Three-dimensional surface geometries of the rabbit soleus muscle during contraction: input for biomechanical modelling and its validation

Influence of muscle length on the three-dimensional architecture and aponeurosis dimensions of rabbit calf muscles

The function of a muscle is highly dependent on its architecture, which is characterized by the length, pennation, and curvature of the fascicles, and the geometry of the aponeuroses. During in vivo function, muscles regularly undergo changes in length, thereby altering their architecture. During passive muscle lengthening, fascicle length (FL) generally increases and the angle of fascicle pennation (FP) and the fascicle curvature (FC) decrease, while the aponeuroses increase in length but decrease in width. Muscles are differently structured, making their change during muscle lengthening complex and multifaceted. To obtain comprehensive data on architectural changes in muscles during passive length, the present study determined the three-dimensional fascicle geometry of rabbit M. gastrocnemius medialis (GM), M. gastrocnemius lateralis (GL), and M. plantaris (PLA). For this purpose, the left and right legs of three rabbits were histologically fixed at targeted ankle joint angles of 95° (short muscle length [SML]) and 60° (long muscle length [LML]), respectively, and the fascicles were tracked by manual three-dimensional digitization. In a second set of experiments, the GM aponeurosis dimensions of ten legs from five rabbits were determined at varying muscle lengths via optical marker tracking. The GM consisted of a uni-pennated compartment, whereas the GL and PLA contained multiple compartments of differently pennated fascicles. In the LML compared to the SML, the GM, GL, and PLA had on average a 41%, 29%, and 41% increased fascicle length, and a 30%, 25%, and 33% decrease in fascicle pennation and a 32%, 11%, and 35% decrease in fascicle curvature, respectively. Architectural properties were also differentiated among the different compartments of the PLA and GL, allowing for a more detailed description of their fascicle structure and changes. It was shown that the compartments change differently with muscle length. It was also shown that for each degree of ankle joint angle reduction, the proximal GM aponeurosis length increased by 0.11%, the aponeurosis width decreased by 0.22%, and the area was decreased by 0.20%. The data provided improve our understanding of muscles and can be used to develop and validate muscle models.

3D ultrasound-based determination of skeletal muscle fascicle orientations

Architectural parameters of skeletal muscle such as pennation angle provide valuable information on muscle function, since they can be related to the muscle force generating capacity, fiber packing, and contraction velocity. In this paper, we introduce a 3D ultrasound-based workflow for determining 3D fascicle orientations of skeletal muscles. We used a custom-designed automated motor driven 3D ultrasound scanning system for obtaining 3D ultrasound images. From these, we applied a custom-developed multiscale-vessel enhancement filter-based fascicle detection algorithm and determined muscle volume and pennation angle. We conducted trials on a phantom and on the human tibialis anterior (TA) muscle of 10 healthy subjects in plantarflexion (157 ± 7∘ ), neutral position (109 ± 7∘ , corresponding to neutral standing), and one resting position in between (145 ± 6∘ ). The results of the phantom trials showed a high accuracy with a mean absolute error of 0.92 ± 0.59∘ . TA pennation angles were significantly different between all positions for the deep muscle compartment; for the superficial compartment, angles are significantly increased for neutral position compared to plantarflexion and resting position. Pennation angles were also significantly different between superficial and deep compartment. The results of constant muscle volumes across the 3 ankle joint angles indicate the suitability of the method for capturing 3D muscle geometry. Absolute pennation angles in our study were slightly lower than recent literature. Decreased pennation angles during plantarflexion are consistent with previous studies. The presented method demonstrates the possibility of determining 3D fascicle orientations of the TA muscle in vivo.

On a three-dimensional model for the description of the passive characteristics of skeletal muscle tissue

In this work, a three-dimensional model was developed to describe the passive mechanical behaviour of anisotropic skeletal muscle tissue. To validate the model, orientation-dependent axial ([Formula: see text], [Formula: see text], [Formula: see text]) and semi-confined compression experiments (mode I, II, III) were performed on soleus muscle tissue from rabbits. In the latter experiments, specimen deformation is prescribed in the loading direction and prevented in an additional spatial direction, fibre compression at [Formula: see text] (mode I), fibre elongation at [Formula: see text] (mode II) and a neutral state of the fibres at [Formula: see text] where their length is kept constant (mode III). Overall, the model can adequately describe the mechanical behaviour with a relatively small number of model parameters. The stiffest tissue response during orientation-dependent axial compression ([Formula: see text] kPa) occurs when the fibres are oriented perpendicular to the loading direction ([Formula: see text]) and are thus stretched during loading. Semi-confined compression experiments yielded the stiffest tissue ([Formula: see text] kPa) in mode II when the muscle fibres are stretched. The extensive data set collected in this study allows to study the different error measures depending on the deformation state or the combination of deformation states.

Aponeurosis structure-function properties: Evidence of heterogeneity and implications for muscle function

Aponeurosis is a sheath-like connective tissue that aids in force transmission from muscle to tendon and can be found throughout the musculoskeletal system. The key role of aponeurosis in muscle-tendon unit mechanics is clouded by a lack of understanding of aponeurosis structure-function properties. This work aimed to determine the heterogeneous material properties of porcine triceps brachii aponeurosis tissue with materials testing and evaluate heterogeneous aponeurosis microstructure with scanning electron microscopy. We found that aponeurosis may exhibit more microstructural collagen waviness in the insertion region (near the tendon) compared to the transition region (near the muscle midbelly) (1.20 versus 1.12, p = 0.055), which and a less stiff stress-strain response in the insertion versus transition regions (p < 0.05). We also showed that different assumptions of aponeurosis heterogeneity, specifically variations in elastic modulus with location can alter the stiffness (by more than 10x) and strain (by approximately 10% muscle fiber strain) of a finite element model of muscle and aponeurosis. Collectively, these results suggest that aponeurosis heterogeneity could be due to variations in tissue microstructure and that different approaches to modeling tissue heterogeneity alters the behavior of computational models of muscle-tendon units. STATEMENT OF SIGNIFICANCE: Aponeurosis is a connective tissue found in many muscle tendon units that aids in force transmission, yet little is known about the specific material properties of aponeurosis. This work aimed to determine how the properties of aponeurosis tissue varied with location. We found that aponeurosis exhibits more microstructural waviness near the tendon compared to near the muscle midbelly, which was associated with differences in tissue stiffness. We also showed that different variations in aponeurosis modulus (stiffness) can alter the stiffness and stretch of a computer model of muscle tissue. These results show that assuming uniform aponeurosis structure and modulus, which is common, may lead to inaccurate models of the musculoskeletal system.

Three-dimensional multi-field modelling of gastric arrhythmias and their effects on antral contractions

The contraction activation of smooth muscle in the stomach wall (SW) is coordinated by slow electrical waves. The interstitial cells of Cajal (ICC), specialised pacemaker cells, initiate and propagate these slow waves. By establishing an electrically coupled network, each ICC adjusts its intrinsic pacing frequency to a single dominant frequency, to be a key aspect in modelling the electrophysiology of gastric tissue. In terms of modelling, additional fields associated with electrical activation, such as voltage-dependent calcium influx and the resulting deformation, have hardly been considered so far. Here we present a three-dimensional model of the electro-chemomechanical activation of gastric smooth muscle contractions. To reduce computational costs, an adaptive multi-scale discretisation strategy for the temporal resolution of the electric field is used. The model incorporates a biophysically based model of gastric ICC pacemaker activity that aims to simulate stable entrainment and physiological conduction velocities of the electrical slow waves. Together with the simulation of concomitant gastric contractions and the inclusion of a mechanical feedback mechanism, the model is used to study dysrhythmias of gastric slow waves induced by abnormal stretching of the antral SW. The model is able to predict the formation of stretch-induced gastric arrhythmias, such as the emergence of an ectopic pacemaker in the gastric antrum. The results show that the ectopic event is accompanied by smooth muscle contraction and, although it disrupts the normal propagation pattern of gastric slow electrical waves, it can also catalyse the process of handling indigestible materials that might otherwise injure the gastric SW.

On multiscale tension-compression asymmetry in skeletal muscle

Skeletal muscle tissue shows a clear asymmetry with regard to the passive stresses under tensile and compressive deformation, referred to as tension-compression asymmetry (TCA). The present study is the first one reporting on TCA at different length scales, associated with muscle tissue and muscle fibres, respectively. This allows for the first time the comparison of TCA between the tissue and one of its individual components, and thus to identify the length scale at which this phenomenon originates. Not only the passive stress-stretch characteristics were recorded, but also the volume changes during the axial tension and compression experiments. The study reveals clear differences in the characteristics of TCA between fibres and tissue. At tissue level TCA increases non-linearly with increasing deformation and the ratio of tensile to compressive stresses at the same magnitude of strain reaches a value of approximately 130 at 13.5% deformation. At fibre level instead it initially drops to a value of 6 and then rises again to a TCA of 14. At a deformation of 13.5%, the tensile stress is about 6 times higher. Thus, TCA is about 22 times more expressed at tissue than fibre scale. Moreover, the analysis of volume changes revealed little compressibility at tissue scale whereas at fibre level, especially under compressive stress, the volume decreases significantly. The data collected in this study suggests that the extracellular matrix has a distinct role in amplifying the TCA, and leads to more incompressible tissue behaviour. STATEMENT OF SIGNIFICANCE: This article analyses and compares for the first time the tension-compression asymmetry (TCA) displayed by skeletal muscle at tissue and fibre scale. In addition, the volume changes of tissue and fibre specimens with application of passive tensile and compressive loads are studied. The study identifies a key role of the extracellular matrix in establishing the mechanical response of skeletal muscle tissue: It contributes significantly to the passive stress, it is responsible for the major part of tissue-scale TCA and, most probably, prevents/balances the volume changes of muscle fibres during deformation. These new results thus shed light on the origin of TCA and provide new information to be used in microstructure-based approaches to model and simulate skeletal muscle tissue.

Age-dependent mechanical and microstructural properties of the rabbit soleus muscle

During growth there are serious changes in the skeletal muscles to compensate for the changed requirements in terms of body weight and size. In this study, the age-dependent (between 21 and 100 days) mechanical and microstructural properties of rabbit soleus muscle tissue were investigated. For this purpose, morphological properties (animal mass, soleus muscle mass, tibial length) were measured at 5 different times during aging. On the other hand, fibre orientation-dependent axial and semi-confined compression experiments were realised. In addition, the essential components (muscle fibres, extracellular matrix, remaining components), dominating the microstructure of muscle tissue, were analysed. While the mechanical results show hardly any age-dependent differences, the morphological and microstructural results show clear age-dependent differences. All morphological parameters increase significantly (animal mass by 839.2%, muscle mass 1050.6%, tibial length 233.6%). In contrast, microstructural parameters change differently. The percentage of fibres (divided into slow-twitch (ST) and fast-twitch (FT) fibres) increases significantly (137.6%), while the proportions of the extracellular matrix and the remaining components (48.2% and 46.1%) decrease. At the same time, the cross-sectional area of the fibres increases significantly (697.9%). The totality of this age-dependent information provides a deeper understanding of age-related changes in muscle structure and function and may contribute to successful development and validation of growth models in the future. STATEMENT OF SIGNIFICANCE: This article reports the first comprehensive data set on age-dependent morphological (animal mass, soleus muscle mass, tibial length), mechanical (axial and semi-confined compression), and microstructural (muscle fibres, extracellular matrix, remaining components) properties of the rabbit soleus muscle. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to understanding of load transfer mechanisms inside the muscle tissue during growth. On the other hand, these results are relevant to the fields of constitutive formulation of age-dependent muscle tissue.

Architectural model for muscle growth during maturation

Muscle architecture, which includes parameters like fascicle length, pennation angle, and physiological cross-sectional area, strongly influences skeletal muscles' mechanical properties. During maturation, the muscle architecture has to adapt to a growing organism. This study aimed to develop an architectural model capable of predicting the complete 3D fascicle architecture for primarily unipennate muscles of an arbitrary age, based on fascicle data for an initial age. For model development, we collected novel data on 3D muscle architecture of the rabbit (Oryctolagus cuniculus) M. plantaris of eight animals ranging in age from 29 to 106 days. Experimental results show that plantaris muscle belly length increases by 73%, whereas mean fascicle length and mean pennation angle increases by 39 and 14%, respectively. Those changes were incorporated into the model. In addition to the data collected for M. plantaris the predictions of the model were compared to existing literature data of rabbit M. soleus and M. gastrocnemius medialis. With an error of −1.0 ± 8.6% for relative differences in aponeurosis length, aponeurosis width, muscle height, and muscle mass, the model delivered good results matching interindividual differences. For future studies, the model could be utilized to generate realistic architectural data sets for simulation studies.

The Energy of Muscle Contraction. III. Kinetic Energy During Cyclic Contractions

During muscle contraction, chemical energy is converted to mechanical energy when ATP is hydrolysed during cross-bridge cycling. This mechanical energy is then distributed and stored in the tissue as the muscle deforms or is used to perform external work. We previously showed how energy is distributed through contracting muscle during fixed-end contractions; however, it is not clear how the distribution of tissue energy is altered by the kinetic energy of muscle mass during dynamic contractions. In this study we conducted simulations of a 3D continuum muscle model that accounts for tissue mass, as well as force-velocity effects, in which the muscle underwent sinusoidal work-loop contractions coupled with bursts of excitation. We found that increasing muscle size, and therefore mass, increased the kinetic energy per unit volume of the muscle. In addition to greater relative kinetic energy per cycle, relatively more energy was also stored in the aponeurosis, and less was stored in the base material, which represented the intra and extracellular tissue components apart from the myofibrils. These energy changes in larger muscles due to greater mass were associated lower mass-specific mechanical work output per cycle, and this reduction in mass-specific work was greatest for smaller initial pennation angles. When we compared the effects of mass on the model tissue behaviour to that of in situ muscle with added mass during comparable work-loop trials, we found that greater mass led to lower maximum and higher minimum acceleration in the longitudinal (x) direction near the middle of the muscle compared to at the non-fixed end, which indicates that greater mass contributes to tissue non-uniformity in whole muscle. These comparable results for the simulated and in situ muscle also show that this modelling framework behaves in ways that are consistent with experimental muscle. Overall, the results of this study highlight that muscle mass is an important determinant of whole muscle behaviour.

Direct measurement of the direction-dependent mechanical behaviour of skeletal muscle extracellular matrix

This paper reports the first comprehensive data set on the anisotropic mechanical properties of isolated endo- and perimysial extracellular matrix of skeletal muscle, and presents the corresponding protocols for preparing and testing the samples. In particular, decellularisation of porcine skeletal muscle is achieved with caustic soda solution, and mechanical parameters are defined based on compressive and tensile testing in order to identify the optimal treatment time such that muscle fibres are dissolved whereas the extracellular matrix remains largely intact and mechanically functional. At around 18 h, a time window was found and confirmed by histology, in which axial tensile experiments were performed to characterise the direction-dependent mechanical response of the extracellular matrix samples, and the effect of lateral pre-compression was studied. The typical, large variability in the experimental stress response could be largely reduced by varying a single scalar factor, which was attributed to the variation of the fraction of extracellular matrix within the tissue. While experimental results on the mechanical properties of intact muscle tissue and single muscle fibres are increasingly available in literature, there is a lack of information on the properties of the collagenous components of skeletal muscle. The present work aims at closing this gap and thus contributes to an improved understanding of the mechanics of skeletal muscle tissue and provides a missing piece of information for the development of corresponding constitutive and computational models.

The Energy of Muscle Contraction. II. Transverse Compression and Work

In this study we examined how the strain energies within a muscle are related to changes in longitudinal force when the muscle is exposed to an external transverse load. We implemented a three-dimensional (3D) finite element model of contracting muscle using the principle of minimum total energy and allowing the redistribution of energy through different strain energy-densities. This allowed us to determine the importance of the strain energy-densities to the transverse forces developed by the muscle. We ran a series of in silica experiments on muscle blocks varying in initial pennation angle, muscle length, and external transverse load. As muscle contracts it maintains a near constant volume. As such, any changes in muscle length are balanced by deformations in the transverse directions such as muscle thickness or muscle width. Muscle develops transverse forces as it expands. In many situations external forces act to counteract these transverse forces and the muscle responds to external transverse loads while both passive and active. The muscle blocks used in our simulations decreased in thickness and pennation angle when passively compressed and pushed back on the load when they were activated. Activation of the compressed muscle blocks led either to an increase or decrease in muscle thickness depending on whether the initial pennation angle was less than or greater than 15°, respectively. Furthermore, the strain energy increased and redistributed across the different strain-energy potentials during contraction. The volumetric strain energy-density varied with muscle length and pennation angle and was reduced with greater transverse load for most initial muscle lengths and pennation angles. External transverse load reduced the longitudinal muscle force for initial pennation angles of β₀ = 0°. Whereas for pennate muscle (β₀ > 0°) longitudinal force changed (increase or decrease) depending on the muscle length, pennation angle and the direction of the external load relative to the muscle fibres. For muscle blocks with initial pennation angles β₀ ≤ 20° the reduction in longitudinal muscle force coincided with a reduction in volumetric strain energy-density.

Mechano-geometrical skeletal muscle fibre characterisation under cyclic and relaxation loading

In the present work, mechano-geometrical characterisations of skeletal muscle fibres in two different deformation states, namely, axial tension and axial compression, were realised. In both cases, cyclic and relaxation tests were performed. Additionally, the changes in the volume of the fibres during deformation were recorded to obtain more detailed information about the muscle fibre load transfer mechanisms. To the best of the authors' knowledge, the present experimental investigation of the mechanical and geometrical characteristics of muscle fibres provides a novel comprehensive data set that can be used to obtain a better understanding of muscle fibre load transfer mechanisms and to construct meaningful models. In the present study, it is shown that muscle fibres exhibit incompressibility (5% volume decrease at maximum deformation) under tension and that this feature is more pronounced under compression loading (37% volume decrease at maximum deformation). These findings are particularly interesting and lead to a further understanding of load transfer mechanisms and to the development of new modelling strategies.

The Energy of Muscle Contraction. I. Tissue Force and Deformation During Fixed-End Contractions

During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

On a coupled electro-chemomechanical model of gastric smooth muscle contraction

The stomach is a central organ in the gastrointestinal tract that performs a variety of functions, in which the spatio-temporal organisation of active smooth muscle contraction in the stomach wall (SW) is highly regulated. In the present study, a three-dimensional model of the gastric smooth muscle contraction is presented, including the mechanical contribution of the mucosal and muscular layer of the SW. Layer-specific and direction-dependent model parameters for the active and passive stress-stretch characteristics of the SW were determined experimentally using porcine smooth muscle strips. The electrical activation of the smooth muscle cells (SMC) due to the pacemaker activity of the interstitial cells of Cajal (ICC) is modelled by using FitzHugh-Nagumo-type equations, which simulate the typical ICC and SMC slow wave behaviour. The calcium dynamic in the SMC depends on the SMC membrane potential via a gaussian function, while the chemo-mechanical coupling in the SMC is modelled via an extended Hai-Murphy model. This cascade is coupled with an additional mechano-electrical feedback-mechanism, taking into account the mechanical response of the ICC and SMC due to stretch of the SW. In this way the relaxation responses of the fundus to accommodate incoming food, as well as the typical peristaltic contraction waves in the antrum for mixing and transport of the chyme, have been well replicated in simulations performed at the whole organ level. STATEMENT OF SIGNIFICANCE: In this article, a novel three-dimensional electro-chemomechanical model of the gastric smooth muscle contraction is presented. The propagating waves of electrical membrane potential in the network ofinterstitial cells of Cajal (ICC) and smooth muscle cells (SMC) lead to a global pattern of change in the calciumdynamics inside the SMC. Taking additionally into account the mechanical response of the ICC and SMC due to stretch of the stomach wall, also referred to as mechanical feedback-mechanism, the result is a complex spatio-temporal regulation of the active contraction and relaxation of the gastric smooth muscle tissue. Being a firstapproach, in future view such a three-dimensional model can give an insight into the complexload transferring system of the stomach wall, as well as into the electro-chemomechanicalcoupling process underlying smooth muscle contraction in health and disease.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Effect of Static Stretching, Dynamic Stretching, and Myofascial Foam Rolling on Range of Motion During Hip Flexion: A Randomized Crossover Trial

Siebert, T, Donath, L, Borsdorf, M, and Stutzig, N. Effect of static stretching, dynamic stretching, and myofascial foam rolling on range of motion during hip flexion: A randomized crossover trial. J Strength Cond Res XX(X): 000-000, 2020-Static and dynamic stretching (DS) are commonly used in sports and physical therapy to increase the range of motion (ROM). However, prolonged static stretching (SS) can deteriorate athletic performance. Alternative methods to increase ROM are thus needed. Foam rolling (FR) may initiate muscle relaxation, improve muscular function, physical performance, and ROM. Previous studies that examined effects of FR on ROM did not control for increased tissue compliance or shifted pain threshold. In this study, the isolated influence of altered tissue compliance on ROM after FR, SS, and DS was investigated using a randomized crossover design. Hip flexion ROM at given joint torques before and after SS, DS, and FR was randomly assessed in 14 young male adults (age: 23.7 +/- 1.3 years; height: 182 +/- 8 cm; body mass: 79.4 +/- 6.9 kg). Hip flexion ROM was measured in the sagittal plane with the subjects lying in a lateral position (no gravitational effects on ROM measurements). Surface electromyographic (EMG) analysis of 2 representative hip extensors (M. biceps femoris and M. semitendinosus) was applied to control for active muscle contribution during ROM measurements. Significant increases in ROM for SS (3.8 +/- 1.1[degrees]; p < 0.001) and DS (3.7 +/- 1.8[degrees]; p < 0.001) were observed, but not for FR (0.8 +/- 3.1[degrees]; p = 0.954). Because stretch forces on tendon and muscle tissue during SS and DS predominately act in longitudinal direction, FR induces mainly transversal forces in the muscle tissue. Thus, increased ROM after FR reported in the literature is more likely due to a shift in the pain threshold. These results provide a better understanding of differential loading conditions during SS, DS, and FR for coaches and practitioners.

Investigating the passive mechanical behaviour of skeletal muscle fibres: Micromechanical experiments and Bayesian hierarchical modelling

Characterisation of the skeletal muscle's passive properties is a challenging task since its structure is dominated by a highly complex and hierarchical arrangement of fibrous components at different scales. The present work focuses on the micromechanical characterisation of skeletal muscle fibres, which consist of myofibrils, by realising three different deformation states, namely, axial tension, axial compression, and transversal compression. To the best of the authors' knowledge, the present study provides a novel comprehensive data set representing of different deformation states. These data allow for a better understanding of muscle fibre load transfer mechanisms and can be used for meaningful modelling approaches. As the present study shows, axial tension and compression experiments reveal a strong tension-compression asymmetry at fibre level. In comparison to the tissue level, this asymmetric behaviour is more pronounced at the fibre scale, elucidating the load transfer mechanism in muscle tissue and aiding in the development of future modelling strategies. Further, a Bayesian hierarchical modelling approach was used to consider the experimental fluctuations in a parameter identification scheme, leading to more comprehensive parameter distributions that reflect the entire observed experimental uncertainty. STATEMENT OF SIGNIFICANCE: This article examines for the first time the mechanical properties of skeletal muscle fibres under axial tension, axial compression, and transversal compression, leading to a highly comprehensive data set. Moreover, a Bayesian hierarchical modelling concept is presented to identify model parameters in a broad way. The results of the deformation states allow a new and comprehensive understanding of muscle fibres' load transfer mechanisms; one example is the effect of tension-compression asymmetry. On the one hand, the results of this study contribute to the understanding of muscle mechanics and thus to the muscle's functional understanding during daily activity. On the other hand, they are relevant in the fields of skeletal muscle multiscale, constitutive modelling.

Passive changes in muscle length

This review, the first in a series of minireviews on the passive mechanical properties of skeletal muscles, seeks to summarize what is known about the muscle deformations that allow relaxed muscles to lengthen and shorten. Most obviously, when a muscle lengthens, muscle fascicles elongate, but this is not the only mechanism by which muscles change their length. In pennate muscles, elongation of muscle fascicles is accompanied by changes in pennation and changes in fascicle curvature, both of which may contribute to changes in muscle length. The contributions of these mechanisms to change in muscle length are usually small under passive conditions. In very pennate muscles with long aponeuroses, fascicle shear could contribute substantially to changes in muscle length. Tendons experience moderate axial strains even under passive loads, and, because tendons are often much longer than muscle fibers, even moderate tendon strains may contribute substantially to changes in muscle length. Data obtained with new imaging techniques suggest that muscle fascicle and aponeurosis strains are highly nonuniform, but this is yet to be confirmed. The development, validation, and interpretation of continuum muscle models informed by rigorous measurements of muscle architecture and material properties should provide further insights into the mechanisms that allow relaxed muscles to lengthen and shorten.

Transverse anisotropy in the deformation of the muscle during dynamic contractions

When pennate muscle fibres shorten, the transverse deformation of fibres results in an increase in pennation angle of fascicles (bundles of fibres) and transverse deformation of muscle belly. Transverse shape changes of a muscle can influence force generation. Recent modelling studies predicted asymmetrical transverse deformations in the muscle fascicles in the gastrocnemii. However, these predictions have not been tested experimentally. As muscle is a 3D entity, it is important to explore the structural changes in a 3D perspective to enhance our understanding of the underlying structural mechanisms that have functional implications. The medial and lateral gastrocnemius muscles from 12 subjects were imaged during plantarflexion movements on a dynamometer. The muscle belly was simultaneously scanned from two orthogonal directions using two ultrasound probes. Fascicle deformations were measured from the two orthogonal ultrasound scans to provide 3D information of muscle geometry. Whilst transverse deformations in the medial gastrocnemius were similar from the two directions, the data for the lateral gastrocnemius confirm that transverse anisotropy can occur in the muscle fascicles. As the lateral gastrocnemius fascicle length shortened, the pennation angle increased and the fascicles bulged transversally in one direction (closest to the typical 2D scanning plane) while thinning in the other orthogonal direction. We suggest that the transverse deformation of the muscle fascicles depends on the stiffness of the aponeuroses, properties of connective tissue structures surrounding muscle, and compressive forces both internal and external to the muscle. These results highlight that muscle fascicles do not bulge uniformly and the implications for this behaviour on muscle function remain largely unexplored.

Experimental and Numerical Characterization of the Mechanical Masseter Muscle Response During Biting

Predictive simulations of the mastication system would significantly improve our understanding of temporomandibular joint (TMJ) disorders and the planning of cranio-maxillofacial surgery procedures. Respective computational models must be validated by experimental data from in vivo characterization of the mastication system's mechanical response. The present pilot-study demonstrates the feasibility of a combined experimental and numerical procedure to validate a computer model of the masseter muscle. An experimental setup is proposed that provides a simultaneous bite force measurement and ultrasound-based visualization of muscle deformation. The direct comparison of the experimentally observed and numerically predicted muscle response demonstrates the predictive capabilities of such anatomically accurate biting models. Differences between molar and incisor biting are investigated; muscle deformation is recorded for three different bite forces in order to capture the effect of increasing muscle fiber recruitment. The three-dimensional (3D) muscle deformation at each bite position and force-level is approximatively reconstructed from ultrasound measurements in five distinct cross-sectional areas (four horizontal and one vertical cross section). The experimental work is accompanied by numerical simulations to validate the predictive capabilities of a constitutive muscle model previously formulated. An anatomy-based, fully 3D model of the masseter muscle is created from magnetic resonance images (MRI) of the same subject. The direct comparison of experimental and numerical results revealed good agreement for maximum bite forces and masseter deformations in both biting positions. The present work therefore presents a feasible in vivo measurement system to validate numerically predicted masseter muscle contractions during mastication.

Geometric models to explore mechanisms of dynamic shape change in skeletal muscle

Skeletal muscle bulges when it contracts. These three-dimensional (3D) dynamic shape changes play an important role in muscle performance by altering the range of fascicle velocities over which a muscle operates. However traditional muscle models are one-dimensional (1D) and cannot fully explain in vivo shape changes. In this study we compared medial gastrocnemius behaviour during human cycling (fascicle length changes and rotations) predicted by a traditional 1D Hill-type model and by models that incorporate two-dimensional (2D) and 3D geometric constraints to in vivo measurements from B-mode ultrasound during a range of mechanical conditions ranging from 14 to 44 N m and 80 to 140 r.p.m. We found that a 1D model predicted fascicle lengths and pennation angles similar to a 2D model that allowed the aponeurosis to stretch, and to a 3D model that allowed for aponeurosis stretch and variable shape changes to occur. This suggests that if the intent of a model is to predict fascicle behaviour alone, then the traditional 1D Hill-type model may be sufficient. Yet, we also caution that 1D models are limited in their ability to infer the mechanisms by which shape changes influence muscle mechanics. To elucidate the mechanisms governing muscle shape change, future efforts should aim to develop imaging techniques able to characterize whole muscle 3D geometry in vivo during active contractions.

Porcine Stomach Smooth Muscle Force Depends on History-Effects

The stomach serves as food reservoir, mixing organ and absorption area for certain substances, while continually varying its position and size. Large dimensional changes during ingestion and gastric emptying of the stomach are associated with large changes in smooth muscle length. These length changes might induce history-effects, namely force depression (FD) following active muscle shortening and force enhancement (FE) following active muscle stretch. Both effects have impact on the force generating capacity of the stomach, and thus functional relevance. However, less is known about history-effects and active smooth muscle properties of stomach smooth muscle. Thus, the aim of this study was to investigate biomechanical muscle properties as force-length and force-velocity relations (FVR) of porcine stomach smooth muscle strips, extended by the analysis of history-effects on smooth muscle force. Therefore, in total n = 54 tissue strips were dissected in longitudinal direction from the ventral fundus of porcine stomachs. Different isometric, isotonic, and isokinetic contraction protocols were performed during electrical muscle stimulation. Cross-sectional areas (CSA) of smooth muscles were determined from cryo-histological sections stained with Picrosirius Red. Results revealed that maximum smooth muscle tension was 10.4 ± 2.6 N/cm². Maximum shortening velocity (V_max) and curvature factor (curv) of the FVR were 0.04 ± 0.01 [optimum muscle length/s] and 0.36 ± 0.15, respectively. The findings of the present study demonstrated significant (P < 0.05) FD [up to 32% maximum muscle force (F_im)] and FE (up to 16% F_im) of gastric muscle tissue, respectively. The FE- and FD-values increased with increasing ramp amplitude. This outstanding muscle behavior is not accounted for in existing models so far and strongly supports the idea of a holistic reflection of distinct stomach structure and function. For the first time this study provides a comprehensive set of stomach smooth muscle parameters including classic biomechanical muscle properties and history-dependent effects, offering the possibility for the development and validation of computational stomach models. Furthermore, this data set facilitates novel insights in gastric motility and contraction behavior based on the re-evaluation of existing contractile mechanisms. That will likely help to understand physiological functions or dysfunctions in terms of gastric accommodation and emptying.

Identification of the mechanical parameters for the human uterus in vivo using intrauterine pressure measurements

There are limited experimental data to characterize the mechanical response of human myometrium. A method is presented in this work to identify mechanical parameters describing the active response of human myometrium from the in vivo intrauterine pressure measurements. The human uterine contraction during labor is simulated by implementing a coupled model in a finite element scheme, and the intrauterine pressure is evaluated as the outcome. A meta-model is developed to approximate the finite element simulation response with a lower computational cost and used to identify model parameters through fitting its prediction to the in vivo measurements. Copyright © 2016 John Wiley & Sons, Ltd.

Intermuscular pressure between synergistic muscles correlates with muscle force

The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle–tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus. Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force–time and pressure–time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).

Force reduction induced by unidirectional transversal muscle loading is independent of local pressure

Transversal unidirectional compression applied to muscles via external loading affects muscle contraction dynamics in the longitudinal direction. A recent study reported decreasing longitudinal muscle forces with increasing transversal load applied with a constant contact area (i.e., leading to a simultaneous increase in local pressure). To shed light on these results, we examine whether the decrease in longitudinal force depends on the load, the local pressure, or both. To this end, we perform isometric experiments on rat M. gastrocnemius medialis without and with transversal loading (i) changing the local pressure from 1.1-3.2Ncm(-2) (n=9) at a constant transversal load (1.62N) and (ii) increasing the transversal load (1.15-3.45N) at a constant local pressure of 2.3Ncm(-2) (n=7). While we did not note changes in the decrease in longitudinal muscle force in the first experiment, the second experiment resulted in an almost-linear reduction of longitudinal force between 7.5±0.6% and 14.1±1.7%. We conclude that the observed longitudinal force reduction is not induced by local effects such as malfunction of single muscle compartments, but that similar internal stress conditions and myofilament configurations occur when the local pressure changes given a constant load. The decreased longitudinal force may be explained by increased internal pressure and a deformed myofilament lattice that is likely associated with the decomposition of cross-bridge forces on the one hand and the inhibition of cross-bridges on the other hand.

Reconstruction of muscle fascicle architecture from iodine-enhanced microCT images: A combined texture mapping and streamline approach

Skeletal muscle models are used to investigate motion and force generation in both biological and bioengineering research. Yet, they often lack a realistic representation of the muscle's internal architecture which is primarily composed of muscle fibre bundles, known as fascicles. Recently, it has been shown that fascicles can be resolved with micro-computed tomography (µCT) following staining of the muscle tissue with iodine potassium iodide (I2KI). Here, we present the reconstruction of the fascicular spatial arrangement and geometry of the superficial masseter muscle of a dog based on a combination of pattern recognition and streamline computation. A cadaveric head of a dog was incubated in I2KI and µCT-scanned. Following segmentation of the masseter muscle a statistical pattern recognition algorithm was applied to create a vector field of fascicle directions. Streamlines were then used to transform the vector field into a realistic muscle fascicle representation. The lengths of the reconstructed fascicles and the pennation angles in two planes (frontal and sagittal) were extracted and compared against a tracked fascicle field obtained through cadaver dissection. Both fascicle lengths and angles were found to vary substantially within the muscle confirming the complex and heterogeneous nature of skeletal muscle described by previous studies. While there were significant differences in the pennation angle between the experimentally derived and µCT-reconstructed data, there was congruence in the fascicle lengths. We conclude that the presented approach allows for embedding realistic fascicle information into finite element models of skeletal muscles to better understand the functioning of the musculoskeletal system.

Three-Dimensional Muscle Architecture and Comprehensive Dynamic Properties of Rabbit Gastrocnemius, Plantaris and Soleus: Input for Simulation Studies

The vastly increasing number of neuro-muscular simulation studies (with increasing numbers of muscles used per simulation) is in sharp contrast to a narrow database of necessary muscle parameters. Simulation results depend heavily on rough parameter estimates often obtained by scaling of one muscle parameter set. However, in vivo muscles differ in their individual properties and architecture. Here we provide a comprehensive dataset of dynamic (n = 6 per muscle) and geometric (three-dimensional architecture, n = 3 per muscle) muscle properties of the rabbit calf muscles gastrocnemius, plantaris, and soleus. For completeness we provide the dynamic muscle properties for further important shank muscles (flexor digitorum longus, extensor digitorum longus, and tibialis anterior; n = 1 per muscle). Maximum shortening velocity (normalized to optimal fiber length) of the gastrocnemius is about twice that of soleus, while plantaris showed an intermediate value. The force-velocity relation is similar for gastrocnemius and plantaris but is much more bent for the soleus. Although the muscles vary greatly in their three-dimensional architecture their mean pennation angle and normalized force-length relationships are almost similar. Forces of the muscles were enhanced in the isometric phase following stretching and were depressed following shortening compared to the corresponding isometric forces. While the enhancement was independent of the ramp velocity, the depression was inversely related to the ramp velocity. The lowest effect strength for soleus supports the idea that these effects adapt to muscle function. The careful acquisition of typical dynamical parameters (e.g. force-length and force-velocity relations, force elongation relations of passive components), enhancement and depression effects, and 3D muscle architecture of calf muscles provides valuable comprehensive datasets for e.g. simulations with neuro-muscular models, development of more realistic muscle models, or simulation of muscle packages.

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

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

Passive skeletal muscle excursion after tendon rupture correlates with increased collagen content in muscle

PURPOSE

This study was designed to measure time-dependent changes in muscle excursion and collagen content after tenotomy, and to analyze the correlation between muscle excursion and collagen content in a rabbit model.

MATERIALS AND METHODS

Twenty-four rabbits underwent tenotomy of the second extensor digitorum longus (EDL) muscles on the right legs and were randomly assigned to three groups based on the period of time after tenotomy (2, 4, and 6 weeks). The second EDL muscles on left legs were used as controls. At each time after tenotomy, passive muscle excursion and collagen content, determined by hydroxyproline content, were measured bilaterally, and the ratio of each value to the normal one was used.

RESULTS

The mean ratio of muscle excursion after tenotomy to the value of the control decreased in a time-dependent fashion: 92.5% at 2 weeks, 78.6% at 4 weeks, and 55.1% at 6 weeks. The mean ratio of hydroxyproline content in muscle to the value of the control increased in a time-dependent fashion: 119.5% at 2 weeks, 157.3% at 4 weeks, and 166.6% at 6 weeks. There was a significant negative correlation between the ratio of hydroxyproline content in muscle after tenotomy to the control values and the ratio of muscle excursion after tenotomy to the control values (r=-0.602, p=0.002).

CONCLUSION

The decrease in muscle excursion seems to correlate with the increase in collagen content in the muscle in a time-dependent fashion following tenotomy.

On the anisotropy of skeletal muscle tissue under compression

This paper deals with the role of the muscle fibres and extracellular matrix (ECM) components when muscle tissue is subjected to compressive loads. To this end, dissected tissue samples were tested in compression modes which induced states of fibres in compression (I), in tension (II) or at constant length (III), respectively. A comparison of the stress responses indicated that the tissue behaviour is significantly different for these modes, including differences between the modes (I) and (III). This contradicts the paradigm of many constitutive models that the stress response can be decomposed into an isotropic part relating to the ECM and an anisotropic fibre part the contribution of which can be neglected under compression. Conversely, the results provide experimental evidence that there is an anisotropic contribution of the fibre direction to the compressive stress. Interpreting these results in terms of recent microscopical studies, potential connections between the observed behaviour and the structure of muscle ECM are established.

Determination of three-dimensional muscle architectures: validation of the DTI-based fiber tractography method by manual digitization

In the last decade, diffusion tensor imaging (DTI) has been used increasingly to investigate three-dimensional (3D) muscle architectures. So far there is no study that has proved the validity of this method to determine fascicle lengths and pennation angles within a whole muscle. To verify the DTI method, fascicle lengths of m. soleus as well as their pennation angles have been measured using two different methods. First, the 3D muscle architecture was analyzed in vivo applying the DTI method with subsequent deterministic fiber tractography. In a second step, the muscle architecture of the same muscle was analyzed using a standard manual digitization system (MicroScribe MLX). Comparing both methods, we found differences for the median pennation angles (P < 0.001) but not for the median fascicle lengths (P = 0.216). Despite the statistical results, we conclude that the DTI method is appropriate to determine the global fiber orientation. The difference in median pennation angles determined with both methods is only about 1.2° (median pennation angle of MicroScribe: 9.7°; DTI: 8.5°) and probably has no practical relevance for muscle simulation studies. Determining fascicle lengths requires additional restriction and further development of the DTI method.