分形分析揭示步态的独立复杂性和可预测性
Fractal Analyses Reveal Independent Complexity and Predictability of Gait
摘要：
运动是一项自然的任务，几十年来一直被评估，并被用作突出各种来源的障碍的代理。大多数研究采用经典的时空步态参数的线性分析。在这里，我们使用更先进的，但不太实用，非线性技术来分析健康受试者的步态时间序列。我们的目的是寻找更多的敏感指标时空步态参数比以前使用的，希望能更好地识别异常运动。我们分析了34名参与者在改变行走方向（向前与向后行走）以及有或没有前庭电刺激的情况下的大规模步幅间隔时间序列和平均步长。计算了Hurst指数$α$和Minkowski分形维数$D$，分别作为步幅间隔时间序列可预测性和复杂性的指标。我们发现，$α$和$D$准确地捕捉步幅间隔的变化的功能的实验条件。向前走表现出最大的复杂性（$D$），因此，适应性。相反，任何干扰（向后走和/或前庭系统的刺激）降低了它。此外，向后走增加了可预测性（$α$）通过一个更刻板的模式的步幅间隔和前庭电刺激降低了可预测性。本研究证明了赫斯特指数和分形维数的互补力量，以改善步行分类。这些整体指标可以很容易地在最佳运动复杂性的框架中解释。我们的发展可能会立即应用于康复，诊断和分类程序。
英文摘要：
Locomotion is a natural task that has been assessed since decades and used as a proxy to highlight impairments of various origins. Most studies adopted classical linear analyses of spatio-temporal gait parameters. Here, we use more advanced, yet not less practical, non-linear techniques to analyse gait time series of healthy subjects. We aimed at finding more sensitive indexes related to spatio-temporal gait parameters than those previously used, with the hope to better identify abnormal locomotion. We analysed large-scale stride interval time series and mean step width in 34 participants while altering walking direction (forward vs. backward walking) and with or without galvanic vestibular stimulation. The Hurst exponent $α$ and the Minkowski fractal dimension $D$ were computed and interpreted as indexes expressing predictability and complexity of stride interval time series, respectively. We show that $α$ and $D$ accurately capture stride interval changes in function of the experimental condition. Walking forward exhibited maximal complexity ($D$) and hence, adaptability. In contrast, any perturbation (walking backward and/or stimulation of the vestibular system) decreased it. Furthermore, walking backward increased predictability ($α$) through a more stereotyped pattern of the stride interval and galvanic vestibular stimulation reduced predictability. The present study demonstrates the complementary power of the Hurst exponent and the fractal dimension to improve walking classification. These holistic indexes can easily be interpreted in the framework of optimal movement complexity. Our developments may have immediate applications in rehabilitation, diagnosis, and classification procedures.
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