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Appropriate mechanical representation of passive muscle tissue is crucial for human body impact modelling. In this paper the experimental and modelling results of compressive loading of freshly slaughtered porcine muscle samples using a drop-tower testing rig are reported. Fibre and cross-fibre compression tests at strain rates varying from 11,600%/s to 37,800%/s were performed. Experimental results show a nonlinear stress-stretch relationship as well as a clear rate dependency of the stress. The mean (standard deviation) engineering stress in the fibre direction at a stretch of 0.7 was 22.47 kPa (5.34 kPa) at a strain rate of 22,000%/s and 38.11k Pa (5.41 kPa) at a strain rate of 37,800%/s. For the cross-fibre direction, the engineering stresses were 5.95 kPa (1.12 kPa) at a strain rate of 11,600%/s, 25.52 kPa (5.12 kPa) at a strain rate of 22,000%/s and 43.66 kPa (6.62 kPa) at a strain rate of 37,800%/s. Significant local strain variations were observed, as well as an average mass loss of 8% due to fluid exudation, highlighting the difficulties in these kinds of tests. The inverse analysis shows for the first time that the mechanical response in terms of both applied load and tissue deformation for each of the strain rates can be captured using a 1st order Ogden hyperelastic material law extended with a three-term quasilinear viscoelastic (QVL) expansion to model viscoelastic effects. An optimisation procedure was used to derive optimal material parameters for which the error in the predicted boundary condition force at maximum compression was less than 3% for all three rates of testing (11,600%/s, 22,000%/s and 37,800%/s). This model may be appropriate for whole body impact modelling at these rates., (© 2013 Elsevier Ltd. All rights reserved.)

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., (Copyright © 2013 Elsevier Ltd. All rights reserved.)