Capturing the chaos of running

An old tool from the nonlinear-dynamics kit has shed new light on how amputations affect gait.

None of us are perfect—and neither are our gaits. In any given stride, we might extend a knee a bit further, swing a leg a bit wider, or raise a foot a bit higher than in the stride before. In nonlinear dynamics, such deviations from perfect periodicity are often characterized by the Lyapunov exponent, a measure of the rate at which small perturbations grow into big ones. A large Lyapunov exponent indicates an unstable, chaotic system prone to large fluctuations; a small exponent indicates a stable system that’s nearly periodic. (See the article by Adilson Motter and David Campbell, Physics Today, May 2013, page 27.) Now Nicole Look, her advisers Elizabeth Bradley and Rodger Kram, and their colleagues at the University of Colorado Boulder have used motion-capture technology to determine Lyapunov exponents associated with human running. The researchers tracked the movements of 17 subjects—six of whom had below-knee amputations and were fitted with prostheses—as they ran at paces varying from a trot to a sprint. (One test subject is pictured here.) As expected, the amputees’ knee and hip motions were less stable than those of nonamputees. But surprisingly, amputees had, on average, a slightly more stable center of mass. Moreover, the center-of-mass dynamics of all subjects tended to grow more stable with increased running speed, even as knee and hip movements grew more chaotic. One proposed explanation: Runners may instinctively compensate for diminished lower-body control by exerting more control over their core. (N. Look et al., Chaos, in press.)—Ashley G. Smart


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