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J Biomech. 2016 May 3;49(7):1170-1179. doi: 10.1016/j.jbiomech.2016.03.005. Epub 2016 Mar 8.

Limit cycle oscillations in standing human posture.

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Department of Mechanical and Manufacturing Engineering, Miami University, 650 East High Street, Oxford, Ohio 45056, United States.
Department of Health and Kinesiology, Purdue University, 800 West Stadium Avenue, West Lafayette, Indiana 47907-2046, United States.
Department of Kinesiology & Physical Education, Wilfrid Laurier University, 75 University Avenue West, Waterloo, Ontario, Canada N2L 3C5.
School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, Indiana 47907-2088, United States. Electronic address:


Limit cycle oscillations (LCOs) are a hallmark of dynamic instability in time-delayed and nonlinear systems such as climate change models, biological oscillators, and robotics. Here we study the links between the human neuromuscular system and LCOs in standing posture. First, we demonstrate through a simple mathematical model that the observation of LCOs in posture is indicative of excessive neuromuscular time-delay. To test this hypothesis we study LCOs in the postural sway of individuals with multiple sclerosis and concussed athletes representing two different populations with chronically and acutely increased neuromuscular time-delays. Using a wavelet analysis method we demonstrate that 67% of individuals with multiple sclerosis and 44% of individuals with concussion exhibit intermittent LCOs; 8% of MS-controls, 0% of older adults, and 0% of concussion-controls displayed LCOs. Thus, LCOs are not only key to understanding postural instability but also may have important applications for the detection of neuromuscular deficiencies.


Balance; Bifurcations; Limit cycle; Model; Neuromuscular disease; Time-delay

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