An experimentalist's approach to accurate localization of phase singularities during reentry

A phase variable that uniquely represents the time course of the action potential has been used to study the mechanisms of cardiac fibrillation. A spatial phase singularity (PS) occurs during reentrant wave propagation and represents the organizing center of the rotating wave. Here, we present an error analysis to investigate how well PSs can be localized. Computer simulations of rotating spiral waves scaled appropriately for cardiac tissue were studied with various levels of noise added. The accuracy in identifying and localizing singularities depended on three factors: (i) the point chosen as the origin in state space used to calculate the phase variable; (ii) signal to noise ratio; and (iii) discretization (number of levels used to represent data). We found that for both simulation as well as experimental data, there existed a wide range for the choice of origin for which PSs could be identified. Discretization coupled with noise affected this range adversely. However, there always existed a range for choice of the origin that was 20% or more of the action potential amplitude within which the accuracy of localizing PSs was better than 2 mm. Thus, a precise determination of origin was not necessary for accurately identifying PSs.