A nystagmus strategy to linearize the vestibulo-ocular reflex

The quick-phase system

Two types of rapid eye movements, saccades and quick phases (QP), share the same neural circuits, but have different purposes. Quick phases reset the eye in the orbit, avoiding an attempt to move the eyes beyond the oculomotor range. In general, QP move the eyes into the direction one is turning. This is useful because it brings the world toward which one is turning into view more quickly. Algorithms for deciding when to begin a QP, and how large it should be, move the eyes, on average, into the direction of turning. This makes it reasonable to assume that the afoveate QP system evolved to provide commands in a head-coordinate system. The saccadic system evolved in foveate animals on top of this system, and thus it is reasonable to assume it also provides commands in head coordinates.

Modeling gaze position-dependent opsoclonus

Opsoclonus/flutter (O/F) is a rare disorder of the saccadic system. Previously, we modeled O/F that developed in a patient following abuse of anabolic steroids. That model, as in all models of the saccadic system, generates commands to make a change in eye position. Recently, we saw a patient who developed a unique form of opsoclonus following a concussion. The patient had postsaccadic ocular flutter in both directions of gaze, and opsoclonus during fixation and pursuit in the left hemifield. A new model of the saccadic system is needed to account for this gaze-position dependent O/F. We started with our prior model, which contains two key elements, mutual inhibition between inhibitory burst neurons on both sides and a prolonged reactivation time of the omnipause neurons (OPNs). We included new inputs to the OPNs from the nucleus prepositus hypoglossi and the frontal eye fields, which contain position-dependent neurons. This provides a mechanism for delaying OPN reactivation, and creating a gaze-position dependence. A simplified pursuit system was also added, the output of which inhibits the OPNs, providing a mechanism for gaze-dependence during pursuit. The rest of the model continues to generate a command to change eye position.

Modeling eye-head gaze shifts in multiple contexts without motor planning

During gaze shifts, the eyes and head collaborate to rapidly capture a target (saccade) and fixate it. Accordingly, models of gaze shift control should embed both saccadic and fixation modes and a mechanism for switching between them. We demonstrate a model in which the eye and head platforms are driven by a shared gaze error signal. To limit the number of free parameters, we implement a model reduction approach in which steady-state cerebellar effects at each of their projection sites are lumped with the parameter of that site. The model topology is consistent with anatomy and neurophysiology, and can replicate eye-head responses observed in multiple experimental contexts: 1) observed gaze characteristics across species and subjects can emerge from this structure with minor parametric changes; 2) gaze can move to a goal while in the fixation mode; 3) ocular compensation for head perturbations during saccades could rely on vestibular-only cells in the vestibular nuclei with postulated projections to burst neurons; 4) two nonlinearities suffice, i.e., the experimentally-determined mapping of tectoreticular cells onto brain stem targets and the increased recruitment of the head for larger target eccentricities; 5) the effects of initial conditions on eye/head trajectories are due to neural circuit dynamics, not planning; and 6) "compensatory" ocular slow phases exist even after semicircular canal plugging, because of interconnections linking eye-head circuits. Our model structure also simulates classical vestibulo-ocular reflex and pursuit nystagmus, and provides novel neural circuit and behavioral predictions, notably that both eye-head coordination and segmental limb coordination are possible without trajectory planning.

Vestibular Compensation in Unilateral Patients Often Causes Both Gain and Time Constant Asymmetries in the VOR

The vestibulo-ocular reflex (VOR) is essential in our daily life to stabilize retinal images during head movements. Balanced vestibular functionality secures optimal reflex performance which otherwise can be distorted by peripheral vestibular lesions. Luckily, vestibular compensation in different neuronal sites restores VOR function to some extent over time. Studying vestibular compensation gives insight into the possible mechanisms for plasticity in the brain. In this work, novel experimental analysis tools are employed to reevaluate the VOR characteristics following unilateral vestibular lesions and compensation. Our results suggest that following vestibular lesions, asymmetric performance of the VOR is not only limited to its gain. Vestibular compensation also causes asymmetric dynamics, i.e., different time constants for the VOR during leftward or rightward passive head rotation. Potential mechanisms for these experimental observations are provided using simulation studies.

Automatic Classification of the Vestibulo-Ocular Reflex Nystagmus: Integration of Data Clustering and System Identification

The vestibulo-ocular reflex (VOR) plays an important role in our daily activities by enabling us to fixate on objects during head movements. Modeling and identification of the VOR improves our insight into the system behavior and improves diagnosis of various disorders. However, the switching nature of eye movements (nystagmus), including the VOR, makes dynamic analysis challenging. The first step in such analysis is to segment data into its subsystem responses (here slow and fast segment intervals). Misclassification of segments results in biased analysis of the system of interest. Here, we develop a novel three-step algorithm to classify the VOR data into slow and fast intervals automatically. The proposed algorithm is initialized using a K-means clustering method. The initial classification is then refined using system identification approaches and prediction error statistics. The performance of the algorithm is evaluated on simulated and experimental data. It is shown that the new algorithm performance is much improved over the previous methods, in terms of higher specificity.

Hybrid model of the context dependent vestibulo-ocular reflex: implications for vergence-version interactions

The vestibulo-ocular reflex (VOR) is an involuntary eye movement evoked by head movements. It is also influenced by viewing distance. This paper presents a hybrid nonlinear bilateral model for the horizontal angular vestibulo-ocular reflex (AVOR) in the dark. The model is based on known interconnections between saccadic burst circuits in the brainstem and ocular premotor areas in the vestibular nuclei during fast and slow phase intervals of nystagmus. We implemented a viable switching strategy for the timing of nystagmus events to allow emulation of real nystagmus data. The performance of the hybrid model is evaluated with simulations, and results are consistent with experimental observations. The hybrid model replicates realistic AVOR nystagmus patterns during sinusoidal or step head rotations in the dark and during interactions with vergence, e.g., fixation distance. By simply assigning proper nonlinear neural computations at the premotor level, the model replicates all reported experimental observations. This work sheds light on potential underlying neural mechanisms driving the context dependent AVOR and explains contradictory results in the literature. Moreover, context-dependent behaviors in more complex motor systems could also rely on local nonlinear neural computations.

Identification of the vestibulo-ocular reflex dynamics

The vestibulo-ocular reflex (VOR) plays an important role in our daily activities by enabling us to fixate on objects during head movements. Modeling and identification of the VOR improves our insight into the system behavior and helps in diagnosing various disorders. However, the switching nature of eye movements, including the VOR, makes the dynamic analysis challenging. In this work we are using integration of subspace and prediction error methods to analyze VOR dynamics. The performance of the method is evaluated using simulation studies and experimental data.

A Comparative Analysis of Speed Profile Models for Ankle Pointing Movements: Evidence that Lower and Upper Extremity Discrete Movements are Controlled by a Single Invariant Strategy

Little is known about whether our knowledge of how the central nervous system controls the upper extremities (UE), can generalize, and to what extent to the lower limbs. Our continuous efforts to design the ideal adaptive robotic therapy for the lower limbs of stroke patients and children with cerebral palsy highlighted the importance of analyzing and modeling the kinematics of the lower limbs, in general, and those of the ankle joints, in particular. We recruited 15 young healthy adults that performed in total 1,386 visually evoked, visually guided, and target-directed discrete pointing movements with their ankle in dorsal-plantar and inversion-eversion directions. Using a non-linear, least-squares error-minimization procedure, we estimated the parameters for 19 models, which were initially designed to capture the dynamics of upper limb movements of various complexity. We validated our models based on their ability to reconstruct the experimental data. Our results suggest a remarkable similarity between the top-performing models that described the speed profiles of ankle pointing movements and the ones previously found for the UE both during arm reaching and wrist pointing movements. Among the top performers were the support-bounded lognormal and the beta models that have a neurophysiological basis and have been successfully used in upper extremity studies with normal subjects and patients. Our findings suggest that the same model can be applied to different "human" hardware, perhaps revealing a key invariant in human motor control. These findings have a great potential to enhance our rehabilitation efforts in any population with lower extremity deficits by, for example, assessing the level of motor impairment and improvement as well as informing the design of control algorithms for therapeutic ankle robots.

Hybrid nonlinear model of the angular vestibulo-ocular reflex

A hybrid nonlinear bilateral model for the horizontal angular vestibulo-ocular reflex (AVOR) is presented in this paper. The model relies on known interconnections between saccadic burst circuits in the brainstem and ocular premotor areas in the vestibular nuclei during slow and fast phase intervals. A viable switching strategy for the timing of nystagmus events is proposed. Simulations show that this hybrid model replicates AVOR nystagmus patterns that are observed in experimentally recorded data.

A sparse matrix approach for simultaneous quantification of nystagmus and saccade

The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.

Automatic classification and robust identification of vestibulo-ocular reflex responses: from theory to practice: introducing GNL-HybELS

The Vestibulo-Ocular Reflex (VOR) stabilizes images of the world on our retinae when our head moves. Basic daily activities are thus impaired if this reflex malfunctions. During the past few decades, scientists have modeled and identified this system mathematically to diagnose and treat VOR deficits. However, traditional methods do not analyze VOR data comprehensively because they disregard the switching nature of nystagmus; this can bias estimates of VOR dynamics. Here we propose, for the first time, an automated tool to analyze entire VOR responses (slow and fast phases), without a priori classification of nystagmus segments. We have developed GNL-HybELS (Generalized NonLinear Hybrid Extended Least Squares), an algorithmic tool to simultaneously classify and identify the responses of a multi-mode nonlinear system with delay, such as the horizontal VOR and its alternating slow and fast phases. This algorithm combines the procedures of Generalized Principle Component Analysis (GPCA) for classification, and Hybrid Extended Least Squares (HybELS) for identification, by minimizing a cost function in an optimization framework. It is validated here on clean and noisy VOR simulations and then applied to clinical VOR tests on controls and patients. Prediction errors were less than 1 deg for simulations and ranged from .69 deg to 2.1 deg for the clinical data. Nonlinearities, asymmetries, and dynamic parameters were detected in normal and patient data, in both fast and slow phases of the response. This objective approach to VOR analysis now allows the design of more complex protocols for the testing of oculomotor and other hybrid systems.

GNL-HybELS: an algorithm to classify and identify VOR responses simultaneously

The Vestibulo-Ocular Reflex (VOR) stabilizes the images of the world on the retinae when the head is in motion. Basic daily activities such as walking or driving depend on the proper functioning of this reflex. For several decades, scientists have developed methods to model and identify this system mathematically. However, traditional methods cannot analyze VOR data comprehensively because they disregard pieces of data (fast phases) which biases estimated reflex dynamics. Here we propose, for the first time, an automated tool to analyze entire VOR responses (slow and fast phases), without apriori classification of nystagmus segments.

Simultaneous identification of oculomotor subsystems using a hybrid system approach: introducing hybrid extended least squares

The oculomotor system plays an essential role in our daily activities. It keeps the images of the world steady on the retina and enables us to track visual targets, or switch between targets. The modeling and identification of this system is key in the diagnosis and treatment of various diseases and lesions. Today, clinical protocols incorporate mathematical techniques to test the functionality of patients' oculomotor modalities through the analysis of the patients' responses to various stimuli. We have developed a new tool for simultaneous identification of the two modes of oculomotor responses, using hybrid extended least squares (HybELS), a novel identification method tailored for hybrid autoregressive moving average with exogenous input models. Previously, modified extended least squares (MELS) was proposed for the identification of vestibular nystagmus dynamics, one mode at a time. It involved searching for segment initial conditions (ICs) to avoid biased results. HybELS identifies both modes simultaneously, and does not require estimation of ICs. Results on experimental vestibuloocular reflex (VOR) data show that HybELS proves to be more robust than MELS with respect to identification of complex models. Furthermore, it is notably less computationally expensive than MELS. In the multi-input case, HybELS outperforms other tested methods, including MELS, both in parameter estimation and prediction error.

Internal models and neural computation in the vestibular system

The vestibular system is vital for motor control and spatial self-motion perception. Afferents from the otolith organs and the semicircular canals converge with optokinetic, somatosensory and motor-related signals in the vestibular nuclei, which are reciprocally interconnected with the vestibulocerebellar cortex and deep cerebellar nuclei. Here, we review the properties of the many cell types in the vestibular nuclei, as well as some fundamental computations implemented within this brainstem-cerebellar circuitry. These include the sensorimotor transformations for reflex generation, the neural computations for inertial motion estimation, the distinction between active and passive head movements, as well as the integration of vestibular and proprioceptive information for body motion estimation. A common theme in the solution to such computational problems is the concept of internal models and their neural implementation. Recent studies have shed new insights into important organizational principles that closely resemble those proposed for other sensorimotor systems, where their neural basis has often been more difficult to identify. As such, the vestibular system provides an excellent model to explore common neural processing strategies relevant both for reflexive and for goal-directed, voluntary movement as well as perception.

A Hybrid Extended Least Squares method (HybELS) for Vestibulo-Ocular Reflex identification

The Vestibulo-Ocular Reflex (VOR) plays an essential role in the majority of daily activities by keeping the images of the world steady on the retina when either the environment or the body is moving. The modeling and identification of this system plays a key role in the diagnosis and treatment of various diseases and lesions, and their associated syndromes. Today, clinical protocols incorporate mathematical techniques for testing the functionality of patients' VORs through the analysis of the patients' responses to various stimuli. We have developed a new tool for simultaneous identification of the two modes of the horizontal VOR, using a novel algorithm. This algorithm, HybELS (Hybrid Extended Least Squares), is a regression-based identification method tailored for hybrid ARMAX (AutoRegressive Moving Average with eXogenous inputs) models, which can also be used for the identification of other neural systems. In the context of the VOR, MELS (Modified Extended Least Squares) has been proposed previously for the identification of vestibular nystagmus dynamics, one mode at a time. It also involved searching for segment initial conditions to avoid biased results. Our hybrid approach identifies the two modes simultaneously, and does not require estimation of initial conditions, since it takes advantage of state continuity in the transitions between fast and slow phases. The results on experimental VOR in the dark show that HybELS outperforms MELS in several aspects: It proves to be more robust than MELS with respect to the system order used for identification, while resulting in more accurate estimates in almost all contexts as well. Furthermore, due to the hybrid nature of the method, its calculations are algebraically more compact, and HybELS turns out to be much less computationally expensive than MELS.

Implications of gain modulation in brainstem circuits: VOR control system

Gain modulation is believed to be a common integration mechanism employed by neurons to combine information from various sources. Although gain fields have been shown to exist in some cortical and subcortical areas of the brain, their existence has not been explored in the brainstem. In the present modeling study, we develop a physiologically relevant simplified model for the angular vestibulo-ocular reflex (VOR) to show that gain modulation could also be the underlying mechanism that modifies VOR function with sensorimotor context (i.e. concurrent eye positions and stimulus intensity). The resulting nonlinear model is further extended to generate both slow and quick phases of the VOR. Through simulation of the hybrid nonlinear model we show that disconjugate eye movements during the VOR are an inevitable consequence of the existence of such gain fields in the bilateral VOR pathway. Finally, we will explore the properties of the predicted disconjugate component. We will demonstrate that the apparent phase characteristics of the disconjugate response vary with the concurrent conjugate component.

A nonlinear model of the neural integrator improves detection of deficits in the human VOR

A nonlinear model has been proposed to describe the set-point-dependent characteristics of the neural integrator (NI) in the oculomotor system. It was shown to yield improved prediction of slow-phase eye position in the vestibulo-ocular reflex (VOR) of normal subjects, when compared to the classical linear model of the NI. In this paper, we compare the parameters of this nonlinear NI model fitted to VOR data from: 1) compensated subjects diagnosed with vestibular deficiencies such as vestibular neuronitis and Meniere's disease and 2) normal (symptom-free) subjects. The identified models exhibit more severe nonlinearity in VOR patients than the normal controls. Several of the identified parameters in patients unmask asymmetries and more context dependence in the NI and in the VOR gain that are consistent with the lesioned side and could serve to support detection of lesions even after compensation.

A functional approach to modeling M1 single-unit activity recorded in three primate motor control studies

When monkeys make movements with or without external force perturbations, or generate isometric forces in different directions from different workspace positions, primary motor cortex (M1) cell activity shows systematic changes in directional tuning and in force-generation gains as a function of arm posture. However, it may be simplistic to assume most control intelligence is in the cortex while the brainstem and especially the spinal cord do little more than passively implement pontifical descending commands. More recent studies like [1-4] do suggest a different perspective. Furthermore, systematic changes in directionality of M1 cell and limb muscle EMG activity may stem partly from the feedback (aka reflex) loops, physical properties of limb biomechanics, muscle anisotropy and force production nonlinearities, and their interplay with task conditions, and not only due to predictive feedforward central commands.

Modeling the nonlinear context dependency of the neural integrator in the vestibuloocular reflex

A neural integrator (NI) is presumed to exist in the oculomotor system to assist in numerous tasks such as maintaining gaze on imaginary targets in the dark. It is shared by all ocular reflexes including the vestibuloocular reflex (VOR). It has been widely accepted that the NI acts as a "perfect" integrator even in the dark with time constants as large as 1950s. However, the NI time constant is often less than ideal and its value can also be dependent on context [W. W. P. Chan and H. L. Galiana, "Integrator function in the oculomotor system is dependent on sensory context," J. Neurophysiol., vol. 93, pp. 3709--3717, Feb. 2005.]. In this paper, a nonlinear feedback model is postulated to model the context-dependent properties of the NI. Algorithms are first developed and validated to fit both linear and nonlinear NI models to experimental data in the presence of ocular nystagmus. Preliminary results indicate that even normal subjects can have a nonlinear VOR and NI.

A non-linear model of the neural integrator in oculomotor control

A Neural Integrator (NI) is presumed to exist in the oculomotor system to assist in numerous tasks such as maintaining gaze on imaginary targets in the dark. It has been widely accepted that the NI acts as a 'perfect' integrator even in the dark with time constants as large as 50s. However, the NI time constant has been found to be much less than ideal and its value can also be dependent on context. In this paper, a nonlinear feedback model is postulated to model the context-dependent properties of NI and its performance is compared to a linear feedback model.

A reevaluation of the inverse dynamic model for eye movements

To construct an appropriate motor command from signals that provide a representation of desired action, the nervous system must take into account the dynamic characteristics of the motor plant to be controlled. In the oculomotor system, signals specifying desired eye velocity are thought to be transformed into motor commands by an inverse dynamic model of the eye plant that is shared for all types of eye movements and implemented by a weighted combination of eye velocity and position signals. Neurons in the prepositus hypoglossi and adjacent medial vestibular nuclei (PH-BT neurons) were traditionally thought to encode the "eye position" component of this inverse model. However, not only are PH-BT responses inconsistent with this theoretical role, but compensatory eye movement responses to translation do not show evidence for processing by a common inverse dynamic model. Prompted by these discrepancies between theoretical notions and experimental observations, we reevaluated these concepts using multiple-frequency rotational and translational head movements. Compatible with the notion of a common inverse model, we show that PH-BT responses are unique among all premotor cell types in bearing a consistent relationship to the motor output during eye movements driven by different sensory stimuli. However, because their responses are dynamically identical to those of motoneurons, PH-BT neurons do not simply represent an internal component of the inverse model, but rather its output. They encode and distribute an estimate of the motor command, a signal critical for accurate motor execution and learning.

A biologically inspired model of binocular control on a free head

A single layer, symmetrical bilateral controller with dual modalities has been developed for a robotic head, based on symmetries in brainstem circuits for the oculomotor control system (OCS). This robotic head controller is unique in the biological approach during its development, and its structural elegance afforded by the single layer organization. Extensions to this controller are based on connections between brainstem and cerebellar structures, and the OCS circuit. To make the robotic head better reflect biology: 1. velocity feedback is added to account for floccular projections to the brainstem OCS, and 2. integral feedback is added to represent findings of vector averaging mechanisms in superior colliculus. The resulting OCS controller has a structure better matched with what has been reported in brainstem premotor-circuit topology. The new bilateral OCS not only retains the structural and analytical simplicity of its precursor, but it now has an improved bandwidth for its pursuit mode, and can track faster objects with smaller errors, while requiring fewer saccades.

Visual-Vestibular Interaction Hypothesis for the Control of Orienting Gaze Shifts by Brain Stem Omnipause Neurons

Models of combined eye-head gaze shifts all aim to realistically simulate behaviorally observed movement dynamics. One of the most problematic features of such models is their inability to determine when a saccadic gaze shift should be initiated and when it should be ended. This is commonly referred to as the switching mechanism mediated by omni-directional pause neurons (OPNs) in the brain stem. Proposed switching strategies implemented in existing gaze control models all rely on a sensory error between instantaneous gaze position and the spatial target. Accordingly, gaze saccades are initiated after presentation of an eccentric visual target and subsequently terminated when an internal estimate of gaze position becomes nearly equal to that of the target. Based on behavioral observations, we demonstrate that such a switching mechanism is insufficient and is unable to explain certain types of movements. We propose an improved hypothesis for how the OPNs control gaze shifts based on a visual-vestibular interaction of signals known to be carried on anatomical projections to the OPN area. The approach is justified by the analysis of recorded gaze shifts interrupted by a head brake in animal subjects and is demonstrated by implementing the switching mechanism in an anatomically based gaze control model. Simulated performance reveals that a weighted sum of three signals: gaze motor error, head velocity, and eye velocity, hypothesized as inputs to OPNs, successfully reproduces diverse behaviorally observed eye-head movements that no other existing model can account for.

A nonlinear model for context-dependent modulation of the binocular VOR

Studies on the behavior of the vestibulo-ocular reflex (VOR) reveal that the monocular reflex gain is adjusted according to target position relative to each eye. In this paper, we present a nonlinear approach in modeling the viewing-context dependency of the slow-phase angular VOR. We show that including appropriate nonlinearities in the responses of premotor neurons in the brainstem is sufficient to account for the online modulation of the VOR with target position. This approach allows very complex behaviors in response to sensory patterns without resorting to currently assumed cortical computations. A local premotor topology with nonlinear properties has repercussions in the study of all ocular reflexes, since it implies context dependent dynamics in all behavioral responses (pursuit, optokinetic, VOR, saccades, etc.) that share this network. Local nonlinearities in spinal circuits could similarly influence the context dependence of other motor systems (such as stretch reflex modulation during rhythmic walking).

An internally switched model of ocular tracking with prediction

Ocular tracking of targets in biological systems involves switching between two strategies: slow pursuit and fast corrective saccades producing pursuit nystagmus. Here, a symmetric (bilateral) controller is used as a model for the oculomotor control system (OCS) to drive two cameras on a robotic head. It relies, as in biology, on internal switching in shared premotor circuits to alternate automatically between the two types of movements comprising nystagmus. The symmetric structural concept is gaining acceptance as evidence points to sharing of both fast phase and slow phase control in brainstem structures previously thought to be solely involved in one mode alone. This bilateral OCS model is a parsimonious design that is at once biomimetic and analytically simple. We extend prior results by incorporating more biological clues from floccular projections to establish rudimentary prediction mechanisms for both slow and fast phases; prediction is achieved by using retinal slip, which contains target velocity information. This provides a more accurate replication of the difference between fast phase and slow phase dynamics, and considers neural activity profiles in the superior colliculus to refine the controller performance. The resulting controller eliminates the need for saccades in steady state for low frequency inputs, and each saccade now has better accuracy, despite visual delays.

A Least-Squares Parameter Estimation Algorithm for Switched Hammerstein Systems With Applications to the VOR

A "Multimode" or "switched" system is one that switches between various modes of operation. When a switch occurs from one mode to another, a discontinuity may result followed by a smooth evolution under the new regime. Characterizing the switching behavior of these systems is not well understood and, therefore, identification of multimode systems typically requires a preprocessing step to classify the observed data according to a mode of operation. A further consequence of the switched nature of these systems is that data available for parameter estimation of any subsystem may be inadequate. As such, identification and parameter estimation of multimode systems remains an unresolved problem. In this paper, we 1) show that the NARMAX model structure can be used to describe the impulsive-smooth behavior of switched systems, 2) propose a modified extended least squares (MELS) algorithm to estimate the coefficients of such models, and 3) demonstrate its applicability to simulated and real data from the Vestibulo-Ocular Reflex (VOR). The approach will also allow the identification of other nonlinear bio-systems, suspected of containing "hard" nonlinearities.

Integrator function in the oculomotor system is dependent on sensory context

The oculomotor integrator is usually defined by the characteristics of decay in gaze after saccades to flashed targets or after spontaneous gaze shifts in the dark. This property is then presumed fixed and accessed by other ocular reflexes, such as the vestibuloocular reflex (VOR) or pursuit, to shape motoneural signals. An alternate view of this integrator proposes that it relies on a distributed network, which should change its properties with sensory-motor context. Here we demonstrate in 10 normal subjects that the function of integration can vary in an individual with the imposed test. The value of the time constant for the decay of gaze holding in the dark can be significantly different from the effective integration time constant estimated from VOR responses. Hence analytical tools for the study of dynamics in ocular reflexes must allow for nonideal and labile integrator function. The mechanisms underlying such labile integration remain to be explored and may be different in various ocular reflexes (e.g., visual versus vestibular).

Superior colliculus encodes distance to target, not saccade amplitude, in multi-step gaze shifts

The superior colliculus (SC) is important for generating coordinated eye-head gaze saccades. Its deeper layers contain a retinotopically organized motor map in which each site is thought to encode a specific gaze saccade vector. Here we show that this fundamental assumption in current models of collicular function does not hold true during horizontal multi-step gaze shifts in darkness that are directed to a goal and composed of a sequence of gaze saccades separated by periods of steady fixation. At the start of a multi-step gaze shift in cats, neural activity on the SC's map was located caudally to encode the overall amplitude of the gaze displacement, not the first saccade in the sequence. As the gaze shift progressed, the locus of activity moved to encode the error between the goal and the current gaze position. Contrary to common belief, the locus of activity never encoded gaze saccade amplitude, except for the last saccade in the sequence.

Neural control of saccades

Quantitative models of the oculomotor plant and control of the saccadic eye movement system are presented in this chapter. Oculomotor plant models described here are linear, including a second-order model by Westheimer (1954), Bahill et al. (1980) and Enderle et al. (2000). The model of the saccade generator is initiated by the superior colliculus and terminated by the cerebellar fastigial nucleus that operates under a time optimal control strategy. A common mechanism for all types of saccades is described, including those with dynamic overshoot and glissadic behavior. Conflicting evidence exists regarding the operation of the excitatory burst neuron during saccades. The excitatory burst neuron operates within two states: complete inhibition, and without inhibition that is characterized by high firing at rates of up to 1000 Hz. While there is direct evidence of projections from the superior colliculus to the paramedian pontine reticular formation, there is conflictory evidence regarding the connections from the superior colliculus to the excitatory burst neuron, with the most recent experimental results supporting no direct connections. A model of the excitatory burst neuron is described using a Hodgkin-Huxley model of the neuron that fires at 1000 Hz automatically and without stimulation when released from inhibition. SIMULINK simulations using this neuron model have all of the characteristics of the excitatory burst neuron firing rate during a saccade. This model eliminates the need to introduce BIAS inputs that causes bursting in some models of the saccade generator. Such a model is also appropriate for modeling the Omnipause neurons.

In multiple-step gaze shifts: omnipause (OPNs) and collicular fixation neurons encode gaze position error; OPNs gate saccades

The superior colliculus (SC), via its projections to the pons, is a critical structure for driving rapid orienting movements of the visual axis, called gaze saccades, composed of coordinated eye-head movements. The SC contains a motor map that encodes small saccade vectors rostrally and large ones caudally. A zone in the rostral pole may have a different function. It contains superior colliculus fixation neurons (SCFNs) with probable projections to omnipause neurons (OPNs) of the pons. SCFNs and OPNs discharge tonically during visual fixation and pause during single-step gaze saccades. The OPN tonic discharge inhibits saccades and its cessation (pause) permits saccade generation. We have proposed that SCFNs control the OPN discharge. We compared the discharges of SCFNs and OPNs recorded while cats oriented horizontally, to the left and right, in the dark to a remembered target. Cats used multiple-step gaze shifts composed of a series of small gaze saccades, of variable amplitude and number, separated by periods of variable duration (plateaus) in which gaze was immobile or moving at low velocity (<25 degrees /s). Just after contralaterally (ipsilaterally) presented targets, the firing frequency of SCFNs decreased to almost zero (remained constant at background). As multiple-step gaze shifts progressed in either direction in the dark, these activity levels prevailed until the distance between gaze and target [gaze position error (GPE)] reached approximately 16 degrees. At this point, firing frequency gradually increased, without saccade-related pauses, until a maximum was reached when gaze arrived on target location (GPE = 0 degrees). SCFN firing frequency encoded GPE; activity was not correlated to characteristics or occurrence of gaze saccades. By comparison, after target presentation to left or right, OPN activity remained steady at pretarget background until first gaze saccade onset, during which activity paused. During the first plateau, activity resumed at a level lower than background and continued at this level during subsequent plateaus until GPE approximately 8 degrees was reached. As GPE decreased further, tonic activity during plateaus gradually increased until a maximum (greater than background) was reached when gaze was on goal (GPE = 0 degrees). OPNs, like SCFNs, encoded GPE, but they paused during every gaze saccade, thereby revealing, unlike for SCFNs, strong coupling to motor events. The firing frequency increase in SCFNs as GPE decreased, irrespective of trajectory characteristics, implies these cells get feedback on GPE, which they may communicate to OPNs. We hypothesize that at the end of a gaze-step sequence, impulses from SCFNs onto OPNs may suppress further movements away from the target.

Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator

The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions in monkeys found that the integration time constant for maintaining fixations decreased, while that for the vestibulo-ocular reflex (VOR) did not. On this basis, it was concluded that saccadic inputs are integrated by the nph, but that the vestibular inputs are integrated elsewhere. We re-analyze the data from which this conclusion was drawn by performing a linear regression of eye velocity on eye position and head velocity to derive the time constant and velocity bias of an imperfect oculomotor neural integrator. The velocity-position regression procedure reveals that the integration time constants for both VOR and saccades decrease in tandem with consecutive nph lesions, consistent with the hypothesis of a single common integrator. The previous evaluation of the integrator time constant relied upon fitting methods that are prone to error in the presence of velocity bias and saccades. The algorithm used to evaluate imperfect fixations in the dark did not account for the nonzero null position of the eyes associated with velocity bias. The phase-shift analysis used in evaluating the response to sinusoidal vestibular input neglects the effect of saccadic resets of eye position on intersaccadic eye velocity, resulting in gross underestimates of the imperfections in integration during VOR. The linear regression method presented here is valid for both fixation and low head velocity VOR data and is easy to implement.

Interaction between visual and vestibular signals for the control of rapid eye movements

To investigate interactions between voluntary and reflexive eye movements, five subjects were asked to make pro- or anti-saccades to various oblique locations cued by a head-fixed flash while being rotated sinusoidally in yaw (0.17 Hz; 73 degrees /s peak velocity) in complete darkness. Eye movements were recorded with the coil technique. In the pro-saccade task, targeting responses showed clear compensation for the intervening nystagmus, but there was a marked increase in horizontal scatter. Most quick phases directed into the hemifield opposite to the flash (away trials) were suppressed from ~100 ms onward. By contrast, quick phases directed into the hemifield of the flash (toward trials) continued virtually unabated until visually triggered saccades began to appear. From 80 ms onward, these vestibularly triggered movements showed signs of metrical modification by the visual signal. In the anti-saccade experiments, suppression of quick phases away from the flash was just as strong as in the pro-saccade experiments, and error rates in these trials were almost as low as in stationary control conditions. Suppression of quick phases directed toward the flash was a new phenomenon that emerged only in anti-saccade experiments. Since this inhibition had a late onset and was only partial, error rates in anti-saccade toward trials were very high. At short latencies, both components of most rapid eye movements were wrongly directed toward the flash. This was followed by a stage with frequent incongruent responses in which unsuppressed quick phases provoked an incorrect horizontal movement, whereas the vertical component showed a correct anti-saccade response. At still longer latencies, most responses were correct in both components. The visual modification of short-latency responses in both tasks showed that rapid eye movements could not simply be classified as either voluntary or reflexive, but suggested that signals underlying each class could merge into a compromise response. That vestibular rotation during the anti-saccade task may cause a wrongly directed horizontal component resembling a quick phase, combined with a vertical component expressing a correct anti-saccade signal, reveals a remarkable independence at the component level. These observations suggest that voluntary and involuntary movements can be programmed in parallel. This behavior is explained most parsimoniously by assuming that the two signals converge at a component-coding stage of the system, rather than at a vectorial coding stage.

Collicular microstimulation during passive rotation does not generate fixed gaze shifts

We investigated whether saccades evoked by electrical stimulation (E-saccades) in the superior colliculus can compensate for passive sinusoidal head rotation in yaw so as to keep the rapid gaze shift constant. After accounting for variations in E-saccade onset position, we found significant horizontal metric changes, proportional to head velocity, in 31 of 37 experiments in 2 monkeys. Vertical effects were small. In a substantial fraction of the experiments (14/37), these metric changes represented significant but often insufficient compensatory adjustments in the horizontal component, opposite to the direction of head movement. However, very robust violations of gaze-shift constancy were remarkably common: significant anticompensatory changes in the horizontal component occurred in 17/37 experiments. In these cases, typically involving larger E-saccades, the horizontal component increased in size with rotation into the half field containing the E-saccade and became smaller during opposite rotation. Further analysis showed that, instead of showing a dichotomy, the metric effect actually varied along a continuum from compensatory to strongly anticompensatory. In addition to these metric changes, we found a robust kinematic effect of head rotation in metrically matched E-saccades. In all experiments where the effect was significant (34/37), horizontal peak velocity increased for rotation into the half field where the E-saccade was directed and decreased for opposite rotation. This kinematic effect was again proportional to head velocity and predominant in the horizontal component. Comparison of yaw and pitch rotation at the same stimulation site showed that both expressions of vestibular-saccade interaction (metric and kinematic) tended to align with the direction of rotation. The component-specific nature of the modulation suggests that the effects may have been caused by convergence of saccadic and vestibular signals at a component-coding stage downstream of the colliculus. We suggest that the quick-phase system got access to the common pulse generator as soon as the collicular stimulation had opened the pause-cell gate. Adding such an anticompensatory signal would act to increase the E-saccade horizontal component when the monkey was rotated in the same direction and bring about a decrease in size and peak velocity when it was opposite. In the large majority of experiments the metric changes failed to maintain gaze-shift constancy, either because they were in the wrong direction or because they were too small. Possible reasons for this major departure from the properties of natural gaze shifts are discussed.

Comparison of human ocular torsion patterns during natural and galvanic vestibular stimulation

Galvanic vestibular stimulation (GVS) is reported to induce interindividually variable tonic ocular torsion (OT) and superimposed torsional nystagmus. It has been proposed that the tonic component results from the activation of otolith afferents. We tested our hypothesis that both the tonic and the phasic OT are mainly due to semicircular canal (SCC) stimulation by examining whether the OT patterns elicited by GVS can be reproduced by pure SCC stimulations. Using videooculography we measured the OT of six healthy subjects while two different stimuli with a duration of 20 s were applied: 1) transmastoidal GVS steps of 2 mA with the head in a pitched nose-down position and 2) angular head rotations around a combined roll-yaw axis parallel to the gravity vector with the head in the same position. The stimulation profile was individually scaled to match the nystagmus properties from GVS and consisted of a sustained velocity step of 4-12 degrees /s on which a velocity ramp of 0.67-2 degrees /s(2) was superimposed. Since blinks were reported to induce transient torsional eye movements, the subjects were also asked to blink once 10 s after stimulus onset. Analysis of torsional eye movements under both conditions revealed no significant differences. Thus we conclude that both the tonic and the phasic OT responses to GVS can be reproduced by pure rotational stimulations and that the OT-related effects of GVS on SCC afferents are similar to natural stimulations at small amplitudes.

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. III. Responses after labyrinthectomy

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in four squirrel monkeys after unilateral labyrinthectomy. Spontaneous nystagmus was measured at the beginning and end of each testing session. During the period that animals were kept in darkness (4 days), the nystagmus at each of these times measured approximately 20 degrees /s. Within 18-24 h after return to the light, the nystagmus (measured in darkness) decreased to 2.8 +/- 1.5 degrees /s (mean +/- SD) when recorded at the beginning but was 20.3 +/- 3.9 degrees /s at the end of the testing session. The latency of the VOR measured from responses to steps of acceleration (3,000 degrees /s(2) reaching a velocity of 150 degrees /s) was 8.4 +/- 0.3 ms for responses to ipsilesional rotations and 7.7 +/- 0.4 ms for contralesional rotations. During the period that animals were kept in darkness after the labyrinthectomy, the gain of the VOR measured during the steps of acceleration was 0.67 +/- 0.12 for contralesional rotations and 0.39 +/- 0.04 for ipsilesional rotations. Within 18-24 h after return to light, the VOR gain for contralesional rotations increased to 0.87 +/- 0.08, whereas there was only a slight increase for ipsilesional rotations to 0.41 +/- 0. 06. A symmetrical increase in the gain measured at the plateau of head velocity was noted after the animals were returned to light. The VOR evoked by sinusoidal rotations of 2-15 Hz, +/-20 degrees /s, showed a better recovery of gain at lower (2-4 Hz) than at higher (6-15 Hz) frequencies. At 0.5 Hz, gain decreased symmetrically when the peak amplitude was increased from 20 to 100 degrees /s. At 10 Hz, gain was decreased for ipsilesional half-cycles and increased for contralesional half-cycles when velocity was raised from 20 to 50 degrees /s. A model incorporating linear and nonlinear pathways was used to simulate the data. Selective increases in the gain for the linear pathway accounted for the recovery in VOR gain for responses at the velocity plateau of the steps of acceleration and for the sinusoidal rotations at lower peak velocities. The increase in gain for contralesional responses to steps of acceleration and sinusoidal rotations at higher frequencies and velocities was due to an increase in the contribution of the nonlinear pathway. This pathway was driven into cutoff and therefore did not affect responses for rotations toward the lesioned side.

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. II. Responses after canal plugging

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in four squirrel monkeys after unilateral plugging of the three semicircular canals. During the period (1-4 days) that animals were kept in darkness after plugging, the gain during steps of acceleration (3, 000 degrees /s(2), peak velocity = 150 degrees /s) was 0.61 +/- 0.14 (mean +/- SD) for contralesional rotations and 0.33 +/- 0.03 for ipsilesional rotations. Within 18-24 h after animals were returned to light, the VOR gain for contralesional rotations increased to 0. 88 +/- 0.05, whereas there was only a slight increase in the gain for ipsilesional rotations to 0.37 +/- 0.07. A symmetrical increase in the gain measured at the plateau of head velocity was noted after animals were returned to light. The latency of the VOR was 8.2 +/- 0. 4 ms for ipsilesional and 7.1 +/- 0.3 ms for contralesional rotations. The VOR evoked by sinusoidal rotations of 0.5-15 Hz, +/-20 degrees /s had no significant half-cycle asymmetries. The recovery of gain for these responses after plugging was greater at lower than at higher frequencies. Responses to rotations at higher velocities for frequencies >/=4 Hz showed an increase in contralesional half-cycle gain, whereas ipsilesional half-cycle gain was unchanged. A residual response that appeared to be canal and not otolith mediated was noted after plugging of all six semicircular canals. This response increased with frequency to reach a gain of 0.23 +/- 0.03 at 15 Hz, resembling that predicted based on a reduction of the dominant time constant of the canal to 32 ms after plugging. A model incorporating linear and nonlinear pathways was used to simulate the data. The coefficients of this model were determined from data in animals with intact vestibular function. Selective increases in the gain for the linear and nonlinear pathways predicted the changes in recovery observed after canal plugging. An increase in gain of the linear pathway accounted for the recovery in VOR gain for both responses at the velocity plateau of the steps of acceleration and for the sinusoidal rotations at lower peak velocities. The increase in gain for contralesional responses to steps of acceleration and sinusoidal rotations at higher frequencies and velocities was due to an increase in the gain of the nonlinear pathway. This pathway was driven into inhibitory cutoff at low velocities and therefore made no contribution for rotations toward the ipsilesional side.

Horizontal vestibuloocular reflex evoked by high-acceleration rotations in the squirrel monkey. I. Normal responses

The horizontal angular vestibuloocular reflex (VOR) evoked by high-frequency, high-acceleration rotations was studied in five squirrel monkeys with intact vestibular function. The VOR evoked by steps of acceleration in darkness (3,000 degrees /s(2) reaching a velocity of 150 degrees /s) began after a latency of 7.3 +/- 1.5 ms (mean +/- SD). Gain of the reflex during the acceleration was 14.2 +/- 5.2% greater than that measured once the plateau head velocity had been reached. A polynomial regression was used to analyze the trajectory of the responses to steps of acceleration. A better representation of the data was obtained from a polynomial that included a cubic term in contrast to an exclusively linear fit. For sinusoidal rotations of 0.5-15 Hz with a peak velocity of 20 degrees /s, the VOR gain measured 0.83 +/- 0.06 and did not vary across frequencies or animals. The phase of these responses was close to compensatory except at 15 Hz where a lag of 5.0 +/- 0.9 degrees was noted. The VOR gain did not vary with head velocity at 0.5 Hz but increased with velocity for rotations at frequencies of >/=4 Hz (0. 85 +/- 0.04 at 4 Hz, 20 degrees /s; 1.01 +/- 0.05 at 100 degrees /s, P < 0.0001). No responses to these rotations were noted in two animals that had undergone bilateral labyrinthectomy indicating that inertia of the eye had a negligible effect for these stimuli. We developed a mathematical model of VOR dynamics to account for these findings. The inputs to the reflex come from linear and nonlinear pathways. The linear pathway is responsible for the constant gain across frequencies at peak head velocity of 20 degrees /s and also for the phase lag at higher frequencies being less than that expected based on the reflex delay. The frequency- and velocity-dependent nonlinearity in VOR gain is accounted for by the dynamics of the nonlinear pathway. A transfer function that increases the gain of this pathway with frequency and a term related to the third power of head velocity are used to represent the dynamics of this pathway. This model accounts for the experimental findings and provides a method for interpreting responses to these stimuli after vestibular lesions.

Hypothesis for shared central processing of canal and otolith signals

A common goal of the translational vestibuloocular reflex (TVOR) and the rotational vestibuloocular reflex (RVOR) is to stabilize visual targets on the retinae during head movement. However, these reflexes differ significantly in their dynamic characteristics at both sensory and motor levels, implying a requirement for different central processing of canal and otolith signals. Semicircular canal afferents carry a signal proportional to angular head velocity, whereas primary otolith afferents modulate approximately in phase with linear head acceleration. Behaviorally, the RVOR exhibits a robust response down to approximately 0.01 Hz, yet the TVOR is only significant above approximately 0.5 Hz. Several hypotheses were proposed to address central processing in the TVOR pathways. All rely on a central filtering process that precedes a "neural integrator" shared with the RVOR. We propose an alternative hypothesis for the convergence of canal and otolith signals that does not impose the requirement for additional low-pass filters for the TVOR. The approach is demonstrated using an anatomically based, simple model structure that reproduces the general dynamic characteristics of the RVOR and TVOR at both ocular and central levels. Differential dynamic processing of otolith and canal signals is achieved by virtue of the location at which sensory information enters a shared but distributed neural integrator. As a result, only the RVOR is provided with compensation for the eye plant. Hence canal and otolith signals share a common central integrator, as in previous hypotheses. However, we propose that the required additional filtering of otolith signals is provided by the eye plant.

Nonlinear dynamic systems evaluation of rhythmic' eye movements (optokinetic nystagmus)

The last decade has seen a surge in the study of nonlinear dynamical behavior in physiologic systems. In this paper, some of the computational techniques most commonly used to investigate the nonlinear dynamics of these systems are described. Applications to eye movement analysis are included, including the validation of a mathematical model of optokinetic nystagmus (OKN) eye movements. OKN appears to have some nonlinear and deterministic component, along with significant randomness. Fast phase starting and ending points are somewhat predictable (deterministic), while so-called 'exceptional events' analysis shows that they also have a large random component. Surrogate data methods suggest that the population of slow and fast phases in OKN is more important than any specific relationship between adjacent slow and fast phases. Analysis of a statistical model for fast phase intervals indicates that the model data are slightly more random than the actual OKN.

Brain stem omnipause neurons and the control of combined eye-head gaze saccades in the alert cat

When the head is unrestrained, rapid displacements of the visual axis-gaze shifts (eye-re-space)-are made by coordinated movements of the eyes (eye-re-head) and head (head-re-space). To address the problem of the neural control of gaze shifts, we studied and contrasted the discharges of omnipause neurons (OPNs) during a variety of combined eye-head gaze shifts and head-fixed eye saccades executed by alert cats. OPNs discharged tonically during intersaccadic intervals and at a reduced level during slow perisaccadic gaze movements sometimes accompanying saccades. Their activity ceased for the duration of the saccadic gaze shifts the animal executed, either by head-fixed eye saccades alone or by combined eye-head movements. This was true for all types of gaze shifts studied: active movements to visual targets; passive movements induced by whole-body rotation or by head rotation about stationary body; and electrically evoked movements by stimulation of the caudal part of the superior colliculus (SC), a central structure for gaze control. For combined eye-head gaze shifts, the OPN pause was therefore not correlated to the eye-in-head trajectory. For instance, in active gaze movements, the end of the pause was better correlated with the gaze end than with either the eye saccade end or the time of eye counterrotation. The hypothesis that cat OPNs participate in controlling gaze shifts is supported by these results, and also by the observation that the movements of both the eyes and the head were transiently interrupted by stimulation of OPNs during gaze shifts. However, we found that the OPN pause could be dissociated from the gaze-motor-error signal producing the gaze shift. First, OPNs resumed discharging when perturbation of head motion briefly interrupted a gaze shift before its intended amplitude was attained. Second, stimulation of caudal SC sites in head-free cat elicited large head-free gaze shifts consistent with the creation of a large gaze-motor-error signal. However, stimulation of the same sites in head-fixed cat produced small "goal-directed" eye saccades, and OPNs paused only for the duration of the latter; neither a pause nor an eye movement occurred when the same stimulation was applied with the eyes at the goal location. We conclude that OPNs can be controlled by neither a simple eye control system nor an absolute gaze control system. Our data cannot be accounted for by existing models describing the control of combined eye-head gaze shifts and therefore put new constraints on future models, which will have to incorporate all the various signals that act synergistically to control gaze shifts.

Eye movement deficits after ibotenic acid lesions of the nucleus prepositus hypoglossi in monkeys. I. Saccades and fixation

It has been suggested that the function of the nucleus prepositus hypoglossi (nph) is the mathematical integration of velocity-coded signals to produce position-coded commands that drive abducens motoneurons and generate horizontal eye movements. In early models of the saccadic system, a single integrator provided not only the signal that maintained steady gaze after a saccade but also an efference copy of eye position, which provided a feedback signal to control the dynamics of the saccade. In this study, permanent, serial ibotenic acid lesions were made in the nph of three rhesus macaques, and their effects were studied while the alert monkeys performed a visual tracking task. Localized damage to the nph was confirmed in both Nissl and immunohistochemically stained material. The lesions clearly were correlated with long-lasting deficits in eye movement. The animals' ability to fixate in the dark was compromised quickly and uniformly so that saccades to peripheral locations were followed by postsaccadic centripetal drift. The time constant of the drift decreased to approximately one-tenth of its normal values but remained 10 times longer than that attributable to the mechanics of the eye. In contrast, saccades were affected minimally. The results are more consistent with models of the neural saccade generator that use separate feedback and position integrators than with the classical models, which use a single multipurpose element. Likewise, the data contradict models that rely on feedback from the nph. In addition, they show that the oculomotor neural integrator is not a single neural entity but is most likely distributed among a number of nuclei.

Providing distinct vergence and version dynamics in a bilateral oculomotor network

Given reported interactions between vergence and version dynamics, ocular reflexes cannot be properly modelled as separate independent subsystems. Using a model structure compatible with known anatomy, we show that a single bilateral system can produce results consistent with observed data both at the central and ocular levels. This model provides for both vergence and conjugate integrators in a single controller, and explains the observed modulation on abducens interneurons and mesencephalic vergence cells during vergence responses. Reported interactions between version and vergence would then be a natural consequence of a shared premotor network. Major implications include: the need to record both eyes in a protocol, since cross-talk is always possible; and adaptation to monocular changes could be distributed in all motor projections to both eyes.

The cerebellum as a predictor of neural messages--I. The stable estimator hypothesis

To describe how the central nervous system combines sensory messages, the hypothesis of a "stable estimator" is proposed: the central nervous system would construct internal estimates of the physical variables characterizing the body movements (e.g. head rotational velocity in space), while a regulating circuit would optimize the process of estimation of each variable, according to the available information and the overall performances of the sensorimotor reactions. The stable estimator of each variable would be embedded in a definite folium of the cerebellar cortex and the related cerebellar and brainstem nuclei. It would be controlled by the related part of the inferior olive. The estimate of each physical variable would be constructed by complementing the message from a dedicated sensory system (e.g. the semi-circular canals, which measure head rotational velocity in space) by neural messages related to the same variable (e.g. eye velocity in the head and retinal slip). Thus, the estimate would be accurate over the widest possible physiological ranges of frequency and velocity. The complementing signals would result from combining estimates of other variables (such as gaze velocity and eye velocity in the orbit), according to rules reproducing the relationships between physical variables. From the same complementing signals, the message from the dedicated sensory system would be predicted, and it is argued that this predictive function resides in the cerebellar cortex. The inferior olive would compare an actual signal about the performance of a sensorimotor reaction to signals of expected performance, computed from the various internal estimates of the variables which determine this performance. Any erroneous setting in a stable estimator would cause differences between the actual and the expected values. Then the inferior olive would compute an error signal directing compensatory functional plasticity. Finally, the whole estimating circuit would be regulated so that the internal coherence between neural messages and the performance of sensorimotor reactions would be achieved. Anatomical identifications and rules of functional plasticity are proposed.

Experimental study and modeling of vestibulo-ocular reflex modulation during large shifts of gaze in humans

An experimental study of head-free and head-fixed gaze shifts explores the role of the vestibulo-ocular reflex (VOR) during saccadic and slow phase components of the gaze shifts. A systematic comparison of head-free and head-fixed gaze shifts in humans revealed that while the VOR is switched off as soon as the saccade starts, its function is progressively restored during the terminal phase of the saccade. The duration of this restoration period is fairly constant; therefore, the faster the gaze saccade, the sooner the VOR function starts to be restored. On the basis of these experimental data, a new eye-head coordination model is proposed. This model is an extension of the one proposed by Laurutis and Robinson (1986) where VOR gain is a function of both the dynamic gaze error signal and head velocity. This extension has also been added to another eye-head coordination model (Guitton et al. 1990). Both modified models yield simulation results comparable to experimental data. This study pinpoints the high efficiency of the gaze control system. Indeed, a fixed period of time (approximately 40 ms) is needed to restore the inhibited VOR; the gaze control system thus must have a knowledge of its own dynamics in order to be able to anticipate the end of the saccadic movement.