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- Title
The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.
- Authors
Qi Guo; Shu-Ting Shen; Guo, Qi; Shen, Shu-Ting
- Abstract
<bold>Background: </bold>There are two major classes of cardiac tissue models: the ionic model and the FitzHugh-Nagumo model. During computer simulation, each model entails solving a system of complex ordinary differential equations and a partial differential equation with non-flux boundary conditions. The reproducing kernel method possesses significant applications in solving partial differential equations. The derivative of the reproducing kernel function is a wavelet function, which has local properties and sensitivities to singularity. Therefore, study on the application of reproducing kernel would be advantageous.<bold>Objective: </bold>Applying new mathematical theory to the numerical solution of the ventricular muscle model so as to improve its precision in comparison with other methods at present.<bold>Methods: </bold>A two-dimensional reproducing kernel function inspace is constructed and applied in computing the solution of two-dimensional cardiac tissue model by means of the difference method through time and the reproducing kernel method through space.<bold>Results: </bold>Compared with other methods, this method holds several advantages such as high accuracy in computing solutions, insensitivity to different time steps and a slow propagation speed of error. It is suitable for disorderly scattered node systems without meshing, and can arbitrarily change the location and density of the solution on different time layers.<bold>Conclusions: </bold>The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.
- Subjects
CHINA; MYOCARDIUM; KERNEL functions; TISSUES; COMPUTER simulation; ORDINARY differential equations; PARTIAL differential equations; ALGORITHMS; BIOLOGICAL models; STATISTICAL models
- Publication
Technology & Health Care, 2016, Vol 24, pS477
- ISSN
0928-7329
- Publication type
journal article
- DOI
10.3233/THC-161171