T+T−調控於鈣耦合模型中心臟交替脈現象之模擬研究

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研究生：	葉思恩 Szu-En Yeh
論文名稱：	T+T−調控於鈣耦合模型中心臟交替脈現象之模擬研究 Simulation studies of T +T− feedback control on cardiac alternans in Ca2+ coupled model
指導教授：	黎璧賢 Pik-Yin Lai 陳志強 Chi-Keung Chan
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 生物物理研究所 Graduate Institute of Biophysics
論文出版年：	2017
畢業學年度：	105
語文別：	中文
論文頁數：	136
中文關鍵詞：	心臟動力學、非線性動力學、非線性調控、分岔、交替脈
外文關鍵詞：	Cardiac dynamics, nonlinear dynamics, feedback control, Bifurcation, Alternans
相關次數：	點閱：19 下載：0
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近年心因性猝死是國人重要死亡因素之一，其中又以由心室顫動所導致之心因性猝死佔了多數。而心臟從正常的跳動到心室顫動之間的演進過程有其動力學之因素，且其動力學系統為一非線性系統。從心臟動力學的觀點認為，心室顫動是心臟的一種混沌且不協調之活動狀態。同時，心臟的動力學特性從正常演化至混沌間會經歷過倍週期分岔 (Bifurcation) 現象。故在倍週期發生後，我們可以在週期二之交替脈(period-2 alternans) 出現時進行控制進以抑制心室顫動的發生。為了解心臟動力學之變化，本研究使用了單細胞與一維纖維結構之 Shiferaw-Fox model(此為一心臟之鈣離子耦合模型) 以模擬心臟之動力學系統，同時引入了一非線性調控方式進行調控模擬。本研究發現這樣的週期二交替脈中可以分成不同階段，並且找到了在不同階段相應的控制方式。此外，研究中亦發現進行控制時能成功控制的臨界強度與心肌組織中被控制之細胞占纖維中之比例的倒數呈現線性關係。這些研究結果有助於未來決定適當之調控參數，進行有效調控，進而避免心因性猝死之發生。

Nowadays, sudden cardiac (SCD) death is one of top 10 causes of
death. Most of them, such as ventricular fibrillation (VF), have a dynamical origin. For example, Ventricular fibrillation has been described as
”chaotic asynchronous fractionated activity of the heart”. According to the
non-linear dynamics, that cardiac dynamic would undergo period doubling
alternans before getting into chaos. As a result, we could try to reduce the
alternans in order to avoid VF. We use single cell and 1-dimension fiber
Shiferaw-Fox model, with APD-calcium coupling, to simulate the dynamics
of heartbeat and the T
+T− feedback control to suppress cardiac alternans.
According to the result of our simulations, we found some relationships
among basic cycle length, control fraction and critical control strength,
and these findings could improve our control to avoid SCD.

㐀要 ix
Abstract xi
娴謝 xiii
目錄 xv
使用符號與定義 xxv
一、 䵺論 1
1.1 心臟結構 .................................................................. 3
1.2 離子通道、動作電位與心跳週期 .................................... 5
1.3 非線性動力學 ............................................................ 8
1.4 Poincaré Map ............................................................ 8
1.5 吸引子 ..................................................................... 9
1.6 分岔現象與交替脈 ...................................................... 10
1.6.1 Pitchfork bifurcation .......................................... 10
1.6.2 倍周期 (Period doubling)..................................... 12
1.6.3 APD 交替脈 (APD Alternans).............................. 13
1.7 吸引子共存 ............................................................... 14
二、 模型 17
2.1 單細胞 Shiferaw-Fox model (SF Model) ........................... 17
2.2 心肌纖維的 Shiferaw-Fox model (SF Model) ..................... 24
xv
ҕᒬ
2.3 T
+T− feedback control.................................................. 31
三、 T+T− 控制模擬結果 35
3.1 單細胞 ..................................................................... 35
3.1.1 τ = α = 500ms.................................................. 35
3.1.2 τ < α.............................................................. 41
3.2 一維纖維結構 ............................................................ 51
3.2.1 Y 字形分岔區域 ................................................ 51
3.2.2 複雜吸引子區域 ................................................ 63
3.2.3 音叉形分岔區域 ................................................ 67
3.2.4 臨界及極小值微擾項之線性關係 ........................... 77
四、 總結 81
4.1 結論 ........................................................................ 81
4.2 未來展望 .................................................................. 82
參考文獻 83
附錄 A 程式䡤 87
A.1 Matlab ..................................................................... 87
                                

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