From single muscle fiber to whole muscle mechanics: a finite element model of a muscle bundle with fast and slow fibers

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.

The need for speed - Does the force-velocity property significantly alter strain distributions within skeletal muscle?

Skeletal muscles are complex structures with nonlinear constitutive properties. This complexity often requires finite element (FE) modeling to better understand muscle behavior and response to activation, especially the fiber strain distributions that can be difficult to measure in vivo. However, many FE muscle models designed to study fiber strain do not include force-velocity behavior. To investigate force-velocity property impact on strain distributions within skeletal muscle, we modified a muscle constitutive model with active and passive force-length properties to include force-velocity properties. We implemented the new constitutive model as a plugin for the FE software FEBio and applied it to four geometries: 1) a single element, 2) a multiple-element model representing a single fiber, 3) a model of tapering fibers, and 4) a model representing the bicep femoris long head (BFLH) morphology. Maximum fiber velocity and boundary conditions of the finite element models were varied to test their influence on fiber strain distribution. We found that force-velocity properties in the constitutive model behaved as expected for the single element and multi-element conditions. In the tapered fiber models, fiber strain distributions were impacted by changes in maximum fiber velocity; the range of strains increased with maximum fiber velocity, which was most noted in isometric contraction simulations. In the BFLH model, maximum fiber velocity had minimal impact on strain distributions, even in the context of sprinting. Taken together, the combination of muscle model geometry, activation, and displacement parameters play a critical part in determining the magnitude of impact of force-velocity on strain distribution.

Changes in the Mechanical Properties of Fast and Slow Skeletal Muscle after 7 and 21 Days of Restricted Activity in Rats

Disuse muscle atrophy is usually accompanied by changes in skeletal muscle structure, signaling, and contractile potential. Different models of muscle unloading can provide valuable information, but the protocols of experiments with complete immobilization are not physiologically representative of a sedentary lifestyle, which is highly prevalent among humans now. In the current study, we investigated the potential effects of restricted activity on the mechanical characteristics of rat postural (soleus) and locomotor (extensor digitorum longus, EDL) muscles. The restricted-activity rats were kept in small Plexiglas cages (17.0 × 9.6 × 13.0 cm) for 7 and 21 days. After this, soleus and EDL muscles were collected for ex vivo mechanical measurements and biochemical analysis. We demonstrated that while a 21-day movement restriction affected the weight of both muscles, in soleus muscle we observed a greater decrease. The maximum isometric force and passive tension in both muscles also significantly changed after 21 days of movement restriction, along with a decrease in the level of collagen 1 and 3 mRNA expression. Furthermore, the collagen content itself changed only in soleus after 7 and 21 days of movement restriction. With regard to cytoskeletal proteins, in our experiment we observed a significant decrease in telethonin in soleus, and a similar decrease in desmin and telethonin in EDL. We also observed a shift towards fast-type myosin heavy chain expression in soleus, but not in EDL. In summary, in this study we showed that movement restriction leads to profound specific changes in the mechanical properties of fast and slow skeletal muscles. Future studies may include evaluation of signaling mechanisms regulating the synthesis, degradation, and mRNA expression of the extracellular matrix and scaffold proteins of myofibers.

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.

Enhancing biomedical data validity with standardized segmentation finite element analysis

Finite element analysis is a powerful computational technique for augmenting biomedical research, prosthetics design, and preoperative surgical assessment. However, the validity of biomechanical data obtained from finite element analysis is dependent on the quality of the preceding data processing. Until now, little information was available about the effect of the segmentation process on finite element models and biomechanical data. The current investigation applied 4 segmentation approaches to 129 femur specimens, yielding a total of 516 finite element models. Biomechanical data including average displacement, pressure, stress, and strain were collected from experimental groups based on the different segmentation approaches. The results indicate that only a 5.0% variation in the segmentation process leads to statistically significant differences in all 4 biomechanical measurements. These results suggest that it is crucial for consistent segmentation procedures to be applied to all specimens within a study. This methodological advancement will help to ensure that finite element data will be more accurate and that research conclusions will have greater validity.

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.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

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.

Increase of resting muscle stiffness, a less considered component of age-related skeletal muscle impairment

Elderly people perform more slowly movements of everyday life as rising from a chair, walking, and climbing stairs. This is in the first place due to the loss of muscle contractile force which is even more pronounced than  the loss of muscle mass. In addition, a secondary, but not negligible, component is the rigidity or increased stiffness which requires greater effort to produce the same movement and limits the range of motion of the joints. In this short review, we discuss the possible determinants of the limitations of joint mobility in healthy elderly, starting with the age-dependent alterations of the articular structure and focusing on the increased stiffness of the skeletal muscles. Thereafter, the possible mechanisms of the increased stiffness of the muscle-tendon complex are considered, among them changes in the muscle fibers, alterations of the connective components (extracellular matrix or ECM, aponeurosis, fascia and tendon) and remodeling of the neural pattern of muscle activation with increased of antagonist co-activation.

Increase of resting muscle stiffness, a less considered component of age-related skeletal muscle impairment

Elderly people perform more slowly movements of everyday life as rising from a chair, walking, and climbing stairs. This is in the first place due to the loss of muscle contractile force which is even more pronounced than the loss of muscle mass. In addition, a secondary, but not negligible, component is the rigidity or increased stiffness which requires greater effort to produce the same movement and limits the range of motion of the joints. In this short review, we discuss the possible determinants of the limitations of joint mobility in healthy elderly, starting with the age-dependent alterations of the articular structure and focusing on the increased stiffness of the skeletal muscles. Thereafter, the possible mechanisms of the increased stiffness of the muscle-tendon complex are considered, among them changes in the muscle fibers, alterations of the connective tissue components, i.e., extracellular matrix (ECM), aponeurosis, tendon and fascia, and remodeling of the neural pattern of muscle activation that increases antagonist co-activation.

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.

Thirty years of translational research in Mobility Medicine: Collection of abstracts of the 2020 Padua Muscle Days

More than half a century of skeletal muscle research is continuing at Padua University (Italy) under the auspices of the Interdepartmental Research Centre of Myology (CIR-Myo), the European Journal of Translational Myology (EJTM) and recently also with the support of the A&CM-C Foundation for Translational Myology, Padova, Italy. The Volume 30(1), 2020 of the EJTM opens with the collection of abstracts for the conference "2020 Padua Muscle Days: Mobility Medicine 30 years of Translational Research". This is an international conference that will be held between March 18-21, 2020 in Euganei Hills and Padova in Italy. The abstracts are excellent examples of translational research and of the multidimensional approaches that are needed to classify and manage (in both the acute and chronic phases) diseases of Mobility that span from neurologic, metabolic and traumatic syndromes to the biological process of aging. One of the typical aim of Physical Medicine and Rehabilitation is indeed to reduce pain and increase mobility enough to enable impaired persons to walk freely, garden, and drive again. The excellent contents of this Collection of Abstracts reflect the high scientific caliber of researchers and clinicians who are eager to present their results at the PaduaMuscleDays. A series of EJTM Communications will also add to this preliminary evidence.

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.

A finite element analysis of diaphragmatic hernia repair on an animal model

The diaphragm is a mammalian skeletal muscle that plays a fundamental role in the process of respiration. Alteration of its mechanical properties due to a diaphragmatic hernia contributes towards compromising its respiratory functions, leading to the need for surgical intervention to restore the physiological conditions by means of implants. This study aims to assess via numerical modeling biomechanical differences between a diaphragm in healthy conditions and a herniated diaphragm surgically repaired with a polymeric implant, in a mouse model. Finite Element models of healthy and repaired diaphragms are developed from diagnostic images and anatomical samples. The mechanical response of the diaphragmatic tendon is described by assuming an isotropic hyperelastic model. A similar constitutive model is used to define the mechanical behavior of the polymeric implant, while the muscular tissue is modeled by means of a three-element Hill's model, specifically adapted to mouse muscle fibers. The Finite Element Analysis is addressed to simulate diaphragmatic contraction in the eupnea condition, allowing the evaluation of diaphragm deformation in healthy and herniated-repaired conditions. The polymeric implant reduces diaphragm excursion compared to healthy conditions. This explains the possible alteration in the mechanical functionality of the repaired diaphragm. Looking to the surgical treatment of diaphragmatic hernia in human neonatal subjects, this study suggests the implementation of alternative approaches based on the use of biological implants.