Multiscale models of skeletal muscle reveal the complex effects of muscular dystrophy on tissue mechanics and damage susceptibility

The role of the extracellular matrix in the reduction of lateral force transmission in muscle bundles: A finite element analysis

BACKGROUND AND OBJECTIVE

Aging is associated with a reduction in muscle performance, but muscle weakness is characterized by a much greater loss of force loss compared to mass loss. The aim of this work is to assess the contribution of the extracellular matrix (ECM) to the lateral transmission of force in humans and the loss of transmitted force due to age-related modifications.

METHODS

Finite element models of muscle bundles are developed for young and elderly human subjects, by considering a few fibers connected through an ECM layer. Bundles of young and elderly subjects are assumed to differ in terms of ECM thickness, as observed experimentally. A three-element-based Hill model is adopted to describe the active behavior of muscle fibers, while the ECM is modeled assuming an isotropic hyperelastic neo-Hookean constitutive formulation. Numerical analyses are carried out by mimicking, at the scale of a bundle, two experimental protocols from the literature.

RESULTS

When comparing numerical results obtained for bundles of young and elderly subjects, a greater reduction in the total transmitted force is observed in the latter. The loss of transmitted force is 22 % for the elderly subjects, while it is limited to 7.5 % for the young subjects. The result for the elderly subjects is in line with literature studies on animal models, showing a reduction in the range of 20-34 %. This can be explained by an alteration in the mechanism of lateral force transmission due to the lower shear stiffness of the ECM in elderly subjects, related to its higher thickness.

CONCLUSIONS

Computational modeling allows to evaluate at the bundle level how the age-related increase of the ECM amount between fibers affects the lateral transmission of force. The results suggest that the observed increase in ECM thickness in aging alone can explain the reduction of the total transmitted force, due to the impaired lateral transmission of force of each fiber.

Duchenne and Becker muscular dystrophy: Cellular mechanisms, image analysis, and computational models: A review

The muscle is the principal tissue that is capable to transform potential energy into kinetic energy. This process is due to the transformation of chemical energy into mechanical energy to enhance the movements and all the daily activities. However, muscular tissues can be affected by some pathologies associated with genetic alterations that affect the expression of proteins. As the muscle is a highly organized structure in which most of the signaling pathways and proteins are related to one another, pathologies may overlap. Duchenne muscular dystrophy (DMD) is one of the most severe muscle pathologies triggering degeneration and muscle necrosis. Several mathematical models have been developed to predict muscle response to different scenarios and pathologies. The aim of this review is to describe DMD and Becker muscular dystrophy in terms of cellular behavior and molecular disorders and to present an overview of the computational models implemented to understand muscle behavior with the aim of improving regenerative therapy.

It's more than the amount that counts: implications of collagen organization on passive muscle tissue properties revealed with micromechanical models and experiments

Collagen accumulation is often used to characterize skeletal muscle fibrosis, but the role of collagen in passive muscle mechanics remains debated. Here we combined finite-element models and experiments to examine how collagen organization contributes to macroscopic muscle tissue properties. Tissue microstructure and mechanical properties were measured from in vitro biaxial experiments and imaging in dystrophin knockout (mdx) and wild-type (WT) diaphragm muscle. Micromechanical models of intramuscular and epimuscular extracellular matrix (ECM) regions were developed to account for complex microstructure and predict bulk properties, and directly calibrated and validated with the experiments. The models predicted that intramuscular collagen fibres align primarily in the cross-muscle fibre direction, with greater cross-muscle fibre alignment in mdx models compared with WT. Higher cross-muscle fibre stiffness was predicted in mdx models compared with WT models and differences between ECM and muscle properties were seen during cross-muscle fibre loading. Analysis of the models revealed that variation in collagen fibre distribution had a much more substantial impact on tissue stiffness than ECM area fraction. Taken together, we conclude that collagen organization explains anisotropic tissue properties observed in the diaphragm muscle and provides an explanation for the lack of correlation between collagen amount and tissue stiffness across experimental studies.

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

Role of Muscle LIM Protein in Mechanotransduction Process

The induction of protein synthesis is crucial to counteract the deconditioning of neuromuscular system and its atrophy. In the past, hormones and cytokines acting as growth factors involved in the intracellular events of these processes have been identified, while the implications of signaling pathways associated with the anabolism/catabolism ratio in reference to the molecular mechanism of skeletal muscle hypertrophy have been recently identified. Among them, the mechanotransduction resulting from a mechanical stress applied to the cell appears increasingly interesting as a potential pathway for therapeutic intervention. At present, there is an open question regarding the type of stress to apply in order to induce anabolic events or the type of mechanical strain with respect to the possible mechanosensing and mechanotransduction processes involved in muscle cells protein synthesis. This review is focused on the muscle LIM protein (MLP), a structural and mechanosensing protein with a LIM domain, which is expressed in the sarcomere and costamere of striated muscle cells. It acts as a transcriptional cofactor during cell proliferation after its nuclear translocation during the anabolic process of differentiation and rebuilding. Moreover, we discuss the possible opportunity of stimulating this mechanotransduction process to counteract the muscle atrophy induced by anabolic versus catabolic disorders coming from the environment, aging or myopathies.

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 passive material influences on deformation and force output of skeletal muscles

Passive materials in human skeletal muscle tissues play an important role in force output of skeletal muscles. This paper introduces a multiscale modeling framework to investigate how age-associated variations on microscale passive muscle components, including microstructural geometry (e.g., connective tissue thickness) and material properties (e.g., anisotropy), influence the force output and deformations of the continuum skeletal muscle. We first define a representative volume element (RVE) for the microstructure of muscle and determine the homogenized macroscale mechanical properties of the RVE from the separate mechanical properties of the individual components of the RVE, including muscle fibers and connective tissue with its associated collagen fibers. The homogenized properties of the RVE are then used to define the elements of the continuum muscle model to evaluate the force output and deformations of the whole muscle. Conversely, the regional deformations of the continuum model are fed back to the RVE model to determine the responses of the individual microscale components. Simulations of muscle isometric contractions at a range of muscle lengths are performed to investigate the effects of muscle architectural changes (e.g., pennation angles) due to aging on force output and muscle deformation. The correlations between the pennation angle, the shear deformation in the microscale connective tissue (an indicator for the lateral force transmission), the angle difference between the fiber direction and principal strain direction and the resulting shear deformation at the continuum scale, as well as the force output of the skeletal muscle are also discussed.

Diaphragm muscle fibrosis involves changes in collagen organization with mechanical implications in Duchenne muscular dystrophy

In Duchenne muscular dystrophy (DMD), diaphragm muscle dysfunction results in respiratory insufficiency, a leading cause of death in patients. Increased muscle stiffness occurs with buildup of fibrotic tissue, characterized by excessive accumulation of extracellular matrix (ECM) components such as collagen, and prevents the diaphragm from achieving the excursion lengths required for respiration. However, changes in mechanical properties are not explained by collagen amount alone and we must consider the complex structure and mechanics of fibrotic tissue. The goals of our study were to 1) determine if and how collagen organization changes with the progression of DMD in diaphragm muscle tissue and 2) predict how collagen organization influences the mechanical properties of the ECM. We first visualized collagen structure with scanning electron microscopy (SEM) images and then developed an analysis framework to quantify collagen organization and generate image-based finite-element models. Image analysis revealed increased collagen fiber straightness and alignment in mdx over wild type (WT) at 3 mo (straightness: mdx = 0.976 ± 0.0108, WT = 0.887 ± 0.0309, alignment: mdx = 0.876 ± 0.0333, WT = 0.759 ± 0.0416) and 6 mo (straightness: mdx = 0.942 ± 0.0182, WT = 0.881 ± 0.0163, alignment: mdx = 0.840 ± 0.0315, WT = 0.759 ± 0.0368). Collagen fibers retained a transverse orientation relative to muscle fibers (70°-90°) in all groups. Mechanical models predicted an increase in the transverse relative to longitudinal (muscle fiber direction) stiffness, with stiffness ratio (transverse/longitudinal) increased in mdx over WT at 3 mo (mdx = 5.45 ± 2.04, WT = 1.97 ± 0.670) and 6 mo (mdx = 4.05 ± 0.985, WT = 1.96 ± 0.506). This study revealed changes in diaphragm ECM structure and mechanics during disease progression in the mdx muscular dystrophy mouse phenotype, highlighting the need to consider the role of collagen organization on diaphragm muscle function.NEW & NOTEWORTHY Scanning electron microscopy images of decellularized diaphragm muscle from WT and mdx, Duchenne muscular dystrophy model, mice revealed that collagen fibers in the epimysium are oriented transverse to muscle fibers, with age- and disease-dependent changes in collagen arrangement. Finite-element models generated from these images predicted that changes in collagen arrangement during disease progression influence the mechanical properties of the extracellular matrix. Thus, changes in collagen fiber-level structure are implicated on tissue-level properties during fibrosis.

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.

Multiscale Computational Modeling of Vascular Adaptation: A Systems Biology Approach Using Agent-Based Models

The widespread incidence of cardiovascular diseases and associated mortality and morbidity, along with the advent of powerful computational resources, have fostered an extensive research in computational modeling of vascular pathophysiology field and promoted in-silico models as a support for biomedical research. Given the multiscale nature of biological systems, the integration of phenomena at different spatial and temporal scales has emerged to be essential in capturing mechanobiological mechanisms underlying vascular adaptation processes. In this regard, agent-based models have demonstrated to successfully embed the systems biology principles and capture the emergent behavior of cellular systems under different pathophysiological conditions. Furthermore, through their modular structure, agent-based models are suitable to be integrated with continuum-based models within a multiscale framework that can link the molecular pathways to the cell and tissue levels. This can allow improving existing therapies and/or developing new therapeutic strategies. The present review examines the multiscale computational frameworks of vascular adaptation with an emphasis on the integration of agent-based approaches with continuum models to describe vascular pathophysiology in a systems biology perspective. The state-of-the-art highlights the current gaps and limitations in the field, thus shedding light on new areas to be explored that may become the future research focus. The inclusion of molecular intracellular pathways (e.g., genomics or proteomics) within the multiscale agent-based modeling frameworks will certainly provide a great contribution to the promising personalized medicine. Efforts will be also needed to address the challenges encountered for the verification, uncertainty quantification, calibration and validation of these multiscale frameworks.

Towards in silico Models of the Inflammatory Response in Bone Fracture Healing

In silico modeling is a powerful strategy to investigate the biological events occurring at tissue, cellular and subcellular level during bone fracture healing. However, most current models do not consider the impact of the inflammatory response on the later stages of bone repair. Indeed, as initiator of the healing process, this early phase can alter the regenerative outcome: if the inflammatory response is too strongly down- or upregulated, the fracture can result in a non-union. This review covers the fundamental information on fracture healing, in silico modeling and experimental validation. It starts with a description of the biology of fracture healing, paying particular attention to the inflammatory phase and its cellular and subcellular components. We then discuss the current state-of-the-art regarding in silico models of the immune response in different tissues as well as the bone regeneration process at the later stages of fracture healing. Combining the aforementioned biological and computational state-of-the-art, continuous, discrete and hybrid modeling technologies are discussed in light of their suitability to capture adequately the multiscale course of the inflammatory phase and its overall role in the healing outcome. Both in the establishment of models as in their validation step, experimental data is required. Hence, this review provides an overview of the different in vitro and in vivo set-ups that can be used to quantify cell- and tissue-scale properties and provide necessary input for model credibility assessment. In conclusion, this review aims to provide hands-on guidance for scientists interested in building in silico models as an additional tool to investigate the critical role of the inflammatory phase in bone regeneration.

Myeloid cell-mediated targeting of LIF to dystrophic muscle causes transient increases in muscle fiber lesions by disrupting the recruitment and dispersion of macrophages in muscle

Leukemia inhibitory factor (LIF) can influence development by increasing cell proliferation and inhibiting differentiation. Because of its potency for expanding stem cell populations, delivery of exogenous LIF to diseased tissue could have therapeutic value. However, systemic elevations of LIF can have negative, off-target effects. We tested whether inflammatory cells expressing a LIF transgene under control of a leukocyte-specific, CD11b promoter provide a strategy to target LIF to sites of damage in the mdx mouse model of Duchenne muscular dystrophy, leading to increased numbers of muscle stem cells and improved muscle regeneration. However, transgene expression in inflammatory cells did not increase muscle growth or increase numbers of stem cells required for regeneration. Instead, transgene expression disrupted the normal dispersion of macrophages in dystrophic muscles, leading to transient increases in muscle damage in foci where macrophages were highly concentrated during early stages of pathology. The defect in inflammatory cell dispersion reflected impaired chemotaxis of macrophages to C-C motif chemokine ligand-2 and local increases of LIF production that produced large aggregations of cytolytic macrophages. Transgene expression also induced a shift in macrophage phenotype away from a CD206+, M2-biased phenotype that supports regeneration. However, at later stages of the disease when macrophage numbers declined, they dispersed in the muscle, leading to reductions in muscle fiber damage, compared to non-transgenic mdx mice. Together, the findings show that macrophage-mediated delivery of transgenic LIF exerts differential effects on macrophage dispersion and muscle damage depending on the stage of dystrophic pathology.

A Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Skeletal muscle: Modeling the mechanical behavior by taking the hierarchical microstructure into account

Skeletal muscles ensure the mobility of mammals and are complex natural fiber-matrix-composites with a hierarchical microstructure. In this work, we analyze the muscle's mechanical behavior on the level of fascicles and muscle fibers. We introduce continuum mechanics hyperelastic material models for the connective tissue endomysium and the embedded muscle fibers. The coupled electrical, chemical and mechanical processes taking place in activated contracting muscle fibers are captured including the temporal change of the activation level and the spatial propagation of the activation potential in fibers. In our model, we investigate the material behavior of fascicle, fiber and endomysium in the fiber direction and examine interactions between muscle fiber and endomysium by considering the temporal and spatial change of muscle fiber activation. In addition, a loading case of normal and shear forces is applied to analyze the fiber lifting force and the lifting height of unipennate muscles with different pennation angles. Moreover, the development of local stresses and strains in fibers and endomysium for different strains are studied. The simulation results allow to identify regions in high risk of damage. Optimal arrangements of unipennate muscle microstructure are found for either very small or very large pennation angles.

MRI and muscle imaging for idiopathic inflammatory myopathies

Although idiopathic inflammatory myopathies (IIM) are a heterogeneous group of diseases nearly all patients display muscle inflammation. Originally, muscle biopsy was considered as the gold standard for IIM diagnosis. The development of muscle imaging led to revisiting not only the IIM diagnosis strategy but also the patients' follow-up. Different techniques have been tested or are in development for IIM including positron emission tomography, ultrasound imaging, ultrasound shear wave elastography, though magnetic resonance imaging (MRI) remains the most widely used technique in routine. Whereas guidelines on muscle imaging in myositis are lacking here we reviewed the relevance of muscle imaging for both diagnosis and myositis patients' follow-up. We propose recommendations about when and how to perform MRI on myositis patients, and we describe new techniques that are under development.

Agent-based model provides insight into the mechanisms behind failed regeneration following volumetric muscle loss injury

Skeletal muscle possesses a remarkable capacity for repair and regeneration following a variety of injuries. When successful, this highly orchestrated regenerative process requires the contribution of several muscle resident cell populations including satellite stem cells (SSCs), fibroblasts, macrophages and vascular cells. However, volumetric muscle loss injuries (VML) involve simultaneous destruction of multiple tissue components (e.g., as a result of battlefield injuries or vehicular accidents) and are so extensive that they exceed the intrinsic capability for scarless wound healing and result in permanent cosmetic and functional deficits. In this scenario, the regenerative process fails and is dominated by an unproductive inflammatory response and accompanying fibrosis. The failure of current regenerative therapeutics to completely restore functional muscle tissue is not surprising considering the incomplete understanding of the cellular mechanisms that drive the regeneration response in the setting of VML injury. To begin to address this profound knowledge gap, we developed an agent-based model to predict the tissue remodeling response following surgical creation of a VML injury. Once the model was able to recapitulate key aspects of the tissue remodeling response in the absence of repair, we validated the model by simulating the tissue remodeling response to VML injury following implantation of either a decellularized extracellular matrix scaffold or a minced muscle graft. The model suggested that the SSC microenvironment and absence of pro-differentiation SSC signals were the most important aspects of failed muscle regeneration in VML injuries. The major implication of this work is that agent-based models may provide a much-needed predictive tool to optimize the design of new therapies, and thereby, accelerate the clinical translation of regenerative therapeutics for VML injuries.

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

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.

A Conceptual Blueprint for Making Neuromusculoskeletal Models Clinically Useful

The ultimate goal of most neuromusculoskeletal modeling research is to improve the treatment of movement impairments. However, even though neuromusculoskeletal models have become more realistic anatomically, physiologically, and neurologically over the past 25 years, they have yet to make a positive impact on the design of clinical treatments for movement impairments. Such impairments are caused by common conditions such as stroke, osteoarthritis, Parkinson’s disease, spinal cord injury, cerebral palsy, limb amputation, and even cancer. The lack of clinical impact is somewhat surprising given that comparable computational technology has transformed the design of airplanes, automobiles, and other commercial products over the same time period. This paper provides the author’s personal perspective for how neuromusculoskeletal models can become clinically useful. First, the paper motivates the potential value of neuromusculoskeletal models for clinical treatment design. Next, it highlights five challenges to achieving clinical utility and provides suggestions for how to overcome them. After that, it describes clinical, technical, collaboration, and practical needs that must be addressed for neuromusculoskeletal models to fulfill their clinical potential, along with recommendations for meeting them. Finally, it discusses how more complex modeling and experimental methods could enhance neuromusculoskeletal model fidelity, personalization, and utilization. The author hopes that these ideas will provide a conceptual blueprint that will help the neuromusculoskeletal modeling research community work toward clinical utility.

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.

Computational Models Provide Insight into In Vivo Studies and Reveal the Complex Role of Fibrosis in mdx Muscle Regeneration

Duchenne muscular dystrophy is a pro-fibrotic, muscle wasting disease. Reducing fibrosis is a potential therapeutic target; however, its effect on muscle regeneration is not fully understood. This study (1) used an agent-based model to predict the effect of increased fibrosis in mdx muscle on regeneration from injury, and (2) experimentally tested the resulting model-derived hypothesis. The model predicted that increasing the area fraction of fibrosis decreased regeneration 28 days post injury due to limited growth factor diffusion and impaired cell migration. WT, mdx, and TGFβ-treated mdx mice were used to test this experimentally. TGFβ injections increased the extracellular matrix (ECM) area fraction; however, the passive stiffness of the treated muscle, which was assumed to correlate with ECM protein density, decreased following injections, suggesting that ECM protein density was lower. Further, there was no cross-sectional area (CSA) difference during recovery between the groups. Additional simulations revealed that decreasing the ECM protein density resulted in no difference in CSA, similar to the experiment. These results suggest that increases in ECM area fraction alone are not sufficient to reduce the regenerative capacity of mdx muscle, and that fibrosis is a complex pathological condition requiring further understanding.

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.

Role of the Extracellular Matrix in Loss of Muscle Force With Age and Unloading Using Magnetic Resonance Imaging, Biochemical Analysis, and Computational Models

The focus of this review is the application of advanced MRI to study the effect of aging and disuse related remodeling of the extracellular matrix (ECM) on force transmission in the human musculoskeletal system. Structural MRI includes (i) ultra-low echo times (UTE) maps to visualize and quantify the connective tissue, (ii) diffusion tensor imaging (DTI) modeling to estimate changes in muscle and ECM microstructure, and (iii) magnetization transfer contrast imaging to quantify the macromolecular fraction in muscle. Functional MRI includes dynamic acquisitions during contraction cycles enabling computation of the strain tensor to monitor muscle deformation. Further, shear strain extracted from the strain tensor may be a potential surrogate marker of lateral transmission of force. Biochemical and histological analysis of muscle biopsy samples can provide "gold-standard" validation of some of the MR findings. The review summarizes biochemical studies of ECM adaptations with age and with disuse. A brief summary of animal models is included as they provide experimental confirmation of longitudinal and lateral force transmission pathways. Computational muscle models enable exploration of force generation and force pathways and elucidate the link between structural adaptations and functional consequences. MR image findings integrated in a computational model can explain and predict subject specific functional changes to structural adaptations. Future work includes development and validation of MRI biomarkers using biochemical analysis of muscle tissue as a reference standard and potential translation of the imaging markers to the clinic to noninvasively monitor musculoskeletal disease conditions and changes consequent to rehabilitative interventions.

Alterations of Extracellular Matrix Mechanical Properties Contribute to Age-Related Functional Impairment of Human Skeletal Muscles

Aging of human skeletal muscles is associated with increased passive stiffness, but it is still debated whether muscle fibers or extracellular matrix (ECM) are the determinants of such change. To answer this question, we compared the passive stress generated by elongation of fibers alone and arranged in small bundles in young healthy (Y: 21 years) and elderly (E: 67 years) subjects. The physiological range of sarcomere length (SL) 2.5-3.3 μm was explored. The area of ECM between muscle fibers was determined on transversal sections with picrosirius red, a staining specific for collagen fibers. The passive tension of fiber bundles was significantly higher in E compared to Y at all SL. However, the resistance to elongation of fibers alone was not different between the two groups, while the ECM contribution was significantly increased in E compared to Y. The proportion of muscle area occupied by ECM increased from 3.3% in Y to 8.2% in E. When the contribution of ECM to bundle tension was normalized to the fraction of area occupied by ECM, the difference disappeared. We conclude that, in human skeletal muscles, the age-related reduced compliance is due to an increased stiffness of ECM, mainly caused by collagen accumulation.

Multi-scale models of lung fibrosis

The architectural complexity of the lung is crucial to its ability to function as an organ of gas exchange; the branching tree structure of the airways transforms the tracheal cross-section of only a few square centimeters to a blood-gas barrier with a surface area of tens of square meters and a thickness on the order of a micron or less. Connective tissue comprised largely of collagen and elastic fibers provides structural integrity for this intricate and delicate system. Homeostatic maintenance of this connective tissue, via a balance between catabolic and anabolic enzyme-driven processes, is crucial to life. Accordingly, when homeostasis is disrupted by the excessive production of connective tissue, lung function deteriorates rapidly with grave consequences leading to chronic lung conditions such as pulmonary fibrosis. Understanding how pulmonary fibrosis develops and alters the link between lung structure and function is crucial for diagnosis, prognosis, and therapy. Further information gained could help elaborate how the healing process breaks down leading to chronic disease. Our understanding of fibrotic disease is greatly aided by the intersection of wet lab studies and mathematical and computational modeling. In the present review we will discuss how multi-scale modeling has facilitated our understanding of pulmonary fibrotic disease as well as identified opportunities that remain open and have produced techniques that can be incorporated into this field by borrowing approaches from multi-scale models of fibrosis beyond the lung.

Skeletal Muscle Extracellular Matrix - What Do We Know About Its Composition, Regulation, and Physiological Roles? A Narrative Review

Skeletal muscle represents the largest body-composition component in humans. In addition to its primary function in the maintenance of upright posture and the production of movement, it also plays important roles in many other physiological processes, including thermogenesis, metabolism and the secretion of peptides for communication with other tissues. Research attempting to unveil these processes has traditionally focused on muscle fibers, i.e., the contractile muscle cells. However, it is a frequently overlooked fact that muscle fibers reside in a three-dimensional scaffolding that consists of various collagens, glycoproteins, proteoglycans, and elastin, and is commonly referred to as extracellular matrix (ECM). While initially believed to be relatively inert, current research reveals the involvement of ECM cells in numerous important physiological processes. In interaction with other cells, such as fibroblasts or cells of the immune system, the ECM regulates muscle development, growth and repair and is essential for effective muscle contraction and force transmission. Since muscle ECM is highly malleable, its texture and, consequently, physiological roles may be affected by physical training and disuse, aging or various diseases, such as diabetes. With the aim to stimulate increased efforts to study this still poorly understood tissue, this narrative review summarizes the current body of knowledge on (i) the composition and structure of the ECM, (ii) molecular pathways involved in ECM remodeling, (iii) the physiological roles of muscle ECM, (iv) dysregulations of ECM with aging and disease as well as (v) the adaptations of muscle ECM to training and disuse.

Intraoperative testing of passive and active state mechanics of spastic semitendinosus in conditions involving intermuscular mechanical interactions and gait relevant joint positions

In cerebral palsy (CP) patients suffering pathological knee joint motion, spastic muscle's passive state forces have not been quantified intraoperatively. Besides, assessment of spastic muscle's active state forces in conditions involving intermuscular mechanical interactions and gait relevant joint positions is lacking. Therefore, the source of flexor forces limiting joint motion remains unclear. The aim was to test the following hypotheses: (i) in both passive and active states, spastic semitendinosus (ST) per se shows its highest forces within gait relevant knee angle (KA) range and (ii) due to intermuscular mechanical interactions, the active state forces elevate. Isometric forces (seven children with CP, GMFCS-II) were measured during surgery over a range of KA from flexion to full extension, at hip angle (HA) = 45° and 20°, in four conditions: (I) passive state, (II) individual stimulation of the ST, simultaneous stimulation of the ST (III) with its synergists, and (IV) also with an antagonist. Gait analyses: intraoperative data for KA = 17-61° (HA = 45°) and KA = 0-33° (HA = 20°) represent the loading response and terminal swing, and mid/terminal stance phases of gait, respectively. Intraoperative tests: Passive forces maximally approximated half of peak force in condition II (HA = 45°). Added muscle activations did increase muscle forces significantly (HA = 45°: on average by 42.0% and 72.5%; HA = 20°: maximally by 131.8% and 123.7%, respectively in conditions III and IV, p < 0.01). In conclusion, intermuscular mechanical interactions yield elevated active state forces, which are well above passive state forces. This indicates that intermuscular mechanical interactions may be a source of high flexor forces in CP.

Microstructural analysis of skeletal muscle force generation during aging

Human aging results in a progressive decline in the active force generation capability of skeletal muscle. While many factors related to the changes of morphological and structural properties in muscle fibers and the extracellular matrix (ECM) have been considered as possible reasons for causing age-related force reduction, it is still not fully understood why the decrease in force generation under eccentric contraction (lengthening) is much less than that under concentric contraction (shortening). Biomechanically, it was observed that connective tissues (endomysium) stiffen as ages, and the volume ratio of connective tissues exhibits an age-related increase. However, limited skeletal muscle models take into account the microstructural characteristics as well as the volume fraction of tissue material. This study aims to provide a numerical investigation in which the muscle fibers and the ECM are explicitly represented to allow quantitative assessment of the age-related force reduction mechanism. To this end, a fiber-level honeycomb-like microstructure is constructed and modeled by a pixel-based Reproducing Kernel Particle Method (RKPM), which allows modeling of smooth transition in biomaterial properties across material interfaces. The numerical investigation reveals that the increased stiffness of the passive materials of muscle tissue reduces the force generation capability under concentric contraction while maintains the force generation capability under eccentric contraction. The proposed RKPM microscopic model provides effective means for the cellular-scale numerical investigation of skeletal muscle physiology. NOVELTY STATEMENT: A cellular-scale honeycomb-like microstructural muscle model constructed from a histological cross-sectional image of muscle is employed to study the causal relations between age-associated microstructural changes and age-related force loss using Reproducing Kernel Particle Method (RKPM). The employed RKPM offers an effective means for modeling biological materials based on pixel points in the medical images and allow modeling of smooth transition in the material properties across interfaces. The proposed microstructure-informed muscle model enables quantitative evaluation on how cellular-scale compositions contribute to muscle functionality and explain differences in age-related force changes during concentric, isometric and eccentric contractions.

A multiscale in silico model of endothelial to mesenchymal transformation in a tumor microenvironment

Endothelial to mesenchymal transformation (EndMT) is a process in which endothelial cells gain a mesenchymal-like phenotype in response to mechanobiological signals that results in the remodeling or repair of underlying tissue. While initially associated with embryonic development, this process has since been shown to occur in adult tissue remodeling including wound healing, fibrosis, and cancer. In an attempt to understand the role of EndMT in cancer progression and metastasis, we present a multiscale, three-dimensional, in silico model. The model couples tissue level phenomena such as extracellular matrix remodeling, cellular level phenomena such as migration and proliferation, and chemical transport in the tumor microenvironment to mimic in vitro tissue models of the cancer microenvironment. The model is used to study the presence of EndMT-derived activated fibroblasts (EDAFs) and varying substrate stiffness on tumor cell migration and proliferation. The simulations accurately model the behavior of tumor cells under given conditions. The presence of EDAFs and/or an increase in substrate stiffness resulted in an increase in tumor cell activity. This model lays the foundation of further studies of EDAFs in a tumor microenvironment on a cellular and subcellular physiological level.

Fibre and extracellular matrix contributions to passive forces in human skeletal muscles: An experimental based constitutive law for numerical modelling of the passive element in the classical Hill-type three element model

The forces that allow body movement can be divided into active (generated by sarcomeric contractile proteins) and passive (sustained by intra-sarcomeric proteins, fibre cytoskeleton and extracellular matrix (ECM)). These are needed to transmit the active forces to the tendon and the skeleton. However, the relative contribution of the intra- and extra- sarcomeric components in transmitting the passive forces is still under debate. There is limited data in the literature about human muscle and so it is difficult to make predictions using multiscale models, imposing a purely phenomenological description for passive forces. In this paper, we apply a method for the experimental characterization of the passive properties of fibres and ECM to human biopsy and propose their clear separation in a Finite Element Model. Experimental data were collected on human single muscle fibres and bundles, taken from vastus lateralis muscle of elderly subjects. Both were progressively elongated to obtain two stress-strain curves which were fitted to exponential equations. The mechanical properties of the extracellular passive components in a bundle of fibres were deduced by the subtraction of the passive tension observed in single fibres from the passive tension observed in the bundle itself. Our results showed that modulus and tensile load bearing capability of ECM are higher than those of fibres and defined their quantitative characterization that can be used in macroscopic models to study their role in the transmission of forces in physiological and pathophysiological conditions.

In Silico Tissue Engineering: A Coupled Agent-Based Finite Element Approach

Over the past two decades, the increase in prevalence of cardiovascular diseases and the limited availability of autologous blood vessels and saphenous vein grafts have motivated the development of tissue-engineered vascular grafts (TEVGs). However, compliance mismatch and poor mechanical properties of the TEVGs remain as two major issues that need to be addressed. Researchers have investigated the role of various culture conditions and mechanical conditioning in deposition and orientation of collagen fibers, which are the key structural components in the vascular wall; however, the intrinsic complexity of mechanobiological interactions demands implementing new engineering approaches that allow researchers to investigate various scenarios more efficiently. In this study, we utilized a coupled agent-based finite element analysis (AB-FEA) modeling approach to study the effect of various loading modes (uniaxial, biaxial, and equibiaxial), boundary conditions, stretch magnitudes, and growth factor concentrations on growth and remodeling of smooth muscle cell-populated TEVGs, with specific focus on collagen deposition and orientation. Our simulations (12 weeks of culture) showed that biaxial cyclic loading (and not uniaxial or equibiaxial) leads to alignment of collagen fibers in the physiological directions. Moreover, axial boundary conditions of the TEVG act as determinants of fiber orientations. Decreasing the serum concentration, from 10% to 5% or 1%, significantly decreased the growth and remodeling speed, but only affected the fiber orientation in the 1% serum case. In conclusion, in silico tissue engineering has the potential to evolve the future of tissue engineering, as it will allow researchers to conceptualize various interactions and investigate numerous scenarios with great speed. In this study, we were able to predict the orientation of collagen fibers in TEVGs using a coupled AB-FEA model in less than 8 h. Impact Statement Tissue-engineered vascular grafts (TEVGs) hold potential to replace the current gold standard of vascular grafting, saphenous vein grafts. However, developing TEVGs that mimic the mechanical performance of the native tissue remains a challenging task. We developed a computational model of the grafts' remodeling processes and studied the effects of various loading mechanisms and culture conditions on collagen fiber orientation, which is a key factor in mechanical performance of the grafts. We were able to predict the fiber orientations accurately and show that biaxial loading and axial boundary conditions are important factors in collagen fiber organization.

Multiscale modeling of the neuromuscular system: Coupling neurophysiology and skeletal muscle mechanics

Mathematical models and computer simulations have the great potential to substantially increase our understanding of the biophysical behavior of the neuromuscular system. This, however, requires detailed multiscale, and multiphysics models. Once validated, such models allow systematic in silico investigations that are not necessarily feasible within experiments and, therefore, have the ability to provide valuable insights into the complex interrelations within the healthy system and for pathological conditions. Most of the existing models focus on individual parts of the neuromuscular system and do not consider the neuromuscular system as an integrated physiological system. Hence, the aim of this advanced review is to facilitate the prospective development of detailed biophysical models of the entire neuromuscular system. For this purpose, this review is subdivided into three parts. The first part introduces the key anatomical and physiological aspects of the healthy neuromuscular system necessary for modeling the neuromuscular system. The second part provides an overview on state-of-the-art modeling approaches representing all major components of the neuromuscular system on different time and length scales. Within the last part, a specific multiscale neuromuscular system model is introduced. The integrated system model combines existing models of the motor neuron pool, of the sensory system and of a multiscale model describing the mechanical behavior of skeletal muscles. Since many sub-models are based on strictly biophysical modeling approaches, it closely represents the underlying physiological system and thus could be employed as starting point for further improvements and future developments. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Analytical and Computational Methods > Computational Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Spatial scaling in multiscale models: methods for coupling agent-based and finite-element models of wound healing

Multiscale models that couple agent-based modeling (ABM) and finite-element modeling (FEM) allow the dynamic simulation of tissue remodeling and wound healing, with mechanical environment influencing cellular behaviors even as tissue remodeling modifies mechanics. One of the challenges in coupling ABM to FEM is that these two domains typically employ grid or element sizes that differ by several orders of magnitude. Here, we develop and demonstrate an interpolation-based method for mapping between ABM and FEM domains of different resolutions that is suitable for linear and nonlinear FEM meshes and balances accuracy with computational demands. We then explore the effects of refining the FEM mesh and the ABM grid in the setting of a fully coupled model. ABM grid refinement studies showed unexpected effects of grid size whenever cells were present at a high enough density for crowding to affect proliferation and migration. In contrast to an FE-only model, refining the FE mesh in the coupled model increased strain differences between adjacent finite elements. Allowing strain-dependent feedback on collagen turnover magnified the effects of regional heterogeneity, producing highly nonlinear spatial and temporal responses. Our results suggest that the choice of both ABM grid and FEM mesh density in coupled models must be guided by experimental data and accompanied by careful grid and mesh refinement studies in the individual domains as well as the fully coupled model.

Extracellular matrix remodelling induced by alternating electrical and mechanical stimulations increases the contraction of engineered skeletal muscle tissues

Engineered skeletal muscles are inferior to natural muscles in terms of contractile force, hampering their potential use in practical applications. One major limitation is that the extracellular matrix (ECM) not only impedes the contraction but also ineffectively transmits the forces generated by myotubes to the load. In the present study, ECM remodelling improves contractile force in a short time, and a coordinated, combined electrical and mechanical stimulation induces the desired ECM remodelling. Notably, the application of single and combined stimulations to the engineered muscles remodels the structure of their ECM networks, which determines the mechanical properties of the ECM. Myotubes in the tissues are connected in parallel and in series to the ECM. The stiffness of the parallel ECM must be low not to impede contraction, while the stiffness of the serial ECM must be high to transmit the forces to the load. Both the experimental results and the mechanistic model suggest that the combined stimulation through coordination reorients the ECM fibres in such a way that the parallel ECM stiffness is reduced, while the serial ECM stiffness is increased. In particular, 3 and 20 minutes of alternating electrical and mechanical stimulations increase the force by 18% and 31%, respectively.

Modelling the role of redox-related mechanisms in musculoskeletal ageing

The decline in the musculoskeletal system with age is driven at the cellular level by random molecular damage. Cells possess mechanisms to repair or remove damage and many of the pathways involved in this response are regulated by redox signals. However, with ageing there is an increase in oxidative stress which can lead to chronic inflammation and disruption of redox signalling pathways. The complexity of the processes involved has led to the use of computational modelling to help increase our understanding of the system, test hypotheses and make testable predictions. This paper will give a brief background of the biological systems that have been modelled, an introduction to computational modelling, a review of models that involve redox-related mechanisms that are applicable to musculoskeletal ageing, and finally a discussion of the future potential for modelling in this field.

Agent-based model illustrates the role of the microenvironment in regeneration in healthy and mdx skeletal muscle

Duchenne muscular dystrophy (DMD) is a progressive muscle-wasting disease with no effective treatment. Multiple mechanisms are thought to contribute to muscle wasting, including increased susceptibility to contraction-induced damage, chronic inflammation, fibrosis, altered satellite stem cell (SSC) dynamics, and impaired regenerative capacity. The goals of this project were to 1) develop an agent-based model of skeletal muscle that predicts the dynamic regenerative response of muscle cells, fibroblasts, SSCs, and inflammatory cells as a result of contraction-induced injury, 2) calibrate and validate the model parameters based on comparisons with published experimental measurements, and 3) use the model to investigate how changing isolated and combined factors known to be associated with DMD (e.g., altered fibroblast or SSC behaviors) influence muscle regeneration. Our predictions revealed that the percent of injured muscle that recovered 28 days after injury was dependent on the peak SSC counts following injury. In simulations with near-full cross-sectional area recovery (healthy, 4-wk mdx, 3-mo mdx), the SSC counts correlated with the extent of initial injury; however, in simulations with impaired regeneration (9-mo mdx), the peak SSC counts were suppressed relative to initial injury. The differences in SSC counts between these groups were emergent predictions dependent on altered microenvironment factors known to be associated with DMD. Multiple cell types influenced the peak number of SSCs, but no individual parameter predicted the differences in SSC counts. This finding suggests that interventions to target the microenvironment rather than SSCs directly could be an effective method for improving regeneration in impaired muscle. NEW & NOTEWORTHY A computational model predicted that satellite stem cell (SSC) counts are correlated with muscle cross-sectional area (CSA) recovery following injury. In simulations with impaired CSA recovery, SSC counts are suppressed relative to healthy muscle. The suppressed SSC counts were an emergent model prediction, because all simulations had equal initial SSC counts. Fibroblast and anti-inflammatory macrophage counts influenced SSC counts, but no single factor was able to predict the pathological differences in SSC counts that lead to impaired regeneration.

Muscle Shear Wave Elastography in Inclusion Body Myositis: Feasibility, Reliability and Relationships with Muscle Impairments

Degenerative muscle changes may be associated with changes in muscle mechanical properties. Shear wave elastography (SWE) allows direct quantification of muscle shear modulus (MSM). The aim of this study was to evaluate the feasibility and reliability of SWE in the severely disordered muscle as observed in inclusion body myositis. To explore the clinical relevance of SWE, potential relationships between MSM values and level muscle impairments (weakness and ultrasound-derived muscle thickness and echo intensity) were investigated. SWE was performed in the biceps brachii at 100°, 90°, 70° and 10° elbow flexion in 34 patients with inclusion body myositis. MSM was assessed before and after five passive stretch-shortening cycles at 4°/s from 70° to 10° elbow angle and after three maximal voluntary contractions to evaluate potential effects of muscle pre-conditioning. Intra-class correlation coefficients and standard errors of measurements were >0.83 and <1.74 kPa and >0.64 and <1.89 kPa for within- and between-day values, respectively. No significant effect of passive loading-unloading and maximal voluntary contractions was found (all p values  >0.18). MSM correlated to predicted muscle strength (all Spearman correlation coefficients (ρ) > 0.36; all p values < 0.05). A significant correlation was found between muscle echo intensity and muscle shear modulus at 70° only (ρ = 0.38, p <0.05). No correlation was found between muscle thickness and MSM (all ρ values > 0.23 and all p values > 0.25, respectively). Within- and between-day reliability of muscle SWE was satisfactory and moderate, respectively. SWE shows promise for assessing changes in mechanical properties of the severely disordered muscle. Further investigations are required to clarify these findings and to refine their clinical value.

NADPH oxidase mediates microtubule alterations and diaphragm dysfunction in dystrophic mice

Skeletal muscle from mdx mice is characterized by increased Nox2 ROS, altered microtubule network, increased muscle stiffness, and decreased muscle/respiratory function. While microtubule de-tyrosination has been suggested to increase stiffness and Nox2 ROS production in isolated single myofibers, its role in altering tissue stiffness and muscle function has not been established. Because Nox2 ROS production is upregulated prior to microtubule network alterations and ROS affect microtubule formation, we investigated the role of Nox2 ROS in diaphragm tissue microtubule organization, stiffness and muscle/respiratory function. Eliminating Nox2 ROS prevents microtubule disorganization and reduces fibrosis and muscle stiffness in mdx diaphragm. Fibrosis accounts for the majority of variance in diaphragm stiffness and decreased function, implicating altered extracellular matrix and not microtubule de-tyrosination as a modulator of diaphragm tissue function. Ultimately, inhibiting Nox2 ROS production increased force and respiratory function in dystrophic diaphragm, establishing Nox2 as a potential therapeutic target in Duchenne muscular dystrophy.

Skeletal muscle mechanics, energetics and plasticity

The following papers by Richard Lieber (Skeletal Muscle as an Actuator), Thomas Roberts (Elastic Mechanisms and Muscle Function), Silvia Blemker (Skeletal Muscle has a Mind of its Own: a Computational Framework to Model the Complex Process of Muscle Adaptation) and Sabrina Lee (Muscle Properties of Spastic Muscle (Stroke and CP) are summaries of their representative contributions for the session on skeletal muscle mechanics, energetics and plasticity at the 2016 Biomechanics and Neural Control of Movement Conference (BANCOM 2016). Dr. Lieber revisits the topic of sarcomere length as a fundamental property of skeletal muscle contraction. Specifically, problems associated with sarcomere length non-uniformity and the role of sarcomerogenesis in diseases such as cerebral palsy are critically discussed. Dr. Roberts then makes us aware of the (often neglected) role of the passive tissues in muscles and discusses the properties of parallel elasticity and series elasticity, and their role in muscle function. Specifically, he identifies the merits of analyzing muscle deformations in three dimensions (rather than just two), because of the potential decoupling of the parallel elastic element length from the contractile element length, and reviews the associated implications for the architectural gear ratio of skeletal muscle contraction. Dr. Blemker then tackles muscle adaptation using a novel way of looking at adaptive processes and what might drive adaptation. She argues that cells do not have pre-programmed behaviors that are controlled by the nervous system. Rather, the adaptive responses of muscle fibers are determined by sub-cellular signaling pathways that are affected by mechanical and biochemical stimuli; an exciting framework with lots of potential. Finally, Dr. Lee takes on the challenging task of determining human muscle properties in vivo. She identifies the dilemma of how we can demonstrate the effectiveness of a treatment, specifically in cases of muscle spasticity following stroke or in children with cerebral palsy. She then discusses the merits of ultrasound based elastography, and the clinical possibilities this technique might hold. Overall, we are treated to a vast array of basic and clinical problems in skeletal muscle mechanics and physiology, with some solutions, and many suggestions for future research.

Spatial and age-related changes in the microstructure of dystrophic and healthy diaphragms

Duchenne muscular dystrophy (DMD) is a progressive degenerative disease that results in fibrosis and atrophy of muscles. The main cause of death associated with DMD is failure of the diaphragm. The diaphragm is a dome-shaped muscle with a fiber microstructure that differs across regions of the muscle. However, no studies to our knowledge have examined spatial variations of muscle fibers in dystrophic diaphragm or how aging affects those variations in DMD. In this study, diaphragms were obtained from mdx and healthy mice at ages three, seven, and ten months in the dorsal, midcostal, and ventral regions. Through immunostaining and confocal imaging, we quantified sarcomere length, interstitial space between fibers, fiber branching, fiber cross sectional area (CSA), and fiber regeneration measured by centrally located nuclei. Because DMD is associated with chronic inflammation, we also investigated the number of macrophages in diaphragm muscle cross-sections. We saw regional differences in the number of regenerating fibers and macrophages during the progression of DMD in the mdx diaphragm. Additionally, the number of regenerating fibers increased with age, while CSA and the number of branching fibers decreased. Dystrophic diaphragms had shorter sarcomere lengths than age-matched controls. Our results suggest that the dystrophic diaphragm in the mdx mouse is structurally heterogeneous and remodels non-uniformly over time. Understanding regional changes in dystrophic diaphragms over time will facilitate the development of targeted therapies to prevent or minimize respiratory failure in DMD patients.

Skeletal muscle contractile properties in a novel murine model for limb girdle muscular dystrophy 2i

Limb-girdle muscular dystrophy (LGMD) 2i results from mutations in fukutin-related protein and aberrant α-dystroglycan glycosylation. Although this significantly compromises muscle function and ambulation, the comprehensive characteristics of contractile dysfunction are unknown. Therefore, we quantified the in situ contractile properties of the medial gastrocnemius in young adult P448L mice, an affected muscle of a novel model of LGMD2i. Normalized maximal twitch force, tetanic force, and power were significantly smaller in P448L mice, compared with sex-matched, wild-type mice. These differences were consistent with the replacement of contractile fibers by passive tissue. The shape of the active force-length relationships were similar in both groups, regardless of sex, consistent with an intact sarcomeric structure in P448L mice. Passive force-length curves normalized to maximal isometric force were steeper in P448L mice, and passive elements contribute disproportionately more to total contractile force in P448L mice. Sex differences were mostly noted in the force-velocity curves, as normalized values for maximal and optimal velocities were significantly slower in P448L males, compared with wild-type, but not in P448L females. This suggests that the dystrophic phenotype, which may include possible changes in cross-bridge kinetics and fiber-type proportions, progresses more quickly in P448L males. These results together indicate that active force and power generation are compromised in both sexes of P448L mice, while passive forces increase. More importantly, the results identified several functional markers of disease pathophysiology that could aid in developing and assessment of novel therapeutics for LGMD2i and possibly other dystroglycanopathies as well. NEW & NOTEWORTHY Comprehensive assessments of muscle contractile function have, until now, never been performed in an animal model for any dystroglycanopathy. This study suggests that skeletal muscle contractile properties are significantly compromised in a recently developed model for limb-girdle muscular dystrophy 2i, the P448L mouse. It further identifies novel pathological markers of muscle function that are suitable for developing therapeutics and for better understanding of disease pathogenesis.

An engineering design approach to systems biology

Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.

In Vivo Multiscale and Spatially-Dependent Biomechanics Reveals Differential Strain Transfer Hierarchy in Skeletal Muscle

Biological tissues have a complex hierarchical architecture that spans organ to subcellular scales and comprises interconnected biophysical and biochemical machinery. Mechanotransduction, gene regulation, gene protection, and structure-function relationships in tissues depend on how force and strain are modulated from macro to micro scales, and vice versa. Traditionally, computational and experimental techniques have been used in common model systems (e.g., embryos) and simple strain measures were applied. But the hierarchical transfer of mechanical parameters like strain in mammalian systems is largely unexplored in vivo. Here, we experimentally probed complex strain transfer processes in mammalian skeletal muscle tissue over multiple biological scales using complementary in vivo ultrasound and optical imaging approaches. An iterative hyperelastic warping technique quantified the spatially-dependent strain distributions in tissue, matrix, and subcellular (nuclear) structures, and revealed a surprising increase in strain magnitude and heterogeneity in active muscle as the spatial scale also increased. The multiscale strain heterogeneity indicates tight regulation of mechanical signals to the nuclei of individual cells in active muscle, and an emergent behavior appearing at larger (e.g. tissue) scales characterized by dramatically increased strain complexity.

A homogenization model of the Voigt type for skeletal muscle

A three-dimensional constitutive model for skeletal muscle incorporating microstructural characteristics is developed and numerically implemented in a general purpose finite element program. The proposed model takes into account explicitly the volume fractions of muscle fibers and connective tissue by using the Voigt homogenization approach to bridge the different length scales of the muscle structure. The model is used to estimate the active and passive homogenized muscle response. Next, the model is validated by experimental data and periodic three-dimensional unit cell calculations comprising various fiber volume fractions and mechanical properties of the constituents. The model is found to be in very good agreement with both the experimental data and the finite element results for all the examined cases. The influence of fiber volume fraction and material properties of constituents on effective muscle response under several loading conditions is examined.