title: The construction of a two-dimensional reproducing kernel function and its application in a biomedical model.
abstract: BACKGROUND
  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.
  
  
  OBJECTIVE
  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.
  
  
  METHODS
  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.
  
  
  RESULTS
  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.
  
  
  CONCLUSIONS
  The reproducing kernel method has higher solution accuracy and stability in the solutions of the two-dimensional cardiac tissue model.
authors.affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang, China.
authors.forename: Qi
authors.initials: Q
authors.lastname: Guo
authors.affiliation: Health Science Center, Peking University, Beijing, China.
authors.forename: Shu-Ting
authors.initials: ST
authors.lastname: Shen
mesh_terms: D000465:Algorithms; D002681:China; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D009206:Myocardium
keywords: Reproducing kernel; cardiac tissue model; compact finite difference; two-dimensional