Biomechanics in posture space: Properties and relevance of principal accelerations for characterizing movement control

Abstract

Human movements, recorded through kinematic data, can be described by means of principal component analysis (PCA) through a small set of variables representing correlated segment movements. The PC-eigenvectors then form a basis in the associated vector space of postural changes. Similar to 3D movements, the kinematics in this posture space can be quantified through 'principal' positions (PPs), velocities (PVs) and accelerations (PAs). The PAs represent a novel set of variables characterizing neuro-muscular control. The aim of the current technical note was to (i) compare the variance explained by PAs with the variance explained by PPs; (ii) clarify the relationship between PAs and segment accelerations; and (iii) compare variability of the first principal acceleration (PA₁) with the local dynamic stability (largest Lyapunov exponent, LyE) of the first principal position (PP₁). A PCA was applied on 3D upper-body positions collected by an Xsens inertial sensor system as nineteen volunteers performed a bimanual repetitive tapping task. The main finding revealed that the PP-explained variance considerably differed from the PA-explained variance, indicating that the latter should be considered when reducing the dimensionality in postural movement analysis through a PCA. Further, the current study formally established that the acceleration curves obtained from differentiating segment positions and from linear combinations of PAs are identical. Finally, a strong correlation, r(17) = 0.92, p < 0.001, was observed between the cycle-to-cycle variability in PA₁ and the LyE calculated for PP₁, supporting the notion that PA variability and LyE share some of the information they provide about movement control.

Keywords: Inertial sensors; Largest Lyapunov exponent LyE; Principal acceleration; Principal component analysis PCA.