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Muscle- specific economy of force 
generation and efficiency of work 
production during human running
Sebastian Bohm1,2*, Falk Mersmann1,2, Alessandro Santuz1,2, Arno Schroll1,2, 
Adamantios Arampatzis1,2
1Humboldt- Universität zu Berlin, Department of Training and Movement Sciences, 
Berlin, Germany; 2Berlin School of Movement Science, Humboldt- Universität zu 
Berlin, Berlin, Germany
Abstract Human running features a spring- like interaction of body and ground, enabled by 
elastic tendons that store mechanical energy and facilitate muscle operating conditions to minimize 
the metabolic cost. By experimentally assessing the operating conditions of two important muscles 
for running, the soleus and vastus lateralis, we investigated physiological mechanisms of muscle 
work production and muscle force generation. We found that the soleus continuously shortened 
throughout the stance phase, operating as work generator under conditions that are considered 
optimal for work production: high force- length potential and high enthalpy efficiency. The vastus 
lateralis promoted tendon energy storage and contracted nearly isometrically close to optimal 
length, resulting in a high force- length- velocity potential beneficial for economical force generation. 
The favorable operating conditions of both muscles were a result of an effective length and velocity- 
decoupling of fascicles and muscle- tendon unit, mostly due to tendon compliance and, in the soleus, 
marginally by fascicle rotation.
Introduction
During locomotion, muscles generate force and perform work in order to support and accelerate 
the body, and the activity of the lower- limb muscles accounts for most of the metabolic energy cost 
needed to walk or run (Kram and Taylor, 1990; Kram, 2000; Dickinson et al., 2000). Running is char-
acterized by a spring- like interaction of the body with the ground, indicating a significant conversion 
of the body’s kinetic and potential energy to strain energy - via the elongation of elastic elements, 
mainly tendons - that can be recovered in the propulsive second half of the stance phase (Dickinson 
et al., 2000; Roberts and Azizi, 2011; Cavagna et al., 1964). In addition, the elasticity of tendons 
influences the operating conditions of the muscles, which in turn are associated with their metabolic 
cost (Roberts, 2002). For a given muscle force, the metabolic cost depends on the muscle’s oper-
ating force- length and force- velocity potential (Bohm et al., 2019; Bohm et al., 2018; Nikolaidou 
et al., 2017) (fraction of maximum force according to the force- length [Gordon et al., 1966] and 
force- velocity [Hill, 1938] curves) because it determines the number of recruited muscle fibers and 
thus the active muscle volume (Roberts, 2002). This means that quasi isometric contractions close the 
optimum of the force- length curve, that is, with a high force- length- velocity potential, are theoreti-
cally most economical for generating a given force. During steady- state running, however, the human 
system does not perfectly conserve all the mechanical energy in each stride. Therefore, muscular work 
by active muscle shortening is needed to maintain the running movement, yet it increases the meta-
bolic cost a) due to the reduced force- velocity potential, which will increase the active muscle volume 
for a given force (Roberts and Azizi, 2011), and b) due to the higher metabolic energy consumption 
RESEARCH ARTICLE
*For correspondence: 
 sebastian. bohm@ hu- berlin. de
Competing interest: The authors 
declare that no competing 
interests exist.
Funding: See page 13
Received: 03 February 2021
Preprinted: 19 February 2021
Accepted: 06 August 2021
Published: 02 September 2021
Reviewing Editor: Carlos Isales, 
Medical College of Georgia at 
Augusta University, United States
   Copyright Bohm et al. This 
article is distributed under the 
terms of the Creative Commons 
Attribution License, which 
permits unrestricted use and 
redistribution provided that the 
original author and source are 
credited.
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of each fiber when actively shortening (Smith et al., 2005; He et al., 2000). The active shorting range 
and velocity of a muscle during movements can be reduced by its tendon and, thus, an important 
benefit of tendon elasticity is a reduction in the metabolic cost of running.
At the muscle level, it has been shown that the triceps surae muscle group produces muscular 
work/energy during the stance phase of steady- state running (Lai et al., 2014). The soleus is the 
largest muscle in this group (Albracht et al., 2008) and does work by active shortening throughout 
the entire stance phase (Bohm et al., 2019; Bohm et al., 2021). In the first part of the stance phase, 
the performed muscular work is stored in the Achilles tendon as elastic strain energy. During the 
later propulsion phase, the tendon strain energy recoil contributes to the muscular energy produc-
tion, suggesting an energy amplification behavior (Roberts and Azizi, 2011) within the triceps surae 
muscle- tendon unit (MTU) during running. On the contrary, the vastus lateralis muscle, as the largest 
muscle of the quadriceps femoris muscle group (Mersmann et al., 2015), operates nearly isometri-
cally despite a lengthening- shortening behavior of the vastus lateralis MTU (Bohm et al., 2018; Monte 
et al., 2020). The almost isometric contraction suggests a negligible mechanical work production by 
the vastus lateralis during running and a spring- like energy exchange between body and vastus later-
alis MTU, which promotes energy conservation (Dickinson et al., 2000; Roberts and Azizi, 2011).
The triceps surae and the quadriceps muscle group are considered to be crucial for running perfor-
mance (Arampatzis et al., 2006; Hamner and Delp, 2013). The quadriceps femoris decelerates and 
supports the body early in stance while the triceps surae accounts for the propulsion later in the stance 
phase (Dorn et al., 2012; Santuz et al., 2020; Hamner and Delp, 2013). The soleus and vastus later-
alis, as the largest muscles of both muscle groups, show marked differences in their morphological 
and architectural properties with shorter fascicles and higher pennation angles in the soleus (Bohm 
et al., 2019; Maganaris et al., 1998) compared to vastus lateralis (Bohm et al., 2018; Marzilger 
et al., 2018). Because of the long fascicles of the vastus lateralis, a unit of force generated by this 
muscle is metabolically more expensive (Biewener and Roberts, 2000) compared to the soleus. Our 
previous findings (Bohm et al., 2018) suggest that the vastus lateralis operates at a high force- length- 
velocity potential during running, which would indicate a fascicle contraction condition that could 
minimize the energetic cost of muscle force generation. The soleus muscle instead operates as a 
muscular work generator through active shortening, though close to the optimum of the force- length 
curve. Operating with increasing shortening velocity decreases the force- velocity potential according 
to the force- velocity relationship (Bohm et al., 2019; Bohm et al., 2021) and may increase the ener-
getic cost of muscle force generation, marking a trade- off between mechanical work production and 
metabolic expenses. The enthalpy efficiency (Barclay, 2015) (or mechanical efficiency; Hill, 1939; Hill, 
1964) quantifies the fraction of chemical energy from ATP hydrolysis that is converted into mechanical 
work and depends on the shortening velocity, with a steep increase at low shortening velocities up to 
a maximum at around 20% of the maximum shortening velocity (Vmax) and a decrease thereafter (Hill, 
1939; Barclay et al., 1993; Hill, 1964). Previous findings suggest that the soleus fascicles continu-
ously shorten at a moderate velocity during the stance phase of running (Bohm et al., 2019), covering 
a range that corresponds to a high efficiency. Therefore, the soleus muscle may operate at fascicle 
conditions that would be beneficial for economical work/energy production.
The muscle fascicle behavior is strongly influenced by the decoupling of the fascicles from the MTU 
excursions due to tendon elasticity and fascicle rotation (Azizi et al., 2008; Alexander, 1991; Zuur-
bier and Huijing, 1992; Wakeling et al., 2011). The previously reported decoupling of the soleus 
muscle indicates that tendon elasticity and fascicle rotation affect the operating fascicle length and 
velocity during running (Bohm et al., 2019; Werkhausen et al., 2019); however, their integration in 
the regulation of the efficiency- fascicle velocity dependency is unclear. Regarding the vastus lateralis 
muscle, it was suggested that proximal muscles like the knee extensors feature less compliant tendons 
compared to the distal triceps surae muscles, thus limiting the decoupling between fascicles and MTU 
(Farris and Sawicki, 2012; Biewener and Daley, 2007; Biewener, 2016). However, in our previous 
study, we found significantly smaller vastus lateralis fascicle length changes compared to the vastus 
lateralis MTU (Bohm et al., 2018), indicating an important decoupling within the vastus lateralis MTU 
due to tendon elasticity.
The purpose of this study was to assess the soleus and the vastus lateralis fascicle behavior with 
regard to the operating force- length- velocity potential and enthalpy efficiency to investigate physi-
ological mechanisms for muscle work production and muscle force generation during running. The 
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soleus muscle actively shortens during the stance phase at moderate velocities, which may match the 
plateau of the enthalpy efficiency- velocity curve, and operates close to the optimum of the force- 
length curve. Therefore, we hypothesized that the soleus muscle as a work generator operates at 
a high force- length potential and a high enthalpy efficiency, minimizing the metabolic cost of work 
production. On the other hand, the vastus lateralis muscle that promotes energy conservation seems 
to operate at a favorable length and almost isometrically. Thus, we hypothesized a high force- length 
and a high force- velocity potential that would reduce the metabolic energy cost of muscle force 
generation. In order to investigate the regulation of the efficiency and force potentials, we further 
quantified the length and velocity- decoupling of the fascicles from the MTU as well as the electro-
myographic (EMG) activity. Because of experimental constrains, the two muscles were measured in 
two groups, respectively.
Results
There were no significant differences in the anthropometric characteristics between groups (age 
p=0.369, height p=0.536, body mass p=0.057). The experimentally assessed optimal fascicle length 
for force generation (L0) of the soleus was on average 41.3 ± 5.2 mm and significantly shorter than L0 
of the vastus lateralis with 94.0 ± 11.6 mm (p<0.001). The forces that corresponded to L0 of soleus and 
vastus lateralis (Fmax) were 2887 ± 724 N and 4990 ± 914 N (p<0.001), respectively. Furthermore, the 
assessed Vmax was 279 ± 35 mm/s for the soleus, significantly lower than the Vmax of the vastus lateralis 
with 1082 ± 133 mm/s (p<0.001).
The stance and swing times during running were 304 ± 23 ms and 439 ± 26 ms for the soleus group 
and 290 ± 22 ms and 448 ± 30 ms for the vastus lateralis group (p=0.075, p=0.369). The EMG compar-
ison showed that the soleus was active throughout the entire stance phase of running while the vastus 
lateralis was mainly active in the first part of the stance and with an earlier peak of activation (soleus 
41 ± 5% of the stance phase, vastus lateralis 35 ± 4% of the stance phase, p<0.001, Figure 1). During 
the stance phase, the MTU of both muscles showed a lengthening- shortening behavior, but the vastus 
lateralis MTU started to shorten earlier (soleus 59 ± 2% of the stance phase, vastus lateralis 50 ± 
2% of the stance phase, p<0.001, Figure 1). The soleus and the vastus lateralis fascicle length were 
clearly decoupled from the MTU length with smaller operating length ranges throughout the whole 
stance phase (Figure 1). The soleus fascicles operated at a length close to L0 at touchdown and then 
shortened continuously until the foot lift- off (0.994–0.752 L/L0, Figure 1). The operating length of the 
vastus lateralis fascicles remained closely above L0 over the entire stance phase and was on average 
significantly longer compared to the soleus fascicles (soleus 0.899 ± 0.104 L/L0, vastus lateralis 1.054 
± 0.082 L/L0, p<0.001, Figure 1).
The stance phase- averaged force- length potential of both muscles was high and not significantly 
different (p=0.689, Figure 2). The average pennation angle of the soleus was significantly greater 
than that of the vastus lateralis (soleus 23.9 ± 5.1°, vastus lateralis 13.3 ± 1.8°, p<0.001) and increased 
continuously throughout stance, whereas it remained almost unchanged in the vastus lateralis 
(Figure 1). The average operating velocity of the soleus fascicles was significantly higher compared 
to the vastus lateralis (soleus 0.799 ± 0.260 L0/s, vastus lateralis 0.084 ± 0.258 L0/s, p<0.001), which 
showed an almost isometric contraction throughout stance. Consequently, the force- velocity potential 
(p<0.001) and thus the overall force- length- velocity potential (p<0.001) of the soleus was significantly 
lower compared to the vastus lateralis during the stance phase (Figure 2). However, the higher short-
ening velocity of the soleus was close to the optimum for maximum enthalpy efficiency, leading to 
a significantly higher enthalpy efficiency over the stance phase in comparison to the vastus lateralis 
(p<0.001, Figure 3).
The fascicle, muscle belly, and MTU length changes throughout stance as well as the resulting 
velocity decoupling coefficients (DC) are illustrated in Figure 4 for both muscles, where DCTendon quan-
tifies the decoupling due to tendon compliance, DCBelly due to fascicle rotation, and DCMTU the overall 
decoupling of MTU and fascicles. There was a clear length and velocity- decoupling of MTU and belly 
due to tendon compliance in both muscles (Figure 4). The statistical parametric mapping (SPM) anal-
ysis revealed a significantly lower DCTendon of the soleus compared to the vastus lateralis between 4% 
and 8% of the stance phase (p=0.032) since decoupling started later for the soleus. Between 20% 
and 57% of the stance phase (p<0.001) and between 65%  of the stance phase until lift- off, the soleus 
DCTendon was significantly higher than vastus lateralis (p<0.001, Figure 4). The DCTendon averaged over 
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the stance phase of the soleus was also significantly greater (p<0.001, Table 1). Furthermore, the 
velocity- decoupling of muscle belly and fascicles due to fascicle rotation progressively increased in the 
second part of the stance phase for the soleus but was negligible for the vastus lateralis (Figure 4). 
The soleus DCBelly was significantly higher from 33%  of the stance phase until lift- off compared to the 
vastus lateralis as shown by the SPM analysis (p<0.001, Figure 4) but also when averaged over the 
entire stance phase (p<0.001, Table 1). DCBelly was markedly lower than DCTendon, indicating that the 
tendon took over the majority of the overall decoupling in both muscles (Figure 4). Accordingly and 
similarly to DCTendon, the SPM analysis for the overall decoupling of MTU and fascicles showed that 
0
20
40
60
80
100
0.6
0.8
1.0
1.2
1.4
Fascicle length Norm (L/L 0)
0
20
40
60
80
100
5.0
6.0
7.0
8.0
9.0
MTU length Norm (L/L 0)
2.5
3.0
3.5
4.0
4.5
0
20
40
60
80
100
0
10
20
30
40
Pennation angle (°)
 
0
20
40
60
80
100
Stance phase (%)
0.0
0.2
0.4
0.6
0.8
1.0
EMG Norm 
SOL MTU length Norm (L/L0)
Fascicle length Norm (L/L 0)
Pennation angle (°)
EMG Norm  
VL MTU length Norm (L/L0)
A
D
C
B
Stance phase (%)
SOL
VL
SOL
VL
SOL
VL
SOL
VL
Stance phase (%)
Stance phase (%)
Stance phase (%)
Figure 1. 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).
The online version of this article includes the following source data for figure 1:
Source data 1. Numerical data represented in the graph 1.
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DCMTU of the soleus was significantly lower between 4% and 8% of the stance phase (p=0.032) and 
significantly higher from 20% to 57% of the stance phase and from 65%  of the stance phase until 
lift- off compared to the vastus lateralis (p<0.001, Figure 4). The stance phase- averaged DCMTU of the 
soleus was significantly greater compared to the vastus lateralis as well (p<0.001, Table 1).
Discussion
We mapped the operating length and velocity of the soleus and the vastus lateralis fascicles during 
running onto the individual force- length, force- velocity, and enthalpy efficiency- velocity curves in order 
to investigate physiological mechanisms for muscle force generation and muscle work production 
SOL
VL
Force-length-velocity potential
*
*
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
Force-velocity potential
Force-length potential
A
B
C
Figure 2. 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).
The online version of this article includes the following source data for figure 2:
Source data 1. Numerical data represented in the graph 2.
0.0
0.2
0.4
0.6
0.8
1.0
Fascicle velocity (V/Vmax)
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
Enthalpy efficiency
*
SOL
VL
Figure 3. 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).
The online version of this article includes the following source data for figure 3:
Source data 1. Numerical data represented in the graph 3.
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Figure 4. 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).
The online version of this article includes the following source data for figure 4:
Source data 1. Numerical data represented in the graph 4.
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 ± 0.128
0.180 ± 0.053*
DCBelly (V/Vmax)
0.016 ± 0.008
0.003 ± 0.002*
DCMTU (V/Vmax)
0.574 ± 0.127
0.179 ± 0.014*
*Statistically significant difference between the two muscles (p<0.05).
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in the two muscles. The soleus continuously shortened throughout the stance phase and produced 
muscular work at a shortening velocity close to the enthalpy efficiency optimum. Vastus lateralis oper-
ated with smaller length changes, almost isometrically, resulting in a high force- velocity potential, 
which is beneficial for economic force generation. Both muscles operated close to L0, that is, at a high 
force- length potential. Tendon compliance was responsible for the majority of the overall decoupling 
of MTU and fascicles in both muscles, enabling favorable conditions for muscle force or muscle work 
production. Only in the soleus muscle did fascicle rotation contribute to the overall decoupling, indi-
cating an additional, yet comparatively minor effect on the fascicle dynamics during locomotion.
The triceps surae and quadriceps muscle groups are the main contributors for locomotion and thus 
responsible for a great portion of the metabolic energy cost of running (Farris and Sawicki, 2012; 
Fletcher and MacIntosh, 2015; Uchida et al., 2016; Hamner and Delp, 2013). While the quadriceps 
mainly decelerates and supports body mass in the early stance phase, the triceps surae contributes 
to the acceleration of the center of mass during the second part of the stance phase (Dorn et al., 
2012; Hamner and Delp, 2013). The soleus is the largest muscle of the triceps surae (Albracht et al., 
2008) and the vastus lateralis of the quadriceps (Mersmann et al., 2015) and thus both muscles are 
important for the running movement. We found that the soleus actively shortened throughout the 
entire stance phase, indicating continuous work/energy production. The average velocity at which the 
soleus shortened was very close to the optimal velocity for maximal enthalpy efficiency. Enthalpy effi-
ciency quantifies the fraction of chemical energy from ATP hydrolysis that is converted into mechanical 
muscular work (Hill, 1964; Barclay, 2015) with a peak at around 20%  of Vmax (Hill, 1939; Barclay 
et al., 1993). Consequently, the mechanical work performed by the soleus muscle, being essential 
during running (Arampatzis et al., 1999; Stefanyshyn and Nigg, 1998; Hamner and Delp, 2013; 
Lai et al., 2015) and high enough in magnitude to significantly influence the overall metabolic energy 
cost of locomotion (Bohm et al., 2019; Sawicki et al., 2020; Beck et al., 2019), was generated at a 
high enthalpy efficiency (94%  of maximum efficiency). Considering that also the soleus force- length 
potential was close to the maximum (0.92) and that a high potential may decrease the active muscle 
volume for a given muscle force (Beck et al., 2019; Biewener and Roberts, 2000; Fletcher and 
MacIntosh, 2017), our results provide evidence of a cumulative contribution of two different mech-
anisms (high force- length potential and high enthalpy efficiency) to an advantageous muscular work 
production of the soleus during running. The vastus lateralis was mainly active in the first part of the 
stance phase and its fascicles operated with very small length changes, that is, almost isometrically, 
confirming earlier reports (Bohm et al., 2018; Monte et al., 2020). This indicates that the vastus 
lateralis dissipates and/or produces negligible amounts of mechanical energy during running, yet 
generating force for the deceleration and support of the body mass. The observed decoupling of the 
vastus lateralis MTU and fascicles showed that the deceleration of the body mass in the early stance 
phase was not a result of an energy dissipation by the contractile element (active stretch) but rather an 
energy absorption by the tendinous tissue. Tendons feature low damping characteristics, resulting in a 
hysteresis of only 10%  (Pollock and Shadwick, 1994; Bennett et al., 1986), and, therefore, the main 
part of the absorbed energy of the body’s deceleration is expected to be stored as elastic tendon 
strain energy, which is then returned later in the second part of the stance phase. The high force- 
length (0.93) and force- velocity (0.96) potential of the vastus lateralis muscle throughout stance indi-
cates an energy exchange within the vastus lateralis MTU under almost optimal conditions for muscle 
force generation during running. Operating at high potentials reduces the active muscle volume for 
a given force (Biewener and Roberts, 2000; Fletcher and MacIntosh, 2017) and thus the metabolic 
energy cost of muscle force generation.
By actively shortening the soleus delivered energy during the entire stance phase to the skeleton, 
providing the main muscular work required for running. On the other side, the contractile elements of 
the vastus lateralis muscle did not contribute to the required muscular work and operated in concert 
with the elastic tendon in favor of energy storage (Roberts and Azizi, 2011). Our findings showed 
that, although the human body interacts with the ground in a spring- like manner during steady- state 
running to store mechanical energy (Dickinson et al., 2000; Roberts and Azizi, 2011), there are 
indeed muscles that operate as work generators, like the soleus, and others that promote energy 
conservations, like the vastus lateralis. Further, our results indicate that the fascicle operating length 
and velocity of the soleus muscle, the main work generator, is optimized for high enthalpy efficiency, 
while of the vastus lateralis muscle, which promote energy conservation, for a high potential of force 
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generation. The consequence of the active shortening of the soleus muscle for work production is a 
decrease of the force- velocity potential during the stance phase, which may increase the active muscle 
volume and shortening- related cost (Hill, 1938; Fenn, 1924; Smith et al., 2005; He et al., 2000). 
However, the soleus muscle features shorter fascicles (L0 = 41 mm) compared to the vastus lateralis 
muscle (L0 = 94 mm), and, for this reason, a given force generated by the soleus is energetically less 
expensive (Biewener and Roberts, 2000). The specific morphology of the soleus muscle certainly 
compensates for the reductions of the force- velocity potential and provides advantages for its function 
as work generator during submaximal steady- state running. Furthermore, operating around the ‘sweet 
spot’ of the shortening velocity for high enthalpy efficiency facilitates the economical muscular work 
production, while either a too high or a too low shortening velocity would be disadvantageous. The 
advantageous operating conditions specific for soleus and vastus lateralis during submaximal running 
shown here for a moderate speed of 2.5 m/s seem to persist at faster running speeds as well. This is 
indicated by recent evidence of a comparable muscle operating length and velocity of the soleus (Lai 
et al., 2015) and vastus lateralis (Monte et al., 2020) over a broad range of running speeds, respec-
tively. In addition, the operating behavior of both muscles seems to reflect their respective muscle 
group. The gastrocnemius muscles, as the second largest plantar flexors, have been shown to operate 
at a length similar to soleus and only at slightly higher velocities (Lai et al., 2018), suggesting efficient 
work production too. For the other monoarticular knee extensors, vastus medialis and intermedius, 
the resting fascicle length is about similar to the vastus lateralis (Ward et al., 2009), and, since they 
share the same single patellar tendon, we also do not expect that those muscles operate substantially 
different (Arnold et al., 2013), that is, likewise at a high force potential.
The almost optimal conditions for muscular work production and muscle force generation of the 
soleus and vastus lateralis were a result of an effective decoupling between MTU and fascicle length 
that was regulated by an appropriate muscle activation. For the soleus, the activation level increased 
in the first part of stance phase, contracting the muscle while the MTU increased in length. This 
activation pattern not only prevented the muscle to be stretched but also induced continuous short-
ening around the plateau of the force- length curve at a high enthalpy efficiency. The respective high 
DCTendon further indicates that a part of the body’s mechanical energy was stored as strain energy in 
the Achilles tendon in addition to the generated work by fascicle shortening. During MTU shortening 
(propulsion phase), the soleus EMG activity decreased and the tendon recoiled, enabling the high 
shortening velocities of the MTU while maintaining the fascicle operating conditions close to the effi-
ciency optimum. The simultaneous release of the stored strain energy from the tendon further added 
to the ongoing muscle work production, that is, energy amplification. The vastus lateralis muscle 
showed higher levels of activation during the initial part of the stance phase and earlier deactivation 
than soleus. The timing and level of activation regulated the decoupling within the vastus lateralis 
MTU during the body mass deceleration in a magnitude that the lengthening and shorting of the MTU 
was fully accomplished by the tendinous tissue. Consequently, the vastus lateralis fascicles operated 
at a high force- length- velocity potential and the body’s energy was stored within the MTU. Although 
being substantial for soleus and vastus lateralis, the SPM analysis revealed higher values of DCTendon 
for soleus during the major part of the stance phase (average value for soleus 0.57 V/Vmax and vastus 
lateralis 0.18 V/Vmax), indicating a greater decoupling within the soleus MTU compared to the vastus 
lateralis MTU. In the soleus muscle, fascicle rotation (changes in pennation angle) had an additional 
effect on the overall decoupling between MTU and fascicles. The results showed an increase in DCBelly 
in the second part of the stance phase where the soleus belly velocity was high during the MTU short-
ening. However, the decoupling by the fascicle rotation was considerably smaller compared to the 
tendon decoupling. Over the stance phase, belly and tendon decoupling were 1.6% Vmax and 57% Vmax 
and during the MTU shortening phase 2.6% Vmax and 72% Vmax, respectively, suggesting a rather minor 
functional role of fascicle rotation during submaximal running. In the vastus lateralis, fascicle rotation 
was virtually absent and consequently DCBelly values showed no relevant decoupling effect at all.
Note that because of the extensive experimental protocol for each muscle it was not possible to 
measure soleus and vastus lateralis in the same participants. However, both groups are a represen-
tative sample and no significant differences were found in anthropometrics and relevant gait param-
eters. Furthermore, for the determination of the vastus lateralis force- length curve, the muscle was 
not isolated, hence the curve also includes the contribution of the vastus medialis and intermedius. 
The underlying assumption for this approach is that the force- length curves of these three synergistic 
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knee extensors are comparable, which is supported by the study of Herzog et al. (Herzog et al., 
1990). Besides, it is currently not possible to measure enthalpy efficiency directly during running. 
Instead, we used an experimentally determined efficiency- velocity curve reported by Hill (Hill, 1964) 
and confirmed by others (Barclay et al., 2010) to relate the measured operating fascicle velocities 
of both muscles to the enthalpy efficiency. We were also not able to directly measure Vmax of both 
muscles and despite using a biologically funded value, its choice affects the force- velocity potential 
and enthalpy efficiency. However, when conducting a sensitivity analysis by substantially reducing or 
increasing Vmax by 30%, the force- velocity potential of vastus lateralis only changed for Vmax -30% and 
Vmax +30 % from 0.96 to 0.94 and 0.98 and of soleus from 0.63 to 0.52 and 0.65 while the enthalpy effi-
ciency changed from 0.082 to 0.081 and 0.016 for vastus lateralis and from 0.425 to 0.439 and 0.403 
for soleus, respectively, without an impact on the significance of the differences between muscles 
(potential p<0.001, efficiency p<0.001). These results support the robustness of our primary outcomes 
and strengthen our conclusions.
In conclusion, the present study demonstrated that during the stance phase of steady- state running, 
when the human body interacts with the environment in a spring- like manner, the soleus muscle acts 
as work generator and the vastus lateralis muscle as energy conservator. Furthermore, our findings 
provide evidence that the soleus operates under conditions optimal for muscular work production 
(i.e., high force- length potential and high enthalpy efficiency) and the vastus lateralis under conditions 
optimal for muscle force generation (i.e., high force- length and high force- velocity potential).
Materials and methods
Participants and experimental design
Thirty- three physically active adults, accustomed to regular running on a recreational basis (i.e., no 
competitive runners), were included in the present investigation. None of the participants reported 
any history of neuromuscular or skeletal impairments in the 6 months prior to the recordings. The 
ethics committee of the university approved the study (EA2/076/15), and the participants gave written 
informed consent in accordance with the Declaration of Helsinki. From the right leg, either the soleus 
(n = 19, 29 ± 6 years, 177 ± 9 cm, 69 ± 9 kg, seven females) or vastus lateralis (n = 14, age 28 ± 4 years, 
height 179 ± 7 cm, body mass 75 ± 8 kg, three females) muscle fascicle length, fascicle pennation 
angle, and EMG activity were recorded during running on a treadmill at 2.5  m/s. Corresponding 
MTU lengths were calculated from the kinematic data and individually measured tendon lever arms. 
We further assessed the soleus and vastus lateralis force- fascicle length and force- fascicle velocity 
relationship to calculate the force- length and force- velocity potential of the soleus and the vastus 
lateralis muscle fascicles during running. The operating fascicle velocity was additionally mapped on 
the enthalpy efficiency- velocity relationship to assess the enthalpy efficiency of both muscles. The 
contribution of the decoupling of the fascicle length and velocity from the MTU to the operating 
force potential and enthalpy efficiency at the level of tendon and muscle belly during running was 
examined for both muscles as well. All data for one participant were collected on the same day and 
sensors (EMG, ultrasound, reflective markers) remained attached between the different parts of the 
experiment.
Joint kinematics, fascicle behavior, and electromyographic activity 
during running
After a familiarization phase, a 4 min running trial on a treadmill (soleus: h/p cosmos mercury, Isny, 
Germany; vastus lateralis: Daum electronic, ergo_run premium8, Fürth, Germany) was performed 
and kinematics of the right leg were captured by a Vicon motion capture system (version 1.8, Vicon 
Motion Systems, Oxford, UK, 250  Hz) using an anatomically referenced reflective marker setup 
(greater trochanter, lateral femoral epicondyle and malleolus, fifth metatarsal, and tuber calcanei). 
The kinematic data were used to determine the touchdown of the foot and the toe- off as consecutive 
minima in knee joint angle over time (Fellin et al., 2010). Furthermore, the kinematics of the ankle 
and knee joint served to calculate the MTU length change of the soleus and vastus lateralis during 
running as the product of ankle joint angle changes and Achilles tendon lever arm as well as knee 
joint angle changes and patellar tendon lever arm (Lutz and Rome, 1996), respectively. We used 
the ultrasound- based tendon- excursion method for the Achilles tendon lever arm determination (An 
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et al., 1984). The patellar tendon lever arm was measured using magnetic resonance imaging in fully 
extended knee joint position and calculated as a function of the knee joint angle change using the 
data by Herzog and Read (Herzog and Read, 1993; for a detailed description of both tendon lever 
arm measurements, see Bohm et al., 2019; Bohm et al., 2018; Bohm et al., 2021). The initial soleus 
and vastus lateralis MTU length was calculated based on the regression equation provided by Hawkins 
and Hull (Hawkins and Hull, 1990) at neutral ankle joint angle for the soleus MTU and at touchdown 
for the vastus lateralis MTU. During the running trial, ultrasound images of either the soleus or vastus 
lateralis muscle fascicles were recorded synchronously to the kinematic data (soleus: Aloka Prosound 
Alpha 7, Hitachi, Tokyo, Japan, 6 cm linear array probe, UST- 5713T, 13.3 MHz, 146 Hz; vastus lateralis: 
My Lab60, Esaote, Genova, Italy, 10 cm linear array probe LA923, 10 MHz, 43 Hz). The ultrasound 
probe was mounted over the medial aspect of the soleus muscle belly or on the vastus lateralis muscle 
belly (≈50%  of femur length) using a custom anti- skid neoprene- plastic cast. The fascicle length was 
post- processed from the ultrasound images using a self- developed semi- automatic tracking algorithm 
(Marzilger et al., 2018) that calculated a representative reference fascicle on the basis of multiple 
muscle fascicle portions identified from the entire displayed muscle (for details, see Bohm et al., 
2018; Marzilger et al., 2018; Figure 5). Visual inspection of each image was conducted and correc-
tions were made if necessary. At least nine steps were analyzed for each participant and then aver-
aged (Bohm et al., 2018; Giannakou et al., 2011). The pennation angle was calculated as the angle 
between the deeper aponeurosis and the reference fascicle (Figure 5). The length changes of the 
muscle belly of soleus and vastus lateralis were calculated as the differences of consecutive products 
of fascicle length and the respective cosine of the pennation angle (Fukunaga et al., 2001). Note 
rF
Fascicle length (mm)
5000
4000
3000
2000
1000
0
Force (N)
20            40            60           80
A
upper 
apon.
deeper 
apon.
1 cm
F
θ
upper aponeurosis
deeper aponeurosis
θ
0
2000
4000
6000
8000
Force (N)
 
Fascicle length (mm)
 
 
60          70           80          90         100
B
F
1 cm
Figure 5. 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).
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that this does not give the length of the entire soleus or vastus lateralis muscle belly but rather the 
projection of the instant fascicle length onto the plane of the MTU, which can be used to calculate 
the changes of the belly length (Bohm et al., 2019). The velocities of fascicles, belly, and MTU were 
calculated as the first derivative of the lengths over time.
Surface EMG of the vastus lateralis and the soleus were measured by means of a wireless EMG 
system (Myon m320RX, Myon AG, Baar, Switzerland, 1000 Hz). A fourth- order high- pass Butterworth 
filter with 50 Hz cut- off frequency, a full- wave rectification, and then a low- pass filter with 20 Hz cut- 
off frequency were applied to the raw EMG data. The EMG activity was averaged over the same 
steps that were analyzed for the soleus parameters and for the vastus lateralis over 10 running steps. 
EMG values were then normalized for each participant to the maximum obtained during a individual 
maximum voluntary contraction.
Assessment of the force-length, force-velocity, and enthalpy efficiency-
velocity relationship
To determine the soleus and the vastus lateralis force- length relationship, eight maximum voluntary 
plantar flexion or knee extension contractions (MVCs) in different joint angles were performed with 
the right leg on an isokinetic dynamometer (Biodex Medical, Syst. 3, Inc, Shirley, NY), following a 
standardized warm- up (Bohm et al., 2019; Bohm et al., 2018; Nikolaidou et al., 2017; Figure 5). For 
the plantar flexion MVCs, the participants were placed in prone position with the knee in fixed flexed 
position (~120°) to restrict the contribution of the bi- articular m. gastrocnemius to the plantar flexion 
moment (Hof and van den Berg, 1977) and the joint angles were set in a randomized equally distrib-
uted order ranging from 10° plantar flexion to the individual maximum dorsiflexion angle. Regarding 
the knee extensions, participants were seated with a hip joint angle of 85° to reduce the contribution 
of the bi- articular m. rectus femoris (Herzog et al., 1990), while the knee joint angle ranged between 
20° to 90° knee joint angle (0° = knee extended) in randomly ordered 10° intervals. The resultant 
moments at the ankle and knee joint were calculated under consideration of the effects of gravita-
tional and passive moments and any misalignment between joint axis and dynamometer axis using 
an established inverse dynamics approach (Arampatzis et al., 2005; Arampatzis et al., 2004). The 
required kinematic data were recorded during the MVCs based on anatomically referenced reflective 
markers (medial and lateral malleoli and epicondyle, calcaneal tuberosity, second metatarsal, and 
greater trochanter) by a Vicon motion capture system (250 Hz). Furthermore, the contribution of the 
antagonistic moment produced by tibialis anterior during the plantar flexion MVCs or by the hamstring 
muscles during the knee extension MVCs was taken into account by means of an EMG- based method 
according to Mademli et al. (Mademli et  al., 2004), considering the force- length dependency of 
the antagonists (Bohm et al., 2021). The force applied to the Achilles or patellar tendon during the 
plantar flexion or knee extension MVCs was calculated as quotient of the joint moment and individual 
tendon lever arm, respectively. The soleus or the vastus lateralis fascicle behavior during the MVCs 
was synchronously captured by ultrasonography and fascicle length was determined using the same 
methodology described above (Figure 5). Accordingly, an individual force- fascicle length relationship 
was calculated for soleus or vastus lateralis by means of a second- order polynomial fit and Fmax and L0 
was derived, respectively (Figure 5).
The force- velocity relationship of the soleus and the vastus lateralis muscle was further assessed 
using the classical Hill equation (Hill, 1938) and the muscle- specific Vmax and constants of arel and brel. 
For Vmax, we took values of human soleus and vastus lateralis type 1 and 2 fibers measured in vitro 
at 15 °C reported by Luden et al. (Luden et al., 2008). The values were then adjusted (Ranatunga, 
1984) for physiological temperature conditions (37 °C) and an average fiber type distribution of the 
human soleus (type 1 fibers: 81%, type 2: 19%) and vastus lateralis muscle (type 1 fibers: 37%, type 2: 
63%) reported in literature (Johnson et al., 1973; Luden et al., 2008; Edgerton et al., 1975; Larsson 
and Moss, 1993) was the basis to derive a representative value of Vmax. For the soleus muscle under 
the in vivo condition, Vmax was calculated as 6.77 L0/s and for the vastus lateralis as 11.51 L0/s. For L0, 
we then referred to the individually measured optimal fascicle length (described above, Figure 5). 
The constant arel was calculated as 0.1 + 0.4 FT, where FT is the fast twitch fiber type percentage, 
which then equals to 0.175 for the soleus and 0.351 for the vastus lateralis (Winters and Stark, 1985; 
Winters and Stark, 1988). The product of arel and Vmax gives the constant brel as 1.182 for the soleus 
and 4.042 for the vastus lateralis (Umberger et al., 2003). Based on the assessed force- length and 
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force- velocity relationships, we calculated the individual force- length and force- velocity potential of 
both muscles as a function of the fascicle operating length and velocity during the stance phase of 
running. The product of both potentials then gives the overall force- length- velocity potential.
Furthermore, we determined the enthalpy efficiency- velocity relationship for the soleus and the 
vastus lateralis muscle fascicles in order to calculate the enthalpy efficiency of both muscles as a 
function of the fascicle operating velocity during running. For this purpose, we used the experimental 
efficiency values provided by the paper of Hill, 1964 in Table 1 for a/P0 = 0.25 (Hill, 1964). By means 
of the classical Hill equation (Hill, 1938), we then transposed the original efficiency values that were 
presented as a function of relative load (relative to maximum tension) to shortening velocity (normal-
ized to Vmax). The values of enthalpy efficiency and shortening velocity were then fitted using a cubic 
spline, giving the right- skewed parabolic- shaped curve with a peak efficiency of 0.45 at a velocity of 
0.18 V/Vmax. The resulting function was then used to calculate the enthalpy efficiency of the soleus and 
the vastus lateralis during running based on the average value of the fascicle velocity over stance, 
accordingly.
Assessment of decoupling within the MTU
To quantify the decoupling of fascicle, belly, and MTU velocities over the time course of stance, 
we calculated a decoupling coefficient to account for the tendon compliance (DCTendon, equation 1), 
fascicle rotation (DCBelly, equation 2), as well as for the overall decoupling of MTU and fascicle veloci-
ties that includes both components (DCMTU, equation 3).
 
DCTendon
(
t
)
=
VMTU
(
t
)
− VBelly
(
t
) /Vmax 
(1)
 
DCBelly
(
t
)
= |VBelly
(
t
)
− VFascicle
(
t
)
|/Vmax 
(2)
 
DCMTU
(
t
)
= |VMTU
(
t
)
− VFascicle
(
t
)
|/Vmax 
(3)
where V(t) is the velocity at each percentage of the stance phase (i.e. t = 0, 1, …, 100% stance). 
We introduced these new decoupling coefficients because previously suggested decoupling ratios 
(i.e., tendon gearing = VMTU/VBelly, belly gearing [or architectural gear ratio] = VBelly/VFascicle, MTU gearing 
= VMTU/VFascicle; Azizi et al., 2008; Wakeling et al., 2011) may feature limitations for the application 
under in vivo conditions, that is, considering that muscle belly and fascicle velocities may be very close 
to or even zero during functional tasks as walking and running (Bohm et al., 2019; Bohm et al., 2018), 
which results in non- physiological gear ratios.
Statistics
A t- test for independent samples was used to test for group differences in anthropometric character-
istics, temporal gait parameters, and differences between the soleus and the vastus lateralis fascicle 
belly, MTU, and EMG parameters. The Mann–Whitney U test was applied in case the assumption of 
normal distribution, tested by the Kolmogorov–Smirnov test with Lilliefors correction, was not met. 
The level of significance was set to α = 0.05, and the statistical analyses were performed using SPSS 
(IBM Corp., version 22, NY). Furthermore, SPM (independent samples t- test, α = 0.05) was used to 
test for differences between the DCTendon, DCBelly, and DCMTU of the soleus and the vastus lateralis 
throughout the stance phase of running. SPM was conducted using the software package spm1D 
(version 0.4, http://www. spm1d. org; Pataky, 2012).
Acknowledgements
Funding for this research was supplied by the German Federal Institute of Sport Science (grant no. 
ZMVI14- 070604/17- 18). The magnetic resonance image acquisition was funded by the foundation 
Stiftung Oskar- Helene- Heim. We further acknowledge support by the German Research Foundation 
(DFG) and the Open Access Publication Fund of Humboldt- Universität zu Berlin.
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Additional information
Funding
Funder
Grant reference number
Author
German Federal Institute 
of Sport Science
ZMVI14-070604/17-18
Adamantios Arampatzis
Stiftung Oskar Helene 
Heim
Sebastian Bohm
The funders had no role in study design, data collection and interpretation, or the 
decision to submit the work for publication.
Author contributions
Sebastian Bohm, Conceptualization, Data curation, Formal analysis, Investigation, Methodology, 
Project administration, Visualization, Writing - original draft, Writing – review and editing; Falk Mers-
mann, Data curation, Methodology, Writing – review and editing; Alessandro Santuz, Methodology, 
Writing – review and editing; Arno Schroll, Methodology, Software, Writing – review and editing; 
Adamantios Arampatzis, Conceptualization, Funding acquisition, Methodology, Supervision, Writing 
- original draft, Writing – review and editing
Author ORCIDs
Sebastian Bohm    http:// orcid. org/ 0000- 0002- 5720- 3672
Falk Mersmann    http:// orcid. org/ 0000- 0001- 7180- 7109
Alessandro Santuz    http:// orcid. org/ 0000- 0002- 6577- 5101
Adamantios Arampatzis    http:// orcid. org/ 0000- 0002- 4985- 0335
Ethics
Human subjects: The ethics committee of the Humboldt- Universität zu Berlin approved the study and 
the participants gave written informed consent in accordance with the Declaration of Helsinki.
Decision letter and Author response
Decision letter https:// doi. org/ 10. 7554/ eLife. 67182. sa1
Author response https:// doi. org/ 10. 7554/ eLife. 67182. sa2
Additional files
Supplementary files
•  Transparent reporting form 
Data availability
The final processed data can be found at: https:// doi. org/ 10. 6084/ m9. figshare. 14046749.
The following dataset was generated:
Author(s)
Year
Dataset title
Dataset URL
Database and Identifier
Bohm S, Mersmann 
F, Santuz A, Schroll A, 
Arampatzis A
2021
Data_Muscle- specific 
economy of force 
generation and efficiency 
of work production during 
human running
https:// doi. org/ 10. 
6084/ m9. figshare. 
14046749
figshare, 10.6084/
m9.figshare.14046749
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Muscle-specific economy of force generation and efficiency of work production during human running.
Bohm, Sebastian,Mersmann, Falk,Santuz, Alessandro,Schroll, Arno,Arampatzis, Adamantios