Numerical Investigation of Blood

Flow in Stented Intracranial

Aneurysm Models

Numerische Untersuchung der

Blutstrmung durch intrakranielle

Aneurysmen mit Stents

Der Technischen Fakultt derUniversitt Erlangen-Nrnberg

zur Erlangung des Grades

DOKTOR-INGENIEUR

vorgelegt von

Efran Lpez Ramrez

Erlangen - 2011

Als Dissertation genehmigt von

der Technischen Fakultt der

Universitt Erlangen-Nrnberg

Tag der Einreichtung : 06.05.2010

Tag der Promotion : 15.02.2011

Dekan: Prof. Dr.-Ing. habil. R. German

Berichterstatter: Prof. Dr.-Ing. A. Delgado

Prof. Dr. rer. nat. habil. U. Rde

Acknowledgments

The present dissertation thesis is the result of my research work carried out during mystay at the Institute of Fluid Mechanics (LSTM), Friedrich-Alexander University Erlangen-Nuremberg, Germany. This thesis would have not been possible without the financial sup-port awarded by the National Council on Science and Technology of Mexico (CONACYT)and the German Academic Exchange Service (DAAD) to conduct my doctoral studies, thissupport is highly acknowledged.

I am heartily thankful to my Ph.D. supervisor Prof. Dr.-Ing. habil. Antonio DelgadoRodriguez for giving me the opportunity to work in his group and for his support, motivationand guidance throughout my research work. His technical and editorial advices were essentialfor the completion of my dissertation. Muchas gracias por todo el apoyo.

I am very much grateful to Prof. Dr. Dr. h.c. F. Durst for supporting my application forthe scholarship that gave me the opportunity to join the LSTM and during the early stagesof my stay in Germany.

I also thank Dr. Kamen Beronov, former head of the Medical application group for hisguidance, helpful discussions and constructive criticism. Furthermore, I would like to extendmy thanks to the members of the dissertation committee and the president of the jury foraccepting this thesis.

Moreover, I would like to thank all colleagues at LSTM for the nice working atmosphere.It was a also a big pleasure to share part of the doctoral studies and life with my friendsChristoph Scheit and Elsy Arratia, and at this point I want to thank them for the lovelymoments we lived together.

I would also like to take this opportunity to thank my friends I met in Erlangen like Estefania,Sal, Fabricio, Poliana, Hesdras, Bianca, Carmen, Ramn, Anke, Jos Luis, Jos and Palomafor the wonderful friendship they offered me, you were a real support.

Quiero expresar mis ms profundos y sinceros agradecimientos a mis padres por todos losaos de apoyo, por todos sus consejos. Gracias por haberme impulsado siempre y por todala dedicacin puesta en m.

A mis hermanos Mirsa, Ardelia, Simn, Rosa y Cecilia y a mi cunada Cecilia Durnmuchas gracias por tantos momentos inovidables que hemos pasado juntos, gracias por lasinagotables ancdotas que nos unen fuertemente como hermanos a pesar de la distancia. Amis sobrinos Monse, Mirsita, Manolo, Ricky y Moni, muchas gracias por ser como son yhacer de nuestras cortas visitas enormes momentos. Muchas gracias Familia!

Quiero agradecer muy especialmente a mi segunda familia, Francisco y Silvia. Les agradezcoinfinitamente el apoyo en todo momento desde que tuve el gusto de conocerlos. A FranciscoJr. por tan elocuentes charlas y buen humor que siempre se agradecen. A mi to Joselito ymis primos.

Sofa, gracias por estar siempre a mi lado, an en la distancia que nos separ al inicio deesta etapa. Gracias por todo el amor y el apoyo en este tiempo que me llev alcanzar estameta. T hiciste que este tiempo del doctorado fuera maravilloso. Gracias por creer en miy estar a mi lado. Te amo!.

Abstract

The present work aims to further advance the understanding of blood flow at and in cere-bral aneurysms. It focuses, in particular, on hemodynamic parameters associated with theformation and rupture of lateral and terminal aneurysms. Aneurysms are abnormally wideor bulging parts of an artery. The work includes also a study of hemodynamic effects ofstent-like implants for treatment of such aneurysms. It was carried out using computationaltomography data from patients, software tools for medical visualization and vessel geometryreconstruction for grid generation, and commercially available software for computationalfluid dynamics (CFD).

The kind of patient-specific results on mechanical and geometric parameters of the kindobtained here can be used to assist the estimation of aneurysm rupture risk as well as themedical planning of endovascular interventions for treating vessels at high risk. The presentwork treats, in particular, the effect of stent placement on hemodynamic parameters such asblood flow velocity and wall shear stress. To that end, virtual stenting is performed andits effects simulated, in synthetic but geometrically representative models of intracranialaneurysms. The effectiveness of stenting in reducing the intra-aneurysmal flow and loweringthe mechanical loads on the weakened aneurysmal wall is quantified. Qualitative knowledgeof hemodynamic changes in cerebral aneurysms after stenting is gained, including e.g. thestrength and location of areas with low flow and shear rates or the considerable significanceof mutual situation of vessel branches and aneurysm. The predictive capability of simplifiednumerical models of stents is estimated against representations of flow through detailedmodels of stents. The work carried out in this thesis allows an estimate of the technicaleffort of CFD modeling of real aneurysms, including their treatment with endovascularimplants, as well as the kind, range, and predictive value of information to be gained fromsuch modeling.

Kurzfassung

Ziel der vorliegenden Arbeit ist die Vertiefung des Verstndnisses fr die Blutstrmungin der Nhe und innerhalb von Gehirnaneurysmen, insbesondere fr hmodynamische Pa-rameter, welche mit der Bildung und Ruptur von lateralen und terminalen Aneurysmenin Verbindung gesetzt werden. Aneurysmen sind krankhafte Erweiterungen von arteriellenAbschnitten. Die Arbeit beinhalten darber hinaus Studien ber die hmodynamischenEffekte, die durch Stent-hnlichen Implantaten, welche zur endovaskulren Behandlung vonGehirnaneurysmen eingesetzt oder untersucht werden, herbeigefhrt werden knnen. DieArbeit wurde anhand von Computertomographie-Daten realer Patienten und mithilfe vonSoftware fr medizinische Bildgebung und Gefgeometrie-Rekonstruktion sowie fr com-putational fluid dynamics (CFD) durchgefhrt.

Die Art von Informationen ber mechanischen und geometrischen Parametern, die auch dieMehrheit der in dieser Arbeit entstandenen Ergebnisse umfasst, kann zur Untersttzung beider Einschtzung des Ruptur-Risikos von gefhrdeten Gefen sowie bei der medizinischenPlanung ihrer endovaskulren Behandlung herangezogen werden. Die vorliegende Arbeit be-fasst sich insbesondere mit der Auswirkung einer Stent-Platzierung auf hmodynamische Pa-rameter wie Blutstromgeschwindigkeit und Wandscherspannung. Dafr wird eine virtuelleStent-Implantation in synthetischen aber geometrisch reprsentativen Gefgeometrien imRechner modelliert und die dadurch vernderte Hmodynamik dann mit CFD simuliert.Dabei wird die Effizienz des Implantats hinsichtlich der Reduzierung des Blutflusses und dermechanischen Wandbelastung in Aneurysmen quantitativ untersucht. Es werden qualitativeEinsichten in weitere Vernderungen der Hmodynamik nach Stent-Platzierung gewonnen,wie z.B. die Strke und Lage von Flecken mit niedriger Flu- bzw. Scherrate oder der oftbetrchtliche Einfluss der Lage eines Aneurysmas bezglich der Krmmung benachbarterGefabschnitte. Vereinfachte numerische Modelle von Stents werden gegenber detail-lierten Darstellungen der Stent-Durchstrmung bezglich ihrer Aussagekraft bewertet. DieLehren aus dieser Arbeit, wenn betrachtet im Zusammenhang, erlauben eine gute Ein-schtzung des fr die CFD Modellierung von realen Aneurysmen erforderlichen technischenAufwands, sowie der Art, der Wertspanne und der Aussagekraft von Informationen, die einesolche Modellierung als Mehrwert zu bringen verspricht.

Contents

Index of Tables v

Index of Figures xiii

Nomenclature xvi

1 Introduction 1

1.1 Historical perspective on cardiovascular function . . . . . . . . . . . . . . . 1

1.2 Cerebral aneurysm, causes and its effects . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Diagnosis and prognosis . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2.1.1 Prognosis of intracranial aneurysms . . . . . . . . . . . . . 11

1.3 Therapy options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.1 Craniotomy with clipping . . . . . . . . . . . . . . . . . . . . . . . . 13

1.3.2 Endovascular treatment . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4 Motivation of the present thesis . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.5 Outline of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

i

CONTENTS ii

2 Hemodynamics modeling 21

2.1 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.1.1 Finite volume method (FVM) . . . . . . . . . . . . . . . . . . . . . . 22

2.1.2 Non-Newtonian blood model . . . . . . . . . . . . . . . . . . . . . . 23

2.1.3 Porous media conditions . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.2 Blood circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.2.1 Fourier transform analysis . . . . . . . . . . . . . . . . . . . . . . . . 28

2.2.2 Cardiac waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.3 Neglected effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Numerical simulations using image-based aneurysm models 35

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.1 Study cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.2 Use of physiologic data . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2 Methods and data used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.2.1 Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.1 Steadystate simulation . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.2 Transient simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.4.1 Technical limitations of imaging techniques . . . . . . . . . . . . . . 58

4 Hemodynamic changes after virtual stenting of a lateral saccular intracra-nial aneurysms - comparison of realistic stent designs 61

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.2.1 Idealized model of saccular aneurysm . . . . . . . . . . . . . . . . . . 66

4.2.2 Stent designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3 Steady state results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.4 Transient results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.4.1 Blood flow changes induced by stents . . . . . . . . . . . . . . . . . . 80

4.4.2 Loads at the aneurysm dome . . . . . . . . . . . . . . . . . . . . . . 86

4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

CONTENTS iii

5 Porous stents modeled in an aneurysm located at the circle of Willis (CW) 91

5.1 Numerical Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.1.1 Idealized model of aneurysms in CW . . . . . . . . . . . . . . . . . . 92

5.1.2 Design of porous stent . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.1.3 Contrast agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.2.1 Blood flow changes induced by stents . . . . . . . . . . . . . . . . . . 97

5.2.2 Loads at the aneurysm dome . . . . . . . . . . . . . . . . . . . . . . 100

5.2.3 Contrast agents sensitivity to flow properties . . . . . . . . . . . . . 102

5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.3.1 Flow characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.3.2 What happens at the dome? . . . . . . . . . . . . . . . . . . . . . . . 105

5.3.3 Contrast agents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

6 Outlook 111

6.1 Perspectives of the CFD in planning aneurysm treatment . . . . . . . . . . 112

6.2 What to look at? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

Bibliography 115

List of Tables

1.1 Risk of rupture of aneurysms. . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 Predominant locations of intracranial aneurysms. . . . . . . . . . . . . . . . 10

2.1 Factors affecting the effective blood viscosity at a location . . . . . . . . . . 24

2.2 Numerical description of the composite wave shown in Figure 2.4, giving theposition (t, p) of the discrete blue points shown along the curve. . . . . . . . 31

2.3 Values of the Fourier coefficients for the cardiac wave shown in Figure 2.5,with n = 1, 2, . . . , 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1 Geometrical characteristics of the real aneurysms computed in this thesis. . 40

3.2 Physical properties of the blood. . . . . . . . . . . . . . . . . . . . . . . . . 40

3.3 Geometrical characteristics of the real aneurysm computed in this thesis andthe ones studied by Jou [43] and Shojima [89]. . . . . . . . . . . . . . . . . . 53

4.1 Porosities of the different stent configurations. . . . . . . . . . . . . . . . . . 70

4.2 Grid parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.3 Outlet velocity at the side vessel. . . . . . . . . . . . . . . . . . . . . . . . . 72

4.4 Values plotted in Figure 4.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

v

List of Figures

1.1 Structure of a muscular artery. . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 Schematic models of a fusiform aneurysm at the aorta (left) and a saccularaneurysm (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 a) Oblique view of a vertebral angiography depicting an aneurysmal dilatationof the distal portion of the left SCA (3 3.5 mm (black arrow head). b) Astereoscopic image for a 3D vertebral angiography depicting an aneurysm inthe hemispheric branch of the left SCA (arrow head). . . . . . . . . . . . . . 9

1.4 a) CT scan 2 weeks after trauma reveals an acute hematoma in the genu ofcorpus callosum, and dense contrast enhancement (black arrow) near the falxedge in the image. b) the newly developed aneurysm (withe arrow) on thenonbranching site of the right ACA in the 3D reconstruction. . . . . . . . . 10

1.5 a) Left vertebral angiography showing VGAM. b) left oblique view of theVGAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6 Anatomy of the brain (posterior vs. anterior circulation and CW) . . . . . . 11

1.7 Clip placed across the neck of the aneurysm to prevent blood from enteringthe dome. The goal of surgical clipping is to isolate an aneurysm from thenormal circulation without blocking off any small perforating arteries nearby. 13

1.8 Microcatheter (shown in blue) deploys platinum coils into the aneurysm untilcomplete occlusion. Coils promote thrombus formation. . . . . . . . . . . . 15

1.9 Saccular aneurysm model and stent placed at the neck. Stent is aimed toreconstruct the parent vessel from which the aneurysm has formed. . . . . . 16

vii

LIST OF FIGURES viii

2.1 Typical 3D unstructured grids of real aneurysms derived from computed to-mographic data and generated with Amira tetra-grid generator from VisageImaging. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Viscosity of blood compared with Casson model for non-Newtonian fluid. . . 24

2.3 Comparison of a composite waveform (blue line) with the simple form of asine wave (red line). While they are both periodic, as seen on the right,the composite wave is highly irregular and is therefore not easy to describeanalytically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Re-synthesis of arterial pressure wave form by summation of the first 20harmonic components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5 Typical composite pressure wave form used as pressure-inlet boundary con-dition. The CFD computation realizes the prescribed pressure. . . . . . . . 32

3.1 Locations of the aneurysms studied in this thesis (arrows) and location, dis-tribution, and median size of a total number of 265 aneurysms reported in [5].View from above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 3D posterior view following left vertebral artery injection of the section ofthe posterior circulation in patient 1. Figure key: 1) left vertebral artery, 2)basilar artery, 3) posterior inferior cerebellar artery (PICA), 4) P1 segmentof posterior cerebral artery, 5) P2 Segment of posterior cerebral artery, 6)right superior cerebellar artery, 7) left superior cerebellar artery, 8) anteriorinferior cerebellar artery, An1) giant basilar tip aneurysms, An2) aneurysmat the PICA junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 The three patterns of blood flow observed in the experimental aneurysmsreported by Moftakhar et al. [68]. a) recirculation, b) Impinging jet, andc) low flow inside aneurysm. Lateral aneurysms like in c) can also haverecirculating flow pattern, similar to and even more complicated than in a). 39

3.4 Computational grids. Based on CT scan data computational grids were gen-erated. left: Case I and right: Case II . . . . . . . . . . . . . . . . . . . . . 41

3.5 Pressure function simulated (Pa) at the inlet boundary condition of thecurved artery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.6 AMIRA GUI including 3 different planes from Case I aneurysm and a 3Dreconstruction of the complete acquired CT data. . . . . . . . . . . . . . . 42

3.7 Streamlines, colored by velocity, illustrate the flow through the parent in-tracranial vessels and the aneurysms in aneurysms. . . . . . . . . . . . . . . 43

3.8 WSS contours at the walls of the aneurysms. Blue arrows show the zoneswhere the lowest values of WSS are found. Red arrows show the points athighest WSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

LIST OF FIGURES ix

3.9 Contour plots and velocity vectors for Case I on planes Y1 (top row) andplane X1 (bottom row), parallel to the Y and X axis respectively. The smalltop left and bottom left figures show the planes Y1 and X1 and the iso-surfaceof velocity v = 0.01 m/s (depicted in the inset figure as a gray surface). Left:Contour plots showing the relatively high velocity inside the aneurysm, thesurface of iso-velocity almost hits the aneurysm dome, but is splited before ittouches the top wall. Right: Velocity vectors plotted on the planes colored byvelocity magnitude (see the color code bar to the left). Velocity fields showthe vortices formed around the jet. The flow leaves the aneurysm mainlyfrom frontal wall (to the right in the top row). Blue arrows show the zoneswhere the lowest values of WSS are found. Red arrows show the points athighest WSS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.10 Contour plots and velocity vectors for Case II on planes Z2 (top row) andplane Y2 (bottom row), parallel to the Z and Y axis espectively. Similar tothe previous figure, both planes and the iso-surface of velocity v = 0.01 m/sare shown in top left and bottom left figures. Left: Contour plots showinglow velocity flow in the aneurysm. The flow preferentially streams from theparent vessel into the left branch. Right: Velocity vectors plotted at the sameplanes colored by velocity magnitude (See the color code bar to the left). Theflow coming back from the aneurysm and enters the right branch is indicatedwith the green arrow. No jet flow is observed, but the isosurface hits directlythe left potion of the neck (red arrow). . . . . . . . . . . . . . . . . . . . . 46

3.11 Time series of Pressure (left) and velocity (right) at the inlet. . . . . . . . . 47

3.12 Case I (middle column) presents a highly vortical flow dominated by the jetcoming from the parent vessel. Case II (right column) is an aneurysm inwhich flow structure inside it does not change substantially during a cardiaccycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

3.13 The velocity average computed inside the aneurysm during the cardiac cycle. 49

3.14 Time series of velocity average at the red planes (neck) shown in the insetfigures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.15 Time series of WSS spatially averaged at the aneurysm surface. . . . . . . 50

3.16 Comparison WSS contours at the wall of the aneurysm sac for different timesand Case I. Left: back view and right: front view. The time gap betweenplots is 0.2 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.17 Alteration of wall shear stress during a cardiac cycle measured along thelight-blue line (at y = 0.00424 m) seen in the inset figure. The compositewave shown in the inset figure is a reference for the time labels. . . . . . . . 52

LIST OF FIGURES x

3.18 Alteration of wall shear stress during a cardiac cycle measured along thelight-blue line (at z = 0.0002754 m) seen in the inset figure. The line wasselected arbitrarily. The inset plot (top left corner) shows the distribution ofWSS along this line, whereas the main plot shows the distribution starting atthe proximal side of the aneurysm (using the inset image view at the center ofthis Figure as reference), so that highest values in this plot are found wherethe aneurysm joints the parent vessel. On the other hand, the highest valuesof WSS are found on the distal wall of the aneurysm in this view, (not shownin the main plot, but labeled in the inset plot). . . . . . . . . . . . . . . . . 53

3.19 Vessel and aneurysm averages WSS over one cycle and maximum values ofWSS recorded at t = 0.95 s (end diastole) in the present study and valuesreported by Jou [43]. The numerical data can be seen in table 3.3. . . . . . 54

3.20 Time series of pressure average at the dome PD. . . . . . . . . . . . . . . . 54

3.21 Left: mean WSS versus the aneurysm surface area, and right: maximal WSSat diastole versus the aneurysm area reported by Jou [43] and values calcu-lated in the present study. WSS is given in Pascals. . . . . . . . . . . . . . . 56

3.22 Bivariate scattergram with regression between the aspect ratio and the WSSof the aneurysms found in the middle cerebral artery. A significant negativecorrelation was observed (r = 0.67). Ruptured aneurysms reported byShojima are shown in red, while unruptured ones are in blue. The greenarrow shows the result from Case II aneurysm (located at the middle cerebralaneurysm). The orange arrow shows the Case I aneurysm (at a differentposition). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.23 Left (Case I): Point A shows an incorrect filling of the aneurysm at the distalwall due to probable thrombus presence. B is an oval-shaped filling defect.Right (Case II):E shows what it could be a marked elongation or daughterloculus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.24 Model of small-necked aneurysm in the MCA bifurcation visualized. Left:continuous flow technique showed an oval-shaped filling defect at the medialwall. Right: improved depiction achieved with bolus injection [25]. Viewfrom above. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.25 Examples of small additional aneurysms missed on DSA, but perfectly de-tected by the 3DRA technique. Left: A very small (0.5 mm) aneurysms(arrow) in a patient with SAH caused by a ruptured middle cerebral arteryaneurysm. Right: An additional intracavernous carotid artery aneurysm (ar-row) to a giant ophthalmic artery aneurysm [98]. . . . . . . . . . . . . . . . 60

4.1 Left: A broad-based basilar tip aneurysm encroaching the P1 segment onthe right side. Right: After intravascular stenting combined with coiling, thestent was placed from the right P1 segment to the basilar artery, overcomingin this manner a very common technical challenge (Figure taken from [105]). 63

4.2 The model used for simulations was based on the real aneurysm shown inthis figure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

LIST OF FIGURES xi

4.3 Skeleton of the 3D model of intracranial aneurysm. . . . . . . . . . . . . . . 66

4.4 Geometry and mesh used for calculations. Front, lateral and top views. . . . 67

4.5 Stent models with aneurysm. a) P 2, b) P 4, c) P 4 X, d) porous stents,and e) Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.6 Detail of the strut designs. The strut thickness is 30 m in all cases. . . . . 69

4.7 Helical stent design. = 2 and 4. . . . . . . . . . . . . . . . . . . . . . . . 70

4.8 Mesh stent design. = 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.9 a) Velocity average inside the aneurysm sac (Vs), b) Velocity average at theaneurysm neck Vn). The mechanical loads at the dome: c) Pressure averagePD), and d) WSS average at the dome WSSD). . . . . . . . . . . . . . . . . 73

4.10 Pathlines colored by the velocity magnitude inside (a) unstented aneurysm,(b) P 2 ,(c) P 4 , (d) P 4 crossed, (e) porous media cases and (f) meshstent. It is important to notice that the features of the flow before and afterthe aneurysm location are qualitatively similar, changes can only be noticedin the intra-aneurysmal flow. The arrows show the blood flow direction. . . 74

4.11 Velocity contour plots on two different planes in the aneurysm and parentvessel at position y = 0 (left) and position x = 0 (right). The planes cross atthe center of the aneurysm. The blood flow direction is from right to left. . 75

4.12 Continuation of velocity contour plots on two different planes in the aneurysmand parent vessel at position y = 0 (left) and position x = 0 (right). Theplanes cross at the center of the aneurysm. It can be noticed that qualitativelyand quantitatively in the intraaneurysmal flow, the patterns obtained in theporous stent model compare to the helical stent. . . . . . . . . . . . . . . . 76

4.13 Dependency of the blood velocity at the neck of the aneurysm on Re number. 77

4.14 Dependency of the blood velocity inside the aneurysmal sac on Re number.Very similar to Figure 4.13, except that Case P 4 seems to be more effectivein reducing the average velocity of blood inside the aneurysm. The porousCase reported better results at higher Re numbers . . . . . . . . . . . . . . 77

4.15 Contours of pressure at the dome for all cases. Letters denote the differentcases as in Figure 4.10. The red spot that appears in the unstented casesindicating high pressure over the distal side of the aneurysmal wall has dis-appeared after stenting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.16 Contours of pressure and WSS at the dome for all 6 cases. Letters denotecases as in Figure 4.10. The red spot that appears in the unstented casesindicating high mechanical load over the dome disappeared after stenting. . 79

4.17 Log-log plot of the Reynolds number (Re) for all cases vs. WSS dependencyof the WSS at the aneurysm dome on Re number. As expected for Low Reflows, very similar trends to Figures 4.13 and 4.14. . . . . . . . . . . . . . . 80

4.18 Comparison of time series of velocities at the aneurysm neck over two seconds. 81

LIST OF FIGURES xii

4.19 Velocity average inside the aneurysm as a function of time over two seconds.Very similar to 4.18, as expected, but the porous stent is slightly more effectivein reducing the velocity inside the aneurysms. In both of the plots, the P 2

stent leads to the lowest reductions. Note that the amplitude of the waves isreduced at lower velocities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.20 Comparison of pathlines at three stages during the cycle. A highly recircu-lation pattern is observed in the interior of the unstented aneurysm, whileP 2 , P 4 and P 4 crossed Cases presented a low flow pattern similarto the one observed in the experimental work by Moftakhar et al. in [68].Hemodynamics into the porous and mesh Cases are more complex. Finally,the pattern of pathlines downstream the aneurysm are more similar in theunstented, porous and mesh Cases . . . . . . . . . . . . . . . . . . . . . . . 82

4.21 Comparison of velocity contours on the plane y = 0.001 and on the plane atthe inlet (neck) of each aneurysm at three stages during the cycle (indicatedin the top figures). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.22 Comparison of velocity vectors colored by the magnitude at plane y = 0.001m (left column) and the iso-surface of iso-velocity = 0.04 m/s, 1/2 ofthe average velocity inside the unstented aneurysms (right column). Thesnapshot were taken at peak systole, time = 0.98 s and the blood flows fromleft to right as illustrated by the black arrows. . . . . . . . . . . . . . . . . . 85

4.23 Velocity at the exit of the side vessel. . . . . . . . . . . . . . . . . . . . . . . 86

4.24 Time series of WSS averaged at the aneurysm sac. . . . . . . . . . . . . . . 87

4.25 Time series of pressure averaged at the aneurysm sac. . . . . . . . . . . . . 87

4.26 WSS average over one cycle along the line shown in the inset figure (at co-ordinate y = 0.001 m or equator of the aneurysm). Higher WSS values arefound at the distal side of the neck. . . . . . . . . . . . . . . . . . . . . . . . 88

5.1 Pressure function simulated (Pa) at the entrance of the CW bounbary con-dition. Data according to Zamir et. al. [111] . . . . . . . . . . . . . . . . . . 93

5.2 Frontal view of the chosen geometrical model of the CW with multiple model-aneurysms. The blue portion of the geometry indicates the stent position. . 93

5.3 Detail of the finite element grid. . . . . . . . . . . . . . . . . . . . . . . . . . 94

5.4 Realistic 3D stent model. The top figure is a representation of what the I stentor single stent case would look like and the bottom figure shows the II stentalso named double stent crossed case, the complexity of this CAD modelsis avoided simulating them as cylindrical layers of porous media. Strutsthickness 30 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.5 Case II configuration and position. The inset figure shows a zoom into thestent configuration, for better visibility, the parent vessel wall is transparent. 96

LIST OF FIGURES xiii

5.6 Averaged blood velocity at the entrance of the aneurysm (neck) as a functionof time for the unstented, single-stented and double-stented aneurysms. . . . 98

5.7 Spatial average of velocity at the equatorial plane of the aneurysm as a func-tion of time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.8 Visualization of flow configuration and instantaneous stream lines of the intra-aneurysmal flow in unstented (top), case I (center) and case II (bottom) stentplacement sac. The color bar ranges from 0 m/s (blue) to 3.2 m/s (red). . . 99

5.9 WSS averaged over the aneurysm wall, where a 10-fold reduction in this scalarcan be seen after stenting with the I stent device and a further reduction wasachieved with the II stent device. As the scales read, the unstented case isplotted using the left scale and the values corresponding to cases I and IIwith stents are plotted with the scale to the right. . . . . . . . . . . . . . . . 100

5.10 Visualizations of WSS (left column) and pressure (right column) distributionat the sac wall for all three cases in Pascals (Pa) and t = 0.28 s. The highWSS present in the unstented case (red spot at top image) disappears afterstenting (center and bottom images). The pressure in the stented cases isvery uniform. Flow direction is from right to left. . . . . . . . . . . . . . . . 101

5.11 Isosurfaces of tracer (in blue) and blood (in red) for all three cases at t = 0.28s. Front view (left column) and back-side view (right column). Unstented -top row, single stent - middle row and two cressed stents - bottom row. . . . 103

5.12 Isosurfaces of tracer (in blue) and blood (in red) for all three cases at t = 0.78s. Front view (left column) and back-side view (right column). Unstented -top row, single stent - middle row and two cressed stents - bottom row. . . . 104

5.13 Distribution of WSS at all grid points on the aneurysm wall averaged over onetime period for all three configurations. Position zero refers to the geometricaxis which lies along and parallel to the parent vessel. Black line shows areference Gaussian shape. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.14 History of the pressure (Pa) averaged at the complete aneurysm wall alongtwo seconds flow time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.15 Rate of sac emptying. It turns out that over most of its span this process islinear in time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Nomenclature

Abbreviations

Angular pitch of mesh-like stents

Dynamic viscosity Pa.s

Kinematic viscosity m2/s

Angular frequency radians per sec

Angular pitch of helical stents

Density Kg/m3

Stress tensor Pa

Wall shear stress Pa

t Time s

3D-RA 3D rotational angiography

AAA Abdominal aortic aneurysm

CFD Computational Fluid Dynamics

CT Computed tomography

CW Circle of Willis

DSA Digital subtraction angiography

xv

LIST OF FIGURES xvi

FDA Food and drug administration

FVM Finite volume method

GCS Glasgow coma scale

ISAT International Subarachnoid Aneurysm Trial

MAP Mean Arterial Pressure

MCA Middle Cerebral Artery

MR Magneto resonance

MRA Magnetic Resonance Angiography

MRI Magnetic Resonance Imaging

N-S Navier-Stokes

PDEs Partial Differential Equations

PICA Posterior inferior cerebellar artery

PIV Particle Image Velocimetry

RBC Red Blood Cells

SAH Subarachnoid hemorrhage

SCA Superior cerebellar artery

WSS Wall Shear Stress

1

Introduction

In the treatment of cerebral aneurysms with stents there is still much research to be done.

1.1 Historical perspective on cardiovascular function

The historical perspective starts with the knowledge that blood moves in a closed circle,which was apparently known in the far east about 2650 B.C., as recorded in the bookby the Yellow Emperor of China written in the Canon of Medicine (Nei Ching). AncientChinese practitioners customarily felt palpable wrist artery (radial artery) pulsations as ameans of diagnosing the cardiac states of their patients. In this approach, the practitionerswere able to obtain both the strength of the pulsation to infer the vigor of contractionof the heart, and the interval duration of the pulses, hence heart rate. This is an earlyindication of the importance of the rate-pressure product, now a popular clinical index ofmyocardial oxygen consumption. The supply and demand of oxygenation, as well as itsproper utilization in terms of energy balance are central to maintaining a healthy bodystatus. The early suggestion of an intrinsic transfer of the energy generated by the heartto the peripheral arteries appears to have been known to different cultures since antiquity,although the theoretical foundation was not established until much later.

In the West, the observation that man must inspire air to sustain life led ancient scientistsand philosophers to toy with the idea that arteries contained air rather than blood. Thiswas the notion originally attributed to Erasistratus in the third century B.C., followingthe teaching of Aristotle. Aristotle and later Herophilus performed numerous anatomicalstudies and the latter discovered the connecting arteries to the contracting heart.

The Greek physician Galen (130-200), through his knowledge of anatomy and great technicalskill, was able to contribute to nearly all the surgical subspecialties including what is nowcalled neurosurgery. Galen was the first to recognize that the walls of arteries are thickerthan those of the veins and that arteries were connected to veins. It was the Persian

1

1.1. HISTORICAL PERSPECTIVE ON CARDIOVASCULAR FUNCTION 2

physician Ibn an-Nafis (1210-1288) who claimed that venous blood of the right ventricle iscarried by the artery-like vein into the lungs, where it mixes with the air and then into theleft ventricle through vein-like artery.

The physicist, astronomer, mathematician, philosopher and inventor Galilei (1564-1642) inhis Dialogue of the Two Sciences, issued in 1637, was the first in suggesting that bloodcirculates in a closed system. Later on, that idea was credited to William Harvey (1578-1657), a contemporary of Galilei, in his De Motu Cordis and De Circulatione Sanguinis(1628). In his Anatomical Exercises he described that blood does continually passesthrough the heart and that blood flows continually out the arteries and into the veins.

Harveys work indicated the pulsatile nature of blood as a consequence of intermittentinflow, during roughly one-third of the heart cycle, now known as systole, in combinationwith essentially steady outflow through the periphery during the remaining cardiac period,the diastole.

Thomas Willis (1621 1675) is known as the pioneer who established neurology as a distinctdiscipline, and is credited with using the word neurology (Neurologie to mean doctrine ofnerves) for the first time in 1664 [108]. This term was initially restricted to denote cranial,spinal, and automatic nerves, but not the central nervous system. The term neuro inGreek refers to tendon or sinew, and not nerves as this term is known today. With time,neurology was used in a broader sense to describe the study of the entire nervous system,both central and peripheral. Willis is thus considered to be the Father of Neurology [83].

Before Willis, the knowledge of brain anatomy was minimal and limited to the works of theItalian school, in particular of da Vinci, Berengario (1522) and others. Willis is rememberedfor the circle of Willis (CW), the arterial anastomosis at the base of the brain. Althoughthis had already been described by Wepfer, Willis is credited with explaining the functionalsignificance of this anastomosis as a safety device against occlusive deficiency thanks topostmortem dye studies.

All this knowledge gave birth to biomechanics, whose definition is the application of engi-neering to biological systems, mostly applied to humans, but has been motivated by cardio-vascular problems in the fisrts place. Biomechanics is very important in different areas ofgrowth, development, tissue remodeling and homeostasis. It deals directly with some directcauses of important diseases, and it suggests ways for the treatment of these diseases.

As an example of biomechanics applied to physiological flow problems, this thesis dealswith the treatment of an arterial disease known as aneurysm, more specifically cerebralaneurysms, which are saccular expansions of the cerebral vascular wall [78].

There is a wide variety of cerebral aneurysms, they can be located in different arteries,can have different forms, and develop for different reasons. Risk factors leading to devel-opment of an aneurysms include age, atherosclerosis, hypertension, smoking, heavy alcoholconsumption, female gender, and Finish or Japanese decent among others. If remain unde-tected or left untreated, cerebral aneurysms can rupture causing subarachnoid hemorrhage(SAH) which can lead to brain damage. Hydrocephalus, rebleeding and cerebral vasospasmwith ischemia are the three major complications following SAH [102], and in worst casesSAH leads to death.

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 3

After a cerebral aneurysm is detected, neurosurgeons enters a decision-making process toselect the best treatment for a particular patient with a particular aneurysm. Despite theincreasing availability of level one evidence (result of prospective randomized studies), thedecision in any medical field of what to do for an individual patient is still more dependenton experience and art than on science [50].

Understanding the blood flow through an aneurysm located in the brain and characterizingthe hemodynamic parameters associated with this vascular malformation is very importantto improve its treatment.

In this thesis, computational fluid dynamic was applied to realistic and synthetic models ofsaccular intracranial aneurysms. The models were treated virtually with the intravasculartherapeutic approach known as stenting. Changes on the aneurysm dome and parent vesselare evaluated prior and post stent placement at the neck of the aneurysm. A novel approachfor stent modeling is also presented in this work, in which stents are modeled as porousmaterials. This approach allows for time saving in the generation of the mesh and thecomputational time is also reduced.

1.2 Cerebral aneurysm, causes and its effects

An aneurysm is a permanent arterial dilatation usually caused by a weakening of the vesselwall.The majority of saccular aneurysms are not considered to be congenital.

Three different hypotheses exist regarding the pathogenesis of the aneurysms 1) congenitalweakness of the muscular layer, 2) degenerative alteration of inner elastic membrane, 3) acombination of both [85].

An intracranial or cerebral aneurysm is a pathological dilatation of an area where a bloodvessel in the brain weakens [57], resulting in a bulging or ballooning out of part of the arterywall. This process of artery remodeling is due to changes in the mechanical stress exertedon the artery wall by flowing blood and inadequacy of reactive mechanisms. Endothelialcells lining the inner arterial surface sense these changes and send signals to cells deeperin the artery wall to enlarge forming the aneurysm [20, 26]. Intracranial aneurysms are acommon clinical disorder. Autopsy studies have shown that the overall frequency in thegeneral population ranges from 0.4% to 10%.

Every year, an estimated 30,000 people in the United States experience a ruptured cerebralaneurysm, and up to 6% of the population (most commonly people between ages 30 and60 years) may have an unruptured aneurysm (approx. 18 millions). The incidence of SAHincreases with age, such that at the third decade of life, the incidence is approximately 1.5to 2.5 per 100,000 per year, at the eighth decade, it is approximately 40 to 78 per 100,000per year [28].

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 4

Simply stated, stroke is a cerebrovascular injury that occurs when blood flow to the brain isinterrupted by a clogged or burst artery. The interruption deprives the brain of blood andoxygen and causes the death of brain cells.

Approximately 50% of patients with aneurysmal SAH will die or suffer severe disability dueto their initial hemorrhages, and another 23-35% will die due to subsequent hemorrhages ifleft untreated.

There are two different types of stroke, ischemic and hemorrhagic.

In an ischemic stroke, blood supply to part of the brain is decreased, leading to dysfunctionand necrosis of the brain tissue in that area. There are four reasons why this might happen:Thrombosis (obstruction of a blood vessel by a clot forming locally), embolism (idem due toa embolus from elsewhere in the body), systemic hypoperfusion (general decrease in bloodsupply) and venous thrombosis (due to locally increased venous pressure).

On the other hand, hemorrhagic stroke is less common, but more deadly. Intracerebralhemorrhage is bleeding directly into the brain tissue itself that usually form a clot. SAHis bleeding within the cerebrospinal fluid spaces surrounding the brain. Bleeding in thesubarachnoid spaces is most often caused by a ruptured aneurysm.

The development of aneurysms in intracranial arteries can be due to properties that makethem different from peripheral arteries. A muscular artery wall consists of three differentlayers. The innermost layer is the tunica intima, the middle layer is the tunica media anthe outermost layer is the tunica adventitia. The structure of a small muscular artery isshown in Figure 1.1. The microscopic structure of intracranial arteries is muscular in type,with media1 thinner than extracranial arteries, but the enclosing layer of tissue (tunicamedia) does not possess elastic and external elastic lamina. Intracranial arteries also havebreaks in the continuity of the media, these defects are normal and unique to intracranialarteries [54, 85].

Fig. 1.1: Structure of a muscular artery.

Brain arteries contain collagen fibers for support and protection, but since they float inthe cerebro-spinal fluid situated under the arachnoid membrane (subarachnoid space), they

1the middle layer of an artery or lymphatic vessel

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 5

have very little support from surrounding tissue [103]. It is believed that cerebral arterieshave much less elastin in the media and adventitia, but more prominent internal elasticlamina than the arteries of extracranial sites [34].

Because most cerebral aneurysms are congenital, this disorder are aggravated or are thedirect result from other conditions such as

older age

high blood pressure

atherosclerosis

head trauma

infection

tumors and other diseases of the vascular system

smoking, heavy alcohol consumption, drug abuse

female gender

Finish or Japanese decent

These factors might contribute to general thickening of the intimal layer in the arterial wall,distal and proximal to branching sites.

Atherosclerosis is a chronic inflammatory, fibroproliferative disease, considered the primarycause of morbidity and mortality in the industrialized world [53], which is a primary causeof other diseases of the modern civilization like heart attacks, stroke and results from acombination of local shear stress patterns and inflammatory processes [19].

Two main kinds of aneurysms can occur in the brain: Fusiform wall dilation and saccularbulging of the artery wall. Fusiform aneurysms (see Figure 1.2 left) are often complicationsof atheroma2. They can be found in any artery, but mostly in the aorta. Abdominal aorticaneurysms (AAA) is an example of fusiform aneurysms, and they are enlargements of atleast 1.5 times the abdominal aorta size.

Saccular aneurysms are balloon-like deformations that protrude from the artery wall (seeFigure 1.2 right). They can be caused by infections of the blood and traumas of the arterialwall. Saccular aneurysms are located either on the vessel edge (side aneurysm), or at abranching region, and are respectively called lateral or terminal.There are also opinionsthat a lateral aneurysm can occur from any of the branches.

Most of the intracranial saccular aneurysms are congenital. Congenital aneurysms are lo-cated at the branching of the brain vessel network, mainly at the branching sites of thearteries afferent to and efferent from the CW.

2a mass of yellowish fatty and cellular material that forms in and beneath the inner lining of the arterialwalls.

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 6

Fig. 1.2: Schematic models of a fusiform aneurysm at the aorta (left) and a saccular aneurysm(right).

Although many experimental and numerical investigations have been carried out, the roles ofblood flow physiologic parameters, morphology, and natural history are poorly understood.A pathogenetic theory is that aneurysms in bifurcations are acquired due to hemodynamicstress on the relatively unsupported bifurcations of cerebral arteries such as wall shear stressand dynamic pressure [94, 46]. This theory has been studied using CFD to compare thehemodynamics conditions before and after aneurysm formation in 3D models of human pa-tient geometric data. Results show significant correlations between functions of the wallshear stress and the location of eventual aneurysm formation [60]. Regarding the forma-tion of saccular aneurysms, the theory of hemodynamics as an important factor promotinganeurysm formation has been also studied in another publication. The results of the studyby Tateshima et al. [92] show that endothelial cells sense and integrate hemodynamic andenvironmental stimuli to produce various mediators that control vascular functions. Thecaliber and also the histologic structure of vessel walls are regulated particularly by fluid-induced wall shear stress.

Researches made on animal models suggest that local hemodynamic forces including fluidinduced wall shear stress (WSS) contribute to the initiation of saccular brain aneurysms [86].Some studies also suggest that focal high WSS induced by certain flow pattern is a predis-posing factor for brain aneurysm formation in healthy arteries [64].

WSS is related to the friction of the adjacent blood flow. The WSS on the endothelial surfaceis proportional to the blood velocity gradient at the wall [76]. A mechanically-induceddegeneration of the wall internal elastic lamina has also been proposed as the initiatingcause of congenital aneurysm with genetic predisposition and within-wall stresses play anobvious role in aneurysm rupture (leading to the previously mentioned scenarios) [93].

Other factors besides hemodynamics and structural alterations of the vessel wall contribut-ing to the development of saccular aneurysms may be either genetic or externaly acquired,mainly due to infection, trauma, neoplasms, radiation or idiopathic [102].

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 7

Because the wall of an aneurysm gets at certain places extremely thin relative to the parentvessel, it has the propensity to rupture. When this happens, it causes hemorrhage into andaround the base of the brain.

Aneurysm rupture is a biomechanical phenomena that occurs when the mechanical stressacting on the dome exceeds the failure strength of the diseased tissue. Since the internalmechanical loads are exerted by the pulsating nature of blood flow inside the vessel andaneurysm.

As already stated, the aneurysm is the product of multi factorial processes, which lead to agradual plastic dilatation of an arterial segment over years. The aneurysm wall stretches andbecomes thinner and weaker than normal artery walls. Eventually an untreated aneurysmcan rupture. The plastic deformation of the arterial wall is associated with structuralchanges, which leads to rupture. The biggest danger from an aneurysm is its rupture andbleeding into the brain, causing subarachnoid hemorrhage (SAH).

SAH will release blood into the space between the skull bone and the brain. A delayedbut serious complication of subarachnoid hemorrhage is hydrocephalus3. Another delayedpost-rupture complication is vasospasm, in which other blood vessels in the brain contractand limit blood flow to vital areas of the brain. This reduced blood flow can cause strokeor tissue damage, severe neurological complications and possibly death. Bleeding is the lessfrequent (10 15%) but much more severe kind of stroke.

For the risk of rupture, the type of aneurysms is an important factor. Incidentally foundaneurysms tend to have a lower risk of rupture than aneurysms found additional to a rup-tured one. Aneurysms causing symptoms, aneurysms larger than 10 mm, and basilar arteryaneurysms have markedly increased risk of rupture. Because symptomatic aneurysms areoften large size and being symptomatic may not be independent risk factor [84]. For theanalysis of risk of SAH in patients with unruptured aneurysms, the previously cited paperreviewed nine studies, totaling 3907 patient-year and published Table 1.1 which representsa resume of the risk of rupture of aneurysms depending on sex, age, type of aneurysm, site,and size.

1.2.1 Diagnosis and prognosis

Unruptured aneurysms may be discovered when they cause symptoms, which depend inthe location and size of the aneurysm, and they can also yield symptoms secondary tocompression of adjoining structures. Sometimes aneurysms are found when angiography4 isperformed. For example in a case report issued by the Surgical Neurology journal [109],a 45-years-old woman was in good health until she suddenly was admitted at the hospitalwith severe headache. When admitted to the hospital the patient was alert and had nofocal neurological deficits except for mild neck stiffness. A computed tomography (CT) scanshowed a small SAH (Figure 1.3). Cerebral angiography disclosed a peripheral aneurysm in

3Excessive buildup of cerebrospinal fluid in the skull dilates fluid pathways called ventricles that canswell and press on the brain tissue

4Medical imaging technique in which an X-ray image is taken to visualize the inside or lumen of bloodvessels and organs of the body, with particular interest in veins, arteries and the heart chambers

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 8

Table 1.1: Risk of rupture of aneurysms.

Risk of rupture per

Patient-Years No. of 100 patient-years Relative risk

investigated ruptures (95% CI) (95% CI)

Overall 3907 75 1.9 (1.5-2.4)

sex

Male 1027 13 1.3 (0.7-2.1) Ref

Female 1304 34 2.6 (1.8-3.6) 2.1 (1.1-3.9)

Age, y

80 No data

Type of aneurysm

Asymptomatic 1145 9 0.8 (0.4-1.5) Ref

Additional 1997 27 1.4 (0.9-2.0) 1.7 (0.8-3.7)

Symptomatic 463 30 6.5 (4.4-9.1) 8.2 (3.9-17)

Site

ACA 464 5 1.1(0.4-2.5) Ref

MCA 1519 17 1.1 (0.7-1.8) 1.0 (0.4-2.8)

ICA 1449 30 1.2 (0.8-1.7) 1.1 (0.4-2.9)

PC 434 19 4.4 (2.7-6.8) 4.1 (1.5-11)

Size, mm

10 3742 27 0.7 (0.5-1.0) Ref>10 675 27 4.0 (2.7-5.8) 5.5 (3.3-9.5)

Ref indicates category; CI, confidence interval; PC, posterior circulation; and NA, not available

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 9

the hemispheric branch of the left superior cerebellar artery (SCA) (see Figure 1.3a). Theaneurysm measured approximately 3 3.5 mm at its largest diameter with incorporation ofthe hemispheric segment (Figure 1.3b).

Fig. 1.3: a) Oblique view of a vertebral angiography depicting an aneurysmal dilatation of the distalportion of the left SCA (3 3.5 mm (black arrow head). b) A stereoscopic image for a 3D vertebralangiography depicting an aneurysm in the hemispheric branch of the left SCA (arrow head).

Aneurysms can also appear as a result of a traumatic experience, this are referred as intratraumatic aneurysms as reported in the same journal [110]. A 5 years old boy was admittedat the department of neurosurgery of the Ajou University School of Medicine in Suwon,South Korea. The boy had suffered from blunt trauma associated with a motor vehicle-related pedestrian accident. The patient presented a stiporous mental state and had GlasgowComa Scale5 (GCS) score of 6, without localized weakness. CT revealed a small hemorrhagein the corpus callosum and a small SAH at the anterior skull base. A 3D reconstruction ofthe 16channel multiscale CT disclosed neither definitive arterial injury nor any underlyingabnormalities in the intracranial vasculature. One week follow-up CT revealed gradualresolution of the clot. At 2 weeks, the patient showed sudden mental deterioration to a deepstuporous mental state and mild weakness of lower extremities accompanied with a seizureattack. CT revealed then the newly developed aneurysm located in the corpus callosum(Figure 1.4). the aneurysm measured 4.5 5mm on the nonbranching site of right anteriorcerebral artery (ACA).

As shown in the previously mentioned case report, aneurysms are also diagnosed afterrupture. In another very interesting case, a 22 years old male patient was admitted intoa hospital reporting mild head trauma [91]. Magneto resonance (MR) imaging revealed alarge midline sac with no apparent clinical symptoms related to it. Angiographic studiesdiscovered a mural vein of Galen aneurysm malformation (VGAM) which is a congenitalanomaly that often manifest in the neonatal period with apparent congestive heart failure.The VGAM was supplied by a single feeder from the medial posterior choroidal artery(MPChA in Figure 1.5)

5neurological scale which aims to give a reliable, objective way of recording the conscious state of aperson, for initial as well as continuing assessment.

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 10

Fig. 1.4: a) CT scan 2 weeks after trauma reveals an acute hematoma in the genu of corpuscallosum, and dense contrast enhancement (black arrow) near the falx edge in the image. b) thenewly developed aneurysm (withe arrow) on the nonbranching site of the right ACA in the 3Dreconstruction.

Eighty-five percent of saccular aneurysms are found at the CW. Table 1.2 contains a list ofthe places where aneurysm are more often located, taken from [85].

Table 1.2: Predominant locations of intracranial aneurysms.

Artery Percentage %

Anterior communicating artery (ACoA) 30 35

Internal carotid artery (ICA) 30

Posterior communicating, carotid bifurcation andophthalmic artery, and the middle cerebral artery(MCA)

22

Aneurysms of the posterior circulation 810

Of the aneurysms in the posterior circulation (back part of the brain), basilar tip is the mostcommon site of origin. Posterior circulation sites often include the top of the basilar artery,the junction of the basilar artery, the superior or anterior inferior cerebellar arteries, and thejunction of the vertebral artery and the posterior inferior cerebellar artery (see Figure 1.6).

In a more recent publication by Baumann et al. in 2008 [5], a study of ninety-nine patientsoperated on for multiple intracranial aneurysms, between 1994 and 2003 is reported. 90%of the patients had SAH and 10% had incidental aneurysms. An important finding of thispublication is that ruptured aneurysms were significantly larger than unruptured ones andmost of the reported ruptured aneurysms were 10 mm or smaller in size.

1.2. CEREBRAL ANEURYSM, CAUSES AND ITS EFFECTS 11

Fig. 1.5: a) Left vertebral angiography showing VGAM. b) left oblique view of the VGAM

Fig. 1.6: Anatomy of the brain (posterior vs. anterior circulation and CW)

1.2.1.1 Prognosis of intracranial aneurysms

This section is devoted to a forecasting of the probable course and outcome of cerebralaneurysms, especially the chances of recovery. Intracranial aneurysm rupture is the majorcause for subarachnoid hemorrhage, which is the most severe form of stroke. In first worldcountries like USA, stroke will affect more than 750,000 Americans. About 150,000 willdie; many will be left permanently disabled or neurologically impaired. Alarmingly, strokeis the third leading cause of death in the United States, and is the number one cause ofadult disability in the same country. An estimated 3.8 million Americans can attribute theirdisability to stroke.

Form the economical point of view, stroke is also devastating, due to its economical impact.In the USA, for example, more than $30 billion are in direct cost related to stroke.

Recent surveys show that Americans fear stroke more than heart diseases, yet the publicremains dangerously unaware of how this disease is caused, treated and prevented. In fact,

1.3. THERAPY OPTIONS 12

many people resign themselves to the fact that stroke is inevitable. People dont know thatmost strokes can be prevented through risk detection, medical management and life stylemodification.

The occurrence of cardiovascular diseases depends on the subject patho-physiological groundand habits. Major cardiovascular risk factors include:

diabetes

hypertension

hypercholesterolemia

obesity

the familial context (family members with heart diseases)

smoking

Minor cardiovascular risk factors are:

age

high-stress job

sedentary habits

lack of daily consumption of fruit and vegetables

high resting heart rate (beating rate above 75 per minute)

1.3 Therapy options

The traditional neurosurgical treatment of intracranial aneurysms involves craniotomy andclipping to avoid SAH or to stop further bleeding. One of the most important causes ofcomplications or death after aneurysm rupture is recurrent rupture; therefore, it is veryimportant to attempt to seal off a ruptured aneurysm from its parent artery and prevent asecond, often fatal bleeding. A relatively new treatment option for intracranial aneurysmsis the endovascular approach, this technique will be addressed in the following section.

1.3. THERAPY OPTIONS 13

1.3.1 Craniotomy with clipping

To prevent aneurysm rupture, neurosurgeons have traditionally performed open cranialsurgery by opening the skull and directly approaching the aneurysm to place a small clipacross the base of the aneurysm (Figure 1.7). Clips are made of titanium and remain onthe artery permanently. Although the surgical procedure has been extremely effective atsealing the aneurysm, the procedure itself is associated with a significant incidence of deathand complications. General complications related to brain surgery include infection, allergicreactions to anesthesia, stroke, and swelling of the brain. Complications specifically relatedto aneurysm clipping include vasospam, stroke, seizure, bleeding. Besides, an imperfectlyplaced clip, which may not completely block off the aneurysm or blocks a normal arteryunintentionally.

Fig. 1.7: Clip placed across the neck of the aneurysm to prevent blood from entering the dome. Thegoal of surgical clipping is to isolate an aneurysm from the normal circulation without blocking offany small perforating arteries nearby.

In an example of clinical experience, Schirmer et al. [87] references to the clinical experiencefrom a series of ruptured aneurysms treated conservatively (craniotomy) reported by Nish-ioka et al. [86], which demonstrated a 37% risk of rebleeding at 4 weeks and a mortality ratefrom repeated hemorrhage and its sequelae of 34% to 42%. The rate of probable recurrentbleeding after six months was 2.2% per year for the first 9 1/2 years and 0.86% per year forthe second decade. Nishioka et al. [70] reported that rebleeding episodes were fatal in 78%.

Another study of the impact of surgical clipping on short-term and long-term mortalityafter intervention of cerebral aneurysms, carried out in 4619 patients (mean age 54.7 15.3, 66.3% female) by Britz et al. [10], reported that survival in patients with ruptures waslower compared with patients with unruptured aneurysms with ratio of death after clipping40% higher in patients with rupture compared with those that were unruptured. Survivalestimates for unruptured patients who underwent clipping were higher than unrupturedpatients who did not undergo clipping. Finally, this paper states that patients with rupturesand aneurysms who underwent clipping have a higher rate of death compared with the

1.3. THERAPY OPTIONS 14

general population in the long term.

Aneurysms that are completely clipped have low risk of regrowth. However, if the aneurysmhas been partially clipped, patients need to have periodic angiograms to make sure theaneurysm is not growing. The possibility of having a rebleed increases to 35% within thefirst 14 days after the first bleed. This is why neurosurgeons prefer to treat the aneurysmas soon as it is diagnosed, so that the risk of a rebleed is lessened.

Patients with aneurysms who underwent clipping surgery may suffer short-term and/orlong-term deficits as a result of a rupture or the treatment itself. Some of these deficits maydisappear over time with healing and therapy. The recovery process may take months oryears to understand the deficits the patient incurred and regain function. Surgical clippingof unruptered cerebral aneurysm are associated with a higher rate of complications thanendovascular treatment [42].

1.3.2 Endovascular treatment

A minimally invasive alternative to aneurysms clipping is endovascular6 surgery. Endovas-cular techniques are aimed at treating a local wall damage in the heart or blood vessel toprevent initial or repeated SAH. Endovascular interventions are minimally invasive becausethey use natural paths. During the endovascular procedure, a catheter is inserted into asuperficial artery and then advanced under image guidance into the diseased segment of thecardiovascular system. This kind of treatment is necessary in aneurysms at high risk forsurgery.

When Guglielmi detachable platinum coils (GDC) were introduced in 1992, endovasculartreatment started its evolution [33, 85] with the aim of providing a therapeutic alternative.

Surgeons began implanting these tiny helical-shaped platinum coils (caliber of 400 mFigure 1.8) in aneurysms that had ruptured. Since coils were introduced, its technologyhas developed substantially as different manufacturers joined the market with an increasingnumber of products.

Of all the coil properties considered prior to fabrication, biocompatibility is the most impor-tant. A biocompatible one is composed of primarily inert material that allows an effectivetreatment without the concern for a systemic host response [107].

To perform coiling, the coils are inserted within a tiny microcatheter that is placed insidethe patients arterial system through a small incision in the femoral artery in the groin7.The microcatheter is advanced through the arterial system all the way up to and insidethe aneurysm; the platinum coils pass then through the microcatheter and delivered insidethe aneurysm cavity, avoiding rupture and embolism. After applying a very low voltageelectric current, the coil is detached. Several coils can be sequentially used until the cavityis correctly filled up with coils. Once the coils are released and fill the aneurysm, it seals off(occlude) the aneurysm, and the blood trapped inside clots.

6Endovascular, meaning inside a blood vessel, refers to using the bodys extensive network of bloodvessels to access and treat abnormalities.

7The fold or hollow on either side of the front of the body where the thigh joins the abdomen

1.3. THERAPY OPTIONS 15

Fig. 1.8: Microcatheter (shown in blue) deploys platinum coils into the aneurysm until completeocclusion. Coils promote thrombus formation.

When endovascular techniques appeared, also the question about which technique offersmore advantages appeared in the decision making process. The International SubarachnoidAneurysm Trial (ISAT) was a multi center prospective randomized trial of surgery com-pared with endovascular coil treatment of aneurysms, that included annual follow-up for atleast five years. It aimed to compare the safety of an endovascular treatment of rupturedintracranial aneurysms [79]. In 2002 the ISAT was stopped early because it showed thatcoiling, was more likely to result in survival without disability at one year compared to neu-rosurgical clipping. Comparing the long-term results of surgical clipping to endovasculartreatment of aneurysms is a major research initiative today.

Although coiling improved the treatment of intracranial aneurysms, it also has some defi-ciencies that limit its effectiveness. GDCs are not effective for the treatment of wide neckedaneurysms, if neck size is < 4 103 m, aneurysm occlusion is achieved in 57 85% of thecases. However, when neck dimension is > 4 103 m, only 15 35% of the aneurysms areeffectively sealed [73].

Another disadvantage of coiling is the partial recanalization of the aneurysm in the firstmonths after successful procedure [52], as reported also in Grunwald et al. (2006). It refersto a prospective analysis on 211 aneurysms treated with coiling. The main conclusion isthat one in four coiled aneurysms will show recurrence [31].

For patients who present unfavorable aneurysm geometry that might limit endovasculartherapy like MCA aneurysm, endovascular coiling is effective and can be performed withacceptable mortality and morbidity in selected patients [24].

Coils can also herniate into the parent vessel and cause thrombi. If the thrombi travels intothe brain, it may cause an ischemic stroke. To overcome this problem, balloon remodeling,complex-shaped coils and self expandable stents have been developed. The first two ap-proaches represent pure mechanical solutions. Stents, on the other hand, may have a larger

1.3. THERAPY OPTIONS 16

potential than simple mechanical protection against coil herniation by inducing healing ofthe aneurysm, specially in the case of wide-necked aneurysms [3, 58, 88].

Intravascular stents have been widely used in the treatment of arterial diseases, usuallycoronary stents, but their stiffness may eventually cause vessel rupture. When flexibleintravascular stents for aneurysms became available (for example the Neuroform and En-terprise stents), another therapeutic approach became also possible in the endovasculartreatment of intracranial aneurysms.

A study in a series of 26 consecutive patients who underwent angioplasty and stenting incarotid dissection with or without associated pseudoaneurysm, reported in Kadkhodayan etal. [44], shows an eight years retrospective review. Twenty-eight stents were deployed in 29procedures on 27 vessels (20 internal carotid arteries and 7 common carotid arteries). CT,sonography or clinical revision were carried out for a mean of 14.6 months, this was used tocalculate procedural and long-term complication rates. Patients underwent diagnostic cere-bral angiography on a dedicated biplanar neuroangiographic unit (Neurostar: Siemens AG,Munich, Germany) and intracranial images were obtained before and after the interventionsto confirm patency of intracranial vessels. The publication concludes that endovascularstent placement is the treatment of choice for patients with failed medical therapy and maybe recommended in asymptomatic patients. Finally it mentions that the technique is safe,with low rates of schemic complications as demonstrated with long-term clinical and imagingfollow up.

A stent is a flexible cylindrical porous tube made of a mesh of struts (shown in Figure. 1.9)typically from stainless steel or alloys [66].

Stents are subject to intensive study world wide to optimize its efficacy and safety in thetreatment of cerebral aneurysmal diseases. The propose of stents is to prevent aneurysmrupture by reconstructing or rebuilding the damaged section of the intracranial artery frominside.

Fig. 1.9: Saccular aneurysm model and stent placed at the neck. Stent is aimed to reconstruct theparent vessel from which the aneurysm has formed.

1.3. THERAPY OPTIONS 17

The first use of stents in aneurysm treatment have been proposed in 1994 [61], but it is onlyrecently that neuro-surgeons started to use this technique in the treatment of intracranialaneurysms.

It is generally admitted that stents reduce the blood flow within the aneurysm and thustrigger blood coagulation therein [55]. As a result, the aneurysm stops growing in volume.The rupture countdown is stopped, as long as it is occluded by the thrombus. Often thelater is gradually formed and complete healing achieved

Apart from lowering the blood flow into the aneurysm, blood clotting is another way ofmeasuring stent efficiency since it is the key to the aneurysm self-repair. A blood clot, alsocalled thrombus, consists of a plug of platelets enmeshed in a network of insoluble fibrin.Clotting is sensitive to the red blood cells behavior, hence the non-Newtonian features of theblood. Indeed, the blood clotting process, clinically observed in stented aneurysms, revealsthe strong dependency of the increase of viscosity with small shear-rate flows.

In first-case reports and case series reported in the literature, stents were mainly used incombination with coils to treat aneurysms that were difficult to treat with coils only. How-ever, experimental studies have also shown that use of stents alone, even without coilsmight hemodynamically uncouple the aneurysm from the parent vessel, leading to throm-bosis of the aneurysm. Vannien et al. described their observations of broad-based saccularaneurysms that showed a spontaneous thrombosis after stent placement only [99].

A disadvantage of stents is that they cause thrombosis and stimulate platelet aggregationinside the main vessel as soon as they are exposed to the blood of the patient [103]. Thedanger of thrombogenesis can be lowered using prophylactic antiplatelet therapy with aspirinand plavix (or an equivalent) during 3 day before stenting in the case of elective treatment.For acute SAH patients, in which the risk of stent thrombogenic reaction is higher, theantiplatelet therapy with aspirin is administrated intravenously, and clopidrogel via gastrictube during the stenting procedure. Additionally, vasospam can be treated with intraarterialnimotop, and acute stent thrombosis with GP IIa/IIIb-antagonists [104].

Although it has been reported that treatment of ruptured aneurysms in a dissecting ver-tebral artery8 with single or double stent placement ends up with total occlusion aftersome time, the effects of endovascular stenting on aneurysmal flow alterations are poorlyunderstood. Control angiography performed three days after stent placing revealed begin-ning aneurysmal thrombosis. Substantial reduction in aneurysmal size was observed after,whereas total occlusion was observed after 3 months without technical complications norneurologic sequelae were observed [7, 23].

Vannien et al. documented three patients with broad-based saccular intracranial aneurysmsin whom aneurysm thrombosis occurred after stent placement alone, with out additionalpacking of the aneurysms with coils. The major finding of the work by Vanien was thefact that coil packing after stenting may not always be necessary during the same ther-apeutic session in small intracranial lateral aneurysms, where the stent alone may leadto spontaneous intra-aneurysmal thrombosis weeks after the procedure. Anticoagulationand antithrombotic medications are generally considered contraindicated immediately after

8Vertebral artery dissection is the development of dissection (a flap-like tear) in the vertebral artery

1.4. MOTIVATION OF THE PRESENT THESIS 18

acute subarachnoid hemorrhage, before the aneurysm is secured. On the other hand, an-tithrombotic medication is considered necessary after the deployment of metallic stents toprevent stent thrombosis and distal thromboembolic complications [99].

The previous examples suggest that when stents are placed at the neck of an aneurysm, theyalter the blood flow pattern inside the aneurysm and reconfigure the shear stress in such away that it may lead to aneurysm thrombosis [103]. In several practical experiences, its highdegree of efficacy has been substantiated. Stents for cerebral aneurysms have transformedthe interventional neurology.

The velocity reduction in the aneurysm resulting from the presence of the stent has beenproposed as a first indicator of its efficiency. Velocity reduction relies on both the geometryof the aneurysm and the structure design of the stent. The efficiency of stent treatmentdepends on several parameters and this thesis is aimed to understand them better usingcomputer simulations.

1.4 Technical motivation and background for the present work

Since the late 1950s, computational fluid dynamics (CFD) has played a major role in thedevelopment of more versatile and efficient aircraft. It has now become a crucial enablingtechnology for the design and development of flight vehicles [2]. Since then, many otherapplications of CFD in science and engineering, among others including the potential to bealso applied in cardiovascular interventions.

As already suggested, the genesis, progression, and rupture of cerebral aneurysms are notwell understood. The evolution of an aneurysm is affected by several factors, including theintra-aneurysmal hemodynamics. It is believed that these factors are important in boththe pathogenesis and thrombosis of cerebral aneurysms. Alteration of hemodynamics inaneurysm models by stenting has already been studied both experimentally and numeri-cally. Aneurysm rupture is a biomechanical phenomenon. Since the internal mechanicalloads are exerted by the pulsating nature of blood flow inside the vessel and aneurysm, thehemodynamics of aneurysms is a key issue in the study for the characterization of the biome-chanics of aneurysms. The understanding of the causes of such malformations and of theeffects of available treatment strategies is improved qualitatively by numerical simulationsof the blood flow using CFD [8].

In the investigations by Baruch et al. [55], flow patterns inside wall aneurysm models werestudied under two different hemodynamic conditions and the influence of stent porosity wasalso investigated. Pulsatile flow patterns in an experimental flow apparatus were visualizedusing laser-induced fluorescence of rhodamine dye.

Computer-aided simulation of intravascular devices allows to easily test different geometriesand structures, with an important requirement: it must be adaptable to unsteady conditionsinduced by cardiac pulsation.

1.4. MOTIVATION OF THE PRESENT THESIS 19

Stents are intravascular medical devices used with higher efficacy than craniotomy or coiling.Today, the stents are subject to intensive study world wide to optimize its efficacy andsafety in the treatment of cerebral aneurysmal diseases. The propose of stents is to preventaneurysm rupture by reconstructing or rebuilding the damaged section of the intracranialartery from inside.

The risk of rupture of fusiform abdominal aortic aneurysms is currently assessed by itsmaximum caliber. Numerical simulations are performed to display the stress field at theaneurysm wall as well as within the aneurysm wall to assist the clinicians. When theaneurysm transverse size exceeds the critical value of 5 cm, abdominal aneurysm repairs useeither open surgery or an endovascular graft technique.

CFD in real geometry is nowadays carried out to give insight of the hemodynamical factorsleading to arterial degradation and subsequent aneurysm formation, as well as aneurysmrupture. This is consistent with an editorial issued in the AJNR American Journal ofNeuroradiology, in which two major tracks are mentioned regarding the study of CFD appliedin aneurysm treatment. The first one is basically what is mentioned above. The secondis to predict the hemodynamics for a specific patient and to predict the flow to assist thephysician in making the optimal therapeutic choice [65]. This thesis adds another track forthe application of CFD towards the study of intravascular treatment of cerebral aneurysm,it is through the simulation and study of stents in CAD models, because it allows thequantification of different parameters (velocity, WSS and pressure) and the efficacy of stentsdesigns when comparing unstented models and virtually treated models using different stentdesigns.

This thesis presents the idea of testing different models of helical stents virtually placed atthe neck of aneurysm models. The stents are modeled as struts with circular transversalsection, the diameter of the stent corresponds to the diameter of stents used in previousstudies.

In order to achieve realistic behavior of blood, a pulsating pressure wave was used at theinlet boundary condition, but results obtained at steady state are also presented.

Focusing on reducing time in CAD modeling, meshing and computing time to make stentmodeling more attractive for the medical community this thesis present result in stentsmodeled as layers of porous material. This can be justified by the fact that stent deploy-ment is done nowadays in a practical manner, making it very difficult for interventionalneuroradiologists to control the position of the struts relative to the aneurysmal neck. Evenwith the modern 3D reconstructions, the working views on the road map remain 2D withonly preprocessed images helping to virtually predict where stents or coils will lie in theanatomy or suggesting the anatomical relationship of implanted stents [45, 38]. It may notbe necessary to carry out numerical simulation in resolved stents, which implies time con-suming pre and post processing of the computations. Rather it is recommended to carryout simulations using porous media layers attached to the parent vessel to represent thestents.

1.5. OUTLINE OF THIS THESIS 20

1.5 Outline of this thesis

In an attempt to cover all aspects related to the hemodynamics in stented aneurysms, thisthesis is divided into six chapters, devoted to subjects of increasing clinical relevance, eachbuilding upon the technical and qualitative knowledge presented in the preceding ones asfollows.

In the next chapter, the physical background, governing equations of blood flow, and CFDare presented. Chapter 2 presents also the basics of the physical aspects of the cardiovascularsystem with focus on hemodynamics. Fourier transform (FT) as a tool for the numericalrepresentation of the cardiac wave form is also given. Finally, the computational tools usedin this thesis are discussed.

Chapter 3 starts with the numerical simulation of hemodynamics in threedimensional mod-els of real aneurysms. This chapter is devoted exclusively to real aneurysms, also calledpatient specific models because the geometry on which simulation is performed is obtainedat a clinic during the examination of the patient. CT scanning was the technique used fordata acquisition of two aneurysms detected in two patients. Later translated onto a tetra-hedral computational grid, which was suitable for computations. The results are validatedby comparison with published data.

Chapter 4 is dedicated to a comparison of numerical simulations of intraaneurysmal bloodflow which have undergone virtual stenting as treatment. It deals with an idealizedmodel of lateral aneurysm that is located in an intracranial curved vessel, the model isbased on a real aneurysm. Three different helical stent designs are simulated. These stentshave different porosities as result of different pitch angles between adjacent struts. A novelapproach for time-effective simulation of stents is presented in this work, in which stentsare simulated as layer of porous material. Comparison of hemodynamic changes insidethe aneurysms prior to and after stenting are given along with a comparison of the stentplacements performance in terms of lowering the aneurysm wall loads (WSS and pressure).

Chapter 5 is dedicated exclusively to evaluate the performance of the porous stent approach,now in a geometrically idealized model of a saccular aneurysm of the CW. The performanceof two different porous stents is compared. Porous stents are modeled as hollow tubes andplaced inside the parent vessel where the saccular aneurysm is found. For comparison,a stent-over-stent is also introduced inside the first stent and hemodynamic changes areevaluated. A study based on passive tracer (contrast media) is also presented in this chapter.

The last chapter contains conclusion is drawn from the results of this numerical study. Anoutlook is then given, as well as a set of recommendations on what to look at in futureworks in the field of numerical simulation of the effects of cardiovascular stents.

2

Hemodynamics modeling

2.1 Governing equations

The development of computational methods to solve nonlinear partial differential equationshas a history of over 70 years. In particular, fluid flow simulations involving mass, momen-tum, and energy balances, typically formulated as partial differential equations (PDEs), butsometimes also as integral or spectral relations.

The continuity and momentum equations can be put in the following PDE form, when theflow is incompressible

Uixi

= 0 (2.1)

(

Uit

+ UkUixk

)

= Pxi

ikxk

(2.2)

In these previous equations, Ui represents the velocity vector, the constant density of thefluid , P the pressure, t the time, ik is the molecular momentum transport tensor and xi isthe coordinate vector. In the case of Newtonian fluids, the stress tensor (ik) reflecting theaveraged exchange of molecular momentum is proportional to the strain-rate tensor

ik = (

Uixk

+Ukxi

)

(2.3)

21

2.1. GOVERNING EQUATIONS 22

where represents the molecular viscosity. Substituting equation 2.3 in equation 2.2, as-suming = is constant and simplifying, the Navier-Stokes (N-S) equations for isothermalflows of incompressible Newtonian fluids results

Uit

+ UkUixk

= 1

P

xi+

2Uixkxk

(2.4)

Here represents the kinematic viscosity. Both equations, 2.1 and 2.4, form a closedsystem of coupled partial differential equations.

The Navier-Stokes equations can not be solved analytically in most cases. It is then necessaryto reduce the continuity PDEs to a discrete finite set of points and hemodynamics quantityvalues. CFD approximately solves the Navier-Stokes equations and there are several dis-cretization techniques to solve numerically this equations. The following section provides anoverview of the discretization technique known as finite volume method (FVM), because itis among the most important and more widely used, and because this method is used in thesoftware applied on the present simulations. This method is in fact based on integral repre-sentations of the conservation equations and then provides for exact conservation of mass,and momentum. If properly applied, this method gives increasingly better approximationsto the actual solution of N-S equations as the number of node points increases [93].

2.1.1 Finite volume method (FVM)

The finite volume method technique discretizes the integral formulation of the conservationlaws directly in the physical space. Its generality, its conceptual simplicity and its ease ofimplementation makes FVM the most widely applied method in CFD. This method can beimplemented in arbitrary grids, structured as well as unstructured [18]. One of the mostimportant features of FVM is their flexibility for unstructured grids. This method is basedon cell-averaged values of hydrodynamic fields like pressure and velocity, which are the mostfundamental quantities in CFD. This makes the FVM different from the finite difference andfinite element methods, in which the main numerical quantities are the pointwise local valuesof the same fields at the mesh points [36].

A grid has to be generated in which a local finite volume also called control volume isassociated to each mesh point (see Figure 2.1). The integral conservation laws are thenapplied to this local volume. This makes a distinction from the finite difference approach,where the discretized space is a set of small cells, one cell is being associated to one meshpoint.

In FVM the conservation of all variables is enforced across the control surfaces. It meansthat when a specific quantity of a conserved variable is transported out of one controlvolume, the same quant