Flexing Computational Muscle: Modeling and Simulation of Musculotendon Dynamics

TLDR

Muscle‑driven simulations are widely used to study movement dynamics, yet the computational speed and biological accuracy of musculotendon models have not been adequately evaluated. The study compares the speed and accuracy of three musculotendon models—two elastic‑tendon equilibrium models and one rigid‑tendon model—and provides OpenSim implementations and benchmark data to facilitate further development. The authors benchmarked the models by simulating muscle dynamics with explicit and implicit integrators, measuring force profiles and computational times. The equilibrium and damped equilibrium models produce similar force profiles but differ in speed, with the damped model up to 29 times faster at low activation, while the rigid‑tendon model matches elastic‑tendon forces for short tendons and is 2–54 times faster with explicit integrators, and all models achieve mean absolute errors below 8.9% for maximal activation and below 18.5% for submaximal activation.

Abstract

Muscle-driven simulations of human and animal motion are widely used to complement physical experiments for studying movement dynamics. Musculotendon models are an essential component of muscle-driven simulations, yet neither the computational speed nor the biological accuracy of the simulated forces has been adequately evaluated. Here we compare the speed and accuracy of three musculotendon models: two with an elastic tendon (an equilibrium model and a damped equilibrium model) and one with a rigid tendon. Our simulation benchmarks demonstrate that the equilibrium and damped equilibrium models produce similar force profiles but have different computational speeds. At low activation, the damped equilibrium model is 29 times faster than the equilibrium model when using an explicit integrator and 3 times faster when using an implicit integrator; at high activation, the two models have similar simulation speeds. In the special case of simulating a muscle with a short tendon, the rigid-tendon model produces forces that match those generated by the elastic-tendon models, but simulates 2–54 times faster when an explicit integrator is used and 6–31 times faster when an implicit integrator is used. The equilibrium, damped equilibrium, and rigid-tendon models reproduce forces generated by maximally-activated biological muscle with mean absolute errors less than 8.9%, 8.9%, and 20.9% of the maximum isometric muscle force, respectively. When compared to forces generated by submaximally-activated biological muscle, the forces produced by the equilibrium, damped equilibrium, and rigid-tendon models have mean absolute errors less than 16.2%, 16.4%, and 18.5%, respectively. To encourage further development of musculotendon models, we provide implementations of each of these models in OpenSim version 3.1 and benchmark data online, enabling others to reproduce our results and test their models of musculotendon dynamics.