A comparison of modelling procedures used to estimate the power–exhaustion time relationship

Abstract

This study aimed to test the consistency of using the power required to elicit maximal oxygen uptake during incremental test (P (t)) to demarcate the range of power intensity in the modelling of the power-exhaustion time relationship. Different mathematical procedures were tested using data from ten subjects exercising on a cycle ergometer. After the determination of P (t) and the power at the ventilatory threshold, the subjects did six tests at constant power to exhaustion within 2-15 min. Estimates were obtained from a segmented model using two distinct equations of the anaerobic contribution to power below and above P (t), respectively. This model fit the overall data with a better adequacy than the simple hyperbolic model (standard error of 29.2 +/- 25.2 vs. 42.3 +/- 25.2 s). The power asymptotes were 225.7 +/- 27.3 W from the segmented model, 226.2 +/- 27.3 and 283.3 +/- 20.5 W from the simple model applied to data below and above P (t), respectively. The estimates from the segmented model were strongly correlated with their analogues from the simple model applied only to data below P (t) (R = 1.00 for power asymptote and curvature coefficient). They were not correlated with their analogues from the simple model applied only to data above P (t). These discrepancies between modelling procedures could arise from the method used to determine P (t) and the oversimplification of the oxygen uptake kinetics. These limitations could lead the segmented model to an overestimation of the anaerobic contribution which was around 15% of total energy expended at P (t).

Different durations within the method of best practice affect the parameters of the speed–duration relationship

“…Our findings are supported by previous works, i.e. that shorter trials tend towards lower estimates of D́ and towards higher estimates of CS (Bishop et al., 1998; Busso et al., 2010; Jenkins et al., 1998; Vandewalle et al., 1997). However, the novel findings of this study were that these differences were also evident when using protocols within the currently recommended testing method of best practice (i.e.…”

Methodological Approaches and Related Challenges Associated With the Determination of Critical Power and Curvature Constant

“…The characteristics of the tests used to define the P-T relationship have a profound effect on CP and W' estimates. For instance, the duration of CWR is known to affect CP and W' (16,26,57,75,102,106,115). If data from five tests to task-failure is rearranged, and only the three tests with the shortest durations are considered, CP has been shown to be 14-20%…”

A phenomenological model of muscle fatigue and the power-endurance relationship

“…We propose a model that predicts both human power output responses during all-out exercise and the time over which a submaximal power output can be sustained at different power outputs (i.e., powerendurance relationship). To test this and enable a unique fit of the model to be achieved, the model was simultaneously fitted to two sets of human data (5,34) collected under these two conditions. Although these two data sets were collected on two groups of subjects by different investigators, they were collected on similar subjects (i.e., untrained, young, and healthy) under similar experimental conditions (i.e., cycle ergometry).…”

“…All-out exercise data for eight subjects were provided by Vanhatalo et al (34), and we analyzed the average power output values measured at 1-s intervals during a 3-min test performed under "control" conditions, but excluded the first 5 s of data during which power output was rising. The power-endurance data were taken directly from the publication by Busso et al (5) (Fig. 2).…”

“…This powerendurance relationship provides a useful framework for understanding exercise tolerance, and parameters derived from it have been used to represent exercise-related constructs, such as "critical power" and "anaerobic work capacity" (23). With respect to these parameters, the research effort has tended to focus on their "energetic basis" (25), construct validity (33), and technical aspects associated with the accuracy of their estimation (5). By contrast, far less research has focused on the physiological mechanisms underlying these parameters and the power-endurance relationship from which they are derived.…”