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INNOVATIVE METHODOLOGY

On the modeling of breath-by-breath oxygen uptake kinetics at the onset of high-intensity exercises: simulated annealing vs. GRG₂ method

¹Laboratoire des Adaptations Physiologiques aux Activités Physiques, Université de Poitiers, Faculté des Sciences du Sport, Poitiers; ²Laboratoire Signal Image Communications, Université de Poitiers, Unité de Formation et de Recherche Sciences Fondamentales et Appliquées, Futuroscope Chasseneuil, France; and ³Institut d'Education Physique et de Réadaptation, Faculté de Médecine, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

Submitted 16 June 2005 ; accepted in final form 19 October 2005

Modeling in the time domain, the non-steady-state O₂ uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG₂ algorithm (a gradient-descent method known for its robustness). Forty simulated O₂ on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG₂ significantly biased two estimated kinetic parameters of the first exponential (the time delay td₁ and the time constant ₁) and impaired the precision (i.e., standard deviation) of the baseline A₀, td₁, and ₁ compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A₂, the time delay td₂, and the time constant ₂). Nevertheless, td₂ was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O₂ uptake on a cycle ergometer and O₂ uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG₂ for A₁ although better with SA for A₂ and ₂. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.

O₂ uptake kinetics; parametric modeling; parameter estimation