The complexity of cardiac fibrillation dynamics can be assessed by analyzing the distribution of phase singularities. The configuration of phase singularities (locations and directions of rotation of spiral waves) can be determined from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase map with a given configuration of phase singularities. We present a constructive mathematical approach to numerically solve this problem in geometries relevant to atrial anatomy.
This method is then applied to generate random phase maps in order to evaluate phase singularity detection algorithms. Since the exact position of phase singularities is known, this provides a statistical model for studying false positive and false negative detection rates as a function of mapping resolution (inter-electrode distance), the level of noise and phase distortion. Monte-Carlo simulations show that, in this model, false detection rates depend on the average distance between neighboring phase singularities, following approximately a power law, in agreement with theoretical arguments.

This work is supported by NSERC grant RGPIN-2015-05658.