CMNE/CILAMCE 2007 Porto, 13 a 15 de Junho, 2007 © APMTAC, Portugal 2007
USE OF THE CONTINUOUS WAVELET TRANSFORM TO CHARACTERIZE THE 30S MAXIMAL TEST IN SWIMMING Leandro Machado1*, Susana Soares2 e J. Paulo Vilas-Boas1, 2 1: Laboratório de Biomecânica Faculdade de Desporto Universidade do Porto Rua Dr. Plácido Costa, 91 – 4200.450 Porto, Portugal e-mail:
[email protected] 2: Gabinete de Natação Faculdade de Desporto Universidade do Porto Rua Dr. Plácido Costa, 91 – 4200.450 Porto, Portugal e-mail: {susana,jpvb}@ fade.up.pt
Key words: Continuous wavelet transform, fatigue thresholds, swimming, velocimetry Summary. A total of 72 swimmers of different maturational status performed a 30s maximal test in front crawl swimming, while their instantaneous speed was being recorded by a cable speedometer. The data treatment begun by the removal of the start, glide and final (wall arrival) phases of the velocity/time curve, performing than a continuous wavelet transform of the remaining signal. It was possible to discriminate two, or more, regions of different spectral content in the instantaneous velocity curve. To the points delimiting those regions, we loosely call fatigue thresholds. To confirm the validity of those fatigue thresholds, a periodogram was computed for each interval upon which the test was divided. Most of the swimmers displayed one or two fatigue thresholds. It was found that the younger swimmers presented more thresholds than the older ones.
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
1. INTRODUCTION The knowledge of the possible existence of a threshold, in time, between dominant participation of alactic and lactic anaerobic energy production systems during short time maximal efforts, is determinant for the anaerobic training planning and control. Moreover, despite a possible theoretical acceptance of this threshold, its application to practical situations is not trivial, due to the lack of a practical and feasible test to assess it. A solution for this inconvenience may be searched on the mechanical response to maximal exertions. Some attempts have been made to compute the anaerobic power and capacity, namely by the use of maximal short efforts. The Wingate test [1], a well known anaerobic evaluation tool, is unfortunately poorly adequate for swimmers, as this is a land test, consequently far from the swimming reality. Even further, it seems that, in short time efforts, the fatigue is more related to neurological and local muscular contraction inhibition factors, than to a reduced capacity of a metabolic pathway. Nonetheless, much more investigation is needed in this area. The purpose of this work was to determine fatigue thresholds from a short time maximal effort, based on the mechanical outcome of the fatigue, namely through the frequency content of the instantaneous velocity, and irrespective of its physiological origin. The wavelet transforms are well known for their uses in signal and image processing [2]. The continuous wavelet transform is used to compute the ‘local’ frequency content of a signal and, in this way, it seems to be a valuable tool to assess the fatigue thresholds present in a velocimetric signal. 2. METHODS A total of 72 swimmers (see characteristics on Table 1) performed a 30s maximal front crawl test, while their instantaneous speed was recorded by a cable speedometer developed by our investigation group [3]. For the older swimmers, the 30s test has been replaced by a 50 meter swim to avoid turning.
n Age (years) Weight (kg) Height (cm) Training
Pre-pubertal Males Females 13 13 9.42±0.82 8.45±0.94 34.20±7.21 28.20±3.22 136.47±4.73 131.33±4.84 Pre-competitive level
Pubertal Males Females 9 9 13.51±0.65 12.63±0.98 55.28±7.04 47.47±5.66 165.53±8.06 160.00±5.18 Regional level
Post-pubertal Males Females 14 14 18.18±2.35 16.54±2.35 69.88±7.03 58.47±7.22 176.27±7.49 165.80±3.32 National level
Table 1. Training level and anthropometric characteristics (mean±SD) of the swimmers.
The individual instantaneous velocity curves corresponding to each swimmer total
2
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
effort time were collected with LabView (Figure 1), and the data was exported to a text file. Data treatment was performed offline using a MatLab routine. The first step consisted in removing the start, glide and final (wall arrival) phases of the velocity curve, as in these phases the swimmer was not actively swimming, i.e., moving the upper and lower limbs in the required way (Figure 2).
Figure 1. Typical velocity curve, as plotted by LabView.
Figure 2. Removing the start, glide and final (wall arrival) phases of the velocity curve. Only the signal between the arrows was considered for further analysis.
The data analysis proceeds by performing a continuous wavelet analysis on the selected signal, through the MatLab routine CWT. To have a better readability of the results from the continuous wavelet transform, instead of presenting a colour coded contour plot, the program presents six contour plots, each at a different fractional height of the wavelet coefficient with maximum amplitude, usually at 40%, 50%, 60%, 70%, 80% and 90% of maximum amplitude (Figure 3). Each of these contour plots has the time in the horizontal axis and the pseudo-frequency in the vertical axis, since wavelets do not have a single well determined frequency. By visual inspection of these contour plots, it is possible to discriminate several time regions with markedly different frequency behaviour, as well as to determine the instant of time separating those regions (Figure 3). In summary, from the wavelet results it is possible to discriminate one, or more, points separating regions (time intervals) of 3
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
different spectral characteristics. To these points we loosely call “fatigue thresholds”.
Figure 3. Contour plots resulting from the continuous wavelet transform of the velocity curve in Figure 2. The arrows mark the position of the boundary between two different spectral content regions.
And why to name these boundary points “fatigues thresholds”? The main reason is because the instantaneous velocity curve has changed its behaviour and the cause for this was a different swimming strategy being performed by the swimmer. As will be seen later, the swimmer starts by swimming accordingly to the rules, with several direction changes of the underwater hand movement, giving rise to several peaks per stroke in the velocity curve (the stroke is the time it takes for a hand to enter the water, do the underwater movements, leave the water, recover, and enter in again); when the swimmer gets tired, the velocity curve displays only two peaks per stroke, suggesting that the swimmer is doing more rectilinear underwater hand movements. The likelihood of the determined point(s) was tested by visual inspection of the velocity behaviour in the selected different frequency content regions (Figure 4). Sometimes this visual procedure was enough to withdraw one or more points and, in this case, the wavelet contour plots were again inspected and new fatigue threshold points considered. In the case being presented in Figure 4, it is obvious that something happened to the velocity pattern in the interval around 14 to 16s. We see that the amplitude of the velocity fluctuations and the maximum velocity per stroke both decrease with time, and that the high frequency features of the velocity curve also disappear to the end of the test. We further see that these changes are more marked around the selected fatigue threshold.
4
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
As it was apparent from the contour plots of Figure 3, it is not possible with the wavelet analysis to get the exact location of the fatigue threshold; we can only obtain a region of changing behaviour in the frequency content, and the corresponding region of changing behaviour in the velocity curve. This was not an unexpected feature, since the swimmer will adjust the swimming technique accordingly to the fatigue felt, or installed, and the adjustment is not instantaneous, but rather takes a certain interval of time.
Figure 4. Part of the velocity curve in Figure 2 that was considered for analysis, with a vertical line marking the fatigue threshold at t=14s.
Upon accepting the fatigue thresholds, the analysis proceeds by computing a periodogram for each of the different regions. Each of these periodograms was normalized to its own maximum amplitude value, and all the normalized periodograms were displayed in a single graph, in order to allow a visual comparison of them (Figure 5). A visual inspection of the periodograms allows us to consider the previously discriminated points as valid fatigue thresholds when the frequencies values of the main lobes, and the respective amplitudes, were markedly different between regions (time intervals). Otherwise, a new analysis of the wavelets contour plots is made and the process is repeated once more.
Figure 5. Normalized periodograms for the two different regions separated by the fatigue threshold of Figure 4. Horizontal lines corresponding to attenuations of 5, 10 and 15dB from maximum amplitude are displayed.
5
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
A text file with the frequencies of the lobes with attenuation between 0 and 5dB from the main lobe, and also of those lobes with attenuation between 5 and 10dB, is created by the program. These frequencies were statistically analyzed between consecutive regions and were found to be statistically different in some cases. A final output consisted in the mean profiles for the velocity per stroke in each of the regions (Figure 6). As anticipated while discussing the term “fatigue threshold”, following the continuous wavelet transform computation, at the beginning of the 30s maximal test the swimmer has a more complex movement of the propulsive segments in the underwater phase, which leads to several phases of acceleration, resulting in the existence of more marked peaks in the velocity/time profile per stroke, and also in a higher mean velocity per stroke. By the end of the test, when fatigue is installed, the underwater hand movements become more rectilinear, there are fewer acceleration peaks in the velocity profile, and lower value for the mean velocity per stroke.
Figure 6. Mean profiles for the velocity per stroke – solid line – and instantaneous standard deviation – vertical lines. The left panels refer to the mean profile for the initial strokes, while the right ones represent that for the final strokes. The top panels refer to the strokes of the right arm, and the bottom ones to the left arm.
6
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
3. RESULTS As can be seen in Table 2, most of the swimmers presented two fatigue thresholds, irrespective of their maturational status. We also see that the older the swimmers are, the fewer thresholds they display. The term “fatigue thresholds” may apply with property to one or two thresholds, but it may hardly be correct for three or more thresholds. The existence of multiple thresholds for the pre-pubertal group may be related with coordination problems associated with the low level of swimming practice and proficiency of these swimmers; they were only trying their best to get to the other side of the swimming pool. Group Number of fatigue thresholds
pre-pubertal
pubertal
post-pubertal
One
1
5
10
Two
16
12
18
Three
8
1
0
Four
1
0
0
Table 2. Distribution of the subjects per maturational group and number of fatigue thresholds Frequency of the main lobe (Hz) Number of fatigue thresholds One
, +, #
*
a
st
nd
1 interval
2
4.58±0.71*
2.67±0.78*
+
Two
2.23±1.74
Three
2.68±2.37
interval
2.08±0.85
+,#
3.05±1.54
rd
3 interval
1.76±0.56
th
4 interval
#
2.33±1.03
1.76±1.04
statistically different
Table 3. Frequency of the main lobe, for each region (interval) based on the position and number of frequency thresholds.
It may be seen in Table 3 that the various regions in which the test is divided, for one or two frequency thresholds, are statistically different from the contiguous one. This indicates that these fatigue thresholds were clearly identified, and therefore have a mechanical basis, most probably in the swimming technique. Maybe they also have a physiological basis, although this was not investigated. 4. CONCLUSIONS The use of the continuous wavelet transform proved to be a valid one in determining the change in the pattern of the swimming velocity. These changes were assigned to
7
Leandro Machado, Susana Soares e João Paulo Vilas-Boas
fatigue thresholds, and were particularly valid for the older (pubertal and pos-pubertal) swimmers, as these are better swimmers than the pre-pubertal ones. In the future, when more tests become available, this may prove to be a valid test to indicate the boundary between the alactic and lactic energy production systems.
REFERENCES [1] Inbar O, Bar-or O, Skinner J (1996). The Wingate Anaerobic Test. Champaign, Illinois: Human Kinetics [2] S. Mallat. (1998). A Wavelet Tour of Signal Processing, Academic Press Inc. [3] Lima, A (2006). Concepção, desenvolvimento de resultados e eficiência no treino da técnica em Natação. PhD Thesis. Porto: Faculty of Sport Sciences and Physical Education, Porto University
8
