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Modeling and Analysis of the Effect of Training on  \(\dot{V}O_{2}\)  Kinetics and Anaerobic Capacity

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Abstract

In this paper, we present an application of a number of tools and concepts for modeling and analyzing raw, unaveraged, and unedited breath-by-breath oxygen uptake data. A method for calculating anaerobic capacity is used together with a model, in the form of a set of coupled nonlinear ordinary differential equations to make predictions of the \(\dot{V}O_{2}\) kinetics, the time to achieve a percentage of a certain constant oxygen demand, and the time limit to exhaustion at intensities other than those in which we have data. Speeded oxygen kinetics and increased time limit to exhaustion are also investigated using the eigenvalues of the fixed points of our model. We also use a way of analyzing the oxygen uptake kinetics using a plot of \(\ddot{V}O_{2}(t)\) vs \(\dot{V}O_{2}(t)\) which allows one to observe both the fixed point solutions and also the presence of speeded oxygen kinetics following training. A method of plotting the eigenvalue versus oxygen demand is also used which allows one to observe where the maximum amplitude of the so-called slow component will be and also how training has changed the oxygen uptake kinetics by changing the strength of the attracting fixed point for a particular demand.

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Authors and Affiliations

  1. Facultad de Ciencias de la Actividad Física y del Deporte-INEF, Universidad Politécnica de Madrid (UPM), c/ Martín Fierro s/n, 28040, Madrid, Spain

    J. R. Stirling & M. S. Zakynthinaki

  2. Instituto de Ciencias Matemáticas, CSIC–UAM–UC3M–UCM, c/ Serrano 121, 28006, Madrid, Spain

    M. S. Zakynthinaki

  3. Laboratoire d’Étude de la Physiologie de l’Exercice, Université d’Évry Val-D’Essonne, Boulevard François Mitterrand, 91025, Evry Cedex, France

    V. Billat

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  1. J. R. Stirling
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  2. M. S. Zakynthinaki
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  3. V. Billat
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Correspondence to J. R. Stirling.

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Stirling, J.R., Zakynthinaki, M.S. & Billat, V. Modeling and Analysis of the Effect of Training on  \(\dot{V}O_{2}\)  Kinetics and Anaerobic Capacity. Bull. Math. Biol. 70, 1348–1370 (2008). https://doi.org/10.1007/s11538-008-9302-9

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  • DOI: https://doi.org/10.1007/s11538-008-9302-9

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