Ventilatory efficiency: Physiological modelling and mechanistic validation

Traditional indices such as the ${\dot{V}}_E$ - ${\dot{V}}_{C{O}_2}$ slope describe ventilatory efficiency within the submaximal, near-linear domain of exercise but underrepresent the nonlinear ventilatory behaviour emerging beyond the first ventilatory threshold (VT₁). We applied a semi-logarithmic model that linearizes the post-VT₁ response by relating CO₂ output to log-transformed ventilation, extracting an empirical slope (b_emp) and normalizing it to a theoretical upper limit of CO₂ clearance anchored to predicted maximal voluntary ventilation (MVV_pred), yielding the bounded ventilatory efficiency index $\eta {\dot{V}}_E$ . In 1150 rigorously screened healthy adults (52.4% women; median age 49 years), $\eta {\dot{V}}_E$ exhibited minimal sex-related variation (14.3% vs. 14.7%) and small positive associations with age (β = +0.058 ± 0.007, P < 0.0001) and FEV₁_pred (%) (β = +0.032 ± 0.008, P < 0.0001), accounting for ∼8.5% of total variance (R² = 0.085). Both empirical (median 3.3 [2.7-4.1] L·logL^{- 1}) and theoretical reference slopes (23.1 [19.5-27.3] L logL^{- 1}) declined with age, whereas $\eta {\dot{V}}_E$ remained stable across the lifespan, as confirmed by deterministic simulations demonstrating proportional coupling between ventilatory performance and theoretical capacity. In a post hoc cohort of individuals without cardiopulmonary disease but with isolated diffusive disturbance, multivariable regression identified $\eta {\dot{V}}_E$ as the only significant independent predictor of reduced diffusing capacity (P = 0.016), while age, height, sex and MVV_pred were non-significant (all P > 0.20), indicating physiological, rather than geometric, determinants. By referencing ventilatory performance to a theoretical limit of CO₂ removal, $\eta {\dot{V}}_E$ provides a reproducible, scale-independent descriptor that refines the physiological interpretation of ventilatory efficiency across health, ageing and contrasting ventilatory constraints. KEY POINTS: The ${\dot{V}}_E$ - ${\dot{V}}_{C{O}_2}$ slope and nadir underestimate key ventilatory adjustments during the most decisive phase of the exercise response - from the first ventilatory threshold (VT₁) to peak exercise. This study introduces a semi-logarithmic approach that linearizes the decisive post-VT₁ segment of the ventilatory response, better capturing its underlying physiological behaviour. The resulting slope, when normalized to a theoretical physiological limit for gas exchange and scaled to the predicted maximal voluntary ventilation, yields a bounded efficiency index ( $\eta {\dot{V}}_E$ , %). $\eta {\dot{V}}_E$ remained robustly stable and only weakly associated with age and lung function, while showing no meaningful dependence on sex or height in over 1000 healthy adults, from which valuable normative equations were derived. This framework integrates ventilatory drive, gas exchange and diffusion capacity, offering a unified and easily applicable tool for physiological and clinical evaluation of ventilatory efficiency.