Algebraic study of drifting spiral waves.

Abstract

This two-dimensional study is motivated by cardiac electrophysiology, and focuses on rotating spiral waves in reaction-diffusion (RD) models. Here we deal with a spiral's translational drift under a constant externally imposed gradient G. A long-standing problem may be stated as follows: Given the dimensionless drift velocity V/G, find its nontrivial direction angle Γ relative to G. A deductive algebraic treatment yields a solution, cosΓ=-V/G. Three features are worth noting: the combination of algebraic and RD contexts; a somewhat extensive derivation contrasting with a compact result; and the generality due to the absence of reaction details in the formula. Agreement with a computational database is good to fair, if spirals of very low density are excluded.