Nonlinear DDE Analysis of Repetitive Hand Movements in Parkinson’s Disease

Time series analysis with nonlinear delay differential equations (DDEs) is a very powerful tool since it reveals spectral as well as topological properties of the underlying dynamical system and is robust against noise. Here we apply nonlinear DDEs to examine the nature of the spatiotemporal distortions in repetitive finger tapping movements of mild to moderate Parkinson's disease (PD) patients on and off their dopamine replacement therapy and of age-matched controls. Using DDE analysis, there was a nearly complete separation of the data of all three groups: PD patients were classified separately from control subjects, and PD patients on and off medication were clearly distinguished. The non-linear phase coupling terms were particular important in being able to separate groups. There was an increased degree of multiplicity of frequencies in the temporal patterns when going from control to PD on medication to PD off medication. This analysis was then compared with clinical scores provided by physicians, the UPDRS (United Parkinson's Disease Rating Scale) scores. The values of the nonlinear term of the DDE shows good correlation to this clinical scores. We conclude that such measures may provide a more objective and precise measure of the spatiotemporal disruption of rhythmic movements in PD, and the reversal of these deficits by pharmacological (or surgical) therapies.