Name
Title | ||
|---|---|---|
A Finite Element Method for an Eikonal Equation Model of Myocardial Excitation Wavefront Propagation |
Abstract | ||
|---|---|---|
An efficient finite element method is developed to model the spreading of excitation in ventricular myocardium by treating the thin region of rapidly depolarizing tissue as a propagating wavefront. The model is used to investigate excitation propagation in the full canine ventricular myocardium. An eikonal-curvature equation and an eikonal-diffusion equation for excitation time are compared. A Petrov Galerkin finite element method with cubic Hermite elements is developed to solve the eikonal-diffusion equation on a reasonably coarse mesh. The oscillatory errors seen when using the Galerkin weighted residual method with high mesh Peclet numbers are avoided by supplementing the Galerkin weights with C 0 functions based on derivatives of the interpolation functions. The ratio of the Galerkin and supplementary weights is a function of the Peclet number such that, for one-dimensional propagation, the error in the solution is within a small constant factor of the optimal error achievable in the trial space. An additional no-inflow boundary term is developed to prevent spurious excitation from initiating on the boundary. The need for discretization in time is avoided by using a continuation method to gradually introduce the nonlinear term of the governing equation. A simulation is performed in an anisotropic model of the complete canine ventricular myocardium, with 2355 degrees of freedom for the dependent variable. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0036139901389513 | SIAM JOURNAL ON APPLIED MATHEMATICS |
Keywords | Field | DocType |
eikonal equation,myocardial excitation,wavefront propagation,Petrov-Galerkin method,Hermite interpolation,numerical continuation | Petrov–Galerkin method,Discontinuous Galerkin method,Mathematical optimization,Wavefront,Mathematical analysis,Eikonal equation,Galerkin method,Finite element method,Hermite interpolation,Method of mean weighted residuals,Mathematics | Journal |
Volume | Issue | ISSN |
63 | 1 | 0036-1399 |
Citations | PageRank | References |
13 | 2.25 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Andrew J Pullan | 1 | 69 | 15.32 |
| Karl A. Tomlinson | 2 | 13 | 2.25 |
| Hunter P J | 3 | 1352 | 177.64 |