A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements

In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of BG. Since the kinematic variables are considered as vectors, the proposed model is presented based on the vector calculus. This vector model predicts different neuronal populations in BG which is in accordance with some recent experimental studies. According to the proposed model, the function of the direct pathway is to calculate the necessary rotation of each joint, and the function of the indirect pathway is to control each joint rotation considering the movement of the other joints. In the proposed model, the local feedback loop between Subthalamic Nucleus and Globus Pallidus externus is interpreted as a local memory to store the previous amounts of movements of the other joints, which are utilized by the indirect pathway. In this model, activities of dopaminergic neurons would encode, at short-term, the error between the desired and actual positions of the end-effector. The short-term modulating effect of dopamine on Striatum is also modeled as cross product. The model is simulated to generate the commands of a redundant manipulator. The performance of the model is studied for different reaching movements between 8 points in a plane. Finally, some symptoms of Parkinson's disease such as bradykinesia and akinesia are simulated by modifying the model parameters, inspired by the dopamine depletion.

Fuzzy neuronal model of motor control inspired by cerebellar pathways to online and gradually learn inverse biomechanical functions in the presence of delay

Contrary to forward biomechanical functions, which are deterministic, inverse biomechanical functions are generally not. Calculating an inverse biomechanical function is an ill-posed problem, which has no unique solution for a manipulator with several degrees of freedom. Studies of the command and control of biological movements suggest that the cerebellum takes part in the computation of approximate inverse functions, and this ability can control fast movements by predicting the consequence of current motor command. Limb movements toward a goal are defined as fast if they last less than the total duration of the processing and transmission delays in the motor and sensory pathways. Because of these delays, fast movements cannot be continuously controlled in a closed loop by use of sensory signals. Thus, fast movements must be controlled by some open loop controller, of which cerebellar pathways constitute an important part. This article presents a system-level fuzzy neuronal motor control circuit, inspired by the cerebellar pathways. The cerebellar cortex (CC) is assumed to embed internal models of the biomechanical functions of the limb segments. Such neural models are able to predict the consequences of motor commands and issue predictive signals encoding movement variables, which are sent to the controller via internal feedback loops. Differences between desired and expected values of variables of movements are calculated in the deep cerebellar nuclei (DCN). After motor learning, the whole circuit can approximate the inverse function of the biomechanical function of a limb and acts as a controller. In this research, internal models of direct biomechanical functions are learned and embedded in the connectivity of the cerebellar pathways. Two fuzzy neural networks represent the two parts of the cerebellum, and an online gradual learning drives the acquisition of the internal models in CC and the controlling rules in DCN. As during real learning, exercise and repetition increase skill and speed. The learning procedure is started by a simple and slow movement, controlled in the presence of delays by a simple closed loop controller comparable to the spinal reflexes. The speed of the movements is then increased gradually, and output error signals are used to compute teaching signals and drive learning. Repetition of movements at each speed level allows to properly set the two neural networks, and progressively learn the movement. Finally, conditions of stability of the proposed model as an inverter are identified. Next, the control of a single segment arm, moved by two muscles, is simulated. After proper setting by motor learning, the circuit is able to reject perturbations.

Daily modulation of the speed-accuracy trade-off

Goal-oriented arm movements are characterized by a balance between speed and accuracy. The relation between speed and accuracy has been formalized by Fitts' law and predicts a linear increase in movement duration with task constraints. Up to now this relation has been investigated on a short-time scale only, that is during a single experimental session, although chronobiological studies report that the motor system is shaped by circadian rhythms. Here, we examine whether the speed-accuracy trade-off could vary during the day. Healthy adults carried out arm-pointing movements as accurately and fast as possible toward targets of different sizes at various hours of the day, and variations in Fitts' law parameters were scrutinized. To investigate whether the potential modulation of the speed-accuracy trade-off has peripheral and/or central origins, a motor imagery paradigm was used as well. Results indicated a daily (circadian-like) variation for the durations of both executed and mentally simulated movements, in strictly controlled accuracy conditions. While Fitts' law was held for the whole sessions of the day, the slope of the relation between movement duration and task difficulty expressed a clear modulation, with the lowest values in the afternoon. This variation of the speed-accuracy trade-off in executed and mental movements suggests that, beyond execution parameters, motor planning mechanisms are modulated during the day. Daily update of forward models is discussed as a potential mechanism.

Cerebellum-inspired neural network solution of the inverse kinematics problem

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

Integration of gravitational torques in cerebellar pathways allows for the dynamic inverse computation of vertical pointing movements of a robot arm

BACKGROUND

Several authors suggested that gravitational forces are centrally represented in the brain for planning, control and sensorimotor predictions of movements. Furthermore, some studies proposed that the cerebellum computes the inverse dynamics (internal inverse model) whereas others suggested that it computes sensorimotor predictions (internal forward model).

METHODOLOGY/PRINCIPAL FINDINGS

This study proposes a model of cerebellar pathways deduced from both biological and physical constraints. The model learns the dynamic inverse computation of the effect of gravitational torques from its sensorimotor predictions without calculating an explicit inverse computation. By using supervised learning, this model learns to control an anthropomorphic robot arm actuated by two antagonists McKibben artificial muscles. This was achieved by using internal parallel feedback loops containing neural networks which anticipate the sensorimotor consequences of the neural commands. The artificial neural networks architecture was similar to the large-scale connectivity of the cerebellar cortex. Movements in the sagittal plane were performed during three sessions combining different initial positions, amplitudes and directions of movements to vary the effects of the gravitational torques applied to the robotic arm. The results show that this model acquired an internal representation of the gravitational effects during vertical arm pointing movements.

CONCLUSIONS/SIGNIFICANCE

This is consistent with the proposal that the cerebellar cortex contains an internal representation of gravitational torques which is encoded through a learning process. Furthermore, this model suggests that the cerebellum performs the inverse dynamics computation based on sensorimotor predictions. This highlights the importance of sensorimotor predictions of gravitational torques acting on upper limb movements performed in the gravitational field.

A model of the cerebellar sensory--motor control applied to fast human forearm movements

To address the problem of how the cerebellum processes the premotor orders that control fast movements of the forearm, a model of the cerebellar control is proposed: a cybernetic circuit composed of a model of the cerebellar premotor pathways driving a biomechanical model of the human forearm. Experiments consist of recording electromyographic (EMG) activities and cinematic variables of the human forearm during fast, single joint, point-to-point movements performed in horizontal and vertical directions with and without mass. The biomechanical model of the forearm is first validated by comparing actual movements and movements simulated by using, as inputs to this model, the synthesized EMG signals and of real EMG activities recorded during the experiments. Then the entire control model is validated by comparing actual movements to the desired ones simulated by the model of the cerebellar pathways whose inputs are velocity signals with Gaussian time-courses. The results show that approximate inverse functions can be computed by means of inner models of direct functions placed in feedback loops, and suggest that the orientation of any member segment with respect to gravity is computed as a cinematic variable in the Central Nervous System (CNS).

The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements

An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality criteria may be applied to a large range of biological movements.

When performing reaching and grasping movements, the brain has to choose one trajectory among an infinite set of possibilities. Nevertheless, because human and animal movements provide highly stereotyped features, motor strategies used by the brain were assumed to be optimal according to certain optimality criteria. In this study, we propose a theoretical model for motor planning of arm movements that minimizes a compromise between the absolute work exerted by the muscles and the integral of the squared acceleration. We demonstrate that under these assumptions agonistic and antagonistic muscles are inactivated during overlapping periods of time for quick enough movements. Moreover, it is shown that only this type of criterion can predict these inactivation periods. Finally, experimental evidence is in agreement with the predictions of the model. Indeed, we report the existence of simultaneous inactivation of opposing muscles during fast vertical arm movements. Therefore, this study suggests that biological movements partly optimize the energy expenditure, integrating both inertial and gravitational forces during the motor planning process.

Motion sickness induced by otolith stimulation is correlated with otolith-induced eye movements

This article addresses the relationships between motion sickness (MS) and three-dimensional (3D) ocular responses during otolith stimulation. A group of 19 healthy subjects was tested for motion sickness during a 16 min otolith stimulation induced by off-vertical axis rotation (OVAR) (constant velocity 60 degrees /s, frequency 0.16 Hz). For each subject, the MS induced during the session was quantified, and based on this quantification, the subjects were divided into two groups of less susceptible (MS-), and more susceptible (MS+) subjects. The angular eye velocity induced by the otolith stimulation was analyzed in order to identify a possible correlation between susceptibility to MS and 3D eye velocity. The main results show that: (1) MS significantly correlates in a multiple regression with several components of the horizontal vestibular eye movements i.e. positively with the velocity modulation (P<0.01) and bias (P<0.05) of the otolith ocular reflex and negatively with the time constant of the vestibulo-ocular reflex (P<0.01) and (2) the length of the resultant 3D eye velocity vector is significantly larger in the MS+ as compared with the MS- group. Based on these results we suggest that the CNS, including the velocity storage mechanism, reconstructs an eye velocity vector modulated by head position whose length might predict MS occurrence during OVAR.

WITHDRAWN: A model of the cerebellar sensory-motor control applied to the fast human forearm movements

This article has been withdrawn consistent with Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy). The Publisher apologizes for any inconvenience this may cause.

Computation of inverse functions in a model of cerebellar and reflex pathways allows to control a mobile mechanical segment

The command and control of limb movements by the cerebellar and reflex pathways are modeled by means of a circuit whose structure is deduced from functional constraints. One constraint is that fast limb movements must be accurate although they cannot be continuously controlled in closed loop by use of sensory signals. Thus, the pathways which process the motor orders must contain approximate inverse functions of the bio-mechanical functions of the limb and of the muscles. This can be achieved by means of parallel feedback loops, whose pattern turns out to be comparable to the anatomy of the cerebellar pathways. They contain neural networks able to anticipate the motor consequences of the motor orders, modeled by artificial neural networks whose connectivity is similar to that of the cerebellar cortex. These networks learn the direct biomechanical functions of the limbs and muscles by means of a supervised learning process. Teaching signals calculated from motor errors are sent to the learning sites, as, in the cerebellum, complex spikes issued from the inferior olive are conveyed to the Purkinje cells by climbing fibers. Learning rules are deduced by a differential calculation, as classical gradient rules, and they account for the long term depression which takes place in the dendritic arborizations of the Purkinje cells. Another constraint is that reflexes must not impede voluntary movements while remaining at any instant ready to oppose perturbations. Therefore, efferent copies of the motor orders are sent to the interneurones of the reflexes, where they cancel the sensory-motor consequences of the voluntary movements. After learning, the model is able to drive accurately, both in velocity and position, angular movements of a rod actuated by two pneumatic McKibben muscles. Reflexes comparable to the myotatic and tendinous reflexes, and stabilizing reactions comparable to the cerebellar sensory-motor reactions, reduce efficiently the effects of perturbing torques. These results allow to link the behavioral concepts of the equilibrium-point "lambda model" [J Motor Behav 18 (1986) 17] with anatomical and physiological features: gains of reflexes and sensori-motor reactions set the slope of the "invariant characteristic," and efferent copies set the "threshold of the stretch reflex." Thus, mathematical and physical laws account for the raison d'etre of the inhibitory nature of Purkinje cells and for the conspicuous anatomical pattern of the cerebellar pathways. These properties of these pathways allow to perform approximate inverse calculations after learning of direct functions, and insure also the coordination of voluntary and reflex motor orders.

Cerebellar learning of bio-mechanical functions of extra-ocular muscles: modeling by artificial neural networks

A control circuit is proposed to model the command of saccadic eye movements. Its wiring is deduced from a mathematical constraint, i.e. the necessity, for motor orders processing, to compute an approximate inverse function of the bio-mechanical function of the moving plant, here the bio-mechanics of the eye. This wiring is comparable to the anatomy of the cerebellar pathways. A predicting element, necessary for inversion and thus for movement accuracy, is modeled by an artificial neural network whose structure, deduced from physical constraints expressing the mechanics of the eye, is similar to the cell connectivity of the cerebellar cortex. Its functioning is set by supervised reinforcement learning, according to learning rules aimed at reducing the errors of pointing, and deduced from a differential calculation. After each movement, a teaching signal encoding the pointing error is distributed to various learning sites, as is, in the cerebellum, the signal issued from the inferior olive and conveyed to various cell types by the climbing fibers. Results of simulations lead to predict the existence of a learning site in the glomeruli. After learning, the model is able to accurately simulate saccadic eye movements. It accounts for the function of the cerebellar pathways and for the final integrator of the oculomotor system. The novelty of this model of movement control is that its structure is entirely deduced from mathematical and physical constraints, and is consistent with general anatomy, cell connectivity and functioning of the cerebellar pathways. Even the learning rules can be deduced from calculation, and they reproduce long term depression, the learning process which takes place in the dendritic arborization of the Purkinje cells. This approach, based on the laws of mathematics and physics, appears thus as an efficient way of understanding signal processing in the motor system.

A model of the cerebellar pathways applied to the control of a single-joint robot arm actuated by McKibben artificial muscles

This article describes an expanded version of a previously proposed motor control scheme, based on rules for combining sensory and motor signals within the central nervous system. Classical control elements of the previous cybernetic circuit were replaced by artificial neural network modules having an architecture based on the connectivity of the cerebellar cortex, and whose functioning is regulated by reinforcement learning. The resulting model was then applied to the motion control of a mechanical, single-joint robot arm actuated by two McKibben artificial muscles. Various biologically plausible learning schemes were studied using both simulations and experiments. After learning, the model was able to accurately pilot the movements of the robot arm, both in velocity and position.

Using sensory weighting to model the influence of canal, otolith and visual cues on spatial orientation and eye movements

The sensory weighting model is a general model of sensory integration that consists of three processing layers. First, each sensor provides the central nervous system (CNS) with information regarding a specific physical variable. Due to sensor dynamics, this measure is only reliable for the frequency range over which the sensor is accurate. Therefore, we hypothesize that the CNS improves on the reliability of the individual sensor outside this frequency range by using information from other sensors, a process referred to as "frequency completion." Frequency completion uses internal models of sensory dynamics. This "improved" sensory signal is designated as the "sensory estimate" of the physical variable. Second, before being combined, information with different physical meanings is first transformed into a common representation; sensory estimates are converted to intermediate estimates. This conversion uses internal models of body dynamics and physical relationships. Third, several sensory systems may provide information about the same physical variable (e.g., semicircular canals and vision both measure self-rotation). Therefore, we hypothesize that the "central estimate" of a physical variable is computed as a weighted sum of all available intermediate estimates of this physical variable, a process referred to as "multicue weighted averaging." The resulting central estimate is fed back to the first two layers. The sensory weighting model is applied to three-dimensional (3D) visual-vestibular interactions and their associated eye movements and perceptual responses. The model inputs are 3D angular and translational stimuli. The sensory inputs are the 3D sensory signals coming from the semicircular canals, otolith organs, and the visual system. The angular and translational components of visual movement are assumed to be available as separate stimuli measured by the visual system using retinal slip and image deformation. In addition, both tonic ("regular") and phasic ("irregular") otolithic afferents are implemented. Whereas neither tonic nor phasic otolithic afferents distinguish gravity from linear acceleration, the model uses tonic afferents to estimate gravity and phasic afferents to estimate linear acceleration. The model outputs are the internal estimates of physical motion variables and 3D slow-phase eye movements. The model also includes a smooth pursuit module. The model matches eye responses and perceptual effects measured during various motion paradigms in darkness (e.g., centered and eccentric yaw rotation about an earth-vertical axis, yaw rotation about an earth-horizontal axis) and with visual cues (e.g., stabilized visual stimulation or optokinetic stimulation).

Motion sickness susceptibility correlates with otolith- and canal-ocular reflexes

Since motion sickness (MS) never occurs in individuals who lack functional vestibular apparatus, it has been suggested that MS susceptible individuals have more sensitive vestibular systems than non-susceptible people. However, previous investigations involving only stimulation of the semi-circular canals have been inconclusive. We measured gain and time constant (TC) of horizontal canal-ocular reflex (COR) and magnitude of otolith-ocular reflex (OOR). We found that MS susceptibility was not correlated to COR gain but was negatively correlated to OOR magnitude. Thus, MS susceptible individuals do not have more sensitive vestibular systems. We also found a positive correlation between MS susceptibility and TC. We hypothesize that central vestibular integration (velocity storage mechanism), by increasing low frequency vestibular inputs, would favour MS.

Unilateral vestibular neuritis with otolithic signs and off-vertical axis rotation

Off-vertical axis rotation (OVAR) at constant velocity is a dynamic otolith stimulus that induces horizontal and vertical eye movement responses. To determine the value of this examination as a test for unilateral otolithic hypofunction, we compared the OVAR responses of patients suffering from acute vestibular neuritis (VN) without any sign of otolith affection, with those of patients suffering from acute VN with otolithic signs. The horizontal eye movement bias component shows directional preponderance (DP) significantly higher in patients with otolithic signs than in patients not presenting them. However, as bias DP also reflects the imbalance between right and left horizontal canals activity, this greater bias DP could be explained by the more severe canals impairment-evaluated by caloric test-found in patients with otolithic signs. No significant difference can be shown on horizontal modulation. The DP of vertical modulation is significantly higher in patients presenting otolithic signs than in patients not presenting them: in the case of otolithic signs, the responses are smaller during rotations toward the affected side. Therefore, this variable could be used as an indication of unilateral otolithic hypofunction.

Computation of inverse dynamics for the control of movements

Accuracy of movements requires that the central nervous system computes approximate inverse functions of the mechanical functions of limb articulations. In vertebrates, this is known to be achieved within the cerebellar pathways, and also in the cerebral cortex of primates. A cybernetic circuit achieving this computation allows accurate simulation of fast movements of the eye or forearm. It is consistent with anatomy, and with the classical view of the cerebellum as permanently supervised by the inferior olive. The inferior olive detects over-or under-shoots of movements, and the resulting climbing fiber activity corrects ongoing movements, regulates the function of cerebellar cortex and nuclei, and sets the gains of the sensorimotor reactions.

Unilateral peripheral semicircular canal lesion and off-vertical axis rotation

Off vertical axis rotation (OVAR) is a stimulus that can be used to assess the otolith-ocular reflex. However, experimental data suggest that isolated unilateral lesion of the lateral semicircular canal (SCC) nerve could modify responses to OVAR. Thus, to determine what nystagmus variables are not affected by SCC dysfunction and might be used as indices of otolithic disease, responses to OVAR were compared in 39 healthy controls and in 19 patients suffering from acute unilateral vestibular neuritis (VN), without any sign of otolith dysfunction. Horizontal and vertical slow phase velocities (SPV) were measured during earth vertical axis rotation (EVAR), and during OVAR at a tilt angle of 9 degrees and rotation velocity of 60 degrees/s. During OVAR, horizontal SPV consists of a sinusoidal modulation superimposed on a sustained bias opposite to the rotation. Vertical SPV consists of a sinusoidal modulation without bias. In patients, the bias shows directional preponderance (DP) toward the healthy side, strongly correlated to EVAR nystagmus DP. It would therefore simply reflect an imbalance, produced by the unilateral peripheral vestibular lesion, between right and left vestibular nuclei activity. On the other hand, vertical and horizontal modulations are not significantly different in patients and controls. Since the cause and the site of VN are not known, we cannot be sure that patients had pure SCC deafferentation. However, as all of them had SCC paresis it is concluded that OVAR modulations are not affected by a strong dysfunction of the pathways issued from the SCCs.

Motion sickness during off-vertical axis rotation: prediction by a model of sensory interactions and correlation with other forms of motion sickness

Motion sickness (MS) susceptibility of 108 normal subjects was measured during off-vertical axis rotation (OVAR) as a function of angular velocity (60-180 degrees/s). The chair rotated about a longitudinal axis tilted 30 degrees with respect to gravity. For each velocity, we measured the duration of exposure necessary to evoke a moderate malaise, with a limit of 30 min. MS appeared the fastest at a rotation velocity of 105 degrees/s; higher or lower velocities were less provocative. These results are in good agreement with predictions made by Zupan et al. [in ICANN'94, Springer-Verlag, 1995] by means of a MS mathematical model derived from a model of sensory interactions [Droulez and Darlot, in Attention and Performance, Vol. 13, Lawrence Erlbaum, Hillsdale, 1989]. We also found that MS susceptibility during OVAR is positively correlated with susceptibility to other forms of MS. Since OVAR induces sensory messages very different from those induced by other provocative stimulations, this could suggest that the sensitivity of a common final vegetative locus is an important factor of the individual differences in susceptibility to MS.

Eye movements and motion perception induced by off-vertical axis rotation (OVAR) at small angles of tilt after spaceflight

The nystagmus and motion perception of two astronauts were recorded during Earth-vertical axis rotation and during off-vertical axis rotation (OVAR) before and after 7 days of spaceflight. Postflight, the peak velocity and duration of per- and postrotatory nystagmus during velocity steps about the Earth-vertical axis were the same as preflight values. During OVAR at constant velocity (45/s, tilt angles successively 5, 10, and 15 degrees), the mean horizontal slow-phase eye velocity (bias), produced by the 'velocity storage mechanism' in the vestibular system, and the peak-to-peak amplitude (modulation) in horizontal eye velocity and position, generated from the output of otolith afferents, were also the same before as after flight. There were, however, changes in the vertical eve position and in the perceived body motion during OVAR. The angle of the perceived body path described as a cone was larger in both astronauts postflight. One astronaut experienced either a large cone angle with its axis upright, or a smaller cone angle with its axis tilted backwards, accompanied by an upward vertical eye drift. These results suggest an increase in the sensitivity of the otolithic system after spaceflight and a longer period of readaptation to Earth's gravity for otolith-induced responses than for canal-induced responses. Our data support the hypothesis that just after spaceflight the CNS generally interprets changes in the otolith signals to be due to translation rather than to tilt.

The cerebellum as a predictor of neural messages--II. Role in motor control and motion sickness

The hypothesis of a "stable estimator" was proposed in the preceding article as a circuit computing an internal estimate of a body movement variable and endowed with regulating properties. Such a circuit would exist for each variable, and would be embedded in a particular folium of the cerebellar cortex and the related paths of the brainstem nuclei and the inferior olive. In this article, the action of the premotor orders on the stable estimator circuit is studied, at initiation and during execution of voluntary movements. A feedback loop via the cerebellar cortex would control on-going movements and maintain the efficacy of the stabilizing sensorimotor reaction, while preventing its interfering with the movement. The regulating loop via the inferior olive would have a short-term role in initiating movements and would boost insufficient stabilizing reactions. The discrepancy between internal estimates of the same variable would be reflected in motion sickness.

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.

Nystagmus induced by off-vertical rotation axis in the cat

1) In the alert cat, nystagmus induced by off-vertical axis rotation (OVAR) was recorded following steps in head velocity or ramps of velocity at constant acceleration below canal threshold. Dependence of nystagmus characteristics on tilt angle of rotation axis and head velocity was studied. Similar results were obtained with both types of stimulation. 2) Mean and modulation amplitude of horizontal eye velocity increased with tilt angle in the range 0-30 degrees. 3) Both variables increased also with head velocity, but with different trends, probably because they are set by different mechanisms. When head rotational velocity was increased above 80 degrees/s, mean eye velocity progressively decreased to zero. 4) In spite of variations from one animal to another, some regularity was observed in the phase of eye velocity modulation. In several cases, a reduction in phase lead of eye velocity with respect to conventional origin of phases (nose-down position) was observed when head velocity increased. 5) Time constant of post-OVAR nystagmus decreased with the tilt angle of the rotation axis from gravity, but not with the orientation of the head with respect to rotation axis. 6) The results could be accounted for by a general equation describing the vestibulo-ocular reflex, provided that estimates of kinematic variables of head movement (head rotational and translational velocities), and visual target distance could be computed by the Central Nervous System.

Eye movements induced by off-vertical axis rotation (OVAR) at small angles of tilt

Off-vertical rotation (OVAR) in darkness induced continuous horizontal nystagmus in humans at small tilts of the rotation axis (5 to 30 degrees). The horizontal slow eye velocity had two components: a mean velocity in the direction opposite to head rotation and a sinusoidal modulation around the mean. Mean velocity generally did not exceed 10 deg/s, and was less than or equal to the maximum velocity of optokinetic after-nystagmus (OKAN). Both the mean and modulation components of horizontal nystagmus increased with tilt angle and rotational velocity. Vertical slow eye velocity was also modulated sinusoidally, generally around zero. The amplitude of the vertical modulation increased with tilt angle, but not with rotational velocity. In addition to modulations in eye velocity, there were also modulations in horizontal and vertical eye positions. These would partially compensate for head position changes in the yaw and pitch planes during each cycle of OVAR. Modulations in vertical eye position were regular, increased with increases in tilt angle and were separated from eye velocity by 90 deg. These results are compatible with the interpretation that, during OVAR, mean slow velocity of horizontal nystagmus is produced by the velocity storage mechanism in the vestibular system. In addition, they indicate that the otolith organs induce compensatory eye position changes with regard to gravity for tilts in the pitch, yaw and probably also the roll planes. Such compensatory changes could be utilized to study the function of the otolith organs. A functional interpretation of these results is that nystagmus attempts to stabilize the image on the retina of one point of the surrounding world. Mean horizontal velocity would then be opposite to the estimate of head rotational velocity provided by the output of the velocity storage mechanism, as charged by an otolithic input during OVAR. In spite of the lack of actual translation, an estimate of head translational velocity could, in this condition, be constructed from the otolithic signal. The modulation in horizontal eye position would then be compensatory for the perceived head translation. Modulation of vertical eye velocity would compensate for actual changes in head orientation with respect to gravity.

Motion perceptions induced by off-vertical axis rotation (OVAR) at small angles of tilt

Off-vertical axis rotation in darkness induces a perception of body motion which lasts as long as rotation continues. Perceived body motion is the combination of two simultaneous displacements. The most easily perceived is a translation without rotation along a conical path, at the frequency of the actual rotation. Meanwhile, the subjects feel as if they were always facing towards the same direction. The summit of the cone is generally below the head, from the waist to below the feet, and subjects have a sense of progression in the direction opposite to actual spinning. Some subjects feel, on the contrary, the summit of the cone above their heads, and the progression in the direction of spinning. Subjects also perceived another body motion, although it was faint for some of them. It consists of a rotation at low velocity in the same direction as progression along the cone. The axis of the cone is perceived as slowly rotating along a larger cone. These motion perceptions increase with tilt angle and rotation velocity. They probably result from the analysis by the Central Nervous System of the acceleration acting on the otoliths. The perceived trajectory would be reconstructed from estimates of gravity, and kinematic variables such as head translational acceleration and velocity, and head rotational velocity. The same variables would account for OVAR-induced nystagmus. Motion sickness would result from the impossibility of reconstructing a consistent body movement from most sets of values of these variables.

Modulation by eye position of neck muscle contraction evoked by electrical labyrinthine stimulation in the alert cat

Modulation of vestibulo-spinal reflexes by gaze is a model system for studying interactions between voluntary and reflex motor activity. In the alert cat, the EMG of Splenius and Obliquus capitis muscles increases with ipsilateral gaze eccentricity during spontaneous eye movements. Labyrinth stimulation by current pulses evokes EMGs with latencies consistent with a three neuron vestibulocollic pathway. The amplitude of evoked activity increases with eye position. The directions in which eye movements increase EMG was usually the same for both spontaneous and induced EMG activity, namely, horizontal and ipsilateral. However, sometimes the increase in spontaneous EMG occurred with horizontal eye position, whereas the induced EMG changed with vertical eye position. Spontaneous and evoked EMG are then modulated by different eye position signals. Command signals reflecting eye position probably reach two different types of neurons in the vestibulo-collic pathway, most likely secondary vestibular neurons and neck muscle motoneurons.

Modulation by horizontal eye position of the vestibulo-collic reflex induced by tilting in the frontal plane in the alert cat

In alert cats, during sinusoidal rotations of head and trunk en bloc around a longitudinal axis, in darkness or in light, the vestibulo-collic reflex induces neck muscle contractions. The phase and gain diagrams are consistent, in the frequency range 0.2 to 1.2 Hz, with previous results from anesthetized or decerebrate cats. In addition, neck muscle contractions are modulated by horizontal eye position, as is the case for rotations in the horizontal plane, around the vertical (Z) axis. Neck muscle contraction is consequently under control of both eye position and head tilt angle. This synergy of eye and head could suppress the effects of vestibulo-collic reflex during orienting reactions.

Neuronal activity in prepositus nucleus correlated with eye movement in the alert cat

1. In nine alert chronically prepared cats the activity of 177 neurons was recorded in the prepositus nucleus during either spontaneous eye movement or that induced by natural vestibular and optokinetic stimulation. 2. In 116 cells, eye position and/or eye velocity was precisely and unequivocally encoded whatever the origin of the eye movement. These cells were separated into different populations according to the eye movement variable encoded and the directionality of the neuronal response. The firing rates of the remaining 61 cells were loosely related to eye movements because a variety of discharge patterns were observed during identical eye movements. In the latter case, some other unmeasured variable (e.g., neck or visual) was suggested to be encoded in the firing frequency. 3. Discharge rate changed before the eyes began to move and reached a new steady level during fixation following a saccade into a particular direction of the orbit. The ondirection was horizontal for 59% of the neurons, vertical for 17%, and oblique for 24%. 4. Regardless of their preferred direction, the discharge rate in 19% of the neurons was closely proportional to eye position. The range in sensitivity was from 1.1 to 7.5 spikes X s-1/deg. Weak velocity responses were occasionally observed during the slow phase of vestibular and optokinetic nystagmus including during saccades. This class of neurons exhibited a very regular interspike interval for a given position of fixation. Since mainly eye position was encoded, these cells were called position neurons. 5. Other prepositus neurons showed both position and velocity sensitivity during saccades and fixation. Their firing rate encoded eye position over the same range as above and also coded velocity during the slow phase of vestibular and optokinetic nystagmus. Depending on the weighting between the position and velocity proportionality constants, these neurons were classified into position-velocity (48%) or velocity-position (33%) groups. 6. The distribution of the above responses led to the conclusion that the prepositus nucleus plays a role in vertical and horizontal spatial integration. The predominance of horizontal activity suggested that the nucleus may be a significant site underlying genesis of horizontal eye position.

Asymmetries of vertical vestibular nystagmus in the cat

In the cat, the asymmetry of vertical nystagmus in response to a rotation around the Y-axis has been characterized by measuring the beat frequency and gain of vestibulo-ocular reflexes in each direction (upward and downward). Sinusoidal variations of head velocity or velocity steps have been applied under three visual conditions (a) in darkness (pure vestibular stimulation); (b) in the light (mixed vestibular and optokinetic stimulation); (c) with a mirror placed in front of the animal; since the mirror image moved with the head, the animal was provided with a stable visual cue (stabilized vision). In all three conditions, beat frequency and gain were greater for downward than for upward nystagmus (the direction refers to that of the quick phase). In darkness, the characteristics of postrotatory nystagmus suggested a greater time constant for downward than for upward vestibulo-ocular reflexes. In the light, both stimuli acted synergistically. In stabilized vision, upward vestibular nystagmus was preferentially suppressed, suggesting an algebraic summation of the effects arising from both kinds of stimuli.