Topology Rules the Heart: Simple Wave Mathematics Terminates Atrial Fibrillation in Every Simulation

Atrial fibrillation, the chaotic rhythm disorder that affects tens of millions of people worldwide, has long defied a simple description. Cardiac electrophysiologists have debated for decades whether the arrhythmia is sustained by many wandering wavelets, a single dominant rotor, several stable rotational sources, or electrical dissociation between the layers of the atrial wall. A new computational study from Ghent University and collaborating institutions now argues that all of these seemingly competing pictures may be different faces of one underlying topological reality, and that this reality can be exploited to shut the arrhythmia down completely, at least in silico.

The research, published in Frontiers in Network Physiology by Arthur S. Bezerra, Robin Van Den Abeele, Nele Vandersickel and colleagues, builds on a deceptively simple mathematical observation. When the atrium is treated as a two-dimensional surface, every propagating wavefront must take one of exactly two geometric forms. It is either an open wave, a line-like segment whose two endpoints are anchored to boundaries such as valves, veins, scars or temporarily refractory tissue, or a closed wave, a ring-like structure that encloses a region of tissue and has no endpoints at all. The distinction echoes a theorem first articulated by Norbert Wiener and Arturo Rosenblueth in 1946, but the new work extends it into a complete dynamical framework for atrial fibrillation.

The crucial insight is that these two wave archetypes behave in fundamentally opposite ways. Open waves, the authors show, tend to self-perpetuate: as long as their endpoints remain attached to boundaries, the wave keeps circulating and can sustain reentrant activity indefinitely. Closed waves, by contrast, tend toward self-termination. On a surface topologically equivalent to a sphere, an expanding closed wave must eventually run out of excitable tissue, transition into a shrinking wave, and collapse. The sino-atrial node’s normal heartbeat pulse is itself a closed wave of this kind, expanding through the atrium before dying out.

From this dichotomy, the team derived a remarkably compact set of rules. Every interaction between wavefronts, obstacles and boundaries in their simulations reduced to just five elementary events: open wave creation, open wave annihilation, closed wave creation, closed wave annihilation, and open wave collision. When a closed wave strikes an obstacle and breaks, an open wave is born. When two open waves merge end to end, an open wave is annihilated. When the two endpoints of a single open wave meet, the wave closes into a ring. And when two open waves collide head-on, they pass through one another, producing two new open waves without changing the total count. More complicated-looking interactions, the authors found, are simply combinations of these five primitives occurring in quick succession.

To test whether this tidy taxonomy survives contact with biological realism, the researchers analyzed a cohort of 600 patient-specific atrial fibrillation simulations. The models were built from publicly available three-dimensional atrial meshes of 100 patients with fibrillation, incorporating realistic fibrosis maps derived from late gadolinium-enhanced MRI and patient-specific fiber orientations. Using the openCARP simulation environment and the Courtemanche ionic model with atrial fibrillation remodeling, the team simulated six different initiation conditions per mesh, each running for 3400 milliseconds, with conduction velocity reduced in fibrotic regions in proportion to MRI intensity.

Detecting and classifying hundreds of thousands of wavefronts required a purpose-built algorithm. The team used an extended phase-mapping approach that first computes the phase of the transmembrane voltage at every mesh vertex, then explicitly identifies phase defects, the discontinuities caused by functional block and fibrosis, and removes them from the rotation calculation. Triangles carrying phase jumps in opposite directions were clustered into connected components representing individual wavefronts, and end-triangles touching phase defects served as discrete equivalents of wave endpoints. Each endpoint was assigned a chirality, clockwise or counterclockwise, and wavefronts with exactly two oppositely charged endpoints were tagged as open waves, while those with none were tagged as closed waves.

The results were striking in their consistency. Across all simulations, the algorithm detected 804,085 open waves and 51,039 closed waves, and every single open wave contained exactly two endpoints with opposite chirality, while every closed wave contained none. Tracking the wavefronts over time yielded 132,870 interaction subgraphs containing 274,461 events, with creation and annihilation events each accounting for 45 percent of the total and open wave collisions making up the remaining 9 percent. Critically, when the researchers computed the total topological index, the net rotational charge, at every moment in every simulation, it summed to exactly zero, in perfect agreement with the index theorem that requires counter-rotating pairs on closed surfaces.

The framework’s most dramatic payoff came in the form of a virtual ablation strategy. Because open waves are the self-perpetuating elements that keep fibrillation alive, the team designed an intervention to convert every open wave in the tissue into a closed wave. At three different time points during each simulation, they identified all phase defects and all open waves, then drew instantaneous virtual ablation lines connecting the endpoints of each open wave just ahead of its advancing wavefront, using an A* pathfinding algorithm whose cost function steered the lines through regions of low phase to maximize the chance of intercepting propagation. Of 1,475 ablation procedures performed across the cohort, every single one terminated the arrhythmia, producing complete electrical silence before the end of the simulation window, a 100 percent success rate. The median procedure required only two ablation lines, and the average required the elimination of just over three open waves.

The authors are careful to note what this result does and does not mean. The virtual ablation is not practically implementable as such, since it demands the instantaneous creation of continuous lesion lines that precisely block dynamically moving wavefronts, something no catheter can currently achieve. The team also did not test whether the hearts would remain non-inducible after the intervention; because the strategy was designed only to terminate fibrillation at a moment in time, there is no reason to expect that new induction would not restart the arrhythmia. Instead, the researchers suggest a more realistic translational path: using the wave-detection algorithm during burst pacing with high-density mapping to identify substrate regions prone to generating non-recombining open waves, and targeting those areas prophylactically.

Even with those caveats, the conceptual contribution is substantial. The open-and-closed wave framework reconciles the field’s long-standing competing theories under a single umbrella: the multiple wavelet hypothesis, the mother rotor hypothesis, meandering rotors, and focal sources all emerge as particular dynamic manifestations of open waves constrained by different kinds of boundaries. It also connects to recent work on topological defibrillation, including the so-called teleportation method in which precisely timed stimuli force spiral wave endpoints together to trigger annihilation, and to statistical-physics analogies comparing fibrillation to unbound vortex states. If the framework holds up in experimental and clinical settings, the chaotic electrical storm of atrial fibrillation may turn out to be governed by a handful of rules simple enough to write on a napkin, and simple enough, perhaps, to beat.

Subject of Research: Topological classification of atrial wavefronts and topology-guided ablation for terminating atrial fibrillation in patient-specific simulations

Article Title: Open wavefront ablation terminates rotor-driven atrial fibrillation

Article References: Open wavefront ablation terminates rotor-driven atrial fibrillation. (n.d.). https://doi.org/10.3389/fnetp.2026.1940428

Image Credits: AI Generated

DOI: 10.3389/fnetp.2026.1940428

Keywords: atrial fibrillation, cardiac electrophysiology, topology, wavefront dynamics, ablation, rotors, phase mapping, computational modeling, index theorem, reentry, open waves, closed waves