Bi-exponential modelling of $$W^{^{\prime}}$$ reconstitution kinetics in trained cyclists
Alan Chorley, Richard Bott, Simon Marwood, Kevin Lamb
Abstract
Abstract Purpose The aim of this study was to investigate the individual $$W^{^{\prime}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:msup> </mml:math> reconstitution kinetics of trained cyclists following repeated bouts of incremental ramp exercise, and to determine an optimal mathematical model to describe $$W^{^{\prime}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:msup> </mml:math> reconstitution. Methods Ten trained cyclists (age 41 ± 10 years; mass 73.4 ± 9.9 kg; $$\dot{V}{\text{O}}_{2\max }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mi>V</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:msub> <mml:mtext>O</mml:mtext> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>max</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> 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. $$W^{^{\prime}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:msup> </mml:math> reconstitution was measured following the first and second recovery periods against which mono-exponential and bi-exponential models were compared with adjusted R 2 and bias-corrected Akaike information criterion (AICc). Results A bi-exponential model outperformed the mono-exponential model of $$W^{^{\prime}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>W</mml:mi> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:msup> </mml:math> reconstitution (AICc 30.2 versus 72.2), fitting group mean data well (adj R 2 = 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; τ SC = 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 τ SC to 716 s with τ FC unchanged. Individual bi-exponential models also fit well (adj R 2 = 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.