Time series analysis and modelling of the freezing of gait phenomenon

Résumé : 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 mechanisms underpinning FOG are currently poorly understood. In this paper 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 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.