Purpose Intensity domains are recommended when prescribing exercise. The distinction between heavy and severe domains is made by the critical speed (CS), therefore requiring a mathematically accurate estimation of CS. The different model variants (distance versus time, running speed versus time, time versus running speed, and distance versus running speed) are mathematically equivalent. Nevertheless, error minimization along the correct axis is important to estimate CS and the distance that can be run above CS (d′). We hypothesized that comparing statistically appropriate fitting procedures, which minimize the error along the axis corresponding to the properly identified dependent variable, should provide similar estimations of CS and d′ but that different estimations should be obtained when comparing statistically appropriate and inappropriate fitting procedure. Methods Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of their peak speed on a treadmill. Several fitting procedures (a combination of a two-parameter model variant and regression analysis: weighted least square) were used to estimate CS and d′. Results Systematic biases (P < 0.001) were observed between each pair of fitting procedures for CS and d′, even when comparing two statistically appropriate fitting procedures, though negligible, thus corroborating the hypothesis. Conclusion The differences suggest that a statistically appropriate fitting procedure should be chosen beforehand by the researcher. This is also important for coaches that need to prescribe training sessions to their athletes based on exercise intensity, and their choice should be maintained over the running seasons.

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 &lt; 0.001), but there was no effect of the fitting procedure (P &gt; 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.

Purpose: Intensity domains are recommended when prescribing exercise, and critical power/speed (CP/CS) was designated the “gold standard” when determining maximal metabolic steady state. CS is the running analog of CP for cycle ergometry. However, a CP for running could be useful for controlling intensity when training in any type of condition. Therefore, this study aimed to estimate external, internal, and total CP (CPext, CPint, and CPtot), obtained based on running power calculations, and verified whether they occurred at the same percentage of peak oxygen uptake as the usual CS. Furthermore, this study examined whether selecting strides at the start, half, or end of the exhaustive runs to calculate running power influenced the estimation of the 3 CPs. Methods: Thirteen male runners performed a maximal incremental aerobic test and 4 exhaustive runs (90%, 100%, 110%, 120% peak speed) on a treadmill. The estimations of CS and CPs were obtained using a 3-parameter mathematical model fitted using weighted least square. Results: CS was estimated at 4.3 m/s while the estimates of CPext, CPint, and CPtot were 5.2, 2.6, and 7.8 W/kg, respectively. The corresponding for CS was 82.5 percentage of peak oxygen uptake and 81.3, 79.7, and 80.6 percentage of peak oxygen uptake for CPext, CPint, and CPtot, respectively. No systematic bias was reported when comparing CS and CPext, as well as the 3 different CPs, whereas systematic biases of 2.8% and 1.8% were obtained for the comparison among CS and CPint and CPtot, respectively. Nonetheless, the for CS and CPs were not statistically different (P = .09). Besides, no effect of the time stride selection for CPs as well as their resulting was obtained (P ≥ .44). Conclusions: The systematic biases among at CS and CPint and CPtot were not clinically relevant. Therefore, CS and CPs closely represent the same fatigue threshold in running. The knowledge of CP in running might prove to be useful for both athletes and coaches, especially when combined with instantaneous running power. Indeed, this combination might help athletes controlling their targeted training intensity and coaches prescribing a training session in any type of condition.

The aim of this study was to examine how running biomechanics (spatiotemporal and kinetic variables) adapt with exhaustion during treadmill runs at 90, 100, 110, and 120% of the peak aerobic speed (PS) of a maximal incremental aerobic test. Thirteen male runners performed a maximal incremental aerobic test on an instrumented treadmill to determine their PS. Biomechanical variables were evaluated at the start, mid, and end of each run until volitional exhaustion. The change of running biomechanics with fatigue was similar among the four tested speeds. Duty factor and contact and propulsion times increased with exhaustion (P ≤ 0.004; F ≥ 10.32) while flight time decreased (P = 0.02; F = 6.67) and stride frequency stayed unchanged (P = 0.97; F = 0.00). A decrease in vertical and propulsive peak forces were obtained with exhaustion (P ≤ 0.002; F ≥ 11.52). There was no change in the impact peak with exhaustion (P = 0.41; F = 1.05). For runners showing impact peaks, the number of impact peaks increased (P ≤ 0.04; $${\upchi }^{2}$$ χ 2  ≥ 6.40) together with the vertical loading rate (P = 0.005; F = 9.61). No changes in total, external, and internal positive mechanical work was reported with exhaustion (P ≥ 0.12; F ≤ 2.32). Results suggest a tendency towards a “smoother” vertical and horizontal running pattern with exhaustion. A smoother running pattern refers to the development of protective adjustments, leading to a reduction of the load applied to the musculoskeletal system at each running step. This transition seemed continuous between the start and end of the running trials and could be adopted by the runners to decrease the muscle force level during the propulsion phase. Despite these changes with exhaustion, there were no changes in either gesture speed (no alteration of stride frequency) or positive mechanical work, advocating that runners unconsciously organize themselves to maintain a constant whole-body mechanical work output.