You are viewing a javascript disabled version of the site. Please enable Javascript for this site to function properly.
Go to headerGo to navigationGo to searchGo to contentsGo to footer
In content section. Select this link to jump to navigation

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.

References

[1] 

Palladino, Joseph L, , Zukus, Ryan L. Left ventricular model parameters and cardiac rate variability. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, pp. 6817-6820, 2011, 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS 2011.

[2] 

Zhong Liang, , Su Boyang, , Zhang JunMei, et al. FSI simulation of intra-ventricular flow in patient-specific ventricular model with both mitral and aortic valves. Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, pp. 703-706, 2013, 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBC 2013.

[3] 

Su Boyang, , Zhong Liang, , Wang XiKun. Numerical simulation of patient-specific left ventricular model with both mitral and aortic valves by FSI approach. Computer Methods and Programs in Biomedicine, 2014; 113(2): 474-482.

[4] 

Gohean, Jeffrey R, , George, Mitchell J, , Pate, Thomas D. Verification of a computational cardiovascular system model comparing the hemodynamics of a continuous flow to a synchronous valveless pulsatile flow left ventricular assist device. ASAIO Journal, 2013; 59(2): 107-116.

[5] 

Kerckhoffs Roy CP,, , Healy Sarah N. Computational methods for cardiac electromechanics. proceedings of the IEEE, April, 2006; 94(4): 769-779.

[6] 

Zhao Jichao, , Jin Yinbin, , Ma Li. A highly efficient and accurate algorithm for solving the partial differential equation in cardiac tissue models. Proceedings of the 2006 WSEAS International Conference on Mathematical Biology and Ecology, Miami, Florida, USA, January 18-20, 2006; pp. 81-86.

[7] 

Bernus O, , Verschelde H, , Panfilov AV. Modified ionic models of cardiac tissue for efficient large scale computations. Phys. Med. Biol, 2002; 47: 1947-1959.

[8] 

Jin YB, , Yang L, , Zhang H, , Kuo YH, , Huang YC. Numerical algorithm for conduction of action potential in two-dimensional cardiac ventricle tissue. Journal of Xi'an Jiaotong University, 2004; 38(8): 851-854.

[9] 

Guo Qi, , Yuan Ai-ling, , Hong Bing-rong. The Reproducing Kernel Method to Solve Motion Trojectory for the Space Aircraft to Track an Goal. Journal of Astronautics, 2006; 27: 145-150, Sup.

[10] 

Cui Ming-gen, , Wu Bo-ying. Reproducing kernel space numerical analysis. Science Press, China, 2004: 1-110.