Phase singularity detection through phase map interpolation : theory, advantages and limitations

Abstract

Background During a cardiac arrhythmia, reentrant waves rotate around critical points called phase singularities (PS). PS detection is relevant to the quantitative description of the dynamics and to the identification of potential targets for ablation. Phase interpolation techniques have been proposed to increase the accuracy of PS localization. Our aim is to provide a theoretical basis and a comparative analysis of these methods.

Method Different electrode configurations representing mapping systems or catheter multi-electrode arrays were considered: triangular mesh, regular square grid and circular arrays. Linear, spline and inverse squared distance interpolation were used to create a continuous map from discrete measurements of phase. Synthetic phase maps with a PS and background noise were generated. Monte-Carlo simulations were run over millions of realizations to estimate PS locations and calculate the false negative and false positive rates as a function of noise variance.

Results Linear interpolation is shown to be exactly equivalent to the standard discrete approach without interpolation. Spline interpolation had lower false negative rate at the expense of a higher false positive rate in the presence of noise. Inverse squared distance interpolation reduced false positives and was more robust to noise but was more likely to fail to detect a PS. Phase interpolation decreased PS localization error down to 0.17 interelectrode distance. The error was largest when the PS was near an electrode.

Conclusion Phase interpolation methods offer additional flexibility to find the adequate trade-off between reducing false positives and false negatives.