A structural model of passive skeletal muscle shows two reinforcement processes in resisting deformation

Abstract

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

Effects of activation on the elastic properties of intact soleus muscles with a deletion in titin

“…Recent models based on passive material properties of porcine muscle suggest that the contribution of stretched parallel elastic elements to passive stiffness becomes significant only at sarcomere lengths longer than those used in our study (Gindre et al, 2013). As a consequence of constant volume, muscles also expand radially during shortening or compression.…”

“…Radial expansion will also load collagen fibers in the extracellular matrix. However, the increase in stress of collagen fibers due to radial expansion becomes significant only at sarcomere lengths much shorter than the ones used in this study (Gindre et al, 2013).…”

“…Intact skeletal muscles are composed of a variety of elastic elements, both inside and outside muscle sarcomeres (Gindre et al, 2013;Roberts, 2016). Owing to the complexity and integration of these structures, it is difficult to differentiate their roles at the level of intact muscles.…”

Collagen content does not alter the passive mechanical properties of fibrotic skeletal muscle in mdx mice

“…Titin is purported to be the primary contributor to intracellular skeletal muscle passive mechanics, with mechanical stiffness dependent on alternative splicing (48). However, there is evidence that extracellular components bear most of the passive load in whole mammalian muscle, particularly at 10% strain (13,15). It is currently unknown how titin splice variants are affected in mdx skeletal muscle and how titin alteration might affect mdx muscle stiffness.…”

Contribution of elastic tissues to the mechanics and energetics of muscle function during movement

“…Collagen is very resilient; thus, the collagen fibers responsible for passive force production in the ECM would be expected to be efficiently elastic. Viscoelastic behavior in whole muscle may result from the complex interaction of collagen fibers and muscle fluid pressure that occurs as fibers reorient and generate force (Gindre et al, 2013). At the level of both whole muscles and single fibers, the viscoelastic behavior of passive muscle is strain rate dependent (Rehorn et al, 2014); thus, the potential spring-like function of these elements may be variable depending upon the speed of movement.…”