請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74213完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林太家 | |
| dc.contributor.author | Bo-Yun Chen | en |
| dc.contributor.author | 陳博允 | zh_TW |
| dc.date.accessioned | 2021-06-17T08:24:37Z | - |
| dc.date.available | 2020-08-20 | |
| dc.date.copyright | 2019-08-20 | |
| dc.date.issued | 2019 | |
| dc.date.submitted | 2019-08-13 | |
| dc.identifier.citation | [1] A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4):500–544, 1952.
[2] Brian J. Kirby. Micro- and Nanoscale Fluid Mechanics, chapter 11. Cambridge University Press, 2013. [3] Zilong Song, Xiulei Cao, and Huaxiong Huang. Electroneutral models for dynamic poisson-nernst-planck systems. Phys. Rev. E, 97:012411, Jan 2018. [4] RANDALL J. LEVEQUE. Finite Volume Methods for Hyperbolic Problems, chapter 10.4. Cambridge University Press, 2002. [5] Li-Lian Wang Jie Shen, Tao Tang. Spectral Methods: Algorithms, Analysis and Applications, chapter 3.3. Springer Science and Business Media, 2011. [6] Richard Naud Wulfram Gerstner, Werner M. Kistler and Liam Paninski. Neuronal Dynamics. Cambridge University Press, 2014. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/74213 | - |
| dc.description.abstract | 本論文給出了細胞內外離子濃度與電位勢的動態模擬，進而產生出動作電位。動作電位的產生來自於細胞膜兩側的電化學電勢差。我們討論的離子種類包含鈉、鉀及氯離子。這像模擬涉及泊松─能斯特─普朗克方程及霍奇金-赫克斯利模型。前者給出了描述離子擴散和電泳行為的標準模型。後者給出了離子通道機制與電路的轉換關係。我們想要結合並比較兩者的結果，然後試著證實後者可由前者得出。此研究中用到的空間離散方法包含有限體積法及擬譜法。在將偏微分方程以半離散形式轉成系統常微分方程後，透過MATLAB裡的ode15s求解器處理對時間的積分。 | zh_TW |
| dc.description.abstract | This thesis presents a dynamic simulation of intracellular and extracellular ionic concentrations and electric potential, then create an action potential, which is generated by a difference of the electrochemical potential between two sides of a cell membrane. Ion species including Sodium, Potassium and Chlorine. This simulation would involve Poisson-Nernst-Planck (PNP) system and Hodgkin–Huxley (HH) model. The former gives a standard model for describing behaviors of ionic diffusion and electrophoresis. The latter gives a transformation between mechanism of ion channels and a circuit. We want to combine and compare the results of these two models, then try to verify that the PNP equations can reduce to the HH model. In this study, methodologies are based on finite volume method and pseudospectral method for space discretization. After changing the semi-discrete scheme to a system of ODE by method of lines(MOL), we use ode15s solver on MATLAB to handle for time integration. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T08:24:37Z (GMT). No. of bitstreams: 1 ntu-108-R06246001-1.pdf: 1396003 bytes, checksum: 02c1a29a34b29a7e1bd3a25258ed8a95 (MD5) Previous issue date: 2019 | en |
| dc.description.tableofcontents | 口試委員審定書iii
誌謝iii Acknowledgements iv 摘要iv Abstract vi List of Figures ix List of Tables ix 1 Introduction 1 2 Mathematical Models 4 2.1 PNP equations: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 HH model: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Nondimensionalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Dimensionless equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.5 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Interface conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Mapping 11 4 Numerical Method I :Finite Volume Method 13 4.1 Cartesian coordinate: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Numerucal Scheme: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.3 Polar coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.4 Numerical scheme: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Numerical Method II: Pseudospectral Method 21 5.1 Derivative matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Poisson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.1 Cartesian coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.2.2 Polar coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5.3 Nernst-Planck equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3.1 Cartesian coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.3.2 Polar coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.3.3 Treatment for the pole conditions . . . . . . . . . . . . . . . . . . . . 27 6 Numerical Results and Discussions 29 6.1 Comparisons of action potentials . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.2 Comparisons between PNP and HH . . . . . . . . . . . . . . . . . . . . . . . 31 6.2.1 At resting state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 6.2.2 At depolarization stage . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.3 Reduce PNP to HH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.3.1 Cartesian coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.3.2 Polar coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 7 Conclusion 39 References 40 A Notation Table 40 B Initial 42 | |
| dc.language.iso | en | |
| dc.subject | 擬譜法 | zh_TW |
| dc.subject | 泊松─能斯特─普朗克方程 | zh_TW |
| dc.subject | 霍奇金-赫克斯利模型 | zh_TW |
| dc.subject | 有限體積 | zh_TW |
| dc.subject | Poisson-Nernst-Planck equations | en |
| dc.subject | Hodgkin–Huxley model | en |
| dc.subject | finite volume method | en |
| dc.subject | pseudospectral method | en |
| dc.title | 霍奇金-赫克斯利模型與泊松─能斯特─普朗克方程之比較 | zh_TW |
| dc.title | Comparison of Hodgkin Huxley model and Poisson Nernst Planck equations | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 107-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 洪子倫,李俊璋 | |
| dc.subject.keyword | 泊松─能斯特─普朗克方程,霍奇金-赫克斯利模型,有限體積,擬譜法, | zh_TW |
| dc.subject.keyword | Poisson-Nernst-Planck equations,Hodgkin–Huxley model,finite volume method,pseudospectral method, | en |
| dc.relation.page | 42 | |
| dc.identifier.doi | 10.6342/NTU201903092 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2019-08-13 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-108-1.pdf 未授權公開取用 | 1.36 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。