Two-dimensional short-term model of oxygen uptake kinetics

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Abstract
An empirical case is presented for a two-dimensional O2 uptake (VO2) response surface, taking into account both short-term time dependence and the effect of power output. The surface is of the form VO2 = Re + aWt + bW(1-e-kt) where Re is the resting level, 0 less than W less than 2,100 kpm and 0 less than t less than 480 s are the power and time variables, respectively, k is the rate constant for the transient phase of uptake, and a and b are parameters. As a more general test of this expression, VO2 data on six middle-distance runners exercising for 8 min on a cycle ergometer at 1,200, 1,600, 1,850, and 2,100 kpm/min were collected in a respiratory laboratory. Fits of the surface gave coefficients of determination (R2) averaging 0.947, although for one subject a much lower value of 0.807 was obtained. The final fitted equation for the whole group was VO2 = 0.403 + 0.0012Wt + 1.821W(1-e-0.031t) with R2 = 0.857. (VO2 was measured in liters per minute, W in thousands of kilopond-meters per minute and t in seconds). A surface fit to a multirun experiment permits a more comprehensive examination of residuals. In this instance for one subject, such an examination suggests the possibility of a damped cyclic response-control mechanism. Residual variation, however, appears large enough to obscure any possible cycle in the remaining subjects.

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