Millard Matthew, Uchida Thomas, Seth Ajay, Delp Scott L
Department of Bioengineering, Stanford University, Stanford, CA 94305, USA.
J Biomech Eng. 2013 Feb;135(2):021005. doi: 10.1115/1.4023390.
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.
肌肉驱动的人体和动物运动模拟被广泛用于补充研究运动动力学的物理实验。肌肉肌腱模型是肌肉驱动模拟的重要组成部分，但模拟力的计算速度和生物学准确性都尚未得到充分评估。在这里，我们比较了三种肌肉肌腱模型的速度和准确性：两种具有弹性肌腱（平衡模型和阻尼平衡模型），一种具有刚性肌腱。我们的模拟基准表明，平衡模型和阻尼平衡模型产生相似的力分布，但计算速度不同。在低激活状态下，使用显式积分器时，阻尼平衡模型比平衡模型快29倍，使用隐式积分器时快3倍；在高激活状态下，这两种模型具有相似的模拟速度。在模拟肌腱较短的肌肉的特殊情况下，刚性肌腱模型产生的力与弹性肌腱模型产生的力相匹配，但使用显式积分器时模拟速度快2至54倍，使用隐式积分器时快6至31倍。平衡模型、阻尼平衡模型和刚性肌腱模型再现最大激活生物肌肉产生的力时，平均绝对误差分别小于最大等长肌力的8.9%、8.9%和20.9%。与次最大激活生物肌肉产生的力相比，平衡模型、阻尼平衡模型和刚性肌腱模型产生的力的平均绝对误差分别小于16.2%、16.4%和18.5%。为鼓励肌肉肌腱模型的进一步发展，我们在OpenSim 3.1版本中提供了这些模型的实现，并在网上提供了基准数据，使其他人能够重现我们的结果并测试他们的肌肉肌腱动力学模型。
