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系統識別號 U0026-2008202011410300
論文名稱(中文) 神經動作電位之機械表面波與離子通道理論研究
論文名稱(英文) Combined Mechanical Surface Wave and Ion Channel Activation Theories to Nerve Action Potential Propagation
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 108
學期 2
出版年 109
研究生(中文) 易瑞祥
研究生(英文) Ruei-Shiang Yi
學號 N16070162
學位類別 碩士
語文別 中文
論文頁數 75頁
口試委員 指導教授-朱銘祥
口試委員-林宙晴
口試委員-陳重德
中文關鍵字 動作電位  離子通道  具髓鞘神經  有限元素法  機械作用波 
英文關鍵字 action potential  myelin  ion channel,  saltatory conduction 
學科別分類
中文摘要 神經在動作電位期間伴隨許多現象,除了電位的變化之外,還會伴隨著機械特性和熱力學的變化。而神經有無髓鞘包覆也會影響到神經傳導速度。目前文獻所提出的模型雖能描述膜電位變化,機械變化,或同時描述兩者。然而卻無法解釋為何具髓鞘的神經傳導速度比無髓鞘的神經傳導速度快。因此有必要建立一個神經之數值模型,利用此模型描述神經動作電位的產生、傳遞以及模擬具髓鞘神經跳躍式傳導現象。
本研究利用有限元素法建立神經數值之模型以計算動作電位期間在神經軸突傳遞的機械波,引進離子通道的機械模型,並提出機械波與動作電位的轉換機制。由神經軸突的機械波得知當細胞質的剛性較細胞皮質小時,其傳遞機械波效果最好。而細胞膜和細胞質的黏滯性對細胞膜徑向位移有影響,但對軸向應力卻無影響。神經軸突與髓鞘的交互作用為接觸時,其位移波、應力波以及傳導速度皆會增加。離子通道設為二階質量-阻尼-彈簧過阻尼系統時可以模擬出由Hodgkin–Huxley模型所得之離子通道的電壓變化。
本研究提出的模型不僅能夠解釋動作電位如何產生,所模擬出來電位變化也與實驗數據符合,也能模擬動作電位的傳遞,其在細胞膜表面產生的位移也接近實驗值,且能夠模擬具髓鞘神經的跳躍式傳導。
英文摘要 SUMMARY
Several physics phenomena such as membrane potential, mechanical deformation, thermodynamic changes occur during the propagation of action potential on the axons of peripheral nerve. The myelin affects the propagation speed of action potential. In recent years, new models such as Hodgkin-Huxley model and soliton model for the action potential have been proposed. Although these models can describe the action potential and the mechanical changes, the saltatory conduction still can not be explained by these model. In this thesis, the propagation of action potential is modeled as mechanical action wave propagated on the axon of nerve. A mechanical model of ion channels and transduction mechanism of mechanical wave to action potential were proposed. Finite element models of unmyelinated and myelinated axons were built and propagation of the action were simulated. The results show that, when stiffness of cytoplasm is smaller than cortex, the propagation speed are in agreement with experimental results. The viscosities of membrane and cytoplasm have no effect on radial but axial mechanical wave. When the interaction between myelin and axon is contact, the displacement, stress and conduction speed are increased compared to unmyelinated axon. The over-damped 2nd order mechanical model of ion channels could describe the transduction of stress wave to action potential at the distal end of the electro-mechanical model of axon. The model developed in this thesis can simulate not only the propagation and generation of action potential but also the saltatory conduction.
論文目次 目錄
摘要 Ⅰ
致謝 Ⅶ
目錄 Ⅷ
圖目錄 Ⅹ
表目錄 XII
符號表 ⅩⅢ
第一章 緒論 1
1.1 神經電生理學回顧 1
1.2 神經電生理模型 2
1.3 研究動機 4
1.4 研究目的 6
第二章 研究方法 7
2.1 神經的生理學 7
2.2 神經各層之材料性質與交互作用 9
2.2.1細胞膜 9
2.2.2細胞皮質 9
2.2.3細胞質 11
2.2.4髓鞘 11
2.2.5各層間的交互作用力 11
2.3離子通道 12
2.4本研究模型 13
2.4.1神經軸突模型 14
2.4.2統御方程式 16
2.5有限元素法 19
2.5.1有限元素軟體簡介 19
2.5.2有限元素模型 20
2.5.3神經各層交互作用 21
2.5.4邊界條件和作用力 21
2.5.5元素選擇 23
2.5.6網格劃分和模擬案例 23
2.6離子通道模型 25
第三章 結果 29
3.1神經軸突機械波 29
3.1.1模型A 29
3.1.2模型B 38
3.1.3模型C 46
3.2離子通道模型與電導關係 53
第四章 討論 58
4.1模擬結果間比較 58
4.1.1模型A 58
4.1.2模型B 61
4.1.3模型C 63
4.1.4離子通道比較 63
4.2模擬結果和文獻比較 64
4.3本研究模型和其他模型比較 65
4.3.1與Hodgkin-Huxley模型比較 65
4.3.2與孤波模型比較 66
4.3.3與Drapaca的模型比較 66
4.3.4與Hady的模型比較 67
4.4.4綜合比較 67
第五章 結論 68
5.1結論 68
5.2建議 68
參考文獻 70

圖目錄
圖2-1 具髓鞘的神經 7
圖2-2 具髓鞘神經蘭氏節位置 8
圖2-3 無髓鞘的神經軸突組成 8
圖2-4神經細胞皮質蛋白組成影像 10
圖2-5 神經細胞皮質組成 10
圖2-6 離子通道結構 12
圖2-7離子通道活化 12
圖2-8 本研究提出機電系統模型 13
圖2-9 無髓鞘的神經軸突模型 14
圖2-10 具髓鞘的神經軸突模型 15
圖2-11 圓柱膜的幾何形狀與力平衡 16
圖2-12 神經各層間的交互作用 21
圖2-13動作電位時神經所受作用力 22
圖2-14 神經軸突作用力和邊界條件 22
圖2-15 無髓鞘的神經軸突網格 23
圖2-16 具髓鞘的神經軸突網格 24
圖2-17 Hodgkin 與Huxley模型 26
圖2-18 離子電導變化 26
圖2-19 質量-彈簧-阻尼系統 27
圖3-1模型A1的r方向位移 30
圖3-2模型A1的z方向應力 30
圖3-3模型A1的r方向位移比較 31
圖3-4模型A1的z方向應力比較 31
圖3-5模型A2的r方向位移 32
圖3-6模型A2的z方向應力 33
圖3-7模型A2的r方向位移比較 34
圖3-8模型A2的z方向應力比較 34
圖3-9模型A3的r方向位移 35
圖3-10模型A3的z方向應力 35
圖3-11模型A3的r方向位移比較 36
圖3-12模型A3的z方向應力比較 37
圖3-13模型B1的r方向位移 39
圖3-14模型B1的z方向應力 39
圖3-15模型B1與A1的r方向位移比較 40
圖3-16模型B1與A1的的z方向應力比較 40
圖3-17模型B2的r方向位移 41
圖3-18模型B2的z方向應力 41
圖3-19模型B2與A1的的r方向位移比較 42
圖3-20模型B2與A1的的z方向應力比較 42
圖3-21模型B3的r方向位移 43
圖3-22模型B3的z方向應力 44
圖3-23模型B3與A1的的r方向位移比較 44
圖3-24模型B3與A1的的z方向應力比較 45
圖3-25不同黏滯係數下z方向應力 46
圖3-26 模型C1的r方向位移 47
圖3-27 模型C1的z方向應力 47
圖3-28 模型C1的r方向位移傳遞 48
圖3-29 模型C1的z方向應力傳遞 49
圖3-30 模型C2的r方向位移 49
圖3-31 模型C2的z方向應力 50
圖3-32 模型C2的r方向位移傳遞 51
圖3-33 模型C2的z方向應力傳遞 51
圖3-34模型A1(左上)、模型A2(右上)、模型A3(下)應力結果 52
圖3-35 鈉離子通道使用過阻尼系統擬合 53
圖3-36 鈉離子通道使用臨界阻尼系統擬合 54
圖3-37 鉀離子通道使用過阻尼系統擬合 55
圖3-38 鉀離子通道使用臨界阻尼系統擬合 55
圖3-39 鈉離子通道擬合結果驗證 56
圖3-40 鉀離子通道擬合結果驗證 57
圖4-1 細胞質剛性不同r方向位移比較 59
圖4-2 模型A1和模型A2剛性應力比較 59
圖4-3 模型A1和模型A3應力比較 60
圖4-4細胞膜與細胞質有無黏滯性的r方向位移比較 61
圖4-5細胞膜與細胞質有無黏滯性的z方向應力比較 62
圖4-6 不同黏滯係數下最大應力比較 62
圖4-7 Hodgkin-Huxley模型與本模型的電位比較 66

表目錄
表2-1 神經軸突各層材料機械性質 20
表2-2 模擬案例 24
表3-1 模型A比較 38
表4-1 不同模型和真實神經的傳導速度 64
表4-2 各模型間比較 67
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