EFFECTS OF PARENT ARTERY SEGMENTATION AND ANEURISMALWALL ELASTICITY ON PATIENT-SPECIFIC HEMODYNAMIC SIMULATIONS*

CHEN Jia-liang, DING Guang-hong

Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China, E-mail: 051029010@fudan.edu.cn

YANG Xin-jian

Beijing Institute of Neurosurgery, Beijing 100050, China

LI Hai-yun

Department of Biomedical Engineering, Capital Medical University, Beijing 100050, China

EFFECTS OF PARENT ARTERY SEGMENTATION AND ANEURISMALWALL ELASTICITY ON PATIENT-SPECIFIC HEMODYNAMIC SIMULATIONS*

CHEN Jia-liang, DING Guang-hong

Department of Mechanics and Engineering Science, Fudan University, Shanghai 200433, China, E-mail: 051029010@fudan.edu.cn

YANG Xin-jian

Beijing Institute of Neurosurgery, Beijing 100050, China

LI Hai-yun

Department of Biomedical Engineering, Capital Medical University, Beijing 100050, China

It is well known that hemodynamics and wall tension play an important role in the formation, grow th and rupture of aneurysms. In the present study, the authors investigated the influence of parent artery segmentation and aneurismal-wall elasticity on patient-specific hemodynam ic simulations with two patient-specific cases of cerebral aneurysms. Realisticmodels of the aneurysms were constructed from 3-D angiography images and blood flow dynam ics was studied under physiologically representative waveform of inflow. For each aneurysm three computationalmodels were constructed: Model 1 withmore extensive upstream parent artery with the rigid arterial and aneurismal wall, Model 2 with the partial upstream parent artery with the elastic arterial and aneurismal wall, Model 3 withmore extensive upstream parent artery with the rigid wall for arterial wall far from the aneurysm and the elastic wall for arterial wall near the aneurysm. The results show that Model 1 could predict complex intra-aneurismal flow patterns and wall shear stress distribution in the aneurysm, but is unable to give aneurismal wall deformation and tension, Model 2 demonstrates aneurismal wall deformation and tension, but fails to properlymodel inflow pattern contributed by the upstream parent artery, resulting in localmisunderstanding Wall Shear Stress (WSS) distribution, Model 3 can overcome limitations of the former twomodels, and give an overall and accurate analysis on intra-aneurismal flow patterns, wall shear stress distribution, aneurismal-wall deformation and tension. Therefore we suggest that the proper length of extensive upstream parent artery and aneurismal-wall elasticity should be considered carefully in establishing computationalmodel to predict the intra-aneurismal hemodynam ic and wall tension.

cerebral aneurysm, fluid-structure interaction, upstream parent artery, wall tension, hemodynam ics

Introduction

Cerebral aneurysms are pathological dilatations of the cerebral artery wall, generally found in the anterior and posterior circulation region in the circle of W illis[1]. W ith the development of noninvasive cerebrovascular imaging diagnoses,more cerebral aneurysms have been identified because the incidence of these aneurysms in the general population is thought to be from two to five percent[2]. Fortunately,most aneurysms are small and an estimated 50% to 80 % of all aneurysms do not rupture through a life time, but some unruptured aneurysmmay enlarge and grow, resulting in high rate of rupture[3]. Therefore determining accurate criteria for predicting aneurysm grow th and rupture would be important formaking better-informed decisions and avoiding unnecessary surgical operations. In this context, there aremany numerical studies based on image-based Computational FluidDynamics (CFD) focusing on comparing the hemodynamic differences between ruptured and unruptured aneurysms, with special emphasis on the Wall Shear Stress (WSS) differences and intra-aneurismal flow patterns[4-8]. High WSS has recently been demonstrated to initiate aneurysm formation[9-11], whereas low WSS has been demonstrated to associate with the grow th and rupture of cerebral aneurysms[5,12]. The aneurysms with complex or unstable flows, narrow jets and impingement sites are associated with a clinical history of previous rupture[6,13]. However one common limitation of these studies is the neglect of the interaction between blood flow and arterial deformation and unable to give aneurismal wall deformation and tension associated with aneurysm rupture. Therefore Fluid-Structure Interaction (FSI)modeling of cerebral aneurysm has been commonly developed to analyze the interaction between the blood flow and arterial deformation, and predict aneurismal wall deformation and tension[14-19], but because of technical factors, these FSImodeling are not able to include the enough length of upstream parent artery whichmay affect the inflow stream.

The aim of this study is to investigate the influence of parent artery segmentation and aneurismalwall elasticity on patient-specific hemodynamic simulations. This investigation provides valuable insight into the complex interaction between cerebral aneurismal-wall deformation and blood flow from upstream parent artery.

Table 1 Patients and aneurysms data

1. Methods

1.1 Patients and images

Two patients with cerebral aneurysm were included in this study, and w ritten informed consent was obtained from each patient. Characteristics of two aneurysm cases are summarized in Table 1. Patient 1 was from anterior communicating artery (AcomA) that had quite long and straight upstream parent artery in the A1 segment. Patient 2 was from posterior communicating artery (PcomA) that had significant curvature upstream parent artery in the Internal Carotid Artery (ICA). For each patient, 3D-DSA images were obtained with digital subtraction angiography system (GE Medical), and a Region Of Interest (ROI) including the aneurysm and adjacent vessels was reconstructed into 3-D voxel data. The voxel data could produce a series of secondary DICOMformat files.

Fig.1 Fluid and solidmechanicsmesh

1.2 Vascularmodels

The DICOMformat files were imbeded into a special software package[20]developed by the authors in order to create one patientmedical image of stereolithography format including blood vessel luminal surface data. The stereolithography format file was imported into ICEMCFD to create Tetra-Prismmeshes for fluid flow analysis. Themaximummesh size was 0.3mm. Attra-prismmesh had approximately ten layers of high refinement near the arterial wall, and the distance between the first layer and the arterial wall was approximately 0.02mm. The structuralmechanicsmesh for the artery was eight-node hexahedral elements created by ANSYS WORKBENCH, and themesh size was 0.2mm. Figure 1 shows the fluidmechanicsmesh at the fluid-structure interface and the inflow plane, and the structuralmechanicsmesh for computational Model 2 of Patient 1. Three computationalmodels were constructed for each patient case based on different upstream parent arteries and arterial wallmotions. Model 1 had themore extensive upstream parent artery with the rigid arterial and aneurismal wall, Model 2 had the partial upstream parent artery with the elastic arterial and aneurismal wall, Model 3 had themore extensive upstream parent artery with the rigid wall for arterial wall far from the aneurysm and with the elastic wall for arterial wall near the aneurysm. The detailedmesh characteristics for the three computationalmodels of each patient case are summarized in Table 2. The 3D-DSA imagesand the computationalmodels for each patient are shown in Fig.2. From left to right, this figure shows 3D-DSA images, Model 1, Model 2 and Model 3 for each aneurysm case.

Table 2 Number of nodes (Nn) and elements (Ne) used in the computations

Fig.2 Vascularmodels of 2 cerebral aneurysms reconstructed from 3-D digital subtraction angiography images and three computationalmodels for each patient case

1.3 Numerical simulation of fluid-structure interactions

Numerical simulations were performed using a commercial computationalmechanics suit ANSYS and ANSYS CFX. ANSYS is a kind of finite-elementbased software for structuralmechanics analysis, while ANSYS CFX is a kind of finite-volume-based software for fluidmechanics computations. They are coupled and solved iteratively within each time step by applying appropriate kinematic and dynamic conditions at the fluid-structure interface until the residual of the system is below a specified tolerance. For fluidmechanics, the 3-D Navier-Stokes equations for incompressible flow with treatment ofmoving domain were solved with time-dependent physiological velocity and pressure boundary conditions. For structuralmechanics,momentum balance equations were solved with stress boundary conditions at the fluid-structure interface and constraint conditions. The computationalmesh for fluidmechanics was updated with respect to boundary displacement by solving the Laplace equation so that the wall boundary displacement could be propagated through all nodes within the domain.

1.4 Material properties and boundary condition

The governing equations for blood flow are the Navier-Stokes equations under the assumption of lam inar, homogenous, incompressible and New tonian flow. The assumption was based on the fact that the Reynolds numbers in human cerebral arteries are within the laminar regime[21,22]. In addition, since we focused on cerebral arteries with relatively large diameters and high flow rates, the fluid was assumed to be New tonian. The blood density and dynamic viscosity were specified as 1 060 kg/m3and 0.004 Ns/m2respectively. No slip was applied at the arterial wall. The arterial wall in the FSImodel was assumed to be uniform, hyperelastic, isotropic, incompressible and homogeneous. The experimental stress-strain curve from Seshaiyer et al.[23]was given as data for an equibiaxial stretching curve to ANSYS Workbench. We used the two- parameter Mooney-Rivlinmaterial constitutive relations tomake best-fitting baxial stressstrain data. The two- parameter Mooney-Rivlinmodel iswhere C1, C2arematerials constants, and I1and I2are respectively the first and second strain invariants of the Cauchy-Green deformation tensor. The fitting result compared with experimental results is shown in Fig.3.The arterial and aneurismal structure was assumed to have uniform wall thickness of 0.2mm[24]. Figure 2 shows the rigid arterial wall indicated with blue region and the elastic arterial wall indicated with red region.

Fig.3 Stress-strain relationship

Fig.4 Boundary condition

The inlet boundary condition (see Fig.4(a)) is one typical pulsatile velocity waveform of ICA obtained with the transcranial Dopplermeasurement. Based on the velocity waveform, the Womersley solution for the velocity profile in a straight pipe was used at the inlet. For the computational Model 2 for Patient 1and Patient 2, themagnitude of velocity waveform imposed at the inlet was adjusted tomake flow rate identical with that in the same plane of Model 1 and Model 3, which could eliminate the effect of differences in inflow rate on simulation results. The outlet pressure waveform (see Fig.4(b)) was determ ined based on the velocity waveform to obtain the physiological range of pressure by assuming that there was no phase lag[15,24]. The initial pressure and velocity were from a steady-state solution based on end diastolic flow rates. The initial displacements and stress were set to zero. Two cardiac cycles were computed using 800 timesteps per cycle, and all the results presented corresponded to the second cardiac cycle.

Fig.5 Color images of aneurismal wall deformation at the peak systole

2. Results

2.1 Aneurismal wall deformation and tension

Figures 5 and 6 show the contours of aneurismal wall deformation and principal stress at the peak systole in both patients. For each patient, the overall distribution of aneurismal wall deformation and principal stress obtained with Model 2 and Model 3 are very sim ilar. For Patient 1 the aneurismal wall deformation shows the concentrated distribution, where themaximum deformation occurs at the apex and gradually decreases toward the neck of aneurismal wall, but the principal stress shows w idening pattern because of w idely high aneurysm surface curvature region where the high value of principal stress tends to be concentrated. For Patient 2 themaximum deformation occurs at the apex of special part called the bleb indi-cated with the white arrow, which is a small daughter aneurysm on the aneurismal wall. Although themaximum principal stress occurs around the neck that is not identical with the regions withmaximum wall deformation, the relativelymaximum principal stress extends to the bleb body indicated with the white arrow. From a clinical point of view, aneurysm blebs have been identified as a factor formarkedly increased risk of future rupture because previous studies indicated that blebs deform at a larger rate because of a locally weaker aneurismal wall compred with the rest of aneurismal wall[25,26].

Fig.6 Color images of aneurismal wall tension at the peak systole

2.2 Wall shear stress

Figure 7 shows the detailed WSS distribution obtained with three computationalmodels for both patients at the peak systole. For patient 1 the differences in the tendency andmagnitude of overall WSS on the aneurismal and parent arterial wall obtained with Model 1 and Model 3 are not very obvious because the overall aneurismal and arterial wall deformation is very small. However for both computationalmodels with local fluid-structure interaction, Model 2 predicts especially higher value of WSS in the neck andmuch smaller value of WSS in the dome and upstream parent artery due to the differences of inflow stream, which are indicated with the white arrow. For Patient 2, the differences in the tendency of overall WSS on the aneurismal and parent arterial wall obtained with Model 1 and Model 3 are also not obvious because the region with high WSS has small wall deformation and the region with large wall deformation has very small WSS. However some local differences of WSSmagnitude can be seen due to local interaction between aneurismal wall and blood flow: Model 3 predicts higher value of WSS around the aneurysm, especially in the body and dome compared with Model 1, which is indicated with the white arrow. For the both computationalmodels with local fluidstructure interaction, Model 2 predicts smaller value of WSS in the dome of aneurysm due to the differences of inflow stream.

2.3 Local blood flow-wall deformation interaction and overall flow patterns

Figure 8 shows the instantaneous stream lines and cross-sectional velocity contours at the peak systole. In the case of Patient 1, three computationalmodels predict the same conclusion about the impingement region and vortex structure in the aneurysm. The stream lines show that the blood from the upstream parent artery flows into the core of the aneurysm after impinging on the arterial wall near the neck and a complex vortex structure is formed. The comparison of several cross-sectional velocity contours within the aneurysm and parent artery between Model 1 and Model 3 shows that the deformation of the arterial wall does not significantly affect the blood flow speed distribution. The comparison between Model 2 and Model 3 shows that for the upstream parent artery flows, Model 3 predictsmoremixing and sw irling flows, resulting in high velocity region near the blood vessel wall and consequently high WSS, Model 2 predicts the simple lam inar flow in the upstream parentartery, resulting in low velocity region near the blood vessel wall and consequently low WSS. In addition, the impinging flow velocity near the neck is larger for Model 2 than that for Model 3, because higher velocity in the axial direction ismore direct to impinge on the neck of right branch in Model 2, which is indicated with the white arrow. The higher impingement near the neck results in the decrease of velocitymagnitude and low WSS in the dome. Therefore for Patient 1, although the segment A1 has quite long and straight upstream parent artery resulting in the simple laminar flow based on theory analysis, some evident differences in the upstream parent artery flow between Model 2 andmodel 3can be seen based on numerical simulation, which also greatly affects WSSmagnitude near the neck and dome.

Fig.7 Color images of WSS at the peak systole

In the case of Patient 2, three computationalmodels also predict the same conclusion about the impingement region and vortex structure in the aneurysm. The stream lines show that there is a big and fast-spinning vortex at the bifurcation of the parent artery, andmost blood directly leaves through the outlet vessels after rotating on the center of the vortex. Therefore the blood velocity in the aneurysm is relatively low. The comparison of several cross-sectional velocity contours within the aneurysm and parent artery between Model 1 and Model 3 shows that the large aneurismal wall deformation at the apex of bleb in Model 3 greatly raises the blood velocity, resulting in local higher WSS, which is indicated with the yellow arrow. The comparison between Model 2 and Model 3 shows that although the upstream parentartery flows in bothmodels do not change dramatically, some blood in Model 2 do not rotate at the bifurcation of the parent artery and directly leave through the left outlet vessels indicated with the white arrow. For Model 2 the variety of blood flow at the bifurcationmakes less blood impinge on the neck and flow into aneurysm ,which greatly weaken the effect of aneurismal wall deformation at the apex of bleb on raising the blood velocity. Therefore for Patient 2 both local fluid-structure interaction and upstream parent artery flow affect the blood velocity and WSS.

Fig.8 Blood flow velocitymagnitude on interior cuts and stream lines at the peak systole

3. Discussion

Although hemodynamics and wall tension in cerebral aneurysms have been predicted by numerous image-based patient-specific computationalmodels, each of these computationalmodels has several limitations thatmay affect the simulation results and thereby result inmisunderstanding of a particular system. Especially, there are still some debates about different computationalmodels. On the one hand, some previous studies indicated that themost important factor for a reliable characterization of the aneurysm hemodynam ics is the geometry, with special emphasis on themore extensive upstream parent artery involved in the computationalmodel to accurately represent the intra-aneurismal hemodynamics, but in these studies the vascular walls were assumed to be rigid because this assumption was not considered to significantly affect themain hemodynamic characteristics of cerebral aneurysms[4,6,11]. Therefore, these studies could not analyze wall deformation and tension, but were limited to simulations of WSS. As a result, even if the details of cell-mediated changes in aneurismal wall structure, properties and geometry remain unknown, wall shear stress has been considered as the primary hemodynamic factor contributing to formation, grow th, and rupture of aneurysms[2]. On the other hand, recent studies based on fluid-structure interactionmodeling of cerebral aneurysms showed that the interaction between the blood flow and arterial deformation significantly altered the hemodynamic forces acting on the arterial wall, and strongly depended on the individual aneurysm shapes[15,17]. In addition, fluid-structure interactionmodeling of cerebral aneurysms is able to describe aneurismal wall deformation and tension which are very important for individualized prediction of aneurysm rupture risk because previous numerical study indicated that high wall deformation and tension correspond to the usual rupture sites[24]. The observation that the site of large deformation is correlated with the site of rupture has also been identified with visualization of aneurysmal pulsations using dynam ic digital subtraction angiography and dynam ic CT angiography[25,26]. These results reinforce the importance of FSI in patient-specific analysis of cerebral aneurysms. But because of technical factors, these previous FSImodels were not able to include the enough length of upstream parent artery, which would affect the results of intra-aneurismal hemodynam icmodel.

In this study, we investigate the influence ofmore extensive parent artery geometry and aneurismal-wall elasticity on patient-specific hemodynamic simulations. The geometricmodels were constructed from 3D-DSA images which provide the highest image resolution and contrast between the arteries and the surrounding tissues. The numerical results demonstrate that aneurismal wall deformation and tension do not vary with the geometry of upstream parent artery because the wall deformation and tension are largely determ ined by the intramural pressure and not somuch by bloodstream impacting force. For both patients themain blood flow patterns within the aneurysm are not greatly affected by the upstream parent artery and local fluid-structure interaction, but the WSS on the aneurismal wall are affected by both aneurismal wall deformation and upstream parent artery. The comparison of Model 1 and Model 3 indicate thatmaximum wall deformation at the tip of aneurysm raises the local WSS, which ismore evident for Patient 2 because of larger wall deformation. The comparison of Model 2 and Model 3 indicate that the variety of overall flow patterns in the upstream parent artery result inmisunderstanding local WSS distribution. For Patient 1, Model 2 predicts especially higher value of WSS near the neck, whereas for Patient 2, Model 2 predictsmuch smaller value of WSS in the dome.

Although some previous numerical studies have discussed the effect of upstream parent artery and wall deformation on WSS, the present study is the first to analyze the effect of coupling these two factors on WSS. Castro et al.[27]compared the differences of WSS between the idealized and realistic upstream parent artery, and found that the idealized parent artery underestimated the WSS in the aneurysms because themore laminar flow pattern within the parent artery in idealizedmodels resulted in a less complex intra-aneurismal flow patterns with fewer vortices and less velocity at the dome. Our results also demonstrate that for both patients the WSS in the aneurysm obtained with Model 2 is smaller than that obtained with Model 3 due to the differences of inflow stream contributed by upstream parent artery, but the extent of WSS decrease is not as obvious as Castro et al.[27]reported because the upstream parent artery in ourmodel is still realistic. Torri et al.[15]investigated the role of FSI in the patient-specificmodeling of cerebral aneurysm using three Y-shaped aneurysms with partial upstream parent artery, and found that when the blood flow impinges strongly on the wall, themaximum WSS tends to decrease due to the flowwall interaction whereas when the blood in the aneurysm is nearly stagnant, a slow flow is induced by the wallmotion, which raises them inimum WSS on the aneurismal wall. In our results, comparison of Model 1 and Model 3 shows that themaximum aneurismal wall deformation at the tip of aneurysm raises the local WSS but aneurismal wall dilation near the neck does not greatly reduce high flow rate because for both patients the region with high flow rate has small wall deformation. However in Model 2 the effect of aneurismal wall deformation on WSS is also greatly influenced by the upstream parent artery. For Patient 1, partial upstream parent arterymakes a higher velocity in the axial directionmore direct to impinge on the neck of right branch, resulting in especially WSS increase on the distensible aneurismal wall. For Patient 2, partial upstream parent arterymakes less blood flow into aneurysm which greatly reduces the effect of aneurismal wall deformation at the apex of bleb on raising WSS. Therefore according to our results, analyzing the effect of aneurismal wall deformation on WSS should be based on the realistic inflow stream contributed by the upstream parent artery.

4. Conclusion

We have investigated the influence ofmore extensive parent artery geometry and aneurismal-wall elasticity on patient-specific hemodynamic simulations, such as intra-aneurismal flow patterns, WSS distribution, aneurismal wall deformation and tension. By comparing the results obtained with three computationalmodels, it is found that the aneurismal wall deformation and tension are independent of upstream parent artery flow, but the WSSmagnitude is greatly influenced by both upstream parent artery flow and local fluid-structure interaction. Therefore in order to give amore accurate prediction of WSS, the proper length of extensive upstream parent artery and aneurismal-wall elasticity should be considered carefully in the computationalmodel.

[1] LASHERAS J. C. The biomechanics of arterial aneurysms[J]. Annual Review of Fluid Mechanics, 2007, 39(1): 293-319.

[2] HUMPHREY J. D., TAYLOR C. A. Intracranial and abdominal aortic aneurysms: Similarities, differences, and need for a new class of computationalmodels[J]. Annual Review of Biomedical Engineering, 2008, 10: 221-246.

[3] BRISMAN J. L., SONG J. K. and NEWELL D. W. Cerebral aneurysms[J]. The New England Journal of Medicine, 2006, 355(9): 928-939.

[4] CEBRAL J. R., CASTRO M. A. and BURGESS J. E. et al. Characterization of cerebral aneurysms for assessing risk of rupture by using patient-specific computational hemodynam icsmodels[J]. American Journal of Neu- roradiology, 2005, 26(10): 2550-2559.

[5] SHOJIMA M., OSHIMA M. and TAKAGI K. et al. Magnitude and role of wall shear stress on cerebral aneurysm computational fluid dynamic study of 20middle cerebral artery aneurysms[J]. Stroke, 2004, 35(11): 2500-2505.

[6] CASTRO M. A., PUTMAN C. M. and SHERIDAN M. J. et al. Hemodynamic patterns of anterior communicating artery aneurysms: A possible association with rupture[J]. American Journal of Neuroradiology, 2009, 30(2): 297-302.

[7] VALENCIA A., MORALES H. and RIVERA R. et al. Blood flow dynam ics in patient-specific cerebral aneurysmmodels: The relationship between wall shear stress and aneurysm area index[J]. Medical Engineering and Physics, 2008, 30(3): 329-340.

[8] WANG Sheng-zhang, CHEN Jia-liang and DING Guang-hong et al. Non-New tonian computational hemodynamics in two patient-specific cerebral aneurysms with daughter saccules[J]. Journal of Hydro- dynam ics, 2010, 22(5): 639-646.

[9] MENG H., WANG Z. and HOI Y. et al. Complex hemodynam ics at the apex of an arterial bifurcation induces vascular remodeling resembling cerebral aneu- rysm initiation[J]. Stroke, 2007, 38(6): 1924-1931.

[10] HOI Y., MENG H. and WOODWARD S. H. et al. Effects of arterial geometry on aneurysm grow th: Three-dimensional computational fluid dynamics study[J]. Journal of Neurosurgery, 2004, 101(4): 676- 681.

[11] CEBRAL J. R., SHERIDAN M. and PUTMAN C. M. Hemodynamics and bleb formation in intracranial aneurysms[J]. American Journal of Neuroradiology, 2010, 31(2): 304-310.

[12] BOUSSEL L., RAYZ V. and MCCULLOCH C. et al. Aneurysm grow th occurs at region of low wall shear stress: Patient-specific correlation of hemodynam ics and grow th in a longitudinal study[J]. Strokes, 2008, 39(11): 2997-3002.

[13] CEBRAL J. R., HENDRICKSON S. and PUTMAN C. M. Hemodynamics in a lethal basilar artery aneurysm just before its rupture[J]. American Journal of Neuro- radiology, 2009, 30(1): 95-98.

[14] TORII R., OSHIMA M. and KOBAYASHI T. et al. Influence of wall elasticity in patient-specific hemodynam ic simulations[J]. Com puters and Fluids, 2007, 36(1): 160-168.

[15] TORII R., OSHIMA M. and KOBAYASHI T. et al. Fluid-structure interactionmodeling of blood flow and cerebral aneurysms: Significance of artery and aneurysm shapes[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(45): 3613- 3621.

[16] TAKIZAWA K., CHRISTOPHER J. and TEZDUYAR T. E. et al. pace-time finite element computation of arterial fluid–structure interactions with patient-specific data[J]. International Journal for Numerical Methods in Biomedical Engineering, 2010, 26(1): 101-116.

[17] BAZILEVS Y., HSU M. C. and ZHANG Y. et al. A fully-coupled fluid-structure interaction simulation of cerebral aneurysms[J]. Com putational Mechanics, 2010, 46(1): 3-16

[18] CHEN Jia-liang, WANG Sheng-zhang and DING Guang-hong et al. The effect of aneurismal-wallmechanical properties on patient-specific hemodynam ic simulations: Two clinical case reports[J]. Acta Mechanica Sinica, 2009, 25(5): 677-688.

[19] CHEN Jia-liang, WANG Sheng-zhang and DING Guang-hong et al. Patient-specific blood dynamic simulations in assessing endovascular occlusion of intracranial aneurysms[J]. Journal of Hydrodynam ics, 2009, 21(2): 271-276.

[20] YU Hong-yu, LI Hai-yun and ZHANG Ying et al. Approach to construction 3D geometricsmodel of cranial aneurysm[J]. Com puter Engineering and App lication, 2008, 44(7): 175-177(in Chinese).

[21] TATESHIMA S., MURAYAMA Y. and VILLABLANCA J. P. et al. In vitromeasurement of fluid induced wall shear stress in unruptured cerebral aneu- rysms harboring blebs[J]. Stroke, 2003, 34(1): 187-192.

[22] WETZEL S., MECKEL S. and FRYDRYCHOW ICZ A. et al. In vivo assessment and visualization of intracranial arterial hemodynamics with flow-sensitized 4D MR imaging at 3T[J]. American Journal of Neuroradio- logy, 2007, 28(3): 433-438.

[23] SESHAIYER P., HSU F. P. K. and SHAH A. D. et al. Multiaxialmechanical behavior of human saccular aneurysms[J]. Com puter Methods in Biomechanics and Biomedical Engineering, 2001, 4(1): 281-289.

[24] ISAKSEN J. G., BAZILEVS Y. and KVAMSDAL T. et al. Determination of wall tension in cerebral arteryaneurysms by numerical simulation[J]. Stroke, 2008, 39(12): 3172-3178.

[25] DEMPERE-MARCO L., OUBEL E. and CASTRO M. A. et al. CFD analysis incorporating the influence of wallmotion: Application to intracranial aneurysms[J]. Lecture Notes Com puter Science, 2006, 9(2): 438- 445.

[26] HAYAKAWA M., KATADA K. and ANNO H. et al. CT angiography with electrocardiographically gated reconstruction for visualizing pulsation of intracranial aneurysms: Identification of aneurysmal protuberance presumably associated with wall thinning[J]. American Journal of Neuroradiology, 2005, 26(6): 1366-1369.

[27] CASTRO M. A., PUTMAN C. M. and CEBRAL J. R. Computational fluid dynamicsmodeling of intracranial aneurysms: Effects of parent artery segmentation on intra-aneurysmal hemodynam ics[J]. Am erican Journal of Neuroradiology, 2006, 27(8): 1703-1709.

March 28, 2011, Revised May 9, 2011)

10.1016/S1001-6058(10)60162-X

* Project supported by the Natioanal Natural Sience Foundation of China (Grant No. 30772234), the Shanghai Leading Academ ic Discipline Project (Grant No. B112).

Biography: CHEN Jia-liang (1982-), Male, Ph. D.

DING Guang-hong, E-mail: ghding@fudan.edu.cn