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研究生： 賴彥合
Lai, Yen-Ho
論文名稱： 單域心肌模擬之數值運算自動化
Automation for Numerical Computations on the Cardiac Monodomain Simulations
指導教授： 陳旻宏
Chen, Min-Hung
共同指導教授: 侯世章
Hou, Su-Chung
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 32
中文關鍵詞： 心臟細胞模型 、單域模型 、數值運算
外文關鍵詞： Cardiac cell models, Monodomain models, Numerical computations
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    • 由於心臟實驗有許多限制，且實現活體細胞的精確控制相當困難，因此數值心臟模型在心臟相關研究扮演著重要的角色。為了因應越來越貼近真實而增加方程式的各種數值模型、精準而複雜的數值方法以及詳細而龐大的數據資料量，傳統以人力編寫程式碼進而計算的過程顯得費時費工。在本篇論文中，我們藉由Python中一個名為BeautifulSoup的爬蟲封包，於國際生理學聯合會(IUPS)生理組學計畫(Physiome Project)網站獲取電生理學模型之相關資料並引用其中C.H. Luo和Y. Rudy分別於1991年及1994年發表的LR91及LR94的心肌細胞模型，再輔以單域心電波方程描述細胞與細胞之間的相互作用，進行數值心肌模擬的程式自動生成。此外，我們以自動生成的程式碼嘗試進行平行化。希望可以透過自動化來部分替代人工生成數值細胞模型程式的繁複過程。

    Numerical cardiac membrane models play an important role in studying membrane-excitable cells, due to the precise control of experiments on living cells and tissue is extremely difficult to achieve. To make the pretend worlds of numerical models close to real life, the models are gradually getting more complex, and so do the numerical methods and amount of data, therefore, it takes more time for humans to learn mathematics and program coding. In this article, we acquire the information of electrophysiological models from the website of International Union of Physiological Sciences(IUPS) Physiome Project via the BeautifulSoup, which is a package for parsing HTML and XML documents in Python, and cite LR91 and LR94, which are established and published by C.H. Luo and Y. Rudy in 1991 and 1994 respectively, as the samples for cardiac cell models, and consider the monodomain models to describe the changing of potential between cells to achieve the automation for numerical cardiac simulation. Besides, we are going to try to parallel computing according to the result of the automation. we are looking forward to simplifying the processing of building a computing code by the automation.

    Contents 摘要. . . . . . . . . . . . . . . . . . . . . . i Abstract. . . . . . . . . . . . . . . . . . . . ii 誌謝. . . . . . . . . . . . . . . . . . . . . . iii 1 Introduction. . . . . . . . . . . . . . . . . .1 2 Cardiac Models. . . . . . . . . . . . . . . . .3 2.1 Cell Models. . . . . . . . . . . . . . . . .3 2.1.1 The LR91 model. . . . . . . . . . . . . . 4 2.1.2 The LR94 model. . . . . . . . . . . . . . 6 2.2 Monodomain model. . . . . . . . . . . . . . 9 3 Automation. . . . . . . . . . . . . . . . . . 10 3.1 Materials for the automation. . . . . . . .10 3.1.1 IUPS Physiome Project. . .. . . . . . . .10 3.1.2 BeautifulSoup in Python. . . . . . . . . 12 3.1.3 MathML. . . . . . . . . . . . . . . . . .13 3.2 Components. . . . . . . . . . . . . . . . .16 3.2.1 Models. . . . . . . . . . . . . . . . . .16 3.2.2 Numerical Methods for ODEs. . . . . . . .16 3.2.3 Numerical Methods for PDEs. . . . . . . .17 3.3 Demonstrations and Results. . . . . . . . .20 3.3.1 Prerequisites. . . . . . . . . . . . . . 20 3.3.2 Processes of Implementation. . . . . . . 21 3.3.3 Results. . . . . . . . . . . . . . . . . 22 4 Conclusion. . . . . . . . . . . . . . . . . . 26 References. . . . . . . . . . . . . . . . . . . 26 Appendices. . . . . . . . . . . . . . . . . . . 27 A Example for Stack. . . . . . . . . . . . . . .28 A.1 Processes for stack. . . . . . . . . . . . .28 A.2 Codes for stack in Python. . . . . . . . . .30 B Accelerating Computations. . . . . . . . . . .31 B.1 Paralleling Computing - PyCUDA. . . . .. . .31

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    [2]Ching-hsing Luo and Yoram Rudy, 1991, ”A Model of the Ventricular Cardiac Action Potential.Depolarisation, Repolarisation and Their Interaction”, Circulation Research, 68, 1501-1526.
    [3]Ching-hsing Luo and Yoram Rudy, 1994, ”A dynamic model of the cardiac ventricular action potential.I. Simulations of ionic currents and concentration changes”, Circulation Research, 74, 1071-1097.
    [4]Ching-hsing Luo and Yoram Rudy, 1994, ”A dynamic model of the cardiac ventricular action potential.II. Afterdepolarizations, triggered activity, and potentiation”, Circulation Research, 74, 1097-1113.
    [5]Chin-hsun Lu, 2018, ”GPU Acceleration on the Cardiac Monodomain Simulation”
    [6]International Union of Physiological Sciences(IUPS). Retrieved March, 2020.http://www.iups.org/
    [7]IUPS Physiome Project : Home. Retrieved March, 2020.https://physiomeproject.org/
    [8]the CellML Project CellML. Retrieved March, 2020.https://www.cellml.org/
    [9]Beautiful Soup Documentation. Retrieved March, 2020.https://www.crummy.com/software/BeautifulSoup/bs4/doc/
    [10]Mathematical Markup Language (MathML) Version 3.0 2nd Edition, the World Wide Web Consor-tium(W3C). Retrieved March, 2020.http://www.w3.org/TR/MathML/
    [11]Keith F. Decker, Jordi Heijman, Jonathan R. Silva, Thomas J. Hund, and Yoram Rudy, 2009,”Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation incanine epicardium”, American Journal of Physiology, 296, (4), H1017-H1026. PubMed ID: 19168720
    [12]Welcome to PyCUDA’s documentation. Retrieved March, 2020.https://documen.tician.de/pycuda/

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