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研究生:蔡岳翰
研究生(外文):Yeuh-Han Tsai
論文名稱:心臟電生理的元胞自動機模擬
論文名稱(外文):Cellular Automata Simulations of Electrophysiology of Heart
指導教授:羅主斌
指導教授(外文):Chu-Pin Lo
學位類別:碩士
校院名稱:靜宜大學
系所名稱:應用數學研究所
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:2008
畢業學年度:97
語文別:中文
論文頁數:56
中文關鍵詞:元胞自動機電生理模擬
外文關鍵詞:ElectrophysiologyCellular AutomataSimulation
相關次數:
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  • 下載下載:13
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針對心臟電生理特性和現象的模擬,經常藉用連續型的微分方程當作模型來進行探討 (如bidomain, monodomain models),但是對於這一類的模型, 其電腦計算的負擔是很大的, 這使得數值模擬與各種現象之探討遇到很大的阻礙。
元胞自動機(cellular automata)是離散型反應擴散方程的一種,利用簡化的規則去代替複雜的數值方法。在心臟模型的建立上,無疑是提供了另一個折衷的計算方法。由於元胞自動機所需要的計算比起解微分方程模型更為容易,因此解更高維度如2D,3D的模型,使元胞自動機在心臟模擬的部分變得更具有可行性。
本文針對元胞自動機的演進歷史做一個介紹,從典型的元胞自動機Wiener and Rosenblueth model和Greenberg and Hastings model、到加入空間的異直性和非等向性以及曲率影響波速的Chernyak, Feldman and Cohen model,透過選擇合適的參數,CA也可以看到在Luo-Rudy model中所看見的現象。
To simulate the electrophysiology of heart, one usually uses continuous type of differential equations such as bidomain or monodomain equations. However, the corresponding computational load is heavy. Therefore the simulation tasks and explorations of various phenomena using such model will meet big difficulties.
As an alternative tool, Cellular Automata (CA) uses a discrete type of reaction-diffusion model allowing the evolution of cells via simple rules which dramatically reduce the computational load. Therefore, the computer simulations in higher space dimension (2D,3D) are more efficient by CA model.
In this article, we will introduce the development of CA models of heart. From the typical Wiener and Rosenblueth model, Greenberg and Hastings model with rigorously validated evolution rules, to Chernyak, Feldman and Cohen model with the factors such as space heterogeneity, anisotropy, curvature effects on propagation speed. When suitably choosing parameters, many important phenomena obtained by monodomain models e.g., Luo-Rudy model can also be reproduced by CA model.
致謝 I
中文摘要 II
英文摘要(ABSTRACT) III
目錄 IV
圖目錄 V
第1章 心臟電生理簡介 1
第1節 心臟電生理的數學模型 1
第2節 心臟的CELLULAR AUTOMATA 1
第2章 心臟的CA模型演進歷史 4
第1節 WIENER AND ROSENBLUETH MODEL(3 STATES OF CA) 4
第2節 J.M. GREENBERG AND S.P. HASTINGS MODEL(5 STATES OF CA) 11
第3節 包含CURVATURE, HETEROGENEITY, ANISOTROPY影響的CA 19
3.1 Effect of Curvature(曲率的影響) 21
3.2 Space Heterogeneity (空間的異質性) 25
3.3 Spatial of Anisotropy(傳導的偏向性) 27
3.4 Dispersion Relation (色散關係) 29
第4節 COHEN, CHERNYAK AND FELDMAN MODEL 33
第3章 CA模型的應用 40
參考文獻 48
[1]. The mathematical formulation of the problem of conduction of impulses in a network of connected excitable element, specifically in cardiac muscle, N. Wiener and A. Rosenblueth, (1946)
[2]. Elementary Differential Geometry, Barrett O’Neill, (1966)
[3]. Spatial Patterns for Discrete Models of Diffusion in Excitable Media, J.M. Greenberg; S.P. Hastings, (1978)
[4]. Pattern Formation and Periodic Structures in Modeled by Reaction-Diffusion Equations, J.M. Greenberg, B.D. Hassard and S.P. Hastings, (1978)
[5]. A cellular automaton model of excitable media including curvature and dispersion, M. Gerhardt, H. Schuster and J. J. Tyson, (1990)
[6]. Isotropic cellular automaton for modeling excitable media, M. Markus and B. Hess, (1990)
[7]. Cellular Automaton Models for Reaction Diffusion Equations, , (1991)
[8]. Third Generation Cellular Automaton for Modeling Excitable Media, , (1992)
[9]. Pattern Formation in Excitable Media, Ehud Meron, (1992)
[10]. Vortex Wave Stabililty in Homogeneous Excitable Media: Simulations on a Randomized Discrete Lattice, A. Feldman, J.Z. Yin, Bo E.H. Saxberg, Y.B. Chernyak, R.J. Cohen, (1995)
[11]. A Cellular Automata Model of the Heart and Its Coupling with a Qualitative Model, P. Siregar, J. P. Sinteff, M. Chahine, and P. Lebeux, (1995)
[12]. Correspondence Between Discrete and Continuous Models of Excitable Media: Trigger Waves, A.B. Feldman, Y.B. Chernyak, R.J. Cohen, (1997)
[13]. Wave-Front Propagation in a Discrete Model of Excitable Media, A.B. Feldman,* Y. B. Chemyak and R.J. Cohen, (1998)
[14]. Cellular automata model of cardiac excitation waves, A.B. Feldman, Y.B. Chernyak, R.J. Cohen, (1999)
[15]. Spiral Wave Generation in Heterogeneous Excitable Media, Gil Bub, Alvin Shrier, and Leon Glass, (2002)
[16]. Multiple Mechanisms of Spiral Wave Breakup in a Model of Cardiac Electrical Activity, Flavio H. Fenton, Elizabeth M. Cherry, Harold M. Hastings, and Steven J. Evans,(2002)
[17]. A Study of CA Applied to an Ecosystem, 吳宜家, (2006)
[18]. Cellular Automata Modeling of Physical Systems (物理系統的元胞自動機模擬), Bastien Chopard, Michel Droz 著 祝玉學 趙學龍
[19]. Mathematical Physiology, James Keener and James Sneyd
[20]. Electrical Restitution and Cardiac Fibrillation, JAMES N. WEISS, M.D., PENG-SHENG CHEN, M.D., ZHILIN QU, PH.D.,HRAYR S. KARAGUEUZIAN, PH.D., SHIN-FONG LIN, PH.D.,and ALAN GARFINKEL, PH.D, (2002)
[21]. Computer Simulations of Electrophysiology of Heart (心臟電生理的相關電腦模擬), 徐宇辰, (2008)
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