Transverse anisotropy in the deformation of the muscle during dynamic contractions

The role of pennation angle and architectural gearing to rate of force development in dynamic and isometric muscle contractions

BACKGROUND

Associations between muscle architecture and rate of force development (RFD) have been largely studied during fixed-end (isometric) contractions. Fixed-end contractions may, however, limit muscle shape changes and thus alter the relationship between muscle architecture an RFD.

AIM

We compared the correlation between muscle architecture and architectural gearing and knee extensor RFD when assessed during dynamic versus fixed-end contractions.

METHODS

Twenty-two recreationally active male runners performed dynamic knee extensions at constant acceleration (2000°s-2) and isometric contractions at a fixed knee joint angle (fixed-end contractions). Torque, RFD, vastus lateralis muscle thickness, and fascicle dynamics were compared during 0-75 and 75-150 ms after contraction onset.

RESULTS

Resting fascicle angle was moderately and positively correlated with RFD during fixed-end contractions (r = 0.42 and 0.46 from 0-75 and 75-150 ms, respectively; p < 0.05), while more strongly (p < 0.05) correlated with RFD during dynamic contractions (r = 0.69 and 0.73 at 0-75 and 75-150 ms, respectively; p < 0.05). Resting fascicle angle was (very) strongly correlated with architectural gearing (r = 0.51 and 0.73 at 0-75 ms and 0.50 and 0.70 at 75-150 ms; p < 0.05), with gearing in turn also being moderately to strongly correlated with RFD in both contraction conditions (r = 0.38-0.68).

CONCLUSION

Resting fascicle angle was positively correlated with RFD, with a stronger relationship observed in dynamic than isometric contraction conditions. The stronger relationships observed during dynamic muscle actions likely result from different restrictions on the acute changes in muscle shape and architectural gearing imposed by isometric versus dynamic muscle contractions.

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.

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.

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.

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.

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.

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.

Skeletal Muscle Shape Change in Relation to Varying Force Requirements Across Locomotor Conditions

Contractions of skeletal muscles to generate in vivo movement involve dynamic changes in contractile and elastic tissue strains that likely interact to influence the force and work of a muscle. However, studies of the in vivo dynamics of skeletal muscle and tendon strains remain largely limited to bipedal animals, and rarely cover the broad spectra of movement requirements met by muscles that operate as motors, struts, or brakes across the various gaits that animals commonly use and conditions they encounter. Using high-speed bi-planar fluoromicrometry, we analyze in vivo strains within the rat medial gastrocnemius (MG) across a range of gait and slope conditions. These conditions require changes in muscle force ranging from decline walk (low) to incline gallop (high). Measurements are made from implanted (0.5–0.8 mm) tantalum spheres marking MG mid-belly width, mid-belly thickness, as well as strains of distal fascicles, the muscle belly, and the Achilles tendon. During stance, as the muscle contracts, muscle force increases linearly with respect to gait–slope combinations, and both shortening and lengthening fiber strains increase from approximately 5 to 15% resting length. Contractile change in muscle thickness (thickness strain) decreases (r² = 0.86; p = 0.001); whereas, the change in muscle width (width strain) increases (r² = 0.88; p = 0.001) and tendon strain increases (r² = 0.77; p = 0.015). Our results demonstrate force-dependency of contractile and tendinous tissue strains with compensatory changes in shape for a key locomotor muscle in the hind limb of a small quadruped. These dynamic changes are linked to the ability of a muscle to tune its force and work output as requirements change with locomotor speed and environmental conditions.

Ultrasound imaging to assess skeletal muscle architecture during movements: a systematic review of methods, reliability, and challenges

B-mode ultrasound is often used to quantify muscle architecture during movements. Our objectives were to 1) systematically review the reliability of fascicle length (FL) and pennation angles (PA) measured using ultrasound during movements involving voluntary contractions; 2) systematically review the methods used in studies reporting reliability, discuss associated challenges, and provide recommendations to improve the reliability and validity of dynamic ultrasound measurements; and 3) provide an overview of computational approaches for quantifying fascicle architecture, their validity, agreement with manual quantification of fascicle architecture, and advantages and drawbacks. Three databases were searched until June 2019. Studies among healthy human individuals aged 17-85 yr that investigated the reliability of FL or PA in lower-extremity muscles during isoinertial movements and that were written in English were included. Thirty studies (n = 340 participants) were included for reliability analyses. Between-session reliability as measured by coefficient of multiple correlations (CMC), and coefficient of variation (CV) was FL CMC: 0.89-0.96; CV: 8.3% and PA CMC: 0.87-0.90; CV: 4.5-9.6%. Within-session reliability was FL CMC: 0.82-0.99; CV: 0.0-6.7% and PA CMC: 0.91; CV: 0.0-15.0%. Manual analysis reliability was FL CMC: 0.89-0.96; CV: 0.0-15.9%; PA CMC: 0.84-0.90; and CV: 2.0-9.8%. Computational analysis FL CMC was 0.82-0.99, and PA CV was 14.0-15.0%. Eighteen computational approaches were identified, and these generally showed high agreement with manual analysis and high validity compared with phantoms or synthetic images. B-mode ultrasound is a reliable method to quantify fascicle architecture during movement. Additionally, computational approaches can provide a reliable and valid estimation of fascicle architecture.

Passive and dynamic muscle architecture during transverse loading for gastrocnemius medialis in man

External forces from our environment impose transverse loads on our muscles. Studies in rats have shown that transverse loads result in a decrease in the longitudinal muscle force. Changes in muscle architecture during contraction may contribute to the observed force decrease. The aim of this study was to quantify changes in pennation angle, fascicle dimensions, and muscle thickness during contraction under external transverse load. Electrical stimuli were elicited to evoke maximal force twitches in the right calf muscles of humans. Trials were conducted with transverse loads of 2, 4.5, and 10 kg. An ultrasound probe was placed on the medial gastrocnemius in line with the transverse load to quantify muscle characteristics during muscle twitches. Maximum twitch force decreased with increased transverse muscle loading. The 2, 4.5, and 10 kg of transverse load showed a 9, 13, and 16% decrease in longitudinal force, respectively. Within the field of view of the ultrasound images, and thus directly beneath the external load, loading of the muscle resulted in a decrease in the muscle thickness and pennation angle, with higher loads causing greater decreases. During twitches the muscle transiently increased in thickness and pennation angle, as did fascicle thickness. Higher transverse loads showed a reduced increase in muscle thickness. Smaller increases in pennation angle and fascicle thickness strain also occurred with higher transverse loads. This study shows that increased transverse loading caused a decrease in ankle moment, muscle thickness, and pennation angle, as well as transverse deformation of the fascicles.