Abstract
   Atrial arrhythmias, such as atrial fibrillation, focal or reentrant tachycardia, and atrial flutter are the most common cardiac arrhythmias in clinical practice, and constitute one of the major health problems today. Different experimental studies have demonstrated that the electrophysiological mechanisms underlying atrial arrhythmias are very varied, highlighting the anatomical and functional reentries, ectopic foci and the existence of spiral waves. Additionally, it has been demonstrated that atrial tachycardias induce electrophysiological alterations that perpetuate them, these changes are called atrial remodeling. Although numerous studies have been performed in this field, the nature of the structural and cellular abnormalities that promote and perpetuate atrial arrhythmias have not been clearly determined, due mainly to the limitations of these experimental studies. A proper understanding of the mechanisms that generate and maintain atrial arrhythmias would allow a selective pharmaco-surgical treatment more optimized and effective, which would cause less secondary damage on the patient. Currently,  mathematical modeling and computer simulations have become a powerful tool to analyze arrhythmogenic processes and even to suggest new experimental or clinical studies and new therapies. 
   In this PhD thesis atrial arrhythmias are simulated and characterized, different factors that promote their initiation and maintenance are evaluated, a new method to localize reentrant and focal sources is propose and evaluated, and finally, the effectiveness of different ablation patterns on termination of atrial arrhythmias is assessed. 
   The modeling is achieved through differential equations, which represent the different currents involved in electrical activity of atrial cells. The effects of electrical remodeling were introduced into this model, which has been integrated into unidimensional and bidimensional atrial tissues and into a threedimensional model of human atria, anatomically realistic. These models were stimulated under different conditions using different predetermined protocols of stimulation. Potential maps of the action potential propagation along the virtual tissues were constructed, and pseudo-electrograms were calculated, to which a spectral analysis was performed. Additionally, dominant frequency maps and organization index maps were developed to characterize atrial arrhythmias. Three different ablation patterns known in clinical practice were simulated and evaluated. The effectiveness of a novel method proposed in this thesis for the location of reentrant and focal sources was also studied. Two different simple ablation patterns were applied and its efficacy in terminating the arrhythmia was assessed. 
   The results show that: 1) Electrical remodeling favours the generation of reentries. 2) The interaction between a continuous ectopic focus and a premature stimulus generates a complex reentrant activity. 3) Factors such as the high frequency of ectopic foci, a larger number of focal stimuli, a decreased conduction velocity and increased anisotropy favor the vulnerability to reentry and the initiation and maintenance of complex reentrant patterns. 4) The highest vulnerability to reentry occurs in the pulmonary veins because they act as anatomical barriers by providing a way for reentrant circuits. 5) Analysis of reentrant patterns, the calculated pseudo-electrograms and the dominant frequency maps and organization index maps, can characterize the different patterns and the simulated atrial arrhythmias. 6) The proposed method in this thesis can locate the stable reentrant sources during reentrant tachycardias and the focal sources. 7) The Maze III ablation technique is the most effective, terminating completely the simulated atrial arrhythmias. The left partial Maze and the mini-Maze techniques are effective in terminating the reentrant tachycardia, in which the reentrant circuit is located in the left atrium. Mini-Maze technique is also effective in the termination of typical atrial flutter. Both patterns applied during atrial fibrillation lead to reentrant tachycardia. Simple ablation patterns, applied in base on the location of reentrant circuits, are effective in the termination of the arrhythmia, which corroborates the importance of locating such circuits. 
   Biophysical modeling can be considered as a useful tool for understanding the underlying mechanisms of therapies for atrial arrhythmias.