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Computational modeling of damage in the hierarchical microstructure of skeletal muscles
Abstract
One of the skeletal muscle’s exceptional properties is its high damage tolerance in terms of its high toughness, which allows the muscle to withstand cracks of millimeter length while maintaining most of its strength (Taylor et al., 2012). In skeletal muscles, damage occurs on different hierarchical levels of the microstructure. We analyze the damage behavior on hierarchy levels 3 (muscle fiber) and 4 (fascicle) on which the most common serious muscle injuries occur. Our model captures damage initiation and rupture of activated muscle fibers resulting from eccentric contractions. We consider the interaction between muscle fibers and endomysium and investigate the influence of the components titin and endomysium on the mechanical behavior in pre-damaged fascicles. Endomysium generally transmits contractile forces. Our results show that high strains in pre-damaged fiber regions are not transferred by the endomysium and, thus, adjacent undamaged fibers are well protected. Moreover, the results show titin’s extraordinary stabilization properties of pre-damaged muscle fibers, so that macroscopic strains of fascicles are hardly reduced in case of strongly pre-damaged fibers and intact titin.
... At the submicron scale a sarcomere from the myofibril, its link to the endomysium, and the endomysium are shown. More specifically, several proteins actin, titin, myosin, troponin, tropomyosin, costameres, laminin, collagen IV, elastin and collagen I are represented] of parallel muscle fibers such as perfectly circular [46][47][48] (Fig. 2.C) or hexagonal [49,50] (Fig. 2.D). Perfectly circular arrangements are simple of use especially considering analytical homogenization methods, as these methods often consider elliptical or cylindrical fiber reinforced composites [51]. ...
... Usually, one macroscopic scale simulation is linked to several microscopic scale simulations. The hierarchical approach is implemented through the use of Finite Element Modeling for skeletal muscle homogenization [36,48,50,[55][56][57][58][59], mostly through the use of computational periodic homogenization [82] which requires the discretized microscopic scale geometry to be periodic in all space directions. Conversely, concurrent methods consider different scales simultaneously in different subvolumes of the same simulation and these scales may exchange information in hand-shake regions. ...
... Using Finite Element Modeling (FEM), Reproducing Kernel Particle Method (RKPM) [37], or analytical frameworks, muscle fibers are usually modeled by separate isotropic and anisotropic contributions. The isotropic behavior accounts for cellular components other than myofibrils and is usually represented by simple hyperelastic laws such as Neo-Hookean [47,48,50,55,56,60,76,87], second order Mooney Rivlin [58], Yeoh model [46,49], or a quadratic polynomial function [37]. ...
Purpose: From the myofibrils to the whole muscle scale, muscle micro-constituents exhibit passive and active mechanical properties, potentially coupled to electrical, chemical, and thermal properties. Experimental characterization of some of these properties is currently not available for all muscle constituents. Multiscale multiphysics models have recently gained interest as a numerical alternative to investigate the healthy and diseased physiological behavior of the skeletal muscle. Methods: This paper refers to the multiscale mechanical models proposed in the literature to investigate the mechanical properties and behavior of skeletal muscles. More specifically, we focus on the scale transition methods, constitutive laws and experimental data implemented in these models. Results: Using scale transition methods such as homogenization, coupled to appropriate constitutive behavior of the constituents, these models explore the mechanisms of ageing, myopathies, sportive injuries, and muscle contraction. Conclusion: Emerging trends include the development of multiphysics simulations and the coupling of modeling with the acquisition of experimental data at different scales, with increasing focus to little known constituents such as the extracellular matrix and the protein titin.
... At the submicron scale a sarcomere from the myofibril, its link to the endomysium, and the endomysium are shown. More specifically, several proteins actin, titin, myosin, troponin, tropomyosin, costameres, laminin, collagen IV, elastin and collagen I are represented] of parallel muscle fibers such as perfectly circular [46][47][48] (Fig. 2.C) or hexagonal [49,50] (Fig. 2.D). Perfectly circular arrangements are simple of use especially considering analytical homogenization methods, as these methods often consider elliptical or cylindrical fiber reinforced composites [51]. ...
... Usually, one macroscopic scale simulation is linked to several microscopic scale simulations. The hierarchical approach is implemented through the use of Finite Element Modeling for skeletal muscle homogenization [36,48,50,[55][56][57][58][59], mostly through the use of computational periodic homogenization [82] which requires the discretized microscopic scale geometry to be periodic in all space directions. Conversely, concurrent methods consider different scales simultaneously in different subvolumes of the same simulation and these scales may exchange information in hand-shake regions. ...
... Using Finite Element Modeling (FEM), Reproducing Kernel Particle Method (RKPM) [37], or analytical frameworks, muscle fibers are usually modeled by separate isotropic and anisotropic contributions. The isotropic behavior accounts for cellular components other than myofibrils and is usually represented by simple hyperelastic laws such as Neo-Hookean [47,48,50,55,56,60,76,87], second order Mooney Rivlin [58], Yeoh model [46,49], or a quadratic polynomial function [37]. ...
Abstract
Purpose : From the myofibrils to the whole muscle scale, muscle micro-constituents exhibit passive and active mechanical properties, potentially coupled to electrical, chemical, and thermal properties. Experimental characterization of some of these properties is currently not available for all muscle constituents. Multiscale multiphysics models have recently gained interest as a numerical alternative to investigate the healthy and diseased physiological behavior of the skeletal muscle.
Methods : This paper refers to the multiscale mechanical models proposed in the literature to investigate the mechanical properties and behavior of skeletal muscles. More specifically, we focus on the scale transition methods, constitutive laws and experimental data implemented in these models.
Results : Using scale transition methods such as homogenization, coupled to appropriate constitutive behavior of the constituents, these models explore the mechanisms of ageing, myopathies, sportive injuries, and muscle contraction.
Conclusion : Emerging trends include the development of multiphysics simulations and the coupling of modeling with the acquisition of experimental data at different scales, with increasing focus to little known constituents such as the extracellular
matrix and the protein titin.
... This question is very challenging to answer through experiments alone; however, computational modelling empowers us to precisely examine how microstructural variations contribute to macroscopic tissue properties. Previous micromechanical models generated from images of muscle cross-sections [21] and using Voronoi tessellation [22] examined how variation in muscle fibre and fascicle geometries influence tissue behaviour [21,23] and focused on cases such as damage [24] and ageing [25]. Micromechanical models that simulated changes in microstructure seen in DMD found that the effect of increased ECM area fraction was highly dependent on the stiffness of the ECM [26]. ...
... Micromechanical models that simulated changes in microstructure seen in DMD found that the effect of increased ECM area fraction was highly dependent on the stiffness of the ECM [26]. These models provided key insights but simplify the representation of the ECM as isotropic [24], transversely isotropic aligned with muscle fibres [21,26], or use a generalized helical assumption to represent collagen direction [22,23,25]. Therefore, they do not account for distinct ECM layers or incorporate the ability to examine the role of changes in collagen microstructure on muscle tissue properties. ...
... Therefore, they do not account for distinct ECM layers or incorporate the ability to examine the role of changes in collagen microstructure on muscle tissue properties. These models also rely on integrating measurements from several studies across different skeletal muscle groups [22][23][24][25], so it would be impossible to use these models to answer specific questions about variations in the structure and function of a particular muscle. ...
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.
... 36 In particular, ST coupled with a distal compliant tendon, and given its parallel fiber arrangement, may lower the risk of muscle strain injuries. 5,8,37 On the contrary, the BF connected to a stiffer distal tendon and characterized by its pennated fiber orientation, is more susceptible to strain injuries, especially when subjected to high force and multiaxial loading conditions. 5,8,37 However, others have suggested that a reduction in tendon compliance could contribute to an increase in injury risk during sprinting, unless the changes in running posture enable the musculotendon complex to function at a shorter length. ...
... 5,8,37 On the contrary, the BF connected to a stiffer distal tendon and characterized by its pennated fiber orientation, is more susceptible to strain injuries, especially when subjected to high force and multiaxial loading conditions. 5,8,37 However, others have suggested that a reduction in tendon compliance could contribute to an increase in injury risk during sprinting, unless the changes in running posture enable the musculotendon complex to function at a shorter length. 6 Despite the similar morphological characteristics and tendon properties with the SM, the BFlh is more susceptible to injury due to greater changes in MTU length during sprinting. ...
Tendon properties impact human locomotion, influencing sports performance, and injury prevention. Hamstrings play a crucial role in sprinting, particularly the biceps femoris long head (BFlh), which is prone to frequent injuries. It remains uncertain if BFlh exhibits distinct mechanical properties compared to other hamstring muscles. This study utilized free‐hand three‐dimensional ultrasound to assess morphological and mechanical properties of distal hamstrings tendons in 15 men. Scans were taken in prone position, with hip and knee extended, at rest and during 20%, 40%, 60%, and 80% of maximal voluntary isometric contraction of the knee flexors. Tendon length, volume, cross‐sectional area (CSA), and anteroposterior (AP) and mediolateral (ML) widths were quantified at three locations. Longitudinal and transverse deformations, stiffness, strain, and stress were estimated. The ST had the greatest tendon strain and the lowest stiffness as well as the highest CSA and AP and ML width strain compared to other tendons. Biceps femoris short head (BFsh) exhibited the least strain, AP and ML deformation. Further, BFlh displayed the highest stiffness and stress, and BFsh had the lowest stress. Additionally, deformation varied by region, with the proximal site showing generally the lowest CSA strain. Distal tendon mechanical properties differed among the hamstring muscles during isometric knee flexions. In contrast to other bi‐articular hamstrings, the BFlh high stiffness and stress may result in greater energy absorption by its muscle fascicles, rather than the distal tendon, during late swing in sprinting. This could partly account for the increased incidence of hamstring injuries in this muscle.
... Besides the basic modeling of physiologically realistic behavior of healthy skeletal muscle, the study of specific (pathological) biological processes is an ongoing research topic. Examples include models for damage [96], fatigue [18,19] and age-related loss of activation [97]. ...
The shoulder joint is one of the functionally and anatomically most sophisticated articular systems in the human body. Both complex movement patterns and the stabilization of the highly mobile joint rely on intricate three-dimensional interactions among various components. Continuum-based finite element models can capture such complexity, and are thus particularly relevant in shoulder biomechanics. Considering their role as active joint stabilizers and force generators, skeletal muscles require special attention regarding their constitutive description. In this contribution, we propose a constitutive description to model active skeletal muscle within complex musculoskeletal systems, focusing on a novel continuum shoulder model. We thoroughly review existing material models before analyzing three selected ones in detail: an active-stress, an active-strain, and a generalized active-strain approach. To establish a basis for comparison, we identify the material parameters based on experimental stress-strain data obtained under various active and passive loading conditions. We discuss the concepts to incorporate active contractile behavior from a mathematical and physiological perspective, address analytical and numerical challenges arising from the mathematical formulations, and analyze the included biophysical principles of force generation in terms of physiological correctness and relevance for human shoulder modeling. Based on these insights, we present an improved constitutive model combining the studied models' most promising and relevant features. Using the example of a fusiform muscle, we investigate force generation, deformation, and kinematics during active isometric and free contractions. Eventually, we demonstrate the applicability of the suggested material model in a novel continuum mechanical model of the human shoulder.
... Different material models can be used for the models on each hierarchical level generated by the Python codes to model different physical processes on the microstructure, e.g. the chemoelectromechanical behavior during muscle fiber activation [15] or the damage behavior of muscle fibers [16]. ...
Python codes are provided for generating computer models of the skeletal muscle on all five hierarchical levels. All scripts are parametrized to generate a large variation of muscle structures. On hierarchical levels 3 (muscle fiber), 4 (fascicle) and 5 (muscle), we use Voronoi tessellation in combination with the sunflower seed arrangement to obtain fiber–matrix-composite models with similar-sized fibers having polygonal cross-sections. The muscle and its microstructure can be studied at a given length scale or in multiscale analysis. The codes provide the basis for a large variety of possible FEM simulations of different phenomena due to full parametrization and flexibility.
A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues suitable at high pressures and low to very high strain rates. Tissues consist of one or more solid and fluid phases and can demonstrate nonlinear anisotropic elastic, viscoelastic, thermoelastic, and poroelastic physics. Under extreme deformations or shock loading, tissues may fracture, tear, or rupture. Existing models do not account for all physics simultaneously, and most poromechanics and soft-tissue models assume incompressibility of some or all constituents, generally inappropriate for modeling shock waves or extreme compressions. Motivated by these prior limitations, a thermodynamically consistent formulation that combines a continuum theory of mixtures, compressible nonlinear anisotropic thermoelasticity, viscoelasticity, and phase-field mechanics of fracture is constructed to resolve the pertinent physics. A metric tensor of generalized Finsler space supplies geometric insight on effects of rearrangements of microstructure, for example degradation, growth, and remodeling. Shocks are modeled as singular surfaces. Hugoniot states and shock decay are analyzed: Solutions account for concurrent viscoelasticity, fracture, and interphase momentum and energy exchange not all contained in previous analyses. Suitability of the framework for representing blood, skeletal muscle, and liver is demonstrated by agreement with experimental data and observations across a range of loading rates and pressures. Insight into previously unresolved physics is obtained, for example importance of rate sensitivity of damage and quantification of effects of dissipation from viscoelasticity and phase interactions on shock decay.
Consistent and reasonable characterization of the material behavior under the coupled effects of strain, strain rate and temperature on the material flow stress is remarkably crucial in order to design as well as optimize the process parameters in the metal forming industrial practice. The objective of this work was to formulate an appropriate flow stress model to characterize the flow behavior of AISI-1045 medium carbon steel over a practical range of deformation temperatures (650–950 ∘ C) and strain rates (0.05–1.0 s − 1 ). Subsequently, the Johnson-Cook flow stress model was adopted for modeling and predicting the material flow behavior at elevated temperatures. Furthermore, surrogate models were developed based on the constitutive relations, and the model constants were estimated using the experimental results. As a result, the constitutive flow stress model was formed and the constructed model was examined systematically against experimental data by both numerical and graphical validations. In addition, to predict the material damage behavior, the failure model proposed by Johnson and Cook was used, and to determine the model parameters, seven different specimens, including flat, smooth round bars and pre-notched specimens, were tested at room temperature under quasi strain rate conditions. From the results, it can be seen that the developed model over predicts the material behavior at a low temperature for all strain rates. However, overall, the developed model can produce a fairly accurate and precise estimation of flow behavior with good correlation to the experimental data under high temperature conditions. Furthermore, the damage model parameters estimated in this research can be used to model the metal forming simulations, and valuable prediction results for the work material can be achieved.
Muscle strain injury and exercise‐induced muscle damage have been described as a continuum of injury whereby micro tears (muscle damage) lead to muscle strain injury. However, the clinical scenario is one of two mutually exclusive conditions that differ markedly in terms of site of injury, mechanism of injury, associated symptoms, repair process, and re‐injury rate. Muscle strain injury is a tearing of muscle fibers close to the muscle‐tendon junction during the application of a single tensile load, with sudden debilitating symptoms, and a subsequent repair process that is slow, and often incomplete, resulting in a high risk of recurrence. Exercise‐induced muscle damage is a disruption to myofibrils that occurs gradually during eccentrically biased exercise, resulting in delayed symptoms, that typically resolve uneventfully, with a repair process that makes the muscle resistant to a recurrence of damage. Thus muscle strain injury and exercise‐induced muscle damage should be viewed as mutually exclusive clinical entities.
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A novel multiscale modeling framework for skeletal muscles based on analytical and numerical homogenization methods is presented to study the mechanical muscle response at finite strains under three-dimensional loading conditions. First an analytical microstructure-based constitutive model is developed and numerically implemented in a general purpose finite element program. The analytical model takes into account explicitly the volume fractions, the material properties, and the spatial distribution of muscle's constituents by using homogenization techniques to bridge the different length scales of the muscle structure. Next, a numerical homogenization model is developed using periodic eroded Voronoi tessellation to virtually represent skeletal muscle microstructures. The eroded Voronoi unit cells are then resolved by finite element simulations and are used to assess the analytical homogenization model. The material parameters of the analytical model are identified successfully by use of available experimental data. The analytical model is found to be in very good agreement with the numerical model for the full range of loadings, and a wide range of different volume fractions and heterogeneity contrasts between muscle's constituents. A qualitative application of the model on fusiform and pennate muscle structures shows its efficiency to examine the effect of muscle fiber concentration variations in an organ-scale model simulation.
New Biomechatronics-Multiphoton Microscopy predicts the degree of muscle weakness from the cellular structure in 3D A laser-scanning multiphoton microscope that diagnoses cellular-level structural defects in skeletal muscle in 3D has been combined with a miniaturized biomechatronics diagnostic machine developed by German researchers. Structural changes to muscle cells, such as the branching and splitting of individual fibers, or subcellular remodeling of cellular skeleton, have been associated with degenerative ailments in patients. Now, Oliver Friedrich at the Friedrich-Alexander-University in Erlangen and colleagues have developed a technique that links the force a muscle cell can apply with its cellular architecture. The team used a special version of multiphoton microscopy, Second Harmonic Generation, to examine single muscle fibers extracted from wild type mice or muscular dystrophy ones carrying a mutation in the dystrophin gene. Simultaneously, an automated system measures the mechanical properties of contractions induced by defined concentrations of calcium ions, or how fibers react to passive stress. Computer analysis yielded linear correlations between optical images and muscle function that may be useful in predicting biomechanical disease in patients from optical assessment of patient biopsies using multiphoton imaging.
This work reviews state of the art representative volume element (RVE) generation techniques for heterogeneous materials. To this end, we present a systematic classification considering a wide range of heterogeneous materials of engineering interest. Here, we divide heterogeneous solids into porous and non-porous media, with 0 < void volume fraction < 1 and void volume fraction = 0, respectively. Further subdivisions are realized based on various morphological features. The corresponding generation methods are classified into three categories: (i) experimental methods targeting reconstruction through experimental characterization of the microstructure, (ii) physics based methods targeting simulation of the physical process(es) responsible for the microstructure formation and evolution, and (iii) geometrical methods concentrating solely on mimicking the morphology (ignoring the physical basis of the microstructure formation process). These comprise of various mathematical tools such as digital image correlation, tessellation, random field generation, differential equation solvers, etc. For completeness, relevant up-to-date software tools, used at various stages of RVE generation — either commercial or open-source — are summarized. Considered methods are reviewed based on their efficiency and predictive performance with respect to geometrical and topological properties of the microstructures.
In contrast to experimentally observed progressive forces in eccentric contractions, cross-bridge and sliding-filament theories of muscle contraction predict that varying myofilament overlap will lead to increases and decreases in active force during eccentric contractions. Non-cross-bridge contributions potentially explain the progressive total forces. However, it is not clear whether underlying abrupt changes in the slope of the nonlinear force-length relationship are visible in long isokinetic stretches, and in which proportion cross-bridges and non-cross-bridges contribute to muscle force. Here, we show that maximally activated single skinned rat muscle fibres behave (almost across the entire working range) like linear springs. The force slope is about three times the maximum isometric force per optimal length. Cross-bridge and non-cross-bridge contributions to the muscle force were investigated using an actomyosin inhibitor. The experiments revealed a nonlinear progressive contribution of non-cross-bridge forces and suggest a nonlinear cross-bridge contribution similar to the active force-length relationship (though with increased optimal length and maximum isometric force). The linear muscle behaviour might significantly reduce the control effort. Moreover, the observed slight increase in slope with initial length is in accordance with current models attributing the non-cross-bridge force to titin.
Background
To ensure adequate function after orthopedic tumor reconstruction, it is important to reattach the remaining soft tissue to the implant. This study aimed at obtaining mechanical properties of textile muscle-implant and muscle-bone connections in a preliminary test.
Methods
Two groups of soft-tissue attachment were mechanically tested and compared: Native bone-muscle samples obtained from human femora and muscles attached to a prosthetic implant by means of Trevira® attachment tubes. Additionally, muscle samples were tested with muscle fibers aligned parallel and perpendicular to the tension load. A uniaxial load was exerted upon all samples.
Results
Failure loads of 26.7 ± 8.8 N were observed for the native bone-muscle group and of 18.1 ± 9.9 N for the Trevira® group. Elongations of 94.8 ± 36.2 % were observed for the native bone-muscle group and 79.3 ± 51.8 % for the Trevira® group. The location of failure was mainly observed in the central area of the muscle fibers. Muscle fibers with parallel fiber orientation (47.6 ± 11.5 N) yielded higher tensile strength than those with perpendicular fiber orientation (14.8 ± 4.1 N).
Conclusions
Our experiments showed that higher forces were transmitted in the origin and insertion areas than in areas of flat soft tissue reconstruction using attachment tubes. The data indicate that the tested material allows reattaching muscles, but without reinforcing the insertion site. Therefore, attachment tubes with region-dependent and potentially anisotropic material behavior might be advantageous to optimize muscle-bone load transmission after surgery, which may allow lower complication rates and shorter physical recovery.
Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin–myosin interactions, force enhancement based on actin–titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin’s free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle’s cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle’s cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.
Background:
Existing studies have included little discussion of anisotropic and material non linearity of muscle tissue, and fiber orientation-based material properties of skeletal muscle tissue are not reported well in literature. There has been some dispute about material response of muscle in different fiber directions. It is necessary to have a better understanding of fiber orientation based material properties of skeletal muscle, to ensure the accuracy of computational models of muscle. To this end, the aim of this study was to investigate fiber orientation-based material properties in vitro and simulate them with finite element analysis (FEA).
Methods:
Tensile testing was performed on 5 samples of skeletal muscle from a goat at a strain rate of 0.15 s-1 with fiber orientation along the length (P) and 45° incline to the fiber direction (I). FEA was completed using the experimental condition to validate the results of the in vitro test. The cross-fiber direction was simulated using FEA.
Results:
The stresses for all fiber directions at maximum stretch were 1,973.2 kPa for fiber direction P, 1,172 kPa for direction I and 430 kPa for the cross-fiber direction. The tensile strengths of the skeletal muscle were 0.44 MPa for P and 0.234 MPa for I. The elastic modulus of muscle tissue in all fiber directions was 1.59 MPa for fiber direction P (Ep), 0.621 MPa for 45° direction I (EI) and 0.43 MPa for the cross-fiber direction (Ec). The displacement of the muscle sample against the maximum load was small along the fiber direction. The results of the present study showed that muscle tissue was stiffer in the fiber direction than in the cross-fiber direction.
Conclusions:
The stiffness of skeletal muscle is changed as the fiber orientation of skeletal muscle tissue changed.
Computational models have been increasingly used to study the tissue-level constitutive properties of muscle microstructure; however, these models were not created to study or incorporate the influence of disease-associated modifications in muscle. The purpose of this paper was to develop a novel multiscale muscle modelling framework to elucidate the relationship between microstructural disease adaptations and modifications in both mechanical properties of muscle and strain in the cell membrane. We used an agent-based model to randomly generate new muscle fibre geometries and mapped them into a finite-element model representing a cross section of a muscle fascicle. The framework enabled us to explore variability in the shape and arrangement of fibres, as well as to incorporate disease-related changes. We applied this method to reveal the trade-offs between mechanical properties and damage susceptibility in Duchenne muscular dystrophy (DMD). DMD is a fatal genetic disease caused by a lack of the transmembrane protein dystrophin, leading to muscle wasting and death due to cardiac or pulmonary complications. The most prevalent microstructural variations in DMD include: lack of transmembrane proteins, fibrosis, fatty infiltration and variation in fibre cross-sectional area. A parameter analysis of these variations and case study of DMD revealed that the nature of fibrosis and density of transmembrane proteins strongly affected the stiffness of the muscle and susceptibility to membrane damage.
Braided pneumatic artificial muscles, and in particular the better known type with a double helical braid usually called the McKibben muscle, seem to be at present the best means for motorizing robot-arms with artificial muscles. Their ability to develop high maximum force associated with lightness and a compact cylindrical shape, as well as their analogical behavior with natural skeletal muscle were very well emphasized in the 1980s by the development of the Bridgestone “soft robot” actuated by “rubbertuators”. Recent publications have presented ways for modeling McKibben artificial muscle as well as controlling its highly non-linear dynamic behavior. However, fewer studies have concentrated on analyzing the integration of artificial muscles with robot-arm architectures since the first Bridgestone prototypes were designed. In this paper we present the design of a 7R anthropomorphic robot-arm entirely actuated by antagonistic McKibben artificial muscle pairs. The validation of the robot-arm architecture was performed in a teleoperation mode.
An extensible, flexible, multiscale, and multiphysics model for nonisometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-of-the-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum flexibility, reproducibility, and extensibility. The results demonstrate the model's capability of simulating different aspects of nonisometric muscle contraction and efficiently simulating the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.
The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening. In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges. Incorporation of a simple 'sticky-spring' mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.
In skeletal muscle fibers, forces must be transmitted between the plasma membrane and the intracellular contractile lattice, and within this lattice between adjacent myofibrils. Based on their prevalence, biomechanical properties and localization, desmin and keratin intermediate filaments (IFs) are likely to participate in structural connectivity and force transmission. We examined the passive load-bearing response of single fibers from the extensor digitorum longus (EDL) muscles of young (3 months) and aged (10 months) wild-type, desmin-null, K19-null, and desmin/K19 double-null mice. Though fibers are more compliant in all mutant genotypes compared to wild-type, the structural response of each genotype is distinct, suggesting multiple mechanisms by which desmin and keratin influence the biomechanical properties of myofibers. This work provides additional insight into the influences of IFs on structure-function relationships in skeletal muscle. It may also have implications for understanding the progression of desminopathies and other IF-related myopathies.
Braided pneumatic artificial muscles, and in particular the better known type with a double helical braid usually called the McKibben muscle, seem to be at present the best means for motorizing robot- arms with artificial muscles. Their ability to develop high maximum force associated with lightness and a compact cylindrical shape, as well as their analogical behavior with natural skeletal muscle were very well emphasized in the 1980s by the development of the Bridge- stone "soft robot" actuated by "rubbertuators". Recent publica- tions have presented ways for modeling McKibben artificial muscle as well as controlling its highly non-linear dynamic behavior. How- ever, fewer studies have concentrated on analyzing the integration of artificial muscles with robot-arm architectures since the first Bridge- stone prototypes were designed. In this paper we present the design of a 7R anthropomorphic robot-arm entirely actuated by antagonis- tic McKibben artificial muscle pairs. The validation of the robot-arm architecture was performed in a teleoperation mode. KEY WORDS—anthropomorphic robot-arm, artificial mus- cle, McKibben muscle
Tensile tests on single muscle fibres from raw and cooked porcine longissimus thoracis muscle were performed to explore the structural mechanisms responsible for their deformation and fracture properties. Measurements of load and deformation were made simultaneously with light microscopy observations of the structural changes which occur on extension. On extending the fibres to fracture, an r-shaped stress-strain curve was observed and the structural changes which occurred during this process could be divided into three phases. Phase one, was characterised by a rapid increase in stress with little change in strain and ended at the yield point. Sarcomere length was uniform along the fibre in this initial phase. Raw fibres yielded at strains of between 2 and 5% of their resting lengths and cooked fibres at strains of between 10 and 20%. In phase two, there was rapid increase in strain with minimal changes in stress. In most fibres this phase was characterised by multiple cracks on the fibre surface and unequal sarcomere stretching. Sarcomeres in the regions where the surface had ruptured extended faster than those in areas still covered by the surface membrane, where sarcomere length remained relatively unchanged. In some cooked fibres, there was little or no surface cracking and all the sarcomeres in these fibres extended almost uniformly. Phase three was characterised by a rise in stress as strain increased and then a final fall in stress at the breaking point. This was accompanied by myofibrillar failure and finally breakage of the whole fibre. The myofibrils did not always fail as one unit; a progressive snapping of small bundles of myofibrils was seen in some raw fibres. Muscle fibres could be stretched to 10·9 ± 1·45% of their resting length before breaking when raw, but to 130 ± 42% of their rest lengths after they were cooked for 1 h at 80°C.
The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.
Recent studies have demonstrated a role for the elastic protein titin in active muscle, but the mechanisms by which titin plays this role remain to be elucidated. In active muscle, Ca(2+)-binding has been shown to increase titin stiffness, but the observed increase is too small to explain the increased stiffness of parallel elastic elements upon muscle activation. We propose a 'winding filament' mechanism for titin's role in active muscle. First, we hypothesize that Ca(2+)-dependent binding of titin's N2A region to thin filaments increases titin stiffness by preventing low-force straightening of proximal immunoglobulin domains that occurs during passive stretch. This mechanism explains the difference in length dependence of force between skeletal myofibrils and cardiac myocytes. Second, we hypothesize that cross-bridges serve not only as motors that pull thin filaments towards the M-line, but also as rotors that wind titin on the thin filaments, storing elastic potential energy in PEVK during force development and active stretch. Energy stored during force development can be recovered during active shortening. The winding filament hypothesis accounts for force enhancement during stretch and force depression during shortening, and provides testable predictions that will encourage new directions for research on mechanisms of muscle contraction.
The classic view of skeletal muscle is that force is generated within its muscle fibers and then directly transmitted in-series, usually via tendon, onto the skeleton. In contrast, recent results suggest thatmuscles aremechanically connected to surrounding structures and cannot be considered as independent actuators. This article will review experiments on mechanical interactions between muscles mediated by such epimuscular myofascial force transmission in physiological and pathological muscle conditions. In a
reduced preparation, involving supraphysiological muscle conditions, it is shown that connective tissues surrounding muscles are capable of transmitting substantial force. Inmore physiologically relevant conditions of intactmuscles, however, it appears that the role of thismyofascial pathway is small. In addition, it is hypothesized that connective tissues can serve as a safety net for traumatic events in muscle or tendon. Future studies are needed to investigate the importance of intermuscular force transmission during
movement in health and disease.
To study the injury characteristics in professional football and to follow the variation of injury incidence during a match, during a season and over consecutive seasons.
Prospective cohort study where teams were followed for seven consecutive seasons. Team medical staff recorded individual player exposure and time-loss injuries from 2001 to 2008.
European professional men's football.
The first team squads of 23 teams selected by the Union of European Football Associations as belonging to the 50 best European teams.
Injury incidence.
4483 injuries occurred during 566 000 h of exposure, giving an injury incidence of 8.0 injuries/1000 h. The injury incidence during matches was higher than in training (27.5 vs 4.1, p<0.0001). A player sustained on average 2.0 injuries per season, and a team with typically 25 players can thus expect about 50 injuries each season. The single most common injury subtype was thigh strain, representing 17% of all injuries. Re-injuries constituted 12% of all injuries, and they caused longer absences than non re-injuries (24 vs 18 days, p<0.0001). The incidence of match injuries showed an increasing injury tendency over time in both the first and second halves (p<0.0001). Traumatic injuries and hamstring strains were more frequent during the competitive season, while overuse injuries were common during the preseason. Training and match injury incidences were stable over the period with no significant differences between seasons.
The training and match injury incidences were stable over seven seasons. The risk of injury increased with time in each half of matches.
Skeletal muscle architecture is defined as the arrangement of fibers in a muscle and functionally defines performance capacity. Architectural values are used to model muscle-joint behavior and to make surgical decisions. The two most extensively used human lower extremity data sets consist of five total specimens of unknown size, gender, and age. Therefore, it is critically important to generate a high-fidelity human lower extremity muscle architecture data set. We disassembled 27 muscles from 21 human lower extremities to characterize muscle fiber length and physiologic cross-sectional area, which define the excursion and force-generating capacities of a muscle. Based on their architectural features, the soleus, gluteus medius, and vastus lateralis are the strongest muscles, whereas the sartorius, gracilis, and semitendinosus have the largest excursion. The plantarflexors, knee extensors, and hip adductors are the strongest muscle groups acting at each joint, whereas the hip adductors and hip extensors have the largest excursion. Contrary to previous assertions, two-joint muscles do not necessarily have longer fibers than single-joint muscles as seen by the similarity of knee flexor and extensor fiber lengths. These high-resolution data will facilitate the development of more accurate musculoskeletal models and challenge existing theories of muscle design; we believe they will aid in surgical decision making.
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 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.
Lesions of the Musculotendinous Unit (MTU, i.e. tendon, myotendinous junction, muscle, aponeurosis and myoaponeurotic junction) are a common injury and a leading cause of functional impairment, long-term pain, and/or physical disability worldwide. Though a large effort has been devoted to macroscopic failure evaluation, these injuries suffer from a lack of knowledge of the underlying tissue-scale micro-mechanisms triggering such lesions. More specifically, there is a strong need for experimental data to better understand and quantify damage initiation and propagation on MTUs.
The present study presents original experimental data on muscle tissue extracted from the hamstring muscle group of rabbits under relevant mechanical solicitations up to rupture, revealing elementary micro-mechanisms and providing quantified values of elastic properties as well as initiation stress and energy release rate.
More specifically, tensile, peeling and shear lap tests were performed to explore cohesion of muscle tissue along the fibre direction or across fibres (mode I) and in shear (mode II), as well as at the muscle/tendon interface.
We show that muscle tissue is weaker in shear than tension (p-value < 0.01) and that the Biceps Femoris had the lowest energy release rate as calculated from mode I peeling tests (G = 0.23 ± 0.16 N/mm) compared to the Semi-Membranous (G = 0.53 ± 0.08 N/mm) and the Semi-Tendinous (0.45 ± 0.20 N/mm), and that this energy is the lowest at the musculotendinous junction.
Our study suggests a preferred damage initiation mechanism based on fibre decohesion in mode I or II and provides quantitative data to model these phenomena. Results also suggest that the Biceps Femoris and more precisely its musculotendinous junction could be the weakest point of the hamstring group.
These findings could be used as a basis to develop mechanical models (e.g. finite element) to better understand and predict the onset of hamstring lesions and help in preventing such events.
Active state titin’s effects have been studied predominantly in sarcomere or muscle fiber segment level and an understanding of its functional effects in the context of a whole muscle, and the mechanism of those is lacking. By representing experimentally observed calcium induced stiffening and actin-titin interaction induced reduced free spring length effects of active state titin in our linked fiber–matrix mesh finite element model, our aim was to study the mechanism of effects and particularly to determine the functionally more effective active state titin model. Isolated EDL muscle of the rat was modeled and three cases were studied: passive state titin (no change in titin constitutive equation in the active state), active state titin-I (constitutive equation involves a higher stiffness in the active state) and active state titin-II (constitutive equation also involves a strain shift coefficient accounting for titin’s reduced free spring length). Isometric muscle lengthening was imposed (initial to long length, lm=28.7mm to 32.7mm). Compared to passive state titin, (i) active state titin-I and II elevates muscle total (lm=32.7mm: 14% and 29%, respectively) and active (lm=32.7mm: 37.5% and 77.4%, respectively) forces, (ii) active state titin-II also shifts muscle’s optimum length to a longer length (lm=29.6mm), (iii) active state titin-I and II limits sarcomere shortening (lm=32.7mm: up to 10% and 20%, respectively). Such shorter sarcomere effect characterizes active state titin’s mechanism of effects. These effects become more pronounced and functionally more effective if not only calcium induced stiffening but also a reduced free spring length of titin is accounted for.
The mechanical behavior of the cortical bone in nanoindentation is a complicated mechanical problem. The finite element analysis has commonly been assumed to be the most appropriate approach to this issue. One significant problem in nanoindentation modeling of the elastic-plastic materials is pile-up deformation, which is not observed in cortical bone nanoindentation testing. This phenomenon depends on the work-hardening of materials; it doesn't occur for work-hardening materials, which suggests that the cortical bone could be considered as a work-hardening material. Furthermore, in a recent study [59], a plastic hardening until failure was observed on the micro-scale of a dry ovine osteonal bone samples subjected to micropillar compression. The purpose of the current study was to apply an isotropic hardening model in the finite element simulations of the nanoindentation of the cortical bone to predict its mechanical behavior. The Johnson-Cook (JC) model was chosen as the constitutive model. The finite element modeling in combination with numerical optimization was used to identify the unknown material constants and then the finite element solutions were compared to the experimental results. A good agreement of the numerical curves with the target loading curves was found and no pile-up was predicted. A Design Of Experiments (DOE) approach was performed to evaluate the linear effects of the material constants on the mechanical response of the material. The strain hardening modulus and the strain hardening exponent were the most influential parameters. While a positive effect was noticed with the Young's modulus, the initial yield stress and the strain hardening modulus, an opposite effect was found with the Poisson's ratio and the strain hardening exponent. Finally, the JC model showed a good capability to describe the elastoplastic behavior of the cortical bone.
This work presents a novel microstructurally-based, multi-scale model describing the passive behaviour of skeletal muscle tissue. The model is based on the detailed description of the mechanically relevant parts of the microstructure. The effective constitutive material response is obtained by a homogenisation of mechanical energies and stresses from the micro- to the macroscale. The key feature of the new model is that it does not require any constitutive assumptions or calibration on the macroscale. The effective mechanical response is a pure consequence of the stiffness and structural arrangement of microscopic components. In this sense, the model inherits its direction-dependent properties directly from the microstructure. This is achieved by employing a Voigt-type homogenisation and by utilising for the complex collageneous network of the extracellular matrix an angular integration method. For physiologically realistic microscopic model parameters, this model reveals that muscle tissue exhibits a tensile stiffness that is larger transverse to the muscle fibre than in muscle fibre direction. This highlights that muscle tissue in general does not obey a classical fibre-reinforcement solely for tensile stretches of the muscle fibres but rather a general transversely isotropic behaviour. Moreover, the formulation of the effective macroscopic energy is provided in terms of well-known macroscopic strain invariants, which allows for an easy application of the model in standard numerical settings.
An extensible, flexible, multiscale and multiphysics model for non-isometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers, and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-ofthe-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum on flexibility, reproducibility, and extensibility. The results demonstrate the model´s capability of simulating different aspects of non-isometric muscle contraction and to efficiently simulate the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle.
Traditional robotic/mechatronic design has successfully exploited the attributes of heavy mechanical systems engineering, but future scientific trends suggest a need for technology that will emulate natural systems - biomimetic operation. This drive for new bio-mimetic principles is particularly prevalent in actuator design. This work will explore the design, using biomimetic principles, of actuators for the bipedal section of a humanoid robot. The paper will consider the design and selection of actuators and their incorporation into the legs of the humanoid. This will for the first stage of a humanoid standing 1.55m at the shoulder and weighing less than 25kg.
This paper presents the authors' investigation results of applying the pneumatic artificial muscle actuation to above-knee prostheses. As a well-known muscle actuator, the pneumatic artificial muscle actuator features a number of unique advantages, including high power density, and similar elastic characteristics to biological muscles. Despite multiple applications in related areas, the application of pneumatic artificial muscle in above-knee prostheses has not been explored. Inspired by this fact, the research presented in this paper aims to develop a pneumatic artificial muscle-actuated above-knee prosthesis, with three specific objectives: (1) demonstrate the pneumatic artificial muscle actuation's capability in generating sufficient torque output to meet the locomotive requirements; (2) develop an effective control approach to enable the restoration of locomotive functions; (3) conduct preliminary testing of the prosthesis prototype on a healthy subject through a specially designed able-body adaptor. In the prosthesis design, an agonist-antagonist layout is utilized to obtain a bidirectional motion. To minimize the radial profile, an open-frame structure is used, with the purpose of allowing the expansion of the muscle actuators into the center space without interference. Also, the muscle actuator parameters are calculated to provide sufficient torque capacity (up to 140 N m) to meet the requirements of level walking. According to this design, the fabricated prototype weighs approximately 3 kg, with a range of motion of approximately 100 degrees. For the control of the prosthesis, a model-based torque control algorithm is developed based on the sliding mode control approach, which provides robust torque control for this highly nonlinear system. Combining this torque control algorithm with an impedance-based torque command generator (higher-level control algorithm), the fabricated prosthesis prototype has demonstrated a capability of providing a natural gait during treadmill walking experiments. [DOI: 10.1115/1.4004417]
Data regarding direct athletic muscle injuries (caused by a direct blunt or sharp external force) compared to indirect ones (without the influence of a direct external trauma) are missing in the current literature-this distinction has clinical implications.
To compare incidence, duration of absence and characteristics of indirect and direct anterior (quadriceps) and posterior thigh (hamstring) muscle injuries.
30 football teams and 1981 players were followed prospectively from 2001 until 2013. The team medical staff recorded individual player exposure and time-loss injuries. Muscle injuries were defined as indirect or direct according to their injury mechanism.
In total, 2287 thigh muscle injuries were found, representing 25% of all injuries. Two thousand and three were valid for further analysis, of which 88% were indirect and 12% direct. The incidence was eight times higher for indirect injuries (1.48/1000 h) compared to direct muscle injuries (0.19/1000 h) (p<0.01). Indirect muscle injuries caused 19% of total absence, and direct injuries 1%. The mean lay-off time for indirect injuries amounted to 18.5 days and differed significantly from direct injuries which accounted for 7 days (p<0.001). 60% of indirect injuries and 76% of direct injuries occurred in match situations. Foul play was involved in 7% of all thigh muscle injuries, as well as in 2% of indirect injuries and 42% of direct injuries.
Muscle anterior and posterior thigh injuries in elite football are more frequent than have been previously described. Direct injuries causing time loss are less frequent than indirect ones, and players can usually return to full activity in under half the average time for an indirect injury. Foul play is involved in 7.5% of all thigh muscle injuries.
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The sliding filament theory of muscle contraction is widely accepted as the means by which muscles generate force during activation. Within the constraints of this theory, isometric, steady-state force produced during muscle activation is proportional to the amount of filament overlap. Previous studies from our laboratory demonstrated enhanced titin-based force in myofibrils that were actively stretched to lengths which exceeded filament overlap. This observation cannot be explained by the sliding filament theory. The aim of the present study was to further investigate the enhanced state of titin during active stretch. Specifically, we confirm that this enhanced state of force is observed in a mouse model and quantify the contribution of calcium to this force. Titin-based force was increased by up to four times that of passive force during active stretch of isolated myofibrils. Enhanced titin-based force has now been demonstrated in two distinct animal models, suggesting that modulation of titin-based force during active stretch is an inherent property of skeletal muscle. Our results also demonstrated that 15% of titin's enhanced state can be attributed to direct calcium effects on the protein, presumably a stiffening of the protein upon calcium binding to the E-rich region of the PEVK segment and selected Ig domain segments. We suggest that the remaining unexplained 85% of this extra force results from titin binding to the thin filament. With this enhanced force confirmed in the mouse model, future studies will aim to elucidate the proposed titin-thin filament interaction in actively stretched sarcomeres.
An advanced shear lag model is developed to analyze the stress-shielding effect in injured muscle fiber by introducing the activation strain. The model considers three muscle fibers connected by the endomysium with the middle muscle fiber injured. Stress shielding describes the function of the lateral transmission of force in protecting the injured muscle fibers from being further injured by transferring force in the injured muscle fiber to its adjacent muscle fibers. Parameter studies demonstrate that the mechanical and geometrical properties of muscle fibers and the endomysium as well as the degree of injury can affect the stress-shielding effect. In conclusion, the model successfully demonstrates and captures, at least in a qualitative manner, the lateral transmission of force between an injured and a normal muscle fiber.
Injuries to the quadriceps muscle of the thigh are frequent in sports and often the cause of serious and prolonged disability. Whether the injury is a contusion or strain of the muscle, the pathology and complications are the same. The most serious complication is myositis ossificans. A rationale of treatment is described based on a division of the injuries into four grades and measures appropriate to each degree are outlined. It is essential to restore normal muscle length as quickly as possible to decrease disability. (C)1969The American College of Sports Medicine
Due to its high power-to-weight ratio, a pleated pneumatic artificial muscle (PPAM) offers an interesting alternative actuation source for robotic devices. Its inherent compliant behaviour excites another broad field of interest: assistive clinical devices such as powered exoskeletons and prosthetics. In this paper, the design of a pneumatically powered transtibial prosthetic device is presented. A first prototype has been built and provides a preliminary test bed for control algorithm development and testing with able-bodied subjects in laboratory conditions. The characteristics and working principle of a PPAM are described. The design specifications and the mechanical model of the prosthesis are discussed. The mechanical design and the control structure are outlined. Furthermore, some initial walking trials with an able-bodied subject wearing the prosthesis prototype are presented and discussed.
In this paper we present a fully three-dimensional finite-strain damage model for fibrous soft tissue. Continuum damage mechanics is used to describe the softening behaviour of soft tissues under large deformation. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. We considered the internal variables associated to damage to correspond to separated contributions of the matrix and fibres. In order to show clearly the performance of the constitutive model, we present 3D simulations of the behaviour of the human medial collateral ligament and of a coronary artery. Results show that the model is able to capture the typical stress–strain behaviour observed in fibrous soft tissues and seems to confirm the soundness of the proposed formulation. Copyright © 2006 John Wiley & Sons, Ltd.
Bone cutting is an essential part of orthopaedic surgery when bone is fractured or damaged by a disease and is used for pins insertion and plates fixation. A finite element model of bone cutting is developed and compared with experimental results. The model allows the interaction between the bone and cutting tool to be studied, hence enabling the evaluation and optimization of the cutting procedure. Results of finite element simulations are obtained for the cutting force as a function of cutting parameters. A strong dependence of cutting parameters on the cutting force was found and described in this paper.
A fully three-dimensional finite-strain viscoelastic model is developed, characterized by: (i) general anisotropic response, (ii) uncoupled bulk and deviatoric response over any range of deformations, (iii) general relaxation functions, and (iv) recovery of finite elasticity for very fast or very slow processes; in particular, classical models of rubber elasticity (e.g. Mooney-Rivlin). Continuum damage mechanics is employed to develop a simple isotropic damage mechanism, which incorporates softening behavior under deformation, and leads to progressive degradation of the storage modulus in a cyclic test with increasing amplitude (Mullins' effect). A numerical integration procedure is proposed which trivially satisfies objectivity and bypasses the use of midpoint configurations. The resulting algorithm can be exactly linearized in closed form, and leads to symmetric tangent moduli. Quasi-incompressible response is accounted for within the context of a three-field variational formulation of the Hu-Washizu type.
Fracture toughness is important for any material, but to date there have been few investigations of this mechanical property in soft mammalian tissues. This paper presents new data on porcine muscle tissue and a detailed analysis of all previous work. The conclusion is that, in most cases, fracture toughness has not in fact been measured for these tissues. Reanalysis of the previous work shows that failure of the test specimens generally occurred at the material's ultimate strength, implying that no information about toughness can be obtained from the results. This finding applied to work on cartilage, artificial neocartilage, muscle and the TMJ disc. Our own data, which was also found to be invalid, gave measured fracture toughness values which were highly variable and showed a strong dependence on the crack growth increment. The net-section failure stress and failure energy were relatively constant in large specimens, independent of crack length, whilst for smaller specimens they showed a strong size effect. These findings are explained by the fact that the process zone size, estimated here using the critical distance parameter L, was similar to, or larger than, critical specimen dimensions (crack length and specimen width). Whilst this analysis casts doubt on much of the published literature, a useful finding is that soft tissues are highly tolerant of defects, able to withstand the presence of cracks several millimetres in length without significant loss of strength.
HERZOG, W., M. DUVALL, and T. R. LEONARD. Molecular mechanisms of muscle force regulation: a role for titin? Exerc. Sport Sci. Rev., Vol. 40, No. 1, pp. 50-57, 2012. Muscle contraction and force regulation is thought to occur exclusively through the interaction of the contractile proteins actin and myosin and in accordance with the assumptions underlying the cross-bridge theory. Here, we demonstrate that a third protein, titin, plays a major role in muscle force regulation, particularly for eccentric contractions and at long muscle and sarcomere lengths.
The aim of this study was to analyse the mechanisms that determine why small groups of muscle fibres may have different mechanical properties than single muscle fibres. The method used combined light microscopy and tensile testing on single fibres and small groups of fibres from raw and cooked (80 °C) meat, from both conditioned and unconditioned porcine longissimus muscle. The results showed that small groups of fibres had different breaking properties than constituent single fibres in raw muscle, but that these differences diminished on cooking. Raw groups of fibres showed a more uniform lengthening along their entire length and a higher extension to rupture than single fibres. Conditioning increased maximum strains in both single fibres and small fibre groups. In unconditioned cooked meat, single fibres and fibre groups showed comparable breaking stresses and extensions. Conditioning resulted in a lower strength in fibre groups than in single fibres. These results show that (endomysial) connective tissue linkages between adjacent muscle fibres in a small group significantly alter the breaking behaviour of single fibres. The effects of these connective tissue linkages are not reduced by conditioning alone, but are largely diminished by cooking to 80 °C.
Finite element models (FEM) dedicated to vertebral fracture simulations rarely take into account the rate dependency of the bone material properties due to limited available data. This study aims to calibrate the mechanical properties of a vertebral body FEM using an inverse method based on experiments performed at slow and fast dynamic loading conditions. A detailed FEM of a human lumbar vertebral body (23,394 elements) was developed and tested under compression at 2,500 and 10 mm s⁻¹. A central composite design was used to adjust the mechanical properties (Young modulus, yield stress, and yield strain) while optimizing four criteria (ultimate strain and stress of cortical and trabecular bone) until the failure load and energy at failure reached experimental results from the literature. At 2,500 mm s⁻¹, results from the calibrated simulation were in good agreement with the average experimental data (1.5% difference for the failure load and 0.1% for the energy). At 10 mm s⁻¹, they were in good agreement with the average experimental failure load (0.6% difference), and within one standard deviation of the reported range of energy to failure. The proposed method provides a relevant mean to identify the mechanical properties of the vertebral body in dynamic loadings.
The goal of this work was to create a finite element micromechanical model of the myotendinous junction (MTJ) to examine how the structure and mechanics of the MTJ affect the local micro-scale strains experienced by muscle fibers. We validated the model through comparisons with histological longitudinal sections of muscles fixed in slack and stretched positions. The model predicted deformations of the A-bands within the fiber near the MTJ that were similar to those measured from the histological sections. We then used the model to predict the dependence of local fiber strains on activation and the mechanical properties of the endomysium. The model predicted that peak micro-scale strains increase with activation and as the compliance of the endomysium decreases. Analysis of the models revealed that, in passive stretch, local fiber strains are governed by the difference of the mechanical properties between the fibers and the endomysium. In active stretch, strain distributions are governed by the difference in cross-sectional area along the length of the tapered region of the fiber near the MTJ. The endomysium provides passive resistance that balances the active forces and prevents the tapered region of the fiber from undergoing excessive strain. These model predictions lead to the following hypotheses: (i) the increased likelihood of injury during active lengthening of muscle fibers may be due to the increase in peak strain with activation and (ii) endomysium may play a role in protecting fibers from injury by reducing the strains within the fiber at the MTJ.
The importance of the extracellular matrix (ECM) in muscle is widely recognized, since ECM plays a central role in proper muscle development (Buck and Horwitz, 1987), tissue structural support (Purslow, 2002), and transmission of mechanical signals between fibers and tendon (Huijing, 1999). Since substrate biomechanical properties have been shown to be critical in the biology of tissue development and remodeling (Engler et al., 2006; Gilbert et al., 2010), it is likely that mechanics are critical for ECM to perform its function. Unfortunately, there are almost no data available regarding skeletal muscle ECM viscoelastic properties. This is primarily due to the impossibility of isolating and testing muscle ECM. Therefore, this note presents a new method to quantify viscoelastic ECM modulus by combining tests of single muscle fibers and fiber bundles. Our results demonstrate that ECM is a highly nonlinearly elastic material, while muscle fibers are linearly elastic.
Peak Ca(2+)-activated specific force (force/fiber cross-sectional area) of human chemically skinned vastus lateralis muscle fiber segments was determined before and after a fixed-end contraction or an eccentric contraction of standardized magnitude (+0.25 optimal fiber length) and velocity (0.50 unloaded shortening velocity). Fiber myosin heavy chain (MHC) isoform content was assayed by SDS-PAGE. Posteccentric force deficit, a marker of damage, was similar for type I and IIa fibers but threefold greater for type IIa/IIx hybrid fibers. A fixed-end contraction had no significant effect on force. Multiple linear regression revealed that posteccentric force was explained by a model consisting of a fiber type-independent and a fiber type-specific component (r(2) = 0.91). Preeccentric specific force was directly associated with a greater posteccentric force deficit. When preeccentric force was held constant, type I and IIa fibers showed identical susceptibility to damage, while type IIa/IIx fibers showed a significantly greater force loss. This heightened sensitivity to damage was directly related to the amount of type IIx MHC in the hybrid fiber. Our model reveals a fiber-type sensitivity of the myofilament lattice or cytoskeleton to mechanical strain that can be described as follows: type IIa/IIx > type IIa = type I. If these properties extend to fibers in vivo, then alterations in the number of type IIa/IIx fibers may modify a muscle's susceptibility to eccentric damage.
The giant muscle protein titin, the "backbone" of the sarcomere, harbors a complex molecular spring whose stiffness is variably tuned in health and disease. Titin is increasingly recognized as a crucial integrator of diverse myocyte signaling pathways. The titin-associated signalosome includes hotspots of protein-protein interactions important for the regulation of protein quality-control mechanisms, hypertrophic gene activation, and mechanosensing.
Post-translational modifications, along with isoform splicing, of titin determine the passive tension development of stretched sarcomeres. It was recently shown that PKCalpha phosphorylates two highly-conserved residues (S26 and S170) of the PEVK region in cardiac titin, resulting in passive tension increase. To determine how each phosphorylated residue affects myocardial stiffness, we generated three recombinant mutant PEVK fragments (S26A, S170A and S170A/S26A), each flanked by Ig domains. Single-molecule force spectroscopy shows that PKCalpha decreases the PEVK persistence length (from 0.99 to 0.68 nm); the majority of this decrease is attributable to phosphorylation of S26. Before PKCalpha, all three mutant PEVK fragments showed at least 40% decrease in persistence length compared to wildtype. Furthermore, Ig domain unfolding force measurements indicate that PEVK's flanking Ig domains are relatively unstable compared to other titin Ig domains. We conclude that phosphorylation of S26 is the primary mechanism through which PKCalpha modulates cardiac stiffness.
The purpose of this study is to develop a constitutive model of skeletal muscle that describes material anisotropy, viscoelasticity and damage of muscle tissue. A free energy function is described as the sum of volumetric elastic, isochoric elastic and isochoric viscoelastic parts. The isochoric elastic part is divided into two types of shear response and the response in the fiber direction. To represent the dependence of the mechanical properties on muscle activity, we incorporate a contractile element into the model. The viscoelasticity of muscle is modeled as a three-dimensional model constructed by extending the one-dimensional generalized Maxwell model. Based on the framework of continuum damage mechanics, the anisotropic damage of muscle tissue is expressed by a second-order damage tensor. The evolution of the damage is assumed to depend on the current strain and damage. The evolution equation is formulated using the representation theorem of tensor functions. The proposed model is applied to the experimental data on tensile mechanical properties in the fiber direction and the compression properties in the fiber and cross-fiber directions in literature. The model can predict non-linear mechanical properties and breaking points.
Skeletal muscle is composed of two primary structural components, contractile myofibrils and extracellular matrix (ECM). The myofibrils adhere to the surrounding endomysium through the basal lamina, sarcolemma and dystrophin, and dystrophin associated glycoprotein (DAG). In this study, a novel shear lag type model is developed to investigate the mechanics of injury to the single muscle fiber due to lengthening contractions. A single muscle fiber is considered as a composite system with reinforced by the contractile myofibrils. The lateral linkages between myofibril and endomysium is modeled as a zero thickness coating layer, that could be injured under high interfacial shear stress. The results shows that the degree of the muscle injury is correlated to the magnitude of the passive stretch during the contraction. Dystrophic muscles are more susceptible to contraction induced injury due to lack of DAG complex in lateral linkage.
Many skeletal muscles, including the feline biceps femoris, are composed of short, tapered myofibers arranged in an overlapping longitudinal series. The endomysium of such muscles transfers tension between overlapping myofibers, and is thus an elastic element in series with them. The endomysium of the cat biceps femoris contains curvilinear collagen fibrils in an approximately isotropic (random) array. The collagen fibrils undergo only a modest reorientation as the myofibers shorten or lengthen within the physiological range. A geometrical model predicts no change in the thickness of the endomysium on changing muscle fiber length and quantifies the expected collagen fibril reorientation in the endomysium as a function of muscle extension. It is also demonstrated that a high proportion of the collagen fibrils will be curvilinear at all sarcomere lengths. The organization of endomysial collagen is appropriate for the transfer of loads between myofibers by means of shear.