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摘 要： 分析椎动脉的动脉瘤血流动力学指标在动脉瘤发生、发展及治疗后的作用，判断引起动脉瘤发生与治疗后复发的特定血流动力学因素，并为动脉瘤的预防、治疗提供理论依据。选取一例颅内动脉瘤患者的CTA影像数据三维建模和仿真计算获取血流动力学指标：time average wall shear stress、time average wall shear stress grade、oscillatory shear index 、aneurysm formation index、relative retention time等参数作为观察指标分析。结果显示：1. 动脉瘤TAWSS及TAWSSG的不稳定，栓塞手术能够降低动脉瘤破裂的风险性，而在栓塞术后的血管交叉处，血管壁则较易受损;2. OSI值较高，改变瘤体内震荡水平导致血流紊乱，OSI值减低，血流趋于稳定;3. 随着动脉瘤AFI值逐渐升高，血液流动可逐渐平稳，可降低动脉瘤破裂危险性。
关键词： 颅内动脉瘤;计算流体力学
中图分类号： TP319 文献标识码： A DOI：10.3969/j.issn.1003-6970.2020.08.028
本文著录格式：刘芳，赵思淇，卢立彬，等. 基于CTA的椎动脉瘤血流动力学分析[J]. 软件，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
顱内动脉瘤（Intracranial aneurysm，IA）是多种因素导致的动脉壁的异常瘤样扩张，常发生于颅内大动脉的分叉及弯曲处，破裂会导致蛛网膜下腔出血，具有极高的致死率及致残率。影响动脉瘤生长和破裂的因素主要包括先天生理性、病理性及血流动力学因素。对于IA的治疗主要包括开颅夹闭术及血管内介入栓塞两种方法[1-3]。无论是哪种方法，由于动脉瘤自身的复杂性及不完全闭塞的发生，即使是有经验的临床医生，术后的复发率依旧很高[4-7]。栓塞手术由于创伤小，操作相对简单等优势和栓塞材料及技术的不断发展进步逐渐被广泛应用于临床。但同时由于弹簧圈具有可压缩性使得动脉瘤复发的可能性大大增加，有研究表明栓塞程度是动动脉瘤复发的重要影响因素，Brzegowy等人回顾性分析破裂与未破裂前交动脉瘤的栓塞治疗，同样得出影响颅内动脉瘤复发的最大因素就是栓塞密度，初始栓塞的不完全极易引起动脉瘤的复发[8-9]。栓塞程度低，弹簧圈会随着血流的冲击逐渐压缩，进而向远侧移位、复发。赵庆平等提出瘤腔内的血流速度与瘤腔大小呈负相关，即栓塞程度越低，腔内血流速度加快时，血液对壁面产生的力就可能导致动脉瘤的复发[10]。近年来随着计算机的发展及有限元软件的开发，尤其是计算流体动力学数值模拟方法的应用，使得血流建模能更好解释血流动力学在IA发病机制中的作用[11-16]
1 材料与方法
原始影像数据采集：采集解放军第78集团军医院一椎动脉瘤患者CTA影像数据，男性患者，62岁，患者主诉头部持续头痛，临床表现为：行走不稳三个月。经临床诊断为头部椎最动脉瘤。经患者本人知情同意并签署意见书与医院伦理委员会批准。 图像后处理工作站：DELL图像向工作站：DELL 7810/CPU E5/16G内存/英伟达K2200显卡;
图像后处理软件：医学交互式影像控制系统（Materialis’ Interative Medical Image Control System，MIMICS，比利时Materialise公司）、医学建模软件3-matic medical（比利时Materialis公司）;
计算机仿真软件：ANSYS 19.2：流体仿真软件CFX，网格划分软件FLUENT MESHING
计算结果分析软件：ENSIGHT10.6。
椎动脉瘤三维重建：将头部影像DICOM数据导入MIMICS软件，使用MIMICS分割工具：阈值分割等算法，最后三维计算生成动脉瘤三维初步模型以stl格式导入3-matic medical软件中，使用光顺表面、去除细小分支、切好出、入口平面，最后形成动脉瘤三维模型，如图1所示。
网格划分：由于模型结构复杂，使用非结构化的四面体网格划分，为保证计算精度，在动脉瘤管壁进行五层加密。
边界条件：本计算不考虑能量的传递，不考虑重力。血液密度为1056 kg/m3，动力粘度为0.0035 。计算采用瞬态计算，两个入口，两个出口，壁面无滑移。入口采用速度入口，出口采用压力出口。为保证尽快收敛，入口速度采用极小的速度差。出口采用压力出口，压力曲线如图3所示。
血流作用在内皮细胞上的力的血流动力学参数GON，壁面切向和正交向上的向量，如果空间梯度G数值变化，代表对内皮细胞产生震荡张力和压缩力，在一个心动周期内，如果某个点发生较大的梯度变化，单位面积内发生强烈的震荡张力或者壓缩力作用于内皮细胞上，GON是用来量化震荡张力和压缩力的程度。
CFX无法直接实现上述参数指标，使用CFX ccl语言编程，如下为子程序的部分内容：
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
从平均壁面切应力（TAWSS）的云图（图4）上来看，云图颜色越偏红，代表平均壁面切应力越大，越接近蓝色则平均壁面切应力越小。载瘤动脉由于其具有较高的流速，因此载瘤动脉的平均壁面切应力要大于动脉瘤。
2.3 动脉瘤的TAWSSG云图分析
从TAWSSG云图中（图5）可以看出，瘤体的TAWSSG开始时低于载瘤动脉，而后逐渐接近。可能是由于开始时动脉瘤体积较大[18-20]，血液流速较慢，壁面切应力数值变化不变明显，所示动脉瘤偏蓝色，TAWSSG值较低。
2.4 动脉瘤的OSI云图分析
图6为动脉瘤OSI云图，在动脉瘤顶端存在小部分高OSI区域。动脉瘤顶端的高OSI区域较之前扩大，振荡剪切系数代表的是整个心动周期内壁面切应力方向变化快慢的量，OSI不同是反应震荡水平，即流动的强度和方向的改变，越大表示震荡越强，流体在周期内流动的方向不稳定，导致动脉瘤内的血流运动趋于紊乱。
2.5 动脉瘤AFI云图分析
图7为动脉瘤AFI云图，瘤体侧壁上存在部分AFI低区域，即偏蓝色区域。流增多形成涡流并不断的冲击着动脉瘤管壁，壁面切应力的方向变化明显，血液流动不稳定。
2.6 动脉瘤GON云图分析
动脉瘤GON云图（图8）表明在动脉瘤表面存在强烈的震荡力和压缩力，原因是血液在进入瘤腔后形成涡流，导致动脉瘤壁震荡，这种冲击对瘤壁造成膨胀或者扩张。 3 討论与结论
通过血流动力学计算分析，发现完全栓塞手术可以阻断进入动脉瘤内的血液[21-24]，提高TAWSS及降低OSI等，降低了破裂出血的风险。通过本实验对最动脉瘤血流动力学的参数的变化分析可得出以下结论：
（1）动脉瘤TAWSS及TAWSSG的不稳定，栓塞手术能够降低动脉瘤破裂的风险性[25-30]，而在栓塞术后的血管交叉处，血管壁则较易受损;
（2）OSI值较高，改变瘤体内震荡水平导致血流紊乱，OSI值减低，血流趋于稳定;
（3）随着动脉瘤AFI值逐渐升高，血液流动可逐渐平稳，可降低动脉瘤破裂危险性。
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关键词： 颅内动脉瘤;计算流体力学
中图分类号： TP319 文献标识码： A DOI：10.3969/j.issn.1003-6970.2020.08.028
本文著录格式：刘芳，赵思淇，卢立彬，等. 基于CTA的椎动脉瘤血流动力学分析[J]. 软件，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
顱内动脉瘤（Intracranial aneurysm，IA）是多种因素导致的动脉壁的异常瘤样扩张，常发生于颅内大动脉的分叉及弯曲处，破裂会导致蛛网膜下腔出血，具有极高的致死率及致残率。影响动脉瘤生长和破裂的因素主要包括先天生理性、病理性及血流动力学因素。对于IA的治疗主要包括开颅夹闭术及血管内介入栓塞两种方法[1-3]。无论是哪种方法，由于动脉瘤自身的复杂性及不完全闭塞的发生，即使是有经验的临床医生，术后的复发率依旧很高[4-7]。栓塞手术由于创伤小，操作相对简单等优势和栓塞材料及技术的不断发展进步逐渐被广泛应用于临床。但同时由于弹簧圈具有可压缩性使得动脉瘤复发的可能性大大增加，有研究表明栓塞程度是动动脉瘤复发的重要影响因素，Brzegowy等人回顾性分析破裂与未破裂前交动脉瘤的栓塞治疗，同样得出影响颅内动脉瘤复发的最大因素就是栓塞密度，初始栓塞的不完全极易引起动脉瘤的复发[8-9]。栓塞程度低，弹簧圈会随着血流的冲击逐渐压缩，进而向远侧移位、复发。赵庆平等提出瘤腔内的血流速度与瘤腔大小呈负相关，即栓塞程度越低，腔内血流速度加快时，血液对壁面产生的力就可能导致动脉瘤的复发[10]。近年来随着计算机的发展及有限元软件的开发，尤其是计算流体动力学数值模拟方法的应用，使得血流建模能更好解释血流动力学在IA发病机制中的作用[11-16]
1 材料与方法
原始影像数据采集：采集解放军第78集团军医院一椎动脉瘤患者CTA影像数据，男性患者，62岁，患者主诉头部持续头痛，临床表现为：行走不稳三个月。经临床诊断为头部椎最动脉瘤。经患者本人知情同意并签署意见书与医院伦理委员会批准。 图像后处理工作站：DELL图像向工作站：DELL 7810/CPU E5/16G内存/英伟达K2200显卡;
图像后处理软件：医学交互式影像控制系统（Materialis’ Interative Medical Image Control System，MIMICS，比利时Materialise公司）、医学建模软件3-matic medical（比利时Materialis公司）;
计算机仿真软件：ANSYS 19.2：流体仿真软件CFX，网格划分软件FLUENT MESHING
计算结果分析软件：ENSIGHT10.6。
椎动脉瘤三维重建：将头部影像DICOM数据导入MIMICS软件，使用MIMICS分割工具：阈值分割等算法，最后三维计算生成动脉瘤三维初步模型以stl格式导入3-matic medical软件中，使用光顺表面、去除细小分支、切好出、入口平面，最后形成动脉瘤三维模型，如图1所示。
网格划分：由于模型结构复杂，使用非结构化的四面体网格划分，为保证计算精度，在动脉瘤管壁进行五层加密。
边界条件：本计算不考虑能量的传递，不考虑重力。血液密度为1056 kg/m3，动力粘度为0.0035 。计算采用瞬态计算，两个入口，两个出口，壁面无滑移。入口采用速度入口，出口采用压力出口。为保证尽快收敛，入口速度采用极小的速度差。出口采用压力出口，压力曲线如图3所示。
血流作用在内皮细胞上的力的血流动力学参数GON，壁面切向和正交向上的向量，如果空间梯度G数值变化，代表对内皮细胞产生震荡张力和压缩力，在一个心动周期内，如果某个点发生较大的梯度变化，单位面积内发生强烈的震荡张力或者壓缩力作用于内皮细胞上，GON是用来量化震荡张力和压缩力的程度。
CFX无法直接实现上述参数指标，使用CFX ccl语言编程，如下为子程序的部分内容：
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
从平均壁面切应力（TAWSS）的云图（图4）上来看，云图颜色越偏红，代表平均壁面切应力越大，越接近蓝色则平均壁面切应力越小。载瘤动脉由于其具有较高的流速，因此载瘤动脉的平均壁面切应力要大于动脉瘤。
2.3 动脉瘤的TAWSSG云图分析
从TAWSSG云图中（图5）可以看出，瘤体的TAWSSG开始时低于载瘤动脉，而后逐渐接近。可能是由于开始时动脉瘤体积较大[18-20]，血液流速较慢，壁面切应力数值变化不变明显，所示动脉瘤偏蓝色，TAWSSG值较低。
2.4 动脉瘤的OSI云图分析
图6为动脉瘤OSI云图，在动脉瘤顶端存在小部分高OSI区域。动脉瘤顶端的高OSI区域较之前扩大，振荡剪切系数代表的是整个心动周期内壁面切应力方向变化快慢的量，OSI不同是反应震荡水平，即流动的强度和方向的改变，越大表示震荡越强，流体在周期内流动的方向不稳定，导致动脉瘤内的血流运动趋于紊乱。
2.5 动脉瘤AFI云图分析
图7为动脉瘤AFI云图，瘤体侧壁上存在部分AFI低区域，即偏蓝色区域。流增多形成涡流并不断的冲击着动脉瘤管壁，壁面切应力的方向变化明显，血液流动不稳定。
2.6 动脉瘤GON云图分析
动脉瘤GON云图（图8）表明在动脉瘤表面存在强烈的震荡力和压缩力，原因是血液在进入瘤腔后形成涡流，导致动脉瘤壁震荡，这种冲击对瘤壁造成膨胀或者扩张。 3 討论与结论
通过血流动力学计算分析，发现完全栓塞手术可以阻断进入动脉瘤内的血液[21-24]，提高TAWSS及降低OSI等，降低了破裂出血的风险。通过本实验对最动脉瘤血流动力学的参数的变化分析可得出以下结论：
（1）动脉瘤TAWSS及TAWSSG的不稳定，栓塞手术能够降低动脉瘤破裂的风险性[25-30]，而在栓塞术后的血管交叉处，血管壁则较易受损;
（2）OSI值较高，改变瘤体内震荡水平导致血流紊乱，OSI值减低，血流趋于稳定;
（3）随着动脉瘤AFI值逐渐升高，血液流动可逐渐平稳，可降低动脉瘤破裂危险性。
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