Stochastic processes in postural center-of-pressure profiles

Abstract

The stochastic processes of postural center-of-pressure profiles were examined in 3- and 5-year-old children, young adult students (mean 20 years), and an elderly age group (mean 67 years). Subjects stood still in an upright bipedal stance on a force platform under vision and nonvision conditions. The time evolutionary properties of the center-of-pressure dynamic were examined using basic stochastic process models. The amount of motion of the center of pressure decreased with increments of age from 3 to 5 years to young adult but increased again in the elderly age group. The availability of vision decreased the amount of motion of the center of pressure in all groups except the 3-year-old group, where there was less motion of the center of pressure with no vision. The stochastic properties of the center-of-pressure dynamic were assessed using both a two-process, random-walk model of Collins and De Luca and an Ornstein-Uhlenbeck model that is linear and has displacement governed only by a single stiffness term in the random walk. The two-process open- and closed-loop model accounted for about 96% and the Ornstein-Uhlenbeck model 92% of the variance of the diffusion term. Diffusion parameters in both models showed that the data were correlated and that they varied with age in a fashion consistent with developmental accounts of the changing regulation of the degrees of freedom in action. The findings suggest that it is premature to consider the trajectory of the center-of-pressure as a two-process, open- and closed-loop random-walk model given that: (a) the linear Ornstein-Uhlenbeck dynamic equation with only two parameters accommodates almost as much of the variance of the random walk; and (b) the linkage of a discontinuity in the diffusion process with the transition of open- to closed-loop processes is poorly founded. It appears that the nature of the stochastic properties of the random walk of the center-of-pressure trajectory in quiet, upright standing remains to be elucidated.