Gindre Juliette, Takaza Michael, Moerman Kevin M, Simms Ciaran K
Centre for Bioengineering, Trinity College Dublin, Ireland.
J Mech Behav Biomed Mater. 2013 Jun;22:84-94. doi: 10.1016/j.jmbbm.2013.02.007. Epub 2013 Mar 14.
Passive skeletal muscle derives its structural response from the combination of the titin filaments in the muscle fibres, the collagen fibres in the connective tissue and incompressibility due to the high fluid content. Experiments have shown that skeletal muscle tissue presents a highly asymmetrical three-dimensional behaviour when passively loaded in tension or compression, but structural models predicting this are not available. The objective of this paper is to develop a mathematical model to study the internal mechanisms which resist externally applied deformation in skeletal muscle bulk. One cylindrical muscle fibre surrounded by connective tissue was considered. The collagenous fibres of the endomysium and perimysium were grouped and modelled as tension-only oriented wavy helices wrapped around the muscle fibre. The titin filaments are represented as non-linear tension-only springs. The model calculates the force developed by the titin molecules and the collagen network when the muscle fibre undergoes an isochoric along-fibre stretch. The model was evaluated using a range of literature based input parameters and compared to the experimental fibre-direction stress-stretch data available. Results show the fibre direction non-linearity and tension/compression asymmetry are partially captured by this structural model. The titin filament load dominates at low tensile stretches, but for higher stretches the collagen network was responsible for most of the stiffness. The oblique and initially wavy collagen fibres account for the non-linear tensile response since, as the collagen fibres are being recruited, they straighten and re-orient. The main contribution of the model is that it shows that the overall compression/tension response is strongly influenced by a pressure term induced by the radial component of collagen fibre stretch acting on the incompressible muscle fibre. Thus for along-fibre tension or compression the model predicts that the collagen network contributes to overall muscle stiffness through two different mechanisms: (1) a longitudinal force directly opposing tension and (2) a pressure force on the muscle fibres resulting in an indirect longitudinal load. Although the model presented considers only a single muscle fibre and evaluation is limited to along-fibre loading, this is the first model to propose these two internal mechanisms for resisting externally applied deformation of skeletal muscle tissue.
被动骨骼肌的结构响应源于肌纤维中的肌联蛋白丝、结缔组织中的胶原纤维以及由于高含水量导致的不可压缩性的共同作用。实验表明，当骨骼肌组织在拉伸或压缩状态下被动加载时，会呈现出高度不对称的三维行为，但目前尚无预测这种行为的结构模型。本文的目的是建立一个数学模型，以研究骨骼肌整体中抵抗外部施加变形的内部机制。研究考虑了一根被结缔组织包围的圆柱形肌纤维。肌内膜和肌束膜的胶原纤维被分组，并建模为仅受拉力作用的、缠绕在肌纤维周围的波浪状螺旋结构。肌联蛋白丝被表示为仅受拉力作用的非线性弹簧。该模型计算当肌纤维进行等容沿纤维拉伸时，肌联蛋白分子和胶原网络产生的力。使用一系列基于文献的输入参数对该模型进行评估，并与现有的实验性纤维方向应力 - 拉伸数据进行比较。结果表明，该结构模型部分捕捉到了纤维方向的非线性和拉伸/压缩不对称性。在低拉伸状态下，肌联蛋白丝的负载起主导作用，但在更高的拉伸状态下，胶原网络是大部分刚度的来源。倾斜且最初呈波浪状的胶原纤维导致了非线性拉伸响应，因为随着胶原纤维被激活，它们会变直并重新定向。该模型的主要贡献在于，它表明整体压缩/拉伸响应受到胶原纤维拉伸的径向分量作用于不可压缩肌纤维所产生的压力项的强烈影响。因此，对于沿纤维的拉伸或压缩，该模型预测胶原网络通过两种不同机制对整体肌肉刚度做出贡献：（1）直接抵抗拉伸的纵向力；（2）作用在肌纤维上的压力，导致间接的纵向负载。尽管所提出的模型仅考虑了单个肌纤维，且评估仅限于沿纤维加载，但这是第一个提出这两种抵抗骨骼肌组织外部施加变形的内部机制的模型。
