From Mouse to Whale

Abstract

Background— On the ECG, the PR interval measures the time taken by an electrical impulse generated in the sinoatrial node to propagate from atria to ventricles. From mouse to whale, the PR interval increases ≈10 ¹ , whereas body mass (BM) augments ≈10 ⁶ . Scaling of many biological processes (eg, metabolic rate, life span, aortic diameter) is described by the allometric equation Y = Y ₀ · BM ^b , where Y is the biological process and b is the scaling exponent that is an integer multiple of 1/4. Hierarchical branching networks have been proposed to be the underlying mechanism for the 1/4 power allometric law. Methods and Results— We first derived analytically the allometric equation for the PR interval. We assumed that the heart behaves as a set of “fractal-like” networks that tend to minimize propagation time across the conducting system while ensuring a hemodynamically optimal atrioventricular activation sequence. Our derivation yielded the relationship PR ∝ BM ^1/4 . We subsequently obtained previously published values of PR interval, heart rate, and BM of 541 mammals representing 33 species. Double-logarithmic analysis demonstrates that PR interval increases as heart rate decreases, and both variables relate to BM following the 1/4 power law. Most important, the best fit for PR versus BM is described by the equation PR=53 · BM ^0.24 . Hence, the empirically determined exponent (0.24) is close to 1/4, as predicted. Conclusions— We have demonstrated that the PR interval of mammals scales as the 1/4 power of the BM, following the universal law for allometric scaling to ensure an optimal atrioventricular activation sequence.