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 degrees , 10 degrees ) 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.

[1]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[2]  T P Andriacchi,et al.  Correcting for deformation in skin-based marker systems. , 2001, Journal of biomechanics.

[3]  G. Yamaguchi,et al.  Methods for determining spinal flexion/extension, lateral bending, and axial rotation from marker coordinate data: Analysis and refinement , 1996 .

[4]  Jinjun Xiong,et al.  Model-guided derivation of lumbar vertebral kinematics in vivo reveals the difference between external marker-defined and internal segmental rotations. , 2003, Journal of biomechanics.

[5]  Pietro Cerveri,et al.  Combined evolution strategies for dynamic calibration of video-based measurement systems , 2001, IEEE Trans. Evol. Comput..

[6]  M Nissan,et al.  Dimensions of human lumbar vertebrae in the sagittal plane. , 1986, Journal of biomechanics.

[7]  Manohar M. Panjabi,et al.  Clinical Biomechanics of the Spine , 1978 .

[8]  Pascal Fua,et al.  Local and Global Skeleton Fitting Techniques for Optical Motion Capture , 1998, CAPTECH.

[9]  Andrew G. Barto,et al.  Reinforcement learning , 1998 .

[10]  M. Pearcy,et al.  Three-Dimensional X-ray Analysis of Normal Movement in the Lumbar Spine , 1984, Spine.

[11]  S. Gracovetsky,et al.  A Database for Estimating Normal Spinal Motion Derived From Noninvasive Measurements , 1995, Spine.

[12]  G Ferrigno,et al.  Robust recovery of human motion from video using Kalman filters and virtual humans. , 2003, Human movement science.

[13]  W. Chiou,et al.  Predictive model of intersegmental mobility of lumbar spine in the sagittal plane from skin markers , 1995 .

[14]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[15]  G. Ferrigno,et al.  Real-time human motion estimation using biomechanical models and non-linear state-space filters , 2006, Medical and Biological Engineering and Computing.

[16]  H C Schamhardt,et al.  Determination of 3D spinal kinematics without defining a local vertebral coordinate system. , 1999, Journal of biomechanics.

[17]  R Allen,et al.  Lumbar spine visualisation based on kinematic analysis from videofluoroscopic imaging. , 2003, Medical engineering & physics.

[18]  A. Schache,et al.  Three-dimensional angular kinematics of the lumbar spine and pelvis during running. , 2002, Human movement science.

[19]  Arne Lundberg.  On the use of bone and skin markers in kinematics research , 1996 .

[20]  Micheline Gagnon,et al.  A Geometric Model of the Lumbar Spine in the Sagittal Plane , 1993, Spine.

[21]  Sahan Gamage,et al.  New least squares solutions for estimating the average centre of rotation and the axis of rotation. , 2002, Journal of biomechanics.

[22]  M M Panjabi,et al.  Three-Dimensional Movements of the Whole Lumbar Spine and Lumbosacral Joint , 1989, Spine.

[23]  Paolo Bifulco,et al.  Estimation of out-of-plane vertebra rotations on radiographic projections using CT data: a simulation study. , 2002, Medical engineering & physics.

[24]  A Leardini,et al.  Position and orientation in space of bones during movement: experimental artefacts. , 1996, Clinical biomechanics.

[25]  M. Panjabi,et al.  An Analysis of Errors in Kinematic Parameters Associated with in Vivo Functional Radiographs , 1992, Spine.