Modeling 3-D Slow Phase Velocity Estimation During Off-Vertical-Axis Rotation (OVAR)

Off-vertical-axis rotation (OVAR) in darkness generates continuous compensatory eye velocity. No model has yet been presented that defines the signal processing necessary to estimate head velocity in three dimensions for arbitrary rotations during OVAR. The present study develops a model capable of estimating all 3 components of head velocity in space accurately. It shows that processing of two patterns of otolith activation, one delayed with respect to the other, for each plane of eye movement is not sufficient. (A pattern in this context is an array of signals emanating from the otoliths. Each component of the array is a signal corresponding to a class of otolith hair cells with a given polarization vector as described by Tou and Gonzalez in 1974.) The key result is that estimation of head velocity in space can be achieved by processing three temporally displaced patterns, each representing a sampling of gravity as the head rotates. A vector cross product of differences between pairs of the sampled gravity vectors implements the estimation. An interesting property of this model is that the component of velocity about the axis of rotation reduces to that derived previously using the pattern estimator model described by Raphan and Schnabolk in 1988 and Fanelli et al in 1990. This study suggests that the central nervous system (CNS) maintains a current as well as 2 delayed representations of gravity at every head orientation during rotation. It also suggests that computing vector cross products and implementing delays may be fundamental operations in the CNS for generating orientation information associated with motion.