Forward models and state estimation in compensatory eye movements

Abstract

The compensatory eye movement (CEM) system maintains a stable retinal image, integrating information from different sensory modalities to compensate for head movements. Inspired by recent models of the physiology of limb movements, we suggest that CEM can be modeled as a control system with three essential building blocks: a forward model that predicts the effects of motor commands; a state estimator that integrates sensory feedback into this prediction; and, a feedback controller that translates a state estimate into motor commands. We propose a specific mapping of nuclei within the CEM system onto these control functions. Specifically, we suggest that the Flocculus is responsible for generating the forward model prediction and that the Vestibular Nuclei integrate sensory feedback to generate an estimate of current state. Finally, the brainstem motor nuclei - in the case of horizontal compensation this means the Abducens Nucleus and the Nucleus Prepositus Hypoglossi - implement a feedback controller, translating state into motor commands. While these efforts to understand the physiological control system as a feedback control system are in their infancy, there is the intriguing possibility that CEM and targeted voluntary movements use the same cerebellar circuitry in fundamentally different ways.

Keywords: cerebellum; control systems; eye movements; forward model; model; okr; vestibular nucleus; vor.

Figure 1

The horizontal compensatory eye movement (CEM) system. Generally, this is described as two separate reflexes. The optokinetic reflex (OKR) uses visual input from the retina to stabilize the eye while the vestibulo-ocular reflex (OKR) responds to vestibular information from the labyrinth. This figure emphasizes the distinction between sensory feedback (black) and motor signals (red).Blue and purple represent central stages of processing, and are added for comparison with other figures. Cblm: cerebellar cortex; AOS/NRTP: accessory optic system and nucleus reticularis tegmentum pontis; VN: vestibular nucleus; NPH: neuclus prepositus hypoglossi; OMN/AB: oculomotor nucleus and abducens.

Figure 2

(A) Inverse and (B) forward models. The plant takes motor commands and produces movement. The inverse model inverts this process, producing the motor commands that are appropriate for a given movement. A forward model mimics this process, estimating the movement that will be produced by the plant.

Figure 3

The SPFC framework proposes that a feedback controller is optimized to produce motor commands that achieve task goals. In order to do this effectively, it uses an estimate of the current situation that is derived from a combination of feedback from the sensory system and forward model estimation that depends on efferent copy.

Figure 4

NPH neurons (dashed, orange) behave like the motor command, represented by the solid, red curve. The black lines show the activity of a hypothetical neuron that would encode eye position, with a constant gain and phase. NPH and Ab activity were taken from (Green et al., 2007).

Figure 5

Timing of cerebellar activity. (A) Shows a simple spike triggered average of eye velocity in response to white noise optokinetic stimulation. The white noise stimulus was provided by a panaromic projector system and consisted of a hexagonal matrix of green patches that were rotated coherently around the animal according to a three dimensional gaussian white noise process filtered through a 20-Hz low-pass filter. Note that the curve of this neuron peaks slightly before 0 ms, i.e. the P-cell is active slightly after the actual movement. (B) Summarizes the timing of the peak in 71 Purkinje cells, showing activity that more or less coincides with the movement (Winkelman and Frens, 2007).

Estimated position and actual position as tracked by three different Kalman filters.

Figure 6

Timing of activity of FTNs in the VN, compared to non-FTNs, Abducens nucleus, vestibular efferents, and the actual eye movement. All phases are given with respect to a vestibular stimulus that was either given in the dark (left panel), or in the light (right panel). Data from Stahl and Simpson (1995).

Figure 7

Complex spike (CS) Modulation as a result of sinusoidal optokinetic stimulation. In (A) the stimulus was an oscillating pattern. In (B) the same pattern moved transparently over a static background. The behavior of the animal varied with the relative luminances of the moving and the static pattern. The frequency of the fitted sine wave equals the frequency of the stimulus (0.1 Hz). Note that the modulation in (A) and (B) is virtually identical, as are the CEM made by the animal (gain 0.60 and 0.58, respectively). Consequently the predicted slip (caused by the eye movement over the static pattern) is not reflected in the CS (Frens et al., 2001).