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

A methodological approach for collecting simultaneous measures of muscle, aponeurosis, and tendon behaviour during dynamic contractions

Skeletal muscles and the tendons that attach them to bone are structurally complex and deform non-uniformly during contraction. While these tissue deformations dictate force production during movement, our understanding of this behaviour is limited due to challenges in obtaining complete measures of the constituent structures. To address these challenges, we present an approach for simultaneously measuring muscle, fascicle, aponeurosis, and tendon behaviour using sonomicrometry. To evaluate this methodology, we conducted isometric and dynamic contractions in in situ rabbit medial gastrocnemius. We found comparable patterns of strain in the muscle belly, fascicle, aponeurosis, and tendon during the isometric trials to those published in the literature. For the dynamic contractions, we found that our measures using this method were consistent across all animals and aligned well with our theoretical understanding of muscle-tendon unit behaviour. Thus, this method provides a means to fully capture the complex behaviour of muscle-tendon units across contraction types.

Finite Element Model of the Shoulder with Active Rotator Cuff Muscles: Application to Wheelchair Propulsion

The rotator cuff is prone to injury, remarkably so for manual wheelchair users. To understand its pathomechanisms, finite element models incorporating three-dimensional activated muscles are needed to predict soft tissue strains during given tasks. This study aimed to develop such a model to understand pathomechanisms associated with wheelchair propulsion. We developed an active muscle model associating a passive fiber-reinforced isotropic matrix with an activation law linking calcium ion concentration to tissue tension. This model was first evaluated against known physiological muscle behavior; then used to activate the rotator cuff during a wheelchair propulsion cycle. Here, experimental kinematics and electromyography data was used to drive a shoulder finite element model. Finally, we evaluated the importance of muscle activation by comparing the results of activated and non-activated rotator cuff muscles during both propulsion and isometric contractions. Qualitatively, the muscle constitutive law reasonably reproduced the classical Hill model force-length curve and the behavior of a transversally loaded muscle. During wheelchair propulsion, the deformation and fiber stretch of the supraspinatus muscle-tendon unit pointed towards the possibility for this tendon to develop tendinosis due to the multiaxial loading imposed by the kinematics of propulsion. Finally, differences in local stretch and positions of the lines of action between activated and non-activated models were only observed at activation levels higher than 30%. Our novel finite element model with active muscles is a promising tool for understanding the pathomechanisms of the rotator cuff for various dynamic tasks, especially those with high muscle activation levels.

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.

In vivo human medial gastrocnemius fascicle behaviour and belly gear during submaximal eccentric contractions are not affected by concentric fatiguing exercise

Changes in muscle geometry and belly gearing during eccentric contractions influence fibre strain and susceptibility to muscle damage. They are modulated by the interaction between connective tissues and intracellular-intrafascicular fluid pressures and external pressures from neighbouring structures. Fatiguing exercise triggers fluid shifts (muscle swelling) and muscle activation changes that may influence these modulators. Our purpose was to measure medial gastrocnemius (MG) geometric changes in vivo during eccentric contractions before and after maximal concentric muscle work to test the hypothesis that fatigue would reduce fascicle rotation and muscle gear and provoke greater fascicle strain. Submaximal eccentric plantar flexor contractions at 40% and 60% of maximal eccentric torque were performed on an isokinetic dynamometer at 5°.s-1 before and immediately after the fatiguing exercise. MG fascicles and muscle-tendon junction were captured using ultrasonography during contractions, allowing quantification of geometric changes, whole-MG length, and belly gear (Δmuscle length/Δfascicle length). Triceps surae (TS) activation was estimated using surface electromyography and the distribution of activations between synergistic muscles was then determined. After exercise, concentric torque decreased ∼39% and resting muscle thickness increased by 4%, indicating muscle fatigue and swelling, respectively. While soleus (Sol) activation and the Sol/TS ratio increased, no changes in MG, MG/TS ratio or fascicle rotation during the contraction were detected. Thus, fascicle lengthening and belly gear remained unaltered. Changes in muscle thickness during contraction was also similar before and after exercise, suggesting that changes in muscle shape were relatively unaffected by the exercise. Consequently, the muscle maintained mechanical integrity after the fatiguing muscle work.

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.

Slow or fast: Implications of myofibre type and associated differences for manifestation of neuromuscular disorders

Many neuromuscular disorders can have a differential impact on a specific myofibre type, forming the central premise of this review. The many different skeletal muscles in mammals contain a spectrum of slow- to fast-twitch myofibres with varying levels of protein isoforms that determine their distinctive contractile, metabolic, and other properties. The variations in functional properties across the range of classic 'slow' to 'fast' myofibres are outlined, combined with exemplars of the predominantly slow-twitch soleus and fast-twitch extensor digitorum longus muscles, species comparisons, and techniques used to study these properties. Other intrinsic and extrinsic differences are discussed in the context of slow and fast myofibres. These include inherent susceptibility to damage, myonecrosis, and regeneration, plus extrinsic nerves, extracellular matrix, and vasculature, examined in the context of growth, ageing, metabolic syndrome, and sexual dimorphism. These many differences emphasise the importance of carefully considering the influence of myofibre-type composition on manifestation of various neuromuscular disorders across the lifespan for both sexes. Equally, understanding the different responses of slow and fast myofibres due to intrinsic and extrinsic factors can provide deep insight into the precise molecular mechanisms that initiate and exacerbate various neuromuscular disorders. This focus on the influence of different myofibre types is of fundamental importance to enhance translation for clinical management and therapies for many skeletal muscle disorders.

Spatially repeatable components from ultrafast ultrasound are associated with motor unit activity in human isometric contractions. J Neural Eng 2023;20:046016. [PMID: 37437598 DOI: 10.1088/1741-2552/ace6fc]

Objective.Ultrafast ultrasound (UUS) imaging has been used to detect intramuscular mechanical dynamics associated with single motor units (MUs). Detecting MUs from ultrasound sequences requires decomposing a velocity field into components, each consisting of an image and a signal. These components can be associated with putative MU activity or spurious movements (noise). The differentiation between putative MUs and noise has been accomplished by comparing the signals with MU firings obtained from needle electromyography (EMG). Here, we examined whether the repeatability of the images over brief time intervals can serve as a criterion for distinguishing putative MUs from noise in low-force isometric contractions.Approach.UUS images and high-density surface EMG (HDsEMG) were recorded simultaneously from 99 MUs in the biceps brachii of five healthy subjects. The MUs identified through HDsEMG decomposition were used as a reference to assess the outcomes of the ultrasound-based components. For each contraction, velocity sequences from the same eight-second ultrasound recording were separated into consecutive two-second epochs and decomposed. To evaluate the repeatability of components' images across epochs, we calculated the Jaccard similarity coefficient (JSC). JSC compares the similarity between two images providing values between 0 and 1. Finally, the association between the components and the MUs from HDsEMG was assessed.Main results.All the MU-matched components had JSC > 0.38, indicating they were repeatable and accounted for about one-third of the HDsEMG-detected MUs (1.8 ± 1.6 matches over 4.9 ± 1.8 MUs). The repeatable components (JSC > 0.38) represented 14% of the total components (6.5 ± 3.3 components). These findings align with our hypothesis that intra-sequence repeatability can differentiate putative MUs from noise and can be used for data reduction.Significance.This study provides the foundation for developing stand-alone methods to identify MU in UUS sequences and towards real-time imaging of MUs. These methods are relevant for studying muscle neuromechanics and designing novel neural interfaces.

A review of the efforts to develop muscle and musculoskeletal models for biomechanics in the last 50 years

Both the Hill and the Huxley muscle models had already been described by the time the International Society of Biomechanics was founded 50 years ago, but had seen little use before the 1970s due to the lack of computing. As computers and computational methods became available in the 1970s, the field of musculoskeletal modeling developed and Hill type muscle models were adopted by biomechanists due to their relative computational simplicity as compared to Huxley type muscle models. Muscle forces computed by Hill type muscle models provide good agreement in conditions similar to the initial studies, i.e. for small muscles contracting under steady and controlled conditions. However, more recent validation studies have identified that Hill type muscle models are least accurate for natural in vivo locomotor behaviours at submaximal activations, fast speeds and for larger muscles, and thus need to be improved for their use in understanding human movements. Developments in muscle modelling have tackled these shortcomings. However, over the last 50 years musculoskeletal simulations have been largely based on traditional Hill type muscle models or even simplifications of this model that neglected the interaction of the muscle with a compliant tendon. The introduction of direct collocation in musculoskeletal simulations about 15 years ago along with further improvements in computational power and numerical methods enabled the use of more complex muscle models in simulations of whole-body movement. Whereas Hill type models are still the norm, we may finally be ready to adopt more complex muscle models into musculoskeletal simulations of human movement.

Advances in imaging for assessing the design and mechanics of skeletal muscle in vivo

Skeletal muscle is the engine that powers what is arguably the most essential and defining feature of human and animal life-locomotion. Muscles function to change length and produce force to enable movement, posture, and balance. Despite this seemingly simple role, skeletal muscle displays a variety of phenomena that still remain poorly understood. These phenomena are complex-the result of interactions between active and passive machinery, as well as mechanical, chemical and electrical processes. The emergence of imaging technologies over the past several decades has led to considerable discoveries regarding how skeletal muscles function in vivo where activation levels are submaximal, and the length and velocity of contracting muscle fibres are transient. However, our knowledge of the mechanisms of muscle behaviour during everyday human movements remains far from complete. In this review, we discuss the principal advancements in imaging technology that have led to discoveries to improve our understanding of in vivo muscle function over the past 50 years. We highlight the knowledge that has emerged from the development and application of various techniques, including ultrasound imaging, magnetic resonance imaging, and elastography to characterise muscle design and mechanical properties. We emphasize that our inability to measure the forces produced by skeletal muscles still poses a significant challenge, and that future developments to accurately and reliably measure individual muscle forces will promote newfrontiers in biomechanics, physiology, motor control, and robotics. Finally, we identify critical gaps in our knowledge and future challenges that we hope can be solved as a biomechanics community in the next 50 years.

In-vivo along muscle fascicle strain heterogeneity is not affected by image registration parameters: Robustness testing of combined magnetic resonance-diffusion tensor imaging method

Coupled with diffusion tractography, non-rigid registration of high-resolution anatomical MR images allows the calculation of local strains along human skeletal muscle fascicles in-vivo. A reference study (passively imposed lengthening of gastrocnemius medial muscle) reported local shortening and lengthening occurring along the same muscle fascicles. However, the robustness of strain amplitudes and distribution patterns should be studied, as the heterogeneity of local length changes has major implications for muscle function. Using a previous image set of human medial gastrocnemius (GM) we aimed at testing: (1) the consistency of our MRI-DTI analysis workflow against changes made to the software environments, (2) the hypothesis that non-rigid demons algorithm tuning parameters (16 paired combinations were tested) are not a significant determinant of muscle fiber direction strain heterogeneity caused by passive knee extension. A profoundly altered analysis workflow did reproduce the original results well, showing a general pattern of proximally lengthened and distally shortened muscle fascicles (strain amplitude range: 21%-67%). Hierarchical shift function analyses and pairwise comparison of strain distributions between 10 equal parts of the tracked GM fascicles confirmed the hypothesis showing no significant effects of tuning parameters determining the in-vivo deformation field inhomogeneity. The findings show the robustness of the MRI-DTI method, and confirming the hypothesis, also the consistency of along muscle fascicle strain heterogeneity patterns against parameter selection. However, the strain amplitudes do vary with parameter choices. New studies are indicated to determine optimal tuning parameters to achieve accurate strain amplitudes compared to exact strains.

Intrafasciomembranal Fluid Pressure: A Novel Approach to the Etiology of Myalgias, Part II

The fascia forms a hierarchy of spaces (small and large compartments) that contain and enclose muscle fibers, fiber bundles, skeletal muscles, and compartments of several skeletal muscles. Solid fascia serves as a membrane that enables an increased volume and fluid pressure within such a fasciomembrane, an intrafasciomembrial fluid pressure (IFMFP). Increased IFMFP provides a theoretical model and a common explanation for the etiology of the myalgias: trigger point (TrP), chronic exertional compartment syndrome (CECS), overtraining syndrome (OTS), and delayed onset muscle soreness (DOMS). Many myalgias and their symptoms are poorly understood, and this review aims to provide an extension to this theoretical model and novel approach. This review suggests that the swelling from elevated IFMFP also likely leads to a longitudinal shortening of the same affected tissue. This model of swelling and shortening provides additional explanations for the changes in the lines of force through the body that can lead to changes in the body's posture and, thus, to compensatory movements. This new approximation also provides a biomechanical explanation for the thickening of the fascia and referred pain, and also suggests that IFMFP is a factor in weather-related pain.

Shorter muscle fascicle operating lengths increase the metabolic cost of cyclic force production

During locomotion, force-producing limb muscles are predominantly responsible for an animal's whole body metabolic energy expenditure. Animals can change the length of their force-producing muscle fascicles by altering body posture (e.g., joint angles), the structural properties of their biological tissues over time (e.g., tendon stiffness), or the body's kinetics (e.g., body weight). Currently, it is uncertain whether relative muscle fascicle operating lengths have a measurable effect on the metabolic energy expended during cyclic locomotion-like contractions. To address this uncertainty, we quantified the metabolic energy expenditure of human participants, as they cyclically produced two distinct ankle moments at three ankle angles (90°, 105°, and 120°) on a fixed-position dynamometer using their soleus. Overall, increasing participant ankle angle from 90° to 120° (more plantar flexion) reduced minimum soleus fascicle length by 17% (both moment levels, P < 0.001) and increased metabolic energy expenditure by an average of 208% across both moment levels (both P < 0.001). For both moment levels, the increased metabolic energy expenditure was not related to greater fascicle positive mechanical work (higher moment level, P = 0.591), fascicle force rate (both P ≥ 0.235), or model-estimated active muscle volume (both P ≥ 0.122). Alternatively, metabolic energy expenditure correlated with average relative soleus fascicle length (r = -0.72, P = 0.002) and activation (r = 0.51, P < 0.001). Therefore, increasing active muscle fascicle operating lengths may reduce metabolic energy expended during locomotion.NEW & NOTEWORTHY During locomotion, active muscles undergo cyclic length-changing contractions. In this study, we isolated confounding variables and revealed that cyclically producing force at relatively shorter fascicle lengths increases metabolic energy expenditure. Therefore, muscle fascicle operating lengths likely have a measurable effect on the metabolic energy expenditure during locomotion.

ZAKβ is activated by cellular compression and mediates contraction-induced MAP kinase signaling in skeletal muscle

Mechanical inputs give rise to p38 and JNK activation, which mediate adaptive physiological responses in various tissues. In skeletal muscle, contraction‐induced p38 and JNK signaling ensure adaptation to exercise, muscle repair, and hypertrophy. However, the mechanisms by which muscle fibers sense mechanical load to activate this signaling have remained elusive. Here, we show that the upstream MAP3K ZAKβ is activated by cellular compression induced by osmotic shock and cyclic compression in vitro, and muscle contraction in vivo. This function relies on ZAKβ's ability to recognize stress fibers in cells and Z‐discs in muscle fibers when mechanically perturbed. Consequently, ZAK‐deficient mice present with skeletal muscle defects characterized by fibers with centralized nuclei and progressive adaptation towards a slower myosin profile. Our results highlight how cells in general respond to mechanical compressive load and how mechanical forces generated during muscle contraction are translated into MAP kinase signaling.

Physical and electrophysiological motor unit characteristics are revealed with simultaneous high-density electromyography and ultrafast ultrasound imaging

Electromyography and ultrasonography provide complementary information about electrophysiological and physical (i.e. anatomical and mechanical) muscle properties. In this study, we propose a method to assess the electrical and physical properties of single motor units (MUs) by combining High-Density surface Electromyography (HDsEMG) and ultrafast ultrasonography (US). Individual MU firings extracted from HDsEMG were used to identify the corresponding region of muscle tissue displacement in US videos. The time evolution of the tissue velocity in the identified region was regarded as the MU tissue displacement velocity. The method was tested in simulated conditions and applied to experimental signals to study the local association between the amplitude distribution of single MU action potentials and the identified displacement area. We were able to identify the location of simulated MUs in the muscle cross-section within a 2 mm error and to reconstruct the simulated MU displacement velocity (cc > 0.85). Multiple regression analysis of 180 experimental MUs detected during isometric contractions of the biceps brachii revealed a significant association between the identified location of MU displacement areas and the centroid of the EMG amplitude distribution. The proposed approach has the potential to enable non-invasive assessment of the electrical, anatomical, and mechanical properties of single MUs in voluntary contractions.

The Contributions of Extracellular Matrix and Sarcomere Properties to Passive Muscle Stiffness in Cerebral Palsy

Cerebral palsy results from an upper motor neuron lesion and significantly affects skeletal muscle stiffness. The increased stiffness that occurs is partly a result of changes in the microstructural components of muscle. In particular, alterations in extracellular matrix, sarcomere length, fibre diameter, and fat content have been reported; however, experimental studies have shown wide variability in the degree of alteration. Many studies have reported changes in the extracellular matrix, while others have reported no differences. A consistent finding is increased sarcomere length in cerebral palsy affected muscle. Often many components are altered simultaneously, making it difficult to determine the individual effects on muscle stiffness. In this study, we use a three dimensional modelling approach to isolate individual effects of microstructural alterations typically occurring due to cerebral palsy on whole muscle behaviour; in particular, the effects of extracellular matrix volume fraction, stiffness, and sarcomere length. Causation between the changes to the microstructure and the overall muscle response is difficult to determine experimentally, since components of muscle cannot be manipulated individually; however, utilising a modelling approach allows greater control over each factor. We find that extracellular matrix volume fraction has the largest effect on whole muscle stiffness and mitigates effects from sarcomere length.

A new framework for analysis of three-dimensional shape and architecture of human skeletal muscles from in vivo imaging data

A new framework is presented for comprehensive analysis of the three-dimensional shape and architecture of human skeletal muscles from magnetic resonance and diffusion tensor imaging data. The framework comprises three key features: (1) identification of points on the surface of and inside a muscle that have a correspondence to points on and inside another muscle, (2) reconstruction of average muscle shape and average muscle fibre orientations, and (3) utilization of data on between-muscle variation to visualize and make statistical inferences about changes or differences in muscle shape and architecture. The general use of the framework is demonstrated by its application to three case studies. Analysis of data obtained before and after eight weeks of strength training revealed there was little regional variation in hypertrophy of the vastus medialis and vastus lateralis, and no systematic change in pennation angle. Analysis of passive muscle lengthening revealed heterogeneous changes in shape of the medial gastrocnemius, and confirmed the ability of the methods to detect subtle changes in muscle fibre orientation. Analysis of the medial gastrocnemius of children with unilateral cerebral palsy showed that muscles in the more-affected limb were shorter, thinner and less wide than muscles in the less-affected limb, and had slightly more pennate muscle fibres in the central and proximal part of the muscle. Amongst other applications, the framework can be used to explore the mechanics of muscle contraction, investigate adaptations of muscle architecture, build anatomically realistic computational models of skeletal muscles, and compare muscle shape and architecture between species.

Regional variation in lateral and medial gastrocnemius muscle fibre lengths obtained from diffusion tensor imaging

Assessment of regional muscle architecture is primarily done through the study of animals, human cadavers, or using b-mode ultrasound imaging. However, there remain several limitations to how well such measurements represent in vivo human whole muscle architecture. In this study, we developed an approach using diffusion tensor imaging and magnetic resonance imaging to quantify muscle fibre lengths in different muscle regions along a muscle's length and width. We first tested the between-day reliability of regional measurements of fibre lengths in the medial (MG) and lateral gastrocnemius (LG) and found good reliability for these measurements (intraclass correlation coefficient [ICC] = 0.79 and ICC = 0.84, respectively). We then applied this approach to a group of 32 participants including males (n = 18), females (n = 14), young (24 ± 4 years) and older (70 ± 2 years) adults. We assessed the differences in regional muscle fibre lengths between different muscle regions and between individuals. Additionally, we compared regional muscle fibre lengths between sexes, age groups, and muscles. We found substantial variability in fibre lengths between different regions within the same muscle and between the MG and the LG across individuals. At the group level, we found no difference in mean muscle fibre length between males and females, nor between young and older adults, or between the MG and the LG. The high variability in muscle fibre lengths between different regions within the same muscle, possibly expands the functional versatility of the muscle for different task requirements. The high variability between individuals supports the use of subject-specific measurements of muscle fibre lengths when evaluating muscle function.

The influence of in vivo mechanical behaviour of the Achilles tendon on the mechanics, energetics and apparent efficiency of bouncing gaits

In this study, we used kinematic, kinetic, metabolic and ultrasound analysis to investigate the role of elastic energy utilization on the mechanical and physiological demands of a movement task (hopping) that primarily involves the plantar-flexor muscles to determine the contribution of tendon work to total mechanical work and its relationship with apparent efficiency (AE) in bouncing gaits. Metabolic power (PMET) and (positive) mechanical power at the whole-body level (PMEC) were measured during hopping at different frequencies (2, 2.5, 3 and 3.5 Hz). The (positive) mechanical power produced during the Achilles tendon recoil phase (PTEN) was obtained by integrating ultrasound data with an inverse dynamic approach. As a function of hopping frequency, PMEC decreased steadily and PMET exhibited a U-shape behaviour, with a minimum at about 3 Hz. AE (PMEC/PMET) showed an opposite trend and was maximal (about 0.50) at the same frequency when PTEN was also highest. Positive correlations were observed: (i) between PTEN and AE (AE=0.22+0.15PTEN, R2=0.67, P<0.001) and the intercept of this relationship indicates the value of AE that should be expected when tendon work is nil; (ii) between AE and tendon gearing (Gt=Δmuscle-tendon unit length/Δmuscle belly length; R2=0.50, P<0.001), where a high Gt indicates that the muscle is contracting more isometrically, thus allowing the movement to be more economical (and efficient); (iii) between Gt and PTEN (R2=0.73, P<0.001), which indicates that Gt could play an important role in the tendon's capability to store and release mechanical power.

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.

Modelling extracellular matrix and cellular contributions to whole muscle mechanics

Skeletal muscle tissue has a highly complex and heterogeneous structure comprising several physical length scales. In the simplest model of muscle tissue, it can be represented as a one dimensional nonlinear spring in the direction of muscle fibres. However, at the finest level, muscle tissue includes a complex network of collagen fibres, actin and myosin proteins, and other cellular materials. This study shall derive an intermediate physical model which encapsulates the major contributions of the muscle components to the elastic response apart from activation-related along-fibre responses. The micro-mechanical factors in skeletal muscle tissue (eg. connective tissue, fluid, and fibres) can be homogenized into one material aggregate that will capture the behaviour of the combination of material components. In order to do this, the corresponding volume fractions for each type of material need to be determined by comparing the stress-strain relationship for a volume containing each material. This results in a model that accounts for the micro-mechanical features found in muscle and can therefore be used to analyze effects of neuro-muscular diseases such as cerebral palsy or muscular dystrophies. The purpose of this study is to construct a model of muscle tissue that, through choosing the correct material parameters based on experimental data, will accurately capture the mechanical behaviour of whole muscle. This model is then used to look at the impacts of the bulk modulus and material parameters on muscle deformation and strain energy-density distributions.

The Effect of Multidirectional Loading on Contractions of the M. Medial Gastrocnemius

Research has shown that compression of muscle can lead to a change in muscle force. Most studies show compression to lead to a reduction in muscle force, although recent research has shown that increases are also possible. Based on methodological differences in the loading design between studies, it seems that muscle length and the direction of transverse loading influence the effect of muscle compression on force production. Thus, in our current study we implement these two factors to influence the effects of muscle loading. In contrast to long resting length of the medial gastrocnemius (MG) in most studies, we use a shorter MG resting length by having participant seated with their knees at a 90° angle. Where previous studies have used unidirectional loads to compress the MG, in this study we applied a multidirectional load using a sling setup. Multidirectional loading using a sling setup has been shown to cause muscle force reductions in previous research. As a result of our choices in experimental design we observed changes in the effects of muscle loading compared to previous research. In the present study we observed no changes in muscle force due to muscle loading. Muscle thickness and pennation angle showed minor but significant increases during contraction. However, no significant changes occurred between unloaded and loaded trials. Fascicle thickness and length showed different patterns of change compared to previous research. We show that muscle loading does not result in force reduction in all situations and is possibly linked to differences in muscle architecture and muscle length.

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.