Time series analysis and modelling of the freezing of gait phenomenon

Abstract

Freezing of Gait (FOG) is one of the most debilitating symptoms of Parkinson’s Disease and is associated with falls and loss of independence. The patho-physiological mecha- nisms underpinning FOG are currently poorly understood. In this thesis we combine time series analysis and mathematical modelling to study the FOG phenomenon’s dynamics. We focus on the transition from stepping in place into freezing and treat this phenomenon in the context of an escape from an oscillatory attractor into an equilibrium attractor state. We analyze the experimental data by two different approaches. In the first approach we use a stochastic Hopf bifurcation normal form model to study the escape time from oscillatory behavior to small-amplitude fluctuations. For the other approach we extract a discrete-time discrete-space Markov chain from experimental data and divide its state space into communicating classes to identify the transition into freezing. This allows us to develop a methodology for computationally estimating the time to freezing as well as the phase along the oscillatory (stepping) cycle of a patient experiencing Freezing Episodes (FE). The developed methodology is general and could be applied to any time series featuring transitions between different dynamic regimes including time series data from forward walking in people with FOG.