Analyses of joint variance related to voluntary whole-body movements performed in standing

Abstract

This article investigates two methodological issues resulting from a recent study of center of mass positional stability during performance of whole-body targeting tasks (Freitas et al., 2006): (1) Can identical results be obtained with uncontrolled manifold (UCM) variance analysis when it is based on estimating the Jacobian using multiple linear regression (MLR) analysis compared to that using typical analytic formal geometric model? (2) Are kinematic synergies more related to stabilization of the instantaneous anterior–posterior position of the center of mass (COMAP) or the center of pressure (COPAP)? UCM analysis was used to partition the variance of the joint configuration into ‘bad’ variance, leading to COMAP or COPAP variability, and ‘good’ variance, reflecting the use of motor abundance. Findings indicated (1) nearly identical UCM results for both methods of Jacobian estimation; and (2) more ‘good’ and less ‘bad’ joint variance related to stability of COPAP than to COMAP position. The first result requires further investigation with more degrees of freedom, but suggests that when a formal geometric model is unavailable or overly complex, UCM analysis may be possible by estimating the Jacobian using MLR. Correct interpretation of the second result requires analysis of the singular values of the Jacobian for different performance variables, which indicates how certain amount of joint variance affects each performance variable. Thus, caution is required when interpreting differences in joint variance structure among various performance variables obtained by UCM analysis without first investigating how the different relationships captured by the Jacobian translate those variances into performance-level variance.