Simulation of adaptive mechanisms in the vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR), which stabilizes the eyes in space during head movements, can undergo adaptive modification to maintain retinal stability in response to natural or experimental challenges. A number of models and neural sites have been proposed to account for this adaptation but these do not fully explain how the nervous system can detect and correct errors in both gain and phase of the VOR. This paper presents a general error correction algorithm based on the multiplicative combination of three signals (retinal slip velocity, head position, head velocity) directly relevant to processing of the VOR. The algorithm is highly specific, requiring the combination of particular sets of signals to achieve compensation. It is robust, with essentially perfect compensation observed for all gain (0.25X–4.0X) and phase (-180°–+180°) errors tested. Output of the model closely resembles behavioral data from both gain and phase adaptation experiments in a variety of species. Imposing physiological constraints (no negative activation levels or changes in the sign of unit weights) does not alter the effectiveness of the algorithm. These results suggest that the mechanisms implemented in our model correspond to those implemented in the brain of the behaving organism. Predictions concerning the nature of the adaptive process are specific enough to permit experimental verification using electrophysiological techniques. In addition, the model provides a strategy for adaptive control of any first order mechanical system.     

Simulation of adaptive modification of the vestibulo-ocular reflex with an adaptive filter model of the cerebellum

An adaptive linear filter model of the cerebellum (Fujita, 1982), which functions as a phase lead or lag compensator with learning capability, is applied to a problem of the cerebellar control of the vestibuloocular reflex (VOR). Under the assumption that the cerebellar flocculus accounts for adaptive modification of dynamic characteristics of the VOR, the cerebellar model was incorporated into a linear control model of the oculomotor system. The results of a simulation study are in good agreement with experimental data on eye movement.     

Plasticity in the adult vestibulo-ocular reflex arc.

Human subjects with maintained reversal of their horizontal field of vision exhibit very substantial adaptive changes in their 'horizontal' vestibulo-ocular reflex (v.o.r.). Short durations (8 min) of vision reversal during natural head movement led to 20% v.o.r. attenuation while long periods (4 weeks) eventually led to approximate reversal of the reflex. The reversed condition is approached by a complex, but highly systematic, series of changes in gain and phase of the reflex response relative to normal. Recovery after return to normal vision exhibits a similar duration, but different pattern, to that of the original adaptation. A chronic cat preparation with long-term optical reversal of vision has now been developed and shows similar adaptive and recovery changes at low test stimulus amplitudes, but different patterns of adaptive response at high amplitudes. An adaptive neural model employing known vestibulo-ocular pathways is proposed to account for these experimentally observed plastic changes. The model is used to predict the adapted response to patterns of stimulation extending beyond the range of experimental investigation.     

Decorrelation control by the cerebellum achieves oculomotor plant compensation in simulated vestibulo-ocular reflex

We introduce decorrelation control as a candidate algorithm for the cerebellar microcircuit and demonstrate its utility for oculomotor plant compensation in a linear model of the vestibulo-ocular reflex (VOR). Using an adaptive-filter representation of cerebellar cortex and an anti-Hebbian learning rule, the algorithm learnt to compensate for the oculomotor plant by minimizing correlations between a predictor variable (eye-movement command) and a target variable (retinal slip), without requiring a motor-error signal. Because it also provides an estimate of the unpredicted component of the target variable, decorrelation control can simplify both motor coordination and sensory acquisition. It thus unifies motor and sensory cerebellar functions.     

Visuomotor transformation in the fly gaze stabilization system

For sensory signals to control an animal's behavior, they must first be transformed into a format appropriate for use by its motor systems. This fundamental problem is faced by all animals, including humans. Beyond simple reflexes, little is known about how such sensorimotor transformations take place. Here we describe how the outputs of a well-characterized population of fly visual interneurons, lobula plate tangential cells (LPTCs), are used by the animal's gaze-stabilizing neck motor system. The LPTCs respond to visual input arising from both self-rotations and translations of the fly. The neck motor system however is involved in gaze stabilization and thus mainly controls compensatory head rotations. We investigated how the neck motor system is able to selectively extract rotation information from the mixed responses of the LPTCs. We recorded extracellularly from fly neck motor neurons (NMNs) and mapped the directional preferences across their extended visual receptive fields. Our results suggest that-like the tangential cells-NMNs are tuned to panoramic retinal image shifts, or optic flow fields, which occur when the fly rotates about particular body axes. In many cases, tangential cells and motor neurons appear to be tuned to similar axes of rotation, resulting in a correlation between the coordinate systems the two neural populations employ. However, in contrast to the primarily monocular receptive fields of the tangential cells, most NMNs are sensitive to visual motion presented to either eye. This results in the NMNs being more selective for rotation than the LPTCs. Thus, the neck motor system increases its rotation selectivity by a comparatively simple mechanism: the integration of binocular visual motion information.     

Eye stabilization by statocyst mediated oculomotor reflex inNautilus

Summary Nautilus pompilius can rotate its eye relative to its body so as to compensate for changes in its body orientation and maintain its eye fixed with respect to gravity. An ocular compensation reflex stabilizes its eye about the pitch axis against the rocking motions that occur as the animal swims by jet propulsion. The eye is not held absolutely still, as 1–2° spontaneous rotations occur even if the animal is clamped.If the animal is held in an unnatural orientation (rotated about the axis through its laterally directed eyes) the counterrotation of the eye is maintained for many minutes; it may compensate for 50–90% of imposed tilts up to ±30°. If the nautilus is tilted suddenly forward or backward, its compensation reflex is 50% complete within 0.3 s, and is complete in 1–2 s. The time course of the responses explains how the eye, during the 1 Hz rocking caused by swimming, can be held fixed in space to within 1–4°. The ocular compensation of each eye is mediated largely by the homolateral statocyst, as is shown by unilateral and bilateral ablation. The effect of ocular compensation is to keep image orientation on the retina fixed relative to gravity, and to prevent large rotational image motions from being caused by the nautilus's own swimming.This work would not have been possible without the fishing skill and the hospitality of the people of Bindoy, Negros Oriental, The Republic of the Philippines. We especially thank Mr. Wilson Vailoces who arranged for capture of experimental animals. We are indebted to Mr. Walter Schneider for his technical assistance on shipboard. This study, a part of the RV Alpha Helix Southeast Asian Expedition was supported by the National Science Foundation under grants of 74-01883 and OCE 74-02888 to the Scripps Institution of Oceanography and BM 575-01149 to Iowa State University. NIH Grant R01-EY01539 to P. Hartline supported data analyses.     

Neural network models of velocity storage in the horizontal vestibulo-ocular reflex

The vestibulo-ocular reflex (VOR) produces compensatory eye movements by utilizing head rotational velocity signals from the semicircular canals to control contractions of the extraocular muscles. In mammals, the time course of horizontal VOR is longer than that of the canal signals driving it, revealing the presence of a central integrator known as velocity storage. Although the neurons mediating VOR have been described neurophysiologically, their properties, and the mechanism of velocity storage itself, remain unexplained. Recent models of integration in VOR are based on systems of linear elements, interconnected in arbitrary ways. The present study extends this work by modeling horizontal VOR as a learning network composed of nonlinear model neurons. Network architectures are based on the VOR arc (canal afferents, vestibular nucleus (VN) neurons and extraocular motoneurons) and have both forward and lateral connections. The networks learn to produce velocity storage integration by forming lateral (commissural) inhibitory feedback loops between VN neurons. These loops overlap and interact in a complex way, forming both fast and slow VN pathways. The networks exhibit some of the nonlinear properties of the actual VOR, such as dependency of decay rate and phase lag upon input magnitude, and skewing of the response to higher magnitude sinusoidal inputs. Model VN neurons resemble their real counterparts. Both have increased time constant and gain, and decreased spontaneous rate as compared to canal afferents. Also, both model and real VN neurons exhibit rectification and skew. The results suggest that lateral inhibitory interactions produce velocity storage and also determine the properties of neurons mediating VOR. The neural network models demonstrate how commissural inhibition may be organized along the VOR pathway.     

A linear canal-otolith interaction model to describe the human vestibulo-ocular reflex

A control systems model of the vestibulo-ocular reflex (VOR) originally derived for yaw rotation about an eccentric axis (Crane et al. 1997) was applied to data collected during ambulation and dynamic posturography. The model incorporates a linear summation of an otolith response due to head translation scaled by target distance, adding to a semi-circular canal response that depends only on angular head rotation. The results of the model were compared with human experimental data by supplying head angular velocity as determined by magnetic search coil recording as the input for the canal branch of the model and supplying linear acceleration as determined by flux gate magnetometer measurements of otolith position. The model was fit to data by determining otolith weighting that enabled the model to best fit the data. We fit to the model experimental data from normal subjects who were: standing quietly, walking, running, or making active sinusoidal head movements. We also fit data obtained during dynamic posturography tasks of: standing on a platform sliding in a horizontal plane at 0.2 Hz, standing directly on a platform tilting at 0.1 Hz, and standing on the tilting platform buffered by a 5-cm thick foam rubber cushion. Each task was done with the subject attending a target approximately 500, 100, or 50 cm distant, both in light and darkness. The model accurately predicted the observed VOR response during each test. Greater otolith weighting was required for near targets for nearly all activities, consistent with weights for the otolith component found in previous studies employing imposed rotations. The only exceptions were for vertical axis motion during standing, sliding, and tilting when the platform was buffered with foam rubber. In the horizontal axis, the model always fit near target data better with a higher otolith component. Otolith weights were similar with the target visible and in darkness. The model predicts eye movement during both passive whole-body rotation and free head movement in space implying that the VOR is controlled by a similar mechanism during both situations. Factors such as vision, proprioception, and efference copy that are available during head free motion but not during whole-body rotation are probably not important to gaze stabilization during ambulation and postural stabilizing movement. The linearity of the canal-otolith interaction was tested by re-analysis of the whole body rotation data on which the model is based (Crane et al. 1997). Normalized otolith-mediated gain enhancement was determined for each axis of rotation. This analysis uncovered minor non-linearities in the canal-otolith interaction at frequencies above 1.6 Hz and when the axis of rotation was posterior to the head. Received: 11 March 1998 / Received in revised form: 1 March 1999     

The use of matrices in analyzing the three-dimensional behavior of the vestibulo-ocular reflex

The vestibulo-ocular reflex rotates the eye about the axis of a head rotation at the same speed but in the opposite direction to make the visual axes in space independent of head motion. This reflex works in all three degrees of freedom: roll, pitch, and yaw. The rotations may be described by vectors and the reflex by a transformation in the form of a matrix. The reflex consists of three parts: sensory, central, and motor. The transduction of head rotation into three neural signals, which may also be described by a vector, is described by a canal matrix. The neural, motorcommand vector is transformed to an eye rotation by a muscle matrix. Since these two matrices are known, one can solve for the central matrix which gives the strength of the connections between all the vestibular neurons and all the eye-muscle motoneurons. The role of the metric tensor in these transformations is described. This method of analysis is used in three applications. A lesion may be simulated by altering the elements in any or all of the three component matrices. By matrix multiplication, the resulting abnormal behavior of the reflex can be described quantitatively in all degrees of freedom. The method is also used to directly compare the differences in brain-stem connections between humans and rabbits that accommodate the altered actions of the muscles of the two species. Finally the method allows a quantitative assessment of the changes that take place in the brainstem connections when plastic changes are induced by artificially dissociating head movements from apparent motion of the visual environment.     

A biologically inspired controller for hexapod walking: simple solutions by exploiting physical properties

The locomotor system of slowly walking insects is well suited for coping with highly irregular terrain and therefore might represent a paragon for an artificial six-legged walking machine. Our investigations of the stick insect Carausius morosus indicate that these animals gain their adaptivity and flexibility mainly from the extremely decentralized organization of the control system that generates the leg movements. Neither the movement of a single leg nor the coordination of all six legs (i.e., the gait) appears to be centrally pre-programmed. Thus, instead of using a single, central controller with global knowledge, each leg appears to possess its own controller with only procedural knowledge for the generation of the leg's movement. This is possible because exploiting the physical properties avoids the need for complete information on the geometry of the system that would be a prerequisite for explicitly solving the problems. Hence, production of the gait is an emergent property of the whole system, in which each of the six single-leg controllers obeys a few simple and local rules in processing state-dependent information about its neighbors.     

The cerebellar nodulus/uvula integrates otolith signals for the translational vestibulo-ocular reflex

BACKGROUND: The otolith-driven translational vestibulo-ocular reflex (tVOR) generates compensatory eye movements to linear head accelerations. Studies in humans indicate that the cerebellum plays a critical role in the neural control of the tVOR, but little is known about mechanisms of this control or the functions of specific cerebellar structures. Here, we chose to investigate the contribution of the nodulus and uvula, which have been shown by prior studies to be involved in the processing of otolith signals in other contexts. METHODOLOGY/PRINCIPAL FINDINGS: We recorded eye movements in two rhesus monkeys during steps of linear motion along the interaural axis before and after surgical lesions of the cerebellar uvula and nodulus. The lesions strikingly reduced eye velocity during constant-velocity motion but had only a small effect on the response to initial head acceleration. We fit eye velocity to a linear combination of head acceleration and velocity and to a dynamic mathematical model of the tVOR that incorporated a specific integrator of head acceleration. Based on parameter optimization, the lesion decreased the gain of the pathway containing this new integrator by 62%. The component of eye velocity that depended directly on head acceleration changed little (gain decrease of 13%). In a final set of simulations, we compared our data to the predictions of previous models of the tVOR, none of which could account for our experimental findings. CONCLUSIONS/ SIGNIFICANCE: Our results provide new and important information regarding the neural control of the tVOR. Specifically, they point to a key role for the cerebellar nodulus and uvula in the mathematical integration of afferent linear head acceleration signals. This function is likely to be critical not only for the tVOR but also for the otolith-mediated reflexes that control posture and balance.     

Interaction of the angular and linear components of the horizontal vestibulo-ocular reflex in the pigeon

Pigeons were exposed to centric and eccentric horizontal rotations in darkness by velocity trapezoid. Different in sign the duration alterations of the opposite directed horizontal eye nystagmus occurred during otolith membrane shifts in sagittal as well as frontal planes. A direct dependence was found between the duration alterations of the primary nystagmus phase and the peak value alterations of its slow phase velocity under increased (but not decreased) centrifugal force. In the both cases, if duration of the primary nystagmus phase was enlarged, duration of its secondary phase was diminished and vice versa. It suggests the otolith component does not decay up to zero by constant velocity and at once after rotation; by deceleration it is biphasic. In affirms the own hypothesis that the linear component is asymmetric central neuronal activity that modifies the canal component even if this activity by itself is not enough for eye movement initiation.     

The development of the static vestibulo-ocular reflex in the Southern Clawed Toad,Xenopus laevis

In the clawed toad, Xenopus laevis, the static vestibulo-ocular reflex appears in 3 days old tadpoles (developmental stage 42) (Fig. 2). The amplitude and gain of this reflex increase up to stage 52, and then decrease to an almost constant value at stage 60 and older tadpoles (Fig. 3). The most effective roll angle gradually increases during development (Fig. 4). The size of the sensory epithelia reaches the final value at the end of the premetamorphic period (stage 56) (Fig. 5). The small-cellular medial ventral vestibular nucleus (VVN) reaches its maximal number of neurons before the large-cellular lateral VVN. Cell death is more pronounced in the medial than in the lateral part of the VVN. In the dorsal vestibular nucleus (DVN), the numerical development of the small and large neurons is similar to that in the small-cellular medial and large-cellular lateral portion of the VVN (Fig. 7). The results demonstrate that labyrinth and oculomotor centres are anatomically connected before the labyrinth and the vestibular nuclei are fully developed. We discuss the possibility that the ciliary polarity pattern of the sensory epithelium is radial during the first period of life, and changes to the vertebrate fan-type pattern during the second week of life. According to the increase of gain during the first three weeks of life, an increase of the spontaneous activity of vestibular neurons may occur during this period.     

The development of the static vestibulo-ocular reflex in the Southern Clawed Toad,Xenopus laevis

The static vestibulo-ocular reflex was investigated in tadpoles at different times following unilateral destruction of the labyrinth during the period of early organogenesis and premetamorphosis. Balance compensation is completed after a few weeks, while gain compensation only occurs partially (Figs. 2-4). Tadpoles hemilabyrinthectomized in the age of 2.5 days (stage 38) develop no vestibular nuclei on their lesioned side, while tadpoles operated later in their life, possess these nuclei (Figs. 5, 6) even if they were not detectable at the operation day (Fig. 7). For their dorsal vestibular nucleus (DVN), the number of neurons is usually larger on the intact than on the lesioned side; while for the ventral vestibular nucleus (VVN), there is either numerical symmetry or a transient decrease of cell number on the intact side (Fig. 5). The results demonstrate that vestibular compensation occurs even if vestibular nuclei have developed only on one side, i.e. the vestibular commissure is not a prerequisite for a successful compensation process. It is discussed whether the use of extra-vestibular error signals for balance but not for gain compensation may cause the differences in time courses of both compensation processes.     

The development of the static vestibulo-ocular reflex in the Southern Clawed Toad,Xenopus laevis

Summary Acute hemilabyrinthectomized tadpoles of the Southern Clawed Toad (Xenopus laevis), younger than stage 47 (about 6 days old), perform no static vestibulo-ocular reflex (Fig. 1). Older acute lesioned animals respond with compensatory movements of both eyes during static roll. Their threshold roll angle, however, depends on the developmental stage. For lesioned stages 60 to 64, it is 75° while stage 52 to 56 tadpoles respond even during a lateral roll of 15° (Figs. 1 and 2). Selective destruction of single macula and crista organs revealed that the static vestibulo-ocular reflex is evoked by excitation of the macula utriculi (Figs. 3 and 4) even in young tadpoles.The results demonstrate that bilateral projections of the vestibular apparatus must have developed at the time of occurrence of the static VOR, that during the first week of life the excitation of a single labyrinth is subthreshold (Fig. 1). We discuss the possibility whether the loss of the static VOR during the prometamorphic period of life (Fig. 2) is caused by increasing formation of multimodal connections in the vestibular pathway.Abbreviations eye angle - roll angle - () response characteristic - A response amplitude - G response gain - VOR vestibulo-ocular reflex     

A neural network model of the vestibulo-ocular reflex using a local synaptic learning rule.

Vertebrates use the vestibulo-ocular reflex to maintain clear vision during head movements. This reflex requires eye-velocity commands from the semicircular canals to be integrated (mathematically) to produce eye-position commands for the extraocular muscles. This is accomplished by a neural network in the caudal pons. A model of this network is proposed using positive feedback via lateral inhibition. The model has been adapted to a learning network. We have developed a synaptic learning rule using only local information to make the model more physiological.     

A biophysical approach to the Spatial Function of eye movements extraocular proprioception and the vestibulo-ocular reflex

The eyeball and the extraocular muscles are used as a paradigm to design a linear spatial model of a single joint with a redundant set of muscles. On the basis of this model relations are derived between orientation, torque, motor commands, and proprioceptive signals. These relations show that the tenet underlying the tensorial interpretation of neural signals in sensorimotor systems does not have general validity. A mechanism is proposed to show how proprioception may play a role in optimizing the coordination of muscles during spatial tasks. Further, a new concept is suggested that allows one to predict the neural connectivities mediating the redundant spatial vestibulo-ocular reflex. This concept has the advantage of minimizing both sensorial error and motor effort.