1
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  
| https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports
Shorter heels are linked 
with greater elastic energy storage 
in the Achilles tendon
A. D. Foster 
1*, B. Block2, F. Capobianco III2, J. T. Peabody2, N. A. Puleo2, A. Vegas2 & 
J. W. Young 
3
Previous research suggests that the moment arm of the m. triceps surae tendon (i.e., Achilles tendon), 
is positively correlated with the energetic cost of running. This relationship is derived from a model 
which predicts that shorter ankle moment arms place larger loads on the Achilles tendon, which 
should result in a greater amount of elastic energy storage and return. However, previous research has 
not empirically tested this assumed relationship. We test this hypothesis using an inverse dynamics 
approach in human subjects (n = 24) at speeds ranging from walking to sprinting. The spring function of 
the Achilles tendon was evaluated using specific net work, a metric of mechanical energy production 
versus absorption at a limb joint. We also combined kinematic and morphological data to directly 
estimate tendon stress and elastic energy storage. We find that moment arm length significantly 
determines the spring-like behavior of the Achilles tendon, as well as estimates of mass-specific 
tendon stress and elastic energy storage at running and sprinting speeds. Our results provide support 
for the relationship between short Achilles tendon moment arms and increased elastic energy 
storage, providing an empirical mechanical rationale for previous studies demonstrating a relationship 
between calcaneal length and running economy. We also demonstrate that speed and kinematics 
moderate tendon performance, suggesting a complex relationship between lower limb geometry and 
foot strike pattern.
The role of the Achilles tendon (AT) in elastic energy storage with subsequent return during stance phase is well 
 established1–7. Recovery of elastic energy imparted to the AT is potentially influenced by AT morphology in three 
ways: (1) material properties of the tendon, (2) cross-sectional area of the tendon, and (3) the moment arm of 
the calcaneal tuberosity loading the tendon against the muscle force of the m. triceps surae (i.e., foot geometry). 
Previous work suggests that foot geometry may explain variation in how much potential energy is stored in the 
tendon, finding that a shorter AT moment arm is correlated with lower mass-specific energy costs of locomotion 
(COL; L  O2  kg−1  s−1)8, 9. This finding suggests that shorter AT moment arms are associated with greater elastic 
loads imparted to the tendon, which are then recovered as kinetic energy during the support phase of each gait 
 cycle9, thereby reducing COL. Scholz et al.9 also suggest that the length of the AT moment arm is a more signifi-
cant factor in explaining COL than variation in material properties of the tendon itself or size-related variation 
in the cost of swinging the leg forward during the aerial phase of the gait  cycle9. However, assumptions about the 
interacting roles of AT moment arm length, tendon cross-sectional dimensions, and tendon material properties 
on variation in elastic energy storage have yet to tested in an integrated manner. Moreover, Scholz et al.9 doesn’t 
directly measure the variables in the model which predict variation in elastic energy storage, including muscle 
force and the external moment arm. Finally, because previous studies of how AT moment arm length influences 
COL have used trained runners running on a treadmill at a speed of 16 km/h, it is still unknown how variation in 
speed and athletic training impacts elastic loading to the tendon in relation to moment arm length. While previ-
ous work has explored elastic loading of the AT at different speeds and under different loading  conditions10–21, 
this study is the first to investigate the potential correlation between foot geometry like the AT moment arm 
length and spring-like behavior of this tendon in humans.
In this study, we model elastic loading of the AT by characterizing the spring-like behavior over the support 
phase of each gait cycle using two metrics. First, we calculate specific net work (SNW) at the ankle joint. SNW is 
OPEN
1Department of Anatomy, School of Osteopathic Medicine, Campbell University, PO Box 4280, Buies Creek, 
NC 27506, USA. 2School of Osteopathic Medicine, Campbell University, PO Box 4280, Buies Creek, NC 27506, 
USA. 3Department of Anatomy and Neurobiology, Northeast Ohio Medical University (NEOMED), Rootstown, 
OH 44272, USA. *email: afoster@campbell.edu
2
Vol:.(1234567890)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
a ratio of net joint work to total joint work that results in values from 0, comparable to a perfect spring, to 1, com-
parable to a perfect motor or brake (see “Methods” section)22. SNW values of 1.0 are the result of a step with solely 
positive or negative work at the joint during stance phase, whereas a value of 0 indicates commensurate levels of 
positive and negative work, consistent with spring-like behavior. We use SNW to test whether AT moment arm 
length predicts spring-like behavior of the tendon. Second, we also measure individual AT cross-sectional area 
and tendon length using ultrasonography along with the muscle force impulse at the ankle over stance phase to 
estimate the magnitude of energy storage in the  AT23 (see “Methods” section). We test the following hypotheses:
H1: Subjects with shorter AT moment arms should exhibit more spring-like behavior (lower SNW values) 
in running gaits.
H2: AT moment arm length should be negatively correlated with tendon stress (i.e., force per unit cross-
sectional area).
H3: AT moment arm length should be negatively correlated with tendon energy storage.
Results
Specific net work. 
AT moment arm lengths ranged from 3.12 to 5.01 cm (see boxplot in Supplementary 
Fig. S1) and are significantly correlated with body mass (r = 0.624,  t[22] = 3.748, p < 0.001). SNW values at the hip 
are moderately high in all gaits, whereas values at the knee become more spring-like (i.e., lower values of SNW) 
in gaits lacking double-limb support periods, such as jogging, running, and sprinting. At the ankle, subjects 
have the lowest values of SNW when jogging and the highest values when sprinting (see Table 1 for summary 
statistics for each speed; see Fig. 1 for density plot and histogram of SNW values by joint and speed). We find 
that AT moment arm length is positively correlated with SNW for running and sprinting gaits, which supports 
hypothesis  H1. However, this relationship is not significant for jogging gaits (see Table 2; Fig. 2). Additionally, 
while sprinting gaits exhibit higher mean SNW values at the ankle compared to walking gaits, the length of the 
AT moment arm appears to still have a significant effect on spring-like behavior at sprint speeds, but not during 
walking gaits.
Using a mixed-effect multiple regression model with the average moment arm of the GRF vector at the ankle 
(RAnkle), tendon cross-sectional area (CSA), the GRF impulse (J), Froude number, and body mass as fixed effect 
predictors, we find that AT moment arm length does not significantly explain variation in SNW at running 
speeds. Nevertheless, AT moment arm length and RAnkle are significant predictors at sprinting speeds (see Table 3). 
Standardized partial correlation coefficients (i.e., β-weights) demonstrate that RAnkle plays a more significant role 
than AT moment arm length, which suggests that tendon elastic energy storage is particularly sensitive to vari-
ation in postural variation across steps. However, average RAnkle is also correlated with AT moment arm length 
at sprint speeds (r = 0.370,  t[70] = 3.336, p = 0.001). This result is consistent with the finding that AT moment arm 
length is correlated with foot length at sprint speeds (i.e., individuals with longer feet have longer AT moment 
arms; r = 0.684,  t[22]  = 4.394, p < 0.001), which should translate to a longer external moment arm (RAnkle) of the 
GRF. There were also no sex-based differences when sex was added as a fixed-effect (p = 0.680).
Tendon stress and elastic energy storage. 
Both mass-specific tendon stress (MPa/kg) and mass-spe-
cific elastic energy storage (Joules/kg) are negatively correlated with AT moment arm length at running and 
sprint speeds (see Fig. 3; Table 3). These variables are not correlated at walking, fast walking, and jogging speeds. 
Subject means are located in Supplementary Tables S1 and S2.
Discussion
We predicted that subjects with smaller AT moment arm lengths would exhibit lower SNW values in running 
gaits (i.e., more spring-like joint behavior). The overall pattern is that there is significant variation across gait 
cycles, but that AT moment arm length does appear to result in greater mass-specific tendon stress, and there-
fore more spring-like behavior (i.e., lower SNW values), resulting in greater mass-specific energy storage at 
running and sprinting speeds. The design for this study was derived from a model proposed by Scholz et al.9, 
which predicts that tendon material properties and foot geometry explain inter-individual differences in COL, 
with AT moment arm length explaining most of this variation. The mixed-effect model analyzing sprint speed 
kinematics, subject morphology, body size, and tendon CSA, a determinant of tendon strength and stiffness, 
suggests that CSA does not play a significant role in determining spring-like behavior. Indeed, our results suggest 
Table 1.  SNW values for each joint at each speed. Mean Froude numbers and specific net work (SNW) values 
with standard deviations (SD) for each joint at each speed.
Gait
Froude
Hip SNW
Knee SNW
Ankle SNW
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Walk
0.130
0.041
0.669
0.251
0.653
0.170
0.450
0.199
Fast Walk
0.245
0.054
0.640
0.292
0.571
0.153
0.367
0.232
Jog
0.362
0.086
0.834
0.178
0.297
0.220
0.231
0.200
Run
0.662
0.179
0.930
0.124
0.428
0.245
0.447
0.252
Sprint
1.086
0.283
0.935
0.148
0.450
0.299
0.755
0.201
3
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
that AT moment arm length and kinematics (i.e., ankle joint posture) play the largest role in determining elastic 
loading of the tendon. Additionally, the results of the mixed-effect model demonstrate that when holding body 
size constant, AT moment arm length is still a significant predictor. If subjects had similar tendon properties 
for their mass, mass-specific measures of elastic loading to the tendon would not vary with AT moment arm 
length. Therefore, these results provide robust support for the hypothesis that heel allometry is a significant 
factor in moderating elastic energy storage. It is also worth noting that there is variation about the regression 
line in ways that differ from scatter about the regression line when looking at COL in previous  work8, 9. This is 
likely attributed to step-to-step variation among and between subjects. COL calculations are an average over 
two minutes, containing multiple steps, whereas values for SNW, tendon stress, and elastic strain energy in this 
study are averages over stance phase for multiple sequential steps.
Figure 1.  Density plot of individual specific net work (SNW) values for the hip, knee, and ankle for each step, 
for all subjects, at each speed. Peaks represent the most concentrated distribution of SNW values for each joint, 
at each speed. Plot rugs (vertical lines) are histograms of SNW values from all subjects and all steps.
Table 2.  Pearson’s correlation coefficient comparisons between ankle SNW, mass-specific stress, and mass-
specific elastic energy storage and the Achilles tendon moment arm at different speeds. Bolded values indicate 
significance at p ≤ 0.05.
Variable
Speed
Statistic
R
p-value
SNW
Walk
t144 =  − 0.796
 − 0.066
0.786
Fast walk
t96 =  − 1.051
 − 0.107
0.852
Jog
t103 = 0.675
0.066
0.251
Run
t85 = 3.367
0.343
0.001
Sprint
t70 = 4.094
0.440
 < 0.001
AT stress/BM
Run
t165 =  − 9.185
 − 0.582
 < 0.001
Sprint
t102 =  − 5.190
 − 0.457
 < 0.001
AT tendon energy/BM
Run
t165 =  − 4.938
 − 0.359
 < 0.001
Sprint
t102 =  − 2.319
 − 0.224
0.011
4
Vol:.(1234567890)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
This study also builds upon previous work by exploring how speed and AT moment arm length moderates 
elastic energy storage. AT moment arm length does not explain variation in tendon performance during walk-
ing gaits, which is consistent with predictions and results from Scholz et al.9 and Raichlen et al.8. AT moment 
arm length does explain variation in tendon performance in running and sprinting gaits, though not in jogging 
gaits, despite jogging gaits having the lowest mean value for SNW at the ankle for all subjects (0.231). The mean 
SNW values for running and sprinting were higher, at 0.447 and 0.755, respectively (see Table 1). However, while 
sprint speed SNW values are more motor/brake-like at sprinting speeds, the relationship between AT moment 
arm length and SNW is stronger at sprint speeds (r = 0.440,  t[70] = 4.094, p < 0.001) than running speeds (r = 0.343, 
 t[85] = 3.367, p = 0.001) (see Table 2). We interpret these findings to indicate that subjects need to generate more 
positive work at all lower limb joints as speed increases, but that individuals with short calcanei are nonethe-
less able to harness relatively more energy from the spring-like return of the AT in running gaits. However, our 
results demonstrate that AT moment arm length is not correlated with spring-like behavior during walking 
gaits, which supports previous work showing no correlation between AT moment arm length and metabolic 
costs in walking  gaits8.
It is notable that the subject-determined sprint speeds used in this study are on average slower than the tread-
mill speed used in Scholz et al.9 and Raichlen et al.8. Subject sprinting speeds in this study are 3.02 ± 0.478 m/s 
(Froude 1.04 ± 0.309). Subjects from previous studies ran at a sustained pace of 16 km/h (4.44 m/s) on a treadmill, 
while  shod8, 9. However, the results from this study suggest a relationship between AT moment arm length and 
spring-like behavior at speeds above a jog, which may include at 4.44 m/s (16 km/h). The subject population is 
also different. Raichlen et al.8 used trained endurance runners whose 10 K personal best runs were under 36 min 
and Scholz et al.9 used subjects who self-identified as runners. In this study, subjects were recruited based on 
being recreationally fit but are not necessarily regular runners. Additionally, these previous studies only sampled 
Figure 2.  Scatter plots of SNW and the Achilles tendon moment arm length at running (A) and sprinting 
speeds (B) against AT moment arm length. The black lines are least squares best fit lines and the gray bands 
represent 95% confidence intervals.
Table 3.  Mixed-effect model of variation in ankle SNW with morphological and kinematic variables as fixed 
effects at sprint speed. Bolded p-values indicate significant fixed-effect predictors. β are the partial regression 
coefficients (i.e., β-weights). CSA is the cross-sectional area of the AT. RAnkle is the mean external moment arm 
of the ground reaction force. J is the GRF impulse.
Predictor variable
β
Statistic
p-value
Intercept
 − 0.002
F1,45 = 0.003
0.954
Ankle moment arm
0.229
F1,20 = 15.491
0.001
RAnkle
0.336
F1,45 = 7.074
0.011
Body mass
0.151
F1,20 = 0.536
0.473
Froude
0.191
F1,45 = 3.271
0.067
J
 − 0.236
F1,45 = 3.520
0.077
CSA
0.020
F1,20 = 0.001
0.976
5
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
males, whereas this study has both males and females (and has more females than males) and a larger sample size. 
Broadly, our comprehensive sampling methods and sample size provide strong empirical support for previous 
models which suggest that heel morphology moderates AT tendon performance in running gaits.
The mixed-effect model results expand on this relationship by exploring how kinematic variables and tendon 
CSA are correlated with spring-like behavior of the AT. When these variables are included as fixed effects, AT 
moment arm length is not a significant predictor of SNW at running speeds. However, at sprint speeds both 
the AT moment arm and the external moment arm of the GRF (RAnkle) are significant predictors, with RAnkle 
explaining more variation. Posture and footfall pattern (e.g., mid- vs. forefoot striking) may play a role in elastic 
loading, perhaps as reflected in the inter- and intra-subject variation in SNW values from step to step. RAnkle may 
also play a role in elastic energy storage by altering tendon stiffness depending on foot strike pattern (e.g., heel 
vs. fore-foot strike). Hof et al.25 found that subjects with the highest ankle moments exhibited greater stiffness 
in the elastic series component of the m. triceps surae.
Results from tendon stress and estimates of elastic energy storage are consistent with measures of spring-like 
behavior (i.e., SNW). These results demonstrate that smaller AT moment arm lengths are correlated with higher 
mass-specific tendon stress values, which in turn result in greater amounts of mass-specific elastic energy storage. 
These data support previous models and empirical findings demonstrating a correlation between AT moment 
arm length and COL. The differences between the smallest and largest values of AT moment arm length in our 
sample are substantial. Values of AT moment arm lengths in our study varied from 3.12 to 5.01 cm, a 37.7% 
difference that can lead to as much as a 60.7% increase in mass-specific elastic energy storage between subjects 
with the shortest and longest moment arms.
In this study, tendon stress is calculated using the force impulse (time integrated force). This has the advantage 
of reflecting force imparted to the AT over the entirety of stance phase. Peak values, by contrast, only reflect 
instantaneous loads and are more relevant to estimating safety factor and injury risk. Previous work calculated 
peak stresses of 111 MPa measured from turnbuckles on the AT while  running26. Stress data measured in this 
study are similar. The mean value for peak stress from this study (using an inverse dynamics approach) from 
all subjects is 110.58 MPa at sprint speeds and 101.66 MPa for running speeds (see subject means in Table S1 
and S2). There have been a range of estimates for failure stress in the  AT26–30. Wren et al.30 found a mean failure 
stress of 79 MPa when straining Achilles tendons at 1–10% per second. While the mean stress values from this 
study exceed the mean failure stress from Wren et al.30, loading rates measured in this study were not of the 
same magnitude and duration as tests for plastic deformation and failure. Overall, the AT has similar material 
properties to other tendons, but receives a much higher load during running, with an estimated safety factor 
of 1.5, compared to other tendons that have safety factors of ~  428, 31. However, because of the relationship with 
AT moment arm length and tendon stress, it is possible that foot geometry may be predictive of risk for ten-
dinopathy. Achilles tendinopathy (i.e., pain and swelling of the Achilles tendon) is one of the most common 
sports-related  injuries32. Ex vivo data from human ATs suggest that excessive tendon strain (the result of tendon 
Figure 3.  Scatter plots of AT moment arm length and mass-specific tendon stress (MPa/kg) for running (a) 
and sprinting (b) trials. Scatter plot of AT moment arm and mass-specific tendon energy storage (Joules/kg) for 
running (c) and sprinting (d) trials. The black line is a least squares best fit line and the gray band represents the 
confidence interval.
6
Vol:.(1234567890)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
stress) is a primary factor responsible for tendon damage, and that repetitive loading contributes to AT injury 
and  tendinopathy33. Moreover, a majority of AT ruptures are sub-clinical34, which suggests that intrinsic factors 
may play a significant role in explaining tendon strain and predicting risk for injury. Future work should explore 
this association. Additionally, athletic training is linked with changes to AT material properties which is relevant 
to injury prevention and may play a role in the capacity for elastic energy storage in the  AT29, 35.
Previous work has characterized elastic energy storage of the m. gastrocnemius  and Achilles tendon during 
walking and running gaits using inverse dynamics and  ultrasonography13, 14, 16–19, 36, 37. This is the first study to 
measure how AT moment arm length moderates tendon stress and elastic energy storage. However, it is impor-
tant to note there are some limitations imposed by the study design and that a detailed understanding of the 
relationship between foot geometry and the spring-like function of the AT requires further work. In particular, 
future work should incorporate non-invasive imaging methods (e.g., ultrasonography) to measure instantane-
ous changes in AT length and moment arm dimensions. Increased temporal precision may offer greater insight 
into how foot geometry may impact elastic energy storage at different points in stance phase. Indeed, previous 
work has demonstrated that accounting for tendon curvature at different points of stance phase may provide 
more precision in both measurements of tendon dimensions and moment arm  length38. Rasske et al.39 found 
that during walking gaits, AT moment arm length changed 10% at toe-off relative to heel strike. Recent work by 
Harkness-Armstrong et al. found that assuming a straight (as opposed to curved) AT led to larger estimates of 
moment arm length than actual  size38. In this study, joint work was calculated using moment arm lengths which 
vary with joint angle (and scaled to each subject; see “Methods” section). However, future work which measures 
how the AT moment arm changes with joint angle, load, and speed for each individual using ultrasonography 
may increase precision for estimating joint work across stance  phase40–42. For statistical comparisons of spring-
like behavior (SNW), joint stress, strain, and elastic energy storage, a static measure of AT moment arm length 
was used following Scholz et al.9. Previous work from other studies suggests that this method provides reliable 
measures of the AT moment  arm43. However, exploring how tendon performance changes at different points 
of stance phase in relation to ankle moment arm length may also provide further insight into this relationship.
Exploring how AT moment arm length moderates tradeoffs between muscle work and elastic energy storage 
would also provide further clarification. For example, holding all else equal, a shorter moment arm should result 
in less muscle fiber work (shortening) for a given joint rotation. Any decrease in muscle fiber work should result 
in a reduction in metabolic cost, which is consistent with results from previous work demonstrating a negative 
correlation between AT moment arm length and  COL8, 9. The model proposed by Scholz et al.9 (and explored in 
this study), also predicts that shorter AT moment arms will result in increased tendon load. However, any increase 
in tendon load should be a result of an increase in muscle force. This creates a potential conflict in interpreting 
the relationship between AT moment arm length, metabolic cost, and muscle force. The results from this study 
suggest that shorter AT moment arms increase tendon load and elastic energy storage such that the balance of 
this tradeoff still favors a shorter AT moment arm, holding all else equal. However, future work which explores 
how AT moment arm length moderates muscle fiber work, muscle force, tendon load, elastic energy storage, 
and metabolic cost would provide further insight into the tradeoffs imposed between muscle force and elastic 
energy storage in individuals with shorter AT moment arm lengths.
Individual measures of tendon material properties and elastic modulus may also offer greater clarification on 
how anatomy predicts elastic energy storage. Previous research indicates that material properties of the AT and 
force generating capacity of muscles varies between individuals and is correlated with elastic energy  storage15, 18, 
44–46. Additionally, tendon CSA may change with deformation of the tendon as force is applied throughout stance 
phase and should be accounted for in future  studies47. The stiffness of the m. gastrocnemius aponeurosis is also 
a significant factor in contributing to muscle work and elastic energy  storage17, 48–50. Methods which measure 
gearing and muscle–tendon stiffness, which vary with speed and torque development, also have been shown to 
influence elastic energy storage at different points of stance phase, and therefore may also be moderated by foot 
geometry like the AT moment  arm13, 14, 19, 36.
In conclusion, the results from this study suggest that there is a significant correlation between moment arm 
length and spring-like behavior of the AT. This spring-like behavior also corresponds with greater tendon stress 
and elastic energy storage in subjects with smaller AT moment arm sizes. Overall, our findings provide empirical 
mechanical support for the energetic model proposed by Scholz et al.9, suggesting that calcaneal length may be 
an important skeletal determinant of variation in COL during human bipedal running.
Methods
To test how AT moment arm length predicts spring-like behavior of the AT, we collected morphometric, kin-
ematic, kinetic, and ultrasound data from 24 recreationally fit adults (see Table 4 for summary information). 
Subjects were asked to walk, fast walk, jog, run, and sprint at self-determined speeds across 6 force platforms 
Table 4.  Subject morphometrics and summary statistics. Subject morphometrics and statistics presented as 
the number of males and females and all numeric variables represent the mean and the standard deviation (AT: 
Achilles tendon).
Sex
Age
Body mass
AT moment arm
AT cross-sectional area
Male
Female
Years
kg
cm
cm2
7
17
23.50 ± 2.80
64.15 ± 9.84
4.27 ± 0.48
0.61 ± 0.15
7
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
embedded in the floor (2 platforms in width, 3 platforms in length), which allowed for multiple support phases to 
be measured per trial. Subjects were unshod and repeated each speed three times. Subject speeds were calculated 
as the mean velocity of the marker placed on the greater trochanter of each leg during the support phase of each 
gait cycle, which were then standardized using Froude numbers (see Eq. (1))51:
Ultrasound. 
The cross-sectional area of the AT was measured with B-mode ultrasound (SonoSite M-Turbo, 
Fujifilm SonoSite, Bothell, Washington, USA) using a 6 cm linear array transducer operating at 15 MHz (HFL50; 
Fujifilm SonoSite, Bothell, Washington, USA), with a depth set to 2.7 cm. The resolution of the ultrasound 
image is 100 pixels/cm. To measure the cross-sectional area of the AT, the probe was placed in a transverse plane 
at the level of the malleoli while subjects were prone on an examination table and the ankle was fixed at 160° 
(plantarflexed), which was measured with a goniometer. The cross-sectional area of the tendon was measured 
in ImageJ, by tracing the outline of the tendon using the polygon area selection tool and measuring the  area52 
(see Fig. 4). To measure tendon length, subjects lay prone with their foot in a neutral position (i.e., 90°). Using 
the same ultrasonographic technique, the myotendinous junction of the medial head of m. gastrocnemius on the 
left and right leg was located by placing it in the center of the image. A washable marker was used to place a dot 
on the skin at this location using the midpoint guide on the probe. This same procedure was used to determine 
the most inferior extent of the insertion of the tendon on the calcaneal tuberosity. Tendon length was measured 
using a flexible measuring tape and is defined as the distance of the myotendinous junction to the insertion on 
the calcaneal tuberosity. Tendon length for each subject is an average of the lengths of the left and right sides.
Morphometrics. 
Subject body mass and height were recorded using a digital scale and segment lengths (hip 
height and foot length) were measured using a flexible measuring tape. Hip height was defined as the distance 
from the greater trochanter to the floor while standing. Foot length was defined as the most anterior point of 
the first digit to the most posterior point of the calcaneal tuberosity. Subject values for segment lengths are an 
average of the left and right sides.
To compare tendon performance data collected in this study to previous work, we measured the moment 
arm of the AT using photographic  methods9. Subjects stood with their ankle at an angle of 90° (where the leg is 
perpendicular to the foot) on a board that was affixed with a measuring tape (see Supplementary Fig. S2). The 
location of the footboard and camera were standardized and the malleoli were centered in the image to reduce 
the effects of parallax distortion. The moment arm was defined as the most medially or laterally prominent point 
of the medial or lateral malleolus, respectively, to the most posterior edge of the skin covering the tendon. Dis-
tances were measured in  ImageJ52 using the measuring tape as a scale. The medial and lateral values for both the 
left and right foot were averaged from three repeated measurements, then those averages from the medial and 
lateral side were averaged for each subject to obtain a single mean value for the AT moment arm. These moment 
arm values are used as the dependent variable when exploring the relationship between kinematic variables and 
elastic loading. See Table 4 for subject summary statistics and Supplementary Fig. S1 for a boxplot of subject 
AT moment arm lengths.
Kinematics and kinetics. 
Subjects were fitted with retro-reflective markers placed on joint centers of the 
hip, knee, and ankle, in addition to other standardized locations (see Supplementary Fig. S3). Subjects were 
(1)
velocity2
gravitational acceleration · hip height
Figure 4.  The cross-sectional area of the Achilles tendon measured using ultrasound. Example of the cross-
sectional area of the Achilles tendon measured at the level of the malleoli using B-mode ultrasound. The area of 
the tendon outlined by the dashed white line and shaded in blue was calculated using ImageJ. A is anterior and P 
is posterior. The hyperechoic region anterior to the shaded ellipse around the tendon is Kager’s fat pad.
8
Vol:.(1234567890)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
asked to walk, fast walk, jog, run, and sprint at self-determined speeds. Runway distances were sufficient for 
subjects to reach steady state locomotion when crossing force plates. Force data were collected using six force 
platforms (BTS P6000D, BTS Bioengineering Corp., Quincy, MA, USA) that were embedded in the floor, with 
a sampling rate of 1 kHz. Kinematic data were recorded using a 12-camera motion capture system (BTS Bioen-
gineering Corp., Quincy, MA, USA), with a sampling rate of 500 Hz. Force data were deprecated to 500 Hz to 
synchronize force and kinematic data which were processed using custom routines in MATLAB (version 2018b; 
Mathworks, Natick, MA, USA). A zero-lag Butterworth, low-pass filter was used to smooth kinematic data 
(fourth-order, with a 6 Hz cutoff) and force data (fourth-order, with a 100 Hz cutoff).
An inverse dynamics approach was used to calculate joint work for the hip, knee, and ankle over the sup-
port phase of each gait cycle using 2D kinematics and ground reaction forces (GRF). We calculated the exter-
nal moment arm of the GRF (R) as the fore-aft and vertical distance from the center of pressure (COP). Net 
joint moments were calculated using the GRF vector, limb segment accelerations, and joint moments following 
Biewener et al.53 and  Winter54. Because mediolateral forces have a negligible impact on joint moments, these 
moments were ignored in the calculation of biomechanical variables. Net joint moments, M, were determined 
for each kinematic frame, at the hip, knee, and ankle joint using the free-body method described in  Winter54. 
Limb segment accelerations were calculated using the second-order finite differences  method54. Extensor muscle 
forces (Fankle, Fknee, and Fhip) to generate these moments were determined by solving a system of equations from 
Biewener et al.53:
Subtracted terms represent flexor actions of bi-articular muscles gastrocnemius (G), hamstrings (H), and 
rectus femoris (RF). Flexor and extensor moments were calculated assuming the force produced by each muscle 
is proportional to its physiological cross-sectional area (PCSA)53. Muscle force impulse at the hip, knee, and 
ankle was calculated as the finite integral of instantaneous muscle force throughout each support phase. Human 
extensor moment arms, r, for the hip, knee, and ankle, were calculated as instantaneous values that vary with 
joint angle using equations from the literature for the hip and knee from  Visser55 and ankle from Rugg et al.56.
To calculate the average moment arm of the GRF vector (R) at the ankle (RAnkle) for each support phase, we 
used the GRF impulse (J), AT moment arm length (rAnkle; calculated following Rugg et al.56) and the ankle force 
impulse (FImpulse) following equations from Biewener et al.53 [see Eq. (5)]:
Using equations from  Winter54, we calculated work, which is the finite integral of joint power (Watts/kg) 
over time, at the hip, knee, and ankle joint. Positive and negative values for work were used to calculate SNW, 
which is a ratio of the sum of positive and negative work to the sum of the total work, to characterize the spring-
like behavior of lower limb joints [see Eq. (6)]. Negative values (instantaneous values less than 0) for work are 
summed as WorkNeg and positive values for work are summed as WorkPos.
Tendon stress, strain, and energy storage. 
We calculate tendon stress, which is defined as the force 
impulse imparted to the AT, scaled to the cross-sectional area of the AT, for each subject:
Here, FAnkle is the instantaneous value of muscle force at the ankle joint for each support phase of a gait cycle 
(ankle force impulse, FImpulse), and  t1 and  t2 represent the beginning and end of the support phase interval. Tendon 
CSA is calculated as the cross-sectional area and converted to square meters  (m2) from ultrasound images of the 
AT for each subject (see ultrasound methods).
Tendon strain is calculated by dividing tendon stress by the elastic modulus of the AT. Here, we use 819 MPa 
for the elastic modulus, which is the mean value of a sample of human ATs from Wren et al.30. Tendon strain is 
then multiplied by the resting tendon length for each subject (see ultrasound methods) to calculate the estimated 
change in the length of the tendon. Strain energy, or the amount of elastic energy storage in the tendon, is mod-
eled following Hooke’s law [see Eq. (8)].
Here, FAnkle is the ankle force impulse and L is the change in length of the AT. Following Moore et al.23, we 
multiplied the amount of energy recovered by 0.93, which is an estimate of tendon resilience (i.e., 93%).
(2)
Mankle = Fankle · rAnkle
(3)
MKnee = FKnee · rKnee− FG,Knee · rG,Knee−FH,Knee · rH,Knee
(4)
MHip = FHip · rHip − FRF,Hip · rRF,Hip
(5)
RAnkle =
 t2
t1GRF · rAnkle
 t2
t1FAnkle
(6)
|WorkPos + WorkNeg|
|WorkPos| + |WorkNeg|
(7)
Tendonstress =
 t2
t1FAnkle
TendonCSA
(8)
W = 1
2FAnkL
9
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
Statistics. 
All statistical analyses for this study were conducted in the R statistical platform (version 3.6.1, 
’Action of the Toes’)57. We used one-tailed Pearson product-moment correlations to test for positive association 
between SNW and AT moment arm lengths and negative association between AT moment arm lengths and 
stress and elastic energy storage. Mixed-effect models were used to explore the correlation between SNW and 
AT moment arm lengths with kinematic and morphometric variables as fixed effects (using the lme function)58. 
A mixed-effect model is used for testing hypotheses in this study as it allows for adjustment of degrees of free-
dom to account for variation between individuals, and error terms to account for repeated measures of multiple 
steps from the same subject. Raw variates were scaled and centered (converted to z-scores) to permit direct 
comparisons of resulting partial regression coefficients (β weights) to allow for comparison of which predictors 
best explain variance in the dependent variable. Results for all tests were significant at p < 0.05. Plots were made 
using  ggplot259.
Institutional oversight and compliance. 
Institutional Review Board approval was obtained by Camp-
bell University (Protocols 376 and 472) and all study methods and procedures in this study followed the approved 
protocols and all IRB guidelines. Informed consent was obtained prior to subject participation.
Data availability
Data and the R code used for statistical analysis and generating figures and tables in this study are available at: 
https:// github. com/ adfos ter/ achil leste ndon
Received: 8 September 2020; Accepted: 16 April 2021
References
 1. Alexander, R. M. Elastic energy stores in running vertebrates. Integr. Comp. Biol. 24, 85–94 (1984).
 2. Alexander, R. M. Energy-saving mechanisms in walking and running. J. Exp. Biol. 160, 55–69 (1991).
 3. Alexander, R. M. Tendon elasticity and muscle function. Comp. Biochem. Physiol. A Mol. Integr. Physiol. 133, 1001–1011 (2002).
 4. Fukunaga, T. et al. In vivo behaviour of human muscle tendon during walking. Proc. R. Soc. Lond. Ser. B Biol. Sci. 268, 229–233 
(2001).
 5. Lichtwark, G. A. & Wilson, A. M. Is Achilles tendon compliance optimised for maximum muscle efficiency during locomotion?. 
J. Biomech. 40, 1768–1775 (2007).
 6. Sawicki, G. S., Lewis, C. L. & Ferris, D. P. It pays to have a spring in your step. Exerc. Sport Sci. Rev. 37, 130–138 (2009).
 7. Zelik, K. E. & Franz, J. R. It’s positive to be negative: achilles tendon work loops during human locomotion. PLoS ONE 12, e0179976 
(2017).
 8. Raichlen, D. A., Armstrong, H. & Lieberman, D. E. Calcaneus length determines running economy: implications for endurance 
running performance in modern humans and Neandertals. J. Hum. Evol. 60, 299–308 (2011).
 9. Scholz, M. N., Bobbert, M. F., van Soest, A. J., Clark, J. R. & van Heerden, J. Running biomechanics: shorter heels, better economy. 
J. Exp. Biol. 211, 3266–3271 (2008).
 10. Kharazi, M., Bohm, S., Theodorakis, C., Mersmann, F. & Arampatzis, A. Quantifying mechanical loading and elastic strain energy 
of the human Achilles tendon during walking and running. Sci. Rep. 11, 5830 (2021).
 11. Peltonen, J., Cronin, N. J., Stenroth, L., Finni, T. & Avela, J. Viscoelastic properties of the Achilles tendon in vivo. Springerplus 2, 
212 (2013).
 12. Pożarowszczyk, B., Gołaś, A., Chen, A., Zając, A. & Kawczyński, A. The impact of post activation potentiation on achilles tendon 
stiffness, elasticity and thickness among basketball players. Sports 6, 117 (2018).
 13. Monte, A. & Zignoli, A. Muscle and tendon stiffness and belly gearing positively correlate with rate of torque development during 
explosive fixed end contractions. J. Biomech. 114, 110110 (2021).
 14. Monte, A., Nardello, F. & Zamparo, P. Mechanical advantage and joint function of the lower limb during hopping at different 
frequencies. J. Biomech. 118, 110294 (2021).
 15. Maganaris, C. N. & Paul, J. P. Tensile properties of the in vivo human gastrocnemius tendon. J. Biomech. 35, 1639–1646 (2002).
 16. Lichtwark, G. A., Cresswell, A. G. & Newsham-West, R. J. Effects of running on human Achilles tendon length–tension properties 
in the free and gastrocnemius components. J. Exp. Biol. 216, 4388–4394 (2013).
 17. Lichtwark, G. A. & Wilson, A. M. Interactions between the human gastrocnemius muscle and the Achilles tendon during incline, 
level and decline locomotion. J. Exp. Biol. 209, 4379–4388 (2006).
 18. Lichtwark, G. A. & Wilson, A. M. In vivo mechanical properties of the human Achilles tendon during one-legged hopping. J. Exp. 
Biol. 208, 4715–4725 (2005).
 19. Lai, A. K. M., Biewener, A. A. & Wakeling, J. M. Muscle-specific indices to characterise the functional behaviour of human lower-
limb muscles during locomotion. J. Biomech. https:// doi. org/ 10. 1016/j. jbiom ech. 2019. 04. 027 (2019).
 20. Monte, A., Baltzopoulos, V., Maganaris, C. N. & Zamparo, P. Gastrocnemius Medialis and Vastus Lateralis in vivo muscle-tendon 
behavior during running at increasing speeds. Scand. J. Med. Sci. Sports 30, 1163–1176 (2020).
 21. Monte, A., Maganaris, C., Baltzopoulos, V. & Zamparo, P. The influence of Achilles tendon mechanical behaviour on “apparent” 
efficiency during running at different speeds. Eur. J. Appl. Physiol. 120, 2495–2505 (2020).
 22. Lee, D. V., McGuigan, M. P., Yoo, E. H. & Biewener, A. A. Compliance, actuation, and work characteristics of the goat foreleg and 
hindleg during level, uphill, and downhill running. J. Appl. Physiol. (Bethesda, Md.: 1985) 104, 130–141 (2008).
 23. Moore, T. Y., Rivera, A. M. & Biewener, A. A. Vertical leaping mechanics of the Lesser Egyptian Jerboa reveal specialization for 
maneuverability rather than elastic energy storage. Front. Zool. 14, 32 (2017).
 24. Kouno, M., Ishigaki, T., Ikebukuro, T., Yata, H. & Kubo, K. Effects of the strain rate on mechanical properties of tendon structures 
in knee extensors and plantar flexors in vivo. Sports Biomech. 1–14 (2019).
 25. Hof, A. L., Zandwijk, J. P. V. & Bobbert, M. F. Mechanics of human triceps surae muscle in walking, running and jumping. Acta 
Physiol. Scand. 174, 17–30 (2002).
 26. Komi, P. V., Fukashiro, S. & Järvinen, M. Biomechanical loading of Achilles tendon during normal locomotion. Clin. Sports Med. 
11, 521–531 (1992).
 27. Butler, D. L., Grood, E. S., Noyes, F. R., Zernicke, R. F. & Brackett, K. Effects of structure and strain measurement technique on 
the material properties of young human tendons and fascia. J. Biomech. 17, 579–596 (1984).
 28. Ker, R. F., Alexander, R. M. C. N. & Bennett, M. B. Why are mammalian tendons so thick?. J. Zool. 216, 309–324 (1988).
 29. Kongsgaard, M., Aagaard, P., Kjaer, M. & Magnusson, S. P. Structural Achilles tendon properties in athletes subjected to different 
exercise modes and in Achilles tendon rupture patients. J. Appl. Physiol. 99, 1965–1971 (2005).
10
Vol:.(1234567890)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
 30. Wren, T. A. L., Yerby, S. A., Beaupré, G. S. & Carter, D. R. Mechanical properties of the human achilles tendon. Clin. Biomech. 16, 
245–251 (2001).
 31. Biewener, A. A. & Roberts, T. J. Muscle and tendon contributions to force, work, and elastic energy savings: a comparative perspec-
tive. Exerc. Sport Sci. Rev. 28, 99 (2000).
 32. Raikin, S. M., Garras, D. N. & Krapchev, P. V. Achilles tendon injuries in a United States population. Foot Ankle Int. 34, 475–480 
(2013).
 33. Wren, T. A. L., Lindsey, D. P., Beaupré, G. S. & Carter, D. R. Effects of creep and cyclic loading on the mechanical properties and 
failure of human achilles tendons. Ann. Biomed. Eng. 31, 710–717 (2003).
 34. Davis, J. J., Mason, K. T. & Clark, D. A. Achilles tendon ruptures stratified by age, race, and cause of injury among active duty U.S. 
military members. Mil Med. 164, 872–873 (1999).
 35. Mersmann, F., Bohm, S., Schroll, A., Marzilger, R. & Arampatzis, A. Athletic training affects the uniformity of muscle and tendon 
adaptation during adolescence. J. Appl. Physiol. 121, 893–899 (2016).
 36. Qiao, M. & Jindrich, D. L. Leg joint function during walking acceleration and deceleration. J. Biomech. 49, 66–72 (2016).
 37. Cronin, N. J. & Lichtwark, G. The use of ultrasound to study muscle–tendon function in human posture and locomotion. Gait 
Posture 37, 305–312 (2013).
 38. Harkness-Armstrong, C. et al. Effective mechanical advantage about the ankle joint and the effect of achilles tendon curvature 
during toe-walking. Front. Physiol. 11, 407 (2020).
 39. Rasske, K., Thelen, D. G. & Franz, J. R. Variation in the human Achilles tendon moment arm during walking. Comput. Methods 
Biomech. Biomed. Eng. 20, 201–205 (2017).
 40. Fath, F., Blazevich, A. J., Waugh, C. M., Miller, S. C. & Korff, T. Direct comparison of in vivo Achilles tendon moment arms obtained 
from ultrasound and MR scans. J. Appl. Physiol. 109, 1644–1652 (2010).
 41. Maganaris, C. N. Imaging-based estimates of moment arm length in intact human muscle-tendons. Eur. J. Appl. Physiol. 91, 130–139 
(2004).
 42. Olszewski, K., Dick, T. J. M. & Wakeling, J. M. Achilles tendon moment arms: the importance of measuring at constant tendon 
load when using the tendon excursion method. J. Biomech. 48, 1206–1209 (2015).
 43. Gallinger, T. L., Fletcher, J. R. & MacIntosh, B. R. Mechanisms of reduced plantarflexor function in Cerebral palsy: smaller triceps 
surae moment arm and reduced muscle force. J. Biomech. 110, 109959 (2020).
 44. Fukunaga, T. et al. Muscle volume is a major determinant of joint torque in humans. Acta Physiol. Scand. 172, 249–255 (2001).
 45. Hof, A. L. In vivo measurement of the series elasticity release curve of human triceps surae muscle. J. Biomech. 31, 793–800 (1998).
 46. Muraoka, T., Muramatsu, T., Fukunaga, T. & Kanehisa, H. Elastic properties of human Achilles tendon are correlated to muscle 
strength. J. Appl. Physiol. 99, 665–669 (2005).
 47. Reeves, N. D. & Cooper, G. Is human Achilles tendon deformation greater in regions where cross-sectional area is smaller?. J. Exp. 
Biol. 220, 1634–1642 (2017).
 48. Maganaris, C. N., Kawakami, Y. & Fukunaga, T. Changes in aponeurotic dimensions upon muscle shortening: in vivo observations 
in man. J. Anat. 199, 449–456 (2001).
 49. Magnusson, S. P., Aagaard, P., Rosager, S., Dyhre-Poulsen, P. & Kjaer, M. Load-displacement properties of the human triceps surae 
aponeurosis in vivo. J. Physiol. 531, 277–288 (2001).
 50. Magnusson, S. P. et al. Differential strain patterns of the human gastrocnemius aponeurosis and free tendon, in vivo. Acta Physiol. 
Scand. 177, 185–195 (2003).
 51. Alexander, R. M. & Jayes, A. S. A dynamic similarity hypothesis for the gaits of quadrupedal animals. J. Zool. Lond. 201, 135–152 
(1983).
 52. Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).
 53. Biewener, A. A., Farley, C. T., Roberts, T. J. & Temaner, M. Muscle mechanical advantage of human walking and running: implica-
tions for energy cost. J. Appl. Physiol. 97, 2266–2274 (2004).
 54. Winter, D. A. Biomechanics and Motor Control of Human Movement (Wiley, 2009).
 55. Visser, J. J., Hoogkamer, J. E., Bobbert, M. F. & Huijing, P. A. Length and moment arm of human leg muscles as a function of knee 
and hip-joint angles. Eur. J. Appl. Physiol. 61, 453–460 (1990).
 56. Rugg, S. G., Gregor, R. J., Mandelbaum, B. R. & Chiu, L. In vivo moment arm calculations at the ankle using magnetic resonance 
imaging (MRI). J. Biomech. 23, 495–501 (1990).
 57. R Core Team. R: A language and environment for statistical computing. (R Foundation for Statistical Computing, 2019).
 58. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. & R Core Team. nlme: Linear and Nonlinear Mixed Effects Models. R package version 
3.1–137 (2018).
 59. Wickham, H. ggplot2: Elegant Graphics for Data Analysis. (Springer, 2009).
Acknowledgements
The authors wish to thank the Campbell University School of Osteopathic Medicine and the Campbell Univer-
sity Medical Student Summer Research Scholars program. We also thank Dr. Jennifer Bunn and the Campbell 
University College of Pharmacy & Health Sciences for use of the Advanced Interdisciplinary Movement Science 
(AIMS) lab. Finally, we wish to thank the subjects for their participation in this research.
Author contributions
Conceptualization: A.D.F., J.W.Y.; Methodology: A.D.F., J.W.Y.; Software: A.D.F.; Analysis: A.D.F., J.W.Y.; Data 
Collection: A.D.F., F.C., J.T.P., N.A.P., B.B., V.A.; Writing – original draft: A.D.F., J.W.Y.; Writing – editing: A.D.F., 
J.W.Y., F.C., J.T.P., N.A.P., B.B., V.A.
Funding
Funding for this study was provided by the Campbell University School of Osteopathic Medicine and the Medical 
Student Summer Research Scholars program.
Competing interests 
The authors declare no competing interests.
Additional information
Supplementary Information The online version contains supplementary material available at https:// doi. org/ 
10. 1038/ s41598- 021- 88774-8.
Correspondence and requests for materials should be addressed to A.D.F.
11
Vol.:(0123456789)
Scientific Reports |         (2021) 11:9360  | 
https://doi.org/10.1038/s41598-021-88774-8
www.nature.com/scientificreports/
Reprints and permissions information is available at www.nature.com/reprints.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and 
institutional affiliations.
Open Access  This article is licensed under a Creative Commons Attribution 4.0 International 
License, which permits use, sharing, adaptation, 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/.
© The Author(s) 2021

Shorter heels are linked with greater elastic energy storage in the Achilles tendon.
Foster, A D,Block, B,Capobianco, F,Peabody, J T,Puleo, N A,Vegas, A,Young, J W