Authors’ Response to Letter to the Editor: “Running Critical Power: A Comparison of Different Theoretical Models”

Our study recently published in the International Journal of Sports Medicine was designed to (i) compare the critical power (CP) and work capacity over CP (W´) values reported by the different CP models available in current analysis software packages (Golden Cheetah and Stryd platform), (ii) to locate the CP values in the power-duration curve, and (iii) to determine the influence of the CP model used on the W´ balance. Our results revealed that (i) there were significant differences between CP models in the estimated parameters, (ii) the bioenergetic Golden Cheetah model (CP_cheetach) was located between the 10- and 20-minute work rate, and the power-1/time (CP_1/time), Stryd platform (CP_stryd), work-time (CP_work) and Morton hyperbolic models at the 30-minute work rate, and (iii) the accuracy of the W´ balance to predict the time to exhaustion at the severe intensity domain was conditioned to the CP model used, with the two-parameters CP models being the most accurate.

Here, we provide our point-by-point comments to the concerns raised in the Letter to the Editor:

First, it was speculated that different time trials were used in the CP models compared given the differences reported between the CP_1/time and the CP_work models. After revising our database, we detected an error not related to the selected time trials but rather to the applied fitting method. Specifically, we aimed to apply the same fitting called “Ordinary least-squares regression” which, by error, we applied only in one of them, the other using the so-called “Ordinary product regression”. This error has been solved in the published erratum. Lastly, it was criticized that the maximum power of the three-parameter models was not displayed. This is simply due to our decision to focus on the parameters of greatest interest (i. e., CP and W'). Similarly, it was criticized that there was a missing W´ value in the CP_Stryd, which is basically due to the fact that this model does not report it.

Second, it was criticized that our longest time trial duration (i. e., 20-min) was outside the the recommended range of 2- to 15-min. We agree that the time trial selection is an important issue in the mathematical modelling as we have previously explored when determining CP, W´, or long-duration power outputs in running [1] [2]. However, we do not agree that the CP and W´ values were invalid due to this issue. On the one hand, we have shown that simplified combinations within the mentioned range (3- to 10-min) place the CP in a location similar to the same duration range used here (3- to 20-min), which is reinforced by its validity to represent the power output associated with the second ventilatory threshold [3]. Likewise, other studies have considered the use of longer durations [4] [5], particularly, when these were close to peak values representing the maximal aerobic capacities. In this regard, with respect to the power output developed in the 10-min time trial, which could serve as a reference of the athletes’ maximal aerobic power, the 20-min time trial was located at 95 (3)%, thus, being quite probable an intensity within the severe intensity domain. Gorostiaga et al. [6] highlighted that the asymptote is placed just below (95–99%) the longest trial duration introduced to the model. Therefore, the CP location of certain models at the 20–30 min range is a good approach in practical terms and, in particular, for our sample of highly-trained athletes considering the role of endurance performance in placing the critical speed (CS) or CP at a high percentage of their maximal aerobic capacities [7].

Third, with regard to the concerns exposed about using the 30- and 60-min time trials to locate the CP in the power duration curve, it was criticized that these durations are outside the power outputs of a CP model. This is only true for asymptote models, since non-asymptote models can be extrapolated further than CP [8], such as the one used in the present study (i. e., CP_cheetah). As then stated that it would be interesting to determine their location with respect to CP and how it varies between individuals, we derive your attention to table 3 and the confidence intervals reported, as well as to a recent study addressing this issue [9].

Lastly, different issues have been mentioned regarding W´. First, its validity to estimate the time to exhaustion when using the 4-min power duration has been questioned due to the range of durations selected. In this regard, it should be noted that even if we stick to the recommended range, different CS values and distances above CS have been reported when selecting different durations (12-, 7- and 3-min vs. 10-, 5- and 2-min) [10]. Thus, as widely reported in previous studies, the main issue with respect W´ is that rather than a constant it is a variable parameter. Lastly, it has been questioned that the W´ balance method could differ from calculating the time to exhaustion from the CP model equation, which basically is the same procedure during the depleting phase.

Publication History

Article published online:
09 January 2024

• References

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