Christian Darlot

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

Abstract. 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).

Computation of inverse dynamics for the control of movements.

Abstract. 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.

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

Abstract. 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.

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.

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.

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

SummaryModulation 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.

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 that 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.

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.

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.