To the Editor- On the deformation and interpolation of phase maps

Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

Three dimensional reconstruction to visualize atrial fibrillation activation patterns on curved atrial geometry

BACKGROUND

The rotational activation created by spiral waves may be a mechanism for atrial fibrillation (AF), yet it is unclear how activation patterns obtained from endocardial baskets are influenced by the 3D geometric curvature of the atrium or 'unfolding' into 2D maps. We develop algorithms that can visualize spiral waves and their tip locations on curved atrial geometries. We use these algorithms to quantify differences in AF maps and spiral tip locations between 3D basket reconstructions, projection onto 3D anatomical shells and unfolded 2D surfaces.

METHODS

We tested our algorithms in N = 20 patients in whom AF was recorded from 64-pole baskets (Abbott, CA). Phase maps were generated by non-proprietary software to identify the tips of spiral waves, indicated by phase singularities. The number and density of spiral tips were compared in patient-specific 3D shells constructed from the basket, as well as 3D maps from clinical electroanatomic mapping systems and 2D maps.

RESULTS

Patients (59.4±12.7 yrs, 60% M) showed 1.7±0.8 phase singularities/patient, in whom ablation terminated AF in 11/20 patients (55%). There was no difference in the location of phase singularities, between 3D curved surfaces and 2D unfolded surfaces, with a median correlation coefficient between phase singularity density maps of 0.985 (0.978-0.990). No significant impact was noted by phase singularities location in more curved regions or relative to the basket location (p>0.1).

CONCLUSIONS

AF maps and phase singularities mapped by endocardial baskets are qualitatively and quantitatively similar whether calculated by 3D phase maps on patient-specific curved atrial geometries or in 2D. Phase maps on patient-specific geometries may be easier to interpret relative to critical structures for ablation planning.