Evaluation of Synergy Extrapolation for Predicting Unmeasured Muscle Excitations from Measured Muscle Synergies
Electromyography (EMG)-driven musculoskeletal modeling relies on high-quality measurements of muscle electrical activity to estimate muscle forces. However, a critical challenge for practical deployment of this approach is missing EMG data from muscles that contribute substantially to joint moments. This situation may arise due to either the inability to measure deep muscles with surface electrodes or the lack of a sufficient number of EMG electrodes. Muscle synergy analysis is a dimensionality-reduction approach to decompose a large number of muscle excitations into a small number of time-varying synergy excitations along with time-invariant synergy weights that define the contribution of each corresponding synergy excitation to a specific muscle excitation. This study evaluates how accurately missing muscle excitations can be predicted using synergy excitations extracted from muscles with available EMGs (henceforth called "synergy extrapolation"). The results were reported on a gait dataset collected from a stroke survivor walking on an instrumented treadmill at self-selected and fastest-comfortable speeds. The evaluation process started with full calibration of a lower-body EMG-driven model using 16-channel EMGs (including surface and indwelling) in each leg. One indwelling EMG (either iliopsoas or adductor longus) was then treated as unmeasured at a time. The synergy weights associated with the unmeasured muscle were predicted through solving a nonlinear optimization problem where the errors between inverse dynamics and EMG-driven joint moments were minimized. We also quantitatively evaluated how synergy analysis algorithms (principal component analysis (PCA) and non-negative matrix factorization (NMF)), EMG normalization methods, and number of synergies affect the accuracy of the predicted unmeasured muscle excitation. Synergy extrapolation performance was most influenced by the choice of synergy analysis algorithm and number of synergies. PCA with 5 or 6 synergies consistently predicted unmeasured muscle excitations most accurately and with greatest robustness to choice of EMG normalization method. Furthermore, the associated joint moment matching accuracy was comparable to that produced by the full EMG-driven calibration. The synergy extrapolation method described in this study may facilitate the assessment of human neuromuscular control and biomechanics in response to surgical or rehabilitation treatment when important EMG signals are missing.