Predicting cardiac frequencies in mammals

We develop a fluid mechanical model of the arterial tree in order to address the key question of what determines heart rate in mammals. We propose that the frequency of the pulsatile pressure gradient, which minimizes resistance to flow and facilitates fluid movement, coincides with the physiological heart rate. Using data from the literature on heart rate in 95 mammals as a function of body mass, and the radius of the aorta as a function of body mass, we construct a target curve of cardiac frequency versus aortic radius. This curve serves as a benchmark for comparison with our model's results. Our elastic one-dimensional model for pulsatile arterial flow, combined with experimental rheological data for human blood, enables us to calculate the frequency that minimizes flow resistance, which we express as a function of a characteristic vascular scale, in this case, the aorta radius. We find a reasonable agreement with the target curve, confirming a scaling law with the observed exponent for mammals ranging in size from ferrets to elephants. Our model provides a plausible explanation for the resting heart rate frequency in healthy mammals.