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

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.