Mathematical modelling and Data Analysis for Parkinson’s Disease Gait
Parakkal Unni, M
Date: 7 February 2022
Publisher
University of Exeter
Degree Title
PhD in Mathematics
Abstract
Freezing is an involuntary stopping of gait observed in late-stage Parkinson’s disease
(PD) patients. It is a highly debilitating symptom lacking a clear understanding of its
causes and is challenging to predict. This thesis addresses (1) machine-learning-based
prediction of freezing for better management of the disease and (2) ...
Freezing is an involuntary stopping of gait observed in late-stage Parkinson’s disease
(PD) patients. It is a highly debilitating symptom lacking a clear understanding of its
causes and is challenging to predict. This thesis addresses (1) machine-learning-based
prediction of freezing for better management of the disease and (2) neuromechanical
modelling to explain the underpinnings of the symptom.
A data-driven approach is proposed in chapter 4 for predicting freezing events
using a machine learning approach, specifically Random Forrest (RF), Neural Network
(NN), and Naive Bayes (NB). Data sampled using a force platform were used for this
purpose. This data was collected from PD subjects as they stepped in place until they
had at least one freezing episode. The F1 scores of the machine learning algorithms
were computed for different windowing parameters. These parameters represent the
input data length (IL) and how early the freezing event is predicted (GL). The IL that
maximised the F1 score is approximately equal to 1.13 s, indicating the physiological
changes leading to a freeze take effect at least one step before the freezing incident.
The prediction deteriorated as one tried to predict it early, evidenced by a negative
correlation between GL and F1 scores. Our algorithm has the potential to support
the development of devices to detect and then potentially prevent freezing events in
people with Parkinson’s, which might occur if left uncorrected.
As the second contribution, mathematical models of PD-Gait are developed
with varying complexity and generality to explain the observed gait characteristics
of PD. The first mathematical model described in chapter 5 consists of the stance
leg modelled as a simple inverted pendulum acted upon by the ankle-push off forces
from the trailing leg and pathological forces by the plantar-flexors of the stance
leg. Freezing and irregular walking are demonstrated in a biped model as well as the inverted pendulum model. The inverted pendulum model is further studied
semi-analytically to show the presence of horseshoe and chaos to explain the cause
of variability in PD-Gait. The model reveals that these opposing forces generated by
the plantar flexors can induce freezing and variability. The model also explains gait
abnormalities such as reduction in step length close to a freeze and irregular walking
patterns. However, the model proposed in chapter 5 does not explicitly address the
effect of central pattern generators (CPG), feedback from the limbs, and the transition
to walking from FoG observed in PD-Gait. Therefore, a generalisation of the model
is developed in chapter 6 by coupling the hybrid mechanical model with a model of
CPG and event dependent feedback. The model demonstrates gait characteristics
relevant to PD, such as freezing, high variability and stable gait. The model’s ability
to capture the PD-related characteristics across a wide parameter range showed its
robustness. Moreover, the effect of augmented feedback on the model is studied to
understand different FoG management methods, such as sensory and auditory cues.
While this model explains variability, freezing, the effect of feedback, and transitions
from freezing to walking, there is further scope to generalise this model, considering
that phase coordination is affected in PD-Gait. This generalisation requirement is
addressed in chapter 7. Here, a set of maps are derived, combining both the neural
and mechanical aspects of the PD-Gait. Phase reset curves (PRC) that correspond
to the oscillators are used to abstract the neuronal dynamics, and a simple inverted
pendulum model is used to describe the motion. Gait variability, freezing, the effect
of PPN stimulation in PD-Gait are explained using this model. The model is also
extensible to be used with different PRCs. To summarise, the thesis has potential
implications in FoG management using sensory cues, and it takes a step forward
in explaining the underpinnings of PD-Gait characteristics such as freezing and
variability.
Doctoral Theses
Doctoral College
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