The main purpose of this study is to compare two different feedback controllers for the stabilization of quiet standing in humans, taking into account that the intrinsic ankle stiffness is insufficient and that there is a large delay inducing instability in the feedback loop: 1) a standard linear, continuous-time PD controller and 2) an intermittent PD controller characterized by a switching function defined in the phase plane, with or without a dead zone around the nominal equilibrium state. The stability analysis of the first controller is carried out by using the standard tools of linear control systems, whereas the analysis of the intermittent controllers is based on the use of Poincaré maps defined in the phase plane. When the PD-control is off, the dynamics of the system is characterized by a saddle-like equilibrium, with a stable and an unstable manifold. The switching function of the intermittent controller is implemented in such a way that PD-control is ‘off’ when the state vector is near the stable manifold of the saddle and is ‘on’ otherwise. A theoretical analysis and a related simulation study show that the intermittent control model is much more robust than the standard model because the size of the region in the parameter space of the feedback control gains (P vs. D) that characterizes stable behavior is much larger in the latter case than in the former one. Moreover, the intermittent controller can use feedback parameters that are much smaller than the standard model. Typical sway patterns generated by the intermittent controller are the result of an alternation between slow motion along the stable manifold of the saddle, when the PD-control is off, and spiral motion away from the upright equilibrium determined by the activation of the PD-control with low feedback gains. Remarkably, overall dynamic stability can be achieved by combining in a smart way two unstable regimes: a saddle and an unstable spiral. The intermittent controller exploits the stabilizing effect of one part of the saddle, letting the system evolve by alone when it slides on or near the stable manifold; when the state vector enters the strongly unstable part of the saddle it switches on a mild feedback which is not supposed to impose a strict stable regime but rather to mitigate the impending fall. The presence of a dead zone in the intermittent controller does not alter the stability properties but improves the similarity with biological sway patterns. The two types of controllers are also compared in the frequency domain by considering the power spectral density (PSD) of the sway sequences generated by the models with additive noise. Different from the standard continuous model, whose PSD function is similar to an over-damped second order system without a resonance, the intermittent control model is capable to exhibit the two power law scaling regimes that are typical of physiological sway movements in humans.

Postural instability is one of the major symptoms of Parkinson’s disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson’s disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson’s patients and some elderly persons might be characterized as a dynamical disease.

Postural instability is one of the predominant symptoms of Parkinson's disease (PD). Despite its significant impact on the deterioration in quality of life in PD patients, mechanistic causes of the instability have not been clarified. Joint inflexibility at ankle and hip joints might be such a major cause, leading to small variability in the center of pressure (CoP) during quiet stance. However, this conjecture is still controversial. Thus, quantitative characterization of CoP patterns during quiet stance in PD patients remains a matter of research. Here we performed a linear discriminant analysis for CoP data in PD patients and age-matched healthy elderly during quiet stance, and showed that CoP variations in PD patients and those in healthy elderly could be well distinguished with an accuracy of about 90%, to which appropriately selected sway indices characterizing aspects of power spectrum for the CoP variations contributed. Specifically, major factors responsible for the discrimination were all associated with increase in the power at a high-frequency band (near and over 1 Hz) along with reduction at the low-frequency regime (lower than about 0.7 Hz). Then, the power-ratio, defined as the relative spectral power in a band around 1 Hz, was examined, since the power in this band reflects postural sway with anti-phase coordinated motions of the ankle and hip joints. We showed that the power-ratio values were significantly smaller in the PD patients than those in the healthy subjects. This difference as well as the results of the linear discriminant analysis suggest joint inflexibility in PD patients, particularly at hip joint, which diminished anti-phase coordination between trunk and lower extremity, leading to postural instability in PD patients.

The intermittent control during human quiet upright stance is a new hypothesis which claims that the active neural feedback control generating the ankle muscle torque is switched off and on intermittently at appropriate timings. The intermittent strategy is capable of providing compliant posture while ensuring robust stability. Contrastingly, impairment of postural reflexes in patients with Parkinson’s disease (PD) causes postural instability. Here we hypothesize that the instability in PD patients might be due to a loss of appropriate intermittent activations in the feedback muscle torque during stance. In order to provide evidence for this hypothesis, we characterized stochastic postural sway patterns measured as changes in center of pressure (CoP) and activities of ankle muscles during quiet stance in healthy young and elderly subjects as well as PD patients. To this end, sway patterns and associated ankle muscle activities were quantified by several indices including the CoP sway area, scaling factors of double-power-law power spectra of the sway, as well as levels and patterns of the muscle activations. Hierarchical cluster analysis was performed to suggest that the sway patterns could be classified into two major types. The first type consisted mainly of sway and muscle activation patterns from healthy subjects and some PD patients with the mild level of severity, and they showed features indicating the intermittent control. The second type, consisting mainly of PD patients with relatively severe levels of motor symptoms, was accompanied with non-intermittent but tonic muscle activities and sway areas either smaller or larger than those in the first type. Moreover, the major two types were further classified into several subtypes with distinguishable characteristics. Results suggested that a loss of the intermittent activations in the ankle muscles could be a cause of the postural instability for a population of PD patients.

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