A plausible explanation for heart rates in mammals

We consider a simple model to give a plausible mechanical explanation of what are the actual resting heart rates of mammals optimized for. We study what is the optimal frequency for a viscoelastic fluid circulating in a pulsatile way through a network of tubes and conclude that the heart rate is not optimized to transport blood through the whole net. Rather, actual resting heart rates of mammals happen at frequencies that optimize flow in vessels of radii that correspond to large arteries, which bring oxygenated blood rapidly far away from the heart, towards head and limbs. Our results for the optimal frequencies, obtained using observed radii of femoral arteries in mammals, agree best with the heart rates observed. We find a theoretical allometric relation between optimal flow frequency and radius: v similar to R-1. This one, agrees with the exponent obtained when plotting observed heart rates versus radii of both, femoral arteries and carotids in mammals of different sizes, from mice to horses. (C) 2010 Elsevier Ltd. All rights reserved.