Abstract
An accurate estimation of critical speed (CS) is important to accurately define the boundary between heavy and severe intensity domains when prescribing exercise. Hence, our aim was to compare CS estimates obtained by statistically appropriate fitting procedures, i.e., regression analyses that correctly consider the dependent variables of the underlying models. A second aim was to determine the correlations between estimated CS and aerobic fitness parameters, i.e., ventilatory threshold, respiratory compensation point, and maximal rate of oxygen uptake. Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of the peak speed of the incremental test on a treadmill. Then, two mathematically equivalent formulations (time as function of running speed and distance as function of running speed) of three different mathematical models (two-parameter, three-parameter, and three-parameter exponential) were employed to estimate CS, the distance that can be run above CS (d′), and if applicable, the maximal instantaneous running speed (smax). A significant effect of the mathematical model was observed when estimating CS, d′, and smax (P < 0.001), but there was no effect of the fitting procedure (P > 0.77). The three-parameter model had the best fit quality (smallest Akaike information criterion) of the CS estimates but the highest 90% confidence intervals and combined standard error of estimates (%SEE). The 90% CI and %SEE were similar when comparing the two fitting procedures for a given model. High and very high correlations were obtained between CS and aerobic fitness parameters for the three different models (r ≥ 0.77) as well as reasonably small SEE (SEE ≤ 6.8%). However, our results showed no further support for selecting the best mathematical model to estimate critical speed. Nonetheless, we suggest coaches choosing a mathematical model beforehand to define intensity domains and maintaining it over the running seasons.
Highlights
The prescription of exercise intensity, one of the most important criteria to induce specific adaptations to training (Maclnnis and Gibala, 2017), is often based on the percentage of the maximal rate of oxygen uptake (V O2max) or maximal heart rate (American College of Sports Medicine, 2000; Burgomaster et al, 2007; Roy et al, 2018)
The average R2 obtained for the linear regression of the V O2 as a function of time relationship recorded during the maximal incremental aerobic test was 0.94 ± 0.04
The linear mixed model with random effects explained almost all variance in the data for critical speed (CS) while a large part of variance in the data was still unexplained for d and smax even with random effects (Table 3). These results were reinforced by the Intraclass correlation coefficients (ICC) of the random effects, which was excellent for CS but poor and moderate for d and smax, respectively (Table 3)
Summary
The prescription of exercise intensity, one of the most important criteria to induce specific adaptations to training (Maclnnis and Gibala, 2017), is often based on the percentage of the maximal rate of oxygen uptake (V O2max) or maximal heart rate (American College of Sports Medicine, 2000; Burgomaster et al, 2007; Roy et al, 2018). Power has been related to time by dividing the original formulation by the exercise duration (Poole et al, 1986; Gaesser and Wilson, 1988; Housh et al, 1989) while Gaesser et al (1990) proposed expressing this exercise duration as function of power, which led to the well-known hyperbolic formulation (Morton and Hodgson, 1996) Another model variant, proposed by Morton (2006), expresses the work performed as function of power, since this work (power multiplied by time to exhaustion) is a dependent variable. This model has, to our knowledge, never been used so far
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