Volterra modeling of the human smooth pursuit system in health and disease

This thesis treats the identification of Volterra models of the human smooth pursuit system from eye-tracking data. Smooth pursuit movements are gaze movements used in tracking of moving targets and controlled by a complex biological network involving the eyes and brain. Because of the neural control of smooth pursuit, these movements are affected by a number of neurological and mental conditions, such as Parkinson's disease. Therefore, by constructing mathematical models of the smooth pursuit system from eye-tracking data of the patient, it may be possible to identify symptoms of the disease and quantify them. While the smooth pursuit dynamics are typically linear in healthy subjects, this is not necessarily true in disease or under influence of drugs. The Volterra model is a classical black-box model for dynamical systems with smooth nonlinearities that does not require much a priori information about the plant and thus suitable for modeling the smooth pursuit system. The contribution of this thesis is mainly covered by the four appended papers. Papers I–III treat the problem of reducing the number of parameters in Volterra models with the kernels parametrized in Laguerre functional basis (Volterra–Laguerre models), when utilizing them to capture the signal form of smooth pursuit movements. Specifically, a Volterra–Laguerre model is obtained by means of sparse estimation and principal component analysis in Paper I, and a Wiener model approach is used in Paper II. In Paper III, the same model as in Paper I is considered to examine the feasibility of smooth pursuit eye tracking for biometric purposes. Paper IV is concerned with a Volterra–Laguerre model that includes an explicit time delay. An approach to the joint estimation of the time delay and the finite-dimensional part of the Volterra model is proposed and applied to time-delay compensation in eye-tracking data