A dynamical systems approach for the submaximal prediction of maximum heart rate and maximal oxygen uptake

Abstract

This study examines the viability of utilizing a dynamical system model and heuristic parameter estimation algorithm to make predictions for maximum heart rate ( $$\mathrm {HR_{max}}$$ ) and maximal oxygen uptake ( $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ ) using data collected from a submaximal testing protocol. $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ is widely considered to be the best single measurement of overall fitness in humans. When a $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ assessment is not available, $$\mathrm {HR_{max}}$$ is often used to prescribe exercise intensities for training and rehabilitation. In the absence of maximal cardiopulmonary exercise testing (CPET), $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ are typically estimated using traditional submaximal prediction methods with well-known limitations and inaccuracies. For this study, 12 regularly exercising healthy young adult males performed a bout of maximal CPET on a cycle ergometer to determine their true $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ . Participants also performed a submaximal bout of exercise at varied intensities. A dynamical system model and heuristic parameter estimation algorithm were applied to the submaximal data to estimate the participants’ $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ . The submaximal predictions were evaluated by computing the coefficient of determination $${R^2}$$ and the standard error of the estimate (SEE) through comparisons with the true maximal values for $$\mathrm {HR_{max}}$$ ( $${R^2 = 0.96}$$ , SEE = 2.4 bpm) and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ ( $${R^2 = 0.93}$$ , SEE = 2.1 mL kg $$^{-1}$$ min $$^{-1}$$ ). The results from this study suggest that a dynamical system model and heuristic parameter estimation algorithm can provide accurate predictions for $$\mathrm {HR_{max}}$$ and $$\dot{\mathrm {V}}{\mathrm {O_{2max}}}$$ using data collected from a submaximal testing protocol.