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BACKGROUND: Macroreentry stands as the predominant mechanism of typical and atypical flutter. Despite advances in mapping, many aspects of macroreentrant atrial tachycardia remain unsolved. In this translational study, we applied principles of topology to understand the activation patterns, entrainment characteristics, and ablation responses in a large clinical macroreentrant atrial tachycardia database. METHODS: Because the atrium can be topologically seen as a closed sphere with holes, we used a computational fixed spherical mesh model with a finite number of holes to induce and analyze macroreentrant atrial tachycardia. The ensuing insights were used to interpret high-density activation maps, postpacing interval-tachycardia cycle length values (difference between postpacing interval and tachycardia cycle length), and ablation response in 131 cases of typical and atypical flutter (n=106 left atrium, n=25 right atrium). RESULTS: Modeling of macroreentrant atrial tachycardia revealed that reentry on closed surfaces consistently manifests itself as paired rotation and that an odd number of critical boundaries is mathematically impossible. Together with mathematical confirmation by the index theorem, this led to a unifying construct that could explain the number of loops, difference between postpacing interval and tachycardia cycle length values, and ablation outcomes (termination, no change, or prolongation in tachycardia cycle length) in all 131 cases. CONCLUSIONS: Combining topology with the index theorem offers a novel and cohesive framework for understanding and managing typical and atypical flutter. [ABSTRACT FROM AUTHOR]