Modeling the spatiotemporal organization of velocity storage in the vestibuloocular reflex by optokinetic studies

1. A generalized three-dimensional state space model of visual vestibular interaction was developed. Matrix and dynamical system operators associated with inputs from the semicircular canals, otolith velocity estimator, and the visual system have been incorporated into the model, which focus on their relationship to the velocity storage integrator. 2. A relationship was postulated between the eigenvalues and the direction of the eigenvectors of the system matrix and the orientation of the spatial vertical. It was assumed that the system matrix for a tilted position was a composition of two linear transformations of the system matrix for the upright position. One transformation modifies the eigenvalues of the system matrix, whereas another rotates the eigenvectors of the system matrix. The pitch and roll eigenvectors rotate with the head, whereas the yaw axis eigenvector remains approximately spatially invariant. 3. Based on the three-dimensional model, a computational procedure was formulated to identify the eigenvalues and eigenvectors of the system matrix with the use of a modification of the Marquardt algorithm. With the use of data obtained from a monkey, it was shown that the three-dimensional behavior of velocity storage cannot be predicted solely in terms of its time constants, i.e., the inverse of its eigenvalues. With the use of the same eigenvalues the data could either be fit or not fit, depending on the eigenvector directions. Therefore, it is necessary to specify eigenvector directions when characterizing velocity storage in three dimensions. 4. Parameters found with the use of the Marquardt algorithm were incorporated into the model. Diagonal matrices in a head coordinate frame were introduced for coupling the visual system to the integrator and to the direct optokinetic pathway. Simulations of optokinetic nystagmus (OKN) and optokinetic after-nystagmus (OKAN) were run. The model predicted the behavior of yaw and pitch OKN and OKAN when the animal is upright. It also predicted the cross-coupling in the side down position. The trajectories in velocity space were also accurately simulated. 5. One of the predictions of the model is that when the stimulus direction is along an eigenvector, the trajectory in velocity space is a straight line. Using the 'spectral width' of the residuals from a straight line sequence during OKAN, we developed a methodology to estimate how close the OKAN decay was to an eigenvector trajectory. 6. Thus we have developed a model-based approach for studying and interpreting the response characteristics of velocity storage in three dimensions. The relationship between the orientation of the state space eigenvector basis of the velocity storage integrator and three dimensional space should be useful in studying structures in the central nervous system responsible for maintaining spatial orientation.