  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.
