Data power law scaling behavior is observed in many fields. Velocity of fully developed turbulent flow, telecommunication
traffic in networks, financial time series are some examples among many others. The goal of the
present contribution is to show the scaling behavior of physiological time series in marathon races using wavelet
leaders and the Detrended Fluctuation Analysis.
Marathon race is an exhausting exercise, it is referenced as being a model for studying the limits of human
We analyzed the athlete's heart rate and speed time series recorded simultaneously. We find that the heart cost
time series, number of heart beats per meter, increases with the fatigue appearing during the marathon race, its
tendency grows in the second half of the race for all athletes.
For most physiological time series, we observed a concave behavior of the wavelet leaders scaling exponents which
suggests a multifractal behavior. Otherwise, the Detrended Fluctuation Analysis shows short and long range
time-scale power law exponents with the same break point for each physiological time series and each athlete.
The short range time-scale exponent increases with fatigue in most physiological signals.