Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, British Columbia, Canada.
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada.
PLoS Comput Biol. 2018 Apr 16;14(4):e1006123. doi: 10.1371/journal.pcbi.1006123. eCollection 2018 Apr.
Hill-type muscle models are widely used within the field of biomechanics to predict and understand muscle behaviour, and are often essential where muscle forces cannot be directly measured. However, these models have limited accuracy, particularly during cyclic contractions at the submaximal levels of activation that typically occur during locomotion. To address this issue, recent studies have incorporated effects into Hill-type models that are oftentimes neglected, such as size-dependent, history-dependent, and activation-dependent effects. However, the contribution of these effects on muscle performance has yet to be evaluated under common contractile conditions that reflect the range of activations, strains, and strain rates that occur in vivo. The purpose of this study was to develop a modelling framework to evaluate modifications to Hill-type muscle models when they contract in cyclic loops that are typical of locomotor muscle function. Here we present a modelling framework composed of a damped harmonic oscillator in series with a Hill-type muscle actuator that consists of a contractile element and parallel elastic element. The intrinsic force-length and force-velocity properties are described using Bézier curves where we present a system to relate physiological parameters to the control points for these curves. The muscle-oscillator system can be geometrically scaled while preserving dynamic and kinematic similarity to investigate the muscle size effects while controlling for the dynamics of the harmonic oscillator. The model is driven by time-varying muscle activations that cause the muscle to cyclically contract and drive the dynamics of the harmonic oscillator. Thus, this framework provides a platform to test current and future Hill-type model formulations and explore factors affecting muscle performance in muscles of different sizes under a range of cyclic contractile conditions.
Hill 型肌肉模型在生物力学领域中被广泛用于预测和理解肌肉行为，并且在无法直接测量肌肉力的情况下通常是必不可少的。然而，这些模型的准确性有限，尤其是在通常发生在运动过程中的亚最大激活水平的周期性收缩期间。为了解决这个问题，最近的研究已经将 Hill 型模型中经常被忽略的效应（如大小相关、历史相关和激活相关效应）纳入其中。然而，这些效应对肌肉性能的贡献在反映体内发生的激活、应变和应变速率范围的常见收缩条件下尚未得到评估。本研究的目的是开发一种建模框架，以评估在类似于运动肌肉功能的周期性循环中收缩时对 Hill 型肌肉模型的修改。在这里，我们提出了一个建模框架，该框架由一个阻尼谐振荡器与一个由收缩元件和并联弹性元件组成的 Hill 型肌肉执行器串联而成。固有力-长度和力-速度特性使用 Bezier 曲线描述，我们提出了一种将生理参数与这些曲线的控制点相关联的系统。肌肉-振荡器系统可以进行几何缩放，同时保持动态和运动学相似性，以研究肌肉大小效应，同时控制谐振荡器的动力学。该模型由随时间变化的肌肉激活驱动，这些激活导致肌肉周期性收缩并驱动谐振荡器的动力学。因此，该框架提供了一个平台，可以测试当前和未来的 Hill 型模型公式，并探索在不同大小的肌肉中在一系列周期性收缩条件下影响肌肉性能的因素。
