The anisotropic mechanical behaviour of passive skeletal muscle tissue subjected to large tensile strain, Journal of the Mechanical Behavior of Biomedical Materials, http://dx.doi.org/10. 1016/j.jmbbm.2012.09.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe passive mechanical properties of muscle tissue are important for many biomechanics applications. However, significant gaps remain in our understanding of the three-dimensional tensile response of passive skeletal muscle tissue to applied loading. In particular, the nature of the anisotropy remains unclear and the response to loading at intermediate fibre directions and the Poisson's ratios in tension have not been reported. Accordingly, tensile tests were performed along and perpendicular to the muscle fibre direction as well as at 30, 45 and 60 degrees to the muscle fibre direction in samples of Longissimus dorsi muscle taken from freshly slaughtered pigs. Strain was measured using an optical non-contact method. The results show the transverse or cross fibre (TT') direction is broadly linear and is the stiffest (77kPa stress at a stretch of 1.1), but that failure occurs at low stretches (approximately λ = 1.15). In contrast the longitudinal or fibre direction (L) is nonlinear and much less stiff (10kPa stress at a stretch of 1.1) but failure occurs at higher stretches (approximately λ = 1.65). An almost sinusoidal variation in stress response was observed at intermediate angles. The following Poisson's ratios were measured: Ѵ LT = Ѵ LT' = 0.47, Ѵ TT' = 0.28 and Ѵ TL = 0.74. These observations have not been previously reported and they contribute significantly to our understanding of the three dimensional deformation response of skeletal muscle tissue.

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 tensiononly 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.2

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