IJPAM: Volume 30, No. 3 (2006)

A BIDOMAIN MODEL OF HUMAN CARDIAC TISSUE
INCORPORATING A CAPILLARY MICROSTRUCTURE

John C. Clements$^1$, B. Milan Horácek$^2$
$^1$Department of Mathematics and Statistics
School of Biomedical Engineering
Chase Building, Dalhousie University
Halifax, Nova Scotia, B3H 3J5, CANADA
e-mail: john.clements@dal.ca
$^2$Department of Physiology and Biophysics and Department of Medicine
Tupper Building, Dalhousie University
Halifax, Nova Scotia, B3H 4H7, CANADA
e-mail: milan.horacek@dal.ca


Abstract.Experimental evidence has shown that during propagation of activation in mammalian cardiac tissue, fast action potential upstrokes ($\dot{V}_{max}$) and slower wave velocities are associated with transverse propagation while slow upstrokes and higher wave speeds are associated with longitudinal propagation. Standard bidomain models of cardiac dynamics cannot reproduce this behaviour nor do they incorporate the potentially important properties of the cardiac capillary network. In this study the standard continuous, anisotropic bidomain model for the propagation of electrical activation in the human myocardium $H$ is extended to incorporate both a directionally dependent bulk membrane capacitance $C_{blk}$ and a distributed parallel resistance-capacitance capillary network. Using a simple model for the cardiac membrane dynamics, numerical simulations are conducted to determine the propagation properties of the activation wavefronts for this modified formulation and to examine the extent to which the incorporation of this capillary microstructure affects the action potential profile.

Received: June 1, 2006

AMS Subject Classification: 35K60, 92C05, 35Q80, 92C30

Key Words and Phrases: mammalian cardiac tissue, anisotropic bidomain model, human myocardium, cardiac membrane dynamics, capillary microstructure

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 3