Dynamic Time Warping compared to established methods for validation of musculoskeletal models

By means of Multi-Body musculoskeletal simulation, important variables such as internal joint forces and moments can be estimated which cannot be measured directly. Validation can ensued by qualitative or by quantitative methods. Especially when comparing time-dependent signals, many methods do not perform well and validation is often limited to qualitative approaches. The aim of the present study was to investigate the capabilities of the Dynamic Time Warping (DTW) algorithm for comparing time series, which can quantify phase as well as amplitude errors. We contrast the sensitivity of DTW with other established metrics: the Pearson correlation coefficient, cross-correlation, the metric according to Geers, RMSE and normalized RMSE. This study is based on two data sets, where one data set represents direct validation and the other represents indirect validation. Direct validation was performed in the context of clinical gait-analysis on trans-femoral amputees fitted with a 6 component force-moment sensor. Measured forces and moments from amputees' socket-prosthesis are compared to simulated forces and moments. Indirect validation was performed in the context of surface EMG measurements on a cohort of healthy subjects with measurements taken of seven muscles of the leg, which were compared to simulated muscle activations. Regarding direct validation, a positive linear relation between results of RMSE and nRMSE to DTW can be seen. For indirect validation, a negative linear relation exists between Pearson correlation and cross-correlation. We propose the DTW algorithm for use in both direct and indirect quantitative validation as it correlates well with methods that are most suitable for one of the tasks. However, in DV it should be used together with methods resulting in a dimensional error value, in order to be able to interpret results more comprehensible.