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Human Balance Control: Dead Zones, Intermittency, and Micro-chaos

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Mathematical Approaches to Biological Systems

Abstract

The development of strategies to minimize the risk of falling in the elderly represents a major challenge for aging in industrialized societies. The corrective movements made by humans to maintain balance are small amplitude, intermittent and ballistic. Small-amplitude, complex oscillations (“micro-chaos”) frequently arise in industrial settings when a time-delayed digital processor attempts to stabilize an unstable equilibrium. Taken together, these observations motivate considerations of the effects of a sensory threshold on the stabilization of an inverted pendulum by time-delayed feedback. In the resulting switching-type delay differential equations, the sensory threshold is a strong small-scale nonlinearity which has no effect on large-scale stabilization but may produce complex, small-amplitude dynamics including limit cycle oscillations and micro-chaos. A close mathematical relationship exists between a scalar model for balance control and the micro-chaotic map that arises in some models of digitally controlled machines. Surprisingly, transient, time-dependent, bounded solutions (“transient stabilization”) can arise even for parameter ranges where the equilibrium is asymptotically unstable. In other words, the combination of a sensory threshold with a time-delayed sampled feedback can increase the range of parameter values for which balance can be maintained, at least transiently. Neurobiological observations suggest that sensory thresholds can be manipulated either passively by changing posture or actively using efferent feedback. Thus it may be possible to minimize the risk of falling by means of strategies that manipulate sensory thresholds by using physiotherapy and appropriate exercises.

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Acknowledgements

JM was supported by the William R. Kenan Jr. Charitable Trust, the National Science Foundation (NS-1028970), and the Invitation Award to Distinguished Scientists by the Hungarian Academy of Sciences. TI and GS were supported by the Hungarian National Science Foundation (OTKA-K105433 and OTKA-K101714).

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Authors and Affiliations

  1. W. M. Keck Science Center, The Claremont Colleges, Claremont, CA, 91711, USA

    John Milton

  2. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Tamas Insperger & Gabor Stepan

  3. MTA-BME Research Group on Dynamics of Machines and Vehicles, Hungarian Academy of Sciences, Budapest, 1521, Hungary

    Gabor Stepan

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  1. Graduate School of Mathematics, Nagoya University, Nagoya, Aichi, Japan

    Toru Ohira

  2. Graduate School of Mathematics, Nagoya University, Nagoya, Aichi, Japan

    Tohru Uzawa

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Milton, J., Insperger, T., Stepan, G. (2015). Human Balance Control: Dead Zones, Intermittency, and Micro-chaos. In: Ohira, T., Uzawa, T. (eds) Mathematical Approaches to Biological Systems. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55444-8_1

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