A framework for structured modeling of skeletal muscle

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.

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.

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.

Modeling Skeletal Muscle Stress and Intramuscular Pressure: A Whole Muscle Active-Passive Approach

Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.

An Efficient Inverse Dynamics Optimization Formulation for Musculoskeletal Motion Prediction

In this study, an inverse dynamics optimization formulation and solution procedure is developed for musculoskeletal simulations. The proposed method has three main features: high order recursive B-spline interpolation, partition of unity, and inverse dynamics formulation. First, joint angle and muscle force profiles are represented by recursive B-splines. The formula for high order recursive B-spline derivatives are derived for state variables calculation. Second, partition of unity is used to handle the multi-contact indeterminacy between human and environment during the motion. The global forces and moments are distributed to each contacting point through the corresponding partition ratio. Third, joint torques are inversely calculated from equations of motion based on state variables and contacts to avoid numerical integration of equations of motion. Therefore, the design variables for the optimization problem are joint angle control points, muscle force control points, knot vector, and partition ratios for contacting points. The sum of muscle stress/activity squared is minimized as the cost function. The constraints are imposed for human physical constraints and task-based constraints. The proposed formulation is demonstrated by simulating a trajectory planning problem of a planar musculoskeletal arm with six muscles. In addition, the gait motion of a two-dimensional musculoskeletal model with sixteen muscles is also optimized by using the approach developed in this paper. The gait optimal solution is obtained in about 1 minute CPU time. The predicted kinematics, kinetics, and muscle forces have general trends that are similar to those reported in the literature.

A continuum-mechanical skeletal muscle model including actin-titin interaction predicts stable contractions on the descending limb of the force-length relation

Contractions on the descending limb of the total (active + passive) muscle force-length relationship (i. e. when muscle stiffness is negative) are expected to lead to vast half-sarcomere-length inhomogeneities. This is however not observed in experiments-vast half-sarcomere-length inhomogeneities can be absent in myofibrils contracting in this range, and initial inhomogeneities can even decrease. Here we show that the absence of half-sarcomere-length inhomogeneities can be predicted when considering interactions of the semi-active protein titin with the actin filaments. Including a model of actin-titin interactions within a multi-scale continuum-mechanical model, we demonstrate that stability, accurate forces and nearly homogeneous half-sarcomere lengths can be obtained on the descending limb of the static total force-length relation. This could be a key to durable functioning of the muscle because large local stretches, that might harm, for example, the transverse-tubule system, are avoided.

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.

Three-dimensional finite element analysis of unilateral mastication in malocclusion cases using cone-beam computed tomography and a motion capture system

Purpose

Stress distribution and mandible distortion during lateral movements are known to be closely linked to bruxism, dental implant placement, and temporomandibular joint disorder. The present study was performed to determine stress distribution and distortion patterns of the mandible during lateral movements in Class I, II, and III relationships.

Methods

Five Korean volunteers (one normal, two Class II, and two Class III occlusion cases) were selected. Finite element (FE) modeling was performed using information from cone-beam computed tomographic (CBCT) scans of the subjects’ skulls, scanned images of dental casts, and incisor movement captured by an optical motion-capture system.

Results

In the Class I and II cases, maximum stress load occurred at the condyle of the balancing side, but, in the Class III cases, the maximum stress was loaded on the condyle of the working side. Maximum distortion was observed on the menton at the midline in every case, regardless of loading force. The distortion was greatest in Class III cases and smallest in Class II cases.

Conclusions

The stress distribution along and accompanying distortion of a mandible seems to be affected by the anteroposterior position of the mandible. Additionally, 3-D modeling of the craniofacial skeleton using CBCT and an optical laser scanner and reproduction of mandibular movement by way of the optical motion-capture technique used in this study are reliable techniques for investigating the masticatory system.

Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli

Skeletal muscle undergoes continuous turnover to adapt to changes in its mechanical environment. Overload increases muscle mass, whereas underload decreases muscle mass. These changes are correlated with, and enabled by, structural alterations across the molecular, subcellular, cellular, tissue, and organ scales. Despite extensive research on muscle adaptation at the individual scales, the interaction of the underlying mechanisms across the scales remains poorly understood. Here, we present a thorough review and a broad classification of multiscale muscle adaptation in response to a variety of mechanical stimuli. From this classification, we suggest that a mathematical model for skeletal muscle adaptation should include the four major stimuli, overstretch, understretch, overload, and underload, and the five key players in skeletal muscle adaptation, myosin heavy chain isoform, serial sarcomere number, parallel sarcomere number, pennation angle, and extracellular matrix composition. Including this information in multiscale computational models of muscle will shape our understanding of the interacting mechanisms of skeletal muscle adaptation across the scales. Ultimately, this will allow us to rationalize the design of exercise and rehabilitation programs, and improve the long-term success of interventional treatment in musculoskeletal disease.

Anisotropic Compressive Properties of Passive Porcine Muscle Tissue

The body has approximately 434 muscles, which makes up 40–50% of the body by weight. Muscle is hierarchical in nature and organized in progressively larger units encased in connective tissue. Like many soft tissues, muscle has nonlinear visco-elastic behavior, but muscle also has unique characteristics of excitability and contractibility. Mechanical testing of muscle has been done for crash models, pressure sore models, back pain, and other disease models. The majority of previous biomechanical studies on muscle have been associated with tensile properties in the longitudinal direction as this is muscle's primary mode of operation under normal physiological conditions. Injury conditions, particularly high rate injuries, can expose muscle to multiple stress states. Compressive stresses can lead to tissue damage, which may not be reversible. In this study, we evaluate the structure–property relationships of porcine muscle tissue under compression, in both the transverse and longitudinal orientations at 0.1 s−1, 0.01 s−1, or 0.001 s−1. Our results show an initial toe region followed by an increase in stress for muscle in both the longitudinal and transverse directions tested to 50% strain. Strain rate dependency was also observed with the higher strain rates showing significantly more stress at 50% strain. Muscle in the transverse orientation was significantly stiffer than in the longitudinal orientation indicating anisotropy. The mean area of fibers in the longitudinal orientation shows an increasing mean fiber area and a decreasing mean fiber area in the transverse orientation. Data obtained in this study can help provide insight on how muscle injuries are caused, ranging from low energy strains to high rate blast events, and can also be used in developing computational injury models.

Realization of masticatory movement by 3-dimensional simulation of the temporomandibular joint and the masticatory muscles

Masticatory muscles are closely involved in mastication, pronunciation, and swallowing, and it is therefore important to study the specific functions and dynamics of the mandibular and masticatory muscles. However, the shortness of muscle fibers and the diversity of movement directions make it difficult to study and simplify the dynamics of mastication. The purpose of this study was to use 3-dimensional (3D) simulation to observe the functions and movements of each of the masticatory muscles and the mandible while chewing. To simulate the masticatory movement, computed tomographic images were taken from a single Korean volunteer (30-year-old man), and skull image data were reconstructed in 3D (Mimics; Materialise, Leuven, Belgium). The 3D-reconstructed masticatory muscles were then attached to the 3D skull model. The masticatory movements were animated using Maya (Autodesk, San Rafael, CA) based on the mandibular motion path. During unilateral chewing, the mandible was found to move laterally toward the functional side by contracting the contralateral lateral pterygoid and ipsilateral temporalis muscles. During the initial mouth opening, only hinge movement was observed at the temporomandibular joint. During this period, the entire mandible rotated approximately 13 degrees toward the bicondylar horizontal plane. Continued movement of the mandible to full mouth opening occurred simultaneously with sliding and hinge movements, and the mandible rotated approximately 17 degrees toward the center of the mandibular ramus. The described approach can yield data for use in face animation and other simulation systems and for elucidating the functional components related to contraction and relaxation of muscles during mastication.

A Multilevel Hierarchical Finite Element Model for Capillary Failure in Soft Tissue

Bruising, the result of capillary failure due to trauma, is a common indication of abuse. However, the etiology of capillary failure has yet to be determined as the scale change from tissue to capillary represents several orders of magnitude. As a first step toward determining bruise etiology, we have developed a multilevel hierarchical finite element model (FEM) of a portion of the upper human arm using a commercial finite element tool and a series of three interconnected hierarchical submodels. The third and final submodel contains a portion of the muscle tissue in which a single capillary is embedded. Nonlinear, hyperelastic material properties were applied to skin, adipose, muscle, and capillary wall materials. A pseudostrain energy method was implemented to subtract rigid-body-like motion of the submodel volume experienced in the global model, and was critical for convergence and successful analyses in the submodels. The deformation and hoop stresses in the capillary wall were determined and compared with published capillary failure stress. For the dynamic load applied to the skin of the arm (physiologically simulating a punch), the model predicted that approximately 8% volume fraction of the capillary wall was above the reference capillary failure stress, indicating bruising would likely occur.

A 3D electro-mechanical continuum model for simulating skeletal muscle contraction

A thermodynamically consistent three-dimensional electro-mechanical continuum model for simulating skeletal muscle contraction is presented. Active and passive responses are accounted for by means of a decoupled strain energy function into passive and active contributions. The active force is obtained as the maximum tetanic force penalized by two functions that consider the external stimulus frequency and the overlap between actin and myosin filaments. Passive response is modelled by a transversely isotropic strain energy function. The robustness of the model is analyzed by means of finite element simulations that reproduce the one-dimensional isometric, concentric and eccentric contractions in a simplified model of a muscle. The model has also been implemented to reproduce isometric and concentric contractions on a three-dimensional finite element model of the rat tibialis anterior (TA) muscle. The finite element model was obtained from magnetic resonance imaging and the preferential directions associated with the collagen and muscular fibres were considered. The proposed model was able to reproduce the observed experimental response of the active force generated by the isolated rat TA muscle during isometric and concentric contractions. In addition, the predicted force-velocity relationship is in good agreement with experimental data reported for the fast-twitch extensor digitorum longus (e.d.l) muscle of male rats.

Intramuscular architecture of the autochthonous back muscles in humans

Many training concepts take muscle properties such as contraction speed or muscle topography into account to achieve an optimal training outcome. Thus far, the internal architecture of muscles has largely been neglected, although it is well known that parameters such as pennation angles or the lengths of fascicles but also the proportions of fleshy and tendinous fascicle parts have a major impact on the contraction behaviour of a muscle. Here, we present the most detailed description of the intramuscular fascicle architecture of the human perivertebral muscles available so far. For this, one adult male cadaver was studied. Our general approach was to digitize the geometry of each fascicle of the muscles of back proper (Erector spinae) - the Spinalis thoracis, Iliocostalis lumborum, Longissimus thoracis and the Multifidus thoracis et lumborum - and of the deep muscles of the abdomen - Psoas minor, Psoas major and Quadratus lumborum - during a layerwise dissection. Architectural parameters such as fascicle angles to the sagittal and the frontal planes as well as fascicle lengths were determined for each fascicle, and are discussed regarding their consequences for the function of the muscle. For example, compared with the other dorsovertebral muscles, the Longissimus thoracis can produce greater shortening distances because of its relatively long fleshy portions, and it can store more elastic energy due to both its relatively long fleshy and tendinous fascicle portions. The Quadratus lumborum was outstanding because of its many architectural subunits defined by distinct attachment sites and fascicle lengths. The presented database will improve biomechanical models of the human trunk by allowing the incorporation of anisotropic muscle properties such as the fascicle direction into finite element models. This information will help to increase our understanding of the functionality of the human back musculature, and may thereby improve future training concepts.

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.

A micromechanical model of skeletal muscle to explore the effects of fiber and fascicle geometry

Computational models of muscle generally lump the material properties of connective tissue, muscle fibers, and muscle fascicles together into one constitutive relationship that assumes a transversely isotropic microstructure. These models do not take into account how variations in the microstructure of muscle affect its macroscopic material properties. The goal of this work was to develop micromechanical models of muscle to determine the effects of variations in muscle microstructure on the macroscopic constitutive behavior. We created micromechanical models at the fiber and fascicle levels based on histological cross-sections of two rabbit muscles, the rectus femoris (RF) and the soleus, to determine the effects of microstructure geometry (fiber and fascicle shapes) on the along-fiber shear modulus of muscle. The two fiber-level models predicted similar macroscopic shear moduli (within 13.5% difference); however, the two fascicle-level models predicted very different macroscopic shear moduli (up to 161% difference). We also used the micromechanical models to test the assumption that the macroscopic properties of muscle are transversely isotropic about the fiber (or fascicle) direction. The fiber-level models exhibited behavior consistent with the transverse isotropy assumption; however, the fascicle-level models exhibited transversely anisotropic behavior. Micromechanical models, combined with fiber and fiber bundle mechanical experiments, are needed to understand how normal or pathological variations in microstructure give rise to the observed macroscopic behavior of muscle.

Modeling of skeletal muscle: the influence of tendon and aponeuroses compliance on the force-length relationship

The aim of this study was to investigate the influence of changing elastic properties of tendon and aponeuroses on force production and muscle geometry. A three-dimensional, structural, continuum mechanics model of the cat medial gastrocnemius was used for this purpose. Increasing compliance in tendon and aponeuroses caused a decrease in the peak isometric force and a shift of the force-length relationship to the right of the length axis (i.e. toward greater muscle lengths). This result can be explained with the stability condition of the force-length relationship which produced a history dependence of force production that is conceptually in agreement with experimental observations.

Computational model of the movement of the human muscles of mastication during opening and closing of the jaw

Muscle fibre bundles comprising the four major muscles of mastication in the human being were studied in cadavers. Markers were placed along each muscle fibre bundle by means of serial dissections. The 3D coordinates of each marker were tabulated and imported to Cinema 4D, a software animation program. Origins and insertions of each fibre bundle were also digitized and imported, as were the coordinates of the surface of the skull, the mandible and temporomandibular joint. It was then possible to visualize the movement of all relevant fibre bundles during the passive motions of the mandible. An animated film depicts the positions of all relevant muscle fibres during passive movement of the mandible. The properties of the masseter muscle were documented as a prototype for the eventual study of all the muscles of mastication. One can now proceed to study the inverse problem, namely the forces within each fibre bundle that actively generate mandibular motion. It is hoped that these studies will aid in the management of conditions affecting the temporomandibular joint.