Numerical methods for the detection of phase defect structures in excitable media

Abstract

Electrical waves that rotate in the heart organize dangerous cardiac arrhythmias. Finding the region around which such rotation occurs is one of the most important practical questions for arrhythmia management. For many years, the main method for finding such regions was so-called phase mapping, in which a continuous phase was assigned to points in the heart based on their excitation status and defining the rotation region as a point of phase singularity. Recent analysis, however, showed that in many rotation regimes there exist phase discontinuities and the region of rotation must be defined not as a point of phase singularity, but as a phase defect line. In this paper, we use this novel methodology and perform a comparative study of three different phase definitions applied to in silico data and to experimental data obtained from optical voltage mapping experiments on monolayers of human atrial myocytes. We introduce new phase defect detection algorithms and compare them with those that appeared in literature already. We find that the phase definition is more important than the algorithm to identify sudden spatial phase variations. Sharp phase defect lines can be obtained from a phase derived from local activation times observed during one cycle of arrhythmia. Alternatively, similar quality can be obtained from a reparameterization of the classical phase obtained from observation of a single timeframe of transmembrane potential. We found that the phase defect line length was (35.9 ± 6.2)mm in the Fenton-Karma model and (4.01 ± 0.55)mm in cardiac human atrial myocyte monolayers. As local activation times are obtained during standard clinical cardiac mapping, the methods are also suitable to be applied to clinical datasets. All studied methods are publicly available and can be downloaded from an institutional web-server.

The Ithildin library for efficient numerical solution of anisotropic reaction-diffusion problems in excitable media

“…4.1 for further details. The class also allows for the simulation and filament tracking in a domain with an arbitrary number of spatial dimensions [14, 27, 43, 50, 51].…”

“…2. The first and third row display the transmembrane voltage u at selected frames in time, and the second and fourth row the state space phase [14, 43]. The first stimulus is applied in the first frame in the hatched region at the left edge.…”

“…9. Both display four frames over time of the transmembrane voltage V m , the activation time phase φ , and the phase defect ϱ computed via the cosine method [14, 47]. In fig.…”

“…1. By recording the activation times of the transmembrane voltage V m (top row), the activation time phase φ [14, 47] can be computed (middle row). Where this phase is discontinuous, a phase defect is localized.…”

“…While we have selected these file formats to be easy to read using a wide variety of software, we have also developed the Python module for Ithildin to facilitate interacting with the results of an Ithildin simulation and converting them to a variety of file formats, for instance writing files in the extensible data model and format (XDMF) that can be used to view simulation results in ParaView [14,17,22,23]. The Python module also offers post-processing and analysis methods, for instance the computation of action potential duration (APD), conduction velocity (CV), various phases, phase defect DRAFT from 2024-04-29 11:19 UTC+02 7/31 detection, functions acting on filaments and filament trajectories, and several plotting functions [14,22].…”