Assessing the microstructural response to applied deformation in porcine passive skeletal muscle

Skeletal muscle extracellular matrix structure under applied deformation observed using second harmonic generation microscopy

The mechanical and structural properties of passive skeletal muscle are important for musculoskeletal models in impact biomechanics, rehabilitation engineering and surgical simulation. Passive properties of skeletal muscle depend strongly on the architecture of the extracellular matrix (ECM), but the structure of ECM and its realignment under applied deformation remain poorly understood. We apply second harmonic generation (SHG) microscopy to study muscle ECM in intact muscle samples both under deformation and in the undeformed state. A method for regional relocation was developed, so that the same ECM segment could be viewed before and after applying deformations. Skeletal muscle ECM was viewed at multiple scales and in three states: undeformed, under compression and under tension. Results show that second harmonic generation microscopy provides substantial detail of skeletal muscle ECM over a wide range of length scales, especially the perimysium structure. We present images of individual portions of skeletal muscle ECM both undeformed and subjected to tensile/compressive deformation. We also present data showing the response of the perimysium to a partial thickness cut applied to a section under tensile deformation. STATEMENT OF SIGNIFICANCE: Second Harmonic Generation (SHG) microscopy is an imaging technique which takes advantage of a non-linear and coherent frequency doubling optical effect that is present in a small number of biological molecules, primarily collagen Type I, II and myosin. Collagen I is the most abundant collagen type in skeletal muscle, making SHG a promising option for visualisation of the skeletal muscle extracellular matrix (ECM). SHG microscopy does not require fixing or staining. This short communication presents the application of SHG microscopy to skeletal muscle ECM to improve our understanding of how collagen fibres reorganise under applied tensile and compression, including microscopic observations of collagen fibre reorganisation for intact samples by using a method to re-identify specific regions in repeated deformation tests.

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.

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

This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.

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.

3D finite element models from serial section histology of skeletal muscle tissue - The role of micro-architecture on mechanical behaviour

In this contribution we create three-dimensional (3D) finite element models from a series of histological sections of porcine skeletal muscle tissue. Image registration is performed on the stained sections by affinely aligning them using auxiliary markers, followed by image segmentation to determine muscle fibres and the extracellular matrix in each section, with particular regard to the continuity of the fibres through the stack. With this information, 3D virtual tissue samples are reconstructed, discretised, and associated with appropriate non-linear elastic anisotropic material models. While the gross anatomy is directly obtained from the images, the local directions of anisotropy were determined by the use of an analogy with steady state diffusion. The influence of the number of histological sections considered for reconstruction on the numerically simulated mechanical response of the virtual tissue samples is then studied. The results show that muscle tissue is fairly heterogeneous along the fascicles, and that transverse isotropy is inadequate in describing their material symmetry at the typical length scale of a fascicle. Numerical simulations of different load cases suggest that ignoring the undulations of fibres and their non-uniform cross-sections only moderately affects the passive response of the tissue in tensile and compressive modes, but can become crucial when predicting the response to generic loads and activation.

In vitro compressive properties of skeletal muscles and inverse finite element analysis: Comparison of human versus animals

Virtual finite element human body models have been widely used in biomedical engineering, traffic safety injury analysis, etc. Soft tissue modeling like skeletal muscle accounts for a large portion of a human body model establishment, and its modeling method is not enough explored. The present study aims to investigate the compressive properties of skeletal muscles due to different species, loading rates and fiber orientations, in order to obtain available parameters of specific material laws as references for building or improving the human body model concerning both modeling accuracy and computational cost. A series of compressive experiments of skeletal muscles were implemented for human gastrocnemius muscle, bovine and porcine hind leg muscle. To avoid long-time preservation effects, all experimental tests were carried out in 24 h after that the samples were harvested. Considering computational cost and generally used in the previous human body models, one-order hyperelastic Ogden model and three-term simplified viscoelastic quasi-linear viscoelastic (QLV) were selected for numerical analysis. Inverse finite element analysis was employed to obtain corresponding material parameters. With good fitting records, the simulation results presented available material parameters for human body model establishment, and also indicated significant differences of muscle compressive properties due to species, loading rates and fiber orientations. When considering one-order Ogden law, it is worthy of noting that the inversed material parameters of the porcine muscles are similar to those of the human gastrocnemius regardless of fiber orientations. In conclusion, the obtained material parameters in the present study can be references for global human body and body segment modeling.

An inverse model of the mechanical response of passive skeletal muscle: Implications for microstructure

The constitutive response of passive skeletal muscle is important for many human body modelling applications, but modelling the tension-compression asymmetry and the anisotropy observed in ex-vivo samples is challenging. Existing microstructural models do not capture the full three-dimensional response while models suitable for application in finite element environments mostly have a limited microstructural basis and cannot capture the observed Poisson's ratios. The aim of this paper is to derive an inverse model based on the microstructure of a skeletal muscle that can predict its passive mechanical response. The model parameters and predictions were derived and assessed by comparison with published experimental stress-strain response and Poisson's ratio data. Results show a close match for both predicted stress-strain response for fibre and cross-fibre direction deformations and similar Poisson's ratio values. Some microstructural observations which strengthen our understanding of the role of the collagen network and intramuscular pressure are also provided.

Visualisation of Collagen in fixed skeletal muscle tissue using fluorescently tagged Collagen binding protein CNA35

Detection and visualisation of Collagen structure are important to understand the relationship between mechanical behaviour and microstructure in skeletal muscle since Collagen is the main structural protein in animal connective tissues, and is primarily responsible for their passive load-bearing properties. In the current study, the direct detection and visualization of Collagen using fluorescently tagged CNA35 binding protein (fused to EGFP or tdTomato) is reported for the first time on fixed skeletal muscle tissue. This Technical Note also establishes a working protocol by examining tissue preparation, dilution factor, exposure time etc. for sensitivity and specificity. Penetration of the binding protein into intact mature skeletal muscle was found to be very limited, but detection works well on tissue sections with higher sensitivity on wax embedded sections compared to frozen sections. CNA35 fused to tdTomato has a higher sensitivity than CNA35 fused to EGFP but both show specific detection. Best results were obtained with 15μm wax embedded sections, with blocking of non-specific binding in 1% BSA and antigen retrieval in Sodium Citrate. There was a play-off between dilution of the binding protein and time of incubation but both CNA35-tdTomato and CNA35-EGFP worked well with approximately 100μg/ml of purified protein with overnight incubation, while CNA35-tdTomato could be utilized at 5 fold less concentration. This approach can be applied to study the relationship between skeletal muscle micro-structure and to observe mechanical response to applied deformation. It can be used more broadly to detect Collagen in a variety of fixed tissues, useful for structure-functions studies, constitutive modelling, tissue engineering and assessment of muscle tissue pathologies.