Comparison of Synergy Extrapolation and Static Optimization for Estimating Multiple Unmeasured Muscle Activations...

Calibrated electromyography (EMG)-driven musculoskeletal models can provide great insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unclear.

This study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing "gold standard" muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient $r$ values to quantify shape similarity, each calculated with respect to "gold standard" muscle activations and forces.

On average, SynX produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. $0.15,r$ value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. $174.4 N,r$ value 0.53 vs. 0.07) compared to SO. SynX yielded calibrated Hill-type muscle-tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to "gold standard" calibrated model parameter values.

These findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.