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Dierckx H, Wellner M, Bernus O, et al. Generalized minimal principle for rotor filaments. Phys Rev Lett. 2015;114(17):178104doi: 10.1103/PhysRevLett.114.178104.
Dierckx, H., Wellner, M., Bernus, O., & Verschelde, H. (2015). Generalized minimal principle for rotor filaments. Physical review letters, 114(17), 178104. https://doi.org/10.1103/PhysRevLett.114.178104
Dierckx, Hans, et al. "Generalized minimal principle for rotor filaments." Physical review letters vol. 114,17 (2015): 178104. doi: https://doi.org/10.1103/PhysRevLett.114.178104
Dierckx H, Wellner M, Bernus O, Verschelde H. Generalized minimal principle for rotor filaments. Phys Rev Lett. 2015 May 01;114(17):178104. doi: 10.1103/PhysRevLett.114.178104. Epub 2015 Apr 30. PMID: 25978269.
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Phys Rev Lett. 2015 May 01;114(17):178104. doi: 10.1103/PhysRevLett.114.178104. Epub 2015 Apr 30.

Generalized minimal principle for rotor filaments.

Physical review letters

Hans Dierckx, Marcel Wellner, Olivier Bernus, Henri Verschelde

Affiliations

  1. Department of Mathematical Physics and Astronomy, Ghent University, 9000 Ghent, Belgium.
  2. Physics Department, Syracuse University, Syracuse, New York 13244, USA.
  3. L'Institut de Rythmologie et Modélisation Cardiaque, Université de Bordeaux, 33604 Pessac, France.

PMID: 25978269 DOI: 10.1103/PhysRevLett.114.178104

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.

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