1. Physics of Living Systems
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Muscle-specific economy of force generation and efficiency of work production during human running

  1. Sebastian Bohm  Is a corresponding author
  2. Falk Mersmann
  3. Alessandro Santuz
  4. Arno Schroll
  5. Adamantios Arampatzis
  1. Humboldt-Universität zu Berlin, Department of Training and Movement Sciences, Germany
  2. Berlin School of Movement Science, Humboldt-Universität zu Berlin, Germany
Research Article
Cite this article as: eLife 2021;10:e67182 doi: 10.7554/eLife.67182
8 figures, 1 table and 1 additional file


Soleus (SOL, n = 19) and vastus lateralis (VL, n = 14) muscle-tendon unit (MTU) length (A) and muscle fascicle length (normalized to optimal fascicle length L0, B), pennation angle (C), and electromyographic (EMG) activity (normalized to a maximum voluntary isometric contraction, D) during the stance phase of running (mean ± SD).
Soleus (SOL, n = 19) and vastus lateralis (VL, n = 14) force-length potential (A), force-velocity potential (B), and overall force-length-velocity potential (C) averaged over the stance phase of running.

*Significant difference between muscles (p<0.05).

Soleus (SOL, n = 19) and vastus lateralis (VL, n = 14) enthalpy efficiency (mean ± SD) averaged over the stance phase of running onto the enthalpy efficiency-fascicle velocity relationship (dashed line).

*Significant difference between muscles (p<0.05).

Soleus (SOL, n = 19, top row) and vastus lateralis (VL, n = 14, mid row) muscle-tendon unit (MTU) vs. belly length changes (left), belly vs. fascicle length changes (mid), and MTU vs. fascicle length changes (right) over the stance phase of running with respect to the length at touchdown (0% stance phase).

Differences between curves illustrate the length-decoupling due to tendon compliance, fascicle rotation, and the overall decoupling, respectively. The bottom row shows the resulting velocity-decoupling coefficients (DCs) as the absolute velocity differences between fascicles, belly, and MTU normalized to the maximum shorting velocity (see Materials and methods). Intervals of stance with a significant difference between both muscles are illustrated as hatched areas (p<0.05).

Experimental setup for the determination of the soleus (A) and vastus lateralis (B) force-fascicle length relationship.

Maximum isometric plantar flexions (MVC) at eight different joint angles were performed on a dynamometer. During the MVCs, ultrasound images of the soleus and vastus lateralis were recorded and a representative muscle fascicle length (F) was calculated based on multiple fascicle portions (short dashed lines). Accordingly, an individual force-fascicle length relationship for the soleus and vastus lateralis muscle was derived from the MVCs (squares) by means of a second-order polynomial fit (dashed line, bottom graphs, MVCs and curves of one representative participant).

Author response image 1
Predicted efficiency for running at 5.0 m/s.
Author response image 2
Ultrasound-based determination of muscle fascicle length.

upper (uA) and deeper (dA) aponeurosis, representative reference fascicle (rF) calculated from all identified visible features of multiple fascicles (F).

Author response image 3
Comparison of efficiency-velocity curves provided in literature and assessed operating velocities of soleus (SOL) and vastus lateralis (VL).


Table 1
Average tendon (DCTendon), belly (DCBelly), and muscle-tendon unit (DCMTU) decoupling coefficients for the soleus (SOL) and vastus lateralis (VL) muscles during the stance phase of running (mean ± SD).
SOL (n = 19)VL (n = 14)
DCTendon (V/Vmax)0.567 ± 0.1280.180 ± 0.053*
DCBelly (V/Vmax)0.016 ± 0.0080.003 ± 0.002*
DCMTU (V/Vmax)0.574 ± 0.1270.179 ± 0.014*
  1. *

    Statistically significant difference between the two muscles (p<0.05).

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