Skeletal muscles usually wrap over multiple anatomical features, and their mass moves along the curved muscle paths during human locomotion. However, existing musculoskeletal models simply lump the mass of muscles to the nearby body segments without considering the effect of mass flow, which has been shown to induce non-negligible errors. A mass-variable multibody formulation is proposed here to simultaneously characterize muscle wrapping and mass flow effects. To achieve this goal, a novel cable element of the muscle–tendon unit, which integrates the mass flow feature with a typical Hill-type constitutive relationship, was developed based on an arbitrary Lagrangian–Eulerian description. In addition, sliding joints were used to constrain the elements to move over the underlying bone geometries. After validating the proposed modeling method using two benchmark samples, it was applied to build a large-scale lower limb musculoskeletal model, where knee joint moments were calculated and compared with isokinetic dynamometry measurements of 12 healthy males. The results of the comparison confirm that muscular mass distribution play an important role in the force transmission of muscle wrapping, and the proposed mass-variable formulation provides a better way of predicting and understanding the dynamics of musculoskeletal systems.

中文翻译：

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使用质量可变的多体公式对肌肉包裹和质量流进行建模

骨骼肌通常包裹着多个解剖特征，在人体运动过程中，它们的质量沿弯曲的肌肉路径运动。但是，现有的肌肉骨骼模型只是将肌肉块集中到附近的身体部位，而没有考虑质量流的影响，这已被证明会引起不可忽略的误差。本文提出了一种质量可变的多体配方，以同时表征肌肉包裹和质量流量效应。为了实现这一目标，在任意拉格朗日-欧拉描述的基础上，开发了一种新型的肌腱单元电缆，将质量流特征与典型的希尔型本构关系相结合。另外，使用滑动关节来约束元素在下面的骨骼几何形状上移动。在使用两个基准样本验证了所提出的建模方法后，将其用于建立大型下肢肌肉骨骼模型，在该模型中计算了膝关节力矩并将其与12名健康男性的等速测力法进行了比较。比较结果证实，肌肉质量分布在包裹肌肉的力传递中起着重要作用，并且所提出的质量可变公式为预测和理解肌肉骨骼系统的动力学提供了更好的方法。