Passive mechanics of muscle tendinous junction of canine diaphragm.

The diaphragmatic muscle tendon is a biaxially loaded junction in vivo. Stress-strain relations along and transverse to the fiber directions are important in understanding its mechanical properties. We hypothesized that 1) the central tendon possesses greater passive stiffness than adjacent muscle, 2) the diaphragm muscle is anisotropic, whereas the central tendon near the junction is essentially isotropic, and 3) a gradient in passive stiffness exists as one approaches the muscle-tendinous junction (MTJ). To investigate these hypotheses, we conducted uniaxial and biaxial mechanical loading on samples of the MTJ excised from the midcostal region of dog diaphragm. We measured passive length-tension relationships of the muscle, tendon, and MTJ in the direction along the muscle fibers as well as transverse to the fibers. The MTJ was slack in the unloaded state, resulting in a J-shaped passive tension-strain curve. Generally, muscle strain was greater than that of MTJ, which was greater than tendon strain. In the muscular region, stiffness in the direction transverse to the fibers is much greater than that along the fibers. The central tendon is essentially inextensible in the direction transverse to the fibers as well as along the fibers. Our data demonstrate the existence of more pronounced anisotropy in the muscle than in the tendon near the junction. Furthermore, a gradient in muscle stiffness exists as one approaches the MTJ, consistent with the hypothesis of continuous passive stiffness across the MTJ.     

The effects of aponeurosis geometry on strain injury susceptibility explored with a 3D muscle model

In the musculoskeletal system, some muscles are injured more frequently than others. For example, the biceps femoris longhead (BFLH) is the most commonly injured hamstring muscle. It is thought that acute injuries result from large strains within the muscle tissue, but the mechanism behind this type of strain injury is still poorly understood. The purpose of this study was to build computational models to analyze the stretch distributions within the BFLH muscle and to explore the effects of aponeurosis geometry on the magnitude and location of peak stretches within the model. We created a three-dimensional finite element (FE) model of the BFLH based on magnetic resonance (MR) images. We also created a series of simplified models with a similar geometry to the MR-based model. We analyzed the stretches predicted by the MR-based model during lengthening contractions to determine the region of peak local fiber stretch. The peak along-fiber stretch was 1.64 and was located adjacent to the proximal myotendinous junction (MTJ). In contrast, the average along-fiber stretch across all the muscle tissue was 0.95. By analyzing the simple models, we found that varying the dimensions of the aponeuroses (width, length, and thickness) had a substantial impact on the location and magnitude of peak stretches within the muscle. Specifically, the difference in widths between the proximal and distal aponeurosis in the BFLH contributed most to the location and magnitude of peak stretch, as decreasing the proximal aponeurosis width by 80% increased peak average stretches along the proximal MTJ by greater than 60% while slightly decreasing stretches along the distal MTJ. These results suggest that the aponeurosis morphology of the BFLH plays a significant role in determining stretch distributions throughout the muscle. Furthermore, this study introduces the new hypothesis that aponeurosis widths may be important in determining muscle injury susceptibility.     

Interfiber tension transmission in series-fibered muscles of the cat hindlimb

Several muscles of the cat hindlimb, including biceps femoris and tenuissimus, are composed of short, in-series muscle fibers with tapered intrafascicular terminations. Tension generation and transmission within such muscles requires that active fibers should be mechanically coupled in series via myomyous junctions, specialized connective tissue attachments, or the endomysium. This report establishes that the tapered fibers of the cat biceps femoris and tenuissimus muscles have insignificant numbers of either myomyous or specialized connective tissue junctions. Tension appears to be transmitted in a distributed manner across the plasmalemma of the tapered (and probably the non-tapered) portions of the fibers to the connective tissue of the endomysium, which is therefore an essential series elastic element in these muscles. Subplasmalemmal dense plaques were identified and may play a role in transmembrane force transmission. In addition to the endomysium, passive muscle fibers may also serve to transmit tension between active fibers, and therefore should also be considered to be series elastic elements.     

The influence of prior hamstring injury on lengthening muscle tissue mechanics

Hamstring strain injuries often occur near the proximal musculotendon junction (MTJ) of the biceps femoris. Post-injury remodeling can involve scar tissue formation, which may alter contraction mechanics and influence re-injury risk. The purpose of this study was to assess the affect of prior hamstring strain injury on muscle tissue displacements and strains during active lengthening contractions. Eleven healthy and eight subjects with prior biceps femoris injuries were tested. All previously injured subjects had since returned to sport and exhibited evidence of residual scarring along the proximal aponeurosis. Subjects performed cyclic knee flexion–extension on an MRI-compatible device using elastic and inertial loads, which induced active shortening and lengthening contractions, respectively. CINE phase-contrast imaging was used to measure tissue velocities within the biceps femoris during these tasks. Numerical integration of the velocity information was used to estimate two-dimensional tissue displacement and strain fields during muscle lengthening. The largest tissue motion was observed along the distal MTJ, with the active lengthening muscle exhibiting significantly greater and more homogeneous tissue displacements. First principal strain magnitudes were largest along the proximal MTJ for both loading conditions. The previously injured subjects exhibited less tissue motion and significantly greater strains near the proximal MTJ. We conclude that localized regions of high tissue strains during active lengthening contractions may predispose the proximal biceps femoris to injury. Furthermore, post-injury remodeling may alter the in-series stiffness seen by muscle tissue and contribute to the relatively larger localized tissue strains near the proximal MTJ, as was observed in this study.     

A micromechanical muscle model for determining the impact of motor unit fiber clustering on force transmission in aging skeletal muscle

This study used a micromechanical finite element muscle model to investigate the effects of the redistribution of spatial activation patterns in young and old muscle. The geometry consisted of a bundle of 19 active muscle fibers encased in endomysium sheets, surrounded by passive tissue to model a fascicle. Force was induced by activating combinations of the 19 active muscle fibers. The spacial clustering of muscle fibers modeled in this study showed unbalanced strains suggesting tissue damage at higher strain levels may occur during higher levels of activation and/or during dynamic conditions. These patterns of motor unit remodeling are one of the consequences of motor unit loss and reinnervation associated with aging. The results did not reveal evident quantitative changes in force transmission between old and young adults, but the patterns of stress and strain distribution were affected, suggesting an uneven distribution of the forces may occur within the fascicle that could provide a mechanism for muscle injury in older muscle.

     

A nonlinear model of passive muscle viscosity

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.     

Finite element analysis of mechanics of lateral transmission of force in single muscle fiber

Most of the myofibers in long muscles of vertebrates terminate within fascicles without reaching either end of the tendon, thus force generated in myofibers has to be transmitted laterally through the extracellular matrix (ECM) to adjacent fibers; which is defined as the lateral transmission of force in skeletal muscles. The goal of this study was to determine the mechanisms of lateral transmission of force between the myofiber and ECM. In this study, a 2D finite element model of single muscle fiber was developed to study the effects of mechanical properties of the endomysium and the tapered ends of myofiber on lateral transmission of force. Results showed that most of the force generated is transmitted near the end of the myofiber through shear to the endomysium, and the force transmitted to the end of the model increases with increased stiffness of ECM. This study also demonstrated that the tapered angle of the myofiber ends can reduce the stress concentration near the myofiber end while laterally transmitting force efficiently.     

Effect of altering starting length and activation timing of muscle on fiber strain and muscle damage.

Muscle strain injuries are some of the most frequent injuries in sports and command a great deal of attention in an effort to understand their etiology. These injuries may be the culmination of a series of subcellular events accumulated through repetitive lengthening (eccentric) contractions during exercise, and they may be influenced by a variety of variables including fiber strain magnitude, peak joint torque, and starting muscle length. To assess the influence of these variables on muscle injury magnitude in vivo, we measured fiber dynamics and joint torque production during repeated stretch-shortening cycles in the rabbit tibialis anterior muscle, at short and long muscle lengths, while varying the timing of activation before muscle stretch. We found that a muscle subjected to repeated stretch-shortening cycles of constant muscle-tendon unit excursion exhibits significantly different joint torque and fiber strains when the timing of activation or starting muscle length is changed. In particular, measures of fiber strain and muscle injury were significantly increased by altering activation timing and increasing the starting length of the muscle. However, we observed differential effects on peak joint torque during the cyclic stretch-shortening exercise, as increasing the starting length of the muscle did not increase torque production. We conclude that altering activation timing and muscle length before stretch may influence muscle injury by significantly increasing fiber strain magnitude and that fiber dynamics is a more important variable than muscle-tendon unit dynamics and torque production in influencing the magnitude of muscle injury.     

A mathematical model of force transmission from intrafascicularly terminating muscle fibers

Many long skeletal muscles are comprised of fibers that terminate intrafascicularly. Force from terminating fibers can be transmitted through shear within the endomysium that surrounds fibers or through tension within the endomysium that extends from fibers to the tendon; however, it is unclear which pathway dominates in force transmission from terminating fibers. The purpose of this work was to develop mathematical models to (i) compare the efficacy of lateral (through shear) and longitudinal (through tension) force transmission in intrafascicularly terminating fibers, and (ii) determine how force transmission is affected by variations in the structure and properties of fibers and the endomysium. The models demonstrated that even though the amount of force that can be transmitted from an intrafascicularly terminating fiber is dependent on fiber resting length (the unstretched length at which passive stress is zero), endomysium shear modulus, and fiber volume fraction (the fraction of the muscle cross-sectional area that is occupied by fibers), fibers that have values of resting length, shear modulus, and volume fraction within physiologic ranges can transmit nearly all of their peak isometric force laterally through shearing of the endomysium. By contrast, the models predicted only limited force transmission ability through tension within the endomysium that extends from the fiber to the tendon. Moreover, when fiber volume fraction decreases to unhealthy ranges (less than 50%), the force-transmitting potential of terminating fibers through shearing of the endomysium decreases significantly. The models presented here support the hypothesis that lateral force transmission through shearing of the endomysium is an effective mode of force transmission in terminating fibers.     

In-series fiber architecture in long human muscles

The fiber architecture of adult human sartorius and gracilis muscles was examined using a combination of fiber microdissections and histological methods. Intact fibers were dissected from fascicles of muscle strips that were digested in nitric acid. All of these fibers terminate intrafascicularly by tapering to a fine strand at one or both ends. They measure 4–20 cm after correction for shrinkage. Systematic dissections of 1 cm long blocks sampled at intervals along the muscle length suggest that tapered fiber endings occur at all locations along the muscle but are most common centrally; here they accounted for up to 14% of dissected fibers in each block. Transverse sections of muscle confirm that fiber profiles with small diameters occur at all levels of the muscle but are especially common in sections more than 5 cm from its origin or insertion. The architectural arrangement demonstrated here suggests that long human muscles, like muscles in other species, are composed of relatively short, in-series fibers. This has many implications for the neural activation and force-developing behavior of these muscles that must be considered when paralyzed muscles are reanimated using electrical stimulation. Further, it may predispose long muscles to certain types of neuromuscular damage and dysfunction. © 1993 Wiley-Liss, Inc.     

Passive interaction between sliding filaments in the osmotically compressed skinned muscle fibers of the frog.

Shortening and lengthening velocities, instantaneous stiffness, and tension transients after stretch were measured in compressed muscle fibers from the frog in the presence or absence of polyvinylpyrrolidone (PVP K30) or Dextran T70. Both shortening and lengthening velocities clearly decreased with the concentration of polymer. In the presence of polymer, "passive" stiffness was observed in relaxing solution depending on fiber diameter, and stiffness increased further by activation. This increase by activation above "passive" stiffness was nearly constant in the wide range of polymer concentrations. These active and "passive" stiffnesses were found to be dependent on sarcomere length. The stiffness of a compressed rigor fiber was indicated to be composed of constant rigor stiffness and a variable "passive" one. The tension transient after stretch in a compressed active or rigor fiber was also indicated to be composed of two kinds of transients. The above results suggest that (a) there exist two kinds of interactions in parallel in a compressed active or rigor fiber: one active or rigor and another "passive" between sliding filaments, and (b) the decrease in shortening velocity in a compressed fiber may be brought about by this "passive" interaction.     

A model of stress and strain in the interosseous ligament of the forearm based on fiber network theory

Fiber network theory was developed to describe cloth, a thin material with strength in the fiber directions. The interosseous ligament (IOL) of the forearm is a broad, thin ligament with highly aligned fibers. The objectives of this study were to develop a model of the stress and strain distributions in the IOL, based on fiber network theory, to compare the strains from the model with the experimentally measured strains, and to evaluate the force distribution across the ligament fibers from the model. The geometries of the radius, ulna, and IOL were reconstructed from CT scans. Position and orientation of IOL insertion sites and force in the IOL were measured during a forearm compression experiment in pronation, neutral rotation, and supination. An optical image-based technique was used to directly measure strain in two regions of the IOL in neutral rotation. For the network model, the IOL was represented as a parametric ruled three-dimensional surface, with rulings along local fiber directions. Fiber strains were calculated from the deformation field, and fiber stresses were calculated from the strains using average IOL tensile properties from a previous study. The in situ strain in the IOL was assumed uniform and was calculated so that the net force predicted by the network model in neutral rotation matched the experimental result. The net force in the IOL was comparable to experimental results in supination and pronation. The model predicted higher stress and strain in fibers near the elbow in neutral rotation, and higher stresses in fibers near the wrist in supination. Strains in neutral forearm rotation followed the same trends as those measured experimentally. In this study, a model of stress and strain in the IOL utilizing fiber network theory was successfully implemented. The model illustrates variations in the stress and strain distribution in the IOL. This model can be used to show surgeons how different fibers are taut in different forearm rotation positions-this information is important for understanding the biomechanical role of the IOL and for planning an IOL reconstruction.     

A finite element simulation scheme for biological muscular hydrostats

An explicit finite element scheme is developed for biological muscular hydrostats such as squid tentacles, octopus arms and elephant trunks. The scheme is implemented by embedding muscle fibers in finite elements. In any given element, the fiber orientation can be assigned arbitrarily and multiple muscle directions can be simulated. The mechanical stress in each muscle fiber is the sum of active and passive parts. The active stress is taken to be a function of activation state, muscle fiber shortening velocity and fiber strain; while the passive stress depends only on the strain. This scheme is tested by simulating extension of a squid tentacle during prey capture; our numerical predictions are in close correspondence with existing experimental results. It is shown that the present finite element scheme can successfully simulate more complex behaviors such as torsion of a squid tentacle and the bending behavior of octopus arms or elephant trunks.     

CORRELATION BETWEEN FIBER LENGTH, ULTRASTRUCTURE, AND THE LENGTH-TENSION RELATIONSHIP OF MAMMALIAN SMOOTH MUSCLE

The length-tension relationship was determined for strips of guinea pig taenia coli and correlated with the length and ultrastructural organization of the component fibers. The mean fiber length in "stretched" strips (passive ≥ active tension) was 30% greater than that for fibers in "unstretched" strips (active >> passive tension). In stretched fibers the dense bodies and 100 A diameter myofilaments were consolidated into a mass near the center of fibers in cross-sectional profile. The thick myofilaments were segregated into the periphery of the fiber profiles. In unstretched fibers the dense bodies-100 A diameter filaments and the thick myofilaments were uniformly distributed throughout cross-sectional profiles. A tentative model is proposed to account for the change in fiber length and ultrastructural organization that accompanies stretch. The basic features of the model require the dense bodies to be linked together into a network by the 100 A diameter filaments. The functional consequences of stretching the fibers are discussed in relation to the model proposed for this network.     

Stretch-induced,steady-state force enhancement in single skeletal muscle fibers exceeds the isometric force at optimum fiber length

Stretch-induced force enhancement has been observed in a variety of muscle preparations and on structural levels ranging from single fibers to in vivo human muscles. It is a well-accepted property of skeletal muscle. However, the mechanism causing force enhancement has not been elucidated, although the sarcomere-length non-uniformity theory has received wide support. The purpose of this paper was to re-investigate stretch-induced force enhancement in frog single fibers by testing specific hypotheses arising from the sarcomere-length non-uniformity theory. Single fibers dissected from frog tibialis anterior (TA) and lumbricals (n=12 and 22, respectively) were mounted in an experimental chamber with physiological Ringer's solution (pH=7.5) between a force transducer and a servomotor length controller. The tetantic force-length relationship was determined. Isometric reference forces were determined at optimum length (corresponding to the maximal, active, isometric force), and at the initial and final lengths of the stretch experiments. Stretch experiments were performed on the descending limb of the force-length relationship after maximal tetanic force was reached. Stretches of 2.5-10% (TA) and 5-15% lumbricals of fiber length were performed at 0.1-1.5 fiber lengths/s. The stretch-induced, steady-state, active isometric force was always equal or greater than the purely isometric force at the muscle length from which the stretch was initiated. Moreover, for stretches of 5% fiber length or greater, and initiated near the optimum length of the fiber, the stretch-enhanced active force always exceeded the maximal active isometric force at optimum length. Finally, we observed a stretch-induced enhancement of passive force. We conclude from these results that the sarcomere length non-uniformity theory alone cannot explain the observed force enhancement, and that part of the force enhancement is associated with a passive force that is substantially greater after active compared to passive muscle stretch.     

Asynchrony of ventricular activation affects magnitude and timing of fiber stretch in late-activated regions of the canine heart

Abnormal electrical activation of the left ventricle results in mechanical dyssynchrony, which is in part characterized by early stretch of late-activated myofibers. To describe the pattern of deformation during "prestretch" and gain insight into its causes and sequelae, we implanted midwall and transmural arrays of radiopaque markers into the left ventricular anterolateral wall of open-chest, isoflurane-anesthetized, adult mongrel dogs. Biplane cineradiography (125 Hz) was used to determine the time course of two- and three-dimensional strains while pacing from a remote, posterior wall site. Strain maps were generated as a function of time. Electrical activation was assessed with bipolar electrodes. Posterior wall pacing generated prestretch at the measurement site, which peaked 44 ms after local electrical activation. Overall magnitudes and transmural gradients of strain were reduced when compared with passive inflation. Fiber stretch was larger at aortic valve opening compared with end diastole (P < 0.05). Fiber stretch at aortic valve opening was weakly but significantly correlated with local activation time (r(2) = 0.319, P < 0.001). With a short atrioventricular delay, fiber lengths were not significantly different at the time of aortic valve opening during ventricular pacing compared with atrial pacing. However, ejection strain did significantly increase (P < 0.05). We conclude that the majority of fiber stretch occurs after local electrical activation and mitral valve closure and is different from passive inflation. The increased shortening of these regions appears to be because of a reduced afterload rather than an effect of length-dependent activation in this preparation.     

Dependence of local left ventricular wall mechanics on myocardial fiber orientation: a model study.

The dependence of local left ventricular (LV) mechanics on myocardial muscle fiber orientation was investigated using a finite element model. In the model we have considered anisotropy of the active and passive components of myocardial tissue, dependence of active stress on time, strain and strain rate, activation sequence of the LV wall and aortic afterload. Muscle fiber orientation in the LV wall is quantified by the helix fiber angle, defined as the angle between the muscle fiber direction and the local circumferential direction. In a first simulation, a transmural variation of the helix fiber angle from +60 degrees at the endocardium through 0 degrees in the midwall layers to -60 degrees at the epicardium was assumed. In this simulation, at the equatorial level maximum active muscle fiber stress was found to vary from about 110 kPa in the subendocardial layers through about 30 kPa in the midwall layers to about 40 kPa in the subepicardial layers. Next, in a series of simulations, muscle fiber orientation was iteratively adapted until the spatial distribution of active muscle fiber stress was fairly homogeneous. Using a transmural course of the helix fiber angle of +60 degrees at the endocardium, +15 degrees in the midwall layers and -60 degrees at the epicardium, at the equatorial level maximum active muscle fiber stress varied from 52 kPa to 55 kPa, indicating a remarkable reduction of the stress range. Moreover, the change of muscle fiber strain with time was more similar in different parts of the LV wall than in the first simulation. It is concluded that (1) the distribution of active muscle fiber stress and muscle fiber strain across the LV wall is very sensitive to the transmural distribution of the helix fiber angle and (2) a physiological transmural distribution of the helix fiber angle can be found, at which active muscle fiber stress and muscle fiber strain are distributed approximately homogeneously across the LV wall.     

The passive properties of muscle fibers are velocity dependent

The passive properties of skeletal muscle play an important role in muscle function. While the passive quasi-static elastic properties of muscle fibers have been well characterized, the dynamic visco-elastic passive behavior of fibers has garnered less attention. In particular, it is unclear how the visco-elastic properties are influenced by lengthening velocity, in particular for the range of physiologically relevant velocities. The goals of this work were to: (i) measure the effects of lengthening velocity on the peak stresses within single muscle fibers to determine how passive behavior changes over a range of physiologically relevant lengthening rates (0.1–10L_o/s), and (ii) develop a mathematical model of fiber viscoelasticity based on these measurements. We found that passive properties depend on strain rate, in particular at the low loading rates (0.1–3L_o/s), and that the measured behavior can be predicted across a range of loading rates and time histories with a quasi-linear viscoelastic model. In the future, these results can be used to determine the impact of viscoelastic behavior on intramuscular stresses and forces during a variety of dynamic movements.     

Multiple stimulations for muscle–nerve–blood vessel unit in compensatory hypertrophied skeletal muscle of rat surgical ablation model

Tissue inflammation and multiple cellular responses in the compensatory enlarged plantaris (OP Plt) muscle induced by surgical ablation of synergistic muscles (soleus and gastrocnemius) were followed over 10 weeks after surgery. Contralateral surgery was performed in adult Wistar male rats. Cellular responses in muscle fibers, blood vessels and nerve fibers were analyzed by immunohistochemistry and electron microscopy. Severe muscle fiber damage and disappearance of capillaries associated with apparent tissue edema were observed in the peripheral portion of OP Plt muscles during the first week, whereas central portions were relatively preserved. Marked cell activation/proliferation was also mainly observed in peripheral portions. Similarly, activated myogenic cells were seen not only inside but also outside of muscle fibers. The former were likely satellite cells and the latter may be interstitial myogenic cells. One week after surgery, small muscle fibers, small arteries and capillaries and several branched-muscle fibers were evident in the periphery, thus indicating new muscle fiber and blood vessel formation. Proliferating cells were also detected in the nerve bundles in the Schwann cell position. These results indicate that the compensatory stimulated/enlarged muscle is a suitable model for analyzing multiple physiological cellular responses in muscle–nerve–blood vessel units under continuous stretch stimulation. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

The contribution of muscle progenitor cells to maintaining morphological characteristics of unweighted rat soleus muscle during passive stretch

Skeletal muscle work hypertrophy is usually connected with muscle progenitor SC (satellite cells) activation with subsequent incorporation their nuclei into myofibers. Passive stretch of unloaded muscle was earlier established to prevent atrophic processes and be accompanied by enhanced protein synthesis. We hypothesized that elimination of SC proliferation capacity by gamma-irradiation would partly preavent stretched muscle fiber capability to maintain their size under condition of gravitational unloading. To assess the role of muscle progenitor (satellite) cells in development of passive stretch preventive effect SC proliferation was suppressed by local exposure to ionizing radiation (2500 Rad) and then subsequent hindlimb suspension or hindlimb suspension with concomitant passive stretch were carried out. Reduction of myofiber cross-sectional area and decrease in myo-nuclei number accompanying unloaded muscle atrophy were completely abolished by passive stretch both in irradiated and sham-treated animals. We concluded that satellite cells did not make essential contribution to passive stretch preventive action under condition of simulated weightlessness.