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

Abstract

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.

A three-dimensional model of skeletal muscle tissues

“…We ran simulations with the fully dynamic model on a muscle-aponeurosis configuration as in Figure 3, and subjected the +x-face of the top aponeurosis to cyclic contractions; simultaneously, the muscle fibres were activated in a synchronized manner. We found comparable patterns of tissue accelerations in the longitudinal direction across the dynamic model during cyclic contractions [64] to that of the experiments on rat plantaris muscle [67], again scaling the accelerations by a length scale corresponding to the location in the muscle. We found a larger difference in scaled acceleration in the middle of the muscle relative to the end with greater muscle size for the model and greater added mass for the in situ muscle.…”

“…In Figure 4, we present time traces of the x-components of the displacement. These are measured at 4 distinct points along the centerline of the muscle block: at x(L) (the face being pulled), x 1 close to this face, x mid at the midpoint of the block and x 2 close to the clamped and the simplified version of the medium gastrocnemius from [64] (bottom). Note that in the block geometry, the fibres run parallel to the x-axis, whereas in the medium gastrocnemius they run at an angle θ 0 from the x-axis.…”

“…in silica experiments have been performed with the use of our framework for isometric contractions to study the energetics of muscle contractions [88], and of compression loads on muscles [71]. In the dynamic case, the framework has been used to simulate cyclic contraction [64,68]. With this framework it is possible to specify different mechanical properties of various tissues (muscle, aponeurosis, fat, base material and tendon), localized fibre orientation vectors, regionalized activation of muscle fibres, as well as importing custom-made (MRI-derived) meshes.…”

The energy of muscle contraction. IV. Greater mass of larger muscles decreases contraction efficiency

“…We previously found smaller reductions in mass-specific mechanical work due to greater mass in muscles with higher fibre pennation angles at rest [64]. If we assume that pennation angle has little effect on metabolic cost, which may be reasonable given how little muscle mass altered metabolic cost in this study, muscles with higher pennations may be more efficient for larger muscles in larger animals.…”

“…Aponeurosis may also play a role in limiting the effects of muscle mass in larger animals. We previously showed that larger muscles with greater mass store more energy in aponeurosis during cyclic contractions [64]. However, it is not yet clear what role this energy storage has in mitigating the effects of greater muscle mass, and if this role is altered with changes in aponeurosis properties with body size.…”