determinants of preferred ground clearance during swing...
TRANSCRIPT
© 2016. Published by The Company of Biologists Ltd.
Determinants of preferred ground clearance during swing
phase of human walking.
Amy R. Wu* and Arthur D. Kuo
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 U.S.A
Key Words: biomechanics, locomotion, foot-ground clearance, metabolic power, energetic cost
Summary statement: The foot’s ground clearance during each swing phase of walking may be explained by competing costs
of lifting the foot versus scuffing it on the ground, modulated by movement variability.
Abstract
During each step of human walking, the swing foot passes close to the ground with a small but (usually) non-
zero clearance. The foot can occasionally scuff against the ground, with some risk of stumbling or tripping. The
risk might be mitigated simply by lifting the foot higher, but presumably at increased effort, of unknown
amount. Perhaps the normally preferred ground clearance is a trade-off between competing costs, one for lifting
the foot higher, and one for scuffing it. We tested this by measuring the metabolic energy cost of lifting and
scuffing the foot, treating these apparently dissimilar behaviors as part of a single continuum, where scuffing is
a form of negative foot lift. We measured young, healthy adults (N=9) lifting or scuffing the foot by various
amounts mid-swing during treadmill walking, and observed substantial costs, each well capable of doubling the
net metabolic rate for normal walking (gross cost minus that for standing). In relative terms, the cost for scuffing
increased over twice as steeply as that for lifting. That relative difference means that the expected value of cost,
which takes into account movement variability, occurs at a non-zero mean clearance, approximately matching
the preferred clearance we observed. Energy cost alone is only a lower bound on the overall disadvantages of
inadvertent ground contact, but it is sufficient to show how human behavior may be determined not only by the
separate costs of different trade-offs, but also movement variability, which can influence the average cost
actually experienced in practice.
1 Introduction
The foot momentarily passes close to the ground about mid-way through each swing phase of
walking. It does so with a peak speed over a stride, about three times walking speed (Winter, 1992),
thus presenting a risk of unexpected ground contact and therefore susceptibility to tripping or
stumbling, which are leading causes of falls among older adults (Barrett et al., 2010; Begg and
Sparrow, 2006). Inadequate foot-ground clearance may also be an issue for persons with clinical
conditions such as drop-foot or weak hamstrings (Cruz and Dhaher, 2009), leading to compensations
such as hip hiking and swing leg circumduction (Cruz and Dhaher, 2009; Kerrigan et al., 2000),
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http://jeb.biologists.org/lookup/doi/10.1242/jeb.137356Access the most recent version at J Exp Biol Advance Online Articles. First posted online on 29 July 2016 as doi:10.1242/jeb.137356http://jeb.biologists.org/lookup/doi/10.1242/jeb.137356Access the most recent version at
First posted online on 29 July 2016 as 10.1242/jeb.137356
which also have negative consequences. Even healthy individuals avoid unwanted ground contact, for
example on uneven terrain, by lifting the foot higher mid-swing (Gates et al., 2012). Greater ground
clearance may, however also come with a cost, such as greater energy expenditure (Voloshina et al.,
2013). There may thus be two competing trade-offs: a cost for making inadvertent ground contact
(“scuffing”), and one for lifting the foot mid-swing (“lifting”). Together, these could explain the (non-
zero) clearance humans normally prefer. We therefore seek to test the trade-offs between lifting the
foot higher and allowing it to scuff against ground.
There are several reasons why lifting the foot could be costly (Figure 1). For an otherwise
normal gait, lifting the foot higher entails greater potential energy mid-swing, as well as a longer
travel path and thus greater kinetic energy, both entailing more muscular effort. The effort of
swinging the leg could potentially be reduced with the help of elastic tendons (Kuo, 2002; Doke and
Kuo, 2007; Dean and Kuo, 2009), but simple walking models indicate that the elastic energy for
improved ground clearance would nevertheless require more muscular effort (Dean and Kuo, 2011).
In fact, even if the model is driven largely by passive dynamics and elastic tendons, it would attain
greatest economy if the swing foot could pass through the ground without stumbling (Dean and Kuo,
2009, Fig. 7). Of course, any model can only suggest how humans might hypothetically behave. It is
therefore important to test whether lifting the foot higher actually requires more mechanical work
performed by the body, and whether that also increases the metabolic cost.
There are also likely costs to scuffing the ground mid-swing. These go beyond energy
expenditure to include less quantifiable costs such as the consequences of stumbling, for example
recovery actions needed to maintain balance, and consequences of falling, such as pain and injury.
Stumbling and lifting the foot therefore have categorically different costs, and categorically different
motions, making it difficult to compare their respective trade-offs. We therefore propose the
simplification of treating the motions along a single continuum of vertical ground clearance, where
positive values signify lifting the foot higher, and negative, striking the ground harder (as if the foot
could drop through the floor unimpeded). As for the costs, a typical optimization approach is to
consider multiple contributions (e.g., Winters and Helm, 2000), each weighted and summed to yield a
single objective function with arbitrary units. A second simplification is that, rather than contend with
the many costs of scuffing, we measure only the metabolic cost of repeated scuffing, and treat it as a
lower bound on the overall cost of unwanted ground contact. We therefore do not include stumbling
and falling, which would only add to the incentive for greater ground clearance.
Another factor in the foot’s motion is the notion of risk or variability (see probability
distribution in Figure 1). If the foot were controlled with perfect precision, a ground clearance of zero
might be optimal, because it would entail no excess effort to lift the foot, while also avoiding scuffing.
However, the actual foot motion is variable from step to step, perhaps due to imperfect motor control,
and behaves according to a slightly skewed normal distribution (e.g., mean about 1.56 cm, standard
deviation about 0.25 cm; Begg et al., 2007). On some terrains, non-smoothness of the ground surface
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will also present variability and occasionally cause insufficient ground clearance, and even contribute
to a risk of falling (Best and Begg, 2008). This can be accounted for with the expected value function
(Papoulis and Pillai, 2002), which considers both the probability distribution of the foot’s motion and
the costs for various mean clearances, to yield an overall probabilistic cost for ground clearance.
Here we investigate the energetic cost and biomechanical consequences of foot-to-ground
clearance during swing. We propose that the preferred foot-to-ground clearance is governed by
interactions between the two hypothesized cost trade-offs between lifting and scuffing the foot,
mediated by some probability distribution for the step-by-step variability of foot motion. Since much
of gait appears to be energetically optimal (e.g., Donelan et al., 2001; Doke et al., 2005; Elftman,
1966; Ralston, 1958), the preferred clearance height may closely match with the lowest metabolic
cost. We expect that lifting the foot higher should require more muscular effort and come at greater
metabolic cost. We also expect that negative foot lift, meaning greater amounts of scuffing, should
require more effort and lead to greater metabolic cost as well. These costs, along with the probability
distribution of foot motion, may explain the preferred ground clearance during normal walking.
2 Ground Clearance Cost Model
We propose two simple models for the costs of lifting the foot and for scuffing it against ground
(Figure 1). The cost for lifting the foot CLH(z) is modeled as increasing with the maximum height z
above ground, and the cost for scuffing CSI(z) as increasing with the opposite, a virtual negative lift
where the foot would pass below ground if unimpeded. Of course, with the ground as an obstacle, the
actual result is a normal ground reaction force, and hence scuffing, modeled as a proportional drag
force. Because foot motion is imperfect and exhibits variability, an additional element is added to
represent the probability distribution pz(w) for deviations w about a mean ground clearance z. The
total, expected cost for a mean lift height is the probability-weighted sum of the two individual costs,
�̇�(𝑧) = ∫ ∞
−∞((𝐶SI(𝑧 + 𝑤) + 𝐶LH(𝑧 + 𝑤))𝑝𝑧(𝑤)) 𝑑𝑤 (1)
where �̇� represents the average metabolic energy expenditure rate, evaluated as the expected value of
total cost.
A higher energetic cost is expected for either alternative, lifting the foot higher or scuffing the
foot harder as a function of vertical foot lift (Eqn.1). The cost of increasingly positive lift z of the
swing foot could minimally be due to the work needed to lift the swing leg, but also include costs for
the coordinative responses throughout the body to produce that motion while maintaining balance and
forward gait. Regardless of the mechanism, the effort of lifting the foot might be such that least effort
would be achieved with zero, or even negative, foot lift, if not for the obstacle posed by the ground.
However in reality, negative lift is not usually achievable due to scuffing, which is also expected to be
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costly. There may be multiple contributors to that cost, which is nonetheless expected to increase with
more negative lift, due to the drag force produced by ground against foot, which the human must
counteract to avoid stumbling. Indeed, any drag impulse must be counteracted with an equal and
opposite positive impulse from the rest of the body to recover the original walking speed.
We expect that both lifting and scuffing costs should be minimized near zero foot lift z. This
alone would imply that humans should prefer zero foot lift if not for variability of foot motion.
Human motions are not perfectly repeatable, due to imperfect motor control, noisy sensors, actuators,
and neurons, as well as a number of variations in the surrounding environment. With some two-sided
probability distribution pz(w) of deviations about the nominal z, the minimum cost should typically be
biased away from the steeper of lifting and scuffing costs. Here we posit that the cost of scuffing is
steeper than the cost of lifting, therefore favoring slightly positive nominal foot lift.
The present study represents an extreme simplification of foot scuffing. In real life, scuffing is
often an unexpected and singular occurrence, followed by multiple steps for recovery. Instead, we
employ purposeful, continuous scuffing during steady gait, which simplifies experimental control
over the amount of scuffing, as well as measurement of the associated biomechanics and energetics.
Continuous scuffing might adequately reproduce the consequences of relatively light scuffing, which
does not necessarily induce stumbling and recovery. The model (Eqn.1) therefore serves mainly as a
conceptual basis for explaining the trade-offs between lifting and scuffing the foot, rather than an
accurate representation of the complexities of the experimental measurements. The main purpose here
is to test and quantify the hypothesized costs of lifting and scuffing.
3 Experiment
We measured the costs of walking at different foot clearance heights performed by young, healthy
adults. We used real-time visual feedback to enforce varying amounts of foot lift and scuffing during
treadmill walking. We measured metabolic energy expenditure as the cost, and also characterized the
associated gait kinematics and kinetics. Foot lift was measured relative to ground, and additionally
characterized by the overall mechanical work performed on the body center of mass (COM) and by
the joints, while scuffing was characterized by the horizontal impulse (time-integral of fore-aft force)
produced by the foot against the ground surface mid-swing (75% to 100% of stride, defined as starting
from heelstrike). Eight subjects (N=8, 1 female, 7 male) walked at varying levels of ground clearance
during leg swing at a constant speed of 1.25 m/s on an instrumented treadmill. Subjects walked
normally and with three levels of foot lifting and three levels of scuffing during swing phase of
walking (Figure 2). The thresholds, termed Low, Medium, and High, to achieve during swing were
0.1 m, 0.2 m, and 0.3 m for foot lift and 100 N, 200 N, and 300 N for scuff force. Lift thresholds were
measured from the treadmill surface, and scuff force was defined as horizontal force produced by the
foot, measured as the drag ground reaction force mid-swing. One subject’s scuffing data was excluded
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because the scuff continued smoothly into heel strike, making the impulse indistinguishable from
normal heel contact. Subjects received visual feedback of toe marker height during foot lift
conditions, and fore-aft ground reaction force during scuffing conditions. In each case, these were
displayed in real time along with a target threshold for either scuff force or lift height. Trials were
performed in randomized order, and were of 6 minutes in duration. Subjects’ age ranged from 18 to
29 years, and their body mass M was 73.8±11.1 kg (mean±s.d.) and leg length L was 0.93±0.05 m.
All subjects provided written informed consent prior to the study, according to Institutional Review
Board procedures.
We measured metabolic power and gait mechanics using standard procedures. Net metabolic
rate (in W) was estimated from the rate of oxygen consumption and carbon dioxide production using
standard conversion factors (Brockway, 1987). Steady-state metabolic power was averaged over the
last 2 minutes of each 6-minute trial, and the rate for quiet standing (99.2±17.1 W, 0.0467±0.0123
dimensionless) was subtracted from the gross rate to yield net metabolic power. Kinematic and kinetic
data were also recorded over the same time with motion capture (PhaseSpace, San Leandro, CA
USA), using a standard 24-marker set (Zelik and Kuo, 2010). Foot lift was measured from the vertical
height of the toe marker (fifth metatarsal) during swing, relative to its height during quiet standing.
The marker can exhibit one or two peaks, particularly one peak when the foot is lifted, and so Lift
Height zLH was defined as the first peak height after toe-off (Figure 3D). For normal walking, we also
measured the distribution of the minimum clearance (between the two peaks), as an indicator of
pz(w). Scuffing was measured and characterized with the Scuff Impulse �̂�SI, defined as the integral of
drag force (aft ground reaction force) during the swing phase, normally zero when there is no
scuffing. As a point of comparison, we calculated the average total horizontal impulse generated per
stride for normal walking (26.2±4.32 N⋅s), which was many times greater than the scuff impulses
induced experimentally. Also measured was the rate of work performed on the COM, termed
instantaneous COM work rate (Donelan et al., 2002), computed as the inner product of the ground
reaction forces of each leg and the COM velocity. Standard kinematics and inverse dynamics
procedures (Visual3D, C-Motion, Germantown, MD, USA) yielded ankle, knee, and hip angles and
joint moments and powers. As a simple summary of joint actions, we defined summed joint power as
the net power from ankle, knee, and hip of one leg at each point in the stride. The positive intervals of
COM work rate and summed joint power during a stride were integrated to yield positive COM work
and summed joint work per stride. Average positive COM and summed joint work rates for both sides
of the body were calculated from the corresponding positive work per stride, by dividing by stride
time and multiplying by 2. The same computation was performed for negative work rates. Finally,
step lengths and widths were also computed, along with root-mean-square variabilities, for each trial.
We expected that the increasing levels of each condition would affect the corresponding
measure and metabolic cost. Thus, Scuff Impulse was expected to increase with the amount of
scuffing, and Lift Height with the amount of foot lifting. We also tested for simple relationships
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between these measures and metabolic rate. For scuffing, we expected its metabolic cost to be an odd
function of scuff impulse �̂�SI, meaning the cost should decrease as scuffing approaches zero and
would continue to decrease past the origin if a negative (i.e., assistive) drag force were possible. We
therefore performed a linear fit between scuff impulse �̂�SI and net metabolic rate. For foot lift, it was
less clear how it should determine energetic cost, and so we tested for net metabolic rate increasing
both linearly and quadratically with Lift Height zLH. Fits were performed for all of the data from each
condition simultaneously, allowing each subject to have an individual constant offset. Statistical tests
were performed on the coefficients, with a significance level of α=0.05. The effect of each condition
on corresponding measures (�̂�SI and zLH) was also tested (ANOVA followed by post-hoc t-tests with
Holm-Sidak correction for multiple comparisons; Glantz, 2005).
To facilitate comparison between the relative costs of scuffing and lifting, we devised a scaling
factor to translate between the two. Scaling foot lift zLH to scuffing impulse �̂�SI requires a
transformation from units of distance to units of momentum. We defined the scaling factor mf g ⁄ v f,
where mf is the mass of the lower leg and v f is its speed, approximated as 16.1% of body mass M
(Winter, 2004) and 3.75 m⋅s−1 (three times walking speed; Winter, 1992), respectively. This may be
interpreted as transforming the gravitational potential energy of the lifted foot and lower leg into work
as the foot is scuffed against the ground. Such scaling is used to examine the relative metabolic costs
of scuffing and lifting, where scuffing and lifting are plotted opposite each other on a common, scaled
axis. This allows the costs to be compared in terms of the slope of metabolic rate versus either
scuffing or lifting.
Dimensionless measurements are reported here, using the base units of body mass M, standing
leg length L, and gravitational acceleration g. Force was non-dimensionalized by Mg (mean 723.6 N),
moment and work by MgL (mean 670.8 N⋅m), power by Mg1.5L0.5(mean 2182 W), step length and
width by L (mean 0.9265 m), and step time by √L/g (mean 0.3072 s).
4 Results
We found each of the experimental conditions to yield varying levels of scuff impulse or lift height
(Figure 3). The conditions also resulted in substantial changes in metabolic energy expenditure, as
well as with alterations to gait biomechanics. Net metabolic rate increased substantially within the
range of conditions, to about 1.9 and 2.3 times the normal expenditure rate for scuff and foot lift,
respectively. The increase was less steep for increasing lift height (treated as a continuous variable),
than for increasing scuff impulse. Positive and negative joint and COM work rate also increased with
greater foot lift. In contrast, foot scuffing had less obvious effects on biomechanical measures despite
its relatively high energetic cost.
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Significant changes resulted from each of the discrete walking conditions for foot scuffing and
lifting (Figure 3, Table 1). These were observable in the form of aft-directed ground reaction forces
for scuffing and higher foot trajectories for lifting, summarized by significant changes in scuff
impulse �̂�SI and lift height zLH, respectively (all P<0.05). The scuffing conditions resulted in aft-
directed impulses up to 2.13±0.46 N⋅s for the High condition, equivalent to about 8.6% the aft-
directed impulse for an entire normal stride. The lifting conditions resulted in heights about 1.62 to
3.41 times greater than the normal lift of 0.0886 m, referring to the first peaks in toe clearance.
As expected, the preferred, normal lift height approximately coincided with minimum
metabolic cost (Figure 4). Net metabolic rate increased for greater magnitude of lift height or scuff
impulse, treating the two measures as continuous variables (see Table 2). There was an approximately
linear trend for scuff impulse, with slope −7.03±1.99 (metabolic rate per unit impulse, mean ± c.i.,
95% confidence interval) and offset 0.088±0.0316 (mean ± s.d., equivalent to about −69.0 W⋅N−1⋅s−1
and 183 W, respectively), with R2=0.747 (p=3.95E−7). With the aforementioned scaling factor to
convert scuff impulse to negative height, this slope is equivalent to −0.9097±0.2571. There was also a
significant trend for lift height with quadratic coefficient 0.9876±0.2363 and offset 0.0877±0.0409
(equivalent to about 2517 W⋅m−2 and 185 W, respectively), with R2=0.77 (p=1.10E−8). Alternatively
applying a linear rather than quadratic fit for lift height, the trend remained significant, with linear
coefficient 0.4395±0.0928 (metabolic rate per unit lift height) and offset 0.0472±0.0410 with
R2=0.8116 (p=1.12E−9), with approximately half the steepness of the analogous slope for scuffing
(0.9097 after scaling to metabolic rate per negative lift height). Thus, the cost of scuffing was far
steeper than that for lift height, regardless of fitting method. As a simple indicator of magnitude,
dragging the foot with impulse 11% of the normal stance phase ground reaction impulse caused an
approximate doubling of metabolic cost. A similar doubling of cost resulted from lifting the foot
about 23 cm greater than Normal. Minimum clearance during normal walking, as measured from the
trough of the marker trajectory, was 0.0157 ± 0.0046 m (mean ± s.d.).
The major costs above were associated with relatively minor changes in step parameters for
foot lift, and even smaller changes for scuffing (Table 2). Subjects exhibited slightly longer step
length, step width, and step period and shorter double support duration with increasing lift height (for
each 1 m additional lift: 0.53 m longer, 0.17 m wider, and 0.43 s more time, and -0.11 s more time; all
P<0.05). There were also small increases in step length and width RMS variability (0.0504 m and
0.0588 m per 1 m lift, respectively, P<0.05). However, the only changes in step parameters for
scuffing were slightly increased step width and step length variability (-0.0093 m and -0.0036 m per 1
N⋅s additional scuff impulse, respectively, P<0.05).
The effects of foot lifting and scuffing were somewhat more evident in the mechanics of
walking, particularly for lifting. Qualitatively examining force and power trajectories (Figure 5),
greater foot lift appeared to magnify the first peak of the vertical ground reaction force (GRF), the
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positive and negative peaks of the fore-aft GRF, and the magnitudes of COM and summed joint
power. In contrast, scuffing seemed to have much less effect, perhaps slightly reducing the second
peak of the vertical GRF and push-off power (see Figure 3 for representative data, and Figure 5 for
across-subject average data). In terms of joint kinematics (Figure 6), lifting the foot appeared to
require more flexion in knee and hip during swing, while scuffing produced relatively minor changes.
Lift height also produced changes in joint powers while only ankle push-off seemed to reduce for
scuffing.
These observations are supported by quantitative differences in the work performed by the
body (see Figure 7). Scuffing resulted in only minor or non-significant changes in average work rates
on the COM and by the summed joints, whereas foot lifting resulted in much greater and significant
increases in work (see Table 2, for details and individual joint results). In particular, greater foot lift
entailed more positive and negative work on the COM and by the joints, particularly the ankle and
knee for positive work, and hip for negative work.
5 Discussion
We had hypothesized that humans compromise between the additional effort to lift the foot higher
during swing, and that associated with scuffing of the foot on the ground. We found both types of
deviations to be energetically costlier than the normal swing, with scuffing particularly sensitive to
even small amounts of contact. These costs could in part explain the preferred ground clearance, if
movement variability is also taken into account. This is because the average cost of clearing the
ground by a nominal and positive amount can also depend on relatively infrequent but costly scuffing.
Another aspect of this study is the treatment of two dissimilar options, lifting vs. scuffing the foot, in a
continuous fashion. We next consider the implications of this approach, for examining not only limb
swing but also more general movements.
One notable finding was that the costs of scuffing or lifting the foot can be quite high (Figure
4). Within the range of conditions considered, both were well capable of doubling the normal net
metabolic rate. In the case of foot lifting, the cost is partially attributable to mechanical work, as
indicated by two measures: work performed on the body center of mass (which the swing leg
contributes to), and work performed by the lower extremity joints (Figure 7 and Table 2). Work is
needed to lift the leg, direct it on a longer path, and slow its descent as it nears ground (Figure 3) with
each swing phase. It also appears that other adjustments take place throughout the stride, including a
greater overall amplitude of COM power and summed joint power (Figure 5). The apparently simple
act of raising the swing foot therefore entails a coordinated action affecting the entire stride. The same
is true for scuffing, albeit more subtly, with force imparted on the ground through the swing knee and
hip (Figure 6). However this only had modest effect on overall work rates (small or non-significant
effects, Figure 7), suggesting that scuffing is primarily an action peripheral to the COM, perhaps
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accompanied by additional coordination throughout the body and potentially observable at the muscle
level. In fact, both lifting and scuffing appear to entail a complex series of compensations that are
difficult to predict and subtle to measure. It would be challenging to predict a more than doubling of
metabolic cost from gait analysis measurements alone. The gait analysis presented here therefore
serves mainly to illustrate possible indicators of the increased energetic cost, rather than a
comprehensive explanation.
During normal walking, the foot does not undergo the extremes of lifting or scuffing, but rather
clears the ground with a small and usually positive amount. Although the experiment entailed large
extremes, these were intended to reveal continuous trends in metabolic cost from discrete
experimental conditions. The individual costs for lifting and scuffing are difficult to separate from one
another near zero ground clearance, and so the surrounding trends were used to extrapolate the costs
close to that boundary. Here it is evident that, even though the energetic costs were only slightly
elevated above normal, they increased more sharply with scuffing than with lifting. These relative
sensitivities are proposed to determine the optimum clearance, mediated by the variability of foot
motion. The typical variability of foot motion admits the possibility of occasional scuffing with only a
2 degree change in swing ankle angle (Winter, 1992). Scuffing may therefore be costly enough to
make it preferable to avoid it by lifting the foot higher on average. Most humans probably scuff
infrequently on flat, smooth floors, but the incidence likely increases on uneven surfaces. That
scuffing does occasionally happen may be surmised by the wear pattern on shoe soles, or the marks
left on tiled floors. We speculate that scuff happens occasionally because it would be costlier to
completely avoid it.
To address movement variability, we have treated scuffing as if it could lie along a continuum
with lifting the foot. We thus introduced scuffing as a consequence of negative virtual clearance of the
foot, along with a scaling factor between lift height and scuff impulse. It is only with such a
conversion that the relative sensitivities of metabolic cost with respect to lifting and scuffing can be
compared (see opposing sides of Figure 4). While similar results could have been achieved with
summed joint work, this provides a means to compare otherwise dissimilar options, which are not
easily incorporated into an optimization framework. Here they are treated as convertible into a single
independent variable. However, the actual cost of scuffing in the real world is likely considerably
greater than the purely energetic cost measured here (on a flat, constant-speed treadmill), making its
steepness (left side of Figure 4) greater than measured here. The steeper that cost, the more incentive
for higher average ground clearance, despite its higher metabolic cost. It is also possible that many
other human behaviors depend in part on movement variability when determining an optimum or
preference. For example, Begg et al. (2007) speculated that less effort may be needed to increase the
skewness of the distribution (i.e. only tightly control the variability closer to the ground) than to
decrease its variability.
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There are a number of limitations to this study. We attempted to induce lifting and scuffing of
the foot as deviations from normal gait, but this does not necessarily reproduce the adjustments that
occur in real-world situations. For example, actual scuffing is usually unintentional, and could induce
fear, injury avoidance, and recovery actions not examined here. We also did not address the potential
cost of controlling movement variability. We also did not consider the effect of treadmill speed on the
cost of ground clearance. Previous studies have shown that preferred ground clearance increases with
walking speed (De Asha and Buckley, 2015; Schulz et al., 2010). At high walking speeds, scuffing
would be expected to induce greater drag force, and therefore become costlier, thus favoring more
clearance. Conversely, it is possible that scuffing becomes less critical at very low walking speeds,
when it might even be helpful to scuff at the end of the swing to bring the foot to rest. We have also
assumed that scuffing is adequately characterized by the drag force it produces against ground and
have not explored other possible effects. For example, scuffing may also entail some collision work
against ground, assumed small here due to the relatively low vertical ground reaction force (Figure 5).
Another consideration is the possibility of unintended effects from experimental controls, for example
cognitive effort from visual feedback conditions. The present study therefore only represents a simple
characterization of possible contributing factors that determine the average foot-ground clearance.
There are also several possible implications from our findings. One is a potential explanation
for the increased clearance observed on uneven terrain (Gates et al., 2012; Voloshina et al., 2013).
Uneven ground would be expected to increase the cost of scuffing, and perhaps shift it in the direction
of positive foot lift (Figure 1). It may also affect balance and gait steadiness, and cause a wider, and
perhaps skewed, probability distribution for foot motion. Both of these effects would cause the
optimum average foot clearance to increase. There may also be other factors in the opposite direction.
For example, walking on surfaces with low friction could be more forgiving of scuffing, as humans
anecdotally appear more willing to scuff when wearing slippers or walking on sand, grass or light
snow, conditions where the drag force appears low. This also suggests that a potential opportunity to
lift the swing foot less when traversing stepping stones raised above ground. Reduced amount or
probability of drag would be expected to favor reduced foot lift. The approach applied here may also
affect other scenarios, such as the effects of fatigue or age. Older adults tend to walk at slower speeds
and with increased clearance variability compared to younger adults (Begg et al., 2007), which may
be due to differing biomechanics or control, and result in differing costs for scuffing or lifting the
foot, and perhaps contribute to increased risk for stumbling or falling. Although we have explored a
relatively innocuous situation here, the trade-offs between scuffing and lifting the foot may affect the
overall energetic cost of walking as well as risks for injury.
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Acknowledgments
The authors thank Daniel J. Bertoni for assistance in data collection.
Competing Interests
No competing interests declared.
Author Contributions
A.R.W. and A.D.K. conceived the study and drafted the manuscript. A.R.W. designed and carried out
the experiments and data analyses. Both authors read and approved the final manuscript.
Funding
This work was supported in part by the Office of Naval Research (ETOWL program), National
Institutes of Health (AG030815), and Department of Defense (W81XWH-09-2-0142, National
Defense Science & Engineering Graduate Fellowship Program).
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References
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Tables
Table 1: Effects of experimental conditions. Lift height, scuff impulse, and net metabolic rates in both
dimensional SI units and dimensionless form (mean ± s.d.). Statistical significance (*) compared against
Normal indicated if P<0.05.
Lift Height (zLH) Scuff Impulse (�̂�SI) Net Metabolic Rate
SI dimensionless SI dimensionless SI dimensionless
Normal 0.0886±0.0146 0.0956±0.0144 -0.0273±0.0518 -1.264e-4±2.417e-4 176.93±32.357 0.0833±0.0228
Lift Low 0.1436±0.0293* 0.1553±0.0325* -0.0565±0.0557 -2.462e-4±2.385e-4 254.96±67.680* 0.1204±0.0399*
Lift Medium 0.2236±0.0147* 0.2416±0.0150* -0.0320±0.1335 -8.451e-5±6.874e-8 325.08±94.062* 0.1527±0.0503*
Lift Height 0.3018±0.0330* 0.3259±0.0321* -0.1044±0.1371 -4.490e-4±5.833e-4 411.27±114.818* 0.1920±0.0572*
Scuff Low 0.0823±0.0154 0.0888±0.0154 0.7736±0.2669* 0.0037±0.0016* 223.27±66.037* 0.1074±0.0313*
Scuff Medium 0.0861±0.0185 0.0861±0.0185 1.4229±0.3006* 0.0067±0.0015* 290.30±64.790* 0.1394±0.0314*
Scuff High 0.0804±0.0219 0.0867±0.0231 2.1282±0.4629* 0.0102±0.0033* 339.34±88.586* 0.1650±0.0503*
Table 2: Quantitative results for fits to metabolic rate, step parameters, and work and work rate as a
function of lift height and scuff impulse. Fit parameters include trend value (means ± 95% c.i.) and offsets
(means ± s.d.) and are linear unless otherwise noted. R2 values indicate goodness of fit, and P-values
indicate statistical significance of the trend (*P<0.05). Quantities are reported in dimensionless form, with
body mass, gravitational acceleration, and leg length as base variables.
Lift Height Scuff Impulse
Slope (mean±c.i.) Offset (mean ± s.d.) R2 P Slope (mean±c.i.) Offset (mean ± s.d.) R2 P
Net metabolic rate (quadratic fit coefficient) 0.9876±0.2363 0.0877±0.0409 0.7707 1.1e-8* — — — —
Net metabolic rate (linear fit) 0.4395 ±0.0928 0.0472 ±0.0410 0.8116 1.1e-9* -7.0288±1.9864 0.0881±0.0316 0.7475 4.0e-7*
Step length 0.5319±0.1585 0.7032±0.0580 0.6837 4.5e-7* -1.0911±3.0302 0.7479±0.0576 0.0297 0.46
Step width 0.1733±0.0823 0.1532±0.0215 0.4598 2.3e-4* -2.1181±1.0521 0.1663±0.0248 0.4893 4.4e-4*
Step length RMS 0.0504±0.0205 0.0148±0.0083 0.5367 3.8e-5* -0.8175±0.6207 0.0218±0.0079 0.2908 0.012*
Step width RMS 0.0588±0.0196 0.0181±0.0070 0.6338 2.4e-6* -0.2118±0.4866 0.0238±0.0065 0.0428 0.37
Step period 1.2822±0.3793 1.6959±0.1539 0.6869 4.0e-7* -2.6384±7.2691 1.8043±0.1548 0.0302 0.46
Double support duration -0.3217±0.0890 0.5539±0.0203 0.7148 1.3e-7* 0.3518±2.0775 0.5432±0.0147 0.0067 0.73
COM work (pos.) 0.1178±0.0239 0.0200±0.0076 0.8231 5.4e-10* 0.0850±0.2843 0.0325±0.0068 0.0207 0.54
COM work (neg.) -0.1518±0.0239 -0.0248±0.0080 0.8854 3.6e-12* -0.3095±0.3977 -0.0390±0.0108 0.1252 0.12
COM work rate (pos.) 0.0448±0.0076 0.0131±0.0041 0.8685 1.8e-11* 0.0874±0.1214 0.0181±0.0038 0.1093 0.15
COM work rate (neg.) -0.0585±0.0078 -0.0164±0.0053 0.9151 1.1e-13* -0.2079±0.1955 -0.0217±0.0065 0.2110 0.038*
Joint work (pos.) 0.2018±0.0394 0.0358±0.0136 0.8344 2.5e-10* -0.7226±0.4046 0.0587±0.0056 0.4299 0.0013*
Joint work (neg.) -0.1335±0.0236 -0.0276±0.0079 0.8601 3.6e-11* 0.1598±0.4520 -0.0408±0.0115 0.0287 0.4693
Joint work rate (pos.) 0.0802±0.0217 0.0230±0.0096 0.7241 9.2e-8* -0.3471±0.1585 0.0326±0.0041 0.5315 1.9e-4*
Joint work rate (neg.) 0.0501±0.0084 -0.0176±0.0049 0.8719 1.3e-11* 0.0530±0.2150 -0.0226±0.0068 0.0142 0.61
Ankle work (pos.) 0.0659±0.0271 0.0258±0.0095 0.5321 4.3e-5* 0.4780±0.5282 0.0335±0.0102 0.1622 0.0737
Ankle work (neg.) -0.0272±0.0107 -0.0125±0.0043 0.5512 2.6e-5* 0.2016±0.2246 -0.0157±0.0037 0.1600 0.0759
Knee work (pos.) 0.1053±0.0160 0.0059±0.0098 0.8933 1.6e-12* -0.5130±0.3447 0.0177±0.0084 0.3436 0.0056*
Knee work (neg.) -0.0479±0.0197 -0.0264±0.0030 0.5305 4.4e-5* 0.2234±0.3180 -0.0299±0.0053 0.1045 0.1583
Hip work (pos.) 0.0438±0.0349 0.0209±0.0144 0.2323 0.016* -1.3926±0.4001 0.0247±0.0086 0.7412 5.0e-7*
Hip work (neg.) -0.0717±0.0180 -0.0054±0.0101 0.7534 2.5e-8* 0.4399±0.2541 -0.0125±0.0083 0.4147 0.0017*
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Figures
Figure 1: Proposed cost of ground clearance, in terms of metabolic power, including separate
contributions for scuffing the foot on the ground and for lifting the foot higher. Here clearance is treated as
if there were a single range of positive to negative foot lift, the latter causing foot scuff. Expected cost is
sum of these contributions, mediated by variability of foot motion, described by a probability distribution
function (“Distribution”) about a mean foot lift. If cost of scuffing is steeper than cost of lifting near the
origin, the average foot lift with least cost should be positive, thus favoring non-zero average foot lift.
Figure 2: Experimental set-up. Subjects (N=8) walked with varying levels of foot lift and scuff force on a
split-belt treadmill at 1.25 m⋅s−1. During scuffing conditions, subjects were asked to produce a drag force
against ground (aft ground reaction force, plotted in positive direction) during swing phase walking,
indicated by two target thresholds, one for each foot. In the foot lift conditions, they were asked to clear a
target threshold for the height of the lateral toe marker. Visual feedback of both real-time data and
thresholds was projected on a screen visible to subject.
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Figure 3: Measures of scuffing and foot lift observed in experimental conditions. (A) Fore-aft ground
reaction forces vs. time in gait cycle from a representative subject indicate greater drag (aft) force
achieved from low to high scuff threshold levels (solid rectangle). (B) Fore-aft and vertical trajectory of
the lateral toe marker from a representative subject for various lift height thresholds from the treadmill.
Mean ground clearance levels across subjects measured through (C) scuff impulse (N=7) and (D) lift
height (N=8). All levels of ground clearance were significantly different from normal (p<0.05). Left-hand
axes are dimensionless, using body mass, leg length, and gravitational acceleration as base units; right-
hand axes are SI units. Bars denote mean across subjects, and error bars denote s.d. Gait cycle is defined
as a full stride starting from heelstrike.
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Figure 4: Net metabolic cost as a function of measured scuff impulse (left) and lift height (right). Net
metabolic rate increased with greater scuff impulse (N=7) at a rate of −69.0 W⋅N−1⋅s−1 (R2=0.75, p<0.05)
and with greater lift height (N=8) at 2517 W⋅m−2 (R2=0.77, p<0.05). Distribution of minimum toe
clearance during swing indicates movement variability during normal walking. Separate colors denote
each subjects’ data (square for scuffing, circle for foot lift). Net metabolic rate for normal walking also
indicated (dashed), defined as gross metabolic rate minus quiet standing rate. Metabolic rate, scuff
impulse, and lift height are shown in dimensionless units, using body mass, leg length, and gravitational
acceleration as base units; equivalent SI units are also indicated.
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Figure 5: Force and power measures versus time within gait cycle (% of stride) for varying levels of
ground clearance (black for normal, solid for foot lift, dashed for scuff). (A) Vertical and (B) fore-aft
ground reaction force, (C) center of mass (COM) power, and (D) summed joint power from sum of ankle,
knee, and hip power from one leg. More qualitative changes are observed in lift conditions than in scuff
conditions, compared against Normal. Vertical axes are shown in both dimensionless and SI form;
horizontal axes are shown as fraction of gait cycle beginning with heelstrike, with corresponding time
scale for each condition shown in (A). Each trace is a filtered average across subjects; see Fig. 3A for
representative trials.
Figure 6: Joint angle, moment, and power for (A) foot scuff and (B) foot lift conditions. Trajectories vs.
time for ankle, knee, and hip, with gait cycle starting at heelstrike. Left-hand axes are in dimensionless
units, and right-hand axes are SI units.
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Figure 7: Mean positive and negative (A) COM work rate per stride and (B) summed joint work rate per
stride against scuff impulse and lift height. Joint work rates include ankle, knee, and hip. Lift height had a
greater impact on work rate than scuff impulse. Greater lift contributed towards significant increases in
positive and negative COM work rate and joint work rate. However, scuff impulse only affected negative
COM work and positive joint work rates, both at lesser rates than for lift height. Separate colors denote
each subjects’ data (square for scuffing, circle for foot lift). Trend significance indicated by solid lines
(p<0.05) and non-significance by dashed lines.
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