Substrate size as a determinant of fibrillatory activity maintenance in a mathematical model of canine atrium.

Tissue size has been considered an important determinant of atrial fibrillation (AF), but recent work has questioned the critical size hypothesis. Here, we use a previously developed mathematical model of the two-dimensional canine atrium with realistic action potential, ionic, and conduction properties to address substrate size effects on the maintenance of fibrillatory activity. Cholinergic AF was simulated at different acetylcholine (ACh) concentrations ([ACh]) and distributions, with substrate area varied 11.1-fold. Automated phase singularity detection was used to facilitate the analysis of arrhythmic activity. The duration of activity induced by a single extrastimulus increased with increasing substrate dimensions. Two general mechanisms underlying activity were observed and were differentially affected by substrate size. For large mean [ACh], single primary rotors anchored in low-[ACh] zones maintained activity and substrate dimensions were not critical. At lower mean [ACh], extensive spiral wave meander prevented the emergence of single stable rotors. Prolonged activity was favored when substrate size permitted a sufficiently large number of simultaneous longer-lasting rotors that extinction of all was unlikely. Thus either single dominant rotor or multiple reentrant spiral generator mechanisms could maintain fibrillatory activity in this model and were differentially dependent on substrate size. These results speak to recent debates about the role in AF of single driver rotors versus multiple reentrant circuit mechanisms by suggesting that either may maintain fibrillatory atrial activity depending on atrial size and electrophysiological properties.