The effect of tissue geometry on the activation recovery interval of atrial myocytes

The propagation of electric activity inside a realistically-shaped, thick-walled model of the atria was studied. The membrane kinetics was based on the formulations of Courtemanche, Ramirez and Nattel. In spite of the assumed uniformity of all kinetics parameters, diffusion parameters, the activation recovery intervals revealed values in a range of about 20 ms, having a clearly distinct spatial distribution, with higher values close to the site of activation and lower ones at sites where activation ends. This paper presents an analysis of this phenomenon based on similar observations made on propagation along the classic models of cable and disk, as well as along the surface of a spherical shell and a diabolo-shaped shell. Propagation in the latter three geometries is treated under axial-symmetric conditions, for which dedicated analytical expressions of the diffusion term are described. The results indicate that the major effects can be directly attributed to a step discontinuity in the conductivity of the medium surrounding the locations of initial and final depolarization. Overall geometry of the myocardial wall determines the smooth distribution of activation recovery intervals in the medium, showing local maxima around the points of initiation and local minima at locations where depolarization ends. The points are determined by the location of the stimulation sites involved and overall tissue geometry.