Eur J Appl Physiol (2002) 87: 17–27 DOI 10.1007/s00421-002-0582-8
O R I GI N A L A R T IC L E
Franc¸ois Cottin Æ Yves Papelier Æ Franc¸ois Durbin Jean P. Koralsztein Æ Ve´ronique L. Billat
Effect of fatigue on spontaneous velocity variations in human middle-distance running: use of short-term Fourier transformation Accepted: 3 January 2002 / Published online: 12 March 2002 Springer-Verlag 2002
Abstract Best performances in middle-distance running are characterized by coefficients of variation of the velocity ranging from 1% to 5%. This seems to suggest that running at constant velocity is a strain inducing an increase in physiological variables such as oxygen uptake. This study tested three questions. (l) Does velocity variability during a middle-distance all-out run increase with fatigue? (2) Does velocity variability alter the slow phase of the oxygen kinetic because of small spontaneous recoveries, compared with the same distance run at constant velocity? (3) Is a maintained average velocity over a given distance enhanced by a variable-pace rather than by a constant-pace? Ten long-distance runners performed two series of all-out runs over the distance (previously determined) which they could cover maintaining a velocity equal to 90% of that eliciting maximal oxygen consumption. In the first series (free-pace) the subjects were asked to run as fast as possible, without any predetermined velocity profile. In the second series, the same distance was covered at a constant velocity (equal to the average in the previous free-pace run), set by a cyclist
F. Cottin (&) De´partement des Sciences et Techniques en Activite´s Physiques et Sportives, Universite´ d’E´vry Val d’Essonne, Bd F. Mitterrand, 91025 E´vry Cedex, France E-mail:
[email protected] Tel.: +33-01-60876500 Fax: +33-01-60876505 Y. Papelier Laboratoire de Physiologie, Faculte´ de Me´decine Kremlin-Biceˆtre, Hoˆpital Antoine Be´cle`re, 92141 Clamart Cedex, France F. Durbin Commissariat a` l’E´nergie Atomique/Direction des Applications Militaires/Service E´quipements Instruments et Me´trologie, 91680 Bruye`res-le-Chatel, France J.P. Koralsztein Æ V.L. Billat Laboratory in Sport Sciences, Caisse Centrale des Activite´s Sociales d’E´lectricite´ et Gaz de France, 2 avenue Richerand, 75010 Paris. France
preceding the runner. Short-term Fourier transform was used to analyse velocity oscillations. Our results show that: (1) for all subjects, the mean energy spectrum did not change throughout the free-pace runs, suggesting that velocity variability did not increase with fatigue (2-way ANOVA, P=0.557); (2) the kinetic of oxygen uptake and its asymptote were not changed during the free-pace runs compared to the constant-velocity run; (3) performance was not significantly improved by free-pace average velocity [mean (SD) 4.22 (0.47) compared to 4.25 (0.52) mÆs–1 for constant and free-pace respectively, t=–0.58, P=0.57]. These results indicate that during middle-distance running, fatigue does not increase variations in velocity, and free-pace changes neither performance nor the oxygen kinetic. Keywords Spectrum analysis Æ Exercise Æ Running velocity variability
Introduction Fourier transform has commonly been used to analyse physiological responses to pseudo-random binary sequence work change (Hughson et al. 1990; Fukuba et al. 1999), acute exposure to simulated altitude (Yamamoto et al. 1996; Eisele et al. 1992) or to appreciate autonomic control of heart rate variability during exercise (Nakamura et al. 1993; Cottin et al. 1999). At the present time, no study has addressed the occurrence of spontaneous velocity changes with fatigue, using harmonic analysis. However, best performances in middledistance running are usually characterized by relatively large variability in velocity. If one considers indeed the last three world records for middle and long-distance running (1,500 m, 3,000 m, 5,000 m and 10,000 m), it can be noted that the range of coefficients of variation in velocity is 1%–5% (Billat 2001). Even if some studies have already tested the effects of pace variation on performance and physiological responses (Ariyoshi et al. 1979a, b; Foster et al. 1993, 1994), the physiological
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responses have not been examined in exercise where the velocity changes are spontaneous. On the other hand, it is well known that running at constant supra-critical velocity (critical velocity being defined as the horizontal asymptote of the velocity-time relationship) induces a continuous increase in oxygen uptake (V_ O2), heart rate and blood lactate concentration (Billat 2000). Even during an all-out run of 3–15 min, an increase in recruitment of types I and II muscle fibres could increase V_ O2 towards maximal oxygen uptake (V_ O2max). Therefore a spontaneous decrease in velocity around the 3rd min could prevent the development of the V_ O2 slow component (Whipp and Ozyenner 1998). Actually, above critical velocity, V_ O2 rises inexorably towards V_ O2max until fatigue occurs (Barstow and Mole´ 1991). The question arises as to whether the velocity variations become greater with fatigue, in response to metabolic changes occurring during free-pace middledistance runs (3,000 m) performed until exhaustion. Therefore, this study tested three questions: 1. Does velocity variability during a middle-distance allout run increase with fatigue? 2. Does velocity variability alter the slow phase of the oxygen kinetic because of small spontaneous recoveries, compared with the same distance run at constant velocity? 3. Is a maintained average velocity over a given distance enhanced by a variable pace rather than by a constant pace?
second test the distance limit (dlim90, the maximal distance run at constant-pace and at 90% of vV_ O2max), and the time limit (tlim90, the time required to run this distance), were determined. In the third test the subject performed a free-pace all-out run for dlim90. Thus, subjects performed both free- and constant-pace runs for dlim90. Therefore, it was possible to compare the velocity characteristics of constant- and free-pace runs. Data collection procedures Protocol of V_ O2max and vV_ O2max determinations The subjects were instructed to run initially at a velocity of 10 kmÆh–1, the velocity being increased by 1 kmÆh–1 every 2 min. These stages were separated by 30 s rests during which a capillary blood sample was taken from the finger pad and the lactate concentration was measured (YSI 27 analyser, Yellow Spring Instrument, Yellow Spring, Ohio). Measurements of V_ O2 were carried out throughout each test using a telemetric system (K4 b2, Cosmed, Rome, Italy) (McLaughlin et al. 2001). Expired gases were measured breath-by-breath and the results were averaged every 5 s. Before each test, the system for O2 analysis was calibrated using ambient air, whose O2 percentage was assumed to be 20.9%, and a gas of known CO2 percentage (5%) (K4 b2 instruction manual). The turbine flow-meter of the K4 b2 was calibrated using a 3 l syringe. During the incremental test, V_ O2max was defined as the highest V_ O2 measured. During this test, vV_ O2max was defined as the lowest velocity of running that elicited V_ O2max and was maintained for more than 1 min (Billat and Koralsztein 1996). If, during the last stage, an athlete reached a peak in V_ O2 but he could not maintain his run for at least 1 min, the velocity during the previous stage was considered as vV_ O2maxIf this velocity was maintained for more than 1 min, but less than 2 min, vV_ O2max was determined as the average of the velocities of the last and the previous stage [i.e. (1 kmÆh–1)/ 2=0.5 kmÆh–1] (Kuipers et al. 1985). Lactate threshold was defined as the V_ O2 value corresponding to the steeper point of the slope of the plasma lactate measurements, between 3.5 and 5 mmolÆl–1 (Aunola and Rusko 1984).
Methods Subjects Ten male long-distance runners [mean (SD)] [age 41 (10) years, height 175 (5) cm, body mass 71 (5) kg] took part in this investigation. They trained five times a week [70 (20) km a week]. The subjects were all long-distance runners training for the half-marathon. They were chosen as being without long-term planned strategies and to represent random unpredictable paces. Prior to their active participation all subjects provided voluntary written informed consent in accordance with the guidelines of the University. Experiment design Subjects were tested three times until exhaustion,. only one test being performed on any given day. All tests were performed on a synthetic 400 m track at the same time on non-windy days at temperatures ranging from 19 to 22C. On days between two tests, subjects were asked either to rest or to have a sedentary occupation. Prior to the tests, they were asked to refrain from consuming food or beverages containing caffeine. For the second test (see below), the runners followed a pacing cyclist travelling at the required velocity. The cyclist received audio beeps via a Walkman, the beep intervals determining the time required to cover the distance between visual indicators set at 20 m intervals along the track (inside the first lane). In the first test the V_ O2max, the velocity associated with the V_ O2max (vV_ O2max) and the velocity running at the lactate threshold were determined (Aunola and Rusko 1984; Billat et al. 1998). In the
Constant- and free-paces for the distance limit at 90% vV_ O2max The constant- and free-pace runs for the distance limit at 90% vV_ O2max (dlim90) were performed after 15 min of warming-up at 50% vV_ O2max and 5 min rest in order to reach baselines of V_ O2 and blood lactate concentrations. For the constant-pace runs, the subjects were instructed to follow a pacing cyclist travelling at 90% vV_ O2max, as previously determined. Subjects were asked to keep this pace for as long as possible. Thus, this procedure allowed us to determine tlim90 and dlim90. During the free-pace runs, the subjects were asked to optimize their performance for dlim90: they were neither informed of their velocity, nor could they use a watch. For each 20 m interval, the elapsed time was recorded using two moving timekeepers (chronometer Digisports Instruments, Seyssins, France) set exactly at the runner’s side, so avoiding parallax errors when crossing the marks on the track. Thereafter, these data were downloaded into a microcomputer. Since they were manually operated the two recordings were checked that they were similar. This was indeed always the case. Blood samples for lactate determination were collected after warm-up and at 1, 3 and 5 min following exercise. The highest of these values was taken as the maximal blood lactate value for each test. Data processing V_ O2 kinetic As suggested by Barstow and Mole´ (1991) and Barstow (1994), the V_ O2 kinetic was fitted using a double exponential function as follows:
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V_ O2 ðtÞ ¼ V_ O2base þ uðt;d1 Þ A1 1 eðtd1 Þ=s1 þ uðt;d2 Þ A2 1 eðtd2 Þ=s2
ð1Þ
where V_ O2(t) is the oxygen uptake at time t, V_ O2base is the oxygen uptake at the onset of exercise, after the warm-up, A1 and A2 correspond to the amplitude of the V_ O2 of the fast (1) and slow (2) components respectively, d1 and d2 are the time delays before the onsets of components 1 and 2 respectively, u(t, d1 or d2) are the step functions in which t and di are the arguments of the function [u(t, d1 or d2) are equal to 0 for t=d1 or t>=d2 respectively] and s1 and s2 correspond to the time constants of the two components respectively. Estimates of the time constants were determined by examination of the shape of the experiment V_ O2max-time curve. Sigma Plot (SPSS, Chicago, Ill.) was used to determine the best-fit estimates of each parameter. Computation of the time limit at V_ O2max during constantand free-pace for dlim90 Time to attain V_ O2max (TAV_ O2max) during dlim90 was computed according to the method previously described in Billat (2000). Oxygen consumed The aerobic component of the overall energy requirement for dlim90 runs was computed by integrating the area under the curve V_ O2 against time until exhaustion. The integral of Eq. 1 was calculated using Mathcad 8 Pro software (MathSoft, Cambridge, Mass.) (Bearden and Moffatt 2000). Running time analysis During the free-pace runs, the time (ti) required to cover the distance between two interval marks was precisely recorded. The interval marks were all spaced 20 m (Dd) apart. The velocity of running (vi) between two successive interval marks was thus computed as vi=Dd/Dti. Successive vi compared to the distance run for the ten subjects are shown in Fig. 1. Also shown in Fig. 1 are the velocity oscillations over each 20 m interval throughout a 1,280 m run. The average velocities over successive 200 m stretches (SD) were also computed and are given on the same plot. So, it is possible to illustrate alterations in the average or the SD of velocities of running over 200 m stretches. However, this type of analysis does not give any information about the distance-frequency (per metre) variations in velocity of running. Consequently, to obtain further information about velocity variability throughout the running test, we performed spectrum analysis on these specific signals (velocity compared to distance).
Spectrum analysis The fast Fourier transform (FFT) can be used to reveal potential main spectrum harmonics of the velocities of running. However Fourier analysis on a sampled signal is only suitable for stationary signals. A signal is considered stationary when its spectrum does not depend upon the time of analysis. In the present study, we have a priori no information about signal stationarity. Therefore, it seems more suitable to replace simple FFT by short-term Fourier transform (STFT). This signal processing method was first proposed by Gabor (1946). The main principle of STFT consists in choosing a sufficiently small analysis window in which the signal can be considered stationary. Classical FFT can thus be performed on this windowed signal. The same analysis window is applied to another signal block. The STFT consists of all the FFT performed on successive signal blocks that are determined by regular translation of the chosen window (Fig. 2). In the usual case, STFT yields
a 3-dimensional figure called a spectrogram which is a timefrequency analysis (procedure described in a previous study by Cottin et al. 2001). In the present study, the distance run was the only regularly sampled variable as a replacement for time in usual FFT. The signal analysed was the velocity (vi=Dd/Dti) series compared to the distance run. Thus, the three axes of the computed spectrograms were the following: 1. x-axis: distance (metres) 2. y-axis: distance-frequency (per metre) 3. z-axis: spectrum power (metres cubed per second squared) Spectrogram design In principle, FFT only applies to entire discrete signals or signal blocks of n=2n points. In the present study, the initial block comprised the first 32 points. Other blocks were determined by successive 2 point shifts (2 · Dd=40 m). The last signal block was determined when the last point was reached (the 64th). As a result the whole signal of 64 points was divided into 17 blocks of 25=32 points and the spectrogram yielded by these 17 signal blocks consisted of 17 spectra: FFT1, FFT2,. . . FFT17 (Fig. 2). Spectrum limits A usual FFT (i.e. given ordinate compared to time) shows the number of spectrum harmonics as equal to half of the number of points sampled (2n/2). The sharpness of the analysis (time interval between two harmonics) is equal to: fmin ¼ 1=T
where T ¼ Dt 2n
ð2Þ n
and T being the total period corresponding to the chosen 2 points sampled at Dt. The upper frequency limit of a spectrum analysis is given by the Shannon sampling theorem. The rule that ‘‘All the information in a signal, band-limited to a frequency of fmax, can be captured in its samples taken at rates greater than 2fmax’’, is known as Shannon’s sampling theorem. The critical frequency fmax is known as the Nyquist rate: fmax ¼ 1=2Dt
ð3Þ
where Dt is the sampling interval. In the present study the unit of signal, the abscissa, is a distance (metre) instead of time. So: D ¼ Dd 2n ¼ 20 64 ¼ 1280 m
ð4Þ
where Dd is the sampling interval (metres) and D the total distance (metres). Each spectrum consists of (25)/2=16 harmonics and the sharpness unit of the analysis is equal to: fmin ¼ 1=D ¼ 1=1; 280 0:0008 m1
ð5Þ
The upper limit frequency is equal to: fmax ¼ 1=2Dd 0:025 m1 ð1=40 mÞ
ð6Þ
Windowing To avoid major spectrum artefacts due to sampled signal data framing by a rectangular window (Gabor 1946), a Hanning window was applied to the signal. Each signal block of 32 points was multiplied by the corresponding value of the Hanning window prior to computing Fourier spectra (Fig. 2). Spectrum energy Parseval’s theorem states that spectrum energy (ES) of a signal is not dependent on its representation (for instance either ordinate compared to time or compared to frequency), but is equal to signal
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21 variance. Thus, if velocity variability increases with distance (and presumably fatigue), then ES or signal variance of the windowed blocks will increase by the same amount. To answer the question whether ES increases with the distance run, it is necessary to compute all spectrum areas for each subject. The greater these values, the greater are the velocity variations. The areas (ES0, ES1,. . .ES16 ) under each spectrogram spectra were then computed by the following relationship: ESk ¼ Dd
nX ¼16
PSDi
ð7Þ
i¼1
where ESk corresponds to the ES computed for the 20 m between intervals 2k and 2k+32Dd (k being an integer ranging from 0 to 16), PSDi to spectrum power density of harmonic i, and Dd to distance interval (sampling) (Fig. 3). Statistical analysis The results are presented as mean (SD). A Student’s t-test for paired data was used to compare the performances of subjects (i.e. the average velocity maintained for dlim90) and the physiological responses in constant- versus free-pace runs (Table 1). Three 2-way ANOVA were performed (Table 2). Independent variables were the subjects and the distance run. Dependent variables were: 1. The average velocity of running over every 200 m interval 2. The standard deviation (SD) of these average velocities of running 3. Total ES of spectrograms each containing 17 spectra (spaced 40 m apart) in the variable-pace run Significant differences were identified using Tukey’s test. Statistical significance was set at P
