Master thesis Development of a Computational Fluid Dynamics pipeline for patient-specific cerebral aneurysms

Transcription

1 Master thesis Development of a Computational Fluid Dynamics pipeline for patient-specific cerebral aneurysms C.W.C. Stasse August 10, 2007 BMTE07.26 graduation committee: prof. dr. ir. F.N. v.d. Vosse prof. dr. ir. B.M. ter Haar Romeny dr. ir. P.H.M. Bovendeerd advisors: ir. G. Mulder ir. R. Hermans Eindhoven University of Technology Department of Biomedical Engineering

2 2

3 Abstract A cerebral aneurysm is a local dilatation of the arterial wall in the brain. Almost half of all patients with ruptured cerebral aneurysms dies in the first month after rupture. Aneurysm formation is hypothysed to be a consequence of hemodynamically generated forces working on the arterial wall leading to degeneration of the media. When an aneurysm is diagnosed, the risk of rupture versus the risk of treatment needs to be assessed. Currently, aneurysm size is the main criterium. This criterium is not sufficient and new methods to assess the risk of rupture need to be found. Since hemodynamic forces play a role in aneurysm formation and development, a Computational Fluid Dynamics (CFD) pipeline for patient-specific aneurysms is developed. Two cerebral aneurysm geometries are used for this purpose, both supplied by Philips Medical Systems. The first, a geometry based on a model of a lateral saccular aneurysm is used to develop the pipeline. A second geometry is based on a realistic model of an internal carotid artery with a terminal aneurysm and is used to improve and evaluate the pipeline. Both geometries need additional inlet sections, which are added using the Vascular Modeling ToolKit (VMTK). This software is especially designed to manipulate 3D vascular geometries for CFD. Centerlines of the geometries are also obtained with this software. Meshes are generated with NETGEN, which uses tetrahedral elements and can be used for complex geometries. An simplified version of a real pulsatile flow is the input for the flow simulations, which are performed in SEPRAN. A method allowing for standardized visualization of intra-aneurysmal flow is developed. With the method, a plane is created using two centerline points in the parent artery and the top of the aneurysm dome. This plane forms the basis for the creation of several parallel and perpendicular cross sections, used for the visualization of the velocity data. The data is visualized with vectors representing the in-plane velocity and contours representing the absolute in-plane velocity, the out-of-plane velocity and the vorticity. The resulting flow patterns in the idealized geometry show that the flow bends towards the outlet after entering the dome, without the formation of a counterclockwise vortex. Such a vortex was expected based on previous work done with the original model. Flow patterns in the patient-specific geometry were very similar. In conclusion, a pipeline has been developed for CFD, although flow simulation still requires an experienced user to determine mesh properties, boundary conditions and visualization options. 3

4 4

5 Contents Abstract 5 1 Introduction 7 2 Physiology and pathology Physiology of the cerebral arterial system Pathology of cerebral aneurysms Mesh generation Geometries Preprocessing Meshing NETGEN Element conversion Mathematical and CFD model Mathematical model CFD model Data visualization Introduction Idealized geometry ICA geometry Data extraction Results Idealized geometry ICA geometry Discussion 45 8 Conclusion and recommendations Conclusion Recommendations Appendix 49 A VMTK protocol 49 5

6 B NETGEN protocol 53 6

7 Chapter 1 Introduction 7

8 An arterial aneurysm is a local dilatation of the arterial wall. Aneurysm formation is hypothysed to be a consequence of hemodynamically generated forces working on the arterial wall leading to degeneration of the media. This focal degeneration typically occurs at curved arterial segments and at the apex of bifurcations[1]. In the cerebral arterial system aneurysms are most commonly located at the branching points of the circle of Willis[2]. Most of these aneurysms have a saccular shape. The rupture of aneurysms causes over half of all cerebral hemorrhage. Intracranial aneurysm rupture leading to cerebral hemorrhage has a mortality rate of 45% after 30 days. Half of the survivors sustain irreversible brain damage and reoccurrence of hemorrhage is likely if the aneurysm remains untreated[3]. The mean age for cerebral hemorrhage is about 55 years for both males and females and the incidence is slightly higher in males than in females[4]. Risk factors for cerebral hemorrhage include age, hypertension, diabetes, smoking and stress[5]. Autopsies revealed that 25% of the population above 55 years have undetected intracranial saccular aneurysms[6]. In patients where aneurysms are detected, the average annual risk of rupture is 2%. For asymptomatic aneurysms with a diameter of 10 mm or smaller, which is most common, this decreases to below 1%. Symptomatic aneurysms and aneurysms with diameters larger than 10 mm have an increased annual risk of rupture of respectively 8% and 5%[7]. Aneurysms are most frequently diagnosed using visualization modalities such as CT scanning and MR imaging. Upon detection, the risk of rupture versus the risk of treatment needs to be evaluated. Currently, aneurysm size is the main criterium in deciding whether an aneurysm needs to be treated. Treatment options are endovascular coil embolization, surgical clipping and more recently stenting. Coil embolization consists of filling the aneurysm with a platinum coil to decrease blood circulation and promote thrombus formation in the aneurysm. This procedure may be preceded by stenting of the parent artery, especially in wide-necked aneurysms. Clipping consists of placing a clip around the aneurysm neck, preventing blood from flowing into the aneurysm. The choice of treatment depends on the individual risk assessment of each aneurysm, including factors like the patient s condition and characteristics of the aneurysm like location, size and shape[8]. Aneurysm rupture has been associated with aneurysm growth[9]. There are two often used and interconnected mechanisms for aneurysm growth. The first mechanism consists of apoptosis of the smooth muscle cells driven by the wall shear stress (WSS) and originating from the endothelium. Loss of these cells results in a decrease of vascular tone, which is the constriction of the artery relative to the maximum dilated state. The second mechanism consists of the remodelling of the artery due to constant pressure induced tension. This leads to remodeling of the elastine and collagen fibers in the media[10]. Risk assessment based on the critical size of an aneurysm is a topic of controversy, since there is no clear definition of the critical size. Therefore, new methods of risk of rupture assessment need to be developed. Since flow related properties like WSS and pressure are associated with aneurysm growth, it is logical to examine flow in patient-specific aneurysm models. In this project a pipeline for Computational Fluid Dynamics(CFD) in patient-specific cerebral aneurysms is developed for this purpose. In chapter 2 an introduction to the physiology of the cerebral vasculature is given, followed by the pathology of aneurysms. Chapter 3 starts with the preparation of 3D geometry data containing aneurysms. Two geometries are used for the CFD pipeline development in this project. The preparation of the geometry is needed for the meshing process which is the main part of chapter 3 as well as for the flow simulation as described in chapter 4. In this 8

9 chapter a mathematical model and a CFD model are defined. In chapter 5 a standardized process for the visualization of the simulation results is described. The results of the CFD and visualization procedures are presented in chapter 6. 9

10 10

11 Chapter 2 Physiology and pathology 11

12 2.1 Physiology of the cerebral arterial system Blood reaches the brain through the vertebral and the internal carotid arteries as displayed in figure 2.1. The internal carotid arteries mainly supply the cerebrum and the vertebral arteries merge to form the basilar artery that supplies the remainder of the brain. The circle of Willis connects the internal carotid arteries and the basilar artery. The connecting vessels are the anterior cerebral and communicating arteries and the posterior cerebral and communicating arteries. The diameters of these arteries are approximately 2.35 and 2.1 mm for the anterior and posterior cerebral arteries respectively and 1.45 mm for the communicating arteries[11]. The diameter of the internal carotid artery is about 5 mm[12]. The circle of Willis is located at the base of the brain and provides a more uniform blood supply to the brain. It also acts as a safety margin if an occlusion occurs at a location in the circle of Willis due to thrombosis, atherosclerosis or hemorrhage related vasospasms. In this case, blood supply to the affected region of the brain can still be maintained[13]. Anterior communicating artery Internal carotid artery Anterior cerebral artery Middle cerebral artery Posterior cerebral artery Basilar artery Posterior communicating artery Vertebral artery Figure 2.1: The circle of Willis[13] The vessel wall of cerebral arteries has largely the same structure as a systemic arterial wall (figure 2.2). The wall consists of an intima, media and adventitia. The intima consists of endothelial cells and internal elastic lamina. Smooth muscle cells and elastin and collagen fibers make up the media. The outer layer, called the adventitia, is mostly collagen fibers and fibroblasts. Characteristics specifically for cerebral arteries are a well developed internal elastic lamina, few elastic fibers in the media, a thin adventitia, no external elastic lamina separating the media from the adventitia and a smaller wall-to-lumen ratio[14, 15, 13]. The pulsatility of the flow in the circle of Willis depends on the elasticity of the arteries. The flow pulse is the summation of a constant and the pulsatile flow. Flow rate minima and maxima vary approximately between 2.0 and 3.5 ml/s for anterior cerebral arteries and between 1.5 and 2.5 ml/s for middle cerebral arteries[17]. For the internal carotid artery the 12

13 Figure 2.2: Cross section of an arterial wall[16] minimum and maximum flow varies between 2.0 and 11 ml/s[18]. 2.2 Pathology of cerebral aneurysms Intracranial saccular aneurysms are local dilatations of the arterial wall. The process of aneurysm formation and development is not well understood, but hemodynamic factors play an important role[19]. Sustained hemodynamic stresses, especially high blood flow, result in outward remodeling. This adaptive process reduces the wall shear stress in response to a chronic increase in blood flow. Changes in blood pressure and metabolism are also considered factors in aneurysm formation[20]. Saccular aneurysms can be encountered in different locations in the circle of Willis, especially near or at bifurcations. In figure 2.3 three saccular aneurysms are shown at different positions in respect to the parent artery. The geometry of the aneurysm can be described by several characteristic dimensions. These dimensions are the orifice size(l), the neck width(n), the dome width(w), the dome semi-axis height(s) and the dome height(h) as shown in figure 2.4. Characterization of the shape of an aneurysm can be done by determining ratios like w/n, h/n, w/h and h/s. In a study by Parlea et al. (1999) the ratio between dome width and dome height, w/h, was found to have an mean value of 1 for aneurysms in the circle of Willis, indicating that the average intracranial aneurysm has a spherical shape. In figure 2.4 this value and other mean values for various ratios are given for simple-lobed aneurysms on different locations in the circle of Willis[22]. 13

14 A B C Figure 2.3: Saccular aneurysm positions: Lateral(A), Bifurcation(B), Terminal(C)[21] Figure 2.4: Saccular aneurysm dimensions and ratios[22]. 14

15 Chapter 3 Mesh generation 15

16 Computational Fluid Dynamics (CFD) is a widely used technique to simulate blood flow in patient-specific vascular geometries[10, 23, 24, 11, 17]. The technique starts with the acquisition of the patient-specific geometry. There are various ways of obtaining vascular geometries from patients, such as 3D rotational angiography[23], ANGUS[25], MR angiography[24] and multi-slice CT angiography[26]. From this data 3D vascular geometries can be reconstructed and exported as a surface, usually defined by a collection of data points in various file formats. The surface might need some additional preparation, which is called preprocessing. The next step in the CFD process is the subdivision of the 3D geometry into small elements. This is needed for the final step, which is the flow simulation itself. In this chapter the preprocessing and meshing of the geometries is discussed. 3.1 Geometries Several geometries obtained with 3D rotational angiography were provided by Philips Medical Systems(PMS). The files, containing point data which form the geometry surfaces, were provided in the STL format. The geometries ranged from a simple idealized artery to a complex vascular structure (figure 3.1). Both lateral and terminal aneurysms were available. Two of the geometries were selected for this project. The geometry in figure 3.1A is a reconstruction of a real 3D model used previously for Particle Image Velocity(PIV) measurements[27]. In the same project a flow simulation has been made using a mesh made in PATRAN with the same dimensions as the model (figure 3.1A). Results from this simulation can be used to evaluate the results from this project. Because of the simplicity of this idealized geometry, it was chosen as a basis for the development of the CFD pipeline in this project. The parent artery has a diameter of 4 mm, the dome height and width are both 8 mm and the semi-axis height is 3 mm. The dimension of the neck width is 7 mm. The geometry in figure 3.1B is used to validate and expand the CFD pipeline. It is reconstructed by PMS from a scan of a model produced by Elastrat. The model is a realistic resemblance of a right internal carotid artery (ICA) with an aneurysm and will be referred to as the ICA geometry. The terminal aneurysm has a parent artery with two outlets. The diameter of the inlet artery is 4 mm and the dome height and width are 11 and 13 mm respectively. The semi-axis height is 5 mm and the neck width is 10 mm. 16

17 A B inlet aneurysm C D Figure 3.1: Several vascular geometries containing aneurysms were considered; (A) An idealized lateral aneurysm on a parent artery with one outlet. The smaller figure is the model it is based on. (B) A terminal aneurysm on a parent artery with 2 outlets. (C) A terminal aneurysm on a parent artery with multiple inlets and/or outlets. (D) A lateral aneurysm on a parent artery with part of the intracranial vasculature attached. 3.2 Preprocessing The geometry is preprocessed with a software package called the Vascular Modeling ToolKit(VMTK)[28]. VMTK is especially developed to manipulate 3D vascular structures for CFD. Appendix A contains a step by step protocol for preprocessing in VMTK. Four steps can be distinguished: Clipping: In case of complex vascular geometries the geometry is clipped in order to extract the aneurysm with it s parent artery. This is necessary to reduce computation time and avoid computer memory problems. The distal part of the parent artery of the idealized geometry can largely be clipped (figure 3.3A). The proximal part is left virtually intact to ensure a natural inflow in the aneurysm. However, a small strip is clipped such that the inlet surface is perpendicular to the artery. This is required for the addition of extensions. Smoothing: If a geometry displays local irregularities, mostly due to the density of the point data, smoothing is necessary. In VMTK smoothing can be controlled with a cut-off 17

18 value for a low pass filter and a value for the number of iterations the filter is used. Smoothing too much will result in deformation of the geometry, therefore the original and smoothed geometry should always be compared with each other. Both the idealized and the ICA geometries (3.2) have been lightly smoothed to remove possible irregularities. A B Figure 3.2: (A) Bottom view of the ICA model prior to smoothing. (B) Bottom view of the ICA model after smoothing. Adding extensions: Inlet extensions need to be added for both geometries(figure 3.3). The length of the inlet extension is not arbitrary, which is also discussed in the next chapter. An additional advantage of the extensions, is that a circular inlet surface is created. This is convenient for the definition of the inlet flow, defined in the next chapter. The length of the outlet extension can be kept as short as possible to reduce computation time. An extension is also added to the outlet of the idealized geometry. This was done to improve the smoothness of the mesh in the outlet region. For the ICA geometry, no extensions were added to the outlets because it did not have a positive effect on the mesh generation. When VMTK creates extensions, it automatically generates a centerline through the parent artery. The centerline is the path between the center points of the original inlet and outlet(s), were the centerline data points are defined as the subsequent centerpoints of maximal inscribed spheres throughout the artery. Extensions are added based on the direction of the centerline at the geometry inlet and outlet(s). The centerline data can be exported and are essential in the visualization of the simulation results. Capping: Finally, the inlet and outlet(s) are capped. The geometries now have inlet, outlet and wall surfaces. In the next chapter these boundary surfaces are used to define the boundary conditions for the flow simulation. 18

19 outlet inlet A B outlet1 outlet2 inlet C D Figure 3.3: Addition of extensions to the geometries; (A) Clipped idealized geometry. (B) Extended idealized geometry. (C) Clipped ICA geometry. (D) Extended ICA geometry. 3.3 Meshing NETGEN The geometries are meshed using NETGEN [29]. NETGEN is a mesh generator suitable for complex geometries. It uses tetrahedral elements, which are either linear 4-noded or quadratic 10-noded elements. In appendix B a protocol for the mesh generation of vascular geometries with NETGEN is given. The mesh generation can be manipulated through various mesh parameters. The main parameters are STL-chart distance and mesh-size grading. The first parameter defines the approximate overall edge size of the surface elements. The second parameter determines what size difference the edges of adjacent elements can maximally have. For curved geometries these parameters can typically be used by first choosing the overall rib size needed for the surface area with the largest curvature. Next, the grading parameter is applied to allow for larger elements in less curved areas and smaller elements in highly curved areas. Both geometries are meshed with 10-noded quadratic elements. For the idealized and ICA geometry and elements were used respectively (figure 3.4). 19

20 A B Figure 3.4: 3D Mesh of (A) the idealized geometry and (B) the ICA geometry, using and tetrahedral elements respectively Element conversion The 10-noded quadratic elements produced with NETGEN cannot be used by the flow simulation software SEPRAN, since SEPRAN needs 15-noded quadratic elements. Therefore Matlab is used to make the conversion. For each of the four element surfaces in the 10-noded element an extra node is created in it s center of gravity. Together with an extra node in the element s center of gravity this makes 15 nodes in total. In figure 3.5 the creation of 2 nodes on the element surface is shown. SEPRAN requires a prescribed sequence of the nodes in each element. Since the nodes in NETGEN elements have a different sequence, a renumbering process is also included in the Matlab element conversion program. The meshed geometries are now ready to be used for flow simulations in SEPRAN. 20

21 A B Figure 3.5: Conversion of the 10-noded element(a) to a 15-noded element(b), using the center of gravity of the element surfaces. 21

22 22

23 Chapter 4 Mathematical and CFD model 23

24 4.1 Mathematical model The Navier-Stokes equations need to be solved for each element in the geometry. incompressible Newtonian flow the equations are: For an ρ( δ u δt + ( u ) u) = p + µ 2 u (4.1) u = 0 (4.2) Solving these equations in a meshed geometry is referred to as finite element modeling (FEM) and it requires a definition of boundary conditions and fluid properties. The shape of a realistic flow pulse representing the flow in the internal carotid artery is given in figure 4.1. The pulse consists of a stationary and a pulsatile component. The flow pulse used as inlet boundary condition for this project has a stationary and a sinusoidal pulsatile component as is displayed in figure 4.2. Implementation of a more realistic pulse was not realized due to time limitations, but for the purposes of this project the pulse was considered sufficient. In the PIV experiments and CFD analysis in [27] a stationary or mean flow, q mean, of 3.6 ml/s was used. Based on literature findings the height of the pulsatile component was defined as 0.7q mean. This results in a maximum flow, q max, of 4.9 ml/s and a minimum flow, q min, of 2.3 ml/s. These values will also be used in this project, since they are in the range given in section 2.1. Incompressible Newtonian flow can be characterized by the Womersley and Reynolds numbers, α and Re, derived from the dimensionless Navier-Stokes equations. The Reynolds number defines whether the flow is laminar or turbulent. According to (4.3) the Reynolds number for the flow in both geometries is 240. Therefore, the flow is considered laminar for both situations[30]. The Womersley number defines the ratio of the instationary forces and the viscous forces and is defined in (4.4). The density of blood, ρ, is 1060 kg/m 3 and the dynamic viscosity, µ, is 3.5 mpa/s. If a heartbeat of 75 beats per minute is assumed, the characteristic timescale, ω, is 8. With a radius of 2 mm this gives a Womersley number of approximately 3 for both the idealized and the ICA geometry. This value indicates that the flow will assume a Womersly profile if it is fully developed. The entrance length is defined by (4.5) and is about 5 cm. This means the flow in the parent arteries can not be considered fully developed as is generally the case in blood vessels[30]. Because the flow profile is not known at the entrance of the tube and the flow is not fully developed, a parabolic flow profile is used as an approximation. Re = ρu maxr µ (4.3) ρω α = r µ (4.4) L e = O( rre α 2 ) (4.5) 24

25 At the outlet stress free flow is imposed. In case of the ICA geometry this will have an effect on the flow fractions exiting both outlets. For an in vivo situation, the flow fractions will be determined by the resistance of the complete vascular structure distal of the aneurysm. The correct ratio of the flow fractions and the effect it has on the flow in the aneurysm itself is not considered in this project. The geometry is considered rigid and at the wall the no-slip condition is imposed, meaning that all velocity components are zero. max stationary component min Figure 4.1: Shape of the flow pulse in the internal carotid artery[17]. flow [ml/s] time [s] Figure 4.2: Three cycles of the flow pulse, consisting of a stationary and pulsatile part. 25

26 4.2 CFD model The 15-noded quadratic elements are of the Crouzeix Raviart type, which uses a discontinuous pressure interpolation. As mentioned in section (4.1), three cycles of the flow pulse are simulated. The third cycle is assumed to provide flow patterns representative for additional cycles and is used for flow visualization. The Navier-Stokes equations are solved for 31 time increments per cycle. The solution for each step is obtained using an iterative solving method with an incomplete LU decomposition preconditioner. 26

27 Chapter 5 Data visualization 27

28 5.1 Introduction As mentioned before, the aim of this project is to create a CFD pipeline for patient-specific aneurysm models and a flow visualization procedure that can be applied in any such geometry. The basic procedure is developed using the idealized geometry and expanded using the ICA geometry. Although 3D visualizations of flow in 3D geometries are helpfull, quantification of intraaneurysmal flow patterns requires 2D cross sections. These cross sections can be used to plot various flow properties. In this project, in-plane velocity(ipv), absolute in-plane velocity(aipv), out-of-plane velocity(opv) and the vorticity are considered. IPV is a 2D vector indicating the direction and magnitude of the velocity in the cross section. However, the magnitude is more clearly visualized by the AIPV, which is the absolute value of the IPV. The OPV is the magnitude of the velocity component perpendicular to the cross section. The vorticity is the gradient of the 2D velocity field and can be used to characterize the rotation of the velocity field. All visualizations are produced using Matlab. 5.2 Idealized geometry For a symmetric geometry the logical choice would be to create cross sections parallel to and through the planes of symmetry. The centerline and a central point in the aneurysm are used to define a plane through the aneurysm and the parent artery. The centerline is available from the geometry preprocessing as described in section 3.2 (figure 5.1). Figure 5.1: The idealized geometry with centerline as viewed in VMTK. Since we are only interested in the flow in the aneurysm and a small part of the parent artery, the proximal and distal parts are cut off perpendicular to the centerline. This is done by manually selecting points on the centerline that are as close to the aneurysm as possible, without cutting off any of the aneurysm datapoints. The aneurysm s center of gravity is a good point to use as a central point for the definition of cross sections in the geometry. However, obtaining this point is not easy and a more convenient point, the top of the aneurysm 28

29 dome, is manually selected for the same purpose. For a symmetric geometry, like the model that forms the basis for the idealized geometry, the top of the dome is positioned on two planes of symmetry. The plane defined by both cut-off points and the top of the dome is used as a basis for the flow visualization (plane 2 in figure 5.2A). The plane is rotated such that it is in the xy-plane with the cut-off points on the x-axis. After translation of the proximal cut-off point to the origin, additional parallel planes for cross sections are defined at an arbitrary distance of 1.6 mm on either side of the first plane. The resulting planes are displayed in figure 5.2A. A plane perpendicular to plane 2 through the top of the dome gives the second main visualization cross section (plane 5 in figure 5.2B). Again additional cross sections, perpendicular to plane 5, are made at a distance of 1.6 mm A B Figure 5.2: Two sets of three parallel planes are used for the visualization. (A) Plane 2 goes through the two cut-off points and the central point. Planes 1 and 3 are parallel and equidistant to 2. (B) Plane 5 also goes through the central point, but is perpendicular to plane 2. Planes 4 and 6 are parallel and equidistant to ICA geometry The centerline obtained in VMTK is displayed in figure 5.3. For the patient-specific geometry two cut-off points are chosen on the outlet centerlines. The inlet section of the parent artery is also shortened by selecting a point on the centerline. The distance between planes has been doubled to 3.2 mm. The rest of the visualization procedure is the same as for the idealized geometry. The resulting datapoints and planes are shown in figure

30 Figure 5.3: The ICA geometry with centerline as viewed in VMTK A B Figure 5.4: (A) Planes 1, 2 and 3. (B) Planes 4, 5 and 6. 30

31 5.4 Data extraction Dataslices are extracted from the geometries based on the cross sections. The velocity vector components for each datapoint are linearly interpolated over a regular grid for each slice, before the flow properties are computed. If the dataslices are to thick, data might be lost due to the interpolation process. If the dataslices are to thin, not enough datapoints are available. To compromise between the two a slice thickness of 0.4 mm is chosen. 31

32 32

33 Chapter 6 Results 33

34 As is described in chapter 5, the AIPV, OPV and vorticity are visualized on 6 cross sections per geometry. The order of magnitude of the velocity in the upper section of the aneurysm differs from that of the lower section, thereby preventing proper visualization with one scale. Therefore, a version with a different scale for the upper section is made for every plot. Four steps in the flow cycle are used for the visualization, as indicated by the pulse inserts. These steps are the maximum flow acceleration, the absolute maximum flow, the maximum flow deceleration and the absolute minimum flow. A selection of the available plots is made to evaluate the flow patterns in the aneurysms. 6.1 Idealized geometry The AIPV for cross section 2 is displayed in figure 6.1. The flow does not seem to form a counterclockwise vortex around a point in the aneurysm in this plane, but it bends towards the outlet. This becomes more clear in the differently scaled upper sections of the split plots. In figure 6.2 the OPV is given for maximum flow in cross sections 4,5 and 6. In the upper section of cross section 4(A) the velocity field is mainly directed upward. In the upper section of cross section 5(B) the OPV is larger and the velocity vectors are smaller. Cross section 6(C) shows a decrease in the OPV in the upper section and an increase in the lower section, indicating the movement of flow towards the outlet. The results for the other steps are similar. To show the movement of flow perpendicular to the parent artery direction, both the AIPV in cross sections 4, 5 or 6 or the OPV in cross sections 1,2 or 3 can be used. In figure 6.3 the OPV in cross section 3 is given. In these plots it can clearly be seen that the flow moves towards the wall upon entering the aneurysm and back towards the middle (or plane of symmetry ) upon leaving the aneurysm. Vorticity values range from -400 to 400 in the parent artery. The peak values are found just below the neck of the aneurysm. In figure 6.4 the vorticity is plotted for cross sections 2 and 4. Even with a significantly different scale in the upper sections, no obvious vortices can be observed in the both cross sections. 34

35 A E B F C G D H Figure 6.1: The AIPV in cross section 2 for 4 moments in time. Plots (E) through (H) are split at the aneurysm neck and the upper part is differently scaled for both the AIPV contours and the velocity vectors. The pulse inserts indicate the moment in time. The scales are in m/s. 35

36 A B C Figure 6.2: OPV for cross sections 4(A), 5(B) and 6(C) for maximum flow. Scales are in m/s 36

37 x 10 3 x 10 3 x 10 3 x 10 3 A B x 10 3 x 10 3 x 10 3 x 10 3 C D Figure 6.3: OPV for cross section 3 in 4 time steps. Scales are in m/s. 37

38 A E B F C G D H Figure 6.4: Vorticity for cross sections 2(A,B,C,D) and 4(E,F,G,H). 38

39 6.2 ICA geometry The magnitude and direction of the in-plane velocity for cross sections 2 is displayed in figure 6.5. Since cross section 2 lacks the presence of the inlet, the same plots are given for cross section 3 including the inlet. Just like in the idealized geometry the flow seems to bend towards the outlet in both planes, without the formation of intra-aneurysmal vortices. Although the magnitude of the AIPV changes over time, no change in flow pattern is observed. The AIPV plots in figure 6.6 show that the flow in the aneurysm moves upwards and towards the sides of the aneurysm. This resembles the flow pattern observed in the idealized geometry. In figure 6.7 the OPV is plotted for cross section 2. These plots illustrate the movement of flow perpendicular to the parent artery. Since the inlet is not located directly beneath the aneurysm and the flow enters the aneurysm at a slight angle, this OPV pattern is expected. Vorticity values range from -250 to 250 in the parent artery and are highest in the regions below the neck (figure 6.8A) and at the inlet wall just below the point of bifurcation (figure 6.8B). The vorticity in the upper part of the aneurysm does not exceed -5 or 5 and no vortices can be detected. 39

40 x 10 3 x 10 3 A E x 10 3 x 10 3 B F x 10 3 x 10 3 C G x 10 3 x 10 3 D H Figure 6.5: AIPV for cross sections 2(A,B,C,D) and 3(E,F,G,H). Scales are in m/s. 40

41 x 10 3 x 10 3 A B x 10 3 x 10 3 C D Figure 6.6: AIPV for cross section 4. Scales are in m/s. 41

42 x 10 3 x 10 3 A B x 10 3 x 10 3 C D Figure 6.7: OPV for cross section 2. Scales are in m/s. 42

43 A B Figure 6.8: Vorticity plots for cross sections 2(A) and 3(B) at maximum flow. 43

44 44

45 Chapter 7 Discussion 45

46 Both geometries show similar results for the intra-aneurysmal flow patterns. The results in chapter 6 indicate that the flow bends directly towards the outlet upon entering the aneurysm. This results in very small velocities in the upper sections of both aneurysms (figures 6.1, 6.2, 6.5 and 6.6). Vorticity is highest below and around the neck (figure 6.4) and at the walls of the inlet (figure 6.8B). No vortices could be detected in the upper sections of the aneurysms. A single vortex structure was expected there for the idealized geometry, based on the PIV and CFD experiments performed on the original geometry[27]. The idealized geometry provided by PMS differs substantially from the model it is based on. Especially the shape and width of the aneurysm neck seem altered. Figure 3.1 shows both the original model and the scanned and reconstructed version using 3D rotational angiography (3D RA). The change in geometry indicates that the reconstruction of the model using 3D RA is not accurate. Smoothing of the geometry also slightly alters the geometry. The less defined and wider neck might be a reason for the lack of a counterclockwise vortex in the flow patterns and the small velocities observed in the upper part of the aneurysm. Mesh independancy has not been tested. However, for the idealized geometry more than twice as many elements were used in comparison with the CFD analysis in [27], were reasonably accurate results were obtained. At the flattened outlets of the ICA geometry, NETGEN automatically produces a very fine mesh to cope with the curvature. Allowing NETGEN to adapt to curvature resulted in large surface and volume elements in the relatively large and smooth aneurysm dome. Restricting the curvature adaptation resulted in very dense meshes. These could not be used in SEPRAN, probably due to computer memory issues. A compromise had to be made, resulting in a mesh with slightly large elements in the aneurysm dome. This may have had an influence on the accuracy of the results for the ICA geometry. For the idealized geometry, this did not seem to pose a problem. The main point of discussion regarding the mathematical model is the definition of the boundary conditions. Since flow is not fully developed upon entering the aneurysm, the inlet flow profile can only be approximated. The definition of a stress free outflow for the idealized geometry is correct, since rigid walls are assumed. This is not the case for the ICA geometry. The flow fractions exiting both outlets are influenced in vivo by the resistance of the distal vasculature. In the model the resistance is determined by the length and cross section of each outlet. However, the outlet flow fractions may have a large effect on the intra-aneurysmal flow patterns, as reported in an in vitro study on idealized geometries by Kerber et al[31]. According to Cebral et al[32] however, the character of intra-aneurysmal flow patterns does not change significantly due to the variation of flow fractions. Eventually, in vivo measurements of flow fractions may be required to perform reliable flow simulations in aneurysms close to bifurcations. Since aneurysms are common at bifurcations, the flow fraction issue needs to be adressed. The goal of the visualization process is to create standard cross sections for comparison of multiple aneurysms. Two points from the parent artery s centerline and the top of the aneurysm dome form the basis for the cross sections. The points are user-defined and thus subject to interpretation. In stead of the top of the dome a more central, automatically generated point might be preferable. Such a centerpoint might be automatically available as the center of the largest possible sphere bounded by the aneurysm. An additional problem in the case of the ICA geometry is the position of the inlet of the parent artery. Orientation of the aneurysm dome in respect to the inlet centerline might result in a different perception and interpretation of flow patterns. 46

47 Chapter 8 Conclusion and recommendations 47

48 8.1 Conclusion Most importantly, flow visualization with a CFD pipeline for patient-specific cerebral aneurysms is possible. However, an experienced user is needed to determine the appropriate mesh properties, boundary conditions and visualization options. Geometry files in the STL format can be imported, preprocessed and meshed to be used for flow simulations. Limitations are the accuracy of the geometry, the definition of the inlet flow and the flow fraction ratio in case of multiple outlets. The meshing process can be largely automated using a general mesh size and a parameter for curvature adaptation. However, meshing highly curved surfaces proved more difficult. The visualization method works with both the idealized and the ICA geometries. The definition of cross sections is user-dependent, but seems to provide a good standard for visualization of the flow simulation data. Probable flow patterns were observed in the results chapter. 8.2 Recommendations For geometries containing highly curved surfaces local mesh refinement needs to be implemented for the dome region. This is needed to generate meshes that produce meshindependant results. Local mesh refinement is possible with NETGEN, but was not performed in this project due to time limitations. A more realistic approximation of the inlet flow is needed to obtain more realistic flow patterns. Outlet flow fractions are likely to influence the intra-aneurysmal flow patterns. Therefore, methods to determine or approximate these fractions are needed. To obtain the necessary precision of the approximation, the influence of the fractions on the intra-aneurysmal flow need to be examined. The top of the aneurysm dome is a convenient point to use for the definition of cross sections. Other points however, such as the center of gravity of the aneurysm, might also prove usefull for this purpose and must be examined. 48

49 Appendix A VMTK protocol 49

50 The Vascular Modeling ToolKit (VMTK) is a software tool for 3D reconstruction, geometric analysis, mesh generation and surface data analysis for image-based modeling of blood vessels. These vessels may contain bifurcations and/or aneurysms and can have only one inlet. To download the VMTK software and for more information and documentation about installing and using VMTK: luca/vmtk/doku.php This protocol describes the isolation of aneurysms and the preparation of the obtained geometry for meshing, with VMTK version 0.5. A 3D geometry file with the STL-format is used, although multiple file-formats can be imported. Starting: Assuming the installation of VMTK was successful, startup the software by running the vmtk executable file in the installation folder. A screen pops up titled PypePad. Importing: In PypePad commands can be entered in the upper window and output is given in the lower window. First, the geometry file needs to be imported and converted to the format required by VMTK. Because VMTK uses it s installation directory as work directory, the geometry file first needs to be copied to this directory. Now type in the command window: imusurfacewriter -ifile file.stl -ofile file.vtp Next, select run all from the run-menu. The created file can be viewed by running: imusurfaceviewer -ifile file.vtp It is conve- A viewer pops up and the geometry can be controlled with the mouse. nient to combine the above commands using --pipe : imusurfacewriter -ifile file.stl -ofile file.vtp --pipe imusurfaceviewer -ifile file.vtp With the --pipe command multiple commands can be run in sequence, hence the name PypePad. It is usefull to save the commands that you use as scripts. This enable you to open a complete set of commands for running or editing in stead of having to type it manually again. To do this, choose save as in the file-menu. Clipping: To clip the geometry run: imusurfaceclipper -ifile file.vtp -ofile file clipped.vtp Again the viewer pops up, but this time the clipping tool can be activated by pressing i. A cube appears that can be rotated and translated with the mouse. Also the individual surfaces of the cube can be translated, by dragging the associated spheres. Once the cube is placed over the part of the geometry that needs to be clipped, press space. 50

51 Pressing i activates the clipping cube again. Once the clipping is done press q to close the viewer. When clipping, try to clip the artery perpendicular to the longitudinal axis at a location that is mostly circular. This is important for the addition of extensions. Also, clip small sidebranches relatively short because of the smoothing process later on. Extensions: After clipping, the inlet extension can be added with the following commands: imusurfacereader -ifile file clipped.vtp \ --pipe bvgcenterlines -seedselector openprofiles \ --pipe imurenderer \ --pipe bvgflowextensions -adaptivelength 1 -extensionratio 4 -normalestimationratio 0 -interactive 1 \ --pipe imusurfacewriter -ofile file extensions.vtp \ --pipe imusurfaceviewer -opacity 0.3 \ --pipe imusurfaceviewer -array MaximumInscribedSphereRadius \ The \ symbol is used to indicate the end of the line. Because of the --pipe command, -ifile and -ofile only have to be used once. Press q and you are prompted to enter the number corresponding to the inlet as displayed in the viewer. Press Enter. Again you are prompted, now for the numbers corresponding to the outlets. Centerlines will be computed based on the chosen inlet and outlets. Press q twice and you are prompted to again enter the number corresponding to the inlet. Press enter and the extension is created. Press q twice to view the extensions along with the centerlines which they are based upon. In the bvgflowextensions command several variables are used. The extensionratio variable indicates the ratio of the extension length and the inlet s mean radius. The normalestimationratio variable determines the direction the extension has, based on the centerline. A value of 0 means that the centerline isn t used at all, but that the direction of the extension is based on the inlet surface direction. This works better when the centerline is curved towards the inlet surface. The value 1 for interactive lets the user choose which inlet or outlet is extended. For a value of 0 (default) extensions are created at the inlet and all outlets. Depending on the need for varying extension lengths repeat the process for the outlets (mind the ifile and ofile names) or choose interactive 0 for similar extension lengths. The created extensions have to have smooth sidewalls and a smooth connection to the original geometry for the meshing process to work later on! Smoothing: The geometry can be smoothed and compared to the original version with: imusurfacesmoothing -ifile file extensions.vtp -iterations 30 -passband 0.1 -ofile file smoothed.vtp \ --pipe imurenderer \ --pipe imusurfaceviewer -display 0 \ --pipe imusurfaceviewer -color display 1 51

52 The smoothing can be controlled through the iterations and passband values. the viewer the original geometry is colored red and the smoothed geometry is gray. In Capping: Finally the open extensions can be capped. Because of the smoothing procedure the inlet and outlet openings have been slightly deformed. In order to create sharp edges at the openings it is best to first clip a small part of the extensions before capping them. The created surfaces must be very close to perpendicular to the lolongitudinalxis of the artery. If this proves difficult it is also possible to first add small extensions before capping. The small extensions will have surfaces at a 90 o angle. imusurfaceclipper -ifile file smoothed.vtp \ --pipe imusurfacecapper -interactive 0 -ofile file capped.vtp \ Exporting: The geometry can be exported as an STL-file with: imusurfacewriter -ifile file smoothed.vtp -ofile file finished.stl As mentioned before the successful addition of extensions depends on the clipping of the arteries. If it is difficult to make neat in- and outlet surfaces, there is the option of adding extra long extensions. This helps to create smoother transitions from the geometry to the extension. In this case, the clipping of the extensions as mentioned in the capping section has to be done for a larger part of the extensions. 52

53 Appendix B NETGEN protocol 53

54 Netgen is a 3D tetrahedral mesh generator. Geometries described in the STL file format can be imported. The optimization and refinement of the generated meshes can be largely specified by the user. For more information on Netgen and to download and install the software visit: The version of Netgen that was used is 4.4 and is used in a linux environment. Netgen is open source software based on the LGPL license and is available for windows and unix/linux. This protocol is meant for use with vascular geometries. These geometries need to have closed outlets with sharp edges. Starting: Assuming the installation of Netgen was successful, startup the software by running the ng executable file in the installation folder. The main screen of the program appears. Importing: Use File/Load geometry from the menubar to select your geometry file. Geometry preparation: Select Geometry/STL Doctor from the menubar and go to the Edit Edges tab. Use the slidebars for build edges with yellow angle and continue edges with yellow angle to define the edges of the outlet surfaces. Respective values of 89 and 0 degrees will probably work if the outlets are cut off at 90 degrees. The result of changing these values can be seen directly on screen while sliding the bars. Orange edges should appear at the outlets and disappear from the main surface as the build edges with yellow angle value approaches 89. If it is not possible to create edges only at the outlets, then the geometry might be to coarse or the outlets are not well enough defined. Finish with clicking the Build Edges button. Meshing: A default mesh can be generated by clicking the Generate Mesh button in the menubar. If you first want to change the meshing settings select Mesh/Meshing Options from the menubar. The main choice in the General tab is Mesh granularity, where the main coarseness of the mesh is chosen. If quadratic elements need to be used, check the Second order elements box. The values in the Mesh Size tab have been determined by the choice for the Mesh Granularity. However, there are 2 values that influence the meshing processed most and can be used to further specify the meshing process. The mesh-size grading value determines the maximum size difference ratio between adjacent elements. Changing this value predominantly influences the mesh size around the more curved surfaces of the geometry. The second value is the STL - chart distance. This value determines the overall size of elements. Smaller values mean coarser meshes. Finish with clicking Calc New H and the Apply button at the bottom of the menu. Click the Generate Mesh button to create the mesh. Once the mesh is created, check if the number of surfaces is correct by choosing Mesh/Edit Boundary Conditions from the menubar. A menu pops up and by clicking the next button, you scroll through the surfaces. Double-clicking a surface renders it red and the associated surface number is 54

55 displayed in the pop up window. It is of course possible to adjust other parameters in the Meshing Options menu, but most of these have only minor effects on the mesh. Exporting: Go to File/Export Filetype and check if the Neutral Format is selected. This is the file format that will be used to convert the exported mesh to a format suitable forthe finite element program Sepran. Next, go to File/Export Mesh to export your mesh. 55

56 56

57 Bibliography [1] R.J.Sclabassi G.N.Foutrakis, H.Yonas. Saccular aneurysm formation in curved and bifurcating arteries. Am J Neuroradiology, [2] F.I.Ojini. Natural history of cerebral saccular aneurysms. West Afr J Med, [3] E.J.Graves. Detailed diagnosis and procedures, national discharge hospital survey. Vital Health Stat, [4] W.E.Stehbens. Aneurysms and anatomical variation of cerebral arteries. Arch. Pathol, [5] V.Hertzberg T.Brott, K.Thalinger. Hypertension as a risk factor for spontaneous intracerebral hemorrhage. Stroke, [6] J.L.Farber E.Rubin. Pathology. Lippincott-Raven Publishers, East Washington Square, Philadelphia, [7] A.Algra J. van Gijn G.J.E.Rinkel, M.Djibuti. Prevalence and risk of rupture of intracranial aneurysms: a systematic review. Stroke, [8] Johnston et al. Endovascular treatment of intracranial aneurysms. Stroke, [9] Juvela et al. Factors affecting formation and growth of intracranial aneurysms: a longterm follow-up study. Stroke, [10] Chatziprodromou et al. Haemodynamics and wall remodelling of a growing cerebral aneurysm: a computational model. J Biomechanics, [11] J.G.Chasea J.Arnolda J.Fink S.Moorea, T.Davida. 3d models of blood flow in the cerebral vasculature. J Biomechanics, [12] J.Kreyza et al. Carotid artery diameter in men and women and the relation to body and neck size. Stroke, [13] R.M.K.W.Lee. Morphology of cerebral arteries. Pharmac Ther, [14] D.L.Stilwell R.B.Stephens. Arteries and veins of the human brain. Springfield, [15] P.B.Canham J.G.Walmsley. Orientation of nuclei as indicators of smooth muscle cell alignment in the cerebral artery. Blood Vessels, [16] 57