title: Generalized minimal principle for rotor filaments.
abstract: To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.
authors.affiliation: Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium.
authors.forename: Hans
authors.initials: H
authors.lastname: Dierckx
authors.affiliation: Physics Department, Syracuse University, Syracuse, New York 13244, USA.
authors.forename: Marcel
authors.initials: M
authors.lastname: Wellner
authors.affiliation: L'Institut de Rythmologie et Modélisation Cardiaque, Université de Bordeaux, 33604 Pessac, France.
authors.forename: Olivier
authors.initials: O
authors.lastname: Bernus
authors.affiliation: Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium.
authors.forename: Henri
authors.initials: H
authors.lastname: Verschelde