Long-Range Correlations and Complex Regulation of Pacing in Long-Distance Road Racing.

Purpose: To analyse time domain, spectral and fractal properties of speed regulation during half-marathon racing. Methods: In twenty-one male experienced runners high-resolution data on speed (V), stride frequency (SF) and stride length (SL) were assessed during half-marathon competition (21098 m). Performance times, time and frequency domain variability, spectral scaling exponent (beta) and fractal dimension (FD) of V, SF and SL were analysed. Results: V of 3.65±0.41 m·s-1, SF of 1.41±0.05 Hz and SL of 2.58±0.25 m occurred with higher (p<0.05) individual variability in V and SL compared to SF. Beta and FD were always in between 1.04 and 1.88 and 1.56 to 1.99, respectively. Beta and FD differed (p<0.05) in SF and SL compared to V and were correlated in V and SL (r=0.91, p<0.05). Spectral peaks of V, SF and SL occurred at wavelengths in between 3 to 35 min, and those of V and SL were interrelated (r=0.56, p<0.05). Mean SF and mean SL were significantly correlated with performance (r=0.59 and r=0.95, p<0.05). SL accounted for 84±6 % and SF for 16±6 % of speed variability, respectively. Conclusions: The observed non-random fluctuations in V, SF and SL correspond to non-stationary fractional Brownian motion with inherent long-range correlations. This indicates a similar complex regulation process in experienced runners that is primarily mediated via SL.