|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
First published online October 7, 2008
Journal of Experimental Biology 211, 3266-3271 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.018812
Running biomechanics: shorter heels, better economy
1 Research Institute MOVE, VU University Amsterdam, Van der Boechorststraat 9,
1081 BT Amsterdam, The Netherlands
2 Institute of Sport Research, University of Pretoria, PO Box 14622, Hatfield
0028, Pretoria, South Africa
3 School of Sport Science, Physiotherapy and Optometry, Faculty of Health
Sciences, School of Sport Sciences and Optometry, Private Bag X54001, Druban
4000, South Africa
* Author for correspondence (e-mail: m.scholz{at}fbw.vu.nl)
Accepted 7 July 2008
 |
Summary |
|---|
 TOP Summary INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Key words: moment arm, tendon, elastic, energy, strain, stretch, long distance, runner, oxygen uptake
|
INTRODUCTION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
;
Heise and Martin, 2001;
Saunders et al., 2004;
Williams and Cavanagh, 1987).
Previous studies on running economy have revealed that running economy is an
important determinant of running performance
(Anderson, 1996;
di Prampero et al., 1986;
Joyner, 1991;
Saunders et al., 2004).
Training has little or no effect on running economy; the best results were
achieved after high-intensity interval training and resistance training and
were in the order of 5–7% improvement
(Bailey and Pate, 1991;
Billat et al., 2002;
Franch et al., 1998;
Lake and Cavanagh, 1996;
Midgley et al., 2007). This
suggests that running economy is determined by intrinsic morphological and
physiological properties.
Several hypotheses have been put forward to explain the variation in
running economy among participants. First, it has been hypothesized that some
runners are more economical because they require less energy to swing their
legs (Holden, 2004;
Larsen, 2003). However, it is
very unlikely that variations in leg-swing cost can account for 20–30%
variation in running economy because the total metabolic cost of swinging the
legs is only about 20% of the metabolic cost of running
(Marsh et al., 2004;
Modica and Kram, 2005).
Second, it has been proposed that the rate and magnitude of muscular force
generation explain the rate of metabolic energy consumption during running;
this hypothesis is known as the `cost of generating force' hypothesis
(Kram and Taylor, 1990).
Although it accounts for much of the variation in the metabolic cost of
running between different animal species, it is not able to explain
inter-individual differences in running economy for reasons explained
elsewhere (Heise and Martin,
2001). Third, it is generally accepted that storage and
reutilization of elastic energy in tendons substantially reduces energy
demands in running (Cavagna et al.,
1964). However, it is not known if and how economical runners
could store and recover more tendon elastic energy compared with uneconomical
runners. Hence, at this point, there is no conclusive mechanical explanation
for the inter-individual differences in running economy
(di Prampero et al., 1986;
Kyrolainen et al., 2001;
Saunders et al., 2004;
Williams and Cavanagh,
1987).
The amount of energy stored in a tendon depends on the mechanical
properties of the tendon (compliance and rest length) and on the force that
stretches the tendon. For a given kinematic pattern, and hence kinetic
pattern, tendon force is inversely related to the moment arm of the tendon.
The importance of moment arm scaling and locomotion energetics/elastic storage
and return has been pointed out by others
(Biewener, 2005;
Carrier et al., 1994). However,
moment arm length has not been investigated in the context of inter-individual
variations in running economy.
The purpose of the current study was to test if and how tendon mechanical properties and musculoskeletal geometry can account for inter-individual differences in running economy. Since tendon mechanics cannot be changed experimentally without disrupting the integrity of the participant and/or the movement, we first adopted a musculoskeletal modeling approach and addressed the following question: what is the most effective way to enhance storage and release of tendon energy during a given stretch–shortening cycle? A simple musculoskeletal model undergoing stretch-shortening cycles was developed to explore how the storage of energy in the tendon depends on the mechanical properties of the tendon and the length of the muscle moment arm. It will be shown in this paper that for a given joint moment history the moment arm of the muscle–tendon complex is the most important determinant for energy storage in the tendon. Subsequently, we tested experimentally whether a relationship exists between the moment arm of the Achilles tendon and running economy.
|
MATERIALS AND METHODS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Under these assumptions, it is evident that joint moment equals MTU moment, and joint work equals MTU work. Changes in MTU length are a function of both joint angular displacement and moment arm of the MTU at the joint. During the stretch phase, work is done on the MTU (by gravity) and the MTU, as a whole, is lengthening; in this phase, energy can be stored in the tendon. During the subsequent shortening phase, the MTU does work while shortening; in this phase stored energy can be released from the tendon.
The mechanical behavior of a tendon has been described as a quadratic
spring (Rosager et al., 2002;
van Ingen Schenau, 1984) or a
linear spring with a quadratic toe region
(Hof, 1998). To accommodate
quadratic and/or linear spring characteristics, we adopted a generalized model
for a spring of nth order:
 | (1) |
If either F or u is known for a given tendon, tendon
energy (E) can be calculated as follows:
 | (2) |
 | (3a) |
 | (3b) |
 | (4) |
Inserting Eqn 4 into
Eqn 3b yields:
 | (5) |
In biomechanics, k is commonly parametrized in terms of the amount of
stretch at maximal CE force (i.e. van
Soest and Bobbert, 1993):
 | (6) |
Inserting Eqn 6 into
Eqn 5 yields the final equation:
 | (7) |
For a given Mj, Eqn 7 indicates the following: (1) the smaller the moment arm, the more energy is stored elastically; and (2) for any n, the energy stored in a tendon is more sensitive to moment arm than to mechanical properties of the tendon (lse0 and umax), as can be seen by the magnitude of the exponents. The lower the order of spring (n), the more pronounced this difference in sensitivity.
In summary, in a given musculoskeletal system, the amount of tendon energy storage during a given movement increases as lse0 and umax increase and as Fmax and r decrease. Reducing r, which results in a higher tendon force F (Eqn 4), is the most effective way to increase energy storage in the tendon.
Since joint work is assumed constant in the model, increased reutilization
of tendon energy reduces the amount of mechanical work that the CE has to
produce as well as the metabolic energy required to generate CE work. This is
expected to reduce overall metabolic energy cost of the movement because, in
terms of metabolic cost, generating CE work (concentric contraction) is the
most expensive mode of muscle functioning (i.e.
Ryschon et al., 1997).
In humans, the most prominent tendon in the leg is the Achilles tendon. Based on Eqn 7, it was predicted that runners with smaller moment arms of the Achilles tendon can run more economically. To test this prediction, the relationship between running economy and the moment arm of the Achilles tendon was determined in an experiment conducted with a group of experienced runners.
Experiment
Participants
Fifteen highly trained, healthy, male runners gave written informed consent
to participate in this study. All participants had been training for, and
participating in, regional, national and/or international running competitions
for several years. Thirteen participants reported their personal record (PR)
for 10 km, which was 33 min 52 s±3 min 22 s (mean± s.d.). Two
participants reported a PR of less than 30 min. Participant characteristics
are listed in Table 1.
|
This study was performed in accordance with the guidelines of the Declaration of Helsinki and was approved by the ethics committee of the Faculty of Human Movement Sciences, VU University Amsterdam, The Netherlands.
Running economy and 
O2,max
For each participant, running economy was determined as the rate of oxygen
consumption (O2)
per kg body mass when running at 16 km h–1. After several
minutes of habituation to the treadmill (STM-55; Schiller, Baar, Switzerland)
and warming-up, participants ran at 16 km h–1 on the level
for 5 min. For these participants, this was a submaximal task (see 10 km race
times, Table 1). Steady-state
oxygen consumption was recorded during the last minute of running using a gas
analyzer (Cardiovit CS-200 Ergo-Spiro; Schiller, Baar, Switzerland). After
determining anthropometrics (see below), the same setup was used to measure
maximum rate of oxygen consumption
(O2,max) using
an incremental protocol with increasing running speed and treadmill slope.
Moment arm of the Achilles tendon
By definition, the moment arm of the Achilles tendon is the shortest
distance from the line of action of the Achilles tendon to the center of
rotation of the ankle. The center of rotation of the ankle has been shown to
be located close to the midpoint of the line between the tips of the medial
and lateral malleoli (Lundberg et al.,
1989). To estimate the moment arm of the Achilles tendon in our
participants, we marked the malleoli and took standardized photographs of the
medial and lateral side of the foot: each participant was seated on a chair
with their left foot placed on a reference block (see
Fig. 1). The lateral edge of
the foot was aligned with the reference block; this way, the lateral malleolus
was in the same sagittal plane as the edge of the reference block, which
served as a scale object. The leg was positioned so that the anterior border
of the tibia was vertical. We established the vertical position using a spirit
level. The most prominent aspect of the tip of the lateral malleolus was
marked with a small dot of paint. Foot and leg were photographed from the
lateral side (SONY Cybershot W7; Minato, Tokyo, Japan). This procedure was
repeated for the medial side of the same leg; the medial edge of the foot was
aligned with the reference block, the anterior border of the tibia was
positioned vertically, the most prominent aspect of the tip of the medial
malleolus was marked and a photograph was taken. The horizontal distance from
the marked spot to the posterior aspect of the Achilles tendon was determined
on the picture, both on the lateral and on the medial side (Didge Image
Digitizing Software for Windows, courtesy of A. J. Cullum, Omaha, NE, USA).
The moment arm was taken to be the mean of these two distances.
|
We also measured body mass and height, calculated body mass index (BMI) and determined the following anthropometric variables on the left foot and leg of each participant: foot length (measured from the back of the heel to the tip of the longest toe); lower leg length (measured from the tip of the lateral malleolus to caput fibulae); lower leg circumference (determined using a tape measure) at various positions along the leg, including maximal lower leg circumference; and total leg length (measured from the ground to spina iliaca anterior superior).
A truncated cone model of the lower leg was constructed based on the length
of the lower leg and the circumferences of the lower leg at four points along
its length (Crompton et al.,
1996). Assuming a density of 1.1x103 kg
m–3, we derived lower-leg volume and lower-leg moment of
inertia for rotation about the center of mass in the sagittal plane from this
reconstruction.
Statistics
To analyze the relationship between running economy and the anthropometric
characteristics of the foot and lower leg, we calculated the Pearson
correlation coefficients between
O2 at 16 km
h–1 and all anthropometric variables. Partial correlation
(Draper and Smith, 1981) was
used to test and correct for possibly confounding anthropometric variables
that covaried with moment arm.
The relationship between moment arm and
O2 at 16 km
h1 was fitted with a non-linear model of the form
y=ax–2+b, which was derived from
the theoretical relationship between tendon energy and moment arm, assuming
n=1 (Eqn 7).
Inter- and intra-observer reliability for the determination of Achilles tendon moment arm from pictures of the ankle was assessed by comparing two measurements made by the same person several months apart as well as two measurements made by different people, using Pearson correlation.
|
RESULTS |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
|
|
|
|
|
|
DISCUSSION |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Qualitatively, this conclusion does not depend on the order of the spring, which has been reported to be purely quadratic or a combination of linear and quadratic. However, the effect is quantitatively stronger in a linear spring (n=1) than in a quadratic spring (n=2).
An experiment was conducted to test whether there was indeed a relationship
between Achilles tendon moment arm and running economy. Despite the fact that
a low-tech method was used to estimate the moment arm of the Achilles tendon
in vivo, the values we found for the moment arm of the Achilles
tendon are of similar magnitude to those found by Rugg et al. using magnetic
resonance imaging (MRI) data (Rugg et al.,
1990).
A strong relationship was found between running economy and the moment arm
of the Achilles tendon. This relationship was expected: a small moment arm is
associated with high tendon energy storage. Any energy stored in the tendon
does not have to be generated by the CE. Reducing CE energy generation is
expected to lead to lower metabolic cost, because energy generation by CE is
metabolically the most expensive process in muscle contraction. The total
metabolic energy consumption of a muscle, however, also depends on the amount
of force that is generated (Minetti and
Alexander, 1997), and muscle force is higher if the moment arm is
smaller. Nevertheless, we found that participants with small moment arms
required less energy per kg body mass to run at the speed of 16
ms–1. This indicates that inter-individual variations in
running economy were dominated by variations in the metabolic cost associated
with generating CE work not force.
Variations in moment arm explained 56% of the variation in running economy.
As in previous studies, a relationship was found between running economy and
foot length (Anderson, 1996)
and between running economy and BMI or lower-leg volume/moment of inertia
(Anderson, 1996;
Larsen et al., 2004). However,
we showed that these relationships were no longer significant after correcting
each variable (i.e. foot length, BMI, lower-leg volume, lower-leg moment of
inertia) for covariation with moment arm. This means that runners with smaller
moment arms tend to have lighter and more slender limbs
(Table 4) but a light and
slender build does not relate to better running economy if moment arm is held
constant (Table 5). Hence, the
reason for better running economy is mainly attributed to greater energy
storage in the tendon and not smaller leg-swing cost.
Unlike the model, which has a constant size and was shown to store more elastic energy with a relatively short moment arm (relative to all other linear dimensions), the participants in this study were not all of the same size. This must have caused variations in peak ankle moment, which together with muscle–tendon properties determines maximal tendon energy storage. Hence, elastic energy storage did not depend on moment arm length of the Achilles tendon alone. We expect that most of the variation in peak ankle moment can be attributed to the large differences in body mass between participants. To correct for differences in body mass and to bring out the empirical relationship between running economy and moment arm of the Achilles tendon even better, we can normalize moment arm by some linear dimension that correlates well with body mass. Height is an obvious choice: the correlation between height and body mass is very strong (r=0.91, P<0.001). Indeed, the relationship between running economy and moment arm, normalized by height, is stronger than the relationship between running economy and absolute moment arm (r=0.81, P<0.001 vs r=0.75, P<0.001).
Although we lack sufficient information to quantify tendon energy storage
in individual runners, we would like to get an idea regarding the magnitude of
the effect that a difference in moment arm has on metabolic energy consumption
using existing literature. To do so, we assumed that all the extra energy
stored in the tendon is useful and saves CE work and that the extra cost of
activating the triceps surae to generate tension can be ignored. Ker et al.
calculated that 35 J is stored in the Achilles tendon of a 70 kg man when
loaded with 4700 N, describing the tendon as a linear spring
(Ker et al., 1987). The
stiffness (k) of this tendon can be obtained from Eqn
3a,b.
If the moment arm was 10% smaller, force on the tendon would increase from
4700N to 5170N and, hence, energy storage would increase from 35 J to 42.4 J
(Eqn 3), an increase of 7.4 J or 21%. Storing an additional 7.4 J in the
Achilles tendon during every landing while running at 16 km
h–1, with 3 landings s–1
(Scardina et al., 1985),
reduces CE mechanical power requirement by approximately 22 W. Assuming a CE
mechanical efficiency of 25% (Cavagna and
Kaneko, 1977), metabolic power would be reduced by about 88 W.
Given a body mass of 70 kg and an energetic equivalent of 21 kJ
l–1 O2, this yields a difference of 4.2 ml
kg–1 min–1 in
O2. Hence, this
approximation shows that a 10% difference in moment arm of the Achilles tendon
alone can account for a 4.2 ml kg–1 min–1
difference in
O2. This is more
than 8% for a person with a
O2 of 50 ml
kg–1 min–1 at 16 km h–1.
For a 10% difference in moment arm, the predicted difference in
O2 compares
reasonably well to the differences observed in this study. Note that the
moment arm length in the group of runners who participated in the current
study varied by more than 10%, as did
O2
(Table 2).
We expect that some of the residual variation in running economy can be accounted for by inter-individual variations in peak joint moment, which was not measured in the current study. Runners with similar Achilles tendon moment arms might generate different peak ankle joint moments, as reflected by the magnitude of ground reaction forces and the point of application of the ground reaction force with respect to the ankle. Different peak ankle joint moments yield different amounts of tendon energy storage and, hence, differences in running economy. For future studies on running economy, we propose to measure not only the moment arm of the Achilles tendon but also the peak ankle moment so that the maximal amount of energy stored in the tendon can be calculated and related directly to running economy. Unfortunately, the necessary equipment to measure ankle moment during running was not available in the current study.
Peak ankle moment and running economy were measured in a recent study on
midsole stiffness (Roy and Stefanyshyn,
2006). In this study it was shown that running with a shoe with a
stiffer midsole was associated with increased peak ankle moment and improved
running economy. An underlying mechanism for this improvement in running
economy was not proposed by the authors. Based on the results of the current
study, we hypothesize that the stiff midsole, which was associated with a
significantly higher peak ankle moment, resulted in an improvement in running
economy because of increased energy storage in the Achilles tendon. Note that
Roy and Stefanyshyn used two types of alternative midsoles: `stiff' and
`stiffest' (Roy and Stefanyshyn,
2006). Only the stiff midsole resulted in an improvement of
running economy compared with using a normal midsole, the stiffest midsole did
not. It is beyond the scope of this study to speculate on possible causes for
this.
Aside from the positive effect on running economy, a small moment arm of
the Achilles tendon may have less desirable consequences. It has been shown
that a high peak joint moment in combination with a small moment arm of the
tendon [a low effective mechanical advantage (EMA)], compromises the safety
factor of the tendon (Biewener,
2005). The high tendon forces that occur due to a small moment arm
may increase the risk of tendon overuse or rupture or trigger adaptations of
the tendon that will enable it endure higher peak loads but may cause it to be
stiffer and, therefore, to store less energy for the same submaximal force.
This leads to two questions: (1) do runners with small moment arms have
different tendon properties from runners with large moment arms and (2) do
interactions between moment arm and tendon properties affect the proposed
theoretical relationship between moment arm and running economy?
The comparative literature suggests that there is little variation in the
tissue properties of tendons in different species so it is unclear what kind
of interactions, if any exist between joint moment, moment arm length and the
properties of the tendon (Bennett et al.,
1986; Pollock and Shadwick,
1994). However, even if there is an inverse linear relationship
between k and r, which implies that the tendon is stiffer in subjects
with smaller moment arms, it is advantageous to have a small moment arm. This
is seen by multiplying k by r–1 in
Eqn 6 and inserting into
Eqn 5, yielding E
proportional to r–1.
In summary, this study has established a causal relationship between the variation in running economy and the moment arm of the Achilles tendon. Smaller moment arms are associated with better running economy. This relationship was predicted based on a simple musculoskeletal model of tendon energy storage and was confirmed experimentally.
|
References |
|---|
|
TOPSummaryINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
|---|
Anderson, T. (1996). Biomechanics and running economy. Sports Med. 22,76 -89.[Medline]
Bailey, S. P. and Pate, R. R. (1991). Feasibility of Improving Running Economy. Sports Med. 12,228 -236.[CrossRef][Medline]
Bennett, M. B., Ker, R. F., Dimery, N. J. and Alexander, R. M. (1986). Mechanical-Properties of Various Mammalian Tendons. J. Zool. 209,537 -548.
Biewener, A. A. (2005). Biomechanical
consequences of scaling. J. Exp. Biol.
208,1665
-1676.
Billat, V., Demarle, A., Paiva, M. and Koralsztein, J. P. (2002). Effect of training on the physiological factors of performance in elite marathon runners (males and females). Int. J. Sports Med. 23,336 -341.[CrossRef][Medline]
Carrier, D. R., Heglund, N. C. and Earls, K. D.
(1994). Variable gearing during locomotion in the human
musculoskeletal system. Science
265,651
-653.
Cavagna, G. A. and Kaneko, M. (1977).
Mechanical work and efficiency in level walking and running. J.
Physiol. 268,467
-481.
Cavagna, G. A., Saibene, F. P. and Margaria, R.
(1964). Mechanical work in running. J. Appl.
Physiol. 19,249
-256.
Crompton, R. H., Li, Y., Alexander, R. M., Wang, W. and Gunther, M. M. (1996). Segment inertial properties of primates: new techniques for laboratory and field studies of locomotion. Am. J. Phys. Anthropol. 99,547 -570.[CrossRef][Medline]
di Prampero, P. E., Atchou, G., Brueckner, J.-C. and Moia, C. (1986). The energetics of endurance running. Eur. J. Appl. Physiol. 55,259 -266.[CrossRef]
Draper, N. R. and Smith, H. (1981). Applied Regression Analysis. New York: Wiley.
Franch, J., Madsen, K., Djurhuus, M. S. and Pedersen, P. K. (1998). Improved running economy following intensified training correlates with reduced ventilatory demands. Med. Sci. Sports Exerc. 30,1250 -1256.[CrossRef][Medline]
Heise, G. D. and Martin, P. E. (2001). Are variations in running economy in humans associated with ground reaction force characteristics? Eur. J. Appl. Physiol. 84,438 -442.[CrossRef][Medline]
Hof, A. L. (1998). In vivo measurement of the series elasticity release curve of human triceps surae muscle. J. Biomech. 31,793 -800.[CrossRef][Medline]
Holden, C. (2004). Peering under the hood of
Africa's runners. Science
305,637
-639.
Joyner, M. J. (1991). Modeling-optimal marathon
performance on the basis of physiological factors. J. Appl.
Physiol. 70,683
-687.
Ker, R. F., Bennett, M. B., Bibby, S. R., Kester, R. C. and Alexander, R. M. (1987). The spring in the arch of the human foot. Nature 325,147 -149.[CrossRef][Medline]
Kram, R. and Taylor, C. R. (1990). Energetics of running: a new perspective. Nature 346,265 -267.[CrossRef][Medline]
Kyrolainen, H., Belli, A. and Komi, P. V. (2001). Biomechanical factors affecting running economy. Med. Sci. Sports Exerc. 33,1330 -1337.[CrossRef][Medline]
Lake, M. J. and Cavanagh, P. R. (1996). Six weeks of training does not change running mechanics or improve running economy. Med. Sci. Sports Exerc. 28,860 -869.[Medline]
Larsen, H. B. (2003). Kenyan dominance in distance running. Comp. Biochem. Physiol. A Mol. Integr. Physiol. 136,161 -170.[CrossRef][Medline]
Larsen, H. B., Christensen, D. L., Nolan, T. and Sondergaard, H. (2004). Body dimensions, exercise capacity and physical activity level of adolescent Nandi boys in western Kenya. Ann. Hum. Biol. 31,159 -173.[CrossRef][Medline]
Lundberg, A., Svensson, O. K., Nemeth, G. and Selvik, G. (1989). The axis of rotation of the ankle joint. J. Bone Joint Surg. Br. 71,94 -99.[Medline]
Marsh, R. L., Ellerby, D. J., Carr, J. A., Henry, H. T. and
Buchanan, C. I. (2004). Partitioning the energetics of
walking and running: swinging the limbs is expensive.
Science 303,80
-83.
Midgley, A. W., McNaughton, L. R. and Jones, A. M. (2007). Training to enhance the physiological determinants of long-distance running performance? Can valid recommendations be given to runners and coaches based on current scientific knowledge? Sports Med. 37,857 -880.[Medline]
Minetti, A. E. and Alexander, R. M. (1997). A theory of metabolic costs for bipedal gaits. J. Theor. Biol. 186,467 -476.[CrossRef][Medline]
Modica, J. R. and Kram, R. (2005). Metabolic
energy and muscular activity required for leg swing in running. J.
Appl. Physiol. 98,2126
-2131.
Pollock, C. M. and Shadwick, R. E. (1994). Allometry of muscle, tendon, and elastic energy storage capacity in mammals. Am. J. Physiol. 266,R1022 -R1031.[Medline]
Rosager, S., Aagaard, P., Dyhre-Poulsen, P., Neergaard, K., Kjaer, M. and Magnusson, S. P. (2002). Load-displacement properties of the human triceps surae aponeurosis and tendon in runners and non-runners. Scand. J. Med. Sci. Sports 12, 90-98.[CrossRef][Medline]
Roy, J. P. R. and Stefanyshyn, D. J. (2006). Shoe midsole longitudinal bending stiffness and running economy, joint energy, and EMG. Med. Sci. Sports Exerc. 38,562 -569.[CrossRef][Medline]
Rugg, S. G., Gregor, R. J., Mandelbaum, B. R. and Chiu, L. (1990). In vivo moment arm calculations at the ankle using magnetic resonance imaging (MRI). J. Biomech. 23,495 -501.[CrossRef][Medline]
Ryschon, T. W., Fowler, M. D., Wysong, R. E., Anthony, A. and
Balaban, R. S. (1997). Efficiency of human skeletal muscle
in vivo: comparison of isometric, concentric, and eccentric muscle
action. J. Appl. Physiol.
83,867
-874.
Saunders, P. U., Pyne, D. B., Telford, R. D. and Hawley, J. A. (2004). Factors affecting running economy in trained distance runners. Sports Med. 34,465 -485.[CrossRef][Medline]
Scardina, N., Daniels, J., Vanhandel, P., Bradley, P. and Troup, J. (1985). Running cadence, stride length, ve and respiratory frequency during treadmill and track running at sea-level and altitude. Med. Sci. Sports Exerc. 17,249 -249.
van Ingen Schenau, G. J. (1984). An alternative view of the concept of utilisation of elastic energy in human movement. Hum. Mov. Sci. 3,301 -336.[CrossRef]
van Soest, A. J. and Bobbert, M. F. (1993). The contribution of muscle properties in the control of explosive movements. Biol. Cybern. 69,195 -204.[CrossRef][Medline]
Williams, K. R. and Cavanagh, P. R. (1987).
Relationship between distance running mechanics, running economy, and
performance. J. Appl. Physiol.
63,1236
-1245.
CiteULike 
Complore 
Connotea 
Del.icio.us 
Digg 
Reddit 
Technorati 
Twitter What's this?
This article has been cited by other articles:
|
|
 |
|
  S. S. M. Lee and S. J. Piazza Built for speed: musculoskeletal structure and sprinting ability J. Exp. Biol., November 15, 2009; 212(22): 3700 - 3707. [Abstract] [Full Text] [PDF]
|
|
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
