Abstract(s)
Phase singularity analysis provides a quantitative description of spiral wave patterns observed in chemical or
biological excitable media. The configuration of phase singularities (locations and directions of rotation) is easily
derived from phase maps in two-dimensional manifolds. The question arises whether one can construct a phase
map with a given configuration of phase singularities. The existence of such a phase map is guaranteed provided
that the phase singularity configuration satisfies a certain constraint associated with the topology of the supporting
medium. This paper presents a constructive mathematical approach to numerically solve this problem in the plane
and on the sphere as well as in more general geometries relevant to atrial anatomy including holes and a septal
wall. This tool can notably be used to create initial conditions with a controllable spiral wave configuration for
cardiac propagation models and thus help in the design of computer experiments in atrial electrophysiology.