This proposal aims to revolutionize the understanding and treatment of cardiac arrhythmias through a novel topological framework that addresses key limitations in current ablation strategies. Reentries, the primary drivers of arrhythmias, are traditionally seen as isolated phenomena. However, using the index theorem, we demonstrate that reentries occur in pairs, an insight crucial for understanding arrhythmia persistence. Furthermore, incomplete reentry loops, often dismissed, are shown to play a critical role and must be targeted for effective treatment.

A key objective of this project is to enhance our software package, Directed Graph Mapping (DGM), which uses network theory to analyze all types of arrhythmias. By incorporating these novel topological insights, DGM will identify all arrhythmia sources from electro-anatomical maps, whether simulated, experimental, or clinical. Importantly, we will make DGM fully open-source, enabling researchers worldwide to validate our approach.