Modeling the Recovery of W′ in the Moderate to Heavy Exercise Intensity Domain

Abstract

Purpose This study (i) investigates the effect of recovery power (Prec) and duration (t rec) on the recovery of the curvature constant (W′) of the power–duration relationship, (ii) compares the experimentally measured W′ balance to that predicted (W′ bal) by two models (SK2 and BAR), and (iii) presents a case of real-time performance optimization using the critical power (CP) concept. Methods Seven competitive amateur cyclists performed a ramp test to determine their V˙O2peak and gas exchange threshold, two to four 3-min all-out tests to determine CP and W′, and nine intermittent cycling tests to investigate W′ recovery. The intermittent cycling tests involved a 2-min constant work-rate interval above CP, followed by a constant work-rate recovery interval below CP (Prec and t rec were varied), followed by a 3-min all-out interval. Results There was a significant two-way interaction between Prec and t rec on W′ recovery, P = 0.004 (η 2 = 0.52). Simple main effects were present only with respect to Prec at each t rec. The actual W′ balance at the end of the recovery interval was less than the W′ bal predicted by both SK2 (P = 0.035) and BAR (P = 0.015) models. The optimal strategy derived from the subject-specific recovery model reduced the race time by 55 s as compared with the self-strategy. Conclusions This study has shown that in a recovery interval, Prec has a greater influence than t rec on W′ recovery. The overprediction of W′ bal from SK2 and BAR suggests the need for individualized recovery parameters or models for sub-CP exercise. Finally, the optimal strategy results provide encouraging signs for real-time, model-based performance optimization.

Bi-exponential modelling of $$W^{^{\prime}}$$ reconstitution kinetics in trained cyclists

“…The mono-exponential W ′ bal model has been validated using similar intermittent protocols in hypoxia (Shearman et al 2016 ; Townsend et al 2017 ), and by retrofitting to the point of exhaustion during training and race data (Skiba et al 2014a ), where the mono-exponential model proved a successful fit against the measurements of W′ reconstitution over the short intermittent recoveries. Validations of the mono-exponential W ′ bal model via different protocols have, however, found significant differences against longer recovery durations (Chorley et al 2019 ) and partial prior depletion of W ′ (Lievens et al 2021 ; Sreedhara et al 2020 ), albeit without τ being individually fitted. Where τ has been individualised, it has only been done so against W′ reconstitution at specific measured time points (Caen et al 2019 ; Chorley et al 2020 ) rather than against a time-course of W ′ reconstitution.…”

Optimal pacing strategy modeling of cycling individual time trials

“…To simplify the issue, the researchers determine that the CP values of male and female riders are equal to 4.2 W/kg from Figure .2(b). The relationship between CP, AWC, and fatigue time is given [10] :…”

The Application of Critical Power, the Work Capacity above Critical Power (W′), and Its Reconstitution: A Narrative Review of Current Evidence and Implications for Cycling Training Prescription

“…The Skiba1 model has inherent mathematical limitations such as W reconstitution whilst W is being expended and a reported imbalance of units [104]. Perhaps the biggest limitation of Skiba1, however, is that the recovery intensity can only be calculated retrospectively as it is averaged over a recovery interval.…”

“…VO 2 , blood lactate or pH measurements at the end of the depleting bout, further complicating the understanding of W reconstitution. Despite the criticisms of the Skiba models [45,104,108,110], they remain the only examples published to date.…”

“…Uniquely, Caen, et al [ 110 ], found faster rates of W′ reconstitution following the faster depletion of W′ despite no differences in 2 , blood lactate or pH measurements at the end of the depleting bout, further complicating the understanding of W′ reconstitution. Despite the criticisms of the Skiba models [ 45 , 104 , 108 , 110 ], they remain the only examples published to date.…”