Long-Range Correlations in Stride Intervals May Emerge from Non-Chaotic Walking Dynamics

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.

健康人类步行的步间间隔存在长时程时间相关性（long-range temporal correlations）。与脑、心脏活动中观测到的类分形行为类似，步行过程中的长时程相关性通常被认为源于混沌动力学，且可作为健康状态的标志性特征。此前已有多项数学模型通过假定神经中枢模式发生器（central pattern generators, CPG）与/或非线性生物力学发挥主导作用以诱发混沌，复现了这一行为特征。本研究证实，一款不具备CPG或能产生混沌的生物力学机制的简易步行模型，同样能够复现长时程相关性。当该模型具备适度轨道稳定性（orbital stability）时，其步间间隔会呈现健康人类步行中观测到的长时程相关性——这种稳定性可使当前步在历经多步后仍能对后续步幅产生影响。这一结果对“健康人类步行的长时程相关性需以CPG和/或混沌动力学作为解释依据”的主流假说，给出了明确的反例。与之相反，本研究结果提示，长时程相关性或源于生物系统中普遍存在的噪声，与一般节律运动所必需的轨道稳定性二者的共同作用。