Detection of the change point in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance

The purpose of this study was to develop a method to determine the power output at which oxygen uptake (V˙O₂) during an incremental exercise test begins to rise non-linearly. A group of 26 healthy non-smoking men mean age 22.1 (SD 1.4) years, body mass 73.6 (SD 7.4) kg, height 179.4 (SD 7.5) cm, maximal oxygen uptake (V˙O_2max) 3.726 (SD 0.363) l · min⁻¹], experienced in laboratory tests, were the subjects in this study. They performed an incremental exercise test on a cycle ergometer at a pedalling rate of 70 rev · min⁻¹. The test started at a power output of 30 W, followed by increases amounting to 30 W every 3 min. At 5 min prior to the first exercise intensity, at the end of each stage of exercise protocol, blood samples (1 ml each) were taken from an antecubital vein. The samples were analysed for plasma lactate concentration La]_pl, partial pressure of O₂ and CO₂ and hydrogen ion concentration H⁺]_b. The lactate threshold (LT) in this study was defined as the highest power output above which La⁻]_pl showed a sustained increase of more than 0.5 mmol · l⁻¹ · step⁻¹. The V˙O₂ was measured breath-by-breath. In the analysis of the change point (CP) of V˙O₂ during the incremental exercise test, a two-phase model was assumed for the 3rd-min-data of each step of the test: X _i =at _i +b+ɛ _i for i=1,2,…,T, and E(X _i )>at _i +b for i =T+1,…,n, where X ₁, … , X _n are independent and ɛ _i ∼N(0,σ²). In the first phase, a linear relationship between V˙O₂ and power output was assumed, whereas in the second phase an additional increase in V˙O₂ above the values expected from the linear model was allowed. The power output at which the first phase ended was called the change point in oxygen uptake (CP-V˙O₂). The identification of the model consisted of two steps: testing for the existence of CP and estimating its location. Both procedures were based on suitably normalised recursive residuals. We showed that in 25 out of 26 subjects it was possible to determine the CP-O₂ as described in our model. The power output at CP-V˙O₂ amounted to 136.8 (SD 31.3) W. It was only 11 W – non significantly – higher than the power output corresponding to LT. The V˙O₂ at CP-V˙O₂ amounted to 1.828 (SD 0.356) l · min⁻¹ was 48.9 (SD 7.9)% V˙O_{2 max} ]. The La⁻]_pl at CP-V˙O₂, amounting to 2.57 (SD 0.69) mmol · l⁻¹ was significantly elevated (P<0.01) above the resting level 1.85 (SD 0.46) mmol · l⁻¹], however the H⁺]_b at CP-V˙O₂ amounting to 45.1 (SD 3.0) nmol · l⁻¹, was not significantly different from the values at rest which amounted to 44.14 (SD 2.79) nmol · l⁻¹. An increase of power output of 30 W above CP-V˙O₂ was accompanied by a significant increase in H⁺]_b above the resting level (P=0.03). Accepted: 25 March 1998