eye \nvelocity  and  fast-phases  were  removed.  Data were  analyzed  and  simulated  using  MAT(cid:173)\nLAB  and SIMULINK (The Mathworks, Inc.). \n\n3 RESULTS \nProlonged rotation  in  darkness  at frequencies  which  produced  some  habituation  in  naive \ngoldfish  (0.03-0.17  Hz)  could  produce  a  lower-frequency  oscillation  in  slow-phase  eye \nvelocity  that  was  superimposed  on  the  normal  VOR  response  (fig  1).  This  lower(cid:173)\nfrequency  oscillation produced a periodic alternating nystagmus  (PAN).  When PAN oc(cid:173)\ncurred,  it  was  roughly  sinusoidal  and  varied  in  period,  amplitude,  and  onset-time.  Ha(cid:173)\nbituation could  occur simultaneously with  PAN  (fig  IB) or habituation could completely \n\n\f140 \n\n60 \n\nInitial response \n\nE.  R.  Dow and T.  J. Anastasio \n\nA \n\n~ 40 \n~  20 \n\n-~ 'g \n\n0 \ng!  -20 \nQ) \n>-\nQ)  -40 \n\n~-60~------~--------~~--~--~------~--------~ \n\nQ) ; -:8 ~JJJvAvAJ~\\VV~AvA~\u00a5~AvA~\\AvAJv\\Av\u00a5v\u00a5~AJfv\\\u00a5M~\u00a5v\u00a5JvA~ \ni .r; \n\nResponse after 1 h.  rotation \n\nB \n\n60 \n\n~ 40 \n~  20 \n\n-~ '8 \n\nQ) \n\n,A \nv~ \n\nA \nI\u00a5 \n\nA \n\n~j \nv  y~ \n\nl~J \nv~ \n\niJ \n\n~ \n\n~ \n\nV \n\n~ \n\n0 \n>  -20 \ng!. \nQ)  -40 \ntn-60 \nt \n~ 50~A66A6GGGA66666AGGAAG6A666A6GA6AAAA666AGA666GA6A6 \n1 -58  V V vv rv V V IlVlJlJ V V V V V V U V V V rv V V VlJ u vrvvrvwvlv vvrVV V VVt \n'0 al \n\n800 \n\n400 \n\n600 \n\n200 \n\n0 \n\n.r; \n\n1 000 \n\ntime (s) \n\nFigure 1: Initial  1000 s 0.05 Hz rotation showing PAN (A). Slow-phase \neye velocity shows that PAN starts almost immediately and there is a \nslight reduction in VOR gain after 1000 s. Following 1 h continuous ro(cid:173)\n\ntation in the same goldfish (B),  VOR gain has decreased. \n\nsuppress  PAN (fig 4).  PAN observed  at  lower frequencies  (0.03  and  0.05  Hz)  typically \ndecreased in amplitude as rotation continued. \n\nPrevious work has shown that PAN was most likely to occur during prolonged rotations at \nfrequencies  between 0.05  and  0.1  Hz  (Dow and  Anastasio,  1997).  At  these frequencies, \nhabituation also caused a slight decrease in VOR gain (1.3  to  1.8 times,  initial gain I final \ngain) following  1 h of rotation.  At higher frequencies,  neither habituation nor PAN were \nobserved.  At lower frequencies  (0.03  Hz)  PAN could  occur before  habituation  substan(cid:173)\ntially reduced VOR gain (fig 4).  PAN, was not observed in naIve goldfish rotated a lower \nfrequency  (0.01  Hz)  where  VOR gain  fell  by  22 times  due  to  habituation  (Dow and  An(cid:173)\nastasio,  1997). \n\n\fA Model of Periodic Alternating Nystagmus \n\n141 \n\n4 MODEL \n\nPreviously, a non-linear limit cycle  model  was  constructed  by Leigh,  Robinson,  and  Zee \n(1981;  see also  Furman,  1989)  to  simulate  PAN  in  humans.  This  model  included  a  ve(cid:173)\nlocity storage loop with saturation, and  a central adaptation loop.  This second order sys(cid:173)\ntem  would  spontaneously  oscillate,  producing  PAN,  if the  gain  of the  velocity  storage \nloop was greater than  1. \n\nWe adjusted Robinson's model  to  simulate rotation inducible PAN and habituation in the \ngoldfish.  Input to  and output from  the  model  (fig  2)  represent head  and  slow-phase eye \nvelocity,  respectively.  The time  constants of the canal  (S'tc/(S'tc+ 1\u00bb and  velocity-storage \n(g.l(S'ts+l\u00bb  elements  were  set  to  the  value  of the canal  time  constant  as determined  ex(cid:173)\nperimentally in  goldfish ('Cc  = '1:s = 3 s)  (Hartman and  Klinke,  1980).  The time constant of \nthe central adaptation element (l/S'ta)  was  10 times longer ('1:a = 30 s).  The Laplace vari(cid:173)\nable (s) is complex frequency  (s = jro where /  is -1  and ro is frequency in rad/s).  The gain \nof the  velocity-storage loop (gs)  is  1.05  while that of the central  adaptation loop (ga)  is  1. \nThe  central  adaptation  loop  represents  in  part  a  negative  feedback  loop  onto  vestibular \nnucleus neurons through inhibitory Purkinje cells of the NU.  The vestibulo-cerebellum is \nknown  to  modulate  the  gain  of the  VOR  (Wilson  and  Melvill  Jones,  1979).  The  static \nnonlinearity in  the  velocity  storage  loop consists of a threshold  (\u00b1 0.0225)  and  a satura(cid:173)\ntion (\u00b1 1.25).  The threshold was added to  model the decay in PAN following termination \nof rotation (Dow and Anastasio, 1997), which is not modeled here. \n\ncanal \ntransfer \nfunction \n\nIncreases  or decreases  in  the  absolute  value  of ga  will  cause  VOR  habituation  or  PAN, \nrespectively.  However,  it  was  more  common  for  VOR  habituation  and  PAN  to  occur \nsimultaneously (fig  tB).  This behavior could  not be reproduced  with  the  lumped  model \n(fig  2).  It would  be  necessary  on one hand  to  increase ga  to decrease overall  VOR gain \nwhile,  on  the other hand, decrease ga  to  produce PAN.  A distributed  system  would  ad(cid:173)\ndress  this  problem,  with  multiple  parallel  pathways,  each  having  velocity-storage  and \nadaptive control  through  the  NU.  The idea can \nbe  illustrated  using  the  simplest distributed  sys(cid:173)\ntem  which  has  2  lumped  models  in  parallel  (not \nshown), each having an independently adjustable \ngao  The results from such a two  parallel pathway \nmodel  are shown in fig 3.  In one pathway, ga(h) \nwas  increased  to  model  habituation,  and  gio) \nwas  decreased  to  start  oscillations.  Paradoxi(cid:173)\ncally,  although  the  ultimate  effect  of increasing \nga(h)  is to  decrease  VOR gain,  the  initial  effect \nas  ga(h)  is  increased  is to  increase  gain.  This  is \ndue to the resonant frequency  of the system con(cid:173)\ntinuously shifting to  higher frequencies and tem(cid:173)\nporarily  matching the  frequency  of rotation  (see \nDISCUSSION).  Conversely,  when  ga(o)  is  de(cid:173)\ncreased, there is  a temporary decrease  in  gain as \nthe  resonant  frequency  moves  away  from  the \nfrequency  of rotation.  The two results are  com(cid:173)\nbined  after the  gain  is  reduced  by  half (fig  3B). \n\nFigure 2:  Model used \nto simulation PAN \n(Dow and Anastasio \n1997).  Used with \n\ncentral \nadaptation \n\neye velocity \n\nhead velocity \n\nL...--'r---' \n\npermission. \n\n\f142 \n\nE.  R  Dow and T.  1.  Anastasio \n\nThe  combined  result  shows  a  continual  decrease  in  VOR  gain  with  the  oscillations  su(cid:173)\nperimposed. \n\nQ) \n\n8-\n\n5 DISCUSSION \nIf the  nonlinearities  (i.e.  threshold \nand  saturation)  in  the  model  are \nignored, linear analysis shows that \nthe  model  will  be  unstable  when \n[(1  - gs)/ts + gJ'tal \nis  negative, \nand  will  oscillate  with  a period of \n[2m1(tstJga)].  With  the  initial \nparameters,  the  model  is  stable \nbecause \nthe  central  adaptation \nloop  can  compensate  for  the  un(cid:173)\nstable gain  of the  velocity  storage \nloop.  The  natural  frequency  of \nthe  system,  calculated  from  the \nabove equation, is 0.017 Hz.  This \nresonance,  which  peaks  at  the \nis  stiII \nresonant  frequency  but \npronounced at nearby frequencies, \nproduces  an  enhancement  of  the \nVOR  response.  The  hypothesis \nthat  low  frequency  VOR gain  en(cid:173)\nhancement  is  produced  by  a  po(cid:173)\ntentially  unstable  resonance  is  a \nnovel  feature  of our  model.  The \nnatural  frequency  increases  with \nincreases  in  ga  and  can  alter  the \nfrequency  specific  enhancement. \nDecreases  in  ga,  in  addition  to  decreasing the  natural  frequency,  also cause the  model  to \nbecome unstable.  (If ga  is  reduced  to  zero,  the  model  becomes first  order and  the equa(cid:173)\ntions  are  no  longer valid).  The ability  to  get either habituation  or PAN  by  varying  only \none parameter suggests that habituation and PAN are a related phenomena \n\n~  2[---\nB \nil=--~ \nal 4k \n\nFigure 3: Model at 0.03 Hz.  Two \nsimulations with differing values of \nga  (A) are combined in (B) with the \n\nQ)  -2L---------------~------~--------~----\n~ \n\nc \n--=::. ____________ ........ __  \n\n::: \n\n.... \n\n:::l \n> \n< \n~2  /\n\nvalues of ga  in (C). \n\n1000 \n\n2000 \ntime (sec) \n\n3000 \n\n. . \u2022. \n\n..... \n\n..... \n\nI::  0 L _____  \n\no \n\nThrough the process of habituation,  prolonged  low frequency  rotation  (0.01  Hz)  in  gold(cid:173)\nfish  severely decreased VOR gain, often abruptly and unilaterally (Dow and Anastasio, in \npress).  The decrease in  gain due to  habituation can effectively eliminate PAN at the low(cid:173)\nest frequency  at  which PAN  was  observed  (0.03  Hz)  as  shown  in  fig  4.  In  this example \nthe  naive  VOR  responds  symmetrically  for  the  first  cycle  of rotation.  It then  becomes \nmarkedly asymmetrical,  with  a strong,  unilateral response in one direction for  -10 cycles \nfollowed  by another in the opposite direction for -17 cycles.  The VOR response abruptly \nhabituates after that with  no  PAN.  Complete habituation can be simulated  by  further  in(cid:173)\ncreases in the value of ga'  in the limit-cycle model (fig 2).  Unilateral habituation has been \nsimulated previously  with a bilateral network  model of the VOR in which the cerebellum \ninhibits the vestibular nuclei unilaterally (Dow and Anastasio, in press). \n\n\fA Model of Periodic Alternating Nystagmus \n\n143 \n\n60 \n\n40 \n\nQ) \n\n~ 20 \n\"0 ---~ \n\n.l \n~ \n\n0 \n\n\u00b70 \no \nCD \n> \n~-20 \nQ) \n\nbJ  A ~tLL \nr~ I'~ \"'1 \n\n-40 \n\no \n\n200 \n\n400 \n\n600 \n\ntime (5) \n\n800 \n\nFigure 4: PAN superimposed on the VOR response to continuous rotation \nat 0.03 Hz.  Upper trace, slow-phase eye velocity (fast phases removed); \n\nlower trace, head velocity (not to scale). \n\nThe cerebellum has  several circuits which could provide an increase in firing rate of some \nPurkinje  cells  with  a  concurrent decrease  in  the  firing  rate  of other  Purkinje  cells  sug(cid:173)\ngested by  the model.  There are  many  lateral  inhibitory  pathways  including  inhibition of \nPurkinje cells to  neighboring Purkinje cells (Llimis  and Walton,  1990).  Therefore, if one \nPurkinje  cell  were  to  increase  its  firing  rate,  this  circuitry  suggests  that  neighboring \nPurkinje cells  would decrease their firing  rates.  Also, experimental  evidence shows that \nduring habituation, not all  vestibular nuclei gradually decrease their firing rate as might be \nexpected.  Kileny and colleagues (1980) recorded from  vestibular nucleus neurons during \nhabituation.  They  could  divide  the  neurons  into  3  roughly  equal  groups  based  on  re(cid:173)\nsponse over time:  continual decrease,  constant followed  by  a decrease,  and  increase fol(cid:173)\nlowed  by  decrease.  The  cerebellar circuitry  and  the  single-unit  recording  data  support \nmultiple,  variable  levels  of inhibition  from  the  NU.  How this  mechanism  may  work  is \nbeing explored with a more biologically realistic distributed model. \n\n6 CONCLUSION \n\nOur experimental results are consistent with a multi-parallel  pathway  model of the VOR. \nIn each pathway  an  unstable,  positive velocity-storage loop is  stabilized by  an  inhibitory, \ncentral  adaptation  loop,  and  their  interaction  produces  a  low-frequency  resonance  that \nenhances  the  low-frequency  response  of the  VOR.  Prolonged  rotation  at  specific  fre(cid:173)\nquencies could  produce a decrease  in central adaptation  VOR gain  in  some  pathways re(cid:173)\nsulting in  an  unstable,  low-frequency oscillation resembling PAN in  these  pathways.  An \n\n\f144 \n\nE.  R.  Dow and T.  J. Anastasio \n\nincrease in  adaptation loop gain in the other pathways would result in a decrease in VOR \ngain  resembling  habituation.  The  sum  over  the  VOR  pathways  would  show  PAN  and \nhabituation  occurring  together.  We  suggest  that  resonance  enhancement  and  mUltiple \nparallel  (i.e.  distributed)  pathways  are  necessary  to  model  the  interrelationship  between \nPAN and habituation. \n\nAcknowledgments \n\nThe work  was  supported  by  grant MH50577  from  the  National  Institutes  of Health.  We \nthank M. Zelaya and X. Feng for experimental assistance. \n\nReferences \n\nAngelaki DE and Hess BJM. J Neurophysl73 1729-1751  (1995). \n\nBaloh RW, Honrubia V and Konrad HR. Brain 99 11-26 (1976). \n\nDow ER and Anastasio TJ. NeuroReport 71305-1309 (1996). \n\nDow ER and Anastasio TJ. NeuroReport 82755-2759 (1997). \n\nDow ER and Anastasio TJ. J.  Computat.  Neuro.  in press. \n\nDow RS. J Comp Neurol63 527-548 (1936). \n\nDow RS. J Comp Neurol68 297-305 (1938). \n\nFernandez C and Fredrickson lM. Acta Otolaryngol Suppl192 52-62 (1964). \n\nFurman JMR, Wall C and Pang D. Brain 113  1425-1439 (1990). \n\nFurman lMR, Hain TC and Paige GO. 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Mammalian  Vestibular Physiology,  New York: Plenum \nPress, 1979. \n\n\f", "award": [], "sourceid": 1411, "authors": [{"given_name": "Ernst", "family_name": "Dow", "institution": null}, {"given_name": "Thomas", "family_name": "Anastasio", "institution": null}]}