A benchmark of muscle models to length changes great and small

Digital human body models are used to simulate injuries that occur as a result of vehicle collisions, vibration, sports, and falls. Given enough time the body's musculature can generate force, affect the body's movements, and change the risk of some injuries. The finite-element code LS-DYNA is often used to simulate the movements and injuries sustained by the digital human body models as a result of an accident. In this work, we evaluate the accuracy of the three muscle models in LS-DYNA (MAT_156, EHTMM, and the VEXAT) when simulating a range of experiments performed on isolated muscle: force-length-velocity experiments on maximally and sub-maximally stimulated muscle, active-lengthening experiments, and vibration experiments. The force-length-velocity experiments are included because these conditions are typical of the muscle activity that precedes an accident, while the active-lengthening and vibration experiments mimic conditions that can cause injury. The three models perform similarly during the maximally and sub-maximally activated force-length-velocity experiments, but noticeably differ in response to the active-lengthening and vibration experiments. The VEXAT model is able to generate the enhanced forces of biological muscle during active lengthening, while both the MAT_156 and EHTMM produce too little force. In response to vibration, the stiffness and damping of the VEXAT model closely follows the experimental data while the MAT_156 and EHTMM models differ substantially. The accuracy of the VEXAT model comes from two additional mechanical structures that are missing in the MAT_156 and EHTMM models: viscoelastic cross-bridges, and an active titin filament. To help others build on our work we have made our simulation code publicly available.