New method for the mathematical derivation of the ventilatory anaerobic threshold: a retrospective study

BACKGROUND: Ventilatory anaerobic threshold (VAT) is a useful submaximal measure of exercise tolerance; however, it must be visually determined. We developed a new mathematical method to objectively determine VAT. METHODS: We employed two retrospective population data sets (A/B). Data A (from 128 healthy subjects, patients with cardiovascular risk factors, and cardiac subjects at institution A, who underwent symptom-limited cardiopulmonary exercise testing) were used to develop the method. Data B (from 163 cardiac patients at institution B, who underwent pre−/post-rehabilitation submaximal exercise testing) were used to apply the developed method. VAT (by V-slope) was visually determined (vVAT), assuming that the pre-VAT segment is parallel to the respiratory exchange ratio (R) = 1 line. RESULTS: First, from data A, exponential fitting of ramp V-slope data yielded the equation y = ba(x), where a is the slope of the exponential function: a smaller value signified a less steep curve, representing less VCO(2) against VO(2). Next, a tangential line parallel to R = 1 was drawn. The x-axis value of the contact point was the derived VAT, termed the expVAT (VCO(2)) (calculated as LN (1/[b*LN(a)]/LN(a). This point represents an instantaneous ΔVCO(2)/ΔVO(2) of 1.0. Second, in a similar way, the relation of VO2 vs. VE (minute ventilation) was fitted exponentially. The tangent line that crosses zero was drawn and the x-axis value was termed expVAT (VE) (calculated as 1/LN(a). For data A, the correlation coefficients (r) of vVAT versus VAT (CO(2)), and VAT (VE) were 0.924 and 0.903, respectively (p < 0.001), with no significant difference between mean values with the limits of agreement (1.96*SD of the pair difference) being ±276 and ± 278 mL/min, respectively. expVAT (VCO(2)) and expVAT (VE) significantly correlated with VO(2)peak (r = 0.971, r = 0.935, p < 0.001). For data B, after cardiac rehabilitation, expVAT (CO(2)) and exp. (VE) (mL/min) increased from 641 ± 185 to 685 ± 201 and from 696 ± 182 to 727 ± 209, respectively (p < 0.001, p < 0.008), while vVAT increased from 673 ± 191 to 734 ± 226 (p < 0.001). During submaximal testing, expVAT (VCO(2)) underestimated VAT, whereas expVAT (VE) did not. CONCLUSIONS: Two new mathematically-derived estimates to determine VAT are promising because they yielded an objective VAT that significantly correlated with VO(2)peak, and detected training effect as well as visual VAT did. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (10.1186/s13102-019-0122-z) contains supplementary material, which is available to authorized users.