Running performance has a structural basis
1 Locomotion Laboratory, Kinesiology Department, MS545, Rice
University, 6100 Main Street, Houston, TX 77005, USA
2 Center for Human Performance, Texas Medical Center, Houston, TX 77030,
USA
* Author for correspondence (e-mail: pweyand{at}rice.edu)
Accepted 17 March 2005
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Summary |
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Key words: locomotion, mechanics, ground support forces, muscle, tendon, bone, body mass index
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Introduction |
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Classical evaluations of the relationship between structure and function in
cursorial species considered the presumably enormous mechanical power
requirements of fast running on level ground
(Fenn, 1930;
Hill, 1950
;
Gray, 1959
). However, these
early studies considerably overestimated the mechanical power that skeletal
muscle must generate actively from metabolic sources during each stride.
Cavagna's classical experiments later demonstrated that once a runner is up to
speed, the large majority of the mechanical power needed to lift and
accelerate the body and limbs during each stride is provided via
conservative mechanisms of segment energy transfer and elastic recoil (Cavagna
et al., 1964
,
1971
;
van Ingen Schenau, 1998
;
Willems et al., 1995
). These
conservative transfer mechanisms greatly reduce the burden on skeletal muscle
to serve as a de novo generator of mechanical power once a runner is
up to speed (Kram and Taylor,
1990
; Taylor,
1994
). Thus, the possibility that faster specialists might need
additional body and muscle mass to meet mechanical power requirements does not
seem likely.
In contrast to the relatively limited mechanical power muscle must generate
during steady-speed running, musculoskeletal and ground support forces are
considerable and depend directly on a runner's speed. During fast running,
ground and muscle support forces can exceed the body's weight by as much as
2.5 and 5-fold, respectively (Weyand et
al., 2000; Wright and Weyand,
2001
). The large force requirements of high-speed running and the
invariant forcearea relation of skeletal muscle
(Hill, 1950
;
Nelson et al., 2004
) suggest
that faster specialists may require relatively more muscle to generate these
forces, and additional tendon and bone to transmit them safely (Biewener,
1989
,
1993
) to the ground.
Accordingly, we hypothesized that the greater body masses of faster
specialists are directly related to the greater ground support forces required
to run at faster speeds.
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Materials and methods |
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To maximize experimental rigor, we included specialized human runners of both sexes. We anticipated the presence of two sexes would increase the range of body masses and mass-specific support force requirements examined. Additionally, the inclusion of male and female runners who differ in body composition, but not in the forcearea properties of their musculoskeletal tissues, should provide a more stringent test of the generality of the structurefunction relationship proposed.
Our ultimate goal was to relate the body masses of specialized runners to
their mass-specific ground support requirements. This required an appropriate
standardization for the effect of height on body mass. In the simplest, and
nonapplicable case of identically proportioned individuals who differ in
height (H1), mass differences are proportional to height
cubed (H3). However, we knew a priori that the
unique subjects in our sample would be similar in height but not identically
proportioned (Khosla, 1978,
1985
). On the basis of the
well-established forcearea properties of muscle, tendon and bone
(Hill, 1950
; Biewener,
1989
,
1993
;
Nelson et al., 2004
) we
expected the mass variation of these unique subjects would occur largely in
two dimensions (H2) in accordance with their ground
support force requirements. Therefore, we hypothesized that body masses
related to height-standardized areas would vary in direct relation to
mass-specific ground support force requirements. Thus, our hypothesis takes
the following quantitative form:
![]() | (1) |
![]() | (2) |
If the elite runners in our sample provide true body size optima for
specialized human runners as we have assumed, our ideal mass coefficient, D,
should have a slightly lower value for females than males. This result is
expected because the density of the body's tissues varies between males and
females. Given that the sex difference in body density is 2.5% for elite
runners (Pipes, 1977) the
value of D should be 2.5% lower for females than males.
Ground support force requirements
Generalized support forcespeed relationships were formulated from
direct measurements on nine athletic male and female subjects (N=18;
73.2±6.6 and 60.8±5.8 kg, respectively). All subjects provided
written informed consent in accordance with the guidelines of the local
institutional review board. Subjects ran at a series of constant speeds on a
custom high-speed force treadmill. The average vertical force applied to the
ground during the stance phase was determined in accordance with Weyand et al.
(2000) during a series of
constant speed runs from an initial speed of 2.5 m s1
through the fastest speed each runner could attain for eight steps (range:
males 2.511.2 m s1; females 2.58.0 m
s1). The slopes and intercepts of the linear best-fit
relationships for each of the male and female subjects tested were averaged to
obtain generalized supportforce speed relationship for each sex. The
horizontal and lateral forces applied were not included because their
contribution to the total ground reaction force is quite small
(Cavagna, 1975
). The ground
support force requirements of different specialists were estimated from their
average racing speeds using the sex-specific forcespeed equations
formulated.
Body size optima
Mass and stature values for the world's fastest 45 male and female
performers at each of eight standard track racing distances from 100 to 10,000
m (N=275 males and 261 females) during the past 14 years were
compiled from public source data (Track and Field News
19902003). Individual athletes were included once in each event in
which they were among the top 45 performers during this period. Height and
weight values were coincident with each individual's best performance during
this 14 year period.
Relative body masses and ground support force requirements
The hypothesis that a single structurefunction relationship would
apply regardless of sex and distance of specialization was tested by
evaluating the proportion of variation (R2) accounted for
by the linear regression of body mass on the product of height squared and
ground support force (Equation 1; P<0.05). Also computed was the
average difference between the mass predicted by Equation 1 and the actual
mass for each of the 16 group means.
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Results |
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Body size optima
Specialists in shorter distance races were generally more massive than
those in longer ones. Within both sexes, the most massive specialists were
those in the sprint events of 100, 200 and 400 m whose masses were roughly
equal to one another. The body masses of athletes specializing in events of
80010,000 m were inversely related to event distance for both sexes
(Fig. 2A). Within each sex, the
range of body masses among the eight different event specialists was 1.33- and
1.25-fold for males and females, respectively. The male mean from all eight
events combined exceeded that of the females by 22.5% (66.4±0.5
vs 54.2±0.3 kg), with the single event sex differences ranging
from 17.5 to 30.1% for the 3000 m and 100 m specialists, respectively.
|
By comparison with absolute mass, the relation of the body mass index to event distance was more consistent for males and females across the full range of event distances including the 100, 200 and 400 m (Fig. 3A). The mean BMI for all males exceeded that of all females by 8.5% (21.0±0.1 vs 19.4±0.08 kg m2). Because stature has a direct influence on BMI values (among identically proportioned individuals) a 6.0% difference in BMI resulted from the males being 6.0% taller than the females. Thus, male values exceeded female values by 2.5% when the influence of height on BMI was removed.
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The mean ratio of the body mass index to mass-specific ground support force requirements (Equation 2) of different specialists was similar across the full range of event distances and not statistically different for males and females (Fig. 3C; males=10.01±0.04, females=9.81±0.04 kg m2, P=0.06). In relation to the distance of specialization, the best-fit relationship between the BMI Fg1 ratio and distance for all specialists increased by a factor of 1.04, from 100 to 10,000 m [kg m2 (Fg1) = 9.8+0.00004 m, R2=0.27; overall mean = 9.92±0.03] with relatively greater deviation about the overall mean being present among the sprint specialists (range: 10.19.3).
Expressing the body mass means of the different event specialists in relation to the product of their event-specific support force requirements and height squared accounted for 97% of the total variability present among the 16 group means that spanned a 1.5-fold range of absolute values (Fig. 4; Mb=0.006+0.101x; R2=0.97; P<0.0001).
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Discussion |
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How much mass does additional racing speed require?
The specific mass requirement we obtained for human running speed was
relatively small. For male and female runners of the average heights of those
in our sample (1.77 and 1.67 m, respectively) the respective masses required
per one meter per second of racing speed were 2.5 and 1.8 kg. We attribute
this modest mass requirement for speed to two factors. First, the specific
support forces needed to increase speed are not large. Each meter per second
requires an additional force of only one-tenth of the body's weight or less.
Second, skeletal muscle generates force effectively. One kilogram of skeletal
muscle can produce enough force to support 44 kg of mass
(Hill, 1950;
Nelson et al., 2004
) given the
average fiber lengths of the muscles in the human leg
(Wright and Weyand, 2001
).
Given these force capabilities, we might have found mass minimums for human
speed that were considerably smaller.
Biological necessity dictates that the ultimate mass requirement of human
speed must be appreciably greater than any theoretical minimum estimated from
tissue forcearea properties. This is the case because our ideal mass
coefficient includes all the tissues that contribute to the body's mass; not
solely the musculoskeletal tissues involved in locomotion. Elite runners
obviously cannot wholly eliminate the bodily tissues not directly involved in
ground force application to become better adapted for performance. Given this
minimum requirement for non-musculoskeletal tissue mass, effective skeletal
muscle force production allows performance variation to be mediated by
relatively small alterations in the body's musculature. Indeed, available
evidence indicates that tissue adjustments necessary for modifying force
production are present among runners of different performance specializations.
The shorter distance specialists who are able to apply relatively greater
mass-specific ground forces have proportionately more muscle in relation to
body mass (Spenst et al.,
1993), and apply force with individual leg muscles, and muscle
fibers that are a quarter to a third larger in area than those of endurance
specialists (Lorentzon et al.,
1988
; Sjostrom et al.,
1988
).
At the outset of the study we assumed that the nonmusculoskeletal tissue
masses of elite runners would be minimized to the extent genetically possible.
In the case of fat tissue, sex-specific minima are well documented. For elite
female vs male runners, the proportion of the body's mass comprising
fat tissue is 78% greater, and the body's density is 2.5% less
(Pipes, 1977). These body
density differences led us to expect specific differences between males and
females in the body mass to height-standardized area variables used here. In
accordance with these expectations, we found the mean body mass indices of the
elite male and female runners in our sample differed by 2.5%. Similarly, we
found ideal mass coefficients that were 2.0% lower (P=0.06) for
females than males. The agreement of both of our mass to area ratios with the
established sex differences in body densities, as well as the similar
differences before and after body masses were related to ground support force
requirements, supports two of our initial assumptions. First, the body masses
of the elite runners in our sample do represent the optima genetically
possible for elite human male and female runners. Second, for male and female
runners, the body masses that optimize performance are similarly determined by
the ground support forces their racing specializations require.
Why a single-function relationship?
The most basic explanation for why male and female runners of different
specializations have the same mass requirement for providing ground support
forces during running is that the muscles
(Hill, 1950;
Nelson et al., 2004
) used to
generate the necessary support forces, and the tendons and bones (Biewener,
1989
,
1993
) used to transmit these
forces to the ground, have forcearea properties that are essentially
identical. The acute adaptation that these tissues undergo in response to
habitual loading (Biewener,
1993
) provides a mechanism for ongoing matching of tissue
structure to the functional demands imposed by the training and racing
regimens of individual specialists. However, the relationship between the
support force applied to the ground and the functional loads ultimately
imposed on the muscles, tendons and bones is also affected by the locomotor
mechanics used by the individual runner. Any variability in stance limb
posture; either among individuals or at different running speeds, would alter
the muscle and tendon forces required per unit ground support force applied.
Such variability would therefore be expected to have a direct effect on the
mass requirement of running speed.
How variable is the mass requirement for running speed among individual
performers? We cannot evaluate this question without direct measurements of
ground support forces and the limb mechanics used by individual elite runners.
The limited evidence available from non-competitive human runners indicates
that stance limb mechanics vary only moderately between different runners
(Biewener et al., 2004;
Wright and Weyand, 2001
) and
vary little to not at all when the same individuals run at different speeds
(Biewener et al., 2004
).
However, we did find appreciable variability in the two variables that
determine the ideal mass coefficient most directly: the body mass indices of
individual performers of any given sex and specialization, and the ground
support forces required at common speeds for the 18 subjects on whom we
formulated generalized relationships. Whether these factors co-vary so that
the mass coefficients of each individual performer, like those of the 16 group
means, conform closely to the value of 10 kg x m2
obtained cannot be addressed at present. The virtually identical
Fgspeed relationships obtained from independent
samples of athletic male and female subjects supports the likely validity of
our support force estimates for the population means of the large number of
specialists included in each of the 16 groups. Thus, we are confident that we
have correctly identified the biological value of the ideal mass coefficient
even though we do not yet know how precisely this value applies to individual
performers.
While ground support force requirements and the area-dependent properties
of musculoskeletal tissues explain a minimum mass requirement, they do not
explain the performance penalty imposed by having too much mass. We suggest
that the ideal masses observed among specialists represent a functional
trade-off between the body and muscle mass minimums that maximize
mass-specific aerobic power and endurance
(Costill, 1972;
Saltin, 1987
;
Daniels and Daniels, 1992
)
vs the additional musculoskeletal structure required to apply the
greater ground forces necessary to race at faster speeds. This explanation is
consistent with the observation that the capacity of the human cardiovascular
system can be fully taxed when only a sub-fraction of the body's musculature
is activated (Secher et al.,
1974
; Saltin,
1987
). Additionally, the more limited mass-specific aerobic power
maximums of shorter distance specialists are a direct result of their greater
massiveness. When expressed absolutely, rather than in relation to their
different body masses, the aerobic maxima of different specialists are nearly
the same (Svedenhag and Sjodin, 1985; Daniels and Daniels, 1994;
Weyand et al., 1994
). In close
keeping with the principle of economic design
(Weibel et al., 1992
), runners
are optimized for performance when they meet their functional needs with the
least amount of structure possible.
The functional trade-offs responsible for the body mass optima of the
shortest distance specialists are less clear. Mass-specific aerobic power is
relatively unimportant for sprinting
(Weyand et al., 1999) and the
positive relationship between mass, ground support force and speed implies
that additional mass would allow sprinters to apply greater support forces and
reach faster sprinting speeds. Sprinters clearly have not reached an upper
adaptive limit to either muscle or body masses. Body builders and weight
lifters of similar stature and body composition are considerably more massive
than the elite sprinters in our sample
(Spenst et al., 1993
;
Johnson et al., 1990
). At
present, we can conclude that the structural optimum for human speed is set at
an intermediate level of massiveness, but we cannot identify the factors
imposing this moderate upper limit from the data presented here.
Concluding remarks
Previous analyses have noted that the area-dependent properties of the
musculoskeletal tissues involved in locomotion can be challenging and even
performance limiting for larger mammals and dinosaurs
(Biewener 1989;
Bennet and Taylor, 1995
;
Hutchinson and Garcia, 2002
).
Because area to mass ratios scale negatively with body size, larger animals
are faced with the task of supporting relatively more mass with relatively
smaller muscle, tendon and bone cross-sectional areas. To some extent, larger
animals offset their intrinsic disadvantage for mass-specific force production
by adopting a more favourable limb mechanical advantage for applying ground
force. Their more erect stance limb postures reduce the muscle forces and
cross-sectional areas needed to apply any given support force to the ground
(Biewener, 1989
). However,
human runners do not appear to have this option. They suffer negative
mechanical and metabolic consequences
(McMahon et al., 1987
;
Farley and Gonzalez, 1996
)
when they deviate from the stance limb mechanics they choose naturally. In the
absence of a functional option, human runners have simply adjusted
structurally: musculoskeletal tissue areas are closely matched to the support
forces required. Thus, massiveness does not necessarily pose the performance
disadvantages previously noted for large terrestrial vertebrates. Among
runners of similar stature and body composition, being relatively more massive
is not only beneficial for shorter distance specialists, but also appears to
be biologically necessary for attaining faster speeds.
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Acknowledgments |
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