Paired reentries maintain ventricular tachycardia: a topological analysis of arrhythmic mechanisms using the index theorem.

Introduction: In previous research on reentrant atrial tachycardia (AT), the index theorem has proven instrumental in uncovering consistent paired counter-rotating anatomical reentry (either complete or near-complete), driving the arrhythmia rotating around critical boundaries (CB). Furthermore, interconnecting each CB-pair with an ablation line has been shown to terminate the AT. In this study, we extend this approach to scar-related ventricular tachycardia (VT), complicating the calculations as VT is inherently a 3-dimensional problem. We propose that scar-related VT can be topologically simplified to one or more of four basic physiologically distinct scar-types: transmural (I-shaped), epicardially connected or endocardially connected (U-shaped) or intramural (O-shaped). Methods: Six simulations of scar-related VT were created, each featuring a distinct critical scar configuration. From each simulation, three transmural layers (endocardium, mid-myocardium and epicardium) were extracted to create 2-dimensional surfaces, which were analyzed with the index theorem, using the software package Directed Graph Mapping (DGM) extended with novel algorithms to detect the CBs. Results: On each layer, either no CBs were found or pairs of counter-rotating CBs were found, each CB had an opposite sign, adhering to the index theorem. Ablation was performed by connecting each pair of counter-rotating CBs on each layer to form a continuous ablation surface, bounded by scar tissue, the endocardial surface, or the epicardial surface. This ablation strategy consistently terminated all simulations, supporting the applicability of our topology-based approach to VT. Conclusion: The index theorem remains valid for scar-related VT. Successful ablation on VT should include, connecting the CB-pairs in each 2 dimensional surface. Any other type of ablation does not terminate the VT.