Mathematical Modeling of Long-Lasting Persistent Atrial Fibrillation Explains Why Cardioversion Might be the End-Point for Radiofrequency Ablation: Extrapolation of Clinical Results and Mathematical Modeling Data

Aims: 1) to investigate theoretical probability of termination 6- and 4-waves re-entry atrial fibrillation (AF) by mathematical simulation of cardiversion; 2) to extrapolate mathematical modeling data to clinical results of linear ablation in patients with long-lasting persistent AF.

Material and Methods: Clinical phase. Study was conducted on consecutive 20 pts (6 women, 58.2±10.6 years of age) with long-lasting 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 6-wave re-entry AF was performed using Fitzhugh-Nagumo 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 4-wave re-entry.

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 6-wave reentry to 4 wave re-entry. Following mathematical simulation of cardioversion effectively terminated 4-wave AF, whereas did not cease 6-wave reentry AF.

Conclusion: 1) Mathematical modeling of 6-wave reentry and linear ablation formatting may simulate long lasting persistent AF and subsequent AF organization due to antral and linear ablation. Conversion of 6-waves re-entry to 4-waves reentry with following AF termination after cardioversion may be successful ablation end-point recording the mathematical approach. 2) Our clinical results are consistent with ablation formatting data.