The force-length-velocity potential of the human soleus muscle is related to the energetic cost of running

Abstract

According to the force-length-velocity relationships, the muscle force potential is determined by the operating length and velocity, which affects the energetic cost of contraction. During running, the human soleus muscle produces mechanical work through active shortening and provides the majority of propulsion. The trade-off between work production and alterations of the force-length and force-velocity potentials (i.e. fraction of maximum force according to the force-length-velocity curves) might mediate the energetic cost of running. By mapping the operating length and velocity of the soleus fascicles onto the experimentally assessed force-length and force-velocity curves, we investigated the association between the energetic cost and the force-length-velocity potentials during running. The fascicles operated close to optimal length (0.90 ± 0.10 L₀) with moderate velocity (0.118 ± 0.039 V_max [maximum shortening velocity]) and, thus, with a force-length potential of 0.92 ± 0.07 and a force-velocity potential of 0.63 ± 0.09. The overall force-length-velocity potential was inversely related (r = -0.52, p = 0.02) to the energetic cost, mainly determined by a reduced shortening velocity. Lower shortening velocity was largely explained (p < 0.001, R² = 0.928) by greater tendon gearing, shorter Achilles tendon lever arm, greater muscle belly gearing and smaller ankle angle velocity. Here, we provide the first experimental evidence that lower shortening velocities of the soleus muscle improve running economy.

Keywords: biomechanics; force–length–velocity relationships; gear ratio; muscle-tendon unit; running economy.

Figure 1.

Experimental set-up for the determination of the soleus force–fascicle length relationship. (a) Maximum isometric plantar flexions (MVC) in eight different joint angles were performed on a dynamometer. During the MVCs, the soleus muscle fascicle length (F), pennation angle (Θ) and muscle thickness were measured based on ultrasound images. (b) Exemplary force–fascicle length relationship of the soleus muscle by the MVCs (squares) and the respective second-order polynomial fit (dashed line).

Figure 2.

Ankle angle, soleus muscle–tendon unit (MTU) length, muscle fascicle length, pennation angle, thickness and electromyographic (EMG) activity (normalized to maximum voluntary isometric contraction) during the stance phase of running (2.5 m s⁻¹). Individual (n = 19) data are shown in thin grey lines and group averages in thick black lines.

Figure 3.

Operating length and velocity of soleus muscle fascicles during the stance phase of running mapped onto the averaged normalized force–length and force–velocity curve. White circles indicate the average operating length and velocity of the stance phase of each participant and the black circle the respective group average with the standard deviation of all participants (n = 19). The grey shaded areas illustrate the operating range (maximum to minimum) of the operating length and velocity during the stance phase averaged for all participants. Force is normalized to the maximum force during the maximal isometric plantar flexion contractions, fascicle length to the experimentally determined optimal fascicle length and fascicle velocity to the assessed maximum shortening velocity. Dotted lines in the left graph indicate the standard deviation of the individually measured force–length relationships. Note that the data points do not lie on the average curves because the individual force potentials were calculated for each percentage of the stance phase of each step and then averaged step-wise, which makes a difference to the calculation using the overall subject-based average length or velocity due to the non-linearity of the curves.

Figure 4.

Operating velocity of the soleus muscle–tendon unit (MTU) and muscle belly (top) as well as muscle belly and fascicles (bottom) over the stance phase, illustrating the effect of tendon gearing and belly gearing, respectively. Grey shadings indicate the standard deviations (n = 19).

Figure 5.

Association of the force–length–velocity potential, force–velocity potential and force–length potential of the soleus muscle to the energetic cost of running. *Statistically significant correlation (p < 0.05).