Influence of multibody kinematic optimisation pipeline on marker residual errors

Residual errors are used as a goodness-of-fit metric of the musculoskeletal model to the experimental data in multibody kinematic optimisation (MKO) analyses. Despite many studies reporting residual errors as a criterion for evaluating their proposed algorithm or model, the validity of residual errors as a performance metric has been questioned, with studies indicating a non-causal relationship between residual errors and computed joint angles. Additionally, the impact of different parameters of an MKO pipeline on residual errors has not been analysed. In our study, we have investigated the effect of each step of the MKO pipeline on residual errors, and the existence of a causal relationship between residual errors and joint angles. Increases in residual errors from the baseline model (13.84 [12.72, 15.15]mm) were obtained for: models with marker registration errors of 1.25 cm (16.36 [15.37, 17.57]mm); models with segment scaling errors of 1.25 cm (14.84 [13.77, 16.24]mm); variation in marker weighting scheme (15.28[14.00, 16.85]mm); and models with differing joint constraints (18.21[17.37, 19.11]mm). We also observed that significant variation in residual errors results in significant variation in computed joint angles, with increases in residual error positively correlated with increases in joint angle errors when the same MKO pipeline is employed. Our findings support the existence of a causal relationship and present the significant effect the MKO pipeline has on residual errors. We believe our results can further the discussion of residual errors as a goodness-of-fit metric, specifically in the absence of artefact-free bone movement.