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

Abstract

Purpose The aim of this study was to investigate the individual $$W^{^{\prime}}$$ W ′ reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe $$W^{^{\prime}}$$ W ′ reconstitution. Methods Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; $$\dot{V}{\text{O}}_{2\max }$$ V ˙ O 2 max 58.6 ± 7.1 mL kg min−1) completed three incremental ramps (20 W min−1) to the limit of tolerance with varying recovery durations (15–360 s) on 5–9 occasions. $$W^{^{\prime}}$$ W ′ reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R2 and bias-corrected Akaike information criterion (AICc). Results A bi-exponential model outperformed the mono-exponential model of $$W^{^{\prime}}$$ W ′ reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adjR2 = 0.999) for the first recovery when optimised with parameters of fast component (FC) amplitude = 50.67%; slow component (SC) amplitude = 49.33%; time constant (τ)FC = 21.5 s; τSC = 388 s. Following the second recovery, W′ reconstitution reduced by 9.1 ± 7.3%, at 180 s and 8.2 ± 9.8% at 240 s resulting in an increase in the modelled τSC to 716 s with τFC unchanged. Individual bi-exponential models also fit well (adjR2 = 0.978 ± 0.017) with large individual parameter variations (FC amplitude 47.7 ± 17.8%; first recovery: (τ)FC = 22.0 ± 11.8 s; (τ)SC = 377 ± 100 s; second recovery: (τ)FC = 16.3.0 ± 6.6 s; (τ)SC = 549 ± 226 s). Conclusions W′ reconstitution kinetics were best described by a bi-exponential model consisting of distinct fast and slow phases. The amplitudes of the FC and SC remained unchanged with repeated bouts, with a slowing of W′ reconstitution confined to an increase in the time constant of the slow component.

Effect of varying recovery intensities on power outputs during severe intensity intervals in trained cyclists during the Covid-19 pandemic

“…That the mean power output of recoveries at 50% of FTP (MOD) and self-selected intensities were not different explains the similar power outputs generated during the subsequent severe intervals; however, the manner of the self-selected recoveries was markedly different to that of the constant MOD recovery condition; power output was initially reduced before increasing as the recovery phase progressed. This pattern is consistent with recent suggestions of the occurrence of a bi-exponential recovery of W′ [ 17 , 20 ] in which a fast component is highly dependent upon the first 30 s of recovery [ 17 ]. This fast recovery phase shares a similar time course to that of PCr restoration [ 47 ] and is likely facilitated by the low power outputs at the outset of the MOD recoveries, given that PCr restoration has been shown to be greatest during passive recovery [ 48 ].…”

“…This fast recovery phase shares a similar time course to that of PCr restoration [ 47 ] and is likely facilitated by the low power outputs at the outset of the MOD recoveries, given that PCr restoration has been shown to be greatest during passive recovery [ 48 ]. It has been suggested that the slow recovery phase of the bi-exponential model is linked to the removal of the accumulated metabolites such as lactate, inorganic phosphates and hydrogen ions [ 17 ]. Interestingly, no participants in the present study chose passive rest during any point of their self-selected recoveries.…”

“…The rate of W′ reconstitution is dependent upon the time constant ( τ ) which can be estimated using Eq. 2 [ 14 ], indicating that τ (and thus, the rate of W′ reconstitution) is dependent on the difference between CP and recovery power output (D CP ) [ 14 , 16 , 17 ]. This theoretical equation also suggests that the W′ reconstitution rate no longer improves once recovery power output is lower than 316 W below CP; however, this has yet to be verified experimentally.…”

“…It has been suggested that the W′ bal model underestimates the rate of W′ reconstitution in both elite [ 16 ] and non-elite cyclists [ 18 , 19 ]. Furthermore, recent investigations have suggested a bi-exponential model better represents W′ reconstitution kinetics [ 17 , 20 ], although such a model accounting for varying power output has not been proposed. The reconstitution kinetics of W′ appear to be unaffected by sex [ 17 , 21 , 22 ], body mass, or age per se [ 23 ] but is relative to measures of aerobic fitness such as CP and maximum oxygen uptake (V̇O 2max ) [ 20 , 23 ].…”

“…Furthermore, recent investigations have suggested a bi-exponential model better represents W′ reconstitution kinetics [ 17 , 20 ], although such a model accounting for varying power output has not been proposed. The reconstitution kinetics of W′ appear to be unaffected by sex [ 17 , 21 , 22 ], body mass, or age per se [ 23 ] but is relative to measures of aerobic fitness such as CP and maximum oxygen uptake (V̇O 2max ) [ 20 , 23 ]. Published studies investigating W′ reconstitution [ 14 , 18 , 19 , 20 , 22 ] invariably have a fixed power output (intensity) for recovery phases.…”