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Circulation. 2004;110:2802-2808
Published online before print October 25, 2004, doi: 10.1161/01.CIR.0000146785.15995.67
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(Circulation. 2004;110:2802-2808.)
© 2004 American Heart Association, Inc.

Arrhythmia/Electrophysiology

From Mouse to Whale

A Universal Scaling Relation for the PR Interval of the Electrocardiogram of Mammals

Sami F. Noujaim, BSc; Elena Lucca, MD; Viviana Muñoz, BSc; Dharmendra Persaud, MD; Omer Berenfeld, PhD; Frits L. Meijler, MD; José Jalife, MD

From the Institute for Cardiovascular Research and Department of Pharmacology, SUNY Upstate Medical University, Syracuse, NY; and the Interuniversity Cardiology Institute (ICIN) of the Netherlands, Utrecht, Netherlands (F.L.M.).

Correspondence to José Jalife, MD, Department of Pharmacology, SUNY Upstate Medical University, 766 Irving Ave, Syracuse, NY 13210. E-mail jalifej{at}upstate.edu

Received June 28, 2004; revision received July 31, 2004; accepted August 4, 2004.

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 {approx}101, whereas body mass (BM) augments {approx}106. Scaling of many biological processes (eg, metabolic rate, life span, aortic diameter) is described by the allometric equation Y=Y0 · BMb, 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{propto}BM1/4. 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 · BM0.24. 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.


Key Words: atrioventricular node • conduction • electrocardiography


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