Sources of mechanical power for uphill running in humans
Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA
* Author for correspondence at present address: Brown University, Ecology and Evolutionary Biology Department, Box G-B205, Providence, RI 02912, USA (e-mail: Thomas_Roberts{at}Brown.edu)
Accepted 23 February 2005
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Summary |
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Key words: locomotion, biomechanics, muscle, power, mechanical advantage, recruitment, human
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Introduction |
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Low moments of force at the hip must necessarily limit the power produced at this joint. During level, steady-speed running this lack of mechanical power may have little consequence; the net mechanical power required in each step is close to zero, because there is no net change in the runner's average kinetic or potential energy. By contrast, uphill running requires net mechanical work with each step to increase the body's potential energy. During these activities the low forces developed at the hip could potentially limit the power available from the large hip extensor muscle mass. Power might also be transferred from knee extensors to the hip via biarticular hamstrings, but this also requires a net extensor hip moment. Thus, we hypothesized that the average muscle moment at the hip would increase from level to incline running to meet the demands for mechanical power to lift the body.
To determine whether the hip contributes mechanical power to uphill running, we used inverse dynamics to measure hip muscle moments and power during level running and at two running inclines. We also measured muscle moments and power at the ankle and knee to determine the relative contribution of all joints to uphill power output. We predicted that hip net mechanical power output would increase as a function of running incline. We also predicted that increased force and power output at the hip would be associated with a poorer mechanical advantage for force production during incline running.
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Materials and methods |
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Force and video measurements
Force plates (on the level, Kistler model 9261; Amherst, NY, USA; on
inclines, AMTI model OR65-6, Watertown, MA, USA) were used to measure ground
reaction forces during running. These force plates showed less than 0.5%
cross-talk between channels. The inclined force plate was mounted in a stiff
steel chassis similar to the apparatus described by Kram and Powell
(1989). The unloaded natural
frequency of both plates was greater than 150 Hz.
Horizontal and vertical (i.e. parallel and normal to the plate surface) components of the ground reaction force were recorded on computer after A/D conversion on a National Instruments NB MIO 16H A/D board (National Instruments, Austin, TX, USA). Signals were collected through a custom Labview program at 1000 Hz and filtered by a Chebyshev low pass filter with a cut-off frequency of 60 Hz. A manual correction was made for the small phase shift caused by this filter. The force plates used allowed measurement of the center of pressure of the foot. This measurement was calibrated regularly with a known mass and was accurate within 1 cm.
The positions of the hip, knee and ankle joints were marked and recorded
with video. The centers of rotation of the three joints were palpated and
marked on the skin with black felt-tip marker. A NAC high speed video system
operating at 100 fields s-1 was used to videotape the runners. For
the incline runs, the camera was tilted to the same incline as the force
plate, so that the vertical and horizontal axes in the video corresponded to
the vertical and horizontal axes of the force plate. Frames were digitized and
joint locations were measured using NIH Image software. Raw coordinate data
were filtered bidirectionally by a fourth order, zero lag Butterworth filter
with a cut-off frequency of 10 Hz (Winter,
1990). Joint angles were determined trigonometrically from joint
positions. We assumed that the orientation of the trunk was constant during
the stance phase, and used the angle of the leg relative to the horizontal as
a measure of hip angle. Force and video data were synchronized by triggering
both force data acquisition and the video frame counter (using a custom built
circuit) when the runner tripped the first photocell.
Joint moment
We used inverse dynamics to determine net muscle moments
(Mm) at the ankle, knee and hip
(Elftman, 1939;
Winter, 1990
). Our analysis
included both moments due to limb inertia and rotation as well as ground
reaction force-based moments. We used published values of segment masses,
moments of inertia, and center of mass locations
(Winter, 1990
). By convention,
net extensor muscle moments are positive and net flexor moments are
negative.
We also calculated ground reaction force-based moments independently of
limb inertia. This allowed us to determine the moment arm of the ground
reaction force, one of the variables that determines the mechanical advantage
with which muscles generate force to support the body. By this method, net
muscle moments are calculated as the product of the ground reaction force, GRF
(in N), and the moment arm of this force, or out-moment arm, R (in
m).
![]() | (1) |
R is the orthogonal distance between the resultant ground reaction force vector and the joint center of rotation.
Joint power and work
Net joint power P was calculated from joint moment and angular
velocity () according to the equation:
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where is joint angular velocity in radians. By convention extension
velocities are positive. Positive power indicates work performed by muscles
and tendons, while negative power output indicates work absorbed by muscles
and tendons. Net joint work was calculated by integrating the power-time curve
during stance. Because elastic elements cannot release more energy than they
absorb, the net work performed (positive work minus negative work) during the
step represents the minimum work that must be done by muscles.
Statistics
All data are presented as means ± standard deviations
(S.D.) or standard errors
(S.E.M.). Repeated-measures analysis of
variance (ANOVA) was used to determine statistical significance between
running inclines.
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Results |
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At the knee, net work was negative for all inclines, and there was no significant effect of running incline on knee work (Fig. 3A). Although work was unchanged with incline, there was a significant increase in total joint excursion with incline (Fig. 3B), and a decrease in joint moment (Fig. 3C). The increase in joint excursion offset the decrease in joint moment, so that net work produced was independent of incline. Although net work was unchanged with incline, it is clear from the time profiles of joint power during stance that the knee developed less positive power and negative power during incline running (Fig. 4). Net work was unchanged because positive and negative power decreased proportionately.
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Mechanical work produced at the hip increased dramatically with increasing running incline (P<0.001; Fig. 5A). During level running, net work produced at the hip was not significantly different from zero. Significant positive work was produced at the hip during both 6° and 12° incline running (Fig. 5A). The increase in work output at the hip with running incline was due primarily to an increase in the moment of force developed (Figs 5C, 6C). Average angular excursion of the hip during stance also increased with incline, though the change in joint excursion was much smaller than the change in joint moment (Figs 5B, 6B).
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The increase in extensor muscle moment produced at the hip correlated to a change in the out-moment arm R for force production at the hip. The average moment required at the hip to overcome limb segment inertia was independent of incline (P<0.001). Therefore, we compared the GRF based moment across incline to determine whether increases in average hip moment were due to a change in GRF magnitude or R. There was no significant change in GRF magnitude with incline (Fig. 7), nor was there a significant change in impulse with incline (306±25 Nm s, 311±28 Nm s and 295±25 Nm s for 0°,6° and 12°, respectively). There was a large increase in the average out-moment arm at the hip (R, Eqn 1) with incline (Fig. 8). From level to 12° incline running, the out-moment arm increased by more than fourfold (from 0.022±0.011 m to 0.092±0.006 m; P=0.003).
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Discussion |
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Although we find that most of the power necessary to propel a runner uphill
is produced at the hip joint, it cannot be concluded from the methods used
here that hip extensor muscles alone produce this power. Two-joint muscles can
transfer mechanical power from one joint to another
(Bobbert et al., 1986;
Bobbert and van Ingen Schenau,
1988
; van Ingen Schenau et
al., 1992
; Jacobs et al.,
1996
,
1993
;
Prilutsky et al., 1996
).
During cycling, for example, mechanical power produced by contraction of
mono-articular knee extensors can be transferred via the hamstrings to appear
as mechanical power at the hip (van Ingen
Schenau et al., 1992
). Some of the mechanical work observed at the
hip in the present study may be produced by contraction of knee extensors.
Thus, we can conclude from our measurements of net joint moment that an
increase in net moment at the hip is associated with an increase in net work
either produced by hip extensors, or transferred by biarticular hip extensors
from muscles at other joints (e.g. knee extensors). In either case, an
increase in net muscle moment produced at the hip was necessary to increase
net hip work.
Because we found no increase in net power output at the knee or ankle with
running incline, knee extensors contributed to the increase in net work
necessary to run uphill only if they transfer work to the hip via the
biarticular hamstrings. Estimates of muscle activity from other methods
suggest that this may be the case. Sloniger and coworkers
(1997a,b
)
found increased muscle activity, based on Magnetic Resonance Imaging (MRI), in
knee extensors with increasing running incline (Sloniger et al.,
1997a
,b
).
Glycogen depletion studies also suggest an increase in activity in the vasti
group from level to incline running
(Costill et al., 1974
). The
transfer of power from knee extensors to the hip may reflect an important
mechanism for overcoming the constraints of force production in a jointed
limb. Joint moments are interdependent; an increase in net horizontal force,
for example, would tend to decrease knee extensor moments and increase hip
extensor moments. It has been suggested that two joint muscles distribute
external joint moments across different joints to allow for the coordination
of changes in joint moments (van Ingen
Schenau et al., 1992
). In certain stages of cycling, for example,
the transfer of power from the monarticular knee extensors (vasti group) to
the hip via the biarticular hamstrings allows knee extensors to
contribute to pedal power even when net knee moments are low
(van Ingen Schenau et al.,
1992
). Biarticular muscles may play a similar role as the pattern
of ground reaction forces change with running incline.
The low joint moments observed at the hip during level running may reflect
a strategy for minimizing metabolic energy cost. It has been suggested that
the cost of generating muscle force determines the metabolic cost of running,
and that much of the design of the musculoskeletal system has been shaped by
the need to produce force economically (Taylor,
1985,
1994
;
Kram and Taylor, 1990
;
Roberts et al., 1997
). Several
architectural features of the hip extensors suggest that they are poorly
suited for producing force economically
(Biewener and Roberts, 2000
).
First, hip extensors have relatively long fascicles
(Wickiewicz et al., 1983
). For
a given force output, longer-fibered muscles are metabolically more costly
than short-fibered muscles because a greater volume of muscle must be active
(Biewener and Roberts, 2000
).
Hip muscles may also be disadvantageous for producing force economically
because they do not undergo the stretch-shorten cycle that may reduce the
energy cost of running by allowing for elastic energy storage and recovery
(Alexander, 1988
;
Cavagna et al., 1964
;
Taylor, 1994
;
Roberts et al., 1997
).
Further, the capacity for elastic energy storage and recovery is likely
limited in hip extensors by their relatively small tendons.
Although our measurements of joint moments suggest that hip muscles
generate low forces during level running, some values from the literature
suggest higher levels of activity in hip muscles. Winter's results for jogging
humans were consistent with those of the present study; hip moments were
variable, but generally lower than those at the ankle and knee
(Winter, 1983). Thorpe et al.
(1998
) combined measurements
of joint moments and muscle cross-sectional area measured from MRI to estimate
the average stress in different muscle groups. At slow speeds, their results
were generally consistent with the present study; hip muscle stresses were the
lowest of all three joints and were only about half those of knee extensors.
At higher speeds, however, hip stress values were similar to those of the
ankle (Thorpe et al., 1998
).
Belli and coworkers also found that hip moments were low at moderate speeds
but increased substantially with speed, until reaching peak values nearly as
high as those for the ankle and knee at runners' maximum speeds
(Belli et al., 2002
). Sloniger
and coworkers estimated muscle activity during very fast level running using
contrast shifts in magnetic resonance images
(Sloniger et al., 1997a
).
Their results indicate a very high level of activity of all of the hamstrings,
gluteal and adductor muscles (65-90% active;
Sloniger et al., 1997a
) during
horizontal running at an exercise intensity equivalent to 115% of peak oxygen
uptake. Electromyographic (EMG) measurements also indicate activity in hip
extensors during at least some part of stance
(McClay et al., 1990
), but it
is difficult to make quantitative assessments of absolute magnitude of
recruitment and muscle force in different muscle groups from EMG measurements.
Together, these results suggest that the low joint moments at the hip observed
in the present study for moderate speeds may not hold at fast running speeds.
It is unclear from published studies whether the higher hip moments at high
speeds result from an increase in ground reaction force-based moments or an
increase in inertial moments necessary to swing the limbs faster.
Our results suggest that the primary mechanism for altering joint work with
running incline is an increase in joint moment, rather than an increase in
excursion. Some increase in joint excursion occurred for the knee, and there
was a small increase in hip excursion with incline. Our results for joint
excursion at the hip and knee are consistent with Swanson and Caldwell's study
of incline running (Swanson and Caldwell,
2000). They found an increase in joint range of motion during
stance for the hip, knee and ankle. These results are also consistent with the
pattern of change in muscle function observed in individual muscles of running
birds. In turkeys (Roberts et al.,
1997
; Gabaldon et al.,
2004
) and guinea fowl (Daley
and Biewener, 2003
), modulation of muscle force is one of the
mechanisms utilized to alter mechanical work output for uphill running in
distal joint extensors.
Studies of joint moments in running animals have typically used either a
pseudo-static approach, in which only ground reaction force-based moments are
measured (Biewener, 1989;
Roberts et al., 1998
;
Carrier et al., 1998
), or a
true inverse dynamics technique, which includes joint moments necessary to
overcome inertia of limbs that cyclicly accelerate and decelerate. Only a few
studies have reported these values separately to allow evaluation of the
importance of the limb-inertia component of joint moments
(Biewener et al., 2004
;
Clark and Alexander, 1975
). We
found that the inertial component of joint moments was negligible at the ankle
and small at the knee. In level running, the average extensor moment due to
limb inertia at the knee was only 9.39±2.39 Nm, compared with the total
average moment of 162.99±14.94. At the hip, limb inertia moments were
on average the same magnitude as GRF based moments
(Fig. 9). When the rectified
average moment is calculated (to account for moment magnitude independent of
sign), the GRF-based rectified moments at the hip are 49.15±11.68
vs 52.55±8.03 Nm for limb inertia moments only (for level
running). There was no significant change in limb inertia moment with running
incline.
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Variable mechanical advantage with running incline
The increase in joint moment with incline observed at the hip was
associated with a change in the mechanical advantage with which muscles at the
joint produce force against the ground. The mechanical advantage is defined as
the ratio of the average of the muscle moment arms acting at a joint,
r and the effective moment arm of the resultant ground reaction
force, R (Biewener,
1990). In the present study, we measured only the total moment
produced at a joint and did not attempt to account for the muscle moment arm
or changes in the muscle moment arm that may have occurred across incline. At
the hip, the similarity in joint angle patterns across inclines
(Fig. 6B) would suggest that
muscle moment arms were, on average, similar across inclines. It is the
out-moment arm, or the orthogonal distance from the ground reaction force to
the joint center of rotation, that increased dramatically as running incline
increased. During level running the GRF vector passed very near to the joint
center of rotation and as a result the out-moment arm was small and mechanical
advantage favorable. During incline running, the GRF was oriented more forward
of the hip and the out-moment arm increased, i.e. muscles operated with a
poorer mechanical advantage compared with level running
(Fig. 10). The increased
moment arm at the hip during incline running was associated with higher joint
moments and increased work output at the hip for the same change in angle.
|
The mechanical advantage through which muscles transmit force to the
environment is an important determinant of muscle function in nature. Among
mammalian runners there is a regular change in mechanical advantage, averaged
over all the joints of the limbs, with body size (Biewener,
1989,
1990
). The muscle forces
required to support body weight are generally lower in large mammals because
their upright posture reduces the moment arm of the ground reaction force
(R) and improves mechanical advantage
(Biewener, 1990
). Human runners
appear to alter horizontal ground reaction forces to maintain a contstant
mechanical advantage when ground reaction forces are altered by simulated
reduced gravity (Chang et al.,
2000
). Recent work suggests that the higher cost of transport in
human running vs walking may be due in part to runners' poorer
mechanical advantage and higher muscles forces associated with a bent-leg
posture (Biewener et al.,
2004
). It has been proposed that variation in mechanical advantage
during the course of a single stride may allow muscles to maintain relatively
constant contraction velocities even when joint velocity varies
(Carrier, 1994
;
Carrier et al., 1998
), and
during jumping and accelerations variation in mechanical advantage during
single muscle contractions may allow for increased muscle work and enhanced
elastic energy storage (Roberts and Marsh,
2003
; Roberts and Scale, 2004). The present results suggest a
change in muscle mechanical advantage may provide a mechanism for selectively
utilizing different muscles for different locomotor tasks. The hip contributes
little work for level running because it operates with a favorable mechanical
advantage and joint moments are low, while during incline running the
mechanical advantage is less favorable and joint moments and work are
higher.
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Acknowledgments |
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Footnotes |
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