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Available online at www.sciencedirect.com

Medical Engineering & Physics 30 (2008) 329–340

Blood flow dynamics in patient-specific cerebral aneurysm models:The relationship between wall shear stress and aneurysm area index

Alvaro Valencia a,∗, Hernan Morales a, Rodrigo Rivera b, Eduardo Bravo b, Marcelo Galvez b

a Department of Mechanical Engineering, Universidad de Chile, Casilla 2777, Santiago, Chileb Instituto de Neurocirugıa Asenjo, Jose Manuel Infante 553, Santiago, Chile

Received 27 October 2006; received in revised form 13 April 2007; accepted 19 April 2007

bstract

Hemodynamics plays an important role in the progression and rupture of cerebral aneurysms. The temporal and spatial variations in wallhear stress (WSS) within the aneurysmal sac are hypothesized to be correlated with the growth and rupture of the aneurysm. The currentork describes the blood flow dynamics in 34 patient-specific models of saccular aneurysms located in the region of the anterior and posterior

irculation of the circle of Willis. The models were obtained from three-dimensional rotational angiography image data and blood flowynamics was studied under a physiologically representative waveform of inflow. The three-dimensional continuity and momentum equationsor unsteady laminar flow were solved with commercial software using non-structured fine grid sizes. The vortex structure, the wall pressure,

nd the WSS showed large variations, depending on the morphology of the artery, size of the aneurysm, and form. A correlation existedetween the mean WSS on the aneurysmal sac for lateral unruptured and ruptured aneurysms with an aneurysm surface index, which isefined as the ratio between the aneurysm area and the artery area at model inlet, respectively.

2007 IPEM. Published by Elsevier Ltd. All rights reserved.

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eywords: Computational fluid dynamics; Non-Newtonian fluid; Blood flo

. Introduction

Cerebral aneurysms are pathologic dilations of an artery,enerally found in the circle of Willis. Cerebral aneurysmsnvolve both the anterior and posterior circulation. Rupturef a cerebral aneurysm causes subarachnoid hemorrhageith potentially severe neurologic complications [1]. Cere-ral aneurysms are classified as saccular and non-saccularypes, according to their shape and etiology. Typically, sac-ular aneurysms arise at a bifurcation or along a curve ofhe parent vessel. Classic treatments of saccular aneurysmsre direct surgical clipping or endovascular coil insertion. Theoils promote blood coagulation inside the aneurysm, therebyvoiding blood flow and thus excluding the aneurysm fromhe circulation [2].

It is generally accepted that unique structural features ofhe cerebral vasculature contribute to the genesis of theseneurysms. A typical saccular aneurysm has a very thin tunica

∗ Corresponding author.E-mail address: alvalenc@ing.uchile.cl (A. Valencia).

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350-4533/$ – see front matter © 2007 IPEM. Published by Elsevier Ltd. All rightsoi:10.1016/j.medengphy.2007.04.011

bral aneurysm; Wall shear stress; 3D rotational angiography

edia and the internal elastic lamina is absent in most cases1]. Thus, the arterial wall is composed of the intima anddventitia only. The aneurysm wall, which must withstandhe forces of arterial blood pressure, is composed of layeredollagen. The main characteristic of an aneurysm wall is itsultidirectional collagen fibers; under physiologic pressures,

he collagen fibers become straight and thereby govern theverall stiffness of the lesion [3]. Fluid shear stress modulatesndothelial cell remodeling via realignment and elongation,nd the time variation of wall shear stress (WSS) significantlyffects the rates at which endothelial cells are remodeled [4].onsequently, hemodynamic factors, such as blood velocity,SS, pressure, particle residence time, and flow impinge-ent, play important roles in the growth and rupture of cere-

ral aneurysms. Aneurysm hemodynamics are contingent onneurysm geometry and the aneurysm’s relation to the parentessel, volume, and aspect ratio (depth/neck width) [5,6].

Several authors have reported the importance of WSS onhe development, growth, and rupture of cerebral aneurysms7–9]. High WSS is regarded as a major factor in the devel-pment and growth of cerebral aneurysms [7]. Aneurysm

reserved.

330 A. Valencia et al. / Medical Engineering

Nomenclature

a artery radiusA aneurysm areaAi artery areaCFD computational fluid dynamics3D three-dimensionalf frequencyk viscosity constantp pressureR1 ratio of areas = A/Ai�t time stepU mean velocity at the inletv velocityV artery volumeWSS wall shear stress

Greek symbolsα Womersley number = a(2πfρ/μ)1/2

γ strain rateμ fluid viscosityρ densityτ shear stressτw wall shear stress

ratrbsotaodoaoatpa

daoawtbeo

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baeVraaTnsarterial geometry. In terminal aneurysm models, the effects

τ0 yield stress

upture is related to a low level of WSS and therefore it isssociated with low-flow conditions [9]. Localized stagna-ion of blood flow is known to result in the aggregation ofed blood cells, as well as the accumulation and adhesion ofoth platelets and leukocytes along the intimal surface. Thisituation occurs due to dysfunction of flow-induced nitricxide, which is usually released by mechanical stimulationhrough increased shear stress. It is assumed that a WSS ofpproximately 2 Pa is suitable for maintaining the structuref the aneurysmal wall, whereas a lower WSS results in theegeneration of endothelial cells [9]. For this reason, studiesf blood flow dynamics inside models of saccular aneurysmsre important to obtain quantitative criteria for the treatmentf aneurysms [10]. Tateshima et al. [7,11] studied the intra-neurysmal flow dynamics in acrylic models obtained usinghree-dimensional (3D) computerized tomogram angiogra-hy and found a non-uniform distribution of WSS within theneurysmal sac.

Jou et al. [12] examined the relationship between hemo-ynamics and the growth of two fusiform basilar arteryneurysms. One aneurysm grew significantly and the sizef the other aneurysm remained unchanged. The largestneurysmal growth occurred on the surface of the aneurysm,here the WSS was lower than 0.1 N/m2. The flow pat-

erns did not change with time in the aneurysm that grew,

ut the histogram of the WSS changed with time. Steinmant al. [13] reported image-based computational simulationsf the flow dynamics (CFD) for Newtonian fluid in a giant,

a

c

& Physics 30 (2008) 329–340

natomically realistic, human intracranial aneurysm. Com-utational flow dynamics analysis revealed high-speed flowntering the aneurysm at the proximal and distal ends ofhe neck, promoting the formation of both persistent andransient vortices within the aneurysm sac. The pulsatileow in a cerebral arterial segment exhibiting two saccularneurysms was investigated [14]. It was shown that the twoneurysms behaved in a dissimilar manner, since the bloodnflow region oscillated in only one of the aneurysms. Cebralt al. [15] described a pilot clinical study in which the associa-ion between intra-aneurysmal hemodynamic characteristicsrom CFD models and the rupture of cerebral aneurysmsas investigated. A total of 62 patient-specific models of

erebral aneurysms were constructed from 3D angiographymages. The aneurysms were classified into different cate-ories, depending on the complexity and stability of the flowattern, the location and size of the flow impingement region,nd the size of the inflow jet. Cebral et al. [16] presented aensitivity analysis of the hemodynamic characteristics withespect to variations involving several variables in patient-pecific models of cerebral aneurysms; they found that theariable that had the greatest effect on the flow field was theessel geometry. Shojima et al. [9] simulated blood flow in0 patient-specific cerebral aneurysms located in the mid-le cerebral artery; they calculated the WSS acting on theundi of saccular aneurysms to be significantly lower thanhe WSS acting on the surrounding vasculature. Further, theyound an inverse linear relationship between the aneurysmspect ratio and the WSS of the aneurysm region at peakystole.

The influence of the non-Newtonian properties of bloodn an idealized terminal aneurysm model of the basilar arteryas investigated in detail by Valencia et al. [17]. The non-ewtonian fluid assumption yields more stable flow than aewtonian fluid for the same inlet flow rate. The differences

n the WSS distributions between the Newtonian and non-ewtonian fluid models were important only in the aneurysmodel involving unstable flow dynamics. In a patient-specificodel of a saccular aneurysm, we have confirmed that the

ffects of the fluid model on WSS on the aneurysm are notignificant [18].

The effect of arterial compliance has been considered inut few reported studies of hemodynamics in arteries withneurysms. In models of lateral aneurysms, Low et al. [19]xamined the effects of distensible arterial walls. Recently,alencia and Solis [20] have reported the effects of arte-

ial compliance in a saccular aneurysm model of the basilarrtery; the maximal wall displacement on the top of theneurysm at systole was only 10% of the artery diameter.he influence of wall elasticity in patient-specific hemody-amic simulations has been reported [21], in which it washown that the effects of wall elasticity on WSS depend on

re more important than in lateral aneurysm models.Ma et al. [22] have recently performed a 3D geometri-

al characterization of cerebral aneurysms from computed

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A. Valencia et al. / Medical Eng

omogram angiography data, reconstructing the geometry ofon-ruptured human cerebral aneurysms. This geometry cane classified as hemispheric, ellipsoidal, or spherical; it ispparent that quantification of aneurysm shape is more effec-ive than size indices in discriminating between ruptured and

nruptured aneurysms [23].

In the current work, we present detailed numerical simula-ions of unsteady blood flow in 34 saccular aneurysm models

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Fig. 1. Patient-specific CFD mode

& Physics 30 (2008) 329–340 331

btained from 30 patients. The aneurysms were located in dif-erent cerebral arteries and reconstructed from 3D rotationalngiography image data. The purpose of this study was toeport the different flow characteristics, pressure, and WSSf each cerebral aneurysm. This study included 14 unruptured

ateral aneurysms, 15 ruptured lateral aneurysms, and 5 termi-al saccular aneurysms (Fig. 1). This investigation providesaluable insight into the nature of saccular aneurysms sub-

ls of cerebral aneurysms.

3 ineering & Physics 30 (2008) 329–340

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32 A. Valencia et al. / Medical Eng

ect to physiologically realistic pulsatile loads. In addition,re-procedural planning for cerebral aneurysm endovascularreatments will benefit from an accurate assessment of flowatterns and the mean value of WSS in the aneurysm as pre-ented in this work by means of CFD. The goal of this workas to correlate aneurysm geometry with hemodynamics;

uch a correlation would provide information for the diagno-is and treatment of an unruptured aneurysm by elucidatinghe risk of rupture.

. Methods

.1. Reconstruction methodology

Cerebral angiography rotational acquisitions werebtained by using a Phillips Integris Allura system. Themages were obtained during a 180◦ rotation with imagingt 30 frames/s. The corresponding 100 projection imagesere reconstructed into a 3D data set using an isotropicoxel on a dedicated Phillips workstation. The file, inRML format, was exported to the 3DSMax software

or cleaning and exported in STL format to 3D-Doctoroftware. The parameterization of the contours was madesing the software, 3D-Doctor, from different cut planessing B-spline. Contours were obtained and exported inGES format to Rhinoceros software. In the Computerided Design (CAD) software, non-uniform, rational-spline (NURBS) surfaces were generated and the dif-

erent surfaces were pasted to create the 3D geometryf the arteries with the saccular aneurysms. Finally, theeometry was exported from Rhinoceros in STEP formato the mesh generator Gambit (Fluent Inc., Lebanon,H, USA) and an unstructured grid was generated using

etrahedral elements. This reconstruction method is fastnd the influence of the operator on the final geometry isinimal.

.2. Governing equations

The mass and momentum conservation equations for anncompressible fluid can be written as

· v = 0 (1)

(∂v∂t

+ v · ∇v)

= −∇p + ∇ · τ (2)

here ρ is the density, v the velocity field, p the pressure,nd � is the deviatoric stress tensor. This tensor is related

o the strain rate tensor, however, this relationship is usuallyxpressed as an algebraic equation in the form

= μ(γ)γ (3)

amoN

Fig. 2. Physiologic waveform of the mean inlet velocity.

here μ is the viscosity and γ is the strain rate, which isefined for an incompressible fluid as

˙ =(

∂vi

∂xj

+ ∂vj

∂xi

)(4)

Blood is a suspension of red blood cells in plasma. Theiscosity of blood is mainly dependent on the volume frac-ion of red blood cells in the plasma. We considered theffects of a non-Newtonian fluid model on hemodynamics.he Herschel–Bulkley fluid model was selected [24], because

t shows both yield stress and shear-thinning non-Newtonianiscosity, and it is an accurate model to describe the rheologi-al behavior of blood [24]. The Herschel–Bulkley fluid modelf blood assumes that the viscosity, μ, varies according to theaw

= kγn−1 + τ0

γ(5)

The Herschel–Bulkley fluid model of blood extends theimple power law model for non-Newtonian fluids to includehe yield stress, τ0. We have taken the experimental valuesecommended by Kim [24] as k = 8.9721 × 10−3 N sn/m2,= 0.8601, and τ0 = 0.0175 N/m2. The variation of the vis-osity of the Herschel–Bulkley model with the strain rates similar to the Carreau model [25] and the generalizedower law models used by Johnston. The density of bloodas assumed to be constant (ρ = 1050 kg/m3).

.3. Boundary conditions

Physiological flow conditions were imposed at the inletsing flow measurements with pulsed Doppler ultrasoundcquired from the internal carotid artery of a normal patient.he heart rate was 70 beats/min. The mean blood velocity in

he artery was 37.4 cm/s and the peak systolic flow occurred

t t/T = 0.619 (Fig. 2). The time dependency of the inflowean velocity was imposed by a Fourier representation of

rder 10. The Womersley solution for the velocity profile of aewtonian fluid in a straight pipe is used at the inlet [26]. The

A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340 333

Table 1Mesh refinement comparisons of WSS on an aneurysm at systole and diastole for case 20 (artery volume V = 754.5 mm3)

Number of cells WSSmax (Pa) WSSmin (Pa) Error at systole in % Grid density (cells/mm3)

217,086 9.32 2.34 22.4 288481

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56,261 10.52 2.5611,335 11.96 2.57,157,152 12.01 2.63

omersley number, which depended on flow frequency, sizef the artery, and Newtonian fluid viscosity, varied with thertery diameter at the inlet in each case. The outflow bound-ry condition was defined by ∂φ/∂n = 0 for the fluid velocityΦ = V) at the exit of each cerebral artery, and n denotes theirection normal to the surface. The cerebral arteries at thexit were defined as one outflow boundary condition, so thathe flow rate in each artery at the outlet was adjusted to obtainhe total flow rate. A reference relative pressure of 14 kPa wasefined at the inlet to obtain physiologically realistic pressureariations. A no-slip condition was prescribed at the walls andwo consecutive pulsatile flow cycles were considered for theimulations.

.4. Numerical method

Governing equations were solved with FLUENT soft-are, Version 6.0 (Fluent, Inc.), which utilizes the finiteolume method for spatial discretization. The interpola-ions for velocities and pressure were based on power lawnd second order, respectively. The pressure–velocity cou-ling was obtained using the SIMPLEC algorithm [27]. Themplicit time-marching second order scheme with a time step,

t = 1 × 10−4 s, was used for the computations, and the max-mal iterations per time step was set on 200. With this smallime step, the residual of the continuity and Navier–Stokesquations were <0.001 in all temporal iterations. To reducehe residuals, and consequently the numerical errors, andmprove the accuracy of the present numerical results, it wasecessary to make the calculation with this small time step.ase 26, with a time step of �t = 1 × 10−5 s, was also simu-

ated to evaluate the dependence of the implicit scheme withhe time step. The differences on spatially averaged WSS inhe solution domain at the peak systole were <2%.

To verify grid independence, numerical simulations were

erformed on four grids sizes for case 20 and on five gridizes for case 26. We considered these cases as representa-ive of large and small computational domains, respectively.he average WSS on an aneurysmal sac at peak systolic and

cmto

able 2esh refinement comparisons of WSS on an aneurysm at systole and diastole for c

umber of cells WSSmax (Pa) WSSmin (Pa)

38,920 30.7 6.1087,844 33.55 6.9482,789 39.38 7.6740,542 43.90 8.1323,403 45.20 8.23

12.4 6050.4 10750 1534

iastolic times were computed for the different grid sizesTables 1 and 2). The differences in WSS in both cases were3% between the two fine grids. Considering that computa-

ional time increases linearly with grid size, we used a gridensity of approximately 1400 cells/mm3 to determinate therid cells for the 30 models of saccular aneurysms. The largestrid had 1,270,206 cells (case 27) and the smallest grid had40,000 cells (case 6). The WSS was selected to check gridndependence in this work because the average WSS on theneurysmal sac is an important parameter to evaluate pathol-gy. The workstations used to perform the simulations in thisork were based on an Intel Pentium IV processor with a.8 GHz clock speed, 1.5GB RAM memory, and running onhe Linux Redhat operating system (Version 8.0). The simu-ation time depended on grid size, and for the cases with largeomputational domains, was approximately 72 CPU hours.

. Results

The non-Newtonian flow characteristics for one lat-ral unruptured aneurysm (case 17), one lateral rupturedneurysm (case 9), and one terminal ruptured aneurysm (case2), are shown in Figs. 3a, 4a, and 5a, respectively. Forase 17, the intra-aneurysmal flow showed a vortex centeredithin the cavity. The velocities inside the lateral ruptured

neurysm (case 9) were lower compared with the velocitiesnside the unruptured aneurysm sac and the vortex structureas weak. In case 12, high velocity flow entered from the

nferior part of the aneurysm and it washed the wall of theneurysm. This inflow produced zones with high WSS on theneurysm. In case 12, the effect of a stenosis in the principalrtery produced a maximal velocity of 3.64 m/s at systole.

The jet of fluid through the neck of the aneurysm (i.e., thenflow region) varied in size and position, depending on the

ase. This is an important issue for the endovascular treat-ent of cerebral aneurysms, since controlling blood flow at

he inflow region is a critical step in achieving permanentcclusion of an aneurysm [11]. The long-term anatomical

ase 26 (artery volume V = 160.1 mm3)

Error at systole in % Grid density (cells/mm3)

32.1 24325.8 54912.9 1142

2.9 15020 2020

334 A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340

F ed withW s, for ca

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ig. 3. (a) Velocity vectors inside a lateral unruptured aneurysm, color-codSS on the aneurysmal sac. Values obtained at peak systolic time, t = 0.53

urability of coil embolization in cerebral aneurysms byeans of microcoil technology depends on the aneurysm

hape and the blood flow dynamics at the aneurysm neck2]. As such, we have inferred that recanalization is lessikely if the coils are inserted through the inflow region ofhe aneurysm neck.

The wall pressure distributions for cases 17, 9, and 12 arehown in Figs. 3b, 4b, and 5b, respectively. The wall pressuren the lateral unruptured aneurysm showed more variation athe corresponding pressure on the lateral ruptured aneurysm.he effect on wall pressure of the stenosis in the case 12 wasery important (Fig. 5b). The minimal pressure at the outletas 10.5 kPa in case 17, 6.5 kPa in case 9, and only 4.89 kPa in

ase 12. The pressure variation on the surface of the aneurysmor case 17 at peak systole was approximately 1 kPa. Thisariation was only 6% of the peak intravascular pressure,ndicating that the force produced by the intra-aneurysmalow dynamics does not have an important role in the rupturef saccular aneurysms.

The WSS distribution on an artery varies depending on thessociated morphology [15]. The WSS distributions for cases7, 9, and 12 are shown in Figs. 3c, 4c, and 5c, respectively.

he maximal WSS on the artery was 105 Pa in case 17, 190 Pa

n case 9, and 188 Pa in case 12. The effect of stenosis on WSSn case 12 was very important. The WSS distributions on theneurysm sac for cases 17, 9, and 12 are shown in Figs. 3d,

t

tt

the velocity magnitude, (b) wall pressure, (c) WSS on the artery, and (d)se 17.

d, and 5d, respectively. The highest WSS occurred on theneurysm neck in the distal zone for both lateral aneurysms.arge zones with very low WSS were found in the lateral

uptured aneurysm; values of WSS > 2 Pa were found onlyround the distal zone. The situation was different for theerminal aneurysm due to the form of the inflow in this typef aneurysm.

The WSS distributions on the aneurysmal sac for lat-ral unruptured and ruptured aneurysms of different sizesre shown in Fig. 6a–c, and in Fig. 6d–f, respectively. Theneurysm areas for unruptured cases 21.1, 14.1, and 30.1ere 22, 92, and 103 mm2, respectively. The areas of cases4.1 and 30.1 were similar, however, the WSS distributionsere very different. For ruptured cases 16, 27, and 4, the

neurysm areas were 64, 269, and 217 mm2, respectively,owever, the WSS distribution in case 4 had larger zonesith a low WSS, as in the corresponding zones in case 27.his showed that not only the aneurysm area should be con-idered when assessing the WSS on the aneurysm, since thentra-aneurysmal flow dynamics depend on the morphologyf the main artery, aneurysm position, aneurysm neck size,neurysm area, and the presence of secondary arteries near

he aneurysm [15].

For the five cases with terminal unruptured and rup-ured aneurysms, high or low spatially averaged WSS onhe aneurysm at peak systole existed (Table 3). High WSS

A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340 335

F ith theo case 9.

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ig. 4. (a) Velocity vectors inside a lateral ruptured aneurysm, color-coded wn the aneurysmal sac. Values obtained at peak systolic time, t = 0.53 s, for

as found in the cases with aneurysms centered with respecto the main artery (cases 6, 7, and 12) and low WSS wasound in the two cases with the aneurysm displaced withespect to the main artery (cases 13 and 18; Fig. 7b). Moreerminal aneurysms should thus be considered to elucidatehe correlation with WSS.

The lateral unruptured aneurysms had similar formsFig. 1). The aneurysm area had a significant positive linearorrelation with the virtual area (Fig. 8a). The correlation wasbtained using the 14 studied cases with a correlation coef-cient, r, of 0.87. The virtual area was defined as the area of

he artery corresponding to the aneurysm inlet; this area was

alculated by the CAD software for all the cases. For lateraluptured aneurysms, the relationship between the aneurysmrea and its virtual area was weak, since the aneurysm formedfter rupture was deformed due to bleeding and posterior

able 3ean WSS on an aneurysm at systole for terminal saccular aneurysms

ase R1 WSS (Pa)

6 1.0 32.07 8.4 37.7

18 11.4 9.512 18.2 39.313 39.9 8.0

(ntcuats

tsRa

velocity magnitude, (b) wall pressure, (c) WSS on the artery, and (d) WSS

ealing. The average aneurysm area for lateral unruptured (14ases) and ruptured cases (15 cases) was 52 and 134 mm2,espectively. The quantification of the seemingly arbitraryeometry of unruptured cerebral aneurysms can therefore bealuable in predicting rupture risk, operative risk, design ofoils, and in pre-surgical planning.

Linear parameters of the aneurysms, such as neck width,ome diameter, and dome height, were recorded for the 34ases and the corresponding aspect ratios [5,6] were calcu-ated. A correlation of the WSS on the aneurysm (spatiallyveraged at the peak systole) for the lateral unruptured anduptured cases with the aspect ratio could not be establishedthe correlation factor, r, was 0.07). The measurements ofeck width and dome height depended on the rotation ofhe angiographic image, so different aspect ratios could bealculated for the same case. Area-based indices should besed to correlate WSS. We have defined the ratio of areass R1 = aneurysm area/artery area; this coefficient representshe potential of growth of the aneurysm relative to the arteryize.

The spatially averaged WSS on the aneurysm at peak sys-

ole for the lateral unruptured and ruptured aneurysms hadignificant negative linear correlations with the ratio of areas1 (Fig. 8b and c). The range of R1 was greater for ruptureds compared with unruptured aneurysms. The correlation

336 A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340

F ed withW s, for ca

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ig. 5. (a) Velocity vectors inside a terminal ruptured aneurysm, color-codSS on the aneurysmal sac. Values obtained at peak systolic time, t = 0.53

oefficient, r, was 0.7 in both cases. For the lateral unrup-ured aneurysms, three cases were not considered (10, 29,nd 30.2) and for the ruptured aneurysms, four cases wereot considered (2, 5.1, 19, and 25). Case 30.2 was too smallaneurysm area, 4.6 mm2) and case 10 had a deformed siphonf the principal artery. The four ruptured cases not consid-red had deformed aneurysm surfaces (Fig. 7a, case 5.1).he spatially and temporally averaged WSS at peak systole

or lateral unruptured and ruptured aneurysms had weakerorrelations with the ratio of areas, R1. The average WSS onhe aneurysm was used to characterize the hemodynamics inhe aneurysmal sac because it was not possible to define theame precise locations for all the patient-specific models, asn ideal models [17].

. Discussion

Anatomic regions where both the WSS and the wall sheartress gradient (WSSG) are elevated above normal phys-ologic levels have been shown to lead to pre-aneurysm

hanges, such as disruption of the internal elastic lamina andhinning of the media, in artificially produced bifurcationsn canines [28]. Using a CFD model herein has shown thathe combination of two individual mechanisms are indeed of

ohWs

the velocity magnitude, (b) wall pressure, (c) WSS on the artery, and (d)se 12.

mportance for aneurysm growth: (1) loss of vascular toneue to smooth muscle cell apoptosis and (2) reconstitution ofbers after prolonged periods of excessive strain [29].

The mechanism associated with aneurysm rupture is theesponse of the aneurysm wall to low WSS and it can benderstood only when biologic and mechanical factors areonsidered. Low WSS acting in regions of the aneurysmsac has been suggested as a direct cause of aneurysm rupture9]. We have found large regions of an aneurysm surface withow WSS (Figs. 5 and 6) and these regions were larger in rup-ured aneurysms than in unruptured lesions. The biologicalesponse triggered by low WSS causes endothelial cell degen-ration via apoptosis. Pentimalli et al. [30] have observedignificant differences in apoptosis when comparing rupturednd unruptured aneurysms. High levels of apoptosis wereound in 88% of ruptured aneurysms and in only 10% ofnruptured lesions.

This work shows that the WSS for lateral unrupturednd ruptured aneurysms had a significant linear correla-ion with the ratio of areas, R1. As R1 increased, the WSSecreased in a linear fashion, suggesting an increased risk

f rupture with increased aneurysm area-to-artery area. Weave found ruptured aneurysms for a R1 ≥ 5 with an averageSS of approximately 19 Pa on the aneurysm sac at peak

ystole (Fig. 8c) for unruptured aneurysms. It can thus be

A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340 337

Fig. 6. (a) WSS on the aneurysm for case 21.1, (b) WSS on the aneurysm for case 14.1, (c) WSS on the aneurysm for case 30.1, (d) WSS on the aneurysm forcase 16, (e) WSS on the aneurysm for case 27, and (f) WSS on the aneurysm for case 4. Values obtained at peak systole, t = 0.53 s.

Fig. 7. (a) WSS on the aneurysm for case 5.1 and (b) WSS on the aneurysm for case 18. Values obtained at peak systole, t = 0.53 s.

338 A. Valencia et al. / Medical Engineering & Physics 30 (2008) 329–340

F neurysl le, as fu

saod

ig. 8. (a) Aneurysm area, as function of virtual area for lateral unruptured aateral unruptured aneurysms, and (c) spatially averaged WSS at peak systo

uggested, as depicted in Fig. 8b, that cases with a R1 < 5nd a WSS > 19 Pa have a lower risk of rupture. The ratiof areas, R1, can be used to characterize aneurysm hemo-ynamics, along with other indices, as suggested by Ma

eWtb

ms, (b) spatially averaged WSS at peak systole, as function of area ratio fornction of area ratio for lateral ruptured aneurysms.

t al. [22]. The principal difference in our relationship forSS with the ratio of areas, R1, compared with the rela-

ionship of WSS with the aneurysm aspect ratio describedy Oshima and coworkers [9] was that our investigation

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A. Valencia et al. / Medical Eng

as performed on different cerebral arteries with saccularneurysms, and therefore in cases with different morpholo-ies. For this reason, a relationship of WSS with simplearameters, such as the aneurysm aspect ratio, could not bestablished.

Computational flow dynamics simulations using medicalmage-based anatomical vascular geometries have the inher-nt difficulty of irregular arteries with branches of differentizes and without symmetrical characteristics. In addition, theeconstruction methodology produces small areas with highurvature. All these characteristics produce regions in theomputational domain with an extremely high WSS (Figs.c and 5c). However, the areas with extremely high WSSre small and therefore these values of local WSS do notave important effect on average WSS on aneurysm surfaceresented in the present investigation. Changes in the mor-hology of the arteries can significantly alter the flow fieldnd related hemodynamic parameters, and therefore the sim-lations must also include tiny branch of arteries near theneurysms.

Structural failure of the aneurysmal sac due to the WSSan also be produced, especially if the arterial wall is thinningia cell degeneration. In a future investigation we will con-ider the fluid–structure interaction in the simulation of theemodynamics for patient-specific cases. Also, the patient-pecific pulse of the velocity must be considered for the inletoundary condition.

. Conclusions

This work presents numerical investigations involvingemodynamics in 34 patient-specific models of cerebralneurysms reconstructed from 3D rotational angiography,ncluding 14 lateral unruptured, 15 lateral ruptured, and 5erminal saccular aneurysms. The unsteady flow, pressure,nd WSS on the aneurysm were characterized and the dif-erences between unruptured, ruptured, lateral, and terminalneurysms were reported. The WSS on the aneurysm sachowed important differences between the 34 investigatedneurysms. Linear correlations between the spatially aver-ged WSS on the aneurysmal sac at peak systole for lateralnruptured and ruptured aneurysms with an area index wereound. Further studies are necessary to investigate the effectsf arterial compliance on the development, growth, and rup-ure of patient-specific intracranial aneurysms.

All the patients for this investigation gave their informedonsent, that the image data of 3D angiography can be usedor numerical investigation of fluid dynamics.

cknowledgement

The financial support received from CONICYT Chilender grant number 1030679 is recognized and appreciated.

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& Physics 30 (2008) 329–340 339

onflict of interest

The five authors of this investigation do not have conflict ofnterest with other organizations to publish the results of theirnvestigation in the Journal Medical Engineering & Physics.

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