Constructing quasi-linear oxygen uptake responses from non-linear parameters

Abstract

Purpose: Oxygen uptake (VO2) has been shown to be controlled by a nonlinear system, yet the VO2 response to ramp style exercise appears linear. We tested the hypothesis that an integrative model incorporating nonlinear parameter values could accurately estimate actual VO2 responses to ramp style exercise. Methods: Six healthy, men completed three bouts of varying ramp rate exercise (slow ramp (SR): 15 W/min, regular ramp (RR) 30 W/min, fast ramp (FR) 60W/min) and four bouts of extended-step incremental exercise, where each step lasted 5-15 min or until volitional fatigue on a cycle ergometer on separate days. The step-responses were then fit with a simple monoexponential starting at time zero (MONO) or allowing a time delay and using only the first 5 min of data (5TD). The resulting VO2 parameters from the step protocol were incorporated into an integrative model for the estimation of the VO2 response to each of the rates of ramp incremental exercise. The parameters from the actual and model ramp protocols were compared with 2 way repeated-measures ANOVAs. Results: Both Gain (G) and Mean Response Time (MRT) (or time constant) values increased significantly across work rate transitions (mean±SD; Gain:10.0±0.9, 11.6±1.1, 13.1±1.3, 17.6±3.3 ml O2/min/W; MRT:39.4±7.7, 54.0±5.4, 79.6±15.0, 180.1±56.2 s). Up to maximalVO2 the models over-estimated the actual VO2 response for FR (Gain: ACT 8.7±1.0, MONO 9.9±0.4, 5TD 10.3±0.3 ml O2/min/W). Up to 80% maximal VO2 the models accurately predicted the actual VO2 response across all ramp rates (Gain: ACT 10.7±1.1, 10.2±0.5, 9.2±1.0; MONO 11.0±0.8, 10.3±0.6, 9.2±0.5; 5TD 10.4±0.4, 10.2±0.3, 9.8±0.2 ml O2/min/W, values are listed SR,RR,FR). Conclusions: When variable parameter values (G and either MRT or time constant and time delay) were utilized by an integrative model, accurate estimations of the VO2 response to ramp incremental exercise were possible regardless of ramp rate (up to 80% maximal VO2). The increases in both G and MRT (or time constant) appear to balance each other to produce the quasi-linear VO2 responses.