T+T−調控於鈣耦合模型中心臟交替脈現象之模擬研究

簡易檢索 / 詳目顯示

回結果列表

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：18 下載：0
分享至:	分享至facebook 分享至twitter

查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

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
                                

[1] “Physics of cardiac arrhythmogenesis,” Annual Review of Condensed Matter Physics,
vol. 4, no. 1, pp. 313–337, 2013. doi: 10.1146/annurev- conmatphys- 020911-
125112. [Online]. Available: http://dx.doi.org/10.1146/annurev-conmatphys-
020911-125112.
[2] Z. Qu, G. Hu, A. Garfinkel, and J. N. Weiss, “Nonlinear and stochastic dynamics in
the heart,” Physics Reports, Nonlinear and Stochastic Dynamics in the Heart, vol.
543, no. 2, pp. 61–162, Oct. 10, 2014, issn: 0370-1573. doi: 10.1016/j.physrep.
2014.05.002. [Online]. Available: http://www.sciencedirect.com/science/
article/pii/S037015731400204X (visited on 05/01/2017).
[3] D. J. Dosdall, V. G. Fast, and R. E. Ideker, “Mechanisms of defibrillation,” Annual
Review of Biomedical Engineering, vol. 12, pp. 233–258, Aug. 15, 2010, issn: 1545-
4274. doi: 10.1146/annurev-bioeng-070909-105305.
[4] O. College, Illustration from anatomy & physiology, connexions web site. http://
cnx.org/content/col11496/1.6/, jun 19, 2013. [Online]. Available: https://commons.
wikimedia.org/wiki/File:2024_Cardiac_Arrhythmias.jpg.
[5] E. O. Robles de Medina, R. Bernard, P. Coumel, A. N. Damato, C. Fisch, D.
Krikler, N. A. Mazur, F. L. Meijler, L. Mogensen, P. Moret, Z. Pisa, and H. J.
Wellens, “Definition of terms related to cardiac rhythm. WHO/ISFC task force,”
European Journal of Cardiology, vol. 8, no. 2, pp. 127–144, Sep. 1978, issn: 0301-
4711.
[6] T. Quail, “Chaotic dynamics in cardiac aggregates induced by potassium channel
block,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 22, no. 3,
p. 033 140, Sep. 1, 2012, issn: 1054-1500. doi: 10 . 1063 / 1 . 4748854. [Online].
Available: http://aip.scitation.org/doi/abs/10.1063/1.4748854.
[7] D.-M. Le, P.-Y. Lai, and C. K. Chan. (2012). Control by chaotic attractors: Reduction
of cardiac alternans by small perturbations, [Online]. Available: https://opentextbc.
ca/anatomyandphysiology/chapter/19-2-cardiac-muscle-and-electricalactivity/.
83
୍ԬЅᝏ
[8] P. S. Skardal and J. G. Restrepo, “Coexisting chaotic and multi-periodic dynamics
in a model of cardiac alternans,” Chaos: An Interdisciplinary Journal of Nonlinear
Science, vol. 24, no. 4, p. 043 126, Dec. 2014, issn: 1054-1500, 1089-7682. doi:
10.1063/1.4901728. arXiv: 1408.4993. [Online]. Available: http://arxiv.org/
abs/1408.4993.
[9] S. Luther, F. H. Fenton, B. G. Kornreich, A. Squires, P. Bittihn, D. Hornung, M.
Zabel, J. Flanders, A. Gladuli, L. Campoy, E. M. Cherry, G. Luther, G. Hasenfuss,
V. I. Krinsky, A. Pumir, R. F. G. Jr, and E. Bodenschatz, “Low-energy control of
electrical turbulence in the heart,” Nature, vol. 475, no. 7355, pp. 235–239, Jul. 14,
2011, issn: 0028-0836. doi: 10 . 1038 / nature10216. [Online]. Available: http :
//www.nature.com/nature/journal/v475/n7355/full/nature10216.html.
[10] F. Yapari, D. Deshpande, Y. Belhamadia, and S. Dubljevic, “Control of cardiac
alternans by mechanical and electrical feedback,” Physical Review E, vol. 90, no. 1,
p. 012 706, Jul. 25, 2014. doi: 10.1103/PhysRevE.90.012706. [Online]. Available:
http://link.aps.org/doi/10.1103/PhysRevE.90.012706.
[11] (). Conduction system of the heart, Pinterest, [Online]. Available: https://www.
pinterest.com/mastersnowball/conduction-system-of-the-heart/.
[12] O. College, Illustration from anatomy & physiology, connexions web site. http://
cnx.org/content/col11496/1.6/, jun 19, 2013. [Online]. Available: https://commons.
wikimedia.org/wiki/File:2024_Cardiac_Arrhythmias.jpg.
[13] (). Muscular system module 6: Cardiac muscle tissue, [Online]. Available: http:
//archive.cnx.org/contents/8ff1e0a4-661b-4f24-88a2-372a2aee031a@1/
muscular-system-module-6-cardiac-muscle-tissue.
[14] Klabunde. (). CV physiology | sinoatrial node action potentials, [Online]. Available:
http://www.cvphysiology.com/Arrhythmias/A004.
[15] (). CV physiology | non-pacemaker action potentials, [Online]. Available: http:
//www.cvphysiology.com/Arrhythmias/A006.
[16] A. I. Abdelaziz. (). Ahmed ihab abdelaziz: Untersuchungen zur funktion der humanen atrialen essentiellen leichten myosinkette (ALC-1) in einem transgenen rattenmodell, [Online]. Available: http://edoc.hu-berlin.de/dissertationen/
abdelaziz-ahmed-ihab-2004-09-20/HTML/front.html#front.
[17] X. Zhao, “Indeterminacy of spatiotemporal cardiac alternans,” Physical review. E,
Statistical, nonlinear, and soft matter physics, vol. 78, no. 1, p. 011 902, Jul. 2008,
issn: 1539-3755. [Online]. Available: http : / / www . ncbi . nlm . nih . gov / pmc /
articles/PMC2562603/.
84
୍ԬЅᝏ
[18] C. Hirth, U. Borchard, and D. Hafner, “Effects of the calcium antagonist diltiazem
on action potentials, slow response and force of contraction in different cardiac
tissues,” Journal of Molecular and Cellular Cardiology, vol. 15, no. 12, pp. 799–
809, Dec. 1983, issn: 0022-2828. doi: 10.1016/0022- 2828(83)90342- 5. [Online]. Available: http : / / www . sciencedirect . com / science / article / pii /
0022282883903425.
[19] J. I. Goldhaber, L.-H. Xie, T. Duong, C. Motter, K. Khuu, and J. N. Weiss, “Action
potential duration restitution and alternans in rabbit ventricular myocytes: The key
role of intracellular calcium cycling,” Circulation Research, vol. 96, no. 4, pp. 459–
466, Mar. 4, 2005, issn: 1524-4571. doi: 10.1161/01.RES.0000156891.66893.83.
[20] S. H. Strogatz, Nonlinear dynamics and chaos: With applications to physics, biology,
chemistry, and engineering. Westview Press, Jul. 29, 2014, 533 pp., Google-BooksID: aMrSDQAAQBAJ, isbn: 978-0-8133-4910-7.
[21] Yapparina, 日本婆: ΉΡΙΰͷ a=3.2 ̯ͧΚ̯ⶋ⚛̩時系列, Nov. 30, 2014.
[Online]. Available: https://commons.wikimedia.org/wiki/File%3ALogistic_
map_cobweb_and_time_evolution_a%3D3.2.png.
[22] 許庭瑋 and T.-w. Hsu, “在外加振盪磁場中阻尼磁針的非線性動力學分析;Numerical
and theoretical analysis of the nonlinear dynamics of a damped compass under external oscillatory magnetic field,” thesis, 國立中央大學, Jan. 28, 2016. [Online].
Available: http://ir.lib.ncu.edu.tw/handle/987654321/69378 (visited on
02/22/2017).
[23] A. Petrie and X. Zhao, “Estimating eigenvalues of dynamical systems from time
series with applications to predicting cardiac alternans,” Proc. R. Soc. A, vol. 468,
no. 2147, pp. 3649–3666, Nov. 8, 2012, issn: 1364-5021, 1471-2946. doi: 10.1098/
rspa.2012.0098. [Online]. Available: http://rspa.royalsocietypublishing.
org/content/468/2147/3649 (visited on 03/02/2017).
[24] (). A magnetoelastic strange attractor - ScienceDirect, [Online]. Available: http:
//www.sciencedirect.com/science/article/pii/0022460X79905200 (visited
on 05/01/2017).
[25] J. J. Fox, M. L. Riccio, F. Hua, E. Bodenschatz, and R. F. Gilmour, “Spatiotemporal
transition to conduction block in canine ventricle,” Circulation Research, vol. 90, no.
3, pp. 289–296, Feb. 22, 2002, issn: 0009-7330, 1524-4571. doi: 10.1161/hh0302.
104723. [Online]. Available: http://circres.ahajournals.org/content/90/3/
289.
[26] Y. Shiferaw, M. A. Watanabe, A. Garfinkel, J. N. Weiss, and A. Karma, “Model of
intracellular calcium cycling in ventricular myocytes,” Biophysical Journal, vol. 85,
no. 6, pp. 3666–3686, Dec. 2003, issn: 0006-3495. doi: 10.1016/S0006-3495(03)
74784-5. [Online]. Available: http://www.sciencedirect.com/science/article/
pii/S0006349503747845.
85
୍ԬЅᝏ
[27] “Electrical alternans and spiral wave breakup in cardiac tissue,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 4, no. 3, pp. 461–472, Sep. 1,
1994, issn: 1054-1500. doi: 10.1063/1.166024. [Online]. Available: http://aip.
scitation.org/doi/abs/10.1063/1.166024.
[28] S. Sridhar, D.-M. Le, Y.-C. Mi, S. Sinha, P.-Y. Lai, and C. K. Chan, “Suppression
of cardiac alternans by alternating-period-feedback stimulations,” Physical Review.
E, Statistical, Nonlinear, and Soft Matter Physics, vol. 87, no. 4, p. 042 712, Apr.
2013, issn: 1550-2376. doi: 10.1103/PhysRevE.87.042712.
[29] 李度門 and L. D.M., “Predicting Self-terminating Ventricular Fibrillation by Bivariate Data Analysis and Controlling Cardiac Alternans by Chaotic Attractors;
Predicting Self-terminating Ventricular Fibrillation by Bivariate Data Analysis
and Controlling Cardiac Alternans by Chaotic Attractors,” thesis, 國立中央大
學, Jan. 20, 2014. [Online]. Available: http://ir.lib.ncu.edu.tw/handle/
987654321/63487.
[30] Y.-T. Lin, “非線性調控對心臟分岔現象的影響, Nonlinear control on heart bifurcation,” http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=103230006, Aug. 30,
2016. [Online]. Available: http://ir.lib.ncu.edu.tw:88/thesis/view_etd.
asp?URN=103230006.

簡易檢索 / 詳目顯示

相關論文