Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix

Linking myosin heavy chain isoform shift to mechanical properties and fracture modes in skeletal muscle tissue

Muscle fibers play a crucial role in the mechanical action of skeletal muscle tissue. However, it is unclear how the histological variations affect the mechanical properties of tissues. In this study, the shift of myosin heavy chain (MHC) isoforms is used for the first time to establish a linkage between tissue histological variation and passive mechanical properties. The shift of MHC isoform is found not only to induce significant differences in skeletal muscle passive mechanical properties, but also to lead to differences in strain rate responses. Non-negligible rate dependence is observed even in the conventionally defined quasi-static regime. Fidelity in the estimated constitutive parameters, which can be impacted due to variation in MHC isoforms and hence in rate sensitivity, is enhanced using a Bayesian inference framework. Subsequently, scanning electron microscopy and fluorescence microscopy are used to characterize the fracture morphology of muscle tissues and fibers. The fracture mode of both MHC I and II muscle fibers exhibited shearing of endomysium. Results show that the increase in strain rate only leads to stronger rebounding of the muscle fibers during tissue rupture without changing fracture modes.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Automated model discovery for muscle using constitutive recurrent neural networks

The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

Regional variation in the mechanical properties of the skeletal muscle

Regional mechanics of skeletal muscle were investigated from equibiaxial testing in vitro on tissue samples. Samples were collected in three excising zones in transversal direction to the myofibers. Thus, the transverse plane stiffness, likely to be dictated by extracellular matrix collagen (ECM), was studied. For that, distal, middle, and proximal samples of healthy brachial biceps of rats have been tested. Data was used to generate the material parameters of the first order Ogden constitutive model at these different zones of skeletal muscle. In addition to having a nonlinear mechanical behavior, the analysis of the material parameters of the model showed that the stiffness value of the skeletal muscle tissue may on average have doubled depending on the collected sample location (p < 0.001). Furthermore, it was also shown that during the tests, when the storage temperature of the samples increases from 22 °C to 37 °C, the stiffness of the muscle tissue becomes more important (p < 0.05), which may be due to the rigor mortis phenomenon. Thus, these results contribute to investigating the regional change of mechanical properties of skeletal muscle, particularly those of ECM that play a major role in stiffness tissue, which is essential for the development of accurate computational models.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Multiscale modeling of skeletal muscle to explore its passive mechanical properties and experiments verification

The research of the mechanical properties of skeletal muscle has never stopped, whether in experimental tests or simulations of passive mechanical properties. To investigate the effect of biomechanical properties of micro-components and geometric structure of muscle fibers on macroscopic mechanical behavior, in this manuscript, we establish a multiscale model where constitutive models are proposed for fibers and the extracellular matrix, respectively. Besides, based on the assumption that the fiber cross-section can be expressed by Voronoi polygons, we optimize the Voronoi polygons as curved-edge Voronoi polygons to compare the effects of the two cross-sections on macroscopic mechanical properties. Finally, the macroscopic stress response is obtained through the numerical homogenization method. To verify the effectiveness of the multi-scale model, we measure the mechanical response of skeletal muscles in the in-plane shear, longitudinal shear, and tensions, including along the fiber direction and perpendicular to the fiber direction. Compared with experimental data, the simulation results show that this multiscale framework predicts both the tension response and the shear response of skeletal muscle accurately. The root mean squared error (RMSE) is 0.0035 MPa in the tension along the fiber direction; The RMSE is 0.011254 MPa in the tension perpendicular to the fiber direction; The RMSE is 0.000602 MPa in the in-plane shear; The RMSE was 0.00085 MPa in the longitudinal shear. Finally, we obtained the influence of the component constitutive model and muscle fiber cross-section on the macroscopic mechanical behavior of skeletal muscle. In terms of the tension perpendicular to the fiber direction, the curved-edge Voronoi polygons achieve the result closer to the experimental data than the Voronoi polygons. Skeletal muscle mechanics experiments verify the effectiveness of our multiscale model. The comparison results of experiments and simulations prove that our model can accurately capture the tension and shear behavior of skeletal muscle.

Innovation in culture systems to study muscle complexity

Endogenous skeletal muscle development, regeneration, and pathology are extremely complex processes, influenced by local and systemic factors. Unpinning how these mechanisms function is crucial for fundamental biology and to develop therapeutic interventions for genetic disorders, but also conditions like sarcopenia and volumetric muscle loss. Ex vivo skeletal muscle models range from two- and three-dimensional primary cultures of satellite stem cell-derived myoblasts grown alone or in co-culture, to single muscle myofibers, myobundles, and whole tissues. Together, these systems provide the opportunity to gain mechanistic insights of stem cell behavior, cell-cell interactions, and mature muscle function in simplified systems, without confounding variables. Here, we highlight recent advances (published in the last 5 years) using in vitro primary cells and ex vivo skeletal muscle models, and summarize the new insights, tools, datasets, and screening methods they have provided. Finally, we highlight the opportunity for exponential advance of skeletal muscle knowledge, with spatiotemporal resolution, that is offered by guiding the study of muscle biology and physiology with in silico modelling and implementing high-content cell biology systems and ex vivo physiology platforms.

Increasing the resting time between drop jumps lessens delayed-onset muscle soreness and limits the extent of prolonged low-frequency force depression in human knee extensor muscles

PURPOSE

Unaccustomed eccentric contractions generally result in a long-lasting contractile impairment, referred to as prolonged low-frequency force depression (PLFFD), and delayed-onset muscle soreness (DOMS). We here used repeated drop jumps (DJs) as an eccentric contraction model and studied the effects of increasing the time between DJs from 20 s to 5 min. We hypothesized that both PLFFD and DOMS would be less marked at the longer DJ interval due to the longer time to restore structural elements between DJs.

METHODS

Young men (n = 12) randomly performed 50 DJs with either 20-s (DJ-20 s) or 5-min (DJ-5 min) rest between DJs. Voluntary, 20 Hz and 100 Hz electrically stimulated isometric knee extension torques and muscle soreness were monitored before and for 7 days after DJs; serum CK activity was measured to assess muscle fibre protein leakage. In additional experiments, changes in mRNA levels were assessed in muscle biopsies collected before and 1 h after exercise.

RESULTS

A marked PLFFD was observed with both protocols and the extent of 20 Hz torque depression was smaller immediately and 1 day after DJ-5 min than after DJ-20 s (p < 0.05), whereas the MVC and 100 Hz torques were similarly decreased with the two protocols. Markedly larger differences between the two protocols were observed for the muscle soreness score, which 1-4 days after exercise was about two times larger with DJ-20 s than with DJ-5 min (p < 0.01).

CONCLUSIONS

The larger protective effect of the longer DJ interval against DOMS than against PLFFD indicates that their underlying mechanisms involve different structural elements.

Predicting muscle tissue response from calibrated component models and histology-based finite element models

Skeletal muscle is an anisotropic soft biological tissue composed of muscle fibres embedded in a structurally complex, hierarchically organised extracellular matrix. In a recent work (Kuravi et al., 2021) we have developed 3D finite element models from series of histological sections. Moreover, based on decellularisation of fresh tissue samples, a novel set of experimental data on the direction dependent mechanical properties of collagenous ECM was established (Kohn et al., 2021). Together with existing information on the material properties of single muscle fibres, the combination of these techniques allows computing predictions of the composite tissue response. To this end, an inverse finite element procedure is proposed in the present work to calibrate a constitutive model of the extracellular matrix, and supplementary biaxial tensile tests on fresh and decellularised tissues are performed for model validation. The results of this rigorously predictive and thus unforgiving strategy suggest that the prediction of the tissue response from the individual characteristics of muscle cells and decellularised tissue is only possible within clear limits. While orders of magnitude are well matched, and the qualitative behaviour in a wide range of load cases is largely captured, the existing deviations point at potentially missing components of the model and highlight the incomplete experimental information in bottom-up multiscale approaches to model skeletal muscle tissue.