Mathematical Modeling of LongLasting Persistent Atrial Fibrillation Explains Why Cardioversion Might be the EndPoint for Radiofrequency Ablation: Extrapolation of Clinical Results and Mathematical Modeling Data

Andrey Aradshev1,2, Mikhail Mazurov3, Evgeny Zhelyakov1, Ilia Kaluzhny3, Vasily Finko1, Yury Belenkov2 
1 Electrophysilogy, Federal Scientific and Clinical Cenre of Biomedical Agency, Russia 2 Arrhythmology, Lomonosov State University, Russia 3 Mathematical Chair, Moscow State University of Economic, Statistics, and Informatics, Russia

Aims: 1) to investigate theoretical probability of termination 6 and 4waves reentry atrial fibrillation (AF) by mathematical simulation of cardiversion; 2) to extrapolate mathematical modeling data to clinical results of linear ablation in patients with longlasting persistent AF. Material and Methods: Clinical phase. Study was conducted on consecutive 20 pts (6 women, 58.2±10.6 years of age) with longlasting persistent AF who underwent index ablation. Ablation approach consisted of 3 steps. The first step was antral isolation of PVs, the second step included mitral isthmus ablation and the third step was linear roof ablation. We evaluated AF CL into the CS after each step. Mathematical phase. As the first step numeric reconstruction of the autowave process in excitable tissues of the LA and the simulation of 6wave reentry AF was performed using FitzhughNagumo equation. A special scanning method was used for calculating characteristics of autowave processes in a 2D mathematical model in left atrium (LA). Then ablation formatting (corresponding to all ablation lines) was performed. Modeling of cardioversion applied for 6 and 4wave reentry. Results: Clinical phase. Organization of AF cycle length (from 112±24 to 204±35 ms) was verified in 12 of 20 pts during ablation. SR was effectively restored after external cardioversion at the end of procedure in all pts. Mathematical phase. Ablation formatting (corresponding to linear ablation) transformed 6wave reentry to 4 wave reentry. Following mathematical simulation of cardioversion effectively terminated 4wave AF, whereas did not cease 6wave reentry AF.
Conclusion: 1) Mathematical modeling of 6wave reentry and linear ablation formatting may simulate long lasting persistent AF and subsequent AF organization due to antral and linear ablation. Conversion of 6waves reentry to 4waves reentry with following AF termination after cardioversion may be successful ablation endpoint recording the mathematical approach. 2) Our clinical results are consistent with ablation formatting data. 