Stiffness of a wobbling mass models analysed by a smooth orthogonal decomposition of the skin movement relative to the underlying bone.

Abstract

The so-called soft tissue artefacts and wobbling masses have both been widely studied in biomechanics, however most of the time separately, from either a kinematics or a dynamics point of view. As such, the estimation of the stiffness of the springs connecting the wobbling masses to the rigid-body model of the lower limb, based on the in vivo displacements of the skin relative to the underling bone, has not been performed yet. For this estimation, the displacements of the skin markers in the bone-embedded coordinate systems are viewed as a proxy for the wobbling mass movement. The present study applied a structural vibration analysis method called smooth orthogonal decomposition to estimate this stiffness from retrospective simultaneous measurements of skin and intra-cortical pin markers during running, walking, cutting and hopping. For the translations about the three axes of the bone-embedded coordinate systems, the estimated stiffness coefficients (i.e. between 2.3kN/m and 55.5kN/m) as well as the corresponding forces representing the connection between bone and skin (i.e. up to 400N) and corresponding frequencies (i.e. in the band 10-30Hz) were in agreement with the literature. Consistently with the STA descriptions, the estimated stiffness coefficients were found subject- and task-specific.