Where y0 is the baseline V̇o2 (ml·min−1), A1 and A2 are the asymptotic amplitudes for the exponential terms (ml·min−1), τ1 and τ2 are the time constants (minutes), and TD1 and TD2 are the time delay from the onset of exercise (seconds).
The Cr was evaluated during the steady state of oxygen uptake, 30 seconds before its end. The equivalent energetic of lactate (EEL) was equal to 3 mLO2·kg−1·mmol−1·L−1 (6), this value was added to C in order to estimate the contribution of the anaerobic pathway (C + EEL).
Cr was calculated during the 2000-meter run, the warm-up, and the recovery run. V is the average velocity respectively measured with the Optojump during the 2000-meter run, the warm-up, or the recovery run. M is the body mass.
V̇o2max was defined as V̇o2max obtained during the 2000-meter run. This value was expressed in mL·kg−1·min−1 and was only used to give information about the physical characteristics of the runners (Table 1).
Stiffness (Kleg and Kvert.)
From recording the vertical and horizontal forces, the maximal vertical ground reaction force (VGRF) and horizontal ground reaction force (HGRF) were determined. Vertical displacement of the body's center of mass (ΔZ; Figure 1) was also determined from vertical force records. Vertical acceleration during ground contact was first calculated from the following equation:
where Fz(t) is the VGRF during stance, BW is body weight, and M is body mass. Double integration of az(t) with respect to time provided an estimate for the displacement of the center of mass during ground contact (7). It was assumed that the vertical velocity of the center of mass was 0 at the time of peak force. Thus, it was assumed that the peak vertical force coincides with the peak center of mass displacement (10).
Leg spring stiffness, kleg, was determined by the following equation:
ΔL represents the maximum vertical deformation of the leg spring, L0 is the resting leg length, θ0 is the angle swept by the leg spring during the first half of the stance, and V is the running speed in m·s−1 (Figure 1).
The effective vertical stiffness of the leg spring was calculated from the following:
It is important to note that Kleg represents the total stiffness of the runner during stance, whereas Kvert describes the vertical compliance of the running gait (21).
The effect of fatigue was determined by repeated-measures analysis of variance. Relationships between the Cr and the stiffness were determined by standard linear regression and tested using a Spearman test. The significance level was set at p ≤ 0.05.
Fatigue Effects on the Stiffness of the Runner
All the mechanical parameters remain constant when they are measured before and just after the exhaustive 2000-meter run (Table 2). These results show that, on track, rather a significant change between the warm-up, the exercise, and the recovery, fatigue had no significant influence on mechanical parameters such as VGRF, HGRF, Kleg, and Kvert.
Similarly, SR, SL, CT, FT, and the running speed are not modified (Table 3).
The 2000-meter run was performed to the best capability of each runner, and the mean performance obtained was 6 minutes, 33 seconds ± 33 seconds. Table 3 shows that Cr increases significantly after the 2000-meter run. Indeed, after the exhaustive exercise, Cr is 11% higher than during the warm-up. These changes in Cr are accompanied by a significant increase in respiratory frequency and ventilation (V̇E) (P ≤ 0.05).
Relationship Between Energy Cost, Stiffness, and Other Mechanical Parameters
Figure 3A shows that during the 2000-meter run, Kleg correlates with Cr (r = −0.67 and P ≤ 0.05). Before and after the run, Kleg does not correlate with Cr (Figure 3B and C) However, Kvert does not correlate with Cr (r = −0.04; P = 0.93).
The purpose of this study was to measure the effect of fatigue on the spring-mass characteristics. The results obtained show that stiffness remains constant after an exhaustive 2000-meter run. Moreover, leg stiffness was significantly correlated with energetic cost of running but only during the 2000-meter run.
In regard to the literature, only one study has measured the effect of exhaustion on Kleg and Kvert. Dutto and Smith (10) have shown that Kleg and Kvert decrease significantly from 9.3 to 9.0 kN·m−1 for Kleg and from 23.9 to 23.1 kN·m−1 for Kvert. The main result of the present study shows that Kleg and Kvert remain constant after the exhausting run. These differences can be explained by the methods used. First, these authors measured Kleg and Kvert every 5 minutes throughout an exhaustive treadmill exercise. In the present work, stiffness was measured before and just after the exhaustive run performed on the track. Second, the exercise duration was not the same. In our study, this duration was only 6 minutes ± 33 seconds rather than in the study of Dutto and Smith (10) in which this duration was about 57 ± 19 minutes. Six minutes of exercise may be not long enough and does not induce enough eccentric contraction to modify the elastic properties of the leg muscles for trained runners. Indeed, in their study, Dutto and Smith showed that the modification of stiffness appears at around 14 minutes of exercise. However, they did not make any measure of the stiffness between the beginning and the 14th minute of exercise. Third, during treadmill running compared to overground running, specific mechanical adaptations may occur, especially at the end of an exhaustive exercise (11,15,28). These adaptations may concern the step rate and particularly the amplitude of the vertical displacement of the center of mass (28). On a treadmill, the subjects favored a type of running that provided them with a higher level of security. A variation in these parameters between the treadmill and the track, especially in a state of fatigue, could influence the stiffness of the runner (13). Thus, on a track, the effects of fatigue on stiffness may be different from those observed on a treadmill. Indeed, on a treadmill, studies on the effect of fatigue on the stride mechanical parameters show that fatigue induces an increase in the SL and a decrease in the SR. This increase is associated with an increase in the CTr (1,4,15,25). On a track, studies suggest that few mechanical modifications appear at the end of an exhaustive exercise and that they would allow the intensity of the exercise to be maintained (12,25,26,30). Our results confirm these results, showing that for trained runners, no change due to fatigue in SR, SL, or other mechanical parameters is observed on a track. However, no study has directly measured the differences between treadmill running and track running in a fatigued state.
Concerning the increase in Cr after the exhaustive exercise, this increase may be explained by an increase in V̇E and the regeneration of the store of the high-energy phosphate and the transformation of the blood lactate, accumulated during the exercise, in glycogen, CO2, and H2O (5). However, the mechanical parameters do not explain this increase.
Several studies (8,9,17,19,27,29) have observed a direct relationship between lower extremity flexibility and the aerobic demand of running. These studies suggested that stiffer individuals gain more benefit from passive elastic mechanisms than less stiff individuals and thus incur lower energy cost. An extreme case was highlighted by McMahon et al. (20) when they examined the mechanics and the aerobic demand of a runner with exaggerated hip and knee flexion during stance (i.e., Groucho running). The effective vertical stiffness was reduced and the Cr increased by as much as 50%. Researchers argued that the increase in Cr was due to the fact that the subjects used additional muscle force by deliberately overflexing the knees. Although the stiffness was not artificially decreased in the present study, the inverse relationship found between Kleg and Cr would support the hypothesis of McMahon et al. (20) and other researchers (9,17).
However, this relationship was only significant when Cr and Kleg are measured during the exhausting exercise. Surprisingly, Cr and Kleg do not correlate before or after the exhaustive exercise. This result demonstrated that the inverse relationship between Cr and Kleg may depend on the running velocity. Indeed, the 2000-meter run was performed at a velocity near that associated with the velocity that elicits V̇o2max rather than the velocity of the warm-up and the recovery, which was 30% lower (70% of the average speed of the 2000-meter run). During constant-load cycling or running exercise of supralactic threshold intensity, a slow increase in oxygen uptake (V̇o2) has been shown to appear after the third minute of exercise (2,14). This phenomenon is called the V̇o2 slow component and induces an increase in the Cr within the third minute and the end of the exercise. A number of physiological factors have been postulated as contributing to this increase in Cr. However, biomechanical factors have received less attention in the literature. Recently, Borrani et al. (4) showed that the increase in Cr in running is not due to the change in the external mechanical cost under the effect of fatigue. However, change in global mechanical descriptors (e.g., SR and CT) suggested that lower limb stiffness may be associated with the increase in Cr during a supralactic threshold exercise. In the present work, the inverse relationship between Kleg and Cr reported only during the 2000-meter run gives some support to the Borrani et al. (4) hypothesis. However, in the present study, no increase in Cr was measured between the third and last minute of exercise.
To conclude, the increase in Cr after an exhaustive 2000-meter run without an increase in Kleg or Kvert showed that, during overground running, the increase in Cr did not result partly from a change in the stiffness of the runner. However, the inverse correlation between Cr and Kleg observed during the 2000-meter run and not before or after this exercise suggested that the stiffness of the runner may be not associated with the Cr as previously suggested. The runner's stiffness measured with the spring-mass model cannot be identified as a discriminating parameter of running economy.
Running performance over a mile or 3000 meters depends on the capacity of the best athletes to keep a running style unchanged until the end of the race. Indeed, runners who demonstrated stable running styles were able to run longer during an exhaustive exercise performed at the maximal aerobic speed (15). So technical training in a fatigued state could be interesting.
The relationship between the stiffness and Cr during supralactic threshold exercise observed in the present study allows for the hypothesis that an increase in a runner's stiffness can induce an improvement in Cr. A decrease in Cr leads to an improvement of the endurance running performance. From a practical point of view, an increase in a runner's stiffness is associated with two main types of training. The first one is the technique of running and especially in a fatigued state. The technical training can be included during the usual interval training session performed at the anaerobic threshold or at the maximal aerobic speed. For example, in order to increase stiffness, the runner can perform an interval training session with a greater SR (e.g., 3-3.2 Hz) and a lower SL (in order to conserve the same running speed) than usual. The second one is plyometric training (27). These authors have demonstrated that a 6-week plyometric training program led to an increase in lower leg musculotendinous stiffness. This increase generates an improvement in Cr and in 3-km running performance. This training consists of various jumps, bounds, and hops in both horizontal and vertical planes (e.g., squat jump, double leg jump, alternate leg jump, double leg hurdle jump).
The authors gratefully acknowledge the French Athletics Federation and the French Ministry of Sport for their financial support. They also thank Jean-Michel Levêque for his help in editing the manuscript.
1. Avogadro, P, Dolenec, A, and Belli, A. Changes in mechanical work during severe exhausting running. Eur J Appl Physiol
90: 165-170, 2003.
2. Billat, V, Richard, R, Binsse, V, Koralsztein, JP, and Haouzi, P. The V(O2) slow component for severe exercise depends on type of exercise and is not correlated with time to fatigue
. J Appl Physiol
85: 2118-2124, 1998.
3. Blickhan, R. The spring-mass model for running and hopping. J Biomech
22: 1217-1227, 1989.
4. Borrani, F, Candau, R, Perrey, S, Millet, GY, Millet, GP, and Rouillon, JD. Does the mechanical work in running change during the V̇o2
slow component? Med Sci Sports Exerc
35: 50-57, 2003.
5. Borsheim, E and Bahr, R. Effect of exercise intensity, duration and mode on post-exercise oxygen consumption. Sports Med
33: 1037-60, 2003.
6. Candau, R, Belli, A, Millet, G, Georges, D, Barbier, B, and Rouillon, JD. Energy cost and running mechanics during a treadmill run to voluntary exhaustion in humans. Eur J Appl Physiol Occup Physiol
77: 479-485, 1998.
7. Cavagna, GA. Force platforms as ergometers. J Appl Physiol
39: 174-179, 1975.
8. Craib, MW, Mitchell, VA, Fields, KB, Cooper, TR, Hopewell, R, and Morgan, DW. The association between flexibility and running economy in sub-elite male distance runners. Med Sci Sports Exerc
28: 737-743, 1996.
9. Dalleau, G, Belli, A, Bourdin, M, and Lacour, JR. The spring-mass model and the energy cost of treadmill running. Eur J Appl Physiol Occup Physiol
77: 257-263, 1998.
10. Dutto, D and Smith, G. Changes in spring-mass characteristics during treadmill running to exhaustion. Med Sci Sports Exerc
34: 1324-1331, 2002.
11. Elliott, BC and Blanksby, BA. A cinematographic analysis of overground and treadmill running by males and females. Med Sci Sports Exerc
8: 84-87, 1976.
12. Elliott, BC and Roberts, AD. A biomechanical evaluation of the role of fatigue
in middle distance running. Can J Appl Sports Sci
5: 203-207, 1980.
13. Farley, C and Gonzalez, O. Leg stiffness
and stride frequency in human running. J Biomech
29: 181-186, 1996.
14. Gaesser, G and Poole, D. The slow component of oxygen uptake
kinetics in humans. Exerc Sports Sci Rev
24: 35-71, 1996.
15. Gazeau, F, Koralsztein, JP, and Billat, V. Biomechanical events in the time to exhaustion at maximum aerobic speed. Arch Physiol Biochem
6: 1-8, 1997.
16. Gleim, GW, Stachenfeld, NS, and Nicholas, JA. The influence of flexibility on the economy of walking and jogging. J Orthop Res
8: 814-823, 1990.
17. Heise, G and Martin, P. “Leg spring” characteristics and the aerobic demand of running. Med Sci Sports Exerc
30: 750-754, 1998.
18. Komi, P. Stretch-shortening cycle: a powerful model to study normal and fatigued muscle. J Biomech
33: 1197-1206, 2000.
19. McFarlane, D. Automated metabolic gas analysis system. Sports Med
31: 841-861, 2001.
20 McMahon, T, Valiant, G, and Frederick, E. Groucho running. J Appl Physiol
62: 2326-2337, 1987.
21. McMahon, TA and Cheng, GC. The mechanics of running: how does stiffness
couple with speed? J Biomech
22. Morin, JB, Dalleau, G, Kyröläinen, H, Jeannin, T, and Belli, A. A simple method for measuring stiffness
during running. J Appl Biomech
21: 167-80, 2005.
23. Nicol, CK, Komi, PV, and Marconnet, P. Fatigue
effects of marathon running on neuromuscular performance. I. Changes in muscle force and stiffness
characteristics. Scand J Med Sci Sports
1: 10-17, 1991.
24. Noakes, TD. Physiological models to understand exercise fatigue
and the adaptations that predict or enhance athletic performance. Scand J Med Sci Sports
10: 123-125, 2000.
25. Siler, W and Martin, P. Changes in running pattern during a treadmill run to volitional exhaustion: fast versus slower runners. Int J Sport Biomech
7: 12-28, 1991.
26. Slawinski, JS and Billat, VL. Changes in internal mechanical cost during overground running to exhaustion. Med Sci Sports Exerc
37: 1180-1186, 2005.
27. Spurrs, RW, Murphy, AJ, and Watsford, ML. The effect of plyometric training on distance running performance Eur J Appl Physiol
89: 1-7, 2003.
28. Wank, V, Frick, U, and Schmidtbleicher, D. Kinematics and electromyography of lower limb muscles in overground and treadmill running. Int J Sports Med
19: 455-461, 1998.
29. Williams, K and Cavanagh, P. Relationship between distance running mechanics, running economy, and performance. J Appl Physiol
63: 1236-1245, 1987.
30. Williams, K, Snow, R, and Agruss, C. Change in distance running kinematics with fatigue
. Int J Sport Biomech
7: 138-162, 1991.
Keywords:© 2008 National Strength and Conditioning Association
fatigue; stiffness; oxygen uptake; biomechanics