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研究生:何家豪
研究生(外文):Chia-HaoHo
論文名稱:以不連續有限元素法解單域心電波方程
論文名稱(外文):Discontinuous Galerkin Methods for Monodomain Electrocardiac Wave Equations
指導教授:陳旻宏陳旻宏引用關係
指導教授(外文):Min-Hung Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:數學系應用數學碩博士班
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:英文
論文頁數:38
中文關鍵詞:單域心電波方程擴散反應方程不連續有限元素法半顯隱 Runge-Kutta方法
外文關鍵詞:monodomain electrocardiac wave equationreaction-diffusion equationdiscontinuous Galerkin methodimplicit-explicit Runge-Kutta methods
相關次數:
  • 被引用被引用:0
  • 點閱點閱:85
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  • 下載下載:4
  • 收藏至我的研究室書目清單書目收藏:1
本篇論文主要在建構一維數值格式來模擬心臟細胞上之波傳問題。我們考慮的單域心電波方程為一條擴散反應方程式,在反應項的部分包含了許多條常微分方程式。在建構數值格式來解這問題時,我們先用不連續有限元素法將方程式於空間上半離散化,接著將空間離散後的常微分方程用時間積分的方法來解。基於單域心電波方程的一些數學性質,我們將考慮使用 implicit-explicit Runge-Kutta方法。在解決主要問題之前,我們先對建構出來的數值格式做測試問題,並且得到我們預期的數值解收斂結果。最後將本計算格式在於解單域心電波方程的結果和其他研究結果比較並獲得一致的結果。
In this thesis we construct a one-dimensional scheme to simulate the electrocardiac wave propagating in excitable ventricular cells. The monodomain electrocardiac wave equation is a reaction-diffusion equation whose reaction term consists of six ordinary differential equations and those equations are discretized in space into a set of semi-discrete equations by the discontinuous Galerkin method. The resulting ordinary differential equations system can be solved using time-integration methods. Due to the nature of the problem, we consider the implicit-explicit Runge-Kutta methods. The performances of the scheme are illustrated through numerical experiment. The numerical solution to the diffusion equation and the reaction-diffusion equation converge with the expected rates. The result of the monodomain equation with Luo-Rudy phase 1 model is also presented.
1 Introduction(p.4)
2 Cardiac Model (p.6)
2.1 Cell Model (p.6)
2.2 Monodomain Model (p.10)
3 Discontinuous Galerkin Methods (p.11)
3.1 DG methods for diffusion equation (p.11)
3.2 DG methods for reaction-diffusion equation (p.15)
4 Runge-Kutta methods (p.18)
4.1 Diagonally Implicit Runge-Kutta Methods (p.18)
4.2 Additive Runge-Kutta Methods; 4.3 Test problems (p.21)
5 Computational Results (p.24)
5.1 Numerical experiments (p.24)
5.1.1 Test Problem I (p.24)
5.1.2 Test Problem II (p.27)
5.2 Monodomain Model (p.29)
6 Conclusion (p.33)
Bibliography (p.34)
Appendix (p.37)

1.Hodgkin AL, Huxley AF, A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve, J. Physiol(1952), 117, p.500-544.
2.R.E McAllister, D. Noble and R.W. Tsien, Reconstruction of The Electrical Activity of Cardiac Purkinje Fibers, J. Physiol (Lond) (1975), 251, p.1-59.
3.G.W. Beeler, H. Reuter, Reconstruction of The Action Potential of Ventricular Myocardial Fibers, J. Physiol (Lond) (1977), 268, p.177-210.
4.D. DiFrancesco, D Noble, A Model of Cardiac Electrical Activity Incorporating Ionic Pumps and Concentration Changes, Philos. Trans. R. Soc. Lond. [Biol] (1985), 307, p.353-398.
5.C. S. Henriquez, J. V. Tranquillo, D. Weinstein, E. Hsu, C. R. Johnson, Three Dimensional Propagation in Mathematical Models: Integrative Model of the Mouse Heart, Cardiac Electrophysiology: From Cell To Bedside, Saunders; 4 edition (2004).
6.G. Plank, R. A. B. Burton, P. Hales, M. Bishop, T. Mansoori, M.O. Bernabeu, A. Garny, A. J. Prassl, C. Bollensdorff, F. Mason, F. Mahmood. B. Rodriguez, V. Grau, J. E. Schneider, D. Gavaghan and P. Kohl, Generation of histo=anatomically representative models of the individual heart: tools and application, Phil. Trans. R. Soc. A (2009), 367, p.2257-2292.
7.M. Buist, G. Sands, P. Hunter, and A. Pullan,, A Deformable Finite Element Derived Finite Difference Method for Cardiac Activation Problems, Annals of Biomedical Engineering(2003), Vol. 31, p.577-588.
8.M. Trew, I. L. Grice, B. Smaill, and A. Pullan, A Finite Volume Method for Modeling Discontinuous Electrical Activation in Cardiac Tissue, Annals of Biomedical Engineering (2003), Vol. 33, No. 5, p.590-602.
9.D. M. Harrild and C. S. Henriquez, A Finite Volume Model of Cardiac Propagation Annals of Biomedical Engineering(1997), Vol. 24, p.315-334.
10.K. T. Ng R. Yan, Three-dimensional pseudo spectral modeling of cardiac propagation in an inhomogeneous anisotropic tissue, Medical & Biological Engineering & Computing(2003), 41, p.618-624.
11.U.M. Ascher, S. J. Ruuth and B. T. R. Wetton, Implicit-Explicit Methods for Time-Dependent Partial Differential Equations, SIAM J. Numer. Anal. (1995), p. 797-823.
12.U. Ascher, S. J. Ruuth and R. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math (1997), 25, p.151-167.
13.N. I. C. Jawias, F. Ismail, M. Suleiman, A. Jaafar, Diagonally Implicit Runge-Kutta Fourth Order Dour-Stage Method for Linear Ordinary Differential Equations with Minimized Error Norm, J. Fundamental Sciences(2009), 5, p.69-78.
14.C. H. Luo, Y. Rudy, A model of the Ventricular Cardiac Action-Potential -Depolarization, Repolarization, and Their Interaction. Circulation Research (1991) 68: p.1501-1526.
15.B. H. Smaill and P. J. Hunter, Computer Modeling of Electrical Activation: Form Cellular Dynamics to the Whole Heart, Cardiac Electrophysiology Methods and Models, springer (2010), p.159-185.
16.B. Cockburn, and C.W. Shu, Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems, J. Sci. Comput, Vol. 16, No. 3, September 2001.
17.C. A. Kennedy, M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math(2003). 44, p.139-181.
18.T. Koto, IMEX Runge-Kutta schemes for reaction-diffusion equations, J. Comput. Appl. Math (2008), 215, p.182-195.
19.H. Liu, J. Zou, Some new additive Runge-Kutta methods and their applications, J. Comput. Appl. Math (2006), 190,p.74-98.

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