Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion During Long-Range Walking

TL;DR

This study models the vertical center-of-mass motion during walking as a stochastic dynamical system, using phase space diffusion analysis to quantify long-term variability in gait.

Contribution

It introduces a novel application of Fokker-Planck equation modeling to assess gait variability through phase space analysis of human walking.

Findings

Distribution of adiabatic invariants fits Fokker-Planck solution

Vertical motion variability can be characterized by constant diffusion coefficient

Phase space diffusion provides insights into long-range gait variability

Abstract

When a Hamiltonian system undergoes a stochastic, time-dependent anharmonic perturbation, the values of its adiabatic invariants as a function of time follow a distribution whose shape obeys a Fokker-Planck equation. The effective dynamics of the body's centre-of-mass during human walking is expected to represent such a stochastically perturbed dynamical system. By studying, in phase space, the vertical motion of the body's centre-of-mass of 25 healthy participants walking for 10-minutes at spontaneous speed, we show that the distribution of the adiabatic invariant is compatible with the solution of a Fokker-Planck equation with constant diffusion coefficient. The latter distribution appears to be a promising new tool for studying the long-range kinematic variability of walking.