An EMG-marker tracking optimisation method for estimating muscle forces

Abstract

Existing algorithms for estimating muscle forces mainly use least-activation criteria, which do not necessarily lead to physiologically consistent results. Our objective was to assess an innovative forward dynamics-based optimisation, assisted by both electromyography (EMG) and marker tracking, for estimating the upper-limb muscle forces. A reference movement was generated, and EMG was simulated to reproduce the desired joint kinematics. Random noise was added to both simulated EMG and marker trajectories in order to create 30 trials. Then, muscle forces were estimated using (1) the innovative EMG-marker tracking forward optimisation, (2) a marker tracking forward optimisation with a least-excitation criterion, and (3) static optimisation with a least-activation criterion. Approaches (1) and (2) were solved using a direct multiple shooting algorithm. Finally, reference and estimated joint angles and muscle forces for the three optimisations were statistically compared using root-mean-square errors (RMSEs), biases, and statistical parametric mapping. The joint angles RMSEs were qualitatively similar across the three optimisations: (1) $1.63 \pm 0.51$ °; (2) $2.02 \pm 0.64$ °; (3) $0.79 \pm 0.38$ °. However, the muscle forces RMSE for the EMG-marker tracking optimisation ( $20.39 \pm 13.24$ N) was about seven times smaller than those resulting from the marker tracking ( $124.22 \pm 118.22$ N) and static ( $148.15 \pm 94.01$ N) optimisations. The originality of this novel approach is close tracking of both simulated EMG and marker trajectories in the same objective function, using forward dynamics. Therefore, the presented EMG-marker tracking optimisation led to accurate muscle forces estimations.