Scaling in heart rate and speed dynamics of runners in the marathon race . Running Head : Heart rate and speed dynamics in marathon running .

We report the modification of the scaling dynamics of human heart rate (HR in beat.min-1), speed (S in km.hour-1) and cardiac cost (the Heart Rate / Speed ratio, HRS in cardiac beats.m-1) was investigated in ten male subjects (35±5 yrs) who ran a marathon. The scaling power law was observed using the detrended fluctuation analysis (DFA) and the wavelet structure function. The corresponding scaling law exponents α and τ were estimated as the slope of the segment lines which fit respectively the DFA function graph and the wavelet structure function graph in a log-log representation. For all the signals, two distinct regions of DFA scale invariance, [0.4-1.8] and [1.8-2.3] with the corresponding short-range (α ) and long-range scale (α 2) exponents were identified in both half marathon races and α  was significantly higher than α 2 (p<0.0001). α 1 and α 2 of HR increased as the race progressed (p<0.01) and only α  (short scaling) for S. The HR wavelet scaling exponent (τ) increased significantly during the race (p<0.01). These results demonstrate that a long exhaustive run affects the fractal short scaling of heart rate and speed.