Abstract
Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.
Highlights
Humans typically maintain a standing posture by swaying backward and forward by approximately 20 mm at a very low frequency
Body sway in human standing on a stable floor has been successfully explained by the intermittent control model [6,7,8,9], and simulation of a nonlinear posture control model predicted a bifurcation structure [11]
We examined the bifurcation-induced transition of human sway depending on floor stability, and investigated a human posture control mechanism by performing the following analyses: analysis of the bifurcation structure and the contribution of biological noise, measurement of human sway on different floor conditions, and quantitative evaluation of the human control gains and bifurcation
Summary
Humans typically maintain a standing posture by swaying backward and forward by approximately 20 mm at a very low frequency (less than 1 Hz). A control procedure called intermittent control, in which control is exerted intermittently [6,7,8,9], replicates the features of human body sway and is robust against cognitive delay This intermittent control model shows a limit cycle state [10] and a micro-chaos state [9]; and a simulation study of standing on an unstable floor (a wobble board) with a nonlinear control model predicted a bifurcation structure [11]. This bifurcation structure allows involuntary transition of sway state with destabilization of the stationary state. It allows a high degree of manoeuvrability or variability
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