Abstract
Stride intervals of normal human walking exhibit long-range temporal correlations. Similar to the fractal-like behaviors observed in brain and heart activity, long-range correlations in walking have commonly been interpreted to result from chaotic dynamics and be a signature of health. Several mathematical models have reproduced this behavior by assuming a dominant role of neural central pattern generators (CPGs) and/or nonlinear biomechanics to evoke chaos. In this study, we show that a simple walking model without a CPG or biomechanics capable of chaos can reproduce long-range correlations. Stride intervals of the model revealed long-range correlations observed in human walking when the model had moderate orbital stability, which enabled the current stride to affect a future stride even after many steps. This provides a clear counterexample to the common hypothesis that a CPG and/or chaotic dynamics is required to explain the long-range correlations in healthy human walking. Instead, our results suggest that the long-range correlation may result from a combination of noise that is ubiquitous in biological systems and orbital stability that is essential in general rhythmic movements.
Highlights
Though human walking is highly stereotyped, the stride intervals fluctuate from one stride to the with a measurable variance
We show that nonlinear dynamics capable of chaos may not be necessary to explain the phenomenon of long-range correlation
With h0 = p/12, the distributions of a and b reproduced those of normal human walking with long range correlations, whereas the indication of long-range correlations became less evident as h0 increased to p/6
Summary
Though human walking is highly stereotyped, the stride intervals fluctuate from one stride to the with a measurable variance. In healthy adult walking, the variations in stride intervals exhibit long-range correlations [1,2]. This observation has supported the hypothesis that the step-to-step variation exhibits fractal-like behavior rather than uncorrelated stochastic noise superimposed on regular dynamics. The importance of this long-range correlation has been further emphasized since several studies reported that age and neurological disorders decrease the correlations [3,4,5], suggesting that long-range correlations may indicate a healthy locomotor system. The ubiquitous neuromuscular noise combined with essential but non-chaotic biomechanics may be sufficient to explain the observed long-range correlations in stride intervals
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