the score residual: a quality index to assess the accuracy of joint estimations

the determination of an accurate centre of rotation (cor) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. despite the many functional approaches to estimate cors, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. the purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (score) as a reliable indirect measure of the error of the computed joint centre. to evaluate the score residual, numerical simulations were performed to evaluate cor estimations at different ranges of joint motion. a statistical model was developed and used to determine the theoretical relationships among the score residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the cor estimations to the known centre of rotation. we found that the equation err=0.5rs provides a reliable relationship among the cor error, err, and the scaled score residual, rs, providing that any skin marker artefact is first minimised using the optimal common shape technique (ocst). measurements on six healthy volunteers showed a reduction of score residual from 11 to below 6 mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. this study also demonstrates the significant benefit of the ocst for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. for the first time, this understanding of the score residual allows a measure of error in the non-invasive assessment of joint centres. this measure now enables a rapid assessment of the accuracy of the cor as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.