Constructing quasi-linear V̇O2 responses from nonlinear parameters.

Oxygen uptake (V̇O2) kinetics have been shown to be governed by a nonlinear control system across a range of work rates. However, the linearity of the V̇O2 response to ramp incremental exercise would appear to be the result of a linear control system. This apparent contradiction could represent a balancing of changing V̇O2 kinetics parameter values across a range of work rates. To test this, six healthy men completed bouts of ramp incremental exercise at 15, 30, and 60 W/min (15R, 30R, 60R, respectively) and four bouts of an extended-step incremental exercise. V̇O2 parameter values were derived from the step exercise using two monoexponential models: one starting at time zero and encompassing the entire stage (MONO), and the other truncated to the first 5 min and allowing a time delay (5TD). The resulting parameter values were applied to an integrative model to estimate the ramp responses. As work rate increased, gain values increased (P < 0.001 for MONO and 5TD), as did mean response time (or time constant) values (MONO: P < 0.001; 5TD: P = 0.003). Up to maximal V̇O2 (V̇O(2 max)), the gains of the estimated ramp responses from both models were not different from the gains of the actual observed V̇O2 responses for 15R and 30R (15R: 11.3 ± 1.2, 11.7 ± 0.7, 10.9 ± 0.3; 30R: 10.5 ± 0.8, 11.0 ± 0.5, 10.7 ± 0.3 ml O2·min(-1)·W(-1), for actual, MONO, 5TD, respectively) but were significantly greater for 60R (8.7 ± 1.0, 9.9 ± 0.4, 10.3 ± 0.3 ml O2·min(-1)·W(-1) for actual, MONO, 5TD, respectively). Up to 80%V̇O(2 max) gain values were not significantly different for any ramp rate (P > 0.05 for all). We conclude that the apparent linearity of the V̇O2 response to ramp incremental exercise is consequent to a balancing of increasing time constant and gain parameter values.