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A key feature of successful long distance racing is pacing. Pacing is the modulation of running speed (v) for maximal exploitation of the runner´s performance capacity towards the known endpoint finish line. Pacing shall reflect continuous integration of information on previous experience, remaining running distance, environmental conditions and perception of effort. Additionally to this kind of macro pacing profile there is recent evidence that more high frequent modulations in running v are not random but represent a micro profile with scaling behavior and self-similarity of speed regulation. This fractal scaling micro profile defined by non-stationary fractional Brownian motion with inherent long-range correlations of speed regulation suggests non-linear interrelated control mechanisms operating on various time scales. In half marathon running this was primarily mediated via stride length (SL).
Consequently the first part of the study tested the hypothesis that non-stationary fractional Brownian motion with inherent long-range correlations of speed regulation increased with marathon race progression. In the second part of the study, we tested another hypothesis in a laboratory. The subjects should cycle on a bicycle ergometer with invariant power setpoint through their maximum of individual physical exertion.
Part 1: 20 male endurance runners (mean ± SD age: 37 ± 7 yrs, height: 1.78 ± 0.06 m, weight: 73±8,8 kg) participated in four different certified street marathon races. Terrestric profiles resulted in net elevations between start and finish of 15 m to 90 m. Climate conditions were mild and dry. High-resolution data of V (m/s), stride frequency (SF; Hz) and SL (m) were measured with a light-weight accelerometric foot sensor with a telemetric coupling to a wrist watch (Polar RS800sd with s3-senor, Kempele, Finnland).
The spectral scaling exponent (beta), which denotes the slope of the log-power versus log-frequency regression line, was computed from the smoothed CWT spectral powers of each subjects V, SF and SL time series, while only low frequency components below 0.1 Hz were considered. Beta values between 1.04 and 3 were classified as non-stationary fractional Brownian motion (fBm) with long-range correlations, while values between -1 and 0.38 indicated stationary fractional Gaussian noise (fGn). If fBm was detected, the corresponding fractal dimension (FD) was calculated.
Part 2: 19 male cyclists (mean ± SD age: 24.7 ± 3.5 yrs, height: 1.79 ± 0.06m; weight: 74.3 ± 7,4kg) part. The athletes completed on the bicycle ergometer, a submaximal endurance with IANS power through their maximum of individual physical exertion. Every five minutes rating of perceived exertion (RPE, CR-10), blood lactate, oxygen uptake (VO2), HRV and nonlinear dynamics (α1) were analysed relative to the total load time.
All data processing procedures were done using self-programmed routines in Origin 8.0 (OriginLab, Northampton/USA) and Autosignal v1.7 (Seasolve Software, Framingham/USA).
Subsequent statistical analysis (SPSS 20, IBM Chicago) included testing normality of distribution using Kolmogorov-Smirnov testing and the Levene statistics for homoscedasticity, presentation of descriptive results as means and standard deviations (SD).
Mean values of V (3.54 ± 0.38 vs. 3.39 ± 0.44 m·s-1), SF (1.43 ± 0.07 vs. 1.43 ± 0.07 Hz) and SL (2.58 ± 0.22 vs. 2.47 ± 0.24 m) remained unchanged between first and second marathon half. SL explained 94.1 ± 5.9 % of the variance in V.
CV, beta and FD of V, SF and SL were different (p < 0.05) irrespective of race progression. CV of V (4.2 ± 1.1 vs. 5.4 ± 1.7 %, p < 0.05) and SL (3.8 ± 1.0 vs. 4.8 ± 1.5 %, p < 0.05) increased from first to second marathon half but not CV of SF (1.1 ± 0.3 vs. 1.3 ± 0.3 %, n.s.). Beta of V (1.73 ± 0.17 vs. 1.86 ± 0.2, p < 0.05) increased with race progression whilst beta of SF (1.31 ± 0.16 vs. 1.41 ± 0.22, n.s.) and SL (1.52 ± 0.22 vs. 1.65 ± 0.28, n.s.) remained unchanged. FD of V (1.63 ± 0.09 vs. 1.57 ± 0.1, p < 0.05) decreased in the second half of the marathon but FD of SF (1.84 ± 0.08 vs. 1.8 ± 0.09) and SL (1.74 ± 0.11 vs. 1.67 ± 0.11) did not change with race progression.
In the second part of the study total times of 77.53 ± 15,28min show highly significant increase in demand and a high positive correlation between RPE and HRV. In both studies (Laboratory vs. Marathon) occurred in the comparison of the two halves (first vs. second half) to a significant reduction in α1 values (p <0.05).
The present study is the first that analyzed high frequent modulations in running V in terms of a micro pacing profile with scaling behavior and self-similarity with respect to marathon race progression. The hypothesis that with race progression a runner shows a higher level of correlated non-random speed adjustments was confirmed. Fractal and spectral properties show clear, but subtle effects in beta and FD of v only, although variations in v were primarily mediated by SL. The high RPE values at exhaustive endurance exercise go hand in hand both with a loss of overall variability, as well as the fractal scales awareness. This suggests that demand without end orientation and invariant power more prone to loss of scales awareness, as endpoint oriented events with variable power. The present findings provide furthermore evidence supporting the concept that pacing reflects continuous integration of conscious input and additional cumulative sensations which lead to increasing systemic coupling of performance managing factors towards the known endpoint finish line.