Identification Techniques for Mathematical Modeling of the Human Smooth Pursuit System

Sammanfattning: This thesis proposes nonlinear system identification techniques for the mathematical modeling of the human smooth pursuit system (SPS) with application to motor symptom quantification in Parkinson's disease (PD). The SPS refers to the complex neuromuscular system in humans that governs the smooth pursuit eye movements (SPEM). Insight into the SPS and its operation is of importance in a wide and steadily expanding array of application areas and research fields. The ultimate purpose of the work in this thesis is to attain a deeper understanding and quantification of the SPS dynamics and thus facilitate the continued development of novel commercial products and medical devices. The main contribution of this thesis is in the derivation and evaluation of several techniques for SPS characterization. While attempts to mathematically model the SPS have been made in the literature before, several key aspects of the problem have been previously overlooked.This work is the first one to devise dynamical models intended for extended-time experiments and also to consider systematic visual stimuli design in the context of SPS modeling. The result is a handful of parametric mathematical models outperforming current State-of-the-Art models in terms of prediction accuracy for rich input signals. As a complement to the parametric dynamical models, a non-parametric technique involving the construction of individual statistical models pertaining to specific gaze trajectories is suggested. Both the parametric and non-parametric models are demonstrated to successfully distinguish between individuals or groups of individuals based on eye movements.Furthermore, a novel approach to Wiener system identification using Volterra series is proposed and analyzed. It is exploited to confirm that the SPS in healthy individuals is indeed nonlinear, but that the nonlinearity of the system is significantly stronger in PD subjects. The nonlinearity in healthy individuals appears to be well-modeled by a static output function, whereas the nonlinear behavior introduced to the SPS by PD is dynamical.