Muscle shortening velocity depends on tissue inertia and level of activation during submaximal contractions

Abstract

In order to perform external work, muscles must do additional internal work to deform their tissue, and in particular, to overcome the inertia due to their internal mass. However, the contribution of the internal mass within a muscle to the mechanical output of that muscle has only rarely been studied. Here, we use a dynamic, multi-element Hill-type muscle model to examine the effects of the inertial mass within muscle on its contractile performance. We find that the maximum strain-rate of muscle is slower for lower activations and larger muscle sizes. As muscle size increases, the ability of the muscle to overcome its inertial load will decrease, as muscle tension is proportional to cross-sectional area and inertial load is proportional to mass. Thus, muscles that are larger in size will have a higher inertial cost to contraction. Similarly, when muscle size and inertial load are held constant, decreasing muscle activation will increase inertial cost to contraction by reducing muscle tension. These results show that inertial loads within muscle contribute to a slowing of muscle contractile velocities (strain-rates), particularly at the submaximal activations that are typical during animal locomotion.

Keywords: activation; contractile velocity; inertia; modelling; muscle mechanics.

Figure 1.

Second-order dynamic Hill-type muscle model (a). The mass of the model is evenly distributed along its length at rest such that each point mass m has the same mass and each segment has the same initial length. The force of each segment is the sum of the force from the parallel elastic element PEE (b), and the contractile element CE, which in turn is the product of its activation state, force–length (b) and force–velocity characteristics (c). The displacement of each mass depends on the balance of forces from the adjacent segments or from the external force F_e for the end mass.

Figure 2.

Force–velocity relations for fast (a) and slow (b) muscle, calculated from simulation-I. Simulations are shown for maximal (solid lines), and 20% activation (dashed lines), and for muscle mass of 1.05 g (circles) and 16.33 kg (squares). achieved at 0.01F₀ with no external load (c) and the strain-rate achieved at 0.15F₀ with an added external load of 0.6M (d) are shown for a range from maximal (solid lines) through to 20% activation (shortest dashes). Note the similar strain-rates for fast and slow muscles at 20 and 30% activation (open circles), respectively, representing data from Holt et al. [12]. Fast muscle is shown in blue and slow muscle in red for (a–d). The initial lengths required to achieve at L₀ are shown as a function of muscle mass and activation for the fast (e) and slow (f) muscle for simulation-II.