The complex relationship between effort and heart rate: a hint from dynamic analysis

Dynamic analysis can be used to study the changes of self-regulated biological processes driven by external stimuli. Recently, the changes of heart rate during effort tests has successfully been adjusted using a simple first-order differential equation model driven by body power expenditure. Although this approach produces valid estimates and yields pertinent indices for the analysis of such measurements, it suffers from an inability to model the saturation of the heart-rate increase at high power expenditures and the change of heart-rate equilibrium following effort.

We propose a new analysis allowing the estimation of changes of the heart rate in response to effort (gain) as a function of the power expenditure value.

When applied to the measured heart rates of 30 amateur athletes performing a maximum graded-effort treadmill test, the proposed model was able to predict 99% of the heart rate change measured during exercise. The estimated gains decreased with a power increase above the first ventilatory threshold. This trend was stronger above the second ventilatory threshold and was strongly correlated with the maximum oxygen consumption.

The proposed approach yields a highly precise model of heart rate dynamics during variable effort that reflects the changes of metabolic energy systems at play during exercise.