Abstract
Freezing is an involuntary stopping of gait observed in late-stage Parkinson's disease (PD) patients. This is a highly debilitating symptom lacking a clear understanding of its causes. Walking in these patients is also associated with high variability, making both prediction of freezing and its understanding difficult. A neuromechanical model describes the motion of the mechanical (motor) aspects of the body under the action of neuromuscular forcing. In this work, a simplified neuromechanical model of gait is used to infer the causes for both the observed variability and freezing in PD. The mathematical model consists of the stance leg (during walking) modeled 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. We model the effect on walking of the swing leg in the biped model and provide a rationale for using an inverted pendulum model. Freezing and irregular walking is demonstrated in the 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. While the plantar flexors of the swing leg push the center of mass (CoM) forward, the plantar flexors of the stance leg generate an opposing torque. Our study reveals that these opposing forces generated by the plantar flexors can induce freezing. Other gait abnormalities nearer to freezing such as a reduction in step length, and irregular walking patterns can also be explained by the model.
Highlights
Parkinson’s disease results from the loss of neurons in the substantia nigra pars compacta of the basal ganglia (BG) (Davie, 2008), which has projections toward the motor, and cognitive areas (Albin et al, 1989; Alexander and Crutcher, 1990)
Even though the complex freezing behavior can be explained through several possible routes (Nutt et al, 2011) an attempt is made here to explain it in the simplest possible way and to understand the effect of neuromuscular inputs in generating unstable and chaotic walking behavior as observed in Parkinson’s disease (PD) (Heremans et al, 2013)
“gait cycle” in this study has been defined as the process, where the model states evolve from an initial condition of a step (“double support phase”) until the reset condition is met and the initial condition of the step is computed
Summary
Parkinson’s disease results from the loss of neurons in the substantia nigra pars compacta of the basal ganglia (BG) (Davie, 2008), which has projections toward the motor, and cognitive areas (Albin et al, 1989; Alexander and Crutcher, 1990). The first aim is to explain the empirical observations that are seen in PDGait with a minimum number of variables These include (1) a high coefficient of variation in PD subjects (Heremans et al., 2013), (2) a pattern of reduction of step lengths before freezing (Nutt et al, 2011), (3) the ability of sensory and visual cues to help reduce freezing (Rochester et al, 2005; Young et al, 2014; Amini et al, 2019), (4) the difficulty of freezing prediction, and (5) the occurrence of freezing near obstacles and narrow passages (Snijders et al, 2008). The hypothesis investigated in this study is that the variability and the motor symptoms associated with PD (Heremans et al, 2013) can be explained by the experimentally observed premature activation of plantar flexors observed in PD (Nieuwboer et al, 2004)
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