royalsocietypublishing.org/journal/rspb
Research
Cite this article: Bohm S, Mersmann F,
Santuz A, Arampatzis A. 2021 Enthalpy
efficiency of the soleus muscle contributes to
improvements in running economy.
Proc. R. Soc. B 288: 20202784.
https://doi.org/10.1098/rspb.2020.2784
Received: 6 November 2020
Accepted: 5 January 2021
Subject Category:
Morphology and biomechanics
Subject Areas:
biomechanics, physiology
Keywords:
force–length and force–velocity relationship,
enthalpy–velocity relationship, triceps surae,
endurance running, strength training,
tendon stiffness
Author for correspondence:
Sebastian Bohm
e-mail: sebastian.bohm@hu-berlin.de
Electronic supplementary material is available
online at https://doi.org/10.6084/m9.figshare.
c.5271347.
Enthalpy efficiency of the soleus muscle
contributes to improvements in running
economy
Sebastian Bohm1,2, Falk Mersmann1,2, Alessandro Santuz1,2
and Adamantios Arampatzis1,2
1Department of Training and Movement Sciences, Humboldt-Universität zu Berlin, Philippstr. 13,
10115 Berlin, Germany
2Berlin School of Movement Science, Humboldt-Universität zu Berlin, Berlin, Germany
SB, 0000-0002-5720-3672; FM, 0000-0001-7180-7109; AS, 0000-0002-6577-5101;
AA, 0000-0002-4985-0335
During human running, the soleus, as the main plantar flexor muscle, gen-
erates the majority of the mechanical work through active shortening. The
fraction of chemical energy that is converted into muscular work (enthalpy
efficiency) depends on the muscle shortening velocity. Here, we investigated
the soleus muscle fascicle behaviour during running with respect to the
enthalpy efficiency as a mechanism that could contribute to improvements
in running economy after exercise-induced increases of plantar flexor
strength and Achilles tendon (AT) stiffness. Using a controlled longitudinal
study design (n = 23) featuring a specific 14-week muscle–tendon training,
increases in muscle strength (10%) and tendon stiffness (31%) and reduced
metabolic cost of running (4%) were found only in the intervention group
(n = 13, p < 0.05). Following training, the soleus fascicles operated at higher
enthalpy efficiency during the phase of muscle–tendon unit
(MTU)
lengthening (15%) and in average over stance (7%, p < 0.05). Thus, improve-
ments in energetic cost following increases in plantar flexor strength and AT
stiffness seem attributed to increased enthalpy efficiency of the operating
soleus muscle. The results further imply that the soleus energy production
in the first part of stance, when the MTU is lengthening, may be crucial
for the overall metabolic energy cost of running.
1. Introduction
Habitual bipedalism has been recognized as a defining feature of humans [1],
and an exceptional endurance running ability has been linked to the evolution
of the human lineage [2]. Economy, which is the mass-specific rate of oxygen
uptake or metabolic energy consumption at a given speed [3,4], plays a crucial
role in endurance running performance [5]. The cost of generating force and
work through muscles to support and accelerate the body mass is the main
source of metabolic energy expenditure during locomotion [6]. The force–
length–velocity potential of muscles (defined as the fraction of maximum
force according to the force–length [7] and force–velocity relationships [8]) at
which muscles operate during running [9,10] largely dictates the required
active muscle volume and consequently the energetic cost of contraction
[3,9,11].
In human running, the triceps surae is the major contributor to propulsion
and the main plantar flexor muscle group that transmits force through the
Achilles tendon (AT) [12], consuming a significant amount of metabolic
energy [13]. In earlier studies, we provided evidence that both the contractile
capacities of the triceps surae and the mechanical properties of the AT (i.e. its
stiffness) influence running economy [14,15]. We found that the most
© 2021 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution
License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original
author and source are credited.
economical runners feature a combination of higher plantar
flexor muscle strength and AT stiffness [14], and that a
specific training of muscle strength and AT stiffness can, in
fact, improve running economy [15]. Although the associ-
ation of AT stiffness and energetic cost of running has been
confirmed by other research groups [16,17], the underlying
physiological mechanisms remain unclear.
The soleus is the greatest muscle of the triceps surae [18]
and generates the majority of work/energy to lift and accel-
erate the body [12] by actively shortening throughout the
entire stance phase of running [9,19]. In the first part of the
stance phase, the fascicle shortening is paralleled by a
lengthening of the muscle–tendon unit (MTU) [9], indicating
that a part of the body’s mechanical energy is stored as strain
energy in the AT, but also that the fascicles generate work and
save this work as strain energy in the AT. In the second part
of the stance phase, where the MTU shortens (propulsion
phase), the tendon strain energy is returned to the body
and contributes to the ongoing work generation [9]. The
metabolic cost of generating work by active shortening of
muscles depends on the velocity of the shortening [20]. The
enthalpy efficiency (or mechanical efficiency) quantifies the
fraction of chemical energy from ATP hydrolysis that is con-
verted into mechanical muscular work [21]. The relation of
enthalpy efficiency and shortening velocity shows a steep
increase at low velocities with the peak at around 20% of
the maximum shortening velocity [21,22]. During submaxi-
mal running, the soleus operates below the optimal velocity
for maximal efficiency [9], suggesting that small changes in
the shortening velocity may substantially influence the
enthalpy efficiency of the soleus muscular work production.
The mechanical interaction of the soleus muscle with the
series AT regulates the fascicle shortening dynamics. The AT
takes over a great part of the length changes of the entire
soleus MTU, thereby decoupling the muscle fascicle and
MTU behaviour and, beside the storage and release of
strain energy, allowing the fascicles to operate at velocities
favourable for economical force generation [9,19]. The mech-
anical properties of the tendon in combination with the
strength capacity of the muscle may determine the amount
of fascicle decoupling during the stance phase of running.
However, similar to an increase in muscle strength [23], ten-
dons can adapt to periods of higher mechanical loading by
increasing stiffness [24]. Our earlier findings of improved ener-
getic cost after an exercise-induced increase in AT stiffness and
plantar flexor muscle strength evidenced a direct association
between a balanced adaptation of tendon and muscle and
improvements in running economy [15]. Considering a given
work produced by the soleus muscle during the stance
phase, the energetic cost depends on the enthalpy efficiency
under which this muscular work is generated. Assuming
that a combination of increased plantar flexor strength and
AT stiffness may influence the soleus fascicle shortening pat-
tern, the overall enthalpy efficiency might improve. This
would provide an explaining mechanism to the previously
reported improvements in running economy following effec-
tive
muscle–tendon
training
[15].
To
the
best
of
our
knowledge, no study has experimentally examined the operat-
ing soleus muscle fascicles with respect to the enthalpy
efficiency and its association to the energetic cost of running.
Here, we investigated the effect of a specific muscle-
tendon training, which has been shown to increase plantar
flexor strength and AT stiffness [15], on the enthalpy
efficiency of the operating soleus fascicles during running.
Based on our earlier study [15], we expected an improvement
in running economy after 14 weeks of training. We hypoth-
esized that the training-induced increase in plantar flexor
muscle strength and AT stiffness modulates the soleus fascicle
velocity pattern throughout the stance phase towards vel-
ocities associated with a higher enthalpy efficiency, thereby
reducing the energetic cost of running.
2. Methods
(a) Participants and experimental design
A statistical power analysis was performed a priori and revealed a
required sample size of n = 12 for the intervention group (see
electronic supplementary material for details). Considering
potential dropouts, we recruited 36 participants and randomly
assigned them to an intervention (n = 19) or control group
(n = 17). Inclusion criteria were an age of 20–40 years, at least
two running sessions weekly on a recreational basis and no mus-
cular–tendinous injuries in the previous year. Only habitual
rearfoot-striking runners were considered because it is the most
common foot strike pattern [25] and also to avoid potential con-
founding effects of the strike pattern on our outcome measures.
To quantify the foot strike pattern, we assessed the strike index
[26]
(i.e. centre of pressure position with respect to the heel
relative to foot length at touchdown) during a pre-test session
(0 equals rearfoot-striking, <0.3 inclusion threshold). Twenty-
three participants completed the study, of which 13 were the
intervention group (age 29 ± 5 years, height 178 ± 8 cm, body
mass 73 ± 8 kg, four females) and 10 the control group (31 ±
3 years, 175 ± 10 cm, 70 ± 11 kg, seven females). For the interven-
tion group, the same 14-week muscle–tendon training was added
to the regular ongoing training habits as in our earlier study [15].
Before and after the intervention period, the maximal plantar
flexion moment and AT stiffness as well as energetic cost of run-
ning at 2.5 m s−1 were assessed in both groups. To explain the
expected improvements in energetic cost following the training,
we experimentally determined (i) the foot strike pattern, joint
kinematics and temporal gait parameters as well as (ii) the
soleus MTU and fascicle behaviour in addition to the electromyo-
graphic (EMG) activity during running. We further determined
(iii) the soleus force–fascicle length relationship and force–fasci-
cle velocity relationship in order to calculate the force–length
and force–velocity potential of the fascicles during running (i.e.
fraction of maximum force according to the force–length and
force–velocity curve [9,10,27]) and assessed (iv) the enthalpy effi-
ciency–fascicle velocity relationship to calculate the efficiency of
the soleus muscle during running. Because changes in running
economy were not expected without any intervention [15], the
assessment of the fascicle behaviour was not conducted in the
controls. The university ethics committee approved the study,
and participants gave written informed consent in accordance
with the Declaration of Helsinki.
(b) Exercise protocol
The supervised and biofeedback-based resistance training was
performed for 14 weeks and was characterized by five sets of
four repetitive isometric ankle plantar flexion contractions (3 s
loading and 3 s relaxation) at 90% of the maximum voluntary
contraction (MVC) strength (adjusted every two weeks), three
to four times a week (see electronic supplementary material
for illustration). This loading regimen has been shown to pro-
vide a sufficient magnitude and duration of tendon strain to
promote AT adaptation in addition to increases in plantar
flexor muscle strength [15,24,28].
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Proc. R. Soc. B 288: 20202784
2
(c) Strength of the plantar flexors and Achilles
tendon stiffness
The plantar flexor strength of the right leg was measured using
an inverse dynamics approach. For the determination of AT stiff-
ness, ramp-MVCs were conducted and the force applied to the
AT was calculated as quotient of joint moment and individual
tendon lever arm, which was determined using the tendon-
excursion method. The corresponding AT elongation was ana-
lysed
based
on
the
displacement
of
the
gastrocnemius
medialis-myotendinous junction visualized by ultrasonography.
Stiffness was calculated between 50 and 100% of the maximum
tendon force and strain by dividing elongation by resting
length (see electronic supplementary material for details).
(d) Energetic cost of running
During an 8 min running trial on a treadmill at 2.5 m s−1, expired
gas analysis was conducted and the rate of oxygen consumption
( _VO2) and carbon dioxide production ( _VCO2) was calculated as
the average of the last 3 min [15]. Running economy was then
expressed in units of energy as Energetic cost ¼ 16:89  _VO2 þ
4:84  _VCO2, where energetic cost is presented in (W kg−1) and
_VO2 and _VCO2 in (ml s−1 kg−1) [4,29]. The steady state was visually
confirmed by the rate of _VO2 during each trial, and a respiratory
exchange ratio (RER) of <1.0 was controlled for during the post
analysis (see electronic supplementary material for details).
(e) Joint kinematics and foot strike pattern
Kinematics of the right leg were captured (250 Hz) by a Vicon
motion capture system (Nexus 1.8, Vicon, Oxford, UK) using ana-
tomical-referenced markers [9]. The touchdown and the toe-off
were determined from the kinematic data as consecutive minimum
in knee joint angle over time [30]. The foot strike pattern was ana-
lysed by means of the strike index [26]. A self-developed
algorithm [25] was used to calculate the strike index from the plantar
pressure distribution (120 Hz) captured by the integrated pressure
plate (FDM-THM-S, Zebris Medical GmbH, Isny, Germany).
(f) Soleus muscle-tendon unit length changes,
fascicle behaviour and electromyographic activity
during running
During an additional 3 min running trial at the same speed, kin-
ematics of the ankle joint served to calculate the length change of
the soleus MTU as the product of ankle angle changes and the
previously assessed individual AT lever arm [31]. The initial
soleus MTU length was determined at a neutral joint angle
using the previously reported regression equation by Hawkins &
Hull [32]. Ultrasonic images of the soleus muscle fascicles were
obtained
synchronously at
146 Hz (Aloka
Alpha7,
Tokyo,
Japan). The probe (6 cm linear array, 13.3 MHz) was mounted
over the medial soleus muscle belly. The fascicle length was
post-processed from the images using a semi-automatic tracking
algorithm [33] (figure 1), and corrections were made if necessary.
At least nine steps were averaged [10]. The velocities of MTU and
fascicles were calculated as the first derivative of the lengths over
the time. Synchronized surface EMG of soleus was measured
(1000 Hz) by means of a wireless EMG system (Myon m320RX,
Baar, Switzerland) and is presented as normalized to the
maximum EMG value observed from the individual MVCs [9].
(g) Soleus force–length, force–velocity and efficiency–
velocity relationship
To determine the soleus force–fascicle length relationship (for
details [9]), the participants were placed in the prone position on
the bench of the dynamometer (Biodex Medical, Shirley, NY) with
the knee fixed in a flexed position (figure 1) to restrict the contri-
bution of the bi-articular gastrocnemius muscle to the plantar
flexion moment (approx. 120°) [34]. MVCs were performed with
the right leg in eight different joint angles, and the joint moments
and force acting on the AT were calculated as described in section
2c above. The corresponding soleus fascicle behaviour was cap-
tured synchronously at 30 Hz by ultrasonography, and fascicle
length was measured accordingly (figure 1). The probe remained
attached between the running trial and MVCs. An individual
force–fascicle length relationship was calculated by means of a
second-order polynomial fit (figure 1), giving the maximum force
(Fmax) and optimal fascicle length for force generation (L0).
The force–velocity relationship of the soleus was assessed
using the classical Hill equation [8] and the maximum fascicle
shortening velocity (Vmax) and constants of arel and brel. For
Vmax, we took reported values of human soleus type 1 and 2
fibres [35], adjusted those for physiological temperature [36] and
applied an average fibre-type distribution (81% type 1 fibres and
19% type 2 [9]), giving Vmax as 6.77 L0 s−1 [9]. arel was calculated
as 0.1 + 0.4 × type 2 fibre percentage [37], which equals to 0.175.
The product of arel and Vmax gives brel as 1.182 [37]. Based on
the assessed force–length and force–velocity relationships, it
was possible to calculate the individual force–length and force–
velocity potential of soleus as a function of the fascicle length
(figure 1) and velocity during running [9,10,27].
Furthermore,
we
determined
the
enthalpy
efficiency–
shortening velocity relationship for the soleus fascicles to
calculate the enthalpy efficiency of the soleus as a function of
the
fascicle
velocity
during
running.
We
referred
to
the
fascicle length (mm)
5000
4000
3000
2000
1000
0
force (N)
20
40
60
80
(a)
(b)
Figure 1. (a) Experimental set-up for the determination of the soleus force–
fascicle length relationship. MVCs at eight different joint angles were per-
formed on a dynamometer. During the MVCs, the soleus muscle fascicle
length was measured by ultrasonography as an average (F) of multiple
fascicle portions (short-dashed white lines) identified from the images.
(b) Exemplary force–length relationship of the soleus fascicles obtained
from the MVCs (squares) and the respective second-order polynomial fit
(dashed line).
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Proc. R. Soc. B 288: 20202784
3
experimental efficiency values provided by the paper of Hill [20],
where the values are presented as a function of relative load
which we then transposed to the shortening velocity (normalized
to Vmax) using the classical Hill equation [8]. The corresponding
values of enthalpy efficiency and shortening velocity were 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 Vmax.
The resulting function was then used to calculate the soleus
efficiency during running.
(h) Statistics
An analysis of variance for repeated measures including post hoc
analysis (adjusted p-values reported) was performed for the
group comparison. Anthropometric group differences as well
as baseline differences of the plantar flexion moment, AT stiffness
and energetic cost were tested using a t-test for independent
samples. A paired t-test was used to analyse the training effects
on the assessed gait characteristics, kinematics and MTU and fas-
cicle parameters. The level of significance was set to α = 0.05.
Effect sizes (Hedges’s g) assess the strength of the intervention
effects (see electronic supplementary material for details).
3. Results
There were no significant differences in age (p = 0.421), height
( p = 0.361) and body mass ( p = 0.382) between the interven-
tion and control groups. No baseline differences between
groups were observed for the maximum plantar flexion
moment ( p = 0.894), AT stiffness ( p = 0.421) and energetic
cost ( p = 0.143; table 1). Both the plantar flexion moment
and AT stiffness increased significantly in the intervention
group ( p = 0.024, p = 0.048) without significant changes in
the controls ( p = 0.296, p = 0.745; table 1). Furthermore, we
found a significant decrease in the energetic cost of running
following the 14 weeks of training in the intervention group
( p = 0.028) and no significant changes in the control group
( p = 0.688; table 1). Neither group showed any significant
changes in the strike index (intervention p = 0.868, control
p = 0.868), stance time ( p = 0.283, p = 0.283), flight time ( p =
0.981, p = 0.252) and cadence ( p = 0.310, p = 0.384; table 1)
after training, indicating that the training intervention did
not influence the foot strike pattern.
Following the intervention, ankle and knee joint kin-
ematics did not significantly change during the stance
phase, i.e. joint angles at touchdown (ankle p = 0.108, knee
p = 0.064), toe-off ( p = 0.161, p = 0.844), maximal ankle dorsi-
flexion
(p = 0.576)
and
maximal
knee
flexion
(p = 0.138;
table 2 and figure 2). The soleus MTU showed a lengthening–
shortening behaviour during the stance phase, with shortening
starting at 59 ± 2% of the stance phase similarly pre- and post-
intervention (p = 0.266, g = 0.30; see the Statistics section;
figure 3). The training had no effect on the MTU length,
length changes and velocity, neither when averaged over the
entire stance phase (p = 0.943, p = 0.273, p = 0.274) nor over
the
subphase
of
MTU
lengthening
(p = 0.931,
p = 0.893,
p = 0.788) or MTU shortening (p = 0.946, p = 0.470, p = 0.189;
table 3 and figure 3). Despite the MTU lengthening, the
soleus muscle fascicles shortened continuously throughout
the entire stance phase (figure 3). Following the intervention,
the fascicle shortening was not significantly different over the
entire stance phase (p = 0.662) and the phase of MTU
Table 1. Maximal plantar ﬂexion moment and Achilles tendon stiffness as well as energetic cost, foot strike index and temporal step characteristics during
running before and after the training period for the intervention and control group (mean ± s.d., effect size g).
intervention (n = 13)
control (n = 10)
pre
post
g
pre
post
g
moment (Nm kg−1)a
3.12 ± 0.48
3.44 ± 0.37c
0.77
3.10 ± 0.46
2.99 ± 0.32
0.32
stiffness (kN strain−1)a
85 ± 36
111 ± 59c
0.67
73 ± 29
71 ± 28
0.10
energy cost (W kg−1)b
10.6 ± 0.6
10.2 ± 0.7c
0.74
11.2 ± 1.0
11.1 ± 1.0
0.12
strike index
0.08 ± 0.12
0.10 ± 0.16
0.09
0.06 ± 0.03
0.06 ± 0.03
0.05
stance time (ms)
310 ± 23
316 ± 23
0.29
327 ± 17
324 ± 23
0.34
ﬂight time (ms)
53 ± 31
53 ± 24
0.01
50 ± 31
54 ± 31
0.48
cadence (steps min−1)
160 ± 11
159 ± 9
0.39
162 ± 9
161 ± 9
0.26
aSigniﬁcant time by group interaction effect (p < 0.05).
bSigniﬁcant main effect of time (p < 0.05).
cSigniﬁcant difference (post hoc analysis) to pre (p < 0.05).
Table 2. Ankle and knee joint angles at touchdown, toe-off and at the maximal ankle dorsiﬂexion and knee ﬂexion angle, respectively, during running before
and after the training intervention (mean ± s.d., effect size g, n = 13).
touchdown
toe-off
maximum dorsiﬂexion/knee ﬂexion
pre
post
g
pre
post
g
pre
post
g
ankle joint (°)
−1.3 ± 5.1
−0.0 ± 6.2
0.45
13.7 ± 7.8
15.1 ± 6.0
0.39
−18.0 ± 3.7
−18.4 ± 4.4
0.15
knee joint (°)
−3.7 ± 3.9
−6.5 ± 6.0
0.53
−11.6 ± 4.5
−11.3 ± 4.6
0.05
−32.8 ± 5.8
−34.6 ± 5.8
0.41
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Proc. R. Soc. B 288: 20202784
4
lengthening (p = 0.106) but in the phase of MTU shortening
(p = 0.016; table 3). L0 (pre 43.1 ± 5.7 mm, post 44.1 ± 8.9 mm,
p = 0.767, g = 0.08) and thus Vmax (pre 291 ± 38 mm s−1, post
298 ± 17 mm s−1, p = 0.767, g = 0.08) were not significantly
altered due to training. The operating fascicle length averaged
over the stance phase (pre 0.87 ± 0.11 L0, post 0.85 ± 0.13 L0,
p = 0.360, g = 0.16), but also during MTU lengthening (pre
0.92 ± 0.12 L0, post 0.91 ± 0.15 L0, p = 0.772, g = 0.07) and short-
ening (pre 0.81 ± 0.10 L0, post 0.76 ± 0.11 L0, p = 0.226, g =
0.32), was not significantly changed following training. Conse-
quently,
the
force–length
potential
was
not significantly
different between pre- and post-training in the different
phases (stance p = 0.172, g = 0.14, MTU lengthening p = 0.713,
g = 0.10, MTU shortening p = 0.640, g = 0.12; figure 4).
After training, the soleus force–velocity potential was sig-
nificantly lower in the phase of MTU lengthening ( p = 0.030,
g = 0.64) and significantly higher when the MTU shortened
( p = 0.045, g = 0.58) with no significant difference over the
entire stance ( p = 0.249, g = 0.31; figure 4). This was the conse-
quence of a tendency towards higher fascicle shortening
velocity during MTU lengthening (pre −0.088 ± 0.054 Vmax,
post −0.129 ± 0.061 Vmax, p = 0.073, g = 0.51) and a signifi-
cantly lower velocity during MTU shortening after training
(pre −0.174 ± 0.057 Vmax, post −0.127 ± 0.008 Vmax, p =
0.007, g = 0.83). Furthermore, the averaged EMG activation
over the phase of MTU shortening ( p = 0.028, g = 0.67) and
the entire stance phase was significantly reduced following
the intervention ( p = 0.017, g = 0.60; figures 3 and 4). Com-
pared with pre-intervention running, the fascicle velocity in
the phase of MTU lengthening was closer to the velocity
for optimal enthalpy efficiency after the training (figure 5).
Consequently, the fascicles operated at a significantly higher
enthalpy efficiency in the phase of MTU lengthening after
the training ( p = 0.006, g = 0.85; figures 5 and 6), while there
was no significant pre–post difference in the phase of MTU
shortening ( p = 0.640, g = 0.12; figure 6). Over the entire
stance phase of running, the efficiency of the fascicle
0
20
40
60
80
100
stance phase (%)
–30
–20
–10
0
10
20
30
ankle angle (°)
pre
post
0
20
40
60
80
100
stance phase (%)
–50
–40
–30
–20
–10
0
10
knee angle (°)
pre
post
dorsiﬂexion  
plantar flexion 
flexion 
extension 
(a)
(b)
Figure 2. (a) Ankle joint angle and (b) knee joint angle during the stance
phase of running before and after the training intervention (mean ± s.e.m.,
n = 13).
20
40
60
80
100
stance phase (%)
0
0.2
0.4
0.6
0.8
1.0
EMGnorm
pre
post
0
20
40
60
80
100
stance phase (%)
20
30
40
50
60
fascicle length (mm)
pre
post
0
20
40
60
80
100
stance phase (%)
280
300
320
340
360
MTU length (mm)
pre
post
*
(a)
(b)
(c)
Figure 3. (a) Soleus MTU length, (b) muscle fascicle length and (c) EMG
activity (normalized to a maximum voluntary isometric contraction, during
the stance phase of running before and after the training intervention
(mean ± s.e.m., n = 13). *Significant difference of the stance phase-averaged
EMG activation between pre and post (p < 0.05).
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Proc. R. Soc. B 288: 20202784
5
shortening was also significantly increased following the
training ( p = 0.025, g = 0.66; figure 6).
4. Discussion
Our current study showed for the first time that specific
muscle–tendon training that increases plantar flexor muscle
strength and AT stiffness facilitates the enthalpy efficiency
of the soleus muscle during the stance phase of running.
The increased enthalpy efficiency was found in the first
part of the stance phase where the soleus muscle produces
work by active shortening and transfers muscular work to
the tendon as strain energy. Furthermore, the results provide
additional evidence that a combination of greater plantar
flexor muscle strength and AT stiffness decreases the energy
cost of running [14,15] and indicates that the soleus enthalpy
efficiency is a contributive determinant.
Following the intervention, the energetic cost of running
was significantly reduced by about 4%, a quantity reported
to be above test–retest typical errors [38] and to substantially
enhance endurance running performance [39]. At the same
time, the soleus, which is the main muscle for work/energy
production during running [12], operated at a significantly
increased (7%) enthalpy efficiency throughout the stance
phase. The enthalpy efficiency quantifies the portion of
energy from ATP hydrolysis used by a muscle that is con-
verted
into
mechanical
muscular
work
[21].
Enthalpy
efficiency depends on the velocity of muscle shortening
with a steep increase at low velocities until the peak at
around 0.18 Vmax and again decreasing at higher shortening
velocities [20,21]. For the whole stance phase, fascicle short-
ening, the force–length potential and the force–velocity
potential of the soleus muscle were not significantly different
before and after the intervention, indicating a similar energy
production through muscular work of the soleus muscle.
During the propulsion phase of running (i.e. MTU shorten-
ing), where both tendon and muscle transfer energy/work
to the skeleton [19,40], the enthalpy efficiency of the operat-
ing soleus muscle was high pre- and post-intervention (94%
and 93% of the maximum efficiency). By contrast, during
the first part of the stance phase (i.e. MTU lengthening),
where energy is transferred from the contractile element to
the tendon, the efficiency was lower during pre-intervention
running (77% of the maximum efficiency). The relevant part
of the soleus fascicle shortening occurred during this first
part of stance (59% of the entire shortening range). In combi-
nation with the high muscle activation (higher during MTU
lengthening than during MTU shortening), this indicates an
important
energy
production
through
muscular
work
during the phase of MTU lengthening.
The exercise-induced increase in plantar flexor muscle
strength and AT stiffness was associated with an alteration
of the operating fascicle velocity profile and a significant
increase of the enthalpy efficiency of the soleus in the phase
of MTU lengthening (88% of maximum), potentially improv-
ing the enthalpy efficiency of muscular work production. The
significant increase of the enthalpy efficiency following train-
ing in the phase of MTU lengthening demonstrates that a
substantial part of the entire muscular work was generated
more economically. In the second part of the stance phase,
where the MTU shortened, the high efficiency was main-
tained after the intervention and, further, the fascicles
operated at a significantly higher force–velocity potential.
This was possible due to a shift of the shortening velocity
around the plateau of the efficiency–velocity curve, from
the descending part before the training to the ascending
part after training (figure 5), without a significant decline in
the efficiency. Consequently, the overall enthalpy efficiency
throughout the stance phase of each step was increased.
The phase of MTU shortening was accompanied by a
reduced soleus EMG activation after the intervention, and
the overall EMG activity during the stance phase was signifi-
cantly lower as well (12%). However, the higher maximum
plantar flexion moment along with no significant changes
in EMGmax during the MVCs (pre 0.409 ± 0.114 mV, post
0.410 ± 0.092 mV, p = 0.300) and antagonistic co-activation
(tibialis anterior EMG pre 0.034 ± 0.016 mV, post 0.034 ±
0.013 mV, p = 0.923) as measures for neural adaption after
training strongly indicate muscle hypertrophy, resulting in a
13% increase of Fmax. Therefore, the reductions in EMG acti-
vation may not correspond to a reduced active muscle
volume. To examine this possibility, we calculated the aver-
age force of the soleus muscle (Fs) during the stance phase,
adopting a ‘Hill-type muscle model’ as a function of the aver-
age force–length potential (λl), force–velocity potential (λv),
Table 3. Soleus MTU length, length changes and velocity as well as muscle fascicle length, fascicle shortening distance and fascicle velocity averaged over the
phase of MTU lengthening, MTU shortening and over the entire stance phase during running before and after the training intervention (mean ± s.d., effect size
g, n = 13).
MTU lengthening
MTU shortening
stance phase
pre
post
g
pre
post
g
pre
post
g
MTU length (mm)
325 ± 20
325 ± 21
0.02
323 ± 20
323 ± 21
0.02
324 ± 20
324 ± 21
0.02
MTU length changes (mm)
18.4 ± 2.0
18.2 ± 3.2
0.04
−33.9 ± 9.3
−32.5 ± 5.6
0.19
−16.4 ± 9.0
−14.8 ± 5.6
0.30
MTU velocity (mm s−1)
97 ± 15
98 ± 22
0.07
−259 ± 52
−244 ± 33
0.36
−173 ± 29
−164 ± 21
0.30
fascicle length (mm)
39.2 ± 4.4
39.0 ± 5.1
0.03
34.5 ± 4.3
33.1 ± 4.5
0.23
37.2 ± 4.3
36.5 ± 4.8
0.12
fascicle shortening (mm)
−5.21 ± 2.68
−6.75 ± 3.08
0.45
−6.49 ± 2.02
−4.98 ± 1.23a
0.72
−11.05 ± 3.32
−11.53 ± 3.47
0.12
fascicle velocity (mm s−1)
−21.2 ± 16.7
−33.4 ± 17.5
0.52
−49.1 ± 16.7
−35.8 ± 10.1a
0.71
−33.0 ± 10.8
−34.6 ± 11.0
0.10
aSigniﬁcant difference to pre (p < 0.05).
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Proc. R. Soc. B 288: 20202784
6
EMG activity (α) and Fmax (Fs ¼ lllva  FmaxÞ. The average
force of the soleus muscle after the intervention (Fs = 353 ±
122 N) did not show significant differences compared with
the pre-values (Fs = 372 ± 112 N, p = 0.660), indicating a simi-
lar active muscle volume. Similarly, the rate of muscle force
generation during the stance phase (_Fs ¼ Fs=tstance) did not
differ before (_Fs = 1215 ± 413 N s−1) and after the intervention
(_Fs = 1126 ± 400 N s−1, p = 0.498). The above assessments
suggest that the active muscle volume and the rate of
muscle force generation were not the reason for the improved
running economy, but rather the increase in soleus muscle
operating enthalpy efficiency.
Previous studies provided evidence that the cost of force
to support the body mass and the time course of force appli-
cation to the ground are the major determinants of the
energetic cost of running [6,41]. According to the ‘cost of
generating force hypothesis’ [6], the rate of metabolic
energy consumption is directly related to the body mass
and the time available to generate force, which results in a
constant cost coefficient (i.e. energy required per unit force).
However, modifications in the muscle effective mechanical
advantage (i.e. ratio of the muscle moment arm to the
moment arm of the ground reaction force [42]) within the
lower extremities can influence the cost coefficient of loco-
motion [43,44]. In our study, the metabolic energy cost of
running was reduced after the training without any changes
in the contact time and body mass, indicating a decrease of
the cost coefficient. The similar strike index and lower leg kin-
ematics before and after the intervention suggest unchanged
effective mechanical advantages within the lower extremities;
therefore, this would not be the reason for the reduced cost
coefficient. Instead, our findings show that an adjusted time
course of the soleus shortening velocity during the stance
phase following the training can influence the cost coefficient
as a result of increased enthalpy efficiency of the soleus and,
thus, complement the earlier studies on the mechanical
advantage
and
cost
coefficient
interaction
[41,42].
The
observed continuous soleus fascicle shortening during the
stance phase is in agreement with other experiments using
the
ultrasound
methodology
and
comparable
running
speeds [19,45]. The importance of the energy production by
the plantar flexor muscles for the propulsion phase (i.e. short-
ening of the MTU) during running is well accepted [19,46],
because the mechanical power produced at the ankle joint
in this phase is highest and determines running performance
[47]. Our current results regarding the enthalpy efficiency of
muscular energy generation and running economy show for
the first time that also the phase of the MTU lengthening is
crucial for the overall metabolic energy consumption during
running. Recently, findings of our group [9] but also others
[48,49] provided evidence that soleus muscle dynamics may
improve the economy of locomotion by a modulation of the
force–length–velocity potential, thus decreasing the active
muscle volume. In the present study, the soleus force–
length–velocity potential throughout stance was not signifi-
cantly changed following the intervention, while in the same
time the adjusted time course of the shortening velocity
increased the efficiency of muscle work production. Thus,
the present study expands the importance of the soleus fas-
cicle dynamics towards the efficiency–velocity dependency
as a further factor for improvements of locomotor economy.
The findings of the current study provide further evi-
dence [15,16] that strength training of the plantar flexors
has the potential to enhance running economy. We used a
specific high-intensity muscle–tendon training programme
[24,28], targeting an adaptation of both AT stiffness and plan-
tar flexor muscle strength [14,15], to maintain the functional
integrity of the contractile and series elastic element. Strength
increases without concomitant stiffening of the AT after a
period of training can increase levels of operating and maxi-
mum
strain
[24],
which
have
been
associated
with
pathologies [50], and also possible functional decline [51].
On the other hand, increased stiffness without higher
muscle strength may also limit function by reducing relevant
operating tendon strains [51]. In our study, the maximum AT
strain during the MVCs was not affected by the training (pre
6.2 ± 1.6%, post 6.0 ± 1.2%, p = 0.501) despite an increase in
the plantar flexor muscle strength, indicating a balanced
adaptation of muscle and tendon. Therefore, a specific
1.0
0.8
0.6
0.4
0.2
force–length potential
MTU
lengthening
MTU
shortening
stance
phase
MTU
lengthening
MTU
shortening
stance
phase
MTU
lengthening
MTU
shortening
stance
phase
1.0
0.8
0.6
0.4
0.2
EMGnorm 
*
1.0
0.8
0.6
0.4
0.2
force–velocity potential
pre
post
*
*
*
(a)
(b)
(c)
Figure 4. (a) Soleus fascicle force–length potential, (b) force–velocity poten-
tial and (c) EMG activity (normalized to a maximum voluntary isometric
contraction, averaged over the phase of MTU lengthening, MTU shortening
and the entire stance phase of running before and after the training inter-
vention (n = 13). *Significant difference between pre and post ( p < 0.05).
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Proc. R. Soc. B 288: 20202784
7
muscle-tendon training [24,28] can be recommended to
improve running economy.
To assess the enthalpy efficiency–shortening velocity
relationship, we used a biologically founded value of Vmax
(i.e. 6.77 L0 s−1). However, during submaximal running, the
lower activation level and selective slow fibre-type recruit-
ment
may
affect
the
actual
relationship.
Furthermore,
differences in fibre-type distribution may also affect the
shape of the enthalpy efficiency–shortening velocity curve
[22]. We evaluated the effect of (i) decreasing Vmax by 10%
intervals and (ii) replacing the underlying efficiency values
measured at the frog sartorius at 0°C from Hill [20] by the
data presented by Barclay et al. [22] for the predominantly
slow fibre-type soleus mouse muscle at 21°C, comparable
with the human soleus muscle. The significant pre- to post-
enthalpy efficiency increase for the MTU lengthening phase
and the entire stance phase persisted for values till Vmax−30%
both using the data of Hill or Barclay et al. ( p < 0.05), which
confirms and strengthens the observed intervention effect
(for descriptive values and p-values see electronic supplemen-
tary material, S2). Furthermore, since we calculated the
efficiency as a function of the soleus muscle shortening vel-
ocity (adjusted for physiological temperature) and only
discussed our findings in terms of percentage change, any
uncertainties about the magnitude of the enthalpy efficiency
would not affect our results. The soleus fascicle dynamics
were not assessed in the control group because alterations
were not expected with continued training habits as pre-
viously evidenced [45]. Furthermore, the controls did not
show alterations in any of the assessed parameters, giving
strong support for an unchanged fascicle behaviour after the
intervention period.
5. Conclusion
In conclusion, the current study gives new insights into the
soleus muscle mechanics and metabolic energetics during
human running. In support of our earlier study, an exercise-
induced increase of plantar flexor muscle strength and AT
stiffness reduced the metabolic energy cost of running. The
proposed reason for this improvement is an alteration in the
soleus fascicle velocity profile throughout the stance phase,
which led to a significantly higher enthalpy efficiency of the
operating soleus muscle. The enthalpy efficiency was particu-
larly increased in the phase of MTU lengthening, where the
activation is high and the soleus generates an important part
of the mechanical energy required for running.
Ethics. 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.
Data accessibility. The processed datasets generated and analysed
during the current study are available as part of the electronic
supplementary material..
Authors’ contributions. S.B., F.M., A.S. and A.A. designed research. S.B.,
F.M. and A.S. performed research. S.B. analysed data. S.B. and A.A.
drafted the manuscript. F.M. and A.S. made important intellectual
contributions during revision.
Competing interests. We declare we have no competing interests.
0.2
0.4
0.6
0.8
1.0
Vnorm (V/Vmax)
Vnorm (V/Vmax)
0
0.1
0.2
0.3
0.4
enthalpy efficiency
pre
post
0
20
40
60
80
100
stance phase (%)
–0.2
–0.1
0
0.1
0.2
0.3
0.4
pre
post
}*
MTU lengthening
MTU shortening
(a)
(b)
Figure 5. (a) Soleus muscle fascicle operating velocity over the stance phase of running before and after the intervention (mean ± s.e.m.) and velocity of maximum
enthalpy efficiency (i.e. 0.18 Vmax, horizontal dashed line). Following the intervention, the fascicle shortening velocity was closer to the velocity optimal for maxi-
mum enthalpy efficiency during most of the MTU lengthening phase. (b) Enthalpy efficiency–fascicle velocity relationship with average values of the phase of MTU
lengthening, showing that the fascicles operated at a significantly higher enthalpy efficiency following the intervention (*p < 0.05). Circles indicate that the single
participant values before (white) and after (black) the intervention and squares show the respective mean with standard error bars (n = 13). The vertical dotted line
shows the velocity of maximum efficiency.
enthalpy efficiency
0.50
0.45
0.40
0.35
0.30
0.25
pre
post
MTU
lengthening
MTU
shortening
stance
phase
0
*
*
Figure 6. Soleus muscle fascicle enthalpy efficiency averaged over the phase
of MTU lengthening, MTU shortening and the entire stance phase of running
before and after the training intervention (n = 13). *Significant difference
between pre and post ( p < 0.05).
royalsocietypublishing.org/journal/rspb
Proc. R. Soc. B 288: 20202784
8
Funding. Funding for this research was supplied by the German
Federal Institute of Sport Science (grant no. ZMVI14-070604/
17-18).
Acknowledgements. We acknowledge the support of Antonis Ekizos,
Arno Schroll, Leon Brüll and Victor Munoz-Martel for data recording
and analysis.
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Enthalpy efficiency of the soleus muscle contributes to improvements in running economy.
Bohm, Sebastian,Mersmann, Falk,Santuz, Alessandro,Arampatzis, Adamantios