顱內梭狀動脈瘤彈性壁與剛性壁之結構應力與血液動力學之計算分析

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研究生：	蔡嘉瑋
論文名稱：	顱內梭狀動脈瘤彈性壁與剛性壁之結構應力與血液動力學之計算分析 Numerical Simulation on Structure Stress and Hemodynamics of Intracranial Fusiform Aneurysms with Rigid and Flexible Walls
指導教授：	劉通敏
口試委員:	黃柏文林呈林昭安
學位類別：	碩士 Master
系所名稱：	工學院 - 動力機械工程學系 Department of Power Mechanical Engineering
論文出版年：	2013
畢業學年度：	101
語文別：	中文
論文頁數：	228
中文關鍵詞：	顱內梭狀動脈瘤、流固耦合、數值模擬
相關次數：	點閱：3 下載：0
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根據行政院衛生署公布民國75~100年間國人十大死因統計表中，腦血管疾病高居第三名，然而腦血管疾病中又以顱內動脈瘤破裂之致死率最高。先前臨床及數值計算文獻皆偏重於探討囊狀動脈瘤並假設為剛性瘤壁，然而其假設與實際人體內之血管壁、動脈瘤壁相異，故本研究乃藉由數值模擬計算方式探討顱內梭狀動脈瘤脈動流場特性及配合流固耦合 (Fluid-Structure Interaction) 技術探討彈性瘤壁在脈動血流衝擊之下的結構應力。本文於入口輸入一內頸動脈(ICA)生理波形並以雙向流固耦合、暫態分析之方式，分別探討改變瘤體之最大直徑與不對稱性對顱內動脈瘤瘤內流場與血管壁結構應力之影響。流體部分之數值計算採用有限體積離散方法(Finite Volume Method)求解依時性非穩態不可壓縮Navier-Stokes方程組，其中時間項採用二階Backward Euler法，而對流項與擴散項分別採用修正型之二階上風法予以離散，並搭配SIMPLEC演算法解決壓力與速度耦合問題。脈動流場參數中沃門斯里數(Womersley number)為4.0，雷諾數(Reynolds number)變化範圍為202~384，平均值為266。計算結果乃透過探討流體之血液動力因子及固體之彈性力學因子來呈現，血液動力因子包含瘤內主流場速度分布、瘤體壁面剪應力(WSS)及壁面壓力分布等；固體部分則採用有限元素法求解力平衡之運動方程式，探討不同幾何外型之結構應力(Effective stress)變化、血管壁破壞應力以及比較假設為剛性壁與彈性壁之間的異同。結果顯示本文之剛性瘤壁數值模擬結果(瘤內速度向量場與壓力分布)與先前實驗文獻相似及相同外型之對應結果比對吻合，並進一步提供了實驗難以量測之特徵物理量包括彈性瘤壁之血流壁剪應力、壁壓力和彈性瘤壁內、外壁結構應力分布。剛性瘤壁與彈性瘤壁相比，血流壁剪應力與壁壓力分別高10~35%及5~40%，顯示由剛性壁模擬動脈瘤之量值皆較彈性壁高；內與外瘤壁結構應力分布亦有所差異，以反曲點為例，內瘤壁為彈性大於剛性13%，外瘤壁為剛性大於彈性17%。在模擬瘤壁以對稱及不對稱方式成長時，發現相較於對稱外型，不對稱者其血流壁剪應力、壁壓力及瘤壁結構應力有明顯集中於反曲點的趨勢。最後研究結果顯示同時分析血流重新附著點位置、壁剪應力、壁壓力、內與外瘤壁結構應力之最大及最小值範圍較僅考慮壁剪應力更能合理預測破裂位置，本文所模擬之梭狀瘤外型與臨床破裂位置一致。

摘要    I
誌謝    III
目錄    IV
圖表目錄    IX
符號    XXV
第一章  前言    1
1-1 研究背景與動機    1
1-2 文獻探討    3
1-2-1 臨床與模型實驗    3
1-2-2 數值模擬計算    6
1-3 文獻總結    8
1-3-1 臨床與模型實驗    8
1-3-2 數值模擬計算    8
1-4 研究目的    9
第二章  研究方法與理論分析    11
2-1 幾何外型建構與計算模型尺寸    11
2-2 計算模型格點    12
2-3基本假設    13
2-3-1顱內動脈血管之流動現象    13
2-3-2 流體域第一考量參數    15
2-3-3 流體域第二考量參數    16
2-3-4 限制條件    17
2-3-5 固體(血管壁)運動    17
2-4統御方程式    19
2-4-1 流體部分    19
2-4-2 固體部分    20
2-4-3 流固交界面    21
2-5 流體、固體(材料)參數    22
2-6 邊界條件    23
2-6-1流體部分    23
2-6-2 固體部分    23
2-7 起始條件    24
第三章  數值方法    25
3-1 有限體積法    25
3-1-1 積分    25
3-1-2 對流-擴散項(Convection-Diffusion Term)離散化    27
3-1-3 暫態項(Transient Term)離散化    28
3-1-4 源項(Source Term)離散化    30
3-1-5 壓力-速度場耦合(Pressure-Velocity Coupling)    31
3-1-6 疊代求解    35
3-1-7 流體域收斂標準    36
3-2 有限元素法    37
3-2-1 簡介    37
3-2-2 彈性力學理論    39
3-2-3平衡方程式    40
3-2-4應變與位移關係    41
3-2-5應力與應變關係    42
3-2-6有限元素法之基本理論    43
3-2-7有限元素法之基本程序    46
3-2-8 固體域收斂標準    48
3-3流固耦合(Fluid Structure Interaction)    49
3-3-1流固耦合簡介    49
3-3-2流固耦合背景    49
3-3-3整體求解法(MA)與分部求解法(PA)    50
3-3-4單向與雙向耦合    52
3-3-5格點未匹配之流固交界面負載傳遞    53
3-3-6 ALE(Arbitary Lagrangian-Eulerian)我    55
3-3-7 CFD-FEM耦合求解收斂性    56
3-4 格點獨立測試    57
3-4-1 流體域    57
3-4-2 固體域    58
3-5 數值結果與Womersley理論解之數值驗證    59
第四章  結果與討論    62
4-1 剛性壁(Glass)與彈性壁    62
4-2 對稱理想化梭狀動脈瘤(β=1, Model B)模擬結果    65
4-2-1數值模擬與實驗量測之瘤內速度向量場驗證    65
4-2-2瘤內流場(β=1, Model B)－Z*=0剖面之主流流場    67
4-2-3 瘤內流體壁剪應力    68
4-2-4瘤內流體壁壓力    70
4-2-5 血管壁結構應力    71
4-3 對稱理想化梭狀動脈瘤瘤體最大直徑影響    73
4-3-1瘤內流場(β=1)、Z*=0剖面之主流流場    73
4-3-2 瘤內流體壁剪應力    75
4-3-3 瘤內流體壁壓力    78
4-3-4血管壁結構應力    79
4-4 不對稱理想化梭狀動脈瘤瘤體形狀之影響    85
4-4-1模型D(β=1.75)流場驗證    85
4-4-2 模型E(β=2.67)壁面壓力驗證    86
4-4-3瘤內流場(β≠1)－主流流場與二次流    87
4-4-4 瘤內流體壁剪應力    92
4-4-5 瘤內流體壁壓力    96
4-4-6血管壁結構應力    98
4-5 總結與討論    105
4-5-1 剛性(Glass)、彈性管壁差異，以基礎對稱模型B為例    105
4-5-2 彈性壁之基礎對稱模型B(baseline model B)    105
4-5-3 對稱模式一    106
4-5-4 不對稱之模式二    107
4-5-5 總結    109
4-6 顱內梭狀動脈瘤之破裂分析    111
第五章  結論與未來建議    113
5-1 結論    113
5-2    未來建議    116
參考文獻    117
圖表    124
                                

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