predicted from the standard curve individual %HRmax/%v VO_{2}max at the multistage test. In addition, t to exhaustion 90% vVO_{2}max seems more accurate than t to exhaustion 80%vVO_{2}max and also t to exhaustion is more accurate than %VO_{2}max to predict maximum heart rate during rectangular effort. We know no other study attempting to describe and model systematically %HRmax based at %vVO_{2}max and the time of constant effort. Many others [22-25] have studied the drift of HR in constant and prolonged efforts. Thus, previous studies [22, 26-28] also observed that training was associated with a drift less pronounced at lower %HRmax. The best collective model of this study gives an acceptable idea of the average evolution of %HRmax versus time and %vVO_{2}max. But the main problem with the collective equations is that it translates into a slope of drift and vertical positions of %HRmax same for all so individually. The collective models to predict %HRmax are inadequate on an individual basis, we examined individual models. With these models, we can take into account the values of VO_{2}max or t to exhaustion to improve the prediction since these values remain constant for a given individual. We have therefore chosen two models. Regarding random errors, there are not many differences between the two models studied and they are both excellent. Adding the values of %HRmax corresponding to %vVO_{2}max observed in multistage test improves very little the prediction of %HRmax during constant effort on assessment. Nevertheless, individual models are clearly superior to collective models and appear sufficiently accurate to predict the values of %HRmax depending on the intensity (% vVO_{2}max) and time at constant effort with estimated errors type below 2% HRmax. The model used provides a linear increase of %HRmax on depending of time with regular increases in slope between the intensities, which is not always the case. Thus we see especially at 90% vVO_{2}max, significant differences between theoretical %HRmax and real %HRmax. On the other hand, if one relies on data from Figures 3 and 4, it seems that Equation (1) is also less prone to systematic errors than Equation (18), but analysis of data from 5 other subjects not shown shows in this respect, the two equations are equally good. We may question the interest of an individual model, as it must do all necessary tests to each subject to obtain it, in other words it cannot be experimentally a priori defined as the collective models. On the other hand, although it should be measured on at least 3 intensities, %HRmax can subsequently be predicted at other intensities without having to measure the subjects again. Moreover, if t to exhaustion or VO_{2}max topics change, a new %HRmax can be estimated without having to redo the model.

5. CONCLUSION

The interest of this study was to develop equations that will allow calculating the %HR in function of different settings (time, strength, VO_{2}max, 80% t to exhaustion vVO_{2}max ...) in order to better adjust the intensity of training. The main idea is to take into account the data measured at efforts made at constant load to calculate the parameters for training qualitative. Overall the tests used to determine the intensity levels are of multistage type (steady increase of intensity) while training efforts are mainly constant. This study has demonstrated that model predictions of %HRmax from %vVO_{2}max in multistage tests were not suitable for constant efforts. From equations developed, we have find among the indicators of level of endurance, the time limit to 90% vVO_{2}max is a better predictor of %HRmax than the time limit to 80% vVO_{2}max. The application of these relations on real data showed that only the use of individual equations on individual data gives consistent and acceptable results on an individual basis while collective models rather give an average description of the evolution of %HRmax as a function of time, vVO_{2}max% of t to exhaustion, VO_{2}max and a result of conventional multistage test. Additional research is needed to verify the applicability of the % HR max, %HRrest, %VO_{2}max and %VO_{2} rest relationships within the context of actual aerobic training, in different populations and for high intensity intermittent exercise of different sports practices.

6. ACKNOWLEDGEMENTS

This study was supported by the Ministry of Higher Teaching and Scientific Research, Tunisia. We are grateful to all of the players who participated so willingly in the study.

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NOTES

^{*}Corresponding author.