EMG-Driven Optimal Estimation of Subject-SPECIFIC Hill Model Muscle–Tendon Parameters of the Knee Joint Actuators

Objective: the purpose of this paper is to propose an optimal control problem formulation to estimate subject-specific Hill model muscle–tendon (MT-) parameters of the knee joint actuators by optimizing the fit between experimental and model-based knee moments. Additionally, this paper aims at determining which sets of functional motions contain the necessary information to identify the MT-parameters. Methods: the optimal control and parameter estimation problem underlying the MT-parameter estimation is solved for subject-specific MT-parameters via direct collocation using an electromyography-driven musculoskeletal model. The sets of motions containing sufficient information to identify the MT-parameters are determined by evaluating knee moments simulated based on subject-specific MT-parameters against experimental moments. Results: the MT-parameter estimation problem was solved in about 30 CPU minutes. MT-parameters could be identified from only seven of the 62 investigated sets of motions, underlining the importance of the experimental protocol. Using subject-specific MT-parameters instead of more common linearly scaled MT-parameters improved the fit between inverse dynamics moments and simulated moments by about 30% in terms of the coefficient of determination (from <inline-formula><tex-math notation="LaTeX">$\text{0.57} \pm \text{0.20}$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$\text{0.74} \pm \text{0.14}$</tex-math></inline-formula>) and by about 26% in terms of the root mean square error (from <inline-formula><tex-math notation="LaTeX">$\text{15.98} \pm \text{6.85}$</tex-math></inline-formula> to <inline-formula><tex-math notation="LaTeX">$\text{11.85} \pm \text{4.12}\,{\text{N}} \cdot {\text{m}}$</tex-math> </inline-formula>). In particular, subject-specific MT-parameters of the knee flexors were very different from linearly scaled MT-parameters. Conclusion: we introduced a computationally efficient optimal control problem formulation and provided guidelines for designing an experimental protocol to estimate subject-specific MT-parameters improving the accuracy of motion simulations. Significance: the proposed formulation opens new perspectives for subject-specific musculoskeletal modeling, which might be beneficial for simulating and understanding pathological motions.