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

## TL;DR

This paper uses topological analysis to identify and terminate scar-related ventricular tachycardia by connecting critical boundaries in 3D simulations.

## Contribution

The paper extends the index theorem to 3D scar-related ventricular tachycardia and proposes a topology-based ablation strategy.

## Key findings

- Paired counter-rotating critical boundaries were consistently found in each transmural layer of scar-related VT simulations.
- Ablation strategies connecting these boundary pairs successfully terminated all simulated VT cases.
- The index theorem remains valid for scar-related VT when applied to 2D surfaces derived from 3D simulations.

## Abstract

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).

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.

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.

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.