Published Online
on October 25, 2004

A more recent version of this article appeared on November 2, 2004

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Submitted on June 28, 2004
Revised on July 31, 2004
Accepted on August 4, 2004

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, and 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.).

^* To whom correspondence should be addressed. E-mail: jalifej{at}upstate.edu.

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 10¹, whereas body mass (BM) augments 10⁶. Scaling of many biological processes (eg, metabolic rate, life span, aortic diameter) is described by the allometric equation Y=Y₀ · 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 PRBM^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.

Key words: atrioventricular node • conduction • electrocardiography

Related Article:

Circulation 2004 110: 2773. [Full Text]

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