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研究生: 吳尚融
Wu, Shang-Jung
論文名稱: 非線性動力學應用在單顆心肌細胞的鈣循環
Nonlinear Dynamics of Calcium Cycling in a Cardiac cell
指導教授: 吳國安
Wu, Kuo-An
口試委員: 黎璧賢
Lai, Pik-Yin
陳宣毅
Chen, Hsuan-Yi
羅中泉
Lo, Chung-Chuan
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2021
畢業學年度: 109
語文別: 英文
論文頁數: 77
中文關鍵詞: 心肌動力學離子模型非線性動力學心室顫動
外文關鍵詞: cardiac dynamics, ionic model, CICR, ventricular fibrillation, cardiac alternans, non-linear dynamics, nullcline analysis, Iterated map analysis
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  • 我們提出一個從詳細的生理學離子模型簡化後導出的二變數模型,並驗證該二變數動力學系統可以捕抓到與完整離子模型相似的動力學分叉圖。
    將零斜率線分析和疊代圖分析應用在我們提出的二變數模型藉此研究心臟細胞的動力響應和分叉行為。
    理論結果表明,細胞膜內鈣離子在肌質和肌漿網之間的循環在心臟動力學的穩定性中起著至關重要的作用。
    此外,歸功於二變數模型的簡潔,我們可以更容易看到藏在雙週期心臟動力學背後的機制。


    We propose a two-variable reduced model that is derived from a detailed physiological ionic model and show that this two-variable dynamical system captures realistically the essence of the bifurcation behavior as seen in the ionic model. The dynamical response and bifurcation behavior of a cardiac cell are investigated with the proposed two-variable model by nullcline analysis and iterative map analysis. The theoretical results indicate that intracellular calcium cycling between bulk myoplasm and sarcoplasmic reticulum (SR) plays a crucial role in influencing the stability of cardiac dynamics.
    In addition, due to the simplicity of the two-variable model, one can see easily the mechanism behind the period-2 cycle of calcium dynamics.

    Contents ii List of Tables iii List of Figures viii 1 Introduction 1 2 Ionic Model 6 2.1 The structure of a cardiac cell and the ionic model . . . . . . . . . 6 2.2 Membrane potential and ion channels . . . . . . . . . . . . . . . . . 8 2.2.1 Action potential of cardiac cell . . . . . . . . . . . . . . . . 9 2.2.2 Ionic model of membrane potential . . . . . . . . . . . . . . 11 2.2.3 Ionic model of ion channels current . . . . . . . . . . . . . . 12 2.3 Calcium cycling inside the cell . . . . . . . . . . . . . . . . . . . . . 17 2.4 What is alternans? . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3 Reduction Process 27 3.1 Mathematical structure of the ionic model . . . . . . . . . . . . . . 27 3.2 The role of action potential . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Calcium current across the membrane . . . . . . . . . . . . . . . . 34 3.3.1 Simplify L-type calcium current . . . . . . . . . . . . . . . . 34 3.3.2 Simplify sodium calcium exchanger current . . . . . . . . . 38 3.4 Calcium concentration ci and cs . . . . . . . . . . . . . . . . . . . . 40 3.5 linear buffering term . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.6 Release current Ir . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.7 The relation between ci and cj . . . . . . . . . . . . . . . . . . . . . 44 4 Result and analysis 47 4.1 Mechanism of period-2 cycle . . . . . . . . . . . . . . . . . . . . . . 47 4.2 Nullcline analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3 Iterated map analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.3.1 Two-dimensional map . . . . . . . . . . . . . . . . . . . . . 55 4.3.2 Jacobian matrix . . . . . . . . . . . . . . . . . . . . . . . . 60 5 Conclusion and Future Work 64 Appendix 67 A. Ionic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 B. Two-variable model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Reference 75

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