We examined the relationship amongst baseline work rate (WR), phase II pulmonary oxygen uptake (V̇(O2p)) time constant (τV̇(O2p)) and functional gain (G(P)=ΔV̇(O2p)/ΔWR) during moderate-intensity exercise. Transitions were initiated from a constant or variable baseline WR. A validated circulatory model was used to examine the role of heterogeneity in muscle metabolism (V̇(O2m)) and blood flow (Q̇(m)) in determining V̇(O2p) kinetics. We hypothesized that τV̇(O2p) and G(P) would be invariant in the constant baseline condition but would increase linearly with increased baseline WR. Fourteen men completed three to five repetitions of ∆40 W step transitions initiated from 20, 40, 60, 80, 100 and 120 W on a cycle ergometer. The ∆40 W step transitions from 60, 80, 100 and 120 W were preceded by 6 min of 20 W cycling, from which the progressive ΔWR transitions (constant baseline condition) were examined. The V̇(O2p) was measured breath by breath using mass spectrometry and a volume turbine. For a given ΔWR, both τV̇(O2p) (22-35 s) and G(P) (8.7-10.5 ml min(-1) W(-1)) increased (P < 0.05) linearly as a function of baseline WR (20-120 W). The τV̇(O2p) was invariant (P < 0.05) in transitions initiated from 20 W, but G(P) increased with ΔWR (P < 0.05). Modelling the summed influence of multiple muscle compartments revealed that τV̇(O2p) could appear fast (24 s), and similar to in vivo measurements (22 ± 6 s), despite being derived from τV̇(O2p) values with a range of 15-40 s and τQ̇(m) with a range of 20-45 s, suggesting that within the moderate-intensity domain phase II V̇(O2p) kinetics are slowed dependent on the pretransition WR and are strongly influenced by muscle metabolic and circulatory heterogeneity.

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.