The mechanics and energetics of human walking and running: a joint level perspective.

Abstract

Humans walk and run at a range of speeds. While steady locomotion at a given speed requires no net mechanical work, moving faster does demand both more positive and negative mechanical work per stride. Is this increased demand met by increasing power output at all lower limb joints or just some of them? Does running rely on different joints for power output than walking? How does this contribute to the metabolic cost of locomotion? This study examined the effects of walking and running speed on lower limb joint mechanics and metabolic cost of transport in humans. Kinematic and kinetic data for 10 participants were collected for a range of walking (0.75, 1.25, 1.75, 2.0 m s(-1)) and running (2.0, 2.25, 2.75, 3.25 m s(-1)) speeds. Net metabolic power was measured by indirect calorimetry. Within each gait, there was no difference in the proportion of power contributed by each joint (hip, knee, ankle) to total power across speeds. Changing from walking to running resulted in a significant (p = 0.02) shift in power production from the hip to the ankle which may explain the higher efficiency of running at speeds above 2.0 m s(-1) and shed light on a potential mechanism behind the walk-run transition.

Full text

Page 1

doi: 10.1098/rsif.2011.0182
published online 25 May 2011
J. R. Soc. Interface
Dominic James Farris and Gregory S. Sawicki
a joint level perspective
The mechanics and energetics of human walking and running:


References
ref-list-1
http://rsif.royalsocietypublishing.org/content/early/2011/05/20/rsif.2011.0182.full.html#

This article cites 33 articles, 14 of which can be accessed free
P<P
Subject collections
Published online 25 May 2011 in advance of the print journal.
(254 articles)biomechanics
?

Articles on similar topics can be found in the following collections
Email alerting service

here
right-hand corner of the article or click
Receive free email alerts when new articles cite this article - sign up in the box at the top
publication.
Citations to Advance online articles must include the digital object identifier (DOIs) and date of initial
online articles are citable and establish publication priority; they are indexed by PubMed from initial publication.
the paper journal (edited, typeset versions may be posted when available prior to final publication). Advance
Advance online articles have been peer reviewed and accepted for publication but have not yet appeared in

http://rsif.royalsocietypublishing.org/subscriptions
go to: J. R. Soc. InterfaceTo subscribe to
This journal is © 2011 The Royal Society
on May 25, 2011rsif.royalsocietypublishing.orgDownloaded from

Page 2

The mechanics and energetics of
human walking and running:
a joint level perspective
Dominic James Farris* and Gregory S. Sawicki
Department of Biomedical Engineering, North Carolina State University, 4130 EBIII,
911 Oval Drive, NC 27695-7115, USA
Humans walk and run at a range of speeds. While steady locomotion at a given speed requires
no net mechanical work, moving faster does demand both more positive and negative mech-
anical work per stride. Is this increased demand met by increasing power output at all lower
limb joints or just some of them? Does running rely on different joints for power output than
walking? How does this contribute to the metabolic cost of locomotion? This study examined
the effects of walking and running speed on lower limb joint mechanics and metabolic cost of
transport in humans. Kinematic and kinetic data for 10 participants were collected for a
range of walking (0.75, 1.25, 1.75, 2.0 m s21) and running (2.0, 2.25, 2.75, 3.25 m s21)
speeds. Net metabolic power was measured by indirect calorimetry. Within each gait, there
was no difference in the proportion of power contributed by each joint (hip, knee, ankle)
to total power across speeds. Changing from walking to running resulted in a significant
(p ¼ 0.02) shift in power production from the hip to the ankle which may explain the
higher efficiency of running at speeds above 2.0 m s21and shed light on a potential
mechanism behind the walk–run transition.
Keywords: locomotion; speed; mechanical power; efficiency; cost of transport
1. INTRODUCTION
The links between the mechanics and energetics of ter-
restrial locomotion have been studied extensively in a
variety of animals [1,2], including humans [3]. Humans
prefer to walk at speeds that minimize the metabolic
cost of transport (COT) [4]. COT for humans is least
for walking at 1.2–1.4 ms21while it remains constant
across running speeds [3]. Earlier studies attempted to
link the metabolic requirements of walking and running
to the positive mechanical power required to: (i) raise
and accelerate the body’s centre of mass (external
work); and (ii) accelerate the limbs relative to the centre
of mass (internal work) in animals [5,6] and humans [3].
However, it has since been postulated that increases in
mechanical power with speed cannot fully explain the
simultaneous increases in the metabolic cost of animal
locomotion [1]. This led to an alternative hypothesis
that the time course of generating force and the cost of
supporting body weight during locomotion were the
major determinants of the metabolic cost of running [2].
While there is good evidence for the importance of
the ‘cost of generating force’ in animal and human
locomotion [7], a recent study of humans has calculated
that this cost only accounts for ?50 per cent [8] of the
metabolic cost of walking, with work performed on the
centre of mass also accounting for ?50 per cent [8], re-
emphasizing the importance of work as well as force.
However, this and other studies that calculated the
total mechanical work as external and internal work
are limited owing to these measures being a large under-
estimate of total muscular work [9]. An alternative
approach has used inverse dynamics to calculate individ-
ual joint moment contributions to positive and negative
powers and summed joint average powers to get total
limb power output [10]. To date, no study has used this
approach to calculate total mechanical work and power
acrossa range ofspeedsinwalkingorrunningandrelated
the results to metabolic data.
According to existing metabolic and mechanical
power data, the efficiency of positive work (positive
mechanical power/net metabolic power) is highest at
intermediate walking speeds and increases almost line-
arly with running speed [3]. Ultimately this efficiency is
dependent on the efficiency with which all muscles do
positive work and this is dependent upon the intrinsic
force–velocity and force–length properties of skeletal
muscle. Slower shortening velocities of muscle fibres are
optimal for efficient muscular force production [11].
Distal leg muscles such as the triceps surae exhibit mor-
phologies well suited to reducing muscle fibre velocities
[12], because much of the muscle tendon unit length
change during locomotion is taken up by stretch and
recoil of their long compliant series elastic elements
[13,14]. More proximal muscles do nothave these compli-
ant series elastic elements [15] and so must provide most
of their length change from fibre length changes. This
makes the contractile behaviour of proximal muscles
*Author for correspondence (djfarris@ncsu.edu).
J. R. Soc. Interface
doi:10.1098/rsif.2011.0182
Published online
Received 29 March 2011
Accepted 4 May 2011
1
This journal is q 2011 The Royal Society
on May 25, 2011rsif.royalsocietypublishing.org Downloaded from

Page 3

less efficient. Sawicki et al. [16] predicted, based on
morphological differences between proximal and distal
muscles, that power output at the hip and knee joints
during human walking would be provided at lower effi-
ciency than power output at the ankle joint. Therefore,
one possible explanation for variations in the overall effi-
ciency of positive work is that work is redistributed
between distal and proximal muscle groups with chan-
ging locomotor speed. If this were the case, it would be
expected that speeds at which efficiency is less would be
associated with a greater proportion of total power
being provided at more proximal joints within the leg
(e.g. the hip joint). Alternatively, the relative contri-
butions to total power at each joint might not change
with speed and thus, changes in overall efficiency might
be reflective of underlying changes in contractile con-
ditions within muscles across all joints throughout the
lower limbs.
Redistribution of power output to more proximal
muscles has been observed in accelerating running tur-
keys [17] and in humans running on an incline [18] and
sprinting [19]. However, these tasks are associated with
a net positive work requirement and/or a change in
limb posture that alters the effective mechanical advan-
tage (EMA) of hip muscles, requiring them to do
greater work [18]. Although the amount of total positive
work done per stride changes with locomotion speed,
steady-speed locomotion never requires net positive
work and changing speed does not alter the EMA of
hip muscles [20]. Thus, the mechanism by which total
positive work is modulated during faster or slower
steady-state locomotion speeds might be different from
that for incline running or accelerations. In fact, forward
dynamics simulations of human walking suggest that
changes in walking speed are modulated by increasing
the work done by all lower limb muscle groups [21].
Therefore, modelling data support the idea that changes
in locomotion speed do not involve a redistribution of
power output within the lower limb. Experimental
studieswithhumansarerequiredtoconfirmtheseresults.
This study aimed to test how lower limb joint powers
modulate locomotion speed in humans and whether the
chosen strategy could explain trends in the COT and
efficiency of positive work. Inverse dynamics analysis
was combined with metabolic energy consumption
measurements made on humans walking and running
at a range of steady-state speeds. It was hypothesized
that faster speeds would be achieved by proportionally
increasing power output across the ankle, knee and hip
joints, implying that changes in efficiency with speed
are not due to the redistribution of power output
among joints.
2. MATERIAL AND METHODS
2.1. Experimental protocol
Ten healthy individuals (six male (mean+s.d., age ¼
25+5 years;height ¼ 1.76+0.1 m;
12 kg) and four female (age ¼ 25+5 years; height ¼
1.6+0.2 m; mass ¼ 67+5 kg)) gave written informed
consent to participate in this study. Ethical approval
for all experimental procedures was granted by an
mass ¼ 77+
institutional review board and all procedures were in
line with the declaration of Helsinki [22].
All the experimental trials took place on a split belt
treadmill that was instrumented with two separate force
platforms, one under each belt (BERTEC, Columbus,
OH, USA). Participants completed four walking trials
and four running trials. Walking trials were at 0.75,
1.25, 1.75 and 2.0 ms21. Running trials were at 2.0,
2.25, 2.75 and 3.25 ms21, providing a range of speeds
with an overlap at 2.0 ms21for comparison of walking
and running at the same speed. Each trial lasted 7 min
in order to acquire steady-state metabolic data (see
§2.2) and participants were allowed to self-select their
stride frequency and length.
2.2. Metabolic measurements
Rates of oxygen consumption and carbon dioxide pro-
duction during trials were recorded using a portable
metabolicsystem (OXYCON
Healthcare, Yorba Linda, CA, USA). Prior to walking
and running, measurements were made during 5 min of
quiet standing and values from the last 2 min were aver-
aged and used to calculate rates of metabolic energy
consumption (watts) while standing. For the walking
and running trials, data from the last four of the 7 min
were averaged for the calculation of metabolic rate.
Visual inspection of rates of oxygen consumption with
time (averaged over 30 s intervals) confirmed that par-
ticipants were at steady-state during this period. Rates
of oxygen consumption and carbon dioxide production
were converted to metabolic powers using standard
equations detailed by Brockway [23]. Net metabolic
powers during walking and running were calculated by
subtracting metabolic power during standing from meta-
bolic power during the activity and these values were
normalized to individual body mass (Wkg21).
MOBILE, VIASYS
2.3. Kinematics and kinetics
An eight camera motion analysis system (VICON,
Oxford, UK) was used to capture the positions of 22
reflective markers attached to the pelvis and right leg
(modified Cleveland Clinic marker set). Raw marker
positions were filtered using a second-order low-pass
Butterworth filter with a cut-off frequency of 10 Hz.
A static standing trial was captured and the positions
of markers on segment endpoints were used to calibrate
a four segment (pelvis, thigh, shank and foot) model for
each subject using established inertial parameters [24].
Clusters of three or four markers on rigid plates were
attached to the pelvis, thigh and shank segments to
track segment motion during walking and running.
For the foot, a cluster of three markers was attached
directly to the participants’ shoe. Joint angles for the
hip knee and ankle were computed in three dimensions
as the orientation of the distal segment with reference
to the proximal segment and differentiated to calculate
joint velocities.
Force data were recorded during walking and run-
ning, using the two force platforms embedded in the
treadmill (BERTEC, Columbus, OH, USA). For walk-
ing trials, participants were required to walk with
2
Joint power and energetics of locomotion
D. J. Farris and G. S. Sawicki
J. R. Soc. Interface
on May 25, 2011rsif.royalsocietypublishing.orgDownloaded from

Page 4

each foot hitting its ipsilateral force platform, so as to
separate out individual limb contributions during
double support. Raw analogue force platform signals
were filtered with a second-order low-pass Butterworth
filter with a cut-off frequency of 35 Hz. Inverse dynamic
analyses [25] were then used to compute net joint
moments which were multiplied with joint angular vel-
ocities to calculate joint powers at the hip, knee and
ankle. Kinematics and kinetics were calculated for the
right leg only and it was assumed that the left leg
behaved symmetrically. All kinematic and kinetic cal-
culations were performed using Visual 3D software
(C-motion Inc., Germantown, MD, USA).
2.4. Calculation of positive mechanical work and
efficiency of positive work
Toobtainmechanicalworkandpowervaluesmoreclosely
related to actual muscular work and power than from
external and internal work calculations, total positive
work was calculated as the sum of the work done at
each of the lower limb joints. For this, joint power data
for the hip, knee and ankle were individually integrated
with respect to time over discrete periods of positive and
negative work (figure 1), using the trapezium method.
For each stride at each joint, all values of positive work
were summed and all periods of negative work were
summed to give an individual joint total positive and
negative work, respectively (figure 1). Work values rep-
resent the work done by joints of the right limb for an
average stride. Assuming symmetry, this was considered
equal to the work done by joints within both limbs over
an average step. Individual joint positive mechanical
workvaluesweredividedbysteptimetocalculateaverage
positive mechanical joint powers (equation (2.1)).
?Pþ
j¼
Wþ
Tstep;
j
ð2:1Þ
where, Wþ
at a joint, average step time and average positive mech-
anical power at that joint, respectively.
Following this, the average positive powers calcu-
lated for the hip, knee and ankle were summed and
this value was taken as total average positive power
output (equation (2.2)). Each joint’s average positive
power as a percentage of total average positive power
was determined by equation (2.3).
j;Tstepand?Pþ
jare positive mechanical work
?Pþ
tot¼?Pþ
hipþ?Pþ
kneeþ?Pþ
ank
ð2:2Þ
and
Jpercent¼
?Pþ
?Pþ
j
tot
!
? 100%;
ð2:3Þ
where,?Pþ
ankle average positive power, respectively. Jper centis
the percentage contribution of an individual joint to
total average power.
tot;?Pþ
hip;?Pþ
knee;?Pþ
ankare total, hip, knee and
The efficiency of positive mechanical work was
calculated as shown in equation (2.4)
hþ
work¼
?Pþ
Pmet;
tot
ð2:4Þ
where, hþ
?Pþ
is the corresponding net metabolic power.
This definition of efficiency does not account for any
metabolic cost associated with negative work done
during a stride. This was deemed acceptable given
that the efficiency of negative work in muscle is approxi-
mately five times higher than that of positive work [26]
and so it accounts for only a minimal portion of the
total metabolic cost. This may introduce a small error
in the efficiency calculation but this error should be
systematic across conditions given that total negative
and total positive work done during a stride are equal
for level steady-speed locomotion. Other studies have
included negative work in the denominator of equation
(2.4) [10,27] implying that all the negative work done
on the body is stored and returned as positive work
by elastic structures in muscle (e.g. tendons). While
some of the negative work will be absorbed and
returned in this way, exactly what proportion is not cur-
rently known and thus it was not felt that including
negative work would significantly improve the accuracy
of the efficiency calculation.
workis the efficiency of positive mechanical work;
mechis the average positive mechanical power; and Pmet
2.5. Statistical analysis
For each condition for each individual, kinematic and
kinetic data were averaged over a minimum of 10
–60
–40
–20
0
20
40
60
80
K+
1
K+
2
A+
1
A+
2
K+
3
K–
2
K–
1
A–
2
A–
1
power (W)
0
20
40
60
80
100
normalized stride time (%)
Figure 1. Example plots of knee (solid line) and ankle (dashed
line) joint powers for a sample stride of walking at 1.25 ms21.
Dark grey areas are periods when the joint is doing positive
work and light grey indicates when negative work is being
done. Individual periods of positive and negative work are
labelled Aþ
respectively. Work done during each of these periods was cal-
culated separately by integration using the trapezium rule.
Positive and negative work done at each joint per stride was
calculated as the sum of individual work values, e.g.
Wþ
nand A?
nor Kþ
nand K?
nfor the ankle and knee,
ank¼ Aþ
1þ Aþ
2þ ...Aþ
n.
Joint power and energetics of locomotion
D. J. Farris and G. S. Sawicki3
J. R. Soc. Interface
on May 25, 2011 rsif.royalsocietypublishing.org Downloaded from

Page 5

strides. Group means and standard deviations were then
computed and, unless otherwise stated, these are the
values presented. To test for differences in outcome vari-
ables(totalaveragepositivepower,percentcontribution
of individual joints to total average positive power, effi-
ciency of positive work) between speeds for walking or
running a repeated measures ANOVAwith a Bonferroni
adjustment was used. To compare the same variables
between running and walking at 2.0 ms21a paired
Student’s t-test was used. For all statistical tests, an a
level of 0.05 was set as the threshold for significance.
3. RESULTS
3.1. Mechanical power
Generally speaking, the magnitudes of instantaneous
joint powers at the hip, knee and ankle were greater
at faster speeds throughout the entire stride in both
walking and running (figure 2). This is reflected in
the average positive power data (table 1 and figure 3),
which also demonstrated an increasing trend with
speed. The percentage contribution of each lower limb
joint to total average power was not significantly differ-
ent between speeds for walking (ankle (p ¼ 0.90); knee
(p ¼ 0.08); hip (p ¼ 0.39)) or for running (ankle (p ¼
0.16); knee (p ¼ 0.50); hip (p ¼ 0.33); figure 4). For
walking, the hip and ankle joint powers provided the
largest contributions to total average positive power
(both ? 40–50%) while the knee supplied considerably
less (14–17%). For running, knee joint power was still
the smallest contributor (? 20%), followed by hip
power (32–39%) with ankle power providing most
(42–47%) (figures 3 and 4). For walking and running
at the same speed (2.0 m s21), ankle power contributed
a significantly higher (p ¼ 0.02, t-test) and hip power a
0
1020 30 40 5060 708090 100
normalized stride time (%)
power (W kg–1)
power (W kg–1)
power (W kg–1)
0
1
2
3
4
5
–1
–3
–2
0
1
2
3
4
5
–1
–3
–2
0
1
2
3
4
5
(a)
(d)
(b)(e)
(c)(f)
–1
–3
–2
0
10
20
30
40 50
60 70 80 90 100
normalized stride time (%)
0
2
4
6
8
–2
–4
–6
–8
0
2
4
6
8
–2
–4
–6
–8
0
2
4
6
8
–2
–4
–6
–8
Figure 2. (a,d) Group mean instantaneous ankle, (b,e) knee and (c,f) hip joint powers plotted over one complete stride for (a–c)
walking and (d–f ) running at each speed. Dashed lines are the slowest speed for each gait (walk ¼ 0.75 ms21, run ¼ 2.0 m s21);
then, in ascending order, dotted lines (1.25 ms21and 2.25 ms21); solid grey lines (1.75 ms21and 2.75 ms21); solid black lines
(2.0 ms21and 3.25 m s21).
4
Joint power and energetics of locomotion
D. J. Farris and G. S. Sawicki
J. R. Soc. Interface
on May 25, 2011rsif.royalsocietypublishing.org Downloaded from