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Space‐discretization error analysis and stabilization schemes for conduction velocity in cardiac electrophysiology
Author(s) -
Pezzuto S.,
Hake J.,
Sundnes J.
Publication year - 2016
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.2762
Subject(s) - discretization , cardiac electrophysiology , interpolation (computer graphics) , grid , finite difference , mathematics , finite element method , finite difference method , thermal conduction , numerical analysis , algorithm , mathematical analysis , computer science , geometry , physics , electrophysiology , medicine , animation , computer graphics (images) , thermodynamics
Summary In cardiac electrophysiology, the propagation of the action potential may be described by a set of reaction–diffusion equations known as the bidomain model. The shape of the solution is determined by a balance of a strong reaction and a relatively weak diffusion, which leads to steep variations in space and time. From a numerical point of view, the sharp spatial gradients may be seen as particularly problematic, because computational grid resolution on the order of 0.1 mm or less is required, yielding considerable computational efforts on human geometries. In this paper, we discuss a number of well‐known numerical schemes for the bidomain equation and show how the quality of the solution is affected by the spatial discretization. In particular, we study in detail the effect of discretization on the conduction velocity (CV), which is an important quantity from a physiological point of view. We show that commonly applied finite element techniques tend to overestimate the CV on coarse grids, while it tends to be underestimated by finite difference schemes. Furthermore, the choice of interpolation and discretization scheme for the nonlinear reaction term has a strong impact on the CV. Finally, we exploit the results of the error analysis to propose improved numerical methods, including a stabilized scheme that tends to correct the CV on coarse grids but converges to the correct solution as the grid is refined. Copyright © 2016 John Wiley & Sons, Ltd.