Evolutionary optimization for robust hierarchical computation of the rotation centres of kinematic chains from reduced ranges of motion the lower spine case

A novel technique based on evolutionary optimization is proposed here to compute the average rotation centres (RCs) of ball joints linked into kinematic chains using 3D trajectories of the markers attached to the external surface of the corresponding articulated structures. The chain is hierarchically solved by iteratively minimizing the variance of the marker distances from the actual RC through an evolutional strategy method (ESM) from proximal to distal joints. In particular, the technique is compared to the non-rigid sphere-fitting method, recently proposed in literature and implemented through a closed-form solution (CFS), in conditions of random and systematic noise superimposed to the marker coordinates. Results from simulated motions showed that, in case of small range of motion (5°, 10°) the performance of CFS is really unreliable whereas ESM provided satisfactory accuracy. Error propagation along the kinematic chain was found to be negligible. Also in the case of systematic errors, ESM provides an accuracy that is sensibly better than that of the CFS. As a case study, ESM was applied to the in vivo computation of the RCs of the vertebrae in the lower spine region using a specific marker protocol. A set of spine movements by a normal adult male, recorded by an optoelectronic motion capture system, were processed with the developed method. The variability of the estimated average RCs was small (few millimeters) in agreement with the literature data from cadaveric studies and X-ray imaging.