Multidimensional models for predicting muscle structure and fascicle pennation

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.

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.

Short-Term, Equipment-Free High Intensity Interval Training Elicits Significant Improvements in Cardiorespiratory Fitness Irrespective of Supervision in Early Adulthood

Introduction: Serious health implications from having low levels of cardiorespiratory fitness (CRF) and being overweight in young adulthood are carried forward into later life. High-intensity interval training (HIIT) is a time-effective, potent stimulus for improving CRF and indices of cardiometabolic health. To date, few studies have investigated the use of equipment-free HIIT or the impact of supervision for improving CRF via HIIT. Methods: Thirty healthy young adults (18-30 y) were randomised to 4 weeks (12 sessions) equipment-free, bodyweight based supervised laboratory HIIT (L-HIIT), unsupervised home HIIT (H-HIIT) or no-intervention (CON). Utilised exercises were star jumps, squats and standing sprints. Measurements of CRF (anaerobic threshold (AT) and VO₂peak), blood pressure (BP), body mass index (BMI), blood glucose and plasma insulin by oral glucose tolerance test (OGTT), and muscle architecture were performed at baseline and after the intervention. Results: When compared to the control group, both HIIT protocols improved CRF (AT: L-HIIT mean difference compared to the control group (MD) +2.1 (95% CI: 0.34-4.03) ml/kg/min; p = 0.02; H-HIIT MD +3.01 (1.17-4.85) ml/kg/min; p = 0.002), VO₂peak: L-HIIT (MD +2.94 (0.64-5.25) ml/kg/min; p = 0.01; H-HIIT MD +2.55 (0.34-4.76) ml/kg/min; p = 0.03), BMI (L-HIIT MD -0.43 (-0.86 to 0.00) kg/m²; p = 0.05; H-HIIT: MD -0.51 (-0.95 to -0.07) kg/m²; p = 0.03) and m. vastus lateralis pennation angle (L-HIIT MD 0.2 (0.13-0.27)°; p < 0.001; H-HIIT MD 0.17 (0.09 to 0.24)°; p < 0.001). There was no significant change in BP, blood glucose or plasma insulin in any of the groups. Conclusions: Four weeks time-efficient, equipment-free, bodyweight-based HIIT is able to elicit improvements in CRF irrespective of supervision status. Unsupervised HIIT may be a useful tool for counteracting the rise of sedentary behaviours and consequent cardiometabolic disorders in young adults.

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.

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 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.

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.

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.

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.

How does passive lengthening change the architecture of the human medial gastrocnemius muscle?

There are few comprehensive investigations of the changes in muscle architecture that accompany muscle contraction or change in muscle length in vivo. For this study, we measured changes in the three-dimensional architecture of the human medial gastrocnemius at the whole muscle level, the fascicle level and the fiber level using anatomical MRI and diffusion tensor imaging (DTI). Data were obtained from eight subjects under relaxed conditions at three muscle lengths. At the whole muscle level, a 5.1% increase in muscle belly length resulted in a reduction in both muscle width (mean change -2.5%) and depth (-4.8%). At the fascicle level, muscle architecture measurements obtained at 3,000 locations per muscle showed that for every millimeter increase in muscle-tendon length above the slack length, average fascicle length increased by 0.46 mm, pennation angle decreased by 0.27° (0.17° in the superficial part and 0.37° in the deep part), and fascicle curvature decreased by 0.18 m^-1 There was no evidence of systematic variation in architecture along the muscle's long axis at any muscle length. At the fiber level, analysis of the diffusion signal showed that passive lengthening of the muscle increased diffusion along fibers and decreased diffusion across fibers. Using these measurements across scales, we show that the complex shape changes that muscle fibers, whole muscles, and aponeuroses of the medial gastrocnemius undergo in vivo cannot be captured by simple geometrical models. This justifies the need for more complex models that link microstructural changes in muscle fibers to macroscopic changes in architecture.NEW & NOTEWORTHY Novel MRI and DTI techniques revealed changes in three-dimensional architecture of the human medial gastrocnemius during passive lengthening. Whole muscle belly width and depth decreased when the muscle lengthened. Fascicle length, pennation, and curvature changed uniformly or near uniformly along the muscle during passive lengthening. Diffusion of water molecules in muscle changes in the same direction as fascicle strains.

Three-dimensional geometrical changes of the human tibialis anterior muscle and its central aponeurosis measured with three-dimensional ultrasound during isometric contractions

Background. Muscles not only shorten during contraction to perform mechanical work, but they also bulge radially because of the isovolumetric constraint on muscle fibres. Muscle bulging may have important implications for muscle performance, however quantifying three-dimensional (3D) muscle shape changes in human muscle is problematic because of difficulties with sustaining contractions for the duration of an in vivo scan. Although two-dimensional ultrasound imaging is useful for measuring local muscle deformations, assumptions must be made about global muscle shape changes, which could lead to errors in fully understanding the mechanical behaviour of muscle and its surrounding connective tissues, such as aponeurosis. Therefore, the aims of this investigation were (a) to determine the intra-session reliability of a novel 3D ultrasound (3DUS) imaging method for measuring in vivo human muscle and aponeurosis deformations and (b) to examine how contraction intensity influences in vivo human muscle and aponeurosis strains during isometric contractions.

Methods. Participants (n = 12) were seated in a reclined position with their left knee extended and ankle at 90° and performed isometric dorsiflexion contractions up to 50% of maximal voluntary contraction. 3DUS scans of the tibialis anterior (TA) muscle belly were performed during the contractions and at rest to assess muscle volume, muscle length, muscle cross-sectional area, muscle thickness and width, fascicle length and pennation angle, and central aponeurosis width and length. The 3DUS scan involved synchronous B-mode ultrasound imaging and 3D motion capture of the position and orientation of the ultrasound transducer, while successive cross-sectional slices were captured by sweeping the transducer along the muscle.

Results. 3DUS was shown to be highly reliable across measures of muscle volume, muscle length, fascicle length and central aponeurosis length (ICC ≥ 0.98, CV < 1%). The TA remained isovolumetric across contraction conditions and progressively shortened along its line of action as contraction intensity increased. This caused the muscle to bulge centrally, predominantly in thickness, while muscle fascicles shortened and pennation angle increased as a function of contraction intensity. This resulted in central aponeurosis strains in both the transverse and longitudinal directions increasing with contraction intensity.

Discussion. 3DUS is a reliable and viable method for quantifying multidirectional muscle and aponeurosis strains during isometric contractions within the same session. Contracting muscle fibres do work in directions along and orthogonal to the muscle’s line of action and central aponeurosis length and width appear to be a function of muscle fascicle shortening and transverse expansion of the muscle fibres, which is dependent on contraction intensity. How factors other than muscle force change the elastic mechanical behaviour of the aponeurosis requires further investigation.