Introduction: Reentrant activity underlies many cardiac arrhythmias, yet is traditionally interpreted as arising from isolated circuits. We propose a unifying topological framework based on the index theorem, stating that the sum of phase singularity indices on a closed surface equals zero, implying that reentries must occur in pairs.
Methods: We applied the index theorem to atrial tachycardia (AT), ventricular tachycardia (VT), and atrial fibrillation (AF) using computational modeling and clinical data. For AT, 572 simulations were performed on spherical atrial models with varying boundary configurations. Clinical validation included retrospective (n=131) and prospective (n=88) high-density mapping datasets. VT mechanisms were investigated using 3D simulations of different scar topologies. AF dynamics were explored in 600 simulations on anatomically realistic atrial models with fibrosis.
Results: Across all AT simulations and clinical cases, reentrant circuits consistently appeared as paired structures with opposite chirality. Incomplete ("bystander") loops exhibited nonzero index and were essential for arrhythmia maintenance. Ablation targeting only one loop resulted in tachycardia slowing, whereas connecting paired critical boundaries led to termination. In VT, four fundamental scar topologies were identified, each supporting paired reentries across myocardial layers. In AF simulations, the total topological charge remained conserved despite continuous creation, annihilation, and boundary interactions of rotors, supporting the persistence of paired rotational activity.
Conclusion: The index theorem provides a unifying principle across atrial and ventricular arrhythmias, demonstrating that reentries do not exist in isolation but as paired entities. This insight challenges conventional mapping interpretations and suggests a novel ablation strategy targeting connections between critical boundaries. Topology-based analysis may improve mechanistic understanding and guide more effective, substrate-informed therapies.