Long-range correlations and complex regulation of pacing in long-distance road racing

To analyze time-domain, spectral, and fractal properties of speed regulation during half-marathon racing.

In 21 male experienced runners, high-resolution data on speed (V), stride frequency (SF), and stride length (SL) were assessed during half-marathon competition (21,098 m). Performance times, time- and frequency-domain variability, spectral-scaling exponent (beta), and fractal dimension (FD) of V, SF, and SL were analyzed.

V of 3.65 ± 0.41 m/s, SF of 1.41 ± 0.05 Hz, and SL of 2.58 ± 0.25 m occurred with higher (P < .05) individual variability in V and SL than in SF. Beta and FD were always 1.04-1.88 and 1.56-1.99, respectively. Beta and FD differed (P < .05) in SF and SL compared with V and were correlated in V and SL (r = .91, P < .05). Spectral peaks of V, SF, and SL occurred at wavelengths of 3-35 min, and those of V and SL were interrelated (r = .56, P < .05). Mean SF and mean SL were significantly correlated with performance (r = .59 and r = .95, P < .05). SL accounted for 84% ± 6% and SF for 16% ± 6% of speed variability.

The observed nonrandom fluctuations in V, SF, and SL correspond to nonstationary fractional Brownian motion with inherent long-range correlations. This indicates a similar complex regulation process in experienced runners that is primarily mediated via SL.