DOI: https://doi.org/10.21203/rs.3.rs-220974/v1

A two-parameters [a rate constant *k* and a factor *f* (0≤*f* < 1)] modelling, describing satisfactorily the post-exercise oxygen uptake rate (*V*_{O2}) as a function of the recovery time (*t*), is presented. *f* controls the rate equation d*V*_{O2}/d*t*, particularly at *t* = 0 where (d*V*_{O2}/d*t*)_{t=0} ∝ −*k*(1−*f*), a less abrupt decay than (d*V*_{O2}/d*t*)_{t=0} ∝ −*k* expected from an exponential. Fitting the model to a set of experimental *V*_{O2} vs *t* data after a 3MT it was found a set of values with *f* close to 0 and another with *f* > 1/2, with a narrow distribution of values for the half-recovery time *τ*_{1/2}=(1/*k*)ln[(2−*f*)/(1−*f*)] (〈*τ*_{1/2}〉=0.641 min, *σ* = 0.062 min), very similar to that (*T*) found by fitting a model based on a logit transform (〈*T*〉 = 0.672 min, *σ* = 0.081 min). The parameter *f* is a reliable index of the initial acceleration of the oxygen uptake rate recovery (and likely of the heart rate recovery) and, together with the half-recovery time *τ*_{1/2}, may be a useful method in characterizing and monitoring performs and exercise forms, very important in the physiology area.

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