Dynamical systems theory applied to short walking trials

• Published in: Journal of biomechanics Vol. 176; p. 112331
• Main Authors: Bhat, Sandesh G., Kaufman, Kenton R.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.11.2024; Elsevier Limited
• Subjects: Aged; Algorithms; Analytical techniques; Approximation; Biomechanical Phenomena; Data analysis; Data collection; Datasets; Dynamic systems theory; Dynamical systems; Eigenvalues; Exact solutions; Fall risk; Female; Gait; Gait - physiology; Gait analysis; Gait dynamics; Humans; Liapunov exponents; Male; Mathematical analysis; Methods; Middle Aged; Models, Biological; Postural Balance - physiology; Singular value decomposition; Stability; Stability analysis; System theory; Systems Theory; Walking; Walking - physiology; Gait dynamics; Fall risk; Stability; Dynamical systems; Gait analysis
• ISSN: 0021-9290; 1873-2380; 1873-2380
• DOI: 10.1016/j.jbiomech.2024.112331

Human walking is an extremely complex neuromuscular activity whose simplicity disappears when an attempt is made to provide a quantitative description of the process. The dynamical systems theory provides a framework for analyzing the stability and chaotic nature of dynamical systems, employing Floquet multipliers (FM) and long and short-term Lyapunov exponents (LE), respectively. This report compares FM and LE from three methods: method A (false nearest neighbors and numerical approximation), method B (false nearest neighbors and semi-analytical technique) and method C (singular value decomposition and semi-analytical technique). Data from 33 healthy older adults with no history of falls were used to explain the dynamic system. A surrogate center of mass trajectory was calculated for the analysis of sway in the transverse plane. Results revealed methodological differences in LE and FM calculations with semi-analytical solutions providing closer approximations to observed gait behavior. The long-term LE from Methods A and B were similar, but other LE pairings differed. Method A’s short-term LE indicated chaotic gaits for all subjects, while long-term LE from Methods A and B indicated chaos for half the subjects. Method C showed non-chaotic gait for most subjects. Method B’s FM indicated over 30% of subjects had unstable gait. Method C yielded values of LE and FM that most closely matched the subjects’ gait patterns. This study offers a methodological foundation for gait analysis using short time-series data, facilitating deeper insights into both stability and chaos within gait dynamics.