The Foot's Arch and the Energetics of Human Locomotion

Abstract

The energy-sparing spring theory of the foot’s arch has become central to interpretations of the foot’s mechanical function and evolution. Using a novel insole technique that restricted compression of the foot’s longitudinal arch, this study provides the first direct evidence that arch compression/recoil during locomotion contributes to lowering energy cost. Restricting arch compression near maximally (~80%) during moderate-speed (2.7 ms−1) level running increased metabolic cost by + 6.0% (p < 0.001, d = 0.67; unaffected by foot strike technique). A simple model shows that the metabolic energy saved by the arch is largely explained by the passive-elastic work it supplies that would otherwise be done by active muscle. Both experimental and model data confirm that it is the end-range of arch compression that dictates the energy-saving role of the arch. Restricting arch compression had no effect on the cost of walking or incline running (3°), commensurate with the smaller role of passive-elastic mechanics in these gaits. These findings substantiate the elastic energy-saving role of the longitudinal arch during running, and suggest that arch supports used in some footwear and orthotics may increase the cost of running.

Full text

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Scientific RepoRts | 6:19403 | DOI: 10.1038/srep19403
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The Foot’s Arch and the Energetics
of Human Locomotion
Sarah M. Stearne1, Kirsty A. McDonald1, Jacqueline A. Alderson1, Ian North2,
Charles E. Oxnard3 & Jonas Rubenson1,4
The energy-sparing spring theory of the foot’s arch has become central to interpretations of the foot’s
mechanical function and evolution. Using a novel insole technique that restricted compression of
the foot’s longitudinal arch, this study provides the rst direct evidence that arch compression/recoil
during locomotion contributes to lowering energy cost. Restricting arch compression near maximally
(~80%) during moderate-speed (2.7 ms−1) level running increased metabolic cost by + 6.0% (p < 0.001,
d = 0.67; unaected by foot strike technique). A simple model shows that the metabolic energy saved
by the arch is largely explained by the passive-elastic work it supplies that would otherwise be done by
active muscle. Both experimental and model data conrm that it is the end-range of arch compression
that dictates the energy-saving role of the arch. Restricting arch compression had no eect on the cost
of walking or incline running (3°), commensurate with the smaller role of passive-elastic mechanics in
these gaits. These ndings substantiate the elastic energy-saving role of the longitudinal arch during
running, and suggest that arch supports used in some footwear and orthotics may increase the cost of
running.
Running has classically been characterized by the spring-mass paradigm1,2. During running, gravitational poten-
tial and kinetic energy is temporarily stored as elastic strain energy, primarily in tendons, during the rst half of
stance and subsequently returned in the second half of stance, helping to propel the body forward and upward.
is form of elastic energy reduces the metabolic cost of running by sparing mechanical work otherwise required
by active muscle tissue3,4.
Ker and colleagues5, identied the longitudinal arch of the foot as an elastic storage-return mechanism. ese
authors estimated, by simulating the loads experienced during running in cadaver feet, that approximately 17% of
the mechanical work of running could be stored and returned by the foot’s arch as it undergoes compression and
recoil over the stance phase5 and that this contributes to the economy of running. is theory has subsequently
been adopted in numerous investigations ranging from analyses of running mechanics6, the evolution of human
running7, and footwear design8.
Since the initial study by Ker et al.5 the hypothesis that the foot is an energy-saving spring has never been
tested directly during locomotion and it is unknown to what extent the compression, and subsequent storage and
return of elastic energy in the foot’s longitudinal arch aects the metabolic cost of locomotion. Here we propose
that the metabolic energy saved by the arch spring is a function of the amount of positive mechanical work it
supplies passively (non-metabolically) and the cost of performing that work had it instead been done by active
muscle requiring metabolic energy.
We test this hypothesis experimentally using custom-manufactured orthotic insoles designed to restrict arch
compression and thus reduce arch elastic work. To test our predictions about the eect of arch strain on locomo-
tor cost, we used orthotic insoles to vary arch strain during walking and running at dierent inclines and foot
strike types (rearfoot strike [RFS] vs forefoot strike [FFS]).
Two separate custom insoles were designed for each participant. e rst insole was designed to restrict arch
compression near-maximally compared to that during shod running (Full Arch Insole; FAI) and the second
was designed to restrict compression by approximately 50% during stance (Half Arch Insole; HAI). Despite the
nearly two-fold dierence in arch compression between the HAI and FAI, we hypothesized that both would
result in a comparable reduction in elastic energy storage/return during running and thus a similar increase in
1School of Sport Science, Exercise and Health, The University of Western Australia, Perth, WA, 6009, Australia.
2Willetton Podiatry, Willetton, WA, 6155, Australia. 3School of Anatomy, Physiology and Human Biology, The
University of Western Australia, Perth, WA, 6009, Australia. 4Biomechanics Laboratory, Department of Kinesiology,
The Pennsylvania State University, University Park, PA, 16802, USA. Correspondence and requests for materials
should be addressed to J.R. (email: jonas@psu.edu) or S.M.S. (email: sarah.stearne@iinet.net.au)
Received: 02 June 2015
Accepted: 19 November 2015
Published: 19 January 2016
OPEN

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metabolic cost. It is expected that relatively little elastic energy will be stored in the rst 50% of arch compression
based on the non-linear nature of the arch compression-elastic energy relationship identied by Ker et al.5 (see
Online Supplementary Material Fig. S4). Given the modest arch loads at the prescribed testing speed we expected
increases in the energy cost of level running of ~10% based on the arch load vs. energy storage data of Ker et al.5
and our model for metabolic energy expenditure. In this context, the FAI and HAI were designed to test if the pre-
dicted increase in metabolic cost was associated specically with a reduction in the arch elastic energy as opposed
to a more general gait modication linked to the degree of arch restriction.
Compared to level running, we predicted that restricting arch compression during walking and incline run-
ning would not have as pronounced of an impact on metabolic cost. Walking involves lower loads9, is a pendular
as opposed to a spring-mass gait, and relies more on the arch windlass mechanism10 as opposed to an arch spring
mechanism. We consequently hypothesized the arch spring mechanism has a smaller energy-saving eect in
walking compared to running and tested this by restricting arch compression during walking using the FAI.
During incline running, the loads experienced are similar to level running and the arch is able to store and return
elastic energy11. However, the additional positive mechanical work production required to raise the center of mass
vertically during incline running cannot be generated from previously stored elastic energy11. We therefore pre-
dicted that the energetic cost associated with limiting the arch spring relative to the total cost of incline running
would be smaller than that of level running. Finally, we hypothesized that restricting arch compression would
have a greater eect on the energy cost of level running in habitual FFS runners compared with habitual RFS
strike runners, suggesting greater reliance on the arch spring for reducing running costs.
To test these questions we measured metabolic cost (oxygen consumption), arch compression using
three-dimensional (3D) motion capture, and ground reaction forces and joint kinetics on an instrumented tread-
mill. Using this data we estimated the elastic energy stored and returned by the arch, the total mechanical work of
locomotion and the metabolic cost of restricting arch elastic energy storage/return.
Results
Arch Elastic Energy and Metabolic Cost in Level Running. Arch compression (navicular displace-
ment) was signicantly reduced in the insole conditions compared with the minimal shoe-only level running. A
61.4 ± 33.4% reduction in arch compression was observed with the HAI (p < 0.001, d = 1.22) and 78.9 ± 24.7%
reduction when the FAI was worn (p < 0.001, d = 1.46; Fig.1a and Online Supplementary Fig. S2). Estimated
arch elastic energy return per step was also reduced (81.5 ± 26.4% and 97.2 ± 5.4% reductions in the HAI and
FAI, respectively; both p < 0.001, HAI d = 1.53 and FAI d = 1.72; Fig.1b) and per distance traveled (HAI and
FAI both p < 0.001, HAI d = 1.55 and FAI d = 1.72; Table1). FAI arch compression restriction was signicantly
greater than the HAI condition (p = 0.032, d = 0.60; Fig.1a; Table1) but estimated elastic energy return was not
(p = 0.121, d = 0.58; Table1).
e model-predicted increase in metabolic cost of transport (Earch) as a result of reducing arch compression
was statistically signicant in both the HAI (p = 0.001, d = 0.77) and FAI (p = 0.004, d = 0.72) conditions com-
pared with minimal shoe-only level running (Table1, Fig.2b). e metabolic cost of HAI and FAI level running
resulting from our model were not signicantly dierent from one another (p = 0.920, d = 0.01; Table1, Fig.2b).
In line with the modeled metabolic costs, both the HAI and FAI resulted in a statistically signicant increase
in the experimentally-observed metabolic cost of transport during level running (HAI p = 0.012, d = 0.53; FAI
p < 0.001, d = 0.67; Table1, Fig.2a). As with the modeled costs, there was no statistical dierence in the observed
experimental metabolic cost between the HAI and FAI conditions (p = 0.211, d = 0.18). e modeled and exper-
imental metabolic costs were not signicantly dierent from one another for either the HAI or FAI (Table1). e
insoles had a small non-signicant eect on total limb mechanical work (ANOVA main eect p = 0.121; Table1).
Arch Elastic Energy and Metabolic Cost in Walking and Incline Running. Compared to the mini-
mal shoe-only condition, the insole (FAI) reduced arch compression during walking by 82.4 ± 21.1% (p < 0.001,
d = 1.13) and during incline running by 68.5 ± 30.6% (p = 0.001, d = 1.13; Fig.1a). e estimated arch elastic
energy return per step in both conditions was signicantly reduced (96.3 ± 6.9% and 91.6 ± 15.9% reductions
per step in walking and incline running, respectively; both p < 0.001, walking d = 1.12; incline running d = 1.53;
Fig.1b). e model-predicted metabolic cost of transport in FAI walking was not statistically greater compared
to the minimal shoe-only condition (p = 0.131, d = 0.25; Fig.2b, Table1). A statistically signicant increase in the
modelled metabolic cost of transport was calculated for FAI incline running over the minimal shoe-only condi-
tion (p = 0.025, d = 0.59; Fig.2b, Table1). e experimentally observed metabolic cost of transport was likewise
not aected during walking, nor was it aected in incline running (walking p = 0.950, d = 0.01; incline running
p = 0.164, d = 0.18; Table1, Fig.2a). e insoles had a non-signicant eect on the total limb mechanical work
of locomotion in walking and incline running (walking p = 0.782, d = 0.03; incline running p = 0.074, d = 0.23;
Table1).
Arch Elastic Energy and Metabolic Cost in Rearfoot vs Forefoot Running. Arch compression in
the minimal shoe-only level running condition was signicantly greater in FFS compared with RFS runners
(FFS 12.0 mm vs RFS 9.2 mm; p = 0.022, d = 1.10; Table1). However, the estimated arch elastic energy return
(p = 0.490, d = 0.35), total limb mechanical work (p = 0.181, d = 0.43) and metabolic cost of transport (p = 0.584.
d = 0.29) did not dier between foot strike groups in minimal shoe-only level running (Table1). is was also
true for FAI conditions between RFS and FFS runners (p = 0.483, p = 0.092, p = 0.568, respectively). Both the
modelled and experimental metabolic costs were not statistically dierent between foot strike groups in any of
the HAI and FAI conditions (all conditions p > 0.05; Table1).

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Discussion
By examining the eect of restricting compression of the foot’s longitudinal arch on the metabolic cost of loco-
motion, the present study provides direct evidence supporting the energy-sparing spring theory of the arch. Our
analyses and model generally support the hypothesis that the arch spring saves metabolic energy by reducing the
mechanical work that would otherwise need to be generated by active muscle (Fig.2). Indeed, the elevated met-
abolic cost of level running aer restricting arch compression near-maximally (~80%, FAI) and by ~60% (HAI)
was predicted within 1% and 2.5%, respectively, of the measured values based on the cost of replacing lost elastic
arch work with muscular work. e agreement between the modelled and experimental eect on the metabolic
cost of level running was remarkably robust across a nearly two-fold dierence in arch compression (FAI 10 mm
reduction in compression vs HAI 6.5 mm reduction; Fig.1a), strengthening the interpretation that the elevated
metabolic cost results specically from lost arch elastic energy. We propose that energy costs do not show a clearer
dierence between FAI vs HAI because elastic energy storage increases non-linearly with arch loading5, with the
majority of the elastic energy stored in the nal 25% of arch compression (Online Supplementary Material Fig. S4).
erefore, near equal amounts of arch elastic energy storage/return was removed in both the FAI and HAI condi-
tions (Fig.1b), resulting in a non-signicant dierence in the metabolic cost of running (Fig.2, Table1).
Figure 1. (a) Maximum arch compression (mm; mean ± S.E.M.) relative to arch height at minimal shoe-only
level running initial foot contact. (b) Estimated elastic energy (J kg−1, mean ± S.E.M.) returned from the arch
of the foot in one step. *indicates signicantly dierent (p < 0.05) to the minimal shoe-only trial in the same
condition, ^indicates signicant dierence between the half arch insole (HAI) and full arch insole (FAI) (level
running only).

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e estimated reduction in the elastic energy return from the arch in the FAI level running condition equaled
8.8% of the total limb mechanical work of running, similar to the 6.0% increase in the gross locomotor cost (7.4%
net

V
O2). As expected, these values are lower than Ker et al.’s5 estimate of 17% due to our slower running speed
(2.7 m s−1 compared to Ker et al.’s 4.5 m s−1) and therefore lower arch elastic energy storage/release and
Condition
Habitual
foot strike
Arch
compression
(mm)
Estimated elastic
energy returned from
the arch (J kg−1m−1)
Observed metabolic
cost of transport
(J kg−1 m−1)
Modelled metabolic
cost of transport
(J kg−1 m−1)
Total limb
mechanical work
(J kg−1 m−1)
WALK
Minimal shoe-only
RFS 5.9 ± 2.3 0.039 ± 0.032 3.95 ± 0.46 n/a 0.37 ± 0.05
FFS 7.4 ± 5.3 0.043 ± 0.043 4.06 ± 0.33 n/a 0.42 ± 0.08
Average 6.7 ± 4.1 0.041 ± 0.037 4.01 ± 0.39 n/a 0.40 ± 0.07
Full Arch Insole (FAI)
RFS − 1.1 ± 5.1 0.004 ± 0.008 3.98 ± 0.50 4.17 ± 0.56 0.39 ± 0.10
FFS 2.2 ± 4.1 0.003 ± 0.008 4.03 ± 0.42 4.09 ± 0.55 0.38 ± 0.05
Average 0.7 ± 4.8* 0.003 ± 0.007* 4.01 ± 0.44 4.13 ± 0.54 0.39 ± 0.07
LEVEL RUN
Minimal shoe-only
RFS 9.2 ± 2.1§0.110 ± 0.034 4.59 ± 0.39 n/a 1.25 ± 0.11
FFS 12.0 ± 2.4§0.126 ± 0.055 4.48 ± 0.34 n/a 1.36± 0.18
Average 10.6 ± 2.6 0.118 ± 0.045 4.53 ± 0.36 n/a 1.31± 0.15
Half Arch Insole (HAI)
RFS 2.6 ± 4.2 0.017 ± 0.023 4.79 ± 0.38 4.78 ± 0.35 1.20 ± 0.09
FFS 5.7 ± 6.1 0.021 ± 0.045 4.69 ± 0.42 4.93 ± 0.51 1.36 ± 0.15
Average 4.1 ± 5.3*^ 0.019 ± 0.035* 4.74 ± 0.39* 4.86 ± 0.43* 1.28 ± 0.15
Full Arch Insole (FAI)
RFS − 1.3 ± 6.1 0.002 ± 0.004 4.87 ± 0.50 4.83 ± 0.48 1.20 ± 0.14
FFS 2.5 ± 5.8 0.005 ± 0.013 4.74 ± 0.35 4.88 ± 0.50 1.33 ± 0.15
Average 0.6 ± 6.0*^ 0.004 ± 0.009* 4.81 ± 0.42* 4.85 ± 0.48* 1.27 ± 0.15
INCLINE RUN
Minimal shoe-only
RFS 9.1 ± 3.4 0.108 ± 0.055 5.88 ± 0.41 n/a 1.46 ± 0.18
FFS 11.9 ± 4.5 0.116 ± 0.057 5.66 ± 0.26 n/a 1.56 ± 0.17
Average 10.5 ± 4.1 0.112 ± 0.054 5.77 ± 0.35 n/a 1.51 ± 0.18
Full Arch Insole (FAI)
RFS − 0.3 ± 7.7 0.013 ± 0.028 5.89 ± 0.43 6.04 ± 0.46 1.41 ± 0.19
FFS 5.4 ± 4.9 0.009 ± 0.016 5.78 ± 0.31 5.93 ± 0.26 1.53 ± 0.10
Average 2.5 ± 6.8* 0.011 ± 0.022* 5.83 ± 0.37 5.99 ± 0.37* 1.47 ± 0.16
Table 1. Arch and limb mechanics and energetics. Rearfoot strike (RFS), Forefoot strike (FFS), Average
(average of RFS and FFS), Half Arch Insole (HAI), Full Arch Insole (FAI). *Signicantly dierent from minimal
shoe-only within the same condition p < 0.05, §signicant dierence between RFS and FFS p < 0.05. ^Signicant
dierence between HAI and FAI within the same condition p < 0.05.
Figure 2. (a) Experimentally observed and (b) model-predicted percent change in the gross metabolic cost
of locomotion (mean ± S.E.M.) from the minimal shoe-only to insole trial across walking, level running and
incline running conditions. FAI = full arch insole, HAI = half arch insole. * indicates signicant (p < 0.05)
increase in metabolic energy cost [(a) experimental, (b) modeled] between the minimal shoe-only and insole
trial within the same condition.

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subsequent smaller arch compressive loads. If the contribution of the arch spring to the total mechanical cost of
running increases with speed, as the data from Ker et al.5 suggest, the arch may have an even more pronounced
role in reducing locomotor costs at faster running speeds. What makes the arch-spring such an effective
energy-saving mechanism? It is notable that the arch spring, unlike tendon structures (e.g. the Achilles ten-
don;12,13), achieves elastic energy recycling largely in absence of muscle activity. e distinction between this
passive and other primary active spring mechanisms (e.g. triceps surae/Achilles muscle-tendon-unit) is impor-
tant since the later requires metabolic energy to maintain tension in the spring (cost of force). In this regard, the
arch spring may be the most eective energy saving structure in the lower limb.
Despite conrming that arch compression is greater in FFS compared with RFS runners in the minimal shoe
only level run (p = 0.022; Table1), our hypothesis that forefoot runners would be more aected by restricting
arch compression was not supported. e lack of dierence in the metabolic cost resulting from the FAI between
foot strike groups was, however, predicted by our model. e similar model-predicted metabolic costs between
FAI running in RFS and FFS arose because of a non-signicant dierence in the reduction of arch elastic energy
storage/return between groups. ese ndings raise questions regarding dierences in arch compliance between
RFS and FFS runners, although additional analyses in these groups are required to assess arch material properties
in detail.
Our hypotheses that the arch-spring mechanism has a smaller eect on the energy cost of walking and incline
running were supported. For walking, the small energetic eect can be explained to a large extent by the smaller
role of arch elastic energy storage/return in normal gait (Fig.1b). It is also possible that the FAI increased midfoot
rigidity and thus may have improved the eectiveness of the plantar-exion torque,14,15 saving metabolic energy.
e percent increase in metabolic cost of FAI incline running computed from our model was smaller than that
of FAI level running but was nevertheless signicantly greater than the observed experimental eect. We do not
have a denite answer to explain the poorer agreement between the increase in metabolic cost and the predicted
increase in muscle work during incline FAI running. When running uphill the primary function of muscle is to
generate the positive mechanical work of raising the body vertically. erefore, it remains possible that replacing
lost passive-elastic energy recycling may be less important in incline running compared to level running, which
follows spring-mass mechanics.
Orthotic insoles and arch-support footwear are occasionally prescribed to runners to alter foot and lower
limb biomechanics and tissue loading. e ndings of this study suggest that certain arch supports may hin-
der the arch’s elastic energy storage and subsequently lead to an increase in running energy cost. A number of
studies have reported an increase in the energy cost of running when wearing orthotic insoles16–18, although this
eect may in part be due to added weight19. Perl et al.6 found a statistically signicant 3% increase in metabolic
cost when participants ran in traditional arch supporting running shoes compared with minimalist shoes, even
aer controlling for strike technique, shoe mass and stride frequency. e benets of using corrective orthotics
or footwear designed with signicant arch support should therefore be weighed against their possible eect on
running energetics. In contrast to running, our ndings suggest that using rigid supportive shoes or insoles that
prevent arch collapse are likely to have little energetic consequence during walking given the smaller reliance on,
and reductions in, arch elastic energy storage/return.
Finally, the evolution of the longitudinal foot arch is regarded as a key adaptation for obligate hominin biped-
alism20–24. Although the evolution of the arch is debated, recent fossil evidence suggest that Australopithecus
afarensis (~3.2 million years) possessed at least a partial longitudinal arch22. e functional signicance of the
longitudinal arch in the evolution of human bipedal gait has oen been attributed to the rigid mid-tarsal lever
system allowing eective plantar-exion during toe-o25,26. A complementary theory surrounding the evolution
of the longitudinal arch is that its spring like properties lower the energetic cost of endurance running5,7. Our
study provides support for the arch functioning as both a rigid lever in walking and an energy-sparing spring in
running. e insoles had no eect on the metabolic cost of walking despite restricting ~80% of arch compression.
e absence of any energetic dierence might result, in part, because the insoles enhanced the eect of midfoot
rigidity in walking. On the other hand, restricting the arch’s spring function in level running resulted in a clear
increase in metabolic cost. Further, that we only observed an energetic consequence of arch restriction during
level running and not incline running may oer added insight into the movement behavior and environment of
early Homo. e landscape inhabited by early Homo was invariably not limited to horizontal ground, although
given that the arch only provided an energetic advantage during level and not incline running begs questions of
how landscape inuenced the evolution of the human foot and bipedal gait and how early Homo navigated this
landscape.
Methods
Participants. Eight habitual RFS and nine habitual FFS male runners were included in the study. e par-
ticipants had not experienced any lower limb injuries in the six months prior to testing nor presented with any
pre-existing gait abnormalities. No signicant dierences in measured physiological variables, as determined by
a series of independent t-tests, existed between foot strike groups (age- RFS 25.5 ± 4.4 years, FFS 27.6 ± 3.4 years;
height- RFS 185.3 ± 6.9 cm, FFS 181.8 ± 4.8 cm; weight- RFS 79.4 ± 6.8 kg, FFS 75.7 ± 5.9 kg; weekly running
distance- RFS 39.4 ± 21.1 km, FFS 42.2 ± 36.0 km; mean ± SD). Participants did not regularly wear prescriptive
orthotic insoles. Included participants were deemed to have normal foot structure as determined by the Foot
Posture Index27 (FPI) (RFS 1.4 ± 1.4, FFS 1.0 ± 2.8). Measured foot variables did not dier between RFS and FFS
groups; foot length- RFS 277.0 ± 11.4 mm, FFS 272.4 ± 6.1 mm; resting arch height (from sole to navicular tuber-
osity)- RFS 50.3 ± 7.3 mm, FFS 49.5 ± 9.5 mm; and Achilles tendon moment arm (perpendicular distance from
lateral malleolus to Achilles)- RFS 45.3 ± 4.1 mm, FFS 46.8 ± 5.4 mm. All FPI and foot anthropometric measure-
ments were taken by a single experienced clinician (I.N.). Participants provided written, informed consent prior
to inclusion in the study. All procedures were approved by e University of Western Australia Human Research

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Ethics Committee (Approval ID: RA/4/1/4541) and the study was carried out in accordance with the approved
guidelines.
Custom Arch-restricting Insoles. Two pairs of custom-made foot insoles were manufactured for each par-
ticipant from 3D scans of the participants’ feet in a non-weight bearing neutral sub-talar joint position (ScanAny,
Orthotech laboratories, Blackburn, Melbourne). Both insoles were made with the following specication; four
millimeter polypropylene, high density arch ll (shore value ~350–400), four degree intrinsic rear foot grind, a
balanced fore foot, maximum arch congruency and the heel ground to less than one millimeter such that heel-toe
drop was deemed negligible. One insole was designed to ll the participants arch when the foot was positioned in
a neutral non-weight bearing position, theoretically allowing minimal arch compression during locomotion (full
arch insole; FAI). e second insole had a peak arch height ve millimeters lower than the FAI, with the aim of
allowing ~50% arch compression (half arch insole; HAI). e ve millimeter reduction was chosen based on pilot
work and arch compression data from Perl et al.6 and Ker et al.5. Participants were provided the insoles two weeks
prior to testing to become familiar with wearing them.
Testing Conditions. New Balance Minimus road MR00 shoes were provided to all participants to wear for
testing (approx. weight 180 grams, zero heel-toe drop, no medial arch support and a uniform EVA midsole).
Pockets lled with lead weights were axed to the laces of both shoes in order to standardize foot weight across
all shoe and insole conditions. We chose a minimal shoe as a control condition in order to standardize non-insole
eects as much as possible (e.g. eect of shoe sole cushioning28). Prior to testing, participants completed a ve
minute warm-up on a force-plate instrumented split belt treadmill (Bertec Corporation, Columbus OH, USA)
at a slow run.
Testing comprised of the following conditions; i) shoe-only walk, ii) FAI walk, iii) minimal shoe-only level
run, iv) HAI run, v) FAI run, vi) minimal shoe-only incline run, and vii) FAI incline run. All trials were com-
pleted on the force-plate instrumented treadmill and the order of conditions randomized to prevent any fatigue
or order eects. To further ensure fatigue and trial order were not inuencing results, the rst condition was
repeated at the end of the testing session. Participants reported minimal discomfort and no conscious change in
their running technique whilst wearing the insoles (see Online Supplementary Table S3 for questionnaire results).
All running conditions were performed using the runner’s habitual foot strike technique as conrmed by a
sagittal high speed video camera (Casio EXILIM EX-F1, Casio Computer Co. LTD., Shibuya-ku, Tokyo; 300 Hz).
In accordance with the literature, a RFS was dened when the heel of the shoe made initial contact with the
ground and a FFS dened when the ball of the foot made rst contact29,30. A standardized walking speed of
1.1 ms−1 (representing a comfortable speed on the treadmill and within the range of the participants’ pilot tested
preferred walking speeds) was selected to minimize arch compression and subsequently elastic energy contribu-
tion. To ensure our results were not aected by walking speed, a sub-set of participants (n = 8) also performed the
minimal shoe-only and FAI walk at their individually preferred walking speed (average 1.3 ± 0.1 ms−1). Similar
metabolic cost results were found in the preferred walking speed and the 1.1 ms−1 walking trials (13.6 ± 1.3 vs
13.1 ± 1.5 ml kg−1 min−1, respectively; p = 0.190), including a similar minimal eect of the FAI on the metabolic
cost of walking. All running trials were performed at 2.7 ms−1 (level and incline trials were performed at the same
velocity to control for any speed eects). Pilot testing on a sub-set of participants (n = 8) revealed that running at
faster speeds (3.5 ms−1) caused the insoles to compress and thus limited the eect of the insole on arch compres-
sion, likely due to the higher joint loading at this speed. During incline trials the treadmill was set at three degrees
(although not specically instructed to do so, all runners maintained their level habitual foot strike technique).
is inclination was selected to increase the mechanical work and metabolic cost but within aerobic levels as
faster speed/incline combinations risked reliance on anaerobic metabolic pathways31. e chosen running speed
thus represents an optimized speed to test the eect of the insoles in both level and incline conditions.
Metabolic Cost. Participants were asked to abstain from caeine on the day of the testing and to not eat in
the two hours prior to arriving at the laboratory. Expired gasses were collected during rest (standing) and walk-
ing/running trials. Participants were required to breathe into a two-valve mouthpiece connected via two light-
weight exible tubes to a computerized oxygen and carbon dioxide gas analysis system [Morgan ventilation
monitor (Morgan, Reinham, Kent, UK); oxygen and carbon dioxide analyzers (Ametek SOV S-3A11/Ametek
COV CD-3 A, Applied Electrochemistry, Ametek, Pittsburgh, PA)]. e ventilometer and gas analyzers were
calibrated before and immediately aer each test using a one liter syringe pump and reference gas mixtures,
respectively (BOC Gases, Chatswood, Australia). Each treadmill condition was performed until the participant
reached a steady state of oxygen consumption (

V
O2) aer which a further minute of data was collected for anal-
ysis.

V
O2 data was collected for a minimum period of four minutes as per the Australian Institute of Sport
national testing battery for runners32. During the incline conditions, blood lactate concentration levels were
determined (Lactate-Pro, Arkray, LT-1710, Kyoto, Japan) aer steady state was reached to ensure participants
were exercising aerobically (below their previously determined lactate threshold and the

V
O2 at which this
threshold occurred [see Online Supplementary Material]).
In order to compare metabolic and mechanical energy measures,

V
O2 was converted to a metabolic energy cost
of transport (J kg−1 m−1) by using an energy equivalent of 20.1 J ml−1 O2 and dividing by locomotor speed (m s−1)
and body mass (kg).
Arch Compression and 3D Joint Kinematics and Kinetics. We used a custom 3D kinematic foot
model to estimate arch compression, outlined briey here, and in detail in the Online Supplementary Material.
First, a previously established lower body model was used to dene a rearfoot segment and ankle kinematics33.

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Retro-reective markers were axed to the lower limbs in accordance with Besier et al.33, with additional markers
placed on the navicular tuberosity and distal phalanx of the rst metatarsal (Fig.3). e shoe upper was modied
with ve marker ‘windows’ coinciding with the marker positions, allowing markers to be placed directly on the
foot and remain visible. To ensure marker positions remained unchanged aer removing shoes, all foot markers
were detachable by a magnetic base that did not change location. is resulted in the markers being slightly
oset from the anatomical landmark. e frame-to-frame location of the marker relative to the anatomical land-
mark deviated minimally (< 1 mm) within their respective rigid segments during running. e location of the
functionally relevant anatomical landmarks were identied using a six marker wand in static pointer trials and
expressed in the rearfoot or forefoot anatomical coordinate systems (see Online Supplementary Material). A
small marker was also placed on the medial aspect of the insole in line with the maximum insole height and hence
the maximum arch height.
Motion of the retro-reective markers were tracked using a ten-camera near infrared Vicon T-series 3D
motion capture system (T40S, 250 Hz; Oxford Metrics, Oxford, UK) and sagittal plane high-speed video (300 Hz).
Six consecutive right leg strides from the nal minute of data collection were selected for analysis. Arch height
was dened as the distance of the navicular marker relative to the base of the foot and tracked continuously
throughout the stride (see Online Supplementary Material). Arch height at initial foot contact during the mini-
mal shoe-only level run was used as a reference height for each condition. Arch compression was dened as the
dierence between the reference height and the minimum arch height during stance in each condition.
Inverse dynamics (net joint moments and joint reaction forces) were computed for the ankle in accord-
ance with Besier et al.33, as well as for the MTP joint (sagittal plane only), using Vicon BodyBuilder soware
(Oxford Metrics, Oxford, UK). Ground reaction forces (GRFs) from the instrumented treadmill were recorded at
Figure 3. Right foot medial view illustrating (a) foot marker positions used to compute foot and arch kinematics.
e white markers are physical reective markers, the large red circles are pointed landmarks and the small red
circles represent the computed joint centers. e inset illustrates the virtual landmarks relative to the skeleton, the
sole axis and the navicular displacement measure. e inset gure was generated using OpenSim 3.0 (https://simtk.
org/home/opensim), freely available open source musculoskeletal modeling soware42. (b) example of the arch
compression-restricting insole; image displayed is the Full Arch Insole (FAI); photograph by S.M.S. (c) Footwear
illustrating marker ‘windows’, the insole marker and weight pouch used for matching total shoe and insole weight;
photograph by S.M.S. MP1 = rst metatarsophalangeal joint, MP5 = h metatarsophalangeal joint.

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2,000 Hz, and synchronized with the kinematic data using a Vicon MX-Net control box (Oxford Metrics, Oxford,
UK). All marker trajectories were ltered using a zero-lag 4th order low pass Butterworth lter with cut-o fre-
quencies typically at 14 Hz, determined by a custom residual analysis algorithm for each participant (MATLAB,
e MathWorks Inc., USA). GRFs were ltered at the same cut-o frequency as the kinematic data to mitigate any
artefacts in joint moments arising due to un-accounted segment acceleration34,35.
Arch Elastic Energy and Total Mechanical Work of Locomotion. Our hypotheses are based on the
premise that the insoles impede the storage of elastic energy in the arch and its subsequent ability to contribute to
total mechanical work. How these variables changed between conditions was estimated using a simple model to
predict arch elastic energy storage (Fig.4) and a force plate approach to measure total mechanical limb work of
locomotion36. e arch energy storage model was based on the compressive load-energy storage function estab-
lished by Ker et al.5 and calculations of the participants’ individual ankle compressive loads (inverse dynamics)
and arch compression (high-speed motion capture) (Fig.4; see Online Supplementary Material). Using these
data, we developed subject-specic arch load-displacement curves that permitted an estimate of the arch elastic
energy storage during each trial from their arch compression values (Figs1a and 4). Arch elastic energy return
(Warch
+) was predicted based on a hysteresis value of 22% from Ker et al.5. e force plate approach followed the
individual limb work (Wlimb
+) calculations described by Donelan et al.36, whereby limb powers were computed as
the dot product of the force acting on the limb and the body center of mass velocity, and subsequently integrated
with respect to time. Center of mass velocities were computed by time integrating the center of mass accelera-
tions, which were determined from the sum of the ground reaction forces. Both the arch elastic energy and limb
work calculations are described in detail in the Online Supplementary Material.
Modelled Arch Metabolic Energy Saving. e eect of arch elastic energy on the metabolic cost of loco-
motion was predicted by estimating the amount of positive arch elastic work (energy return) that was eliminated
aer restricting arch compression, and the cost of replacing lost mechanical work were it to be performed by
active muscle. is was computed as:
=(∆−∆)/η
()
+++
EWW1
arch arch limb
where Earch is the modelled additional metabolic energy (expressed as a cost of transport; J kg−1 m−1) after
restricting arch compression, ∆Warch+ is the dierence in the amount of returned arch elastic energy between
the minimal shoe-only trial and the corresponding insole trial for level running, incline running and walking (as
computed from our model; J kg−1 m−1). Although they were found to be small (Table1), we incorporated any
dierences in positive limb mechanical work between shoe-only and insole conditions (∆Wlimb+) as these could
aect metabolic cost. Finally, η
+ is the muscular eciency of performing positive work. A constant theoretical
muscle eciency of 0.25 was used for all trials. is assumed that all the lost arch elastic energy was replaced
Figure 4. (a) Arch elastic strain energy – ankle compressive load relationship adapted from Ker et al.5 used
to estimate arch strain energy from the participant’s maximum ankle joint compressive load (see Online
Supplementary Material). (b) Subject specic load-displacement curve used to predict stored arch elastic energy
during dierent conditions from measured arch compression. e subject-specic load-displacement curve
was established using the maximum arch compression from the participant’s trials and the corresponding ankle
compressive load, and by adjusting the optimized control point so that the area under the curve (elastic energy
storage) matched the estimated energy storage from (a).

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Scientific RepoRts | 6:19403 | DOI: 10.1038/srep19403
solely by positive muscle ber work functioning at a high eciency37. For comparison, (presented in the Online
Supplementary Material Table S2) we also made predictions using the locomotor mechanical eciency computed
from the minimal shoe-only trial for each condition (walking, level running and incline running).
Statistics. General linear model two-way repeated measures split-plot ANOVAs were performed to deter-
mine the eect of the custom insoles and foot strike technique on the following variables; arch compression,
estimated arch elastic energy storage, modeled and experimental metabolic cost, and total limb mechanical work
of locomotion. e between subject factors were habitual foot strike technique (RFS and FFS) and the within
subjects factors were minimal shoe-only, HAI (level running only) and FAI. e signicance level was p < 0.05
for ANOVA analyses. 3 × 2 ANOVAs were conducted for level running and 2 × 2 ANOVAs for walking and
incline running. In the 3 × 2 ANOVAs the location of the signicant main eect was determined using a post-hoc
pairwise comparison with a Bonferroni adjustment for multiple comparisons. Cohen’s d eect sizes38 were cal-
culated and interpreted using the eect scale; small (0.2); moderate (0.5); large (0.8). A series of paired samples
t-tests were conducted between RFS and FFS groups in the minimal shoe-only and FAI conditions to determine
if foot strike had an eect. Paired samples t-tests were also conducted to compare modelled versus experimentally
observed increases in metabolic cost of transport.
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Acknowledgements
The authors would like to acknowledge Orthotech laboratories (Blackburn, Melbourne, Australia) for the
manufacture and supply of the insoles used in this study, Robert Day for his assistance testing the insole material
properties, and Tony Roby for constructing the magnetic marker set and the insole material testing piece. e
authors would like to thank Rodger Kram, Daniel Lieberman and Nicholas Brown for their helpful suggestions
and critique of this work, and Robert Eckhardt and Owen Lovejoy for information pertaining to the evolution of
the human foot.
Author Contributions
S.M.S. contributed to the conception and design of the experiment, was the primary author involved in
the collection and analysis of data and contributed critically to data interpretation, draing and editing the
manuscript and figure preparation. K.A.M. contributed to the design of the experiment, data collection,
processing and interpretation, and editing the manuscript. J.A.A. contributed to the conception and design of the
experiment, the analysis and interpretation of data and editing the manuscript. I.N. contributed to the design of
the experiment, data collection and editing the manuscript. C.E.O. contributed to data interpretation and editing
the manuscript. J.R. contributed to the conception and design of the experiment, the collection, analysis and
interpretation of data, draing and editing the manuscript and gure preparation.
Additional Information
Supplementary information accompanies this paper at http://www.nature.com/srep
Competing nancial interests: e authors declare no competing nancial interests.
How to cite this article: Stearne, S. M. et al. e Foots Arch and the Energetics of Human Locomotion. Sci. Rep.
6, 19403; doi: 10.1038/srep19403 (2016).
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