Investigation of the chaotic dynamics of the vertical strance of a human body on the model of an inverted pendulum

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Abstract

Different stances of human body are studied in medicine and biology for quantitative estimation and clinical diagnostics of impairments and diseases of the musculoskeletal, nervous, vestibular systems and functions. Human body is composed of ~200 bones and ~600 muscles, and its upright position is unstable due to high complexity of the system and its control mechanisms. Among different techniques of the body sway recording the stabilography is one of the most simple and cheap unit. It is composed by a force platform that can measure the reaction forces over the contact areas between two feet and the platform. The former is portable and can be connected to any laptop via USB port. In this study the functions controlling the vertical stance of a person are studied accounting for the nonlinear dynamics of oscillations of the projection (XC,YC) of center of mass (CM) of the body on the horizontal plane. The time series {XC(t),YC(t)} have been measured on 28 healthy volunteers (age 21-42, height 156-182 cm, body mass 48-84.8 kg). The volunteers were asked to keep a quiet stance on two feet, similar stances with body mass shifted onto the left and then onto the right leg. Each stance has been repeated during 30 s with open and then with closed eyes. After a short break a test with balancing on the left and then on the right leg has been perfrmed. For each case, based on the mathematical model of the inverted pendulum, the calculated control functions u(t) in the form u(t)=k1(r(t)-r0)+ k2(r/(t)-r/0), where r(t) is the radius-vector of the CM, r0 is its averaged value over time, (.)/ means the time derivative. Using statistical analysis, the absence of correlations between the control functions for both different subjects and for different positions of the body of the same volunteer was shown. Based on the calculations of the Lyapunov exponent, the individuals have been classified into groups with stable, weakly and highly unstable control of the vertical position of the body. The modeling of such systems in the framework of nondeterministic chaos models with nonlinear control is discussed.
基于倒立摆模型的人体垂直距离混沌动力学研究
医学和生物学研究人体的不同姿态,用于定量估计和临床诊断肌肉骨骼、神经、前庭系统和功能的损伤和疾病。人体由约200块骨骼和约600块肌肉组成,由于系统及其控制机制的高度复杂性,其直立位置是不稳定的。在不同的身体摇摆记录技术中,稳定记录技术是最简单、最廉价的一种。它由一个力平台组成,可以测量两脚与平台之间接触区域的反作用力。前者是便携式的,可以通过USB接口连接到任何笔记本电脑。本文研究了人体质心(CM)在水平面上的投影(XC,YC)振荡的非线性动力学,研究了控制人体垂直姿态的函数。对28名健康志愿者(年龄21 ~ 42岁,身高156 ~ 182 cm,体重48 ~ 84.8 kg)的时间序列{XC(t),YC(t)}进行了测量。志愿者被要求保持安静的双脚站立,类似的姿势是身体重心移到左腿,然后移到右腿。每个姿势重复30秒,先睁开眼睛,然后闭上眼睛。短暂休息后,先用左腿平衡,然后用右腿平衡。对于每种情况,根据倒立摆的数学模型,计算出的控制函数u(t)的形式为u(t)=k1(r(t)-r0)+ k2(r/(t)-r/0),其中r(t)为CM的半径矢量,r0为其随时间的平均值,(.)/为时间导数。通过统计分析,显示了不同受试者和同一志愿者身体不同位置的控制功能之间缺乏相关性。根据李雅普诺夫指数的计算,将个体分为对身体垂直位置控制稳定、弱和高度不稳定的三组。在非线性控制的不确定性混沌模型框架下,讨论了这类系统的建模问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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