A modelling approach for exploring muscle dynamics during cyclic contractions

Ross, Stephanie; Nigam, Nilima; Wakeling, James M.

doi:10.1371/journal.pcbi.1006123

Cited by 21 publications

(27 citation statements)

References 51 publications

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“…We formulated the active and passive fibre curves as trigonometric polynomial and second-order piecewise polynomial fits of experimental data (Winters et al, 2011 ). These curves ( Figure 1A ) are similar in shape to the Bézier curves presented in (Ross et al, 2018a ) but are not parametric. To model the base material properties of the muscle, we used a Yeoh model (Yeoh, 1993 ) fit to experimental data for tensile loading of muscle in the across-fibre direction (Mohammadkhah et al, 2016 ) ( Figure 1C ).…”

Section: Methodssupporting

confidence: 78%

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

et al. 2020

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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.

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Section: Methodssupporting

confidence: 78%

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

et al. 2020

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“…Because the initial density was constant at 1060 kg m –3 ( Méndez and Keys, 1960 ), muscle mass (including that of the aponeurosis) also varied with the scale-cubed, as with the volume. This method of scaling is described in more detail in Ross et al (2018b) , although the scale 1 geometry in this study is the approximate size of a human medial gastrocnemius, whereas in our previous studies it was the size of a fibre bundle ( Ross et al, 2018a , b ).…”

Section: Methodsmentioning

confidence: 95%

“…Our previous 3D muscle model ( Wakeling et al, 2020 ) was quasistatic and did not account for the effects of muscle mass, or the effects of local strain rate on muscle fibre force. In addition to considering the stress-strain rate effects to the muscle fibre response ( Ross et al, 2018b ) in our current model, we also considered the kinetic and internal energies and accounted for the external work done on the system. Note that both the kinetic and internal energies depended on the velocity, unlike our previous model in Wakeling et al (2020) and Ryan et al (2020) which assumed quasistatic deformations.…”

Section: Methodsmentioning

confidence: 99%

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

et al. 2021

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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.

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“…This metabolic model has been shown to predict metabolic rates during running that were consistent with complex metabolic models derived from the First Law of Thermodynamics and the free energy liberated by ATP hydrolysis during cross-bridge cycling [38]. Furthermore, this metabolic model was chosen because it was smooth and continuous to the second derivative, and hence was well-suited for dynamic optimization; the method used in this study to predict muscle recruitment patterns [39]. We modified the metabolic rate function to account for muscle fibre type by including a scaling factor so that the mechanical efficiency of purely slow and fast muscle fibre types were consistent with experimentally reported isokinetic concentric contractions in mice [40] as well as another metabolic model that accounted for fibre types in humans [28].…”

Section: Metabolic Energy Modelmentioning

confidence: 99%

Metabolic cost underlies task-dependent variations in motor unit recruitment

Lai

Biewener

Wakeling

2018

J. R. Soc. Interface.

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Mammalian skeletal muscles are comprised of many motor units, each containing a group of muscle fibres that have common contractile properties: these can be broadly categorized as slow and fast twitch muscle fibres. Motor units are typically recruited in an orderly fashion following the ‘size principle’, in which slower motor units would be recruited for low intensity contraction; a metabolically cheap and fatigue-resistant strategy. However, this recruitment strategy poses a mechanical paradox for fast, low intensity contractions, in which the recruitment of slower fibres, as predicted by the size principle, would be metabolically more costly than the recruitment of faster fibres that are more efficient at higher contraction speeds. Hence, it would be mechanically and metabolically more effective for recruitment strategies to vary in response to contraction speed so that the intrinsic efficiencies and contraction speeds of the recruited muscle fibres are matched to the mechanical demands of the task. In this study, we evaluated the effectiveness of a novel, mixed cost function within a musculoskeletal simulation, which includes the metabolic cost of contraction, to predict the recruitment of different muscle fibre types across a range of loads and speeds. Our results show that a metabolically informed cost function predicts favoured recruitment of slower muscle fibres for slower and isometric tasks versus recruitment that favours faster muscles fibres for higher velocity contractions. This cost function predicts a change in recruitment patterns consistent with experimental observations, and also predicts a less expensive metabolic cost for these muscle contractions regardless of speed of the movement. Hence, our findings support the premise that varying motor recruitment strategies to match the mechanical demands of a movement task results in a mechanically and metabolically sensible way to deploy the different types of motor unit.

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A modelling approach for exploring muscle dynamics during cyclic contractions

Cited by 21 publications

References 51 publications

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

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

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

Metabolic cost underlies task-dependent variations in motor unit recruitment

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