Although the standard methods for determination of CP, RCP, MLSS, and [HHb]BP are different, these indices occur at the same V˙O2p, suggesting that i) they may manifest as a result of similar physiological phenomenon and ii) each provides a valid delineation between tolerable and intolerable constant-power exercise.

The pulmonary O2 uptake (V̇o2p) response to ramp-incremental (RI) exercise increases linearly with work rate (WR) after an early exponential phase, implying that a single time constant (τ) and gain (G) describe the response. However, variability in τ and G of V̇o2p kinetics to different step increments in WR is documented. We hypothesized that the "linear" V̇o2p-WR relationship during RI exercise results from the conflation between WR-dependent changes in τ and G. Nine men performed three or four repeats of RI exercise (30 W/min) and two step-incremental protocols consisting of four 60-W increments beginning from 20 W or 50 W. During testing, breath-by-breath V̇o2p was measured by mass spectrometry and volume turbine. For each individual, the V̇o2p RI response was characterized with exponential functions containing either constant or variable τ and G values. A relationship between τ and G vs. WR was determined from the step-incremental protocols to derive the variable model parameters. τ and G increased from 21 ± 5 to 98 ± 20 s and from 8.7 ± 0.6 to 12.0 ± 1.9 ml·min(-1)·W(-1) for WRs of 20-230 W, respectively, and were best described by a second-order (τ) and a first-order (G) polynomial function of WR (lowest Akaike information criterion score). The sum of squared residuals was not different (P > 0.05) when the V̇o2p RI response was characterized with either the constant or variable models, indicating that they described the response equally well. Results suggest that τ and G increase progressively with WR during RI exercise. Importantly, these relationships may conflate to produce a linear V̇o2p-WR response, emphasizing the influence of metabolic heterogeneity in determining the apparent V̇o2p-WR relationship during RI exercise.

What is the main finding and its importance? 31Here we demonstrate how a first-order system can respond with non-first-order response 32

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