A resistor interpretation of general anisotropic cardiac tissue.
This paper describes a spatial discretization scheme for partial differential equation systems that contain anisotropic diffusion. The discretization method uses unstructured finite volumes, or the boxes, that are formed as a secondary geometric structure from an underlying triangular mesh. We show how the discretization can be interpreted as a resistive circuit network, where each resistor is assigned at each edge of the triangular element. The resistor is computed as an anisotropy dependent geometric quantity of the local mesh structure. Finally, we show that under certain conditions, the discretization gives rise to negative resistors that can produce non-physical hyperpolarizations near depolarizing stimuli. We discuss how the proper choice of triangulation (anisotropic Delaunay triangulation) can ensure monotonicity (i.e. all resistors are positive).
Shao
Hai
H
Department of Computer Science, Duke University, Durham, NC 27708-0129, USA.
Sampson
Kevin J
KJ
Pormann
John B
JB
Rose
Donald J
DJ
Henriquez
Craig S
CS
D016880:Anisotropy; D020342:Finite Element Analysis; D006321:Heart / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*