This chapter originated from a paper presented at the eighth Neural Information Processing Systems conference in December 1995 and on work presented at the Society for Neuroscience conference in November of the same year. It is the first of two chapters aimed at: 1) reproducing monkey psychophysical data on the VOR reported by Snyder and King (Snyder92b), and 2) mapping a theoretical model of the VOR onto brain stem nuclei and cerebellum.
A Global VOR Model based on a Kinematic VOR Model is presented. The Global model derives its name from the fact that it suggests a putative mapping of the components of the Kinematic VOR model onto the entire VOR pathway. The Kinematic VOR Model describes the geometrical relationship between head motion and eye rotation in order to stabilize targets on the retina during head motions. It consists of two equations, a velocity equation and an acceleration equation. The velocity equation is introduced and derived in this chapter; the acceleration equation is presented later in chapter 5. The velocity Kinematic VOR Model describes the relation between angular and linear head velocities to angular eye velocity. The model describes how the angular eye velocity changes with target distance, target eccentricity, and the location and orientation of the axis of rotation of the head. It also specifies how linear motion signals reported by the otoliths in the inner ear is combined with the vestibular canal rotation signals.
The Global VOR Model is constructed by adding dynamical components such as time derivatives, time constants and time delays to the Kinematic VOR Model. Although the Kinematic VOR model is a three-dimensional VOR model, the Global model focuses on the computations of the horizontal VOR in two dimensions.
The Global model describes how signals from the nuclei in the VOR pathway may be performing the computations presented in the Kinematic VOR model.
For example, single unit recordings have shown that a group of cells in the vestibular nucleus, the vestibular-eye position cells, discharge to both head velocity and eye position. Although eye position signals have been included in previous VOR models, they have not provided a satisfying explanation for the mixing of these apparently disparate signals. The Global VOR Model presents an explanation for the mixing between the two signals observed in the vestibular nucleus.
The Global VOR model contains many new elements not found in any earlier model of the VOR ([Cova and Galiana1995]; [Galiana1986]; [Ito1984]; [Lisberger1994]; [Robinson1981]; [Robinson1982]; [Quinn et al.1992]; [Quinn, Baker and Peterson1992]; [Viire et al.1986]). It is the first model that provides a complete geometrical description of the VOR in terms of variables having homologous representation in the brain stem, including VOR gain modulation with vergence and location of the rotation axis. It suggests a direct modulatory role of the cerebellum in the VOR beyond a role in VOR adaptation. In December 1995, it provided predictions about the type of signals expected in the cerebellum during VOR modulation with changes in location of rotation axis; some of these predictions have been subsequently verified ([Snyder and King1996]). Finally, the model relates the geometrical vector representation of eye position to a more natural muscle coordinate representation.