Eikonal-Based Construction of Initial Conditions for Simulating Reentries in Patient-Specific Atrial Geometries

Elham Zakeri Zafarghandi and Vincent Jacquemet
Université de Montréal


Abstract

BACKGROUND: Stimulation protocols for arrhythmia induction rely on precise timing adjustments. When studying arrhythmia perpetuation, a computer-generated initial condition may suffice.

METHODS: Cubic meshes and interconnected cable models of the left atrium were created from 98 patient-specific geometries from King's College London public database. Coarser triangulated meshes with 14.9±2.7k vertices were automatically generated using PyMeshLab. Universal atrial coordinates (UAC) were used to continuously map the surface onto a unit square in the plane. A spiral wave at the center of the pulmonary vein area was generated in the UAC plane by an analytical formula. The resulting phase map was projected on the coarse mesh, smoothened and regularized using an eikonal-diffusion solver. The algorithm is provided as an open-source Python package. Simulation of a paced single cell defined a mapping between phase and cell state, from which we constructed an initial condition for the monodomain equation (remodeled Courtemanche kinetics and reduced conductivity) by nearest-neighbor interpolation. Simulations were run for 1 s from that initial condition in the 2x98 models. Phase singularities (PS) were detected, and their UAC coordinates were documented.

RESULTS: Computational time for eikonal-based phase map generation was 2.4±0.8 s per case (n = 98). The initial conditions were comparable despite anatomical variability. The reentry was sustained in 195/196 cases. The spiral consistently migrated toward the left appendage, as demonstrated by a peak in the PS density cumulated over 98 simulations (last 500 ms), both in the cubic and cable models. Half of the PS were located within 0.21 (cubic) and 0.20 (cables) UAC units from the peak density, indicating consistency across patient anatomy. The distance between peak PS density in cubic and cable models was 0.028 UAC units.

CONCLUSION: Eikonal-based initial conditions facilitate automated arrhythmia initiation and enable the investigation of reproducibility across geometries and mesh types.