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Updated: May 13, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
Published on: April 11, 2018
Flexing computational muscle: modeling and simulation of musculotendon dynamics
Matthew Millard1, Thomas Uchida, Ajay Seth
1Department of Bioengineering, Stanford University, Stanford, CA 94305, USA. mjhmilla@stanford.edu
This study benchmarks musculotendon models for muscle-driven simulations. The damped equilibrium model offers speed advantages, while the rigid-tendon model is fastest for short tendons, with all models showing good biological accuracy.
Area of Science:
- Biomechanics
- Computational modeling
- Human and animal motion analysis
Background:
- Muscle-driven simulations are crucial for studying movement dynamics, complementing physical experiments.
- Musculotendon models are essential components of these simulations.
- Previous evaluations of computational speed and biological accuracy of musculotendon models are limited.
Purpose of the Study:
- To compare the computational speed and biological accuracy of three musculotendon models: equilibrium, damped equilibrium (both elastic tendon), and rigid tendon.
- To provide implementations and benchmark data for OpenSim to facilitate further research.
Main Methods:
- Benchmarking simulations of three musculotendon models: equilibrium, damped equilibrium, and rigid tendon.
- Evaluation of computational speed using explicit and implicit integrators.
- Assessment of biological accuracy by comparing simulated forces to those of maximally and submaximally activated biological muscle.
Main Results:
- The damped equilibrium model shows significant speed improvements over the equilibrium model at low activation.
- The rigid-tendon model is substantially faster than elastic-tendon models, especially for short tendons.
- All three models demonstrate acceptable biological accuracy, with mean absolute errors below 20.9% for maximal activation and 18.5% for submaximal activation.
Conclusions:
- Musculotendon model selection involves a trade-off between computational speed and biological accuracy.
- The damped equilibrium and rigid-tendon models offer performance benefits under specific conditions.
- Open-source implementations and benchmark data are provided to advance musculotendon modeling research.
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