Mechanisms underlying the genesis of re-entrant substrate for atrial fibrillation (AF) in the pulmonary veins (PVs) and left atrium (LA) are not well understood. We develop a biophysically detailed computational model for the PVs and surrounding LA tissue. The model integrates canine PV and LA single cell electrophysiology with the respective 3D tissue geometry and fiber orientation reconstructed from micro-CT data. The model simulations demonstrate that a combination of tissue anisotropy and electrical heterogeneity between the PVs and LA causes a break-down of normal electrical excitation wave-fronts. This leads to the generation of a high-frequency re-entrant source near the PV sleeves. Evidence of such sources have been seen clinically in AF patients. In summary, our modeling results provide new insights into the arrhythmogenic mechanisms of re-entrant excitation waves underlying AF.