A review of center of pressure (COP) variables to quantify standing balance in elderly people: Algorithms and open-access code

Abstract

Postural control is often quantified by recording the trajectory of the center of pressure (COP)-also called stabilogram-during human quiet standing. This quantification has many important applications, such as the early detection of balance degradation to prevent falls, a crucial task whose relevance increases with the aging of the population. Due to the complexity of the quantification process, the analyses of sway patterns have been performed empirically using a number of variables, such as ellipse confidence area or mean velocity. This study reviews and compares a wide range of state-of-the-art variables that are used to assess the risk of fall in elderly from a stabilogram. When appropriate, we discuss the hypothesis and mathematical assumptions that underlie these variables, and we propose a reproducible method to compute each of them. Additionally, we provide a statistical description of their behavior on two datasets recorded in two elderly populations and with different protocols, to hint at typical values of these variables. First, the balance of 133 elderly individuals, including 32 fallers, was measured on a relatively inexpensive, portable force platform (Wii Balance Board, Nintendo) with a 25-s open-eyes protocol. Second, the recordings of 76 elderly individuals, from an open access database commonly used to test static balance analyses, were used to compute the values of the variables on 60-s eyes-open recordings with a research laboratory standard force platform.

Keywords: center of pressure; elderly; postural control; quiet standing.

FIGURE 1

Illustration of the calculation of the 95% confidence ellipse. The feature is equal to the area of the ellipse

FIGURE 2

Illustration of the calculation of the principal sway direction. The feature is equal to the angle θ

FIGURE 3

Illustration of the sway density computation and the peaks computation. (a) Illustration of the computation of the sway density at time t. In this example, four consecutive points fall in the circle of radius 3mm, therefore the sway density at time t is equal to 4/ F_s. (b) Example of filtered trajectory of the sway density over time. The black crosses indicate the position of peaks identified using Definition 2

FIGURE 4

An example of velocity signal. The red dots indicate zero‐crossings identified using Definition 3 and the black crosses indicate the position of peaks identified using Definition 4

FIGURE 5

The sway area per second sums the area of the successive triangles OS_nS_{n +1} (in blue) formed at each time n by the points of the signal and the center of the trajectory O

FIGURE 6

Example of stabilogram diffusion analysis and parameters estimation in each regime. The fitted functions in each region are drawn in blue. (Top) Curve of the MSD as a function of the time interval. (Bottom) Curve of the MSD as a function of the time interval on a logarithmic scale and intervals of time used for the estimation of the linear functions in each region