Vol.:(0123456789)
1 3
European Journal of Applied Physiology (2020) 120:2495–2505 
https://doi.org/10.1007/s00421-020-04472-9
ORIGINAL ARTICLE
The influence of Achilles tendon mechanical behaviour on “apparent” 
efficiency during running at different speeds
Andrea Monte1,2  · Constantinos Maganaris2  · Vasilios Baltzopoulos2  · Paola Zamparo1 
Received: 8 April 2020 / Accepted: 10 August 2020 / Published online: 25 August 2020 
© The Author(s) 2020
Abstract
Purpose We investigated the role of elastic strain energy on the “apparent” efficiency of locomotion (AE), a parameter that 
is known to increase as a function of running speed (up to 0.5–0.7) well above the values of “pure” muscle efficiency (about 
0.25–0.30).
Methods In vivo ultrasound measurements of the gastrocnemius medialis (GM) muscle–tendon unit (MTU) were combined 
with kinematic, kinetic and metabolic measurements to investigate the possible influence of the Achilles tendon mechani-
cal behaviour on the mechanics (total mechanical work, WTOT) and energetics (net energy cost, Cnet) of running at different 
speeds (10, 13 and 16 km h−1); AE was calculated as WTOT/Cnet.
Results GM fascicles shortened during the entire stance phase, the more so the higher the speed, but the majority of the 
MTU displacement was accommodated by the Achilles tendon. Tendon strain and recoil increased as a function of running 
speed (P < 0.01 and P < 0.001, respectively). The contribution of elastic energy to the positive work generated by the MTU 
also increased with speed (from 0.09 to 0.16 J kg−1 m−1). Significant negative correlations (P < 0.01) were observed between 
tendon work and metabolic energy at each running speed (the higher the tendon work the lower the metabolic demand) and 
significant positive correlations were observed between tendon work and AE (P < 0.001) at each running speed (the higher 
the tendon work the higher the efficiency).
Conclusion These results support the notion that the dynamic function of tendons is integral in reducing energy expenditure 
and increasing the “apparent” efficiency of running.
Keywords Running efficiency · Tendon mechanics · Elastic energy · Gastrocnemius medialis
Abbreviations
AE 
 Apparent efficiency
BCoM  Body centre of mass
Cnet 
 Net energy cost
Ek 
 Kinetic energy
Ep 
 Potential energy
ET 
 Total energy
F–L 
 Force–length relationship
F–V 
 Force–velocity relationship
GM 
 Gastrocnemius medialis
GRF 
 Ground reaction force
MTU 
 Muscle–tendon unit
PCSA 
 Physiological cross-sectional area
V 
 Velocity
̇VO2net 
 Net oxygen uptake
WEXT 
 External mechanical work (at the whole-body 
level)
Wfas 
 Positive work done by the fascicles
WINT 
 Internal mechanical work (at the whole-body 
level)
WMTU 
 Positive work done by the MTU
Wten 
 Positive work done by the tendon
WTOT 
 Total mechanical work (at the whole body level)
Communicated by Olivier Seynnes.
 * Paola Zamparo 
 
paola.zamparo@univr.it
1 
Department of Neurosciences, Biomedicine and Movement 
Sciences, University of Verona, via Felice Casorati, 43, 
37131 Verona, Italy
2 
Research Institute for Sport and Exercise Sciences (RISES), 
Liverpool John Moores University, Liverpool, UK
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Introduction
Human locomotion entails the motion of the body through 
an environment: air in terrestrial locomotion whilst in con-
tact with the ground, and water in aquatic locomotion. The 
minimum required work that has to be done to maintain 
the motion of any object in its surrounding environment, is 
given by the product of the resistance offered by the environ-
ment and the distance covered during the motion. The effi-
ciency of the locomotor apparatus can thus be expressed as 
the ratio between the work necessary to maintain motion and 
the chemical energy transformed by the muscles. This “loco-
motion” efficiency (i.e. the total mechanical work generated 
at whole-body level as a proportion of metabolic cost), has 
been investigated in several forms of terrestrial and aquatic 
locomotion, such as swimming (e.g. Zamparo et al. 2002), 
cycling (e.g. Minetti et al. 2001), walking and running (e.g. 
Cavagna and Kaneko 1977; Lejeune et al. 1988; Williams 
and Cavanagh 1987).
In the above-mentioned studies, “locomotion” efficiency 
was, actually, calculated as the ratio between (total) mechan-
ical work per unit distance (WTOT) and net energy cost (Cnet, 
the metabolic energy expended per unit distance); in turn, 
Cnet was calculated as the ratio between net oxygen uptake 
and locomotion velocity ( ̇VO2net/v) and WTOT was calculated 
as the sum of two components: WEXT (the work done to raise 
and accelerate the body centre of mass within the environ-
ment) and WINT (the work associated with the acceleration 
of body segments with respect to the centre of mass). As 
calculated, “locomotion” efficiency approximates “pure” 
muscle efficiency values (about 0.25–0.30, as reported by 
Woledge et al. 1985) in the forms of locomotion where elas-
tic recoil is negligible [e.g. swimming or cycling, as reported 
by Zamparo et al. (2002) and Minetti et al. (2001)] whereas 
in the case of running, the efficiency calculated in this man-
ner can reach far larger values [e.g. up to 0.5–0.7, as reported 
by Cavagna and Kaneko (1977)].
“Locomotion” efficiency is, therefore, often referred to 
as “apparent” efficiency because an increase beyond pure 
muscle efficiency values does not indicate that the muscles 
work in a more efficient way (Ettema 2001). Rather, these 
increased efficiency values are an indication of the conver-
sion of metabolic energy into mechanical work at whole-
body level. As suggested by Alexander (1991), measuring 
“apparent” efficiency can thus help in understanding whether 
mechanical work is “recycled” via storage and release of 
elastic energy (an energy saving mechanism).
As an example, when running at steady-state speed, 
tendons stretch and recoil; through this succession of 
stretch–shortening cycles, tendons could play an important 
role as energy savers allowing this form of locomotion to 
be particularly efficient (Roberts and Azizi 2011). In these 
conditions, indeed, “apparent” efficiency (AE = WTOT/Cnet) 
increases linearly with speed because WTOT increases 
whereas Cnet does not show appreciable changes when the 
velocity increases (e.g. Cavagna and Kaneko 1977). In 
other conditions (e.g. shuttle running or uphill running), 
AE is much lower and this could be attributed to the fact 
that, in these conditions, the tendon acts more as a power 
amplifier (Roberts and Azizi 2011). As an example, during 
shuttle running, AE is lowest over short shuttle distances 
covered at maximal speed (e.g. when the accelerations and 
decelerations are larger and the tendons’ capability to save 
metabolic energy is expected to be reduced) and highest over 
long shuttle distances (e.g. in conditions that approximate 
those of constant speed, linear, running where the metabolic 
energy saving mechanism is expected to be more prominent) 
(Zamparo et al. 2019). A further example is that of running 
on sand where AE is lower relatively to running on a hard 
surface and this could be attributable to a decrease in “mus-
cle–tendon efficiency”, the sand acting as a damper which 
reduces the energy that can be recoiled from the stretched 
tendon (Lejeune et al. 1988). Taken together, these findings 
suggest a link between the capability to exploit the elastic 
energy mechanisms in tendons and the values of “apparent” 
efficiency in human running.
The dynamic function of tendons is indeed integral to 
reduce the energy expenditure of steady-state running: ener-
getic savings may occur by shifting the operating regions 
of the muscles on their force–length and force–velocity 
curves (Ramsey and Street 1940), by reducing muscle work 
(Biewener and Roberts 2000), or by reducing active muscle 
volume (Holt et al. 2016). As an example, an active muscle 
uses less metabolic energy and produces more force when 
operating under isometric conditions compared to shorten-
ing (Fenn 1924). In addition, if the muscle operates close 
to optimal length (the length corresponding to optimum 
myofilament overlap) it will produce more force (Gordon 
et al. 1966) for a given activation level. Therefore, a quasi-
isometric behaviour (i.e. slow shortening speed) around opti-
mal muscle length enables the muscle to produce high forces 
more economically. During different forms of locomotion 
(e.g. walking and running), the elastic elements could 
accommodate the largest part of the MTU length changes, 
allowing the fascicles to work at a high force–length–veloc-
ity potential (Fukunaga et al. 2001; Lichtwark et al. 2007; 
Bohm et al. 2019; Monte et al. 2020). Without tendons, the 
fascicle shortening velocity would be higher, increasing the 
cross-bridge turnover and the energy demand for muscle 
contraction (Woledge et al. 1985). Furthermore, since the 
force per cross-bridge decreases with increasing velocity (de 
Tombe and Ter Keurs 1990), a decrease in the muscle force 
potential would require an increased muscle activation to 
maintain the same level of force to support and accelerate 
the body’s centre of mass, thereby increasing the energy 
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cost of locomotion (Fletcher and MacInthos 2017). Based 
on these theoretical considerations, if the whole muscle–ten-
don unit length changes could be attributed to the tendon 
only, the muscle fibres would operate under isometric condi-
tions, reducing the fascicle length changes (and, therefore, 
the mechanical work done by the muscles) and the level 
of muscle activation required for a given force (Fletcher 
and MacInthos 2017). These theoretical notions were sup-
ported by recent studies of Bohm et al. (2019) and Monte 
et al. (2020), which revealed that the plantar flexor mus-
cles operated quasi-isometrically at a high-force potential 
during running at different speeds. Furthermore, Bohm and 
co-workers found a negative significant correlation between 
the force–length–velocity potential of the soleus muscle and 
the energy cost of running at 10 km h−1, suggesting that the 
higher the force potential the lower the energy expended. 
Therefore, the ankle plantar flexors seem to play an impor-
tant role in the mechanical and physiological demand of 
human running.
The human ankle plantar flexors produce forces of up to 
12 times body weight during running at increasing speed 
(Komi 1990) and are the main force producers amongst all 
the major lower limb muscle groups (Dorn et al. 2012). Due 
to their unique design (short muscle fibres connected to the 
heel via a long and compliant Achilles tendon), the ankle 
plantar flexors, have the capacity to generate high amounts 
of power with minimal energy expenditure. Thanks to their 
long tendon, the plantar flexors can store elastic energy up 
to about 60% of the MTU mechanical work during running 
(Monte et al. 2020; Farris and Sawicki 2012; Lai et al. 2014) 
and their contribution increases as a function of speed. This 
behaviour seems to be particularly relevant for determin-
ing energy expenditure, mechanical work and, therefore, 
“apparent” efficiency; however, there are no studies that have 
investigated the role of plantar flexor tendons on “apparent” 
running efficiency.
The aim of this study was to verify experimentally the 
theoretical link between human plantar flexor muscle–ten-
don behaviour and “apparent” running efficiency. In particu-
lar, we combined in vivo ultrasound, kinematic and kinetic 
measurements during running at different speeds and we 
calculated the relative contribution of GM muscle fascicles 
and Achilles tendon to the mechanical work done by the 
MTU to investigate the role of Achilles tendon behaviour 
on the mechanical power output at whole-body level (WTOT) 
and on the energy demands ( ̇VO2net and Cnet) during running 
at increasing speeds. Our main hypothesis was that the con-
tribution of tendon work to the total work done by the MTU 
would increase with running speed and that this increase 
could, at least partially, explain the concurrent increase in 
“apparent” efficiency.
Materials and methods
Ethical approval
All participants received written and oral information and 
instructions before the study and gave their written informed 
consent to the experimental procedure. The experimental 
protocol was approved by the Ethical Committee of Liv-
erpool John Moores University (protocol number: 18/
SPS/028) and was performed in accordance with the Hel-
sinki Declaration.
Participants
The experiments were performed on 15 male endurance 
athletes, as a part of a larger study (Monte et al. 2020). All 
participants (24 ± 2.4 years of age; 74 ± 2.8 kg of body mass; 
1.77 ± 0.04 m of stature; 8.5 ± 2.2 years of training: 5 ± 1 
workouts per week) received written and oral instructions 
before the study and gave their written informed consent 
to participate in the experimental procedures. The experi-
mental protocol was approved by the Ethical Committee of 
Liverpool John Moores University (protocol number: 18/
SPS/028) and performed in accordance with the Helsinki 
Declaration.
Experimental design
During each running trial, the participants ran at steady-state 
speed using a self-selected cadence, step length and running 
technique. All participants used a forefoot running pattern.
The trajectories of 50 reflective markers were recorded 
using 12 camera system (Vicon Vero 2.2, Oxford Metrics, 
United Kingdom), sampling at 250 Hz. The markers were 
placed at specific anatomical position on the subjects’ head, 
trunk, arms, pelvis, lower limbs and foots. This marker set 
was proposed by Lai et al. (2015) to investigate the ankle 
moment generation. Moreover, we added another 14 markers 
(five on the right shank/foot and one at the great trochanter 
and cheekbones, bilaterally) to measure the tendon lever arm 
during running as described by Rasske et al. (2017) and the 
internal work (see below) with the marker set proposed by 
Minetti et al. (1993).
Ground reaction forces (GRFs) were recorded using an 
instrumented treadmill (M-GAIT, MOTEK) with two 3-axial 
(horizontal, vertical and mediolateral) force plates sampling 
at 1500 Hz (Lai et al. 2018). Resultant GRFs, centre of pres-
sure and free moment vectors were measured and recorded 
by the treadmill’s software.
A B-mode ultrasound apparatus (Telemed Echo Blaster 
128) with a linear probe operated at a scanning depth and 
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European Journal of Applied Physiology (2020) 120:2495–2505
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with of 6 cm (sample frequency 7 MHz) was used to record 
the GM fascicles at a sampling rate of 60 Hz. Ultrasound 
images were recorded from the right leg of each athlete dur-
ing each running trial, with the probe placed in the sagittal 
plane at the mid-belly of the muscle. The position of the 
scanning probe was manipulated until the superficial and 
deep aponeuroses and the connective tissue that surrounds 
the muscle fascicles were clearly visible (Lichtwark et al. 
2007; Cronin and Finni 2013).
All signals were synchronized by a digital output gen-
erated by the ultrasound scanner that triggered all instru-
mentations (the Vicon cameras, ground reaction forces and 
ultrasound).
A metabolic gas analysis was performed to measure oxy-
gen consumption during each running trial ( ̇VO2) by means 
of a breath by breath metabolimeter (CORTEX Metalyzer 
3B, CORTEX Biophysik, Germany). Six min of baseline 
data collection in a standing position was performed before 
these tests, the running trials were separated by 5 min of 
rest and data collected in the last minute of rest/exercise 
were averaged and used in further analyses. Net energy cost 
(Cnet) was calculated as ( ̇VO2net/v), by dividing net oxy-
gen uptake ( ̇VO2net = ̇VO2 −  ̇VO2rest), in ml  O2 kg−1 min−1, 
with the treadmill velocity (v, expressed in m min−1) and 
using an energy equivalent that takes into account the res-
piratory exchange ratio (RER): ̇VO2net (4.94·RER + 16.04) 
J ml O2
−1 (Garby and Astrup 1987); Cnet is thus expressed 
in J kg−1 m−1. In previous studies quantifying “apparent” 
efficiency, net energy expenditure ( ̇VO2net instead of over-
all ̇VO2) has invariably been utilized to calculate the cost 
of transport (e.g. Minetti et al. 1993, 2001, 2002; Saibene 
and Minetti 2003; Zamparo et al. 2002, 2016) because, in 
addition to the metabolic cost of locomotion, overall ̇VO2 
also encompasses resting energy expenditure, which is not 
“utilized” to transport the body.
Data analysis
In the last minute of each running trial, kinematic, kinetic 
and ultrasound data were analysed during the stance phase 
of ten consecutive steps for each participant. This timing 
was chosen to coincide with the determination of oxygen 
uptake. Data of each instrumentation (except for the oxygen 
consumption data) were interpolated to 200 sample points.
Kinetics and mechanical work
Marker trajectories were filtered with a forward and reverse 
low-pass Butterworth filter (second order: cut-off 10 Hz), 
whereas GRF was filtered through a forward and reverse low 
pass, fourth-order Butterworth filter with a cut-off frequency 
of 30 Hz (consistent with the Nyquist theorem). Spectral 
analysis showed peaks of noise frequencies at 41, 47 and 
100 Hz, which were speed and gait independent and conse-
quently induced by the treadmill engine.
Inverse kinematics was used to calculate the angular rota-
tion for each body segment (Lai et al. 2015, 2018). The foot 
was modelled as a rigid segment and the ankle joint was 
represented as a universal joint with the centre of rotation at 
the midpoint between the medial and lateral malleoli mark-
ers and was reconstructed relative to the shank line (Schache 
et al. 2011). A standard inverse dynamic approach was used 
to obtain ankle joint torque, while ankle joint power was 
calculated as the product of ankle joint moment and ankle 
joint angular velocity.
To calculate the internal work, the body was considered 
to be composed of 11 body segments: head–trunk, thighs, 
shanks, feet, upper arms and forearms (Minetti et al. 1993). 
Based on the intrinsic characteristics of the limbs (mass of 
each segment and radius of gyration) determined according 
to Dempster inertial parameters (Winter 1979), and their 
3D angular velocity and acceleration, the work necessary to 
rotate and accelerate the limbs with respect to body centre 
of mass (BCoM) (e.g. the internal work, WINT, J kg−1 m−1) 
was calculated (Cavagna and Kaneko 1977; Minetti 
1988; Minetti et al. 1993; Pavei et al. 2017).
The work done to raise and accelerate the body centre of 
mass with respect to the environment (WEXT, J kg−1 m−1) was 
calculated based on the summation of all increases in total 
mechanical energy (ET = EP + EK), where the time course 
of potential (EP) and kinetic (Ek = Ekx + Eky + Ekz) energy 
were calculated based on the BCoM trajectory. The BCoM 
position was calculated by a double integration of the GRF 
signal, according to Cavagna (1975), and using as integra-
tion constant the treadmill speed (as described by Saibene 
and Minetti 2003).
The sum of internal and external work represents the total 
mechanical work generated to move the body over a unit 
distance (WTOT, J kg−1 m−1). “Apparent” efficiency (AE) was 
then calculated from the ratio WTOT/Cnet (both expressed in 
J kg−1 m−1, see above).
Total mechanical work (WTOT, as computed here) is, 
therefore, not the total work done by the muscles or by the 
MTUs but represents the mechanical work at whole-body 
level. Moreover, by means of this method, instead of the 
work of a force, the work done on the body is computed; 
this work, in turn, is calculated based on the work–energy 
principle, which states that the work done on an object is 
equal to the change in its (kinetic and potential) energy (e.g. 
Zatiorsky 2000).
Muscle fascicle and series elastic element behaviour
In vivo muscle fascicle length and pennation angle were 
measured from the ultrasound videos. Pennation angle was 
defined as the angle between the collagenous tissue and 
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the deep aponeurosis (Lichtwark et al. 2007; Seynnes et al. 
2015). A validated automatic tracking algorithm was used to 
quantify muscle fascicle length and pennation angle (Cronin 
and Finni 2013; Gillet et al. 2013). Each frame of the tracked 
muscle fascicle lengths and pennation angles was visually 
examined to check the algorithm’s accuracy. Whenever the 
muscle fascicle length or pennation angle was deemed inac-
curate, the two points on the aponeuroses defining the mus-
cle fascicles were manually repositioned. The instantaneous 
MTU length of GM in the stance phase was computed using 
instantaneous joint angles as proposed by Hawkins and Hull 
(1990); the instantaneous tendon length was calculated as 
the difference between the MTU length and the muscle belly 
length, taking into account the effect of pennation angle 
(Fukunaga et al. 2001). The behavior of the MTU, the fas-
cicles and the Achilles tendon were investigated during the 
absorption phase (where net ankle joint power is negative) 
and the propulsive phase (where net ankle joint power is 
positive) during stance. The average MTU length, fascicle 
length and tendon length during the absorption and propul-
sive phases are reported in Table 1 along with tendon strain 
(the maximum value during the stance phase) and tendon 
recoil (the maximum value during the propulsive phase). 
Fascicle and tendon length velocities were computed by dif-
ferentiating the lengths of each component with respect to 
time in the stance phase (Lai et al. 2015, 2018).
Muscle fascicle and tendon mechanical work
The amounts of mechanical work done by the MTU, by the 
muscle fascicles and by the Achilles tendon were calculated 
by integrating the corresponding power curves over the 
entire stance phase (see Fig. 1). In turn, the power devel-
oped by each component was obtained by multiplying the 
corresponding force and velocity values. Force production 
was determined as proposed by Farris and Sawicki (2012) 
whereas the velocity was calculated as the first derivative of 
the length changes. Briefly, tendon force was calculated as 
the net ankle torque divided by the tendon lever arm (esti-
mated as suggested by Rasske et al. (2017). The force attrib-
utable to GM was estimated by multiplying “overall” tendon 
force by the relative PCSA of this muscle which, according 
to the literature, amounts to ~ 16% of the PCSA of all the 
plantar flexors (Fukunaga et al. 1996). To estimate muscle 
fascicle force, tendon force was divided by the cosine of the 
pennation angle (e.g. Lichtwark and Wilson 2005).
The positive work done by the MTU (WMTU) was cal-
culated in the portion of stance where the MTU generates 
positive power (Fig. 1, upper panel). Positive muscle fibre 
work (Wfas) was calculated as the positive muscle fibre work 
done during the propulsion phase (Fig. 1, middle panel). 
From these data, positive tendon work (Wten) was finally 
calculated, which represents the mechanical energy that can 
be derived from tendon recoil during the propulsion phase 
(Fig. 1, lower panel).
Statistics
A one-way ANOVA for repeated measures was conducted 
to test for possible differences among running speeds for 
all the investigated variables. When significant main effects 
were found, a post hoc pairwise comparison using Fisher’s 
least significant difference was used to determine the effect 
of speed. To determine the relationships between Wten and 
Cnet, AE and WTOT, the Pearson’s correlation coefficient was 
used. Statistical analysis was performed with SPSS (v24.0). 
All data extracted for statistical analysis were normally dis-
tributed (Shapiro–Wilk normality test, P > 0.05).
Results
Table 1 reports the average values of muscle–tendon unit 
length, fascicle length and tendon length during the absorp-
tion and propulsive phases, as well as the values of tendon 
strain and recoil. All these parameters increased signifi-
cantly as a function of speed (main effect: P < 0.001), apart 
from GM fascicle length, which decreased as a function of 
speed both during absorption and propulsion. Significant 
Table 1  Average muscle–tendon unit (MTU) length, fascicle length 
and tendon length during the absorption and propulsive phases of 
ground contact at 10, 13 and 16 km h−1
Tendon strain (the maximum value during the stance phase) and ten-
don recoil (the maximum value during the propulsive phase) are also 
reported. Data are means ± SD and are expressed in cm
Significant differences from 10  km  h−1 (*P < 0.05; **P < 0.01; 
***P < 0.001); significant differences between 13 and 16  km  h−1 
(#P < 0.05; ##P < 0.01; ###P < 0.001)
10 km h−1
13 km h−1
16 km h−1
MTU length
 Absorption phase
47.41 ± 3.4
53.33 ± 3.9**#
58.87 ± 4.2***#
 Propulsive phase
44.32 ± 3.2
42.88 ± 2.7*#
40.04 ± 2.8**#
Fascicle length
 Absorption phase
4.37 ± 1.01
4.28 ± 0.97*#
4.19 ± 0.83**#
 Propulsive phase
3.99 ± 0.98
3.81 ± 0.98*#
3.62 ± 0.98**#
Tendon length
 Absorption phase
22.53 ± 2.2
23.78 ± 1.97*##
24.51 ± 1.89**##
 Propulsive phase
21.12 ± 1.9
20.02 ± 2.01*#
19.48 ± 1.88**#
Tendon strain
 Absorption phase
1.10 ± 0.49
1.35 ± 0.52**##
1.62 ± 0.57***##
Tendon recoil
 Propulsive phase
0.89 ± 0.55
1.11 ± 0.48**##
1.35 ± 0.51***##
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differences were observed among speeds in all investigated 
muscle and tendon parameters.
During the propulsive phase, the average ankle joint 
power was: 5.40 ± 0.88, 7.38 ± 0.96, 9.72 ± 0.91 W kg−1 at 
10, 13 and 16 km h−1, respectively. Significant differences 
were observed among all running velocities (main effect: 
P < 0.001).
In Fig. 1, the profile of negative (absorbed) and positive 
(generated) mechanical power of the MTU (upper panel), 
muscle fascicles (middle panel) and Achilles tendon (bot-
tom panel) during the stance phase are reported in the 
panels on the left. The panels on the right depict the aver-
age values of positive work during the propulsive phase. 
All variables increased as a function of speed (MTU: 
Fig. 1  Panels on the left: profile 
of mechanical power absorbed 
(negative) and generated (posi-
tive) by the MTU (upper panel), 
muscle fascicle (middle panel) 
and Achilles tendon (lower 
panel) during the stance phase 
at the investigated running 
speeds (solid line: 10 km h−1; 
dotted line: 13 km h−1; dashed 
line: 16 km h−1). Note that the 
mechanical power absorbed by 
the Achilles tendon is always 
higher than that returned during 
its recoil. Panels on the right: 
positive mechanical work done 
by the MTU (upper panel), 
muscle fascicle (middle panel) 
and Achilles tendon (lower 
panel) during the stance phase 
at all the investigated run-
ning speed. Positive work was 
calculated as the first integral of 
the positive mechanical power 
generated during the stance
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1 3
P < 0.001; fascicles: P < 0.05; tendon: P < 0.01) and sig-
nificant differences were observed among running speeds 
in all the investigated parameters. The Achilles tendon 
contributed for the 65% of the MTU work.
Table 2 reports mechanical and metabolic data at the 
three investigated running speeds. With running speed, 
 WEXT decreased (main effect: P < 0.001), whereas ̇VO2net, 
AE, WINT and WTOT increased (main effect: P < 0.001, for 
all variables). The comparisons among speeds showed sig-
nificant differences among running trials for each of these 
variables. No differences in Cnet were observed as a function 
of speed.
Figure 2 shows the correlations between (positive) Achil-
les tendon work and WTOT, Cnet and “apparent” efficiency 
(AE) at each running speed (10, 13 and 16 km h−1, from top 
to bottom). Significant correlations were observed for all 
the investigated parameters at all the investigated speeds. 
The subjects with the highest tendon work were those with 
the highest total mechanical work (upper panel, P < 0.01 
in all cases) and with the lower energy cost (middle panel, 
P < 0.01 in all cases). Positive significant correlations were 
observed between tendon work (Wten) and AE at all the 
investigated speeds (lower panel, P < 0.001 in all cases): the 
subjects with the highest tendon work were those with the 
highest “apparent” efficiency.
In Fig. 3, the mean values of AE are reported as a func-
tion of the mean values of (positive) Achilles tendon work, 
at the three investigated speeds; this relationship is described 
by the following equation: AE = 1.56 Wten + 0.33.
Discussion
In this study, we investigated the role of elastic strain energy 
(e.g. the work produced by the Achilles tendon fascicles of 
the GM muscle tendon unit) on locomotion (“apparent”) 
efficiency at increasing running speeds Our results reveal 
that the work provided by the recoil of the Achilles ten-
don at each speed is linked to: (1) a reduction in the energy 
cost of running, (2) an increase in the mechanical work at 
whole-body level and (3) an increase in the “apparent” effi-
ciency. These novel in vivo experimental results support the 
notion of elastic energy reutilization impacting positively on 
the economy/efficiency of running.
“Apparent” efficiency
Although the contribution of the Achilles tendon to the 
economy/efficiency of running through the reutilization of 
elastic energy is a mechanism since long postulated, data 
reported in this paper constitute a novel observation for 
in vivo human running, allowing for a better interpretation 
of the changes in AE in different experimental conditions. 
In this study, AE was calculated based on values of (total) 
mechanical work (i.e. the sum of internal and external work). 
Although the concept of total mechanical work estimation 
has been debated (as also acknowledged for some aspects 
by the original authors, Willems et al. 1995), an increase in 
efficiency attributable to elastic energy reutilization was also 
observed in studies where mechanical work was calculated 
based on a different (joint power) approach. As an example, 
Farris and Sawicki (2011) calculated values of efficiency 
of about 0.45 during running at 11 km h−1 and Voigt et al. 
(1995) reported values of efficiency of about 0.65 during 
hopping (with a frequency of 2 Hz). This supports the idea 
that measuring “apparent” efficiency can help in under-
standing whether mechanical work has been “recycled” via 
storage and release of elastic energy, thus indicating the 
presence of an energy saving mechanism (as suggested by 
Alexander 1991).
Muscle and tendon contribution
Regarding the underpinning mechanisms, a possible expla-
nation for the increase in “apparent” efficiency with speed 
is that the plantar flexor muscles favour the use of tendon 
elastic strain energy over muscle fibre work (Lichtwark et al. 
2007), and that this energy is enhanced when running speed 
advances towards maximum running velocity (Cavagna and 
Kaneko 1977). Our data are in line with these considerations 
Table 2  Mechanical and metabolic data (mean ± SD) during running at 10, 13 and 16 km⋅h−1
WEXT external mechanical work, WINT internal mechanical work, WTOT total mechanical work, ̇VO2net net oxygen uptake, Cnet energy cost of run-
ning, AE “apparent” efficiency
Significant difference from 10  km  h−1 (*P < 0.05; **P < 0.01; ***P < 0.001); significant difference between 13 and 16  km  h−1(#P < 0.05; 
##P < 0.01; ###P < 0.001)
WEXT
(J kg−1 m−1)
WINT
(J kg−1 m−1)
WTOT
(J kg−1 m−1)
̇VO2net
(ml kg−1 min−1)
Cnet
(J kg−1 m−1)
AE
10 km h−1
1.60 ± 0.09
0.31 ± 0.05
1.91 ± 0.04
32.2 ± 5.4
3.98 ± 0.42
0.49 ± 0.03
13 km h−1
1.49 ± 0.08**#
0.67 ± 0.07***###
2.16 ± 0.03**##
42.9 ± 4.6***###
4.04 ± 0.38
0.53 ± 0.03**##
16 km h−1
1.33 ± 0.08***#
0.95 ± 0.08***###
2.28 ± 0.06***##
52.6 ± 04.2***###
4.08 ± 0.34
0.57 ± 0.05***##
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European Journal of Applied Physiology (2020) 120:2495–2505
1 3
and are comparable to those of previous studies that have 
estimated the relative contribution of tendon elastic strain 
energy to the positive work done by the MTU for the ankle 
plantar flexors during running (Hof et al. 2002; Farris and 
Sawicki 2012; Lai et al. 2014).
This mechanism may be a consequence of the plantar 
flexor muscle fibres remaining relatively isometric as run-
ning speed increases, a behaviour that allows to generate 
large muscle forces and facilitates the storage and recovery 
of tendon elastic strain energy. This was recently verified by 
in vivo studies that analysed the muscle and tendon behav-
iour of the plantar flexors during running at increasing speed 
(Lai et al. 2018; Werkhausen et al. 2019; Monte et al. 2020; 
Bohm et al. 2019). For instance, Monte et al. (2020) dem-
onstrated that the gastrocnemius medialis muscle fascicles 
shorten during the entire stance phase, but that the series 
elastic components accommodate much of the displace-
ment of the MTU, allowing the series elastic components 
to provide the larger amount of mechanical power of the 
MTU. This result suggests that fibres in distal limb muscles, 
such as the ankle plantar flexors, act like isometric struts to 
facilitate greater storage and recovery of tendon elastic strain 
energy at fast locomotion speeds (as indicated by Biewener 
and Roberts 2000).
The strong relationship between tendon work and total 
mechanical work at whole-body level we observed (middle 
panel of Fig. 2) suggests that the elastic energy provided 
by the Achilles tendon recoil during the propulsive phase 
would affect the total mechanical work provided by the body. 
Indeed, as showed by Monte et al. (2020) with faster run-
ning speed, the GM muscle fascicle operating range shifts 
towards smaller lengths (on the ascending limb of the F–L 
relationship) yet operating quasi-isometrically and at a high 
force potential (> 80% of the maximum isometric force) 
and this behaviour allows the muscle fascicles to reduce the 
Fig. 2  Correlations between (positive) tendon work and total mechan-
ical work (at the whole-body level), net energy cost of running and 
“apparent” efficiency at the three investigated speeds (blue dots: 
10 km h−1, red squares: 13 km h−1, green triangles: 16 km h−1). At 
each speed, the subjects with the higher tendon work are those with 
the larger WTOT, the lower Cnet and the larger AE. Upper panel: corre-
lations between tendon work and total mechanical work at 10 km h−1 
(WTOT = 3.34⋅Wten + 1.57, N = 15, R2 = 0.65, P < 0.01), 13  km  h−1 
(WTOT = 2.82⋅Wten + 1.81, N = 15, R2 = 0.52, P < 0.05) and 16 km h−1 
(WTOT = 11.40⋅Wten + 0.56, N = 15, R2 = 0.55, P < 0.05). Middle panel: 
correlations between tendon work and net energy cost of running at 
10 km h−1 (Cnet = − 36.56⋅Wten + 7.68, N = 15, R2 = 0.72, P < 0.001), 
13  km  h−1 (Cnet = −  49.43⋅Wten + 10.15, N = 15, R2 = 0.60, P < 0.01) 
and 16 km h−1 (Cnet = − 35.36⋅Wten + 9.49, N = 15, R2 = 52, P < 0.05). 
Lower panel: correlations between tendon work and “apparent” 
efficiency at 10  km  h−1 (AE = 5.61⋅Wten – 0.08, N = 15, R2 = 0.75, 
P < 0.001), 13  km  h−1 (AE = 7.43⋅Wten – 0.38, N = 15, R2 = 0.65, 
P < 0.01) and 16  km  h−1 (AE = 7.96⋅Wten – 0.65, N = 15, R2 = 54, 
P < 0.05)
Fig. 3  Mean values of “apparent” efficiency as a function of the 
mean values of (positive) Achilles tendon work, at the three investi-
gated speeds (blue dots: 10 km h−1, red dots: 13 km h−1, green dots: 
16 km h−1); this relationship is described by the following equation: 
AE = 1.56 Wten + 0.33. The intercept with the “Y” axes (0.33) indi-
cates the value of “apparent” efficiency that could be expected were 
the Achilles tendon not operating as energy saver
2503
European Journal of Applied Physiology (2020) 120:2495–2505 
1 3
amount of mechanical work performed. The series elastic 
components accommodate the largest part of the MTU dis-
placement as they are stretched not only by the muscle force 
but also, and to a much larger degree, by the ground reaction 
forces. This allows the AT to perform the largest amount of 
mechanical work within the MTU.
What is the benefit of a larger tendon work? If the ten-
don makes a contribution to the whole MTU work during 
muscle contraction, the contribution of the active con-
tractile components would be reduced, thus reducing the 
energy expended during the contraction (Roberts and Azizi 
2011). In particular, as also reported in the “Introduction”, 
if the whole MTU length changes were attributable to 
the tendon alone, the muscle fibres would operate under 
“pure” isometric conditions and at a high force potential, 
requiring the lowest level of muscle activation (Fletcher 
and MacIntosh 2017). This phenomenon was recently veri-
fied by Bohm et al. (2019), who observed that the subjects 
with the higher soleus muscle force potential were those 
with the lower energy cost of running, suggesting that, 
the lower the shortening velocity of the soleus muscle the 
lower the energy demand during running. Furthermore, 
these authors suggested that the main mechanism for the 
underlying reduction of the fascicle shortening velocity 
during the stance phase was a greater tendon gearing (i.e. 
larger tendon displacement with respect to the muscle 
fascicles).
However, the utilization of tendon elasticity does not 
come entirely “free-of-charge”. Tendons operate in series 
with muscles and can only act as useful springs when mus-
cles generate force. Force generation by muscles requires 
metabolic energy, and thus there is a cost to operate ten-
don springs (e.g. Fletcher and MacIntosh 2017; Roberts 
and Azizi 2011; Roberts 2002). It has been proposed that 
the net metabolic benefit of tendon elasticity in running is 
best understood in the context of two properties of skel-
etal muscle (Roberts 2002; Roberts and Scales 2002). The 
first is the ‘Fenn effect’, which states that active muscles 
use more energy when performing work than when generat-
ing force isometrically (Fenn 1924). Thus, to the extent that 
tendons allow muscles to generate force without doing work 
(or while doing less work), they reduce the rate of energy 
consumption in the muscle. The second mechanism is the 
influence that tendon mechanics can have on the recruited 
muscle volume during running. Owing to the F–L and F–V 
properties of muscles, force can be produced with fewer 
active muscle fibres if the muscle operates at low or zero 
(i.e. isometric) shortening velocity (Fletcher and MacIntosh 
2017). The fascicles length changes observed in this study 
are probably not sizeable enough to increase the metabolic 
cost of muscle contraction. Indeed, in vitro evidence showed 
that although muscle force is reduced at shorter sarcomere 
lengths and a greater muscle activation is needed to reach 
a given amount of force, the ATPase rate seems not to dif-
fer from the rate at optimal length at least until 0.75 of L0; 
this suggests that if force potential is > 0.75 then muscle 
metabolic requirement is not affected, whereas when mus-
cle length is < 0.75, a higher cost of contraction should be 
expected (Stephenson et al. 1989; Joumaa et al. 2017). As 
shown by Monte et al. (2020) and Bohm et al. (2019), the 
GM and soleus muscle fascicle do not operate below 75% of 
their force potential during running, so the effects of fascicle 
length changes on muscle energy demands could be consid-
ered to be negligible.
Methodological limitations and considerations
In our study, the Achilles tendon length was not directly 
measured; instead, we used a geometric model to calculate 
the deformation of the entire Achilles tendon–aponeuroses 
complex from ankle and knee joint kinematics. However, 
this approach might overestimate the contribution of the 
mechanical work done by the tendon only, as shown by Zelik 
and Franz (2017). In addition, some recent studies (e.g. Kes-
sler et al. 2020) have reported that using a rigid-body foot 
model (as done in this study) could lead to an overestimation 
of ankle joint power, thus affecting Achilles tendon mechani-
cal work estimates. One other limitation is the estimation 
of GM forces based on reported values of relative PCSA, 
assuming consistent force contribution at all running speeds 
and a negligible inter-muscular force transmission between 
the individual plantar flexor muscles. The former assump-
tion has often been used before (e.g. Kurokawa et al. 2001; 
Fukunaga et al. 1996; Farris and Sawicki 2012) to distrib-
ute forces between synergist muscles, but the validity of the 
outcome forces needs to be confirmed, especially during 
dynamic conditions. In support of the latter assumption are 
the findings of Tijs et al. (2015), who have shown that non-
myotendinous forces are likely to have a minimal effect on 
the overall function of muscles.
Besides the Achilles tendon stretch–recoil, there are sev-
eral other parameters that could affect energy expenditure 
as running speed increases and have not been considered in 
our analysis. For instance, higher activation of other agonist 
and antagonist muscles in the lower limbs, torso and upper 
limbs would contribute to the increase in metabolic energy 
expenditure with increasing speed (Arellano and Kram 
2014). Also, elastic mechanisms other than Achilles ten-
don recoil, such as the arch of the foot, could provide extra 
energy savings with increasing speed and make the running 
task less energy demanding. Furthermore, elastic energy 
could be stored also in the transversal plane of the MTU; 
indeed, biaxial loading of aponeuroses allows for variation 
in tendon stiffness and energy storage in a variety of locomo-
tor behaviours (such as running, jumping and landing; e.g. 
Arellano et al. 2019).
2504
 
European Journal of Applied Physiology (2020) 120:2495–2505
1 3
Conclusion
In conclusion, a larger mechanical work provided by the 
tendons is expected to reduce the metabolic demands of run-
ning and to increase locomotion efficiency. Our data support 
this notion. The relationship between AE and tendon work 
supports previous suggestions that a value of “apparent” effi-
ciency close to muscle efficiency values (0.25–0.30) should 
be expected when no elastic energy can be stored in the 
tendon; the intercept of the relationship between AE and 
tendon work (0.33) indeed indicates the value that could be 
expected in the absence of Achilles tendon stretching–recoil-
ing behaviour. As suggested by Alexander (1991), measur-
ing “apparent” efficiency can help in understanding whether 
mechanical work is “recycled” via storage and release of 
elastic energy.
Author contributions AM, CM, VB and PZ contributed to conception 
and design of the study. AM recorded and analyzed the data under 
the supervision of CM, VB and PZ. AM, CM, VB and PZ contrib-
uted to the interpretation of the data, wrote and critically revised the 
manuscript. All authors approved the final version of the manuscript 
and agreed to be accountable for all aspects of the work. All persons 
included as an author qualify for authorship, and all those who qualify 
for authorship are listed.
Funding The authors received no funding for this work. Open access 
funding provided by Università degli Studi di Verona within the CRUI-
CARE Agreement.
Compliance with ethical standards 
Conflict of interest The authors declare there are no competing inter-
ests.
Availability of data and material All relevant data are reported in the 
manuscript.
Open Access This article is licensed under a Creative Commons Attri-
bution 4.0 International License, which permits use, sharing, adapta-
tion, distribution and reproduction in any medium or format, as long 
as you give appropriate credit to the original author(s) and the source, 
provide a link to the Creative Commons licence, and indicate if changes 
were made. The images or other third party material in this article are 
included in the article’s Creative Commons licence, unless indicated 
otherwise in a credit line to the material. If material is not included in 
the article’s Creative Commons licence and your intended use is not 
permitted by statutory regulation or exceeds the permitted use, you will 
need to obtain permission directly from the copyright holder. To view a 
copy of this licence, visit http://creat iveco mmons .org/licen ses/by/4.0/.
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The influence of Achilles tendon mechanical behaviour on "apparent" efficiency during running at different speeds.
Monte, Andrea,Maganaris, Constantinos,Baltzopoulos, Vasilios,Zamparo, Paola