劉芳 趙思淇 盧立彬

摘 ?要： 分析椎動(dòng)脈的動(dòng)脈瘤血流動(dòng)力學(xué)指標(biāo)在動(dòng)脈瘤發(fā)生、發(fā)展及治療后的作用，判斷引起動(dòng)脈瘤發(fā)生與治療后復(fù)發(fā)的特定血流動(dòng)力學(xué)因素，并為動(dòng)脈瘤的預(yù)防、治療提供理論依據(jù)。選取一例顱內(nèi)動(dòng)脈瘤患者的CTA影像數(shù)據(jù)三維建模和仿真計(jì)算獲取血流動(dòng)力學(xué)指標(biāo)：time average wall shear stress、time average wall shear stress grade、oscillatory shear index 、aneurysm formation index、relative retention time等參數(shù)作為觀察指標(biāo)分析。結(jié)果顯示：1. 動(dòng)脈瘤TAWSS及TAWSSG的不穩(wěn)定，栓塞手術(shù)能夠降低動(dòng)脈瘤破裂的風(fēng)險(xiǎn)性，而在栓塞術(shù)后的血管交叉處，血管壁則較易受損;2. OSI值較高，改變瘤體內(nèi)震蕩水平導(dǎo)致血流紊亂，OSI值減低，血流趨于穩(wěn)定;3. 隨著動(dòng)脈瘤AFI值逐漸升高，血液流動(dòng)可逐漸平穩(wěn)，可降低動(dòng)脈瘤破裂危險(xiǎn)性。

關(guān)鍵詞： 顱內(nèi)動(dòng)脈瘤;計(jì)算流體力學(xué)

中圖分類號(hào)： TP319 ? ?文獻(xiàn)標(biāo)識(shí)碼： A ? ?DOI：10.3969/j.issn.1003-6970.2020.08.028

本文著錄格式：劉芳，趙思淇，盧立彬，等. 基于CTA的椎動(dòng)脈瘤血流動(dòng)力學(xué)分析[J]. 軟件，2020，41（08）：97-102

【Abstract】： To analyze the role of vertebral artery aneurysm parameters in the occurrence， development and post treatment of aneurysms， ? ?to determine the specific Hemodynamics that cause the occurrence and recurrence of aneurysms after treatment， and to provide a theoretical basis for the prevention and treatment of aneurysms. Three-dimensional modeling and simulation of CTA images of a patient with cerebral aneurysm were used to obtain Hemodynamics parameters： Time average wall shear stress， time average wall shear stress， Oscillatory Shear Index， Eurasian SM Formation Index and relative retention time. 1. The instability of TAWSS and Tawssg， embolization can reduce the risk of aneurysm rupture， but the vessel wall is more vulnerable at the cross-section after embolization. 2. Osi Value is higher， changes in the level of turbulence in the tumor lead to blood flow disorder， Osi value is reduced， blood flow tends to be stable; 3. With the gradual increase of AFI， the blood flow could be stabilized and the risk of aneurysm rupture could be reduced.

【Key words】： Cerebral aneurysm; Computational fluid dynamics

0 ?引言

顱內(nèi)動(dòng)脈瘤（Intracranial aneurysm，IA）是多種因素導(dǎo)致的動(dòng)脈壁的異常瘤樣擴(kuò)張，常發(fā)生于顱內(nèi)大動(dòng)脈的分叉及彎曲處，破裂會(huì)導(dǎo)致蛛網(wǎng)膜下腔出血，具有極高的致死率及致殘率。影響動(dòng)脈瘤生長(zhǎng)和破裂的因素主要包括先天生理性、病理性及血流動(dòng)力學(xué)因素。對(duì)于IA的治療主要包括開顱夾閉術(shù)及血管內(nèi)介入栓塞兩種方法[1-3]。無(wú)論是哪種方法，由于動(dòng)脈瘤自身的復(fù)雜性及不完全閉塞的發(fā)生，即使是有經(jīng)驗(yàn)的臨床醫(yī)生，術(shù)后的復(fù)發(fā)率依舊很高[4-7]。栓塞手術(shù)由于創(chuàng)傷小，操作相對(duì)簡(jiǎn)單等優(yōu)勢(shì)和栓塞材料及技術(shù)的不斷發(fā)展進(jìn)步逐漸被廣泛應(yīng)用于臨床。但同時(shí)由于彈簧圈具有可壓縮性使得動(dòng)脈瘤復(fù)發(fā)的可能性大大增加，有研究表明栓塞程度是動(dòng)動(dòng)脈瘤復(fù)發(fā)的重要影響因素，Brzegowy等人回顧性分析破裂與未破裂前交動(dòng)脈瘤的栓塞治療，同樣得出影響顱內(nèi)動(dòng)脈瘤復(fù)發(fā)的最大因素就是栓塞密度，初始栓塞的不完全極易引起動(dòng)脈瘤的復(fù)發(fā)[8-9]。栓塞程度低，彈簧圈會(huì)隨著血流的沖擊逐漸壓縮，進(jìn)而向遠(yuǎn)側(cè)移位、復(fù)發(fā)。趙慶平等提出瘤腔內(nèi)的血流速度與瘤腔大小呈負(fù)相關(guān)，即栓塞程度越低，腔內(nèi)血流速度加快時(shí)，血液對(duì)壁面產(chǎn)生的力就可能導(dǎo)致動(dòng)脈瘤的復(fù)發(fā)[10]。近年來(lái)隨著計(jì)算機(jī)的發(fā)展及有限元軟件的開發(fā)，尤其是計(jì)算流體動(dòng)力學(xué)數(shù)值模擬方法的應(yīng)用，使得血流建模能更好解釋血流動(dòng)力學(xué)在IA發(fā)病機(jī)制中的作用[11-16]

1 ?材料與方法

原始影像數(shù)據(jù)采集：采集解放軍第78集團(tuán)軍醫(yī)院一椎動(dòng)脈瘤患者CTA影像數(shù)據(jù)，男性患者，62歲，患者主訴頭部持續(xù)頭痛，臨床表現(xiàn)為：行走不穩(wěn)三個(gè)月。經(jīng)臨床診斷為頭部椎最動(dòng)脈瘤。經(jīng)患者本人知情同意并簽署意見書與醫(yī)院倫理委員會(huì)批準(zhǔn)。

圖像后處理工作站：DELL圖像向工作站：DELL 7810/CPU E5/16G內(nèi)存/英偉達(dá)K2200顯卡;

圖像后處理軟件：醫(yī)學(xué)交互式影像控制系統(tǒng)（Materialis Interative Medical Image Control System，MIMICS，比利時(shí)Materialise公司）、醫(yī)學(xué)建模軟件3-matic medical（比利時(shí)Materialis公司）;

計(jì)算機(jī)仿真軟件：ANSYS 19.2：流體仿真軟件CFX，網(wǎng)格劃分軟件FLUENT MESHING

計(jì)算結(jié)果分析軟件：ENSIGHT10.6。

椎動(dòng)脈瘤三維重建：將頭部影像DICOM數(shù)據(jù)導(dǎo)入MIMICS軟件，使用MIMICS分割工具：閾值分割等算法，最后三維計(jì)算生成動(dòng)脈瘤三維初步模型以stl格式導(dǎo)入3-matic medical軟件中，使用光順表面、去除細(xì)小分支、切好出、入口平面，最后形成動(dòng)脈瘤三維模型，如圖1所示。

網(wǎng)格劃分：由于模型結(jié)構(gòu)復(fù)雜，使用非結(jié)構(gòu)化的四面體網(wǎng)格劃分，為保證計(jì)算精度，在動(dòng)脈瘤管壁進(jìn)行五層加密。

邊界條件：本計(jì)算不考慮能量的傳遞，不考慮重力。血液密度為1056 kg/m3，動(dòng)力粘度為0.0035 。計(jì)算采用瞬態(tài)計(jì)算，兩個(gè)入口，兩個(gè)出口，壁面無(wú)滑移。入口采用速度入口，出口采用壓力出口。為保證盡快收斂，入口速度采用極小的速度差。出口采用壓力出口，壓力曲線如圖3所示。

血流作用在內(nèi)皮細(xì)胞上的力的血流動(dòng)力學(xué)參數(shù)GON，壁面切向和正交向上的向量，如果空間梯度G數(shù)值變化，代表對(duì)內(nèi)皮細(xì)胞產(chǎn)生震蕩張力和壓縮力，在一個(gè)心動(dòng)周期內(nèi)，如果某個(gè)點(diǎn)發(fā)生較大的梯度變化，單位面積內(nèi)發(fā)生強(qiáng)烈的震蕩張力或者壓縮力作用于內(nèi)皮細(xì)胞上，GON是用來(lái)量化震蕩張力和壓縮力的程度。

CFX無(wú)法直接實(shí)現(xiàn)上述參數(shù)指標(biāo)，使用CFX ccl語(yǔ)言編程，如下為子程序的部分內(nèi)容：

IBRARY：

CEL：

EXPRESSIONS：

DOMAIN： FLUIDdom

Coord Frame = Coord 0

Domain Type = Fluid

Location = Assembly

BOUNDARY： INLET1

Boundary Type = INLET

Location = INLET1

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Normal Speed = invel1

Option = Normal Speed

END

END

END

BOUNDARY： INLET2

Boundary Type = INLET

Location = INLET2

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Normal Speed = invel2

Option = Normal Speed

END

END

END

BOUNDARY： OUTLET1

Boundary Type = OPENING

Location = OUTLET1

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW DIRECTION：

Option = Normal to Boundary Condition

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Option = Opening Pressure and Direction

Relative Pressure = OUTLET1f

END

END

END

BOUNDARY： OUTLET2

Boundary Type = OPENING

Location = OUTLET2

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW DIRECTION：

Option = Normal to Boundary Condition

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Option = Opening Pressure and Direction

Relative Pressure = OUTLET2f

END

END

END

BOUNDARY： OUTLET3

Boundary Type = OPENING

Location = OUTLET3

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW DIRECTION：

Option = Normal to Boundary Condition

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Option = Opening Pressure and Direction

Relative Pressure = OUTLET3f

END

END

END

BOUNDARY： OUTLET4

Boundary Type = OPENING

Location = OUTLET4

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Option = Zero Flux

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = 0 [kg m^-1 s^-2]

Option = Value

END

FLOW DIRECTION：

Option = Normal to Boundary Condition

END

FLOW REGIME：

Option = Subsonic

END

MASS AND MOMENTUM：

Option = Opening Pressure and Direction

Relative Pressure = OUTLET4f

END

END

END

BOUNDARY： WALL_VESSEL

Boundary Type = WALL

Location = WALL_PARENT_VESSEL

BOUNDARY CONDITIONS：

ADDITIONAL VARIABLE： WSSField

Additional Variable Value = WallShearMag

Option = Value

END

ADDITIONAL VARIABLE： WSSxF

Additional Variable Value = Wall Shear X

Option = Value

END

ADDITIONAL VARIABLE： WSSyF

Additional Variable Value = Wall Shear Y

Option = Value

END

ADDITIONAL VARIABLE： WSSzF

Additional Variable Value = Wall Shear Z

Option = Value

END

MASS AND MOMENTUM：

Option = No Slip Wall

END

END

END

DOMAIN MODELS：

BUOYANCY MODEL：

Option = Non Buoyant

END

2.2 ?TAWSS云圖分析

從平均壁面切應(yīng)力（TAWSS）的云圖（圖4）上來(lái)看，云圖顏色越偏紅，代表平均壁面切應(yīng)力越大，越接近藍(lán)色則平均壁面切應(yīng)力越小。載瘤動(dòng)脈由于其具有較高的流速，因此載瘤動(dòng)脈的平均壁面切應(yīng)力要大于動(dòng)脈瘤。

2.3 ?動(dòng)脈瘤的TAWSSG云圖分析

從TAWSSG云圖中（圖5）可以看出，瘤體的TAWSSG開始時(shí)低于載瘤動(dòng)脈，而后逐漸接近?？赡苁怯捎陂_始時(shí)動(dòng)脈瘤體積較大[18-20]，血液流速較慢，壁面切應(yīng)力數(shù)值變化不變明顯，所示動(dòng)脈瘤偏藍(lán)色，TAWSSG值較低。

2.4 ?動(dòng)脈瘤的OSI云圖分析

圖6為動(dòng)脈瘤OSI云圖，在動(dòng)脈瘤頂端存在小部分高OSI區(qū)域。動(dòng)脈瘤頂端的高OSI區(qū)域較之前擴(kuò)大，振蕩剪切系數(shù)代表的是整個(gè)心動(dòng)周期內(nèi)壁面切應(yīng)力方向變化快慢的量，OSI不同是反應(yīng)震蕩水平，即流動(dòng)的強(qiáng)度和方向的改變，越大表示震蕩越強(qiáng)，流體在周期內(nèi)流動(dòng)的方向不穩(wěn)定，導(dǎo)致動(dòng)脈瘤內(nèi)的血流運(yùn)動(dòng)趨于紊亂。

2.5 ?動(dòng)脈瘤AFI云圖分析

圖7為動(dòng)脈瘤AFI云圖，瘤體側(cè)壁上存在部分AFI低區(qū)域，即偏藍(lán)色區(qū)域。流增多形成渦流并不斷的沖擊著動(dòng)脈瘤管壁，壁面切應(yīng)力的方向變化明顯，血液流動(dòng)不穩(wěn)定。

2.6 ?動(dòng)脈瘤GON云圖分析

動(dòng)脈瘤GON云圖（圖8）表明在動(dòng)脈瘤表面存在強(qiáng)烈的震蕩力和壓縮力，原因是血液在進(jìn)入瘤腔后形成渦流，導(dǎo)致動(dòng)脈瘤壁震蕩，這種沖擊對(duì)瘤壁造成膨脹或者擴(kuò)張。

3 ?討論與結(jié)論

通過(guò)血流動(dòng)力學(xué)計(jì)算分析，發(fā)現(xiàn)完全栓塞手術(shù)可以阻斷進(jìn)入動(dòng)脈瘤內(nèi)的血液[21-24]，提高TAWSS及降低OSI等，降低了破裂出血的風(fēng)險(xiǎn)。通過(guò)本實(shí)驗(yàn)對(duì)最動(dòng)脈瘤血流動(dòng)力學(xué)的參數(shù)的變化分析可得出以下結(jié)論：

（1）動(dòng)脈瘤TAWSS及TAWSSG的不穩(wěn)定，栓塞手術(shù)能夠降低動(dòng)脈瘤破裂的風(fēng)險(xiǎn)性[25-30]，而在栓塞術(shù)后的血管交叉處，血管壁則較易受損;

（2）OSI值較高，改變瘤體內(nèi)震蕩水平導(dǎo)致血流紊亂，OSI值減低，血流趨于穩(wěn)定;

（3）隨著動(dòng)脈瘤AFI值逐漸升高，血液流動(dòng)可逐漸平穩(wěn)，可降低動(dòng)脈瘤破裂危險(xiǎn)性。

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