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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
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dc.contributor.advisor | 林太家(Tai-Chia Lin) | |
dc.contributor.author | Min-Jhe Lu | en |
dc.contributor.author | 呂旻哲 | zh_TW |
dc.date.accessioned | 2021-06-08T02:07:30Z | - |
dc.date.copyright | 2016-03-08 | |
dc.date.issued | 2015 | |
dc.date.submitted | 2016-02-01 | |
dc.identifier.citation | [1] Y. Mori, J. W. Jerome, and C. S. Peskin, A three-dimensional model of cellular electrical activity, Bull. Inst. Math. Acad. Sin., 2 (2007), pp. 367–390.
[2] A.L. Hodgkin and A.F. Huxley. A quantitative description of the membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117:500–544, 1952. [3] B. Hille. Ion Channels of Excitable Membranes. Sinauer Associates, 3rd edition, 2001. [4] Moore, J. W., Joyner, R. W., Brill, M. H., Waxman, S. G. and Najar-Joa, M. 1978. Simulations of conduction in uniform myelinated fibers: Relative sensitivity to changes in nodal and internodal parameters. Biophys. J. 21:147–160. [5] A. Carpio, I. Peral. Propagation failure along myelinated nerves. J. Nonlinear Sci., 21 (2011), pp. 499–520 [6] Frankenhaeuser, B. and Huxley, A. F. 1964. The action potential in the myelinated fibre of Xenopus laevis as computed on the basis of voltage clamp data. J. Physiol. (Lond.) 171:302–315. [7] Ford M.C., Alexandrova O., Cossell L. et al (2015) Tuning of Ranvier node and internode properties in myelinated axons to adjust action potential timing. Nat Com 6:8073 [8] FitzHugh, R., Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber. Biophys. J. 2, 11–21 (1962) [9] Alwyn C. Scott., The electrophysics of a nerve fiber, Rev. Mod. Phys. 47, 487 – Published 1 April 1975 [10] S. G. Waxman & M.V. L. Bennett, Relative conduction velocities of small myelinated and non-myelinated fibres in the central nervous system, Nature New Biology 238, 217-219 (16 August 1972) [11] Goldman, L. And Albus, J. S. 1968. Computation of impulse conduction in myelinated fibres: Theoretical basis of the velocity diameter relation. Biophys. J. 8:596–607. [12] AF Huxley, R Stämpfli, Evidence for saltatory conduction in peripheral myelinated nerve fibres, The Journal of physiology, 1949, Ix8, 315-339 [13] Rattay, M. Aberham Modeling axon membranes for functional electrical stimulation, IEEE Trans Biomed Eng, 40 (1993), pp. 1201–1209 [14] Frankenhaeuser, B. And Moore, L. E. 1963. The effect of temperature on the sodium and potassium permeability changes in myelinated nerve fibres of Xenopus laevis. J. Physiol. (Lond.) 169:431–437. [15] S.G. Waxman, An ultrastructural study of the pattern of myelination of preterminal fibers in teleost oculomotor nuclei, electromotor nuclei, and spinal cord Brain Res, 27 (1971), pp. 189–201 [16] LN Trefethen, Spectral Methods in Matlab, SIAM (2001) [17] Halter J.A., Clark Jr. J.W, A distributed-parameter model of the myelinated nerve fiber (1991) Journal of Theoretical Biology, 148 (3) , pp. 345-382. [18] Stephen G. Waxman, Axonal conduction and injury in multiple sclerosis: the role of sodium channels, Nature Reviews Neuroscience 7, 932-941 (December 2006) [19] Dodge, F.A. 1978 Impulse propagation in myelinated nerve fiber. Biophys. [20] JP Keener, J Sneyd , Mathematical physiology - 1998 – Springer [21] Stephen G. Waxman, Jeffery D. Kocsis, and Peter K. Stys, The Axon: Structure, Function and Pathophysiology, 1995 – Oxford [22] Lin, T.C. and B. Eisenberg, A new approach to the Lennard-Jones potential and a new model: PNP-steric equations. Communications in Mathematical Sciences, 2014. 12(1): p. 149-173. [23] Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson-Nernst-Planck equations, MS Kilic, MZ Bazant, A Ajdari - Physical review E, 2007 – APS [24] Steric effects in electrolytes: A modified Poisson-Boltzmann equation I Borukhov, D Andelman, H Orland, Physical review letters 79 (3), 435 [25] A simple statistical mechanical approach to the free energy of the electric double layer including the excluded volume effect, V Kralj-Iglič, A Iglič - Journal de Physique II, 1996 [26] Burger, M., Di Francesco, M., Pietschmann, J.-F., Schlake, B.: Nonlinear cross-diffusion with size exclusion. Preprint, Universität Münster, January 2010 [27] Nonlinear Poisson–Nernst–Planck equations for ion flux through confined geometries, M Burger, B Schlake, MT Wolfram - Nonlinearity, 2012 [28] Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limitsG Giacomin, JL Lebowitz - Journal of statistical Physics, 1997 [29] Asymptotic expansions of IV relations via a Poisson-Nernst-Planck system N Abaid, RS Eisenberg, W Liu - SIAM Journal on Applied Dynamical Systems, 2008 [30] Diffusion and kinetic approaches to describe permeation in ionic channels JA Dani, DG Levitt - Journal of theoretical biology, 1990 [31] Solution of the nerve cable equation using Chebyshev approximations TI Toth, V Crunelli - Journal of neuroscience methods, 1999 [32] Approximation by the Legendre collocation method of a model problem in electrophysiology, D.Funaro, J Comput Appl Math, 43 (1992), pp. 261–271 [33] Cellular biophysics, TF Weiss, 1996, MIT press [34] Methods in neuronal modeling: from ions to networks, C Koch, I Segev - 1998 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/19595 | - |
dc.description.abstract | 我們研究一個用以模擬動作電位沿著一具有髓鞘之神經軸突傳遞的電纜型模型。與先前使用有限差分法的結果[4,8,11]相比,我們使用了在穩定性上更好的譜方法。此外,我們解釋了最早由Fitzhugh在[8]中所提出在蘭氏節上的建模,並檢驗其對應之長度參數的影響。這個參數在[5]中被忽略,其作者將蘭氏節的建模視為是一沒有長度的點。還有,關於數值模擬的結果: 第一,被用以與[12]中的青蛙實驗數據比較; 第二,藉著調整神經軸突解剖上的參數來檢驗,發現與一個最近在腦幹的聽覺神經軸突上的實驗結果一致,那裏實驗者使用了一個更加複雜的雙電纜型參數分布模型來作模擬,以包括更詳細的解剖上之參數。第三,這模型被應用在多發性硬化症的疾病上。
由於電纜型模型可以從古典的泊松-能斯特-普朗克模型所推出[1],我們考慮一個最近提出之修正的具位阻效應之泊松-能斯特-普朗克模型[22],並在離子間排斥力很強的假設下藉著能量變分方法在形式上推導出一個新類型的具體積排除效應之泊松-能斯特-普朗克模型。這個修正的泊松-能斯特-普朗克模型因為包括離子離子之間的作用(這在古典的泊松-能斯特-普朗克模型中是被忽略的),並且作為一個連續模型,可以與古典的多離子位障模型這個離散模型比較。因此,用這個連續模型來研究選擇浸透性以及在離子通道中的飽和與結合現象是很有盼望的。 在神經科學一切豐碩的結果中,至今離散模型是更多被研究並應用的[30,31]。這個論文工作的主要貢獻是在於電纜型模型作為一個在不同尺度,包括軸突等級和離子通道等級之中的連續模型上面。 在神經科學一切豐碩的結果中,至今離散模型是更多被研究並應用的[30,31]。這個論文工作的主要貢獻是在於電纜型模型作為一個在不同尺度,包括軸突等級和離子通道等級之中的連續模型上面。雖然文獻上也有使用譜方法在電纜型模型上,但我們的工作是在具有髓鞘之神經軸突上,與在有分支的樹突上[32]或是在不具有髓鞘之神經軸突上[31]的工作不同。也就是說,我們擴大了使用譜方法研究電纜型模型的工作到一具有神經軸突的情況上。 | zh_TW |
dc.description.abstract | A cable-type model for simulating the action potential propagation along a myelinated axon is studied. Compared with the previous works done in [4,8,11], spectral method is used rather than finite difference method and provides better numerical stability; Furthermore, an interpretation of the modeling on Ranvier nodes first given by Fitzhugh in [8] is suggested and the effect of the corresponding parameter on Ranvier node length is examined, which was ignored in [5], therein the author considered the nodes being modeled as points without length. Moreover, the simulation results are firstly obtained to fit the experimental data on frog in [12], and secondly tested by adjusting the anatomical parameters of the axon and found to be in accordance with a recent research on auditory brainstem axons [7], where the authors used a more complicated two-cable distributed-parameter model to include the more detailed anatomical parameters. Thirdly, the model is used to see the application on Multiple Sclerosis disease.
Since the cable model can be derived from the classical Poisson-Nernst-Planck (PNP) equation [1], we may consider a recently modified PNP model with steric effect [22], and formally derive a new PNP-type model using Energetic Variational Approach with volume exclusion effect under strong repulsion assumption between ions. This modified PNP model includes ion-ion interaction, which is lacked in the classical PNP model and may be the continuum model to be compared with the classical multi-ion barrier model which is discrete. Thus it is promising to use this continuum model to study the selective permeability and the phenomena of saturation and bindings in the ion channel. Among all the fruitful results in Neuroscience up to now, where discrete models had much been studied and applied [30,31], the main contribution of this work is on the cable-type model as the continuum model in different scales including axon-level and ion-channel level. While there also exists works using spectral methods on the cable-type model, our work is on the myelinated axon, which is different to the works either on branched dendrites [32] or on unmyelinated axon [31]. That is, we extend the study on cable-type model using spectral methods to a myelinated axon situation. | en |
dc.description.provenance | Made available in DSpace on 2021-06-08T02:07:30Z (GMT). No. of bitstreams: 1 ntu-104-R02221014-1.pdf: 1497537 bytes, checksum: 3f76660af987b1778409f7e73905876d (MD5) Previous issue date: 2015 | en |
dc.description.tableofcontents | 誌謝 i
中文摘要 ii ABSTRACT iii CONTENTS v LIST OF FIGURES vii LIST OF TABLES viii Chapter 1 Introduction 1 1.1 Physiological background 1 1.1.1 Myelinated axon 2 1.1.2 Anatomical facts on myelinated axon with their significance 3 Chapter 2 Model formulations 4 2.1 Cable model 4 2.1.1 Geometry of the axon and the electrical quantities 4 2.2 Two types of description on transmembrane current 10 2.2.1 Hodgkin-Huxley (HH) model (for unmyelinated squid giant axon) 10 2.2.2 Frankenhaeuser-Huxley (FH) model (for myelinated toad axon) 10 2.2.3 The history of membrane models 11 2.3 Temperature effects 11 2.4 Coupling considerations on spatial domain 11 Chapter 3 Numerical methods 13 3.1 Discretization approach 13 3.2 Model setting and numerical scheme 14 3.3 Literature remark 16 3.3.1 Fitzhugh’s work 16 3.3.2 Goldman and Albus’ work 16 3.3.3 Moore el. al. s’ work 16 3.3.4 Toth and Funaro’s work 16 3.3.5 Carpio and Peral’s work 17 3.3.6 Concluding remark 17 Chapter 4 Applications 18 4.1 Action Potential (AP) Propagation velocity 18 4.1.1 Propagation velocity in comparison with frog experiment data 18 4.1.2 Anatomical parameter analysis 20 4.2 Multiple Sclerosis (MS) Disease 23 4.2.1 Simulation for MS on HH-type cable model 23 4.2.2 Simulation for MS on FH-type cable model 24 Chapter 5 A new PNP-type model: PNP-multi-ion 25 5.1 Two types of current description come from PNP model 25 5.2 PNP-steric model 25 5.3 Introducing volume-excluded (VE) effect in PNP-steric 25 5.3.1 Formal derivation of the PNP-steric with VE effect model 26 5.3.2 Comparing with MPNP model [Kilic, Bazant, and Ajdari 2007] 29 5.3.3 Comparing with cross-diffusion equation with size-exclusion effect 30 5.3.4 Comparing with Nonlinear PNP model [M. Burger et.al. 2012] 30 5.3.5 Discussing of possible physiological applications 32 5.3.6 Future works on comparing with classical multi-ion models 32 5.4 A new FH-type cable model: FH-type cable model with steric effects 33 5.4.1 Goldman-Hodgkin-Katz-steric (GHKs) current 33 5.4.2 Modified FH-type cable model 36 REFERENCE 37 | |
dc.language.iso | en | |
dc.title | 電纜型方程及其在一有髓神經軸突中之動作電位傳遞的應用 | zh_TW |
dc.title | Cable Type Model and its Application on Action Potential Propagation in a Myelinated Axon | en |
dc.type | Thesis | |
dc.date.schoolyear | 104-1 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 洪子倫(Tzyy-Leng Horng),柳春(Chun Liu),許文翰(Tony W.H. Sheu) | |
dc.subject.keyword | 電纜型模型,動作電位傳遞,具髓鞘的神經軸突,蘭氏節長度,多發性硬化症疾病,泊松-能斯特-普朗克模型,位阻效應,能量變分方法,多離子位障模型, | zh_TW |
dc.subject.keyword | cable-type model,action potential propagation,myelinated axon,Ranvier node length,Multiple Sclerosis disease,Poisson-Nernst-Planck equation,steric effect,energetic variational method,multi-ion barrier model, | en |
dc.relation.page | 40 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2016-02-02 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 數學研究所 | zh_TW |
顯示於系所單位: | 數學系 |
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