A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry

The majority of models of wavefront propagation in cardiac tissue have assumed relatively simple geometries. Extensions to complicated three-dimensional (3-D) representations are computationally challenging due to issues related both to problem size and to the correct implementation of flux conserva...

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Bibliographic Details
Published in:IEEE transactions on biomedical engineering 2003-04, Vol.50 (4), p.412-420
Main Authors: Zozor, S., Blanc, O., Jacquemet, V., Virag, N., Vesin, J.-M., Pruvot, E., Kappenberger, L., Henriquez, C.
Format: Article
Language:English
Subjects:
Algorithms
Biological and medical sciences
Body Surface Potential Mapping - methods
Cardiac tissue
Cardiology and cardiovascular system
Computation
Computational modeling
Computer Simulation
Conservation
Electrocardiography - methods
Electromagnetic Fields
Engineering Sciences
Finite difference methods
Finite volume methods
Flux
Geometry
Heart - physiology
Heart Conduction System - physiology
Human health and pathology
Humans
Life Sciences
Mathematical models
Medical sciences
Membrane Potentials - physiology
Models, Cardiovascular
Monolayers
Myocytes, Cardiac - physiology
Numerical models
Other
Shape
Solid modeling
Spatial resolution
Wave fronts
Wave propagation
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Summary:The majority of models of wavefront propagation in cardiac tissue have assumed relatively simple geometries. Extensions to complicated three-dimensional (3-D) representations are computationally challenging due to issues related both to problem size and to the correct implementation of flux conservation. In this paper, we present a generalized finite difference scheme (GDFS) to simulate the reaction-diffusion system on a 3-D monolayer of arbitrary shape. GDFS is a vertex-centered variant of the finite-volume method that ensures local flux conservation. Owing to an effectively lower dimensionality, the overall computation time is reduced compared to full 3-D models at the same spatial resolution. We present the theoretical background to compute both the wavefront conduction and local electrograms using a matrix formulation. The same matrix is used for both these quantities. We then give some results of simulation for simple monolayers and complex monolayers resembling a human atria.
ISSN:0018-9294
1558-2531
DOI:10.1109/TBME.2003.809505