We previously demonstrated that an intermittent-feedback control paradigm, originally developed for modeling the stabilization of upright standing, can be applied with success also to the CIP system, but with values of the critical parameters far from the limiting ones (stick length 50 cm and feedback delay 100 ms). Moreover, there is a cybernetic limit related to the delay of the multimodal sensory feedback (about 230 ms) that supports a feedback stabilization strategy. The difficulty of the task grows exponentially with the decrease of the length of the stick and a stick length of 32 cm is considered as a human limit even for well-trained subjects. Stabilization of the CIP (Cart Inverted Pendulum) is an analogy to stick balancing on a finger and is an example of unstable tasks that humans face in everyday life. These findings provide useful insight into the mechanisms responsible for the statistical persistence of stride intervals in human walking. These mechanisms were clarified based on the phase response characteristics of our model. A lack of phase resetting induced a loss of statistical persistence, as observed for aging, neural disorders, and experimental interventions. In this study, we reproduced the statistical persistence in stride intervals using a simplified neuromechanical model composed of a simple compass-type biomechanical model and a simple CPG model that incorporates only phase resetting and a feedforward controller. However, the essential mechanisms remain largely unclear due to the complexity of the neuromechanical model. In particular, a previous study integrated a biomechanical model composed of seven rigid links with a central pattern generator (CPG) model, which incorporated a phase resetting mechanism as sensory feedback as well as feedforward, trajectory tracking, and intermittent feedback controllers, and suggested that phase resetting contributes to the statistical persistence in stride intervals. It has also been hypothesized that the statistical persistence emerges through the dynamic interactions during walking. Human walking is a complex phenomenon generated through the dynamic interactions between the central nervous system and the biomechanical system. It has been hypothesized that the central nervous system is responsible for the statistical persistence. This statistical property is changed by aging, neural disorders, and experimental interventions.
Stride intervals in human walking fluctuate from one stride to the next, exhibiting statistical persistence. The model can be of help in understanding the mechanism of FoG and developing measures to counter its severity. The model allows one to estimate the parameters from the data and thereby personalise the cueing regimes for patients. The model indicates the frequency-dependent behaviours in PD, which are in line with the STN stimulation and external cueing-related studies. The effect of augmented feedback on the model is also studied to understand different FoG management methods, such as sensory and auditory cues.
The model’s robustness is studied by analysing relevant parameters such as gain in the event-dependent feedback and level of activation of the central pattern generator neurons. The proposed hybrid system model has event-dependent feedback and demonstrates PD-relevant behaviours such as freezing, high variability and stable gait. A novel hybrid system model is proposed in this paper, in which a mechanical model is coupled with a neuronal model. The present understanding of PD gait is limited, and there is a need to develop mathematical models explaining PD gait’s underlying mechanisms. Freezing of gait is a late-stage debilitating symptom of Parkinson’s disease (PD) characterised by a sudden involuntary stoppage of forward progression of gait.
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