Volterra modeling of the Smooth Pursuit System with application to motor symptoms characterization in Parkinson´s disease

A new way of modeling the Smooth Pursuit System (SPS) in humans by means of Volterra series expansion is suggested and utilized together with Gaussian Mixture Models (GMMs) to successfully distinguish between healthy controls and Parkinson patients based on their eye movements. To obtain parsimonious Volterra models, orthonormal function expansion of the Volterra kernels in Laguerre functions with the coefficients estimated by SParse Iterative Covariance-based Estimation (SPICE) is used. A combination of these two techniques is shown to greatly reduce the number of model parameters without significant performance loss. In fact, the resulting models outperform the Wiener models of previous research despite the significantly lower number of model parameters. Furthermore, the results of this study indicate that the nonlinearity of the system is likely to be dynamical in nature, rather than static which was previously presumed. The difference between the SPS in healthy controls and Parkinson patients is shown to lie largely in the higher order dynamics of the system. Finally, without the model reduction provided by SPICE, the GMM estimation fails, rendering the model unable to separate healthy controls from Parkinson patients.