Allometric scaling of electrical excitation and propagation in the mammalian heart

Abstract

Variations in body mass impose constraints on the structure and function of mammalian species, including those of the cardiovascular system. Numerous biological processes, including cardiovascular parameters, have been shown to scale with body mass (BM) according to the law of allometric scaling: Y=Y =a∙BMb (Y, biological process; a, normalization constant; b, scaling exponent, which in many instances is a multiple of ¼). These parameters include heart and breathing rates, intervals and subintervals of the electrocardiogram (ECG), action potential duration (APD), metabolic rate, and temporal properties of ventricular fibrillation. For instance, the hierarchical branching networks of the vascular system, and of the specialized conduction system in the heart have been proposed to be important determinants of allometric scaling. A global and unifying molecular mechanism of allometric scaling has not been put forth, but changes in gene expression have been proposed to play an important role. Even though it is accepted that differences in body size have cardiovascular effects, the use of scaling in the clinical setting is limited. An increase in the clinical utilization of scaling is thought to lead to improved cardiovascular disease diagnosis and management in patients.

Copyright © 2017. Published by Elsevier Ltd.

Figures

Fig. 1

A- Double logarithmic plot of heart rate (HR) versus body mass (BM) in 33 species ranging in size from mouse to whale. The best fit line in red is y=5.5–0.22x; R=−0.96, where HR ~ 235·BM−0.25. Green lines are the 95% confidence limits. B- Variation in the heart size across four orders of magnitude in BM (horse, cat, and mouse). Modified with permission from (Noujaim et al., 2004).

Fig. 2

A- Double logarithmic plot of PR interval versus BM in 33 species ranging in size from mouse, spanning six orders of magnitude in BM. The best fit line in red is y=2.4+0.24x; R=0.92, where PR ~ 53·BM0.25. Green lines are the 95% confidence limits. B- Double logarithmic plots of PA, AH, and HV subintervals versus body mass (rat to horse). The best fits (solid black lines) are y=2.6+0.25x for PA, y=3.5+0.22x for AH, and y=2.8+0.22x for HV, where PA ~ 14·BM0.25, AH ~ 33.8·BM0.25, and HV ~ 16.6·BM0.25. Dotted and broken lines are 95% confidence and prediction limits, respectively. Modified with permission from (Noujaim et al., 2004).

Fig. 3

A- Four action-potential-phase snapshots depicting a rotation of rotors during ventricular fibrillation in mouse, guinea pig, sheep, and human hearts. Vortex-like reentry is apparent in all hearts. The white circular arrows show the location of the center and the direction of rotation. Numbers represent time of one cycle in milliseconds. B- Double logarithmic plot of VF frequency vs. BM covering 11 species, from mouse to horse. Best fit (solid line) is y=2.94–0.23x; R =−0.93. VF Frequency ~ 18.9·BM−0.25, and VF cycle length ~ 53·BM0.25. Short dashed lines and long dashed lines indicate 95% confidence and prediction limits, respectively. Modified with permission from (Noujaim et al., 2007).