Ryan David S, Domínguez Sebastián, Ross Stephanie A, Nigam Nilima, Wakeling James M
Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, BC, Canada.
Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada.
Front Physiol. 2020 Nov 12;11:538522. doi: 10.3389/fphys.2020.538522. eCollection 2020.
In this study we examined how the strain energies within a muscle are related to changes in longitudinal force when the muscle is exposed to an external transverse load. We implemented a three-dimensional (3D) finite element model of contracting muscle using the principle of minimum total energy and allowing the redistribution of energy through different strain energy-densities. This allowed us to determine the importance of the strain energy-densities to the transverse forces developed by the muscle. We ran a series of experiments on muscle blocks varying in initial pennation angle, muscle length, and external transverse load. As muscle contracts it maintains a near constant volume. As such, any changes in muscle length are balanced by deformations in the transverse directions such as muscle thickness or muscle width. Muscle develops transverse forces as it expands. In many situations external forces act to counteract these transverse forces and the muscle responds to external transverse loads while both passive and active. The muscle blocks used in our simulations decreased in thickness and pennation angle when passively compressed and pushed back on the load when they were activated. Activation of the compressed muscle blocks led either to an increase or decrease in muscle thickness depending on whether the initial pennation angle was less than or greater than 15°, respectively. Furthermore, the strain energy increased and redistributed across the different strain-energy potentials during contraction. The volumetric strain energy-density varied with muscle length and pennation angle and was reduced with greater transverse load for most initial muscle lengths and pennation angles. External transverse load reduced the longitudinal muscle force for initial pennation angles of β = 0°. Whereas for pennate muscle (β > 0°) longitudinal force changed (increase or decrease) depending on the muscle length, pennation angle and the direction of the external load relative to the muscle fibres. For muscle blocks with initial pennation angles β ≤ 20° the reduction in longitudinal muscle force coincided with a reduction in volumetric strain energy-density.
在本研究中，我们探究了当肌肉受到外部横向负荷时，肌肉内部的应变能与纵向力变化之间的关系。我们运用总能量最小原理，构建了一个收缩肌肉的三维（3D）有限元模型，并允许能量通过不同的应变能密度进行重新分配。这使我们能够确定应变能密度对肌肉产生的横向力的重要性。我们对一系列初始羽状角、肌肉长度和外部横向负荷各不相同的肌肉块进行了实验。随着肌肉收缩，其体积几乎保持不变。因此，肌肉长度的任何变化都由横向方向的变形（如肌肉厚度或宽度）来平衡。肌肉在扩张时会产生横向力。在许多情况下，外力会抵消这些横向力，并且肌肉在被动和主动状态下都会对外部横向负荷做出反应。我们模拟中使用的肌肉块在被动压缩时厚度和羽状角减小，激活时会向负荷施加反作用力。压缩肌肉块的激活导致肌肉厚度增加或减小，这分别取决于初始羽状角是小于还是大于15°。此外，在收缩过程中，应变能增加并在不同的应变能势之间重新分布。体积应变能密度随肌肉长度和羽状角而变化，并且对于大多数初始肌肉长度和羽状角，随着横向负荷的增加而降低。对于初始羽状角β = 0°的情况，外部横向负荷会降低肌肉纵向力。而对于羽状肌（β > 0°），纵向力的变化（增加或减少）取决于肌肉长度、羽状角以及外部负荷相对于肌纤维的方向。对于初始羽状角β≤20°的肌肉块，肌肉纵向力的降低与体积应变能密度的降低相一致。
