{"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. Chapman and Hall, NY. \n\nFunnan J.M., O'Leary D.P. and Wolfe lW. 1982. 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