Master thesis The velocity field in a cerebral aneurysm model: PIV measurements and CFD analysis. G. Mulder September 28, 2006 BMTE06.

Transcription

1 Master thesis The velocity field in a cerebral aneurysm model: PIV measurements and CFD analysis G. Mulder September 28, 2006 BMTE06.43 prof. dr. ir. F.N. v.d. Vosse dr. ir. P.H.M. Bovendeerd Eindhoven University of Technology Department of Biomedical Engineering

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3 Abstract Cerebral aneurysms are localized, thin walled dilatations of the arterial wall in the brain. The major risk involved is rupture of the aneurysm, resulting in a subarachnoid hemorrhage. In order to decide whether or not to operate, the risk of rupture should be estimated more accurately than currently possible. It is known that the shear rate alters the mechanical properties of the arterial wall via the endothelial cells. Therefore, in vivo measurement of the intra-aneurysmal velocity field is required in risk assessment. X-ray system have great potential in in vivo blood flow visualization, although there are some drawbacks. The X-ray image is a projection of 3D flow data. Furthermore, injection of a contrast agent is required in the visualization of blood using X-ray. Since the injection alters the flow, the influence of this injection should be examined. In order to validate the method used in in vivo determination of the velocity field, an in vitro setup is required. The dimensions of the in vitro model, an idealized saccular aneurysm with a curved parent artery, correspond to the dimensions found in vivo. The intra-aneurysmal velocity field is measured particle image velocimetry, during stationary inflow as well as injection. Furthermore, a computational fluid dynamics model is implemented in Sepran and the results are compared to the experimentally obtained velocity field. The intra-aneurysmal velocity field shows a single vortex structure. Inflow is observed in the plane of symmetry, whereas outflow occurs in planes other than the plane of symmetry. During the injection the vortex strength is increased, while the vortex structure shows no evident changes. Furthermore, the characteristics of the experimentally and numerically obtained velocity fields correspond. 3

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5 Contents Abstract 5 1 Introduction 7 2 Design of the aneurysm model Physiological considerations Physiology of the cerebral arterial system Pathology of cerebral aneurysms Mathematical model Geometry Flow characteristics Particle Image Velocimetry Principle of PIV Practical guidelines Stereo PIV Accuracy PIV setup Method Results Experiment Materials and method Setup Phantom repositioning Method Data acquisition and postprocessing Results Stationary flow Injection into stationary flow Discussion Computational Fluid Dynamics Method and materials Results Problem 1: Stationary inflow condition Problem 2: Stationary main flow with injection Discussion

6 6 General conclusion and recommendations Experiment Computation fluid dynamics Future work Appendix 77 A Geometry in vitro model 77 B Flow characterization 79 C Phantom repositioning device: development and testing 81 C.1 Accuracy experimental setup C.1.1 Design repositioning device C.1.2 Method C.1.3 Results D Protocol 85 D.1 Preparing a measurement D.1.1 Calibration flow probe D.1.2 Laser beam alignment D.1.3 Preparing the setup D.2 Performing a measurement D.2.1 Calibration procedure D.3 Processing the images D.3.1 Calibration images D.4 Particle images D.5 Correction broken pixels

7 Chapter 1 Introduction 7

8 Arterial aneurysms are localized dilatations of blood vessels caused by a congenital or acquired weakness of the media. A variety of characteristic geometries can be distinguished. In the cerebral arteries the most common type is the saccular aneurysm, having a bubblelike geometry. Most cerebral aneurysms are asymptomatic and therefore remain undetected [1]. Autopsies have revealed that in as many as 25% of the population older that 55 years undetected saccular aneurysms are found [2]. In the general population approximately 5% is likely to harbor these aneurysms and 15 20% of these persons have multiple lesions [3, 4]. Cerebral aneurysms are highly uncommon in people younger than 20 years, and very common in older people, especially above 65 years old [4]. This indicates that not every aneurysm is life threatening. However, rupture of an intracranial aneurysm results in subarachnoid hemorrhage (SAH), with a 35% mortality during the initial hemorrhage [2]. In case of subsequent hemorrhage the prognosis is even worse. A total 50 to 60% of the patients with SAH will die or suffer severe morbidity [4]. No more than one third of the patients eventually returns to their previous occupation due to severe neuropsychological disabilities [4]. The possible treatments for a patient with an unruptured cerebral aneurysm are surgical clip placement, endovascular coil occlusion and stenting. In surgical clipping blood is prevented from entering the aneurysmal sac by placing a metal clip across the neck of the aneurysm. Endovascular coil occlusion consist of packing platinum coils in the aneurysmal sack, thereby decreasing the intra-aneurysmal flow such that thrombus formation is promoted. Depending on various geometrical factors, such as neck width and orientation of the aneurysm relative to the parent artery, stenting prior to coil placement might be required [5, 6]. There are only a few articles reporting stenting without coil occlusion as endovascular treatment option for cerebral aneurysms [4, 7]. According to Koivisto no significant difference was detected in the outcome one year after surgical or endovascular treatment of ruptured cerebral aneurysms [8]. The first outcomes of the ongoing International Subarachnoid Aneurysm Trial (ISAT), a large scale trial on ruptured aneurysms involving 42 centers in Europe and America, reported that the relative risk of death or significant disability for endovascular patients is 22.6% lower than for surgical patients [9]. In unruptured aneurysms coil embolization resulted in significantly less complications than surgical clipping [10, 11]. The decision whether intervention is recommended depends on the balance between the risk of rupture and the risk related to the intervention itself. The mechanical properties and loading state of the arterial wall are most important in the determination whether rupture of the aneurysm is a serious threat. Since both parameters can not be determined adequately in vivo, accurate estimation of the risk of rupture is not possible yet. At present, the risk of rupture is mainly associated with the maximum dimension of the lesion even though there is controversy over the critical size [3]. The loading state of the arterial wall depends on the pressure load and shear stress. In contrast to shear stress, the pressure load is similar throughout the arterial system. The shear rate introduced by intra-aneurysmal blood flow is known to affect the endothelial cells covering the lumen. This induces adaptation, or in aneurysms, degradation of the arterial wall. Since the shear rate can be determined from the intra-aneurysmal flow, the development of efficient methods for in vivo flow measurements is of interest. X-ray systems have great potential in becoming an important non-invasive method to determine the flow properties. However, injection of contrast agents is required in X-ray flow visualization techniques. Knowledge on the influence of these injections is indispensable for proper interpretation of 8

9 the X-ray images, and can be acquired via computational studies. As the intra-aneurysmal flow patterns are complex, in vitro validation is needed to obtain insight in its accuracy and limitations. Furthermore, the in vitro setup can be used to perform X-ray measurements in a well-controlled way such that the technique can be evaluated. The purpose of this research is to develop an in vitro setup mimicking intra-aneurysmal flow and enabling the analysis the influence of the injection on the flow characteristics in a cerebral aneurysm. The intra-aneurysmal velocity field is determined using both experimental and computational experiments. Chapter 2 describes the physiological and pathological features of the cerebral arterial system and cerebral aneurysms, which are used to determine the geometry and flow characteristics. Particle Image Velocimetry (PIV), which is a non-intrusive technique to measure velocity fields, is used to determine the velocity field in a realistically dimensioned in vitro model. PIV is explained and tested in chapter 3. Chapter 4 discusses the method and results of the measurements on the in vitro model. In chapter 5 the experimental results are compared to those from a computational fluid dynamics (CFD) model in order to validate the measurement technique. 9

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11 Chapter 2 Design of the aneurysm model 11

12 In order to enable numerical and experimental modeling of the blood flow in cerebral aneurysms a realistic geometry and flow should be chosen. To this purpose physiological features of cerebral circulation and cerebral aneurysms are reviewed shortly. The mathematical model is discussed in the last section. 2.1 Physiological considerations Physiology of the cerebral arterial system Both the internal carotid and basilar arteries supply the brain with blood (figure 2.1). The internal carotids and basilar arteries are connected via the Circle of Willis, which allows blood to pass from one system to another in the event of blockage. The blood is then redistributed by the anterior, middle and posterior cerebral arteries. Figure 2.1: The cerebral arterial system in a bottom view of the brain and a schematic representation of the main arteries (left) [12]. Figure 2.2 shows the anatomy of an arterial wall. The innermost layer of the vessel wall, the tunica intima, consists of one layer or endothelial cells and is supported by an internal elastic lamina. The next layer, the tunica media, is made up of layers of smooth muscle cells and elastic fibres. The tunica adventitia is composed of connective tissue and fibroblasts [2]. Endothelial cells are subject to mechanical forces such as blood pressure, cyclic strain and wall shear stress. In response to hemodynamic variations the endothelial cells excrete substances that acutely regulate smooth muscle cell tone and chronically lead to remodeling of the arterial wall. An in vivo study on human common carotid arteries by Irace et al. revealed that changes in wall shear stress resulted in correspondent intima-media thickness variations [14]. In general, remodeling targets a wall shear stress of 1.5 to 2.0 Pa [15, 16]. 12

13 Figure 2.2: The anatomy of a healthy arterial wall [13]. The flow consists of a stationary and pulsatile component. The pulsatility strongly depends on the properties of the vessel wall. If the cerebral arteries are calcified, the damping of the wave will be minimal resulting in a relatively high pulsatile flow. In healthy arteries however, the flow might be almost stationary. Furthermore, pulsatility decreases further down the arterial tree. Figure 2.3 shows the typical shape of flow pulses in the arteries supplying the Circle of Willis, as derived from flow measurements performed with phase-contrast magnetic resonance by Castro et al. [17]. The upper and lower curve represent the flow in the internal carotid artery and basilar artery, respectively. This illustrates the complexity of the system as the large difference in flow pattern is found in two arteries with a similar pressure wave. Various values of the flow rate are reported in literature, a selection of which is shown in table 2.1. The flow data reported by Narracott are obtained from measurements in a 4 mm vessel. Since they assume a flat inflow profile, the reported velocities correspond to a maximum and mean flow of 6.3 and 4.5 ml s 1. The mean flow reported by Liou applies to an artery which is 5 mm in diameter while the Womersley number α 4, resulting in a mean flow of 5 ml s 1 when a plug flow is assumed. Rudin et al. reported that a flow of 175 ml min 1 is characteristic for cerebrovascular blood flow in vessels that are 3.5 mm in diameter[18]. In section this information will be used to derive the characteristic cerebral flow that will be used in this study. 13

14 Figure 2.3: The typical shape of the flow pulse in the internal carotid artery (ICA) and the basilar artery (BAS) [17] Table 2.1: Literature values of flow rates q and velocities v Article q max q min q m Unit Castro[17] [ml s 1 ] Ford[19] [ml s 1 ] Rudin[18] 2.9 [ml s 1 ] v max v min v m Unit Narracott[20] [m s 1 ] Liou[5] 0.40 [m s 1 ] Pathology of cerebral aneurysms Arterial aneurysms are localized dilatations of blood vessels varying in shape, size and location. Cerebral arteries frequently develop saccular aneurysms, a bubble-like pouching of the arterial wall. The great majority of human intracranial aneurysms occur at branching sites of the circle of Willis [21, 2], commonly between the anterior cerebral artery and anterior communicating artery, at the trifurcation of the middle cerebral artery or at the internal carotid artery - posterior communicating artery - anterior cerebral artery complex [2]. Figure 2.5 shows common geometries of saccular aneurysms with respect to their parent artery. Parlea et al. (1999) used the typical basilar and internal carotid artery diameter in an analysis of simple-lobed cerebral aneurysms dimensions using angiograms. The basilar and internal carotid artery are approximately 3.2 and 3.6 mm in diameter, respectively [22, 23]. The angiographic neck (N), dome height (H), dome diameter (D) and semi-axis height (S) were measured in the angiograms. The fractions of those measures define the shape of the 14

15 Quantity Mean ± SD D/N [-] 1.81 ± 0.47 H/N [-] 1.80 ± 0.74 D/H [-] 1.07 ± 0.27 H/S [-] 1.87 ± 0.30 N [mm] 4.24 ± 2.50 D [mm] 7.70 ± 4.77 H [mm] 7.20 ± 4.31 Figure 2.4: The relative and absolute dimensions of intact simple-lobed aneurysms as derived by Parlea et al. The angiographic neck (N), dome height (H), dome diameter (D) and semiaxis height (S), as defined in the figure on the right, were obtained from angiograms of intact cerebral aneurysms. The absolute dimensions are derived from the angiograms using a carotid or basilar artery diameter of 3.3 and 3.6 mm as reference. [22] aneurysms while the absolute dimensions are retrieved by scaling using the basilar or carotid artery as reference. Figure 2.4 shows the dimensions defined and a summary of the dimensions obtained with intact aneurysms from various locations on the circle of Willis [22]. Figure 2.5: Schematic representations of saccular aneurysm geometries in respect to the parent artery: lateral, bifurcation and terminal aneurysm. [21] There are many possible causes of intracranial aneurysms, such as congenital defects, atherosclerosis, chronic hypertension and bacterial infections. Each of those causes reveals itself in aneurysms with specific characteristics [2]. The etiology of cerebral aneurysms is a controversial issue. However, two major hypotheses can be distinguished. One hypothesis states that the aneurysm formation is caused by acquired degenerative changes in the arterial wall, while the other supports the idea that aneurysm formation is caused by congenital defects in the muscular layer of the cerebral arteries [4, 2]. In the embryonic development of Y-shaped bifurcations, the circumferential muscular layer of the parent vessel and the two branches are separate and may fail to connect adequately across the notch of the Y. This results in a point of congenital muscular weakness which is only bridged by endothelium, the internal elastic membrane and adventitia. Forces onto the congenital defect due to the hemodynamics may result in the formation of a saccular aneurysm [2]. Prior to rupture, many intracranial aneurysms are thin-walled ( µm) transparent structures as in figure 2.6. The media and internal elastic lamina are typically absent in saccular lesions, which thereby consists largely of collagen [3]. 15

16 Figure 2.6: A saccular aneurysm revealed in an arteriogram (right) [24] and a thin walled saccular aneurysm in a bifurcation in the circle of Willis collected in an autopsy (left) [2]. 16

17 2.2 Mathematical model Geometry Terminal aneurysms are most common in the human brain [21]. However, the hemodynamic features of lateral aneurysms are better understood and therefore more suitable for this research. In general, the flow characteristics in lateral aneurysms depend upon the geometrical configuration in relation to the parent vessel, the size of the neck and the volume of the aneurysm. The geometry of the in vitro model (Hemolab, CA-boog-01) by used in all experiments is shown in figure 2.7. With H = 8 mm, D = 8 mm, N 3.9 mm and S = 3.5 mm, this geometry is within the reported range (figure 2.4)[22]. The exact dimensions are reported in appendix A Flow characteristics The pulsatility is reduced in arteries localized further down the arterial tree. Therefore, the shape of the flow pulse is assumed to correspond to the flow pulse in the basilar artery rather than the internal carotid artery (figure 2.3). This flow pulse is approximated using two separate sinusoidal functions to describe the fast increase and slow decrease of the flow, with the pulsatility characterized by the time t max at which the maximum is reached, the duration T c of one cardiac cycle, the mean flow q m and the magnitude of the flow pulse q p = q max q min. If the time is defined such that the fast increase in flow starts at t = 0, the flow q(t) is described by q m (1 q p 2q q(t) = m cos(π t t max )) if 0 < t t max q m (1 + qp 2q m cos(π t t (2.1) max T c t max )) if t max < t T c The data from table 2.1 are used to estimate qp q m. The data from Castro, Narracott and Ford [17, 20, 19] result in 0.6, 0.8 and 0.7, respectively. Therefore, qp q m = 0.7 is assumed to be an realistic estimate of the pulse height. A heart rate of 75 beats per minute corresponds to T c = 0.8 seconds. The duration of the steep rise in flow is derived from the pulse shown in figure 2.3, resulting in t max = 0.1 second. The only unknown left is the mean flow, which may be derived from the data in table 2.1. However, seeing the diversity in reported flow rates, the mean flow is estimated using 4 " # # " & Figure 2.7: The geometry of the lateral aneurysm model with dimensions in mm. 17

18 arterial wall remodeling properties. In this approach the vessel wall is assumed to adapt to the stationary component of the flow. For laminar flow in a straight tube the wall shear stress equals τ w = 4νρq πr 3 (2.2) The kinematic viscosity ν and density ρ of blood equal m 2 s 1 and 10 3 kg m 3, respectively. The radius of the parent artery is 2 mm. Using τ w = 2.0 Pa results in a flow of 3.6 ml s 1, which appears to be within the reported range (table 2.1). The blood flow in the parent vessel is characterized using non-dimensional parameters. This enables scaling such that the flow characteristics in the experimental setup corresponds to the in vivo situation. Incompressible Newtonian flow is characterized by the Womersley number α and Reynolds number Re (derived in appendix B). ω α = R ν Re = RV ν Womersley number (2.3) Reynolds number (2.4) The characteristic length is chosen to be radius of the parent vessel. A heart rate of 75 bpm corresponds to ω = 7.9. Assuming plug flow, the characteristic velocity V becomes 0.3 m s 1. This results in: α = 3.0 (2.5) Re = 163 (2.6) Table 2.2: In vivo values used in the characterization of the stationary component of the flow in the parent artery. ν blood m 2 s 1 ρ blood 10 3 kg m 3 heart rate 75 beats per minute R m V 0.3 m s 1 The values used in the determination of the Reynolds and Womersley number are summarized in table 2.2. Figure 2.8 shows one period of this model of the flow pulse. The geometry and flow characteristics are used in the experimental and computational models as described in chapter 4 and 5. 18

19 Figure 2.8: The pulsatile flow q(t) described by equation 2.1. The mean flow q m = 3.6 ml s 1 is derived from arterial wall remodeling properties. The magnitude of the pulse is defined as q p = 0.7q m. Maximum flow is reached at t max = 0.1T c, with T c the duration of one cardiac cycle. 19

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21 Chapter 3 Particle Image Velocimetry 21

22 3.1 Principle of PIV Particle image velocimetry is a technique with which time resolved data on in-plane velocity of a flowing medium can be acquired. The medium is seeded with tracer particles that are sufficiently small to follow the flow closely. The region of interest is illuminated with a thin sheet of light. An image sequence of light scattered by the moving particles is recorded. This setup is summarized in figure 3.1. Figure 3.1: Principle of PIV. The flowing medium is seeded with small particles and illuminated with a thin light sheet. Light scattered by the particles is recorded on time t 1 and t 2. Displacements are determined by correlating particle patterns in two subsequently recorded frames. Since t = t 2 t 1 is known, the velocity field can be derived. Quantitative information on the velocity field can be extracted from the image sequence. In PIV, the displacement of particle patterns between subsequent images is determined. To this purpose the recorded images are divided into rectangular sections, called interrogation areas. The displacement is found by cross correlation of corresponding interrogation areas in two subsequent recordings (figure 3.2). Maximum correlation occurs when the particle image patterns match best. This results in the average displacement within one interrogation area, ( x, y). Since the time t between two subsequent recordings is known, the velocity per interrogation area is found. Advanced PIV codes use iterative methods to improve the accuracy by pre-shifting the interrogation areas with the displacement from a previous PIV computation. Deformation of the interrogation areas using previous PIV computations will further improve the correlation. 22

23 Figure 3.2: Cross correlation. The top squares represent an interrogation area in two subsequently recorded frames, f and f + 1. Maximum correlation occurs when the particle patterns match best, yielding the displacement. 3.2 Practical guidelines There are several aspects to keep in mind when the PIV settings are chosen [25]. 1. The seeding density should be such that within one section sufficient particles are available to obtain a good correlation peak. At least 4 to 8 particles should be present in every interrogation area. However, at high concentrations the particle motion may be affected through interactions of surrounding particles. As long as the distance between particles exceeds several particle diameters this effect is assumed to be negligible. 2. A high maximum velocity increases the possibility that particles in one interrogation area in the first frame will no longer be present in the corresponding section in the second frame. This will reduce the quality of the correlation peak. In general, this problem is avoided as long as the displacement between two frames does not exceed 1/4 of the interrogation area or window width. However, the tracer must move at least twice its diameter between two recordings. The dependency of the maximal and minimal displacement d max and d min (in CCD pixels) on the maximal and minimal velocity v max and v min (in m s 1 ) is mathematically expressed as d max = Mv max t < 1/4L int, d min = Mv min t > 2d p, (3.1) with magnification M = image size object size in pixels per m, time between images t, size of the interrogation area L int in pixels, particle size d p in pixels. 3. A through-plane velocity component introduces an error in the displacement vectors in two ways. Particles present in the light sheet when recording the first image may have left the sheet in the second image. This phenomenon is called signal drop-out, which is a problem that can be avoided by choosing the light sheet thickness and time between pulses such that the through-plane displacement v z t will not exceed one fourth of the sheet thickness h: v z t 1/4 (3.2) h 23

24 The second way in which the accuracy is reduced is by parallax. The image is an projection of the particle positions in the light sheet, the depth at which the particles are present being unknown. This does not introduce an error in the two dimensional vector field when looking straight at the light sheet. However, this is not entirely true for the edges of the image, thereby introducing an error that increases further from the center of the image. 4. The velocity gradient within an interrogation area should be small in order to prevent loss off coherence. In general, less than 5 10% variation in velocity is recommended. 5. The camera should be focused on the middle of the light sheet. It is recommended to focus the camera such that the particle images are at least three pixels in diameter in order to optimize the effectiveness of subpixel interpolation. This is used to resolve particle displacements as small as 1/64 of the pixel pitch, thereby increasing the accuracy of the velocity field. 6. Overlapping of interrogation areas is recommended since loss-of-pairs results in the loss of information at the edges of the interrogation area. Furthermore, overlapping does produce more vectors due to an oversampling of the data, which is useful when computing derived quantities. These guidelines are used in the experiments described in chapter Stereo PIV In the PIV setup described previously, through-plane particle movement is considered a source of error. Since the optical axis of the camera is perpendicular to the laser light sheet the velocity vectors are projected into this plane and the third component is lost. In stereo PIV however, two cameras record the same area from a different point of view, as shown in figure 3.3. The third velocity component can be extracted from the information of two cameras. For each vector in a 3D vector map, the three true displacements ( X, Y, Z) are reconstructed from the corresponding two dimensional displacements ( x, y) from both cameras. A drawback of this setup is the mismatch between the best plane of focus, which is parallel to the image plane (CCD), and the object plane (laser sheet). A complete focus of the object plane can be achieved when the image plane is tilted relative to the lens such that the object plane, the plane of the imaging lens and the image plane intersect at one common point [26, 27]. This so called Scheimpflug arrangement is visualized in figure 3.4. Another disadvantage is the perspective distortion, reducing the field of view when the images from both cameras are combined. In order to enable the computation of the velocity field, it is necessary to determine how coordinates from the object plane are imaged onto the CCD plane. This is achieved by a calibration procedure in which images of a well-defined calibration grid are taken with both cameras at multiple heights. Comparing known marker positions with corresponding marker positions on each camera image, model parameters are adjusted to give the best possible fit. Whether a linear or nonlinear calibration model is used depends on the setup in which the velocity field is measured. 24

25 Figure 3.3: Principle of stereo PIV. The displacements derived from the images recorded by the left and right camera are used to reconstruct the true displacement, including the third component. Figure 3.4: The Scheimpflug arrangement. When the image plane (CCD) is parallel to the imaging lens, the plane of focus is also parallel to the lens. In stereo PIV this means the best plane of focus and object plane do not coincide, since the cameras are viewing the laser sheet from an angle. This is solved by tilting the image plane relative to the plane of the lens such that the image, lens and object planes intersect at one point. The path traveled by the light from the object on the right, through the cameras lens, to the CCD plane is shown. 25

26 3.4 Accuracy PIV setup In PIV, errors are introduced by dysfunctional pixels, camera noise, laser instabilities and the scatter properties of the illuminated particles. Furthermore, increasing displacement between two images leads to reduction of interrogation area overlap, thereby reducing the quality of the correlation (figure 3.2). In order to get an indication of the error, a well-defined displacement is applied on an artificial PIV image. In the first measurement no displacements are applied, the result of which should reveal the random error and the presence of any offset in the velocity measurement. In order to determine the slope of the systematic error both a vertical translation and an in-plane rotation are applied to the artificial PIV image. In this approach the effect of the laser on the accuracy is not included Method The setup is shown in figure 3.5. In order to enable the determination of the third velocity component, two cameras (Kodak Megaplus ES 1.0) are focused on a calibration grid with grid size 0.5 cm. This grid is mounted on a rotation and translation device, enabling rotation in the xy-surface and vertical translation in the z-direction. A calibration is performed over 2 mm (steps of z = 0.25 mm). The artificial PIV image, glued onto a 1 mm thick metal plate as displayed in figure 3.6, is placed on top of the calibration grid. The grid is lowered 1 mm to ensure the measurement is performed within the calibrated range. The top of the metal plate is now located at z = 0. First, a series - 21 image pairs - of the artificial PIV image is obtained without applying any displacements between the images. In the next series of 9 image pairs the plate is translated from z = 0.5 mm to z = +0.5 mm with steps of z = mm between two sequential images. Furthermore, a rotation of 1 degree is applied in every translation step. Dantec software (FlowManager version 3.62) is used to synchronize the laser and cameras. All raw images are exported from FlowManager. The calibration is computed using internally developed (v.d.plas, TUE) software and applied on the flow images. These unwarped images are imported into FlowManager and the 2D velocity fields is computed assuming a t = 1 ms. Interrogation areas of pixels with 50% overlap are used. The displacement and calibration data from both cameras are combined to determine the 3D velocity field in the illuminated plane with internally developed stereo PIV (v.d.plas, TUE) code. A more detailed description of this process is available in appendix D.5. 26

27 Camera 1 & 2 Calibration grid Rotation device Calibration grid Translation device Figure 3.5: Testing the accuracy of the PIV setup: two cameras are focused on the calibration grid (left), which is mounted onto a rotation and translation device (right). A calibration is performed over a vertical range of 2 mm. Figure 3.6: An artificial PIV is image is glued onto metal plate which has a uniform thickness of 1 mm. It is placed on top of the calibration grid after the calibration procedure and the grid is lowered 1 mm to correct for the thickness of the plate. 27

28 3.4.2 Results 0.04 Figure 3.7 shows a representative example of the 2D vector fields obtained when no displacement is applied and when both a verticale translation and in plane rotation is 0.04 applied x [m] x [m] (a) (b) Figure 3.7: Typical 2D velocity fields applying (a) no displacement and (b) in plane rotation. The velocity fields are scaled equally. When no displacements are applied, the velocity in the x-direction equals ± m s 1 and the histogram of u x shows a normal distribution around zero (figure 3.8). This indicates that there is no offset in the measured velocity in the x-direction. The same observations are made for the velocities in y and z-direction, which equal ± m s 1 and ± m s 1, respectively. The cause of the waves observed in the estimated standard error in u x is unknown (figure 3.9). The magnitude of the error is small compared to the magnitude of the velocities. The slope of the fit equals , which indicates that the error is approximately 2% of the measured velocity. This also applies to the velocity in the y-direction. However, one should be aware of the fact that this percentage depents on both the size and overlap of the interrogation areas. Furthermore, pre-shifting of interrogation areas in adaptive PIV methods should reduce the slope. For the velocity in z-direction, no range of velocities is available. The highest peak in the histogram shown in figure 3.10 corresponds to the applied displacement, while the second, much lower, peak is caused by the wave pattern observed in the in-plane velocities. The exact cause of the wave pattern is unknown. However, since other preliminary tests did not show this pattern, it is assumed that this pattern is introduced by the PIV method used here. If another combination of grid size, camera distance, interrogation area size and overlap are be used, the wave pattern is not observed. 28

29 S (a) û 10 4 x [m s 1 ] (b) u x [m s 1 ] Figure 3.8: (a) The estimated standard error S in m s 1 and (b) the histogram of all u x when no displacements are applied. The distribution resembles a normal distribution, with a mean that does not significantly differ from zero S û x [m s 1 ] Figure 3.9: The estimated standard error S (in m s 1 ) in u x when an in-plane rotation and out-of-plane translation are applied. A similar behavior was observed for the error in u y. 29

30 u z [m s 1 ] Figure 3.10: The histogram of all u z when an in-plane rotation and out-of-plane translation are applied. The highest peak corresponds to the applied displacement, while the second peak is erroneous. 30

31 Chapter 4 Experiment 31

32 Stereo PIV is used to determine the velocity field in an in vitro model of an aneurysm and its parent artery. In order to examine the influence of injection, the velocity field obtained in a stationary flow is compared to the velocity field measured during several injections, varying in either rate or volume. 4.1 Materials and method Setup Figure 4.1 shows the experimental setup used. A stationary pump (Verder, type 2032) is used to produce a stationary flow. Based on the geometrical considerations described in chapter 2, an in vitro model (Hemo- Lab, CA-BOOG-01) is made out of two perspex plates joined with bolts as shown in figure 4.2(a). Each plate forms half the lumen of the spherical aneurysm and its curved parent artery. Three beads are mounted on the upper plate for repositioning purposes (see the following section and appendix C for more detailed information). Plug-in couplings are used to attach the tubes connecting the phantom. The dimensions of the phantom are defined in appendix A (see also figure 2.7). The curved walls of the model introduce distortion, especially near the edges and in the neck of the aneurysm. In order to minimize this effect, the refractive indices of the model and fluid should match as closely as possible. The in vitro model is made out of perspex, which has a refractive index of Most fluids either have much lower refractive indices or are impractical (e.g. highly toxic or flammable) to be used in this experiment. Eventually, paraffin oil, which has a refractive index of at 20 o C, has been selected. The optical distortion due to this mismatch of refractive index is visualized using a highly uniform grid (figure 4.2(b)). The size and type of the seeding particles to be used depends on the application. The general requirement is that the particles must be small enough to follow the flow field and at the same time be good scatters. Furthermore, the density of the particles should resemble the density of the fluid in order to minimize gravity effects. A polyamid seeding is used with mean particle size 5 µm and density 1030 kg m 3 [28]. The luminal surface of the model is treated with copper polish (Brasso) in order to prevent fouling.. M F H > A 2 = H = B B E I A E C 1 L E J A + = J D A J A H 2 = H = B B E 2 K F 9 = J A H 1 A? J H Figure 4.1: The experimental setup. The barrel contains seeded paraffin. The catheter tip is situated at 5 cm from the model inlet. 32

33 (a) (b) Figure 4.2: (a) The in vitro model consists of two plates. Each plate forms half the lumen of the spherical aneurysm and its curved parent artery. Plug-in couplings are used to connect the tubes to the phantom. The beads (B) on the upper plate are used in the repositioning of the phantom. The positive x- and y-direction are defined as shown here. (b) The upper plate of the in vitro model is placed onto a uniform grid and the lumen is filled with paraffin. This shows the distortion due to the curved surfaces of the phantom and mismatch in refractive index. In order to examine the influence of an injection on the intra-aneurysmal flow conditions, the velocity field is measured during the injection of paraffin. The tip of the catheter is situated at 5 cm from the model inlet. Since the clinical injector (Mark V Provis, Medrad) used is not suitable for paraffin, a gas bubbler is placed in between the injector and the catheter. This setup is based on the difference in intrinsic density of water and paraffin (ρ H2 O = 1000 kg m 3 vs. ρ p = 800 kg m 3 ) [29, 30]. The bubbler is filled with paraffin and all air is removed. The injector is filled with water and connected to the bubbler. The lid is thoroughly taped onto the container in order to prevent it from being released during the pressure increase due to the injection. When a certain volume of water is injected, it enters the bottom of the bubbler. Since the volume in the bubbler is constant, the amount of paraffin leaving the bubbler is equal to the injected volume. Figure 4.3 shows this setup. All components are connected with rigid tubes. Throughout the experiment, the flow is monitored with an ultrasonic flow meter (Transonic Systems) in order to register the actual injection. A 15 Hz dual-pulse Q-switched Nd:YAG laser (New Wave II; 532 nm; 20 mj per pulse) is used for the illumination of the particles. The laser beams are aligned such that optimal sheet overlap occurs at 38 cm from the laser head. The Kodak cameras as specified in the previous chapter are used to obtain the images. The laser and cameras are situated as shown in figure

34 Figure 4.3: Since the clinical injector (left) is not suitable for paraffin, a gas bubbler (right) is placed between the injector and the catheter. The water from the injector enters at the bottom, resulting in an equal outflow of paraffin. Due to the difference in density and chemical properties, the water and paraffin will not mix even during injection. Phantom Laser Cameras Figure 4.4: The distance between the laser head and the aneurysm is approximately 40 cm. The laser sheet is aligned parallel to and just below the upper half of the phantom, first entering the aneurysm. The particles in the laser sheet are recorded by two cameras. 34

35 4.1.2 Phantom repositioning Stereo PIV is used to determine the velocity field in a plane as close to the plane of symmetry of the aneurysm model as practically possible. In stereo PIV a calibration procedure is required to determine the relation between the object and image coordinates. Furthermore, the calibration procedure enables correction of the distortion due to the mismatch in refractive index in the regions in which the dots of the calibration grid are properly visible. In order to ensure the calibration is valid, the position of the phantom relative to the cameras should be reproducible. Figure 4.5 shows the device that was designed for this purpose. The laser sheet enters the phantom at the side of the aneurysm, parallel to and just below the upper half of the model. Cameras Phantom Spring Translation device Tube guide Micro screw (b) Calibration setup Base plate (a) (c) Measurement setup Figure 4.5: The phantom repositioning device. (a) The laser sheet enters the phantom at the side of the aneurysm, just below and parallel to the upper plate of the phantom. Two cameras are focused on the particles present in the laser sheet, each from a different point of view. (b) The calibration setup. Only the upper plate is placed in the container. A translation device enables vertical movement of the grid which is illuminated via a mirror under 45 o. (c) The measurement setup. The arm holding the grid has been removed and the whole phantom is placed into the container. Light scattered by particles in the laser sheet travels through the upper half of the phantom before entering the cameras. The calibration should be performed with the upper half of the phantom in exactly the same position as during the measurement. Furthermore, the container is filled with paraffin such that the lumen is free of air. The calibration grid is placed directly underneath the upper half and moved downward over a range large enough to contain the full width of the laser sheet. The grid size used equals 0.5 mm. During a measurement, the calibration grid is removed and both halves of the phantom are used. The two halves are connected using bolts and placed into the device. The inflow 35

36 and outflow tubes slide through the brass guiding tubes into the plug-in couplings in the phantom. Filling and tilting of the container reduces background scattering. The laser and cameras are aligned and focused. The success of the measurement depends on the accuracy of repositioning the phantom. Therefore, some preliminary tests have been performed in order to examine the accuracy with which the phantom is repositioned in both the calibration setup and the measurement setup. The estimated standard error in the x-direction is in the order of magnitude 0.3 pixel for both the calibration and measurement setup. In the y-direction the error in the calibration setup is smaller than the error in the measurement setup, order of magnitude 0.4 and 0.6 respectively. This difference is caused by the extra force introduced by the stiff tubes connecting the phantom. More information on the phantom repositioning device and the accuracy tests is provided in appendix C Method A more detailed description of the measurement protocol is provided in appendix D.2.1. Although the physiological flow consists of a stationary and pulsatile component, only the stationary component is considered here. The desired flow characteristics are derived in section 2.2.2, which resulted in Re = 163. The kinematic viscosity of paraffin (ν p = m 2 s 1 ) is lower than the viscosity of blood. Since the geometry of the model is not scaled, the difference in viscosity is compensated by a change in flow from 3.6 ml s 1 to 2.5 ml s 1. The displacements are computed most accurately when the particles shift approximately 1/4 L int pixels between two recordings, with L int the interrogation area size. The flow in the parent artery differs significantly from the flow in the aneurysm, resulting in a different optimal time between image recordings for these two areas. Hence, the velocity fields in the aneurysm and its parent artery are determined using a time between recordings t = 2000 µs and t = 500 µs, respectively. A major disadvantage of this method is the impossibility to couple the velocity field in the aneurysm to the velocity field in the parent artery. Therefore, during injection the velocity field in both the aneurysm and parent artery is measured simultaneously using t = 1000 µs in all injection experiments. In both the stationary and injection experiments 30 image pairs are recorded with 200 ms between each image pair, yielding a sample frequency of 5 Hz and a measurement time of 6 seconds. In X-Ray, injection of a contrast agent is required to visualize blood. The properties of a contrast agent frequently used in cerebral aneurysms, Ultravist, are summarized in table 4.1. Both the viscosity and density differ from those of blood, thereby altering the flow characteristics. Furthermore, the influence of this injection may depend on the injection protocol, including parameters such as injection rate and injected volume. In order to examine the influence of those two parameters, the velocity field is measured during the injection of paraffin. Since the injected fluid has the same properties as the fluid of which one wants to visualize the flow, the only difference is caused by the injection itself. First, a reference injection is defined. In all other injections, either the injection rate or volume are varied. The ratio of the injection rate to the main flow should be such that enough contrast agent is injected to enable visualization of flow patterns with X-Ray. However, if the injection rate is to high, the image will be all black and all information on flow patterns is lost. Preliminary X-ray experiments showed that a fraction of injection rate and main flow of 0.3 to 0.8 gives the desired contrast. Based on this knowledge, three injection flow rates are 36

37 selected (table 4.2). The effect of the injected volume is examined by varying the duration of injection (1, 2 and 3 s). An injection rate of 1.5 ml s 1 and duration of 2 s represents the reference state. Table 4.1: Properties of Ultravist, a contrast agent used in X-Ray experiments. The Ultravist types differ in iodine concentration (the type numbers represent the iodine content in mg I per ml).[31] Ultravist Unit Viscosity 20 o C m 2 s 1 37 o C m 2 s 1 Density 20 o C kg l 1 37 o C kg l 1 Table 4.2: Injection rates and duration used in PIV experiments. The fraction of injection rate to the main flow is varied within the range that leads to good X-Ray results. The settings representing the reference injection are bold. Fraction of main flow Absolute flow rate Duration] [ ] [ml s 1 ] [s] ; 2.0; Data acquisition and postprocessing First the PIV images are corrected for the optical distortion, using the calibration results. Due to the distortion in the aneurysmal neck, the aneurysm and parent artery are processed separately. The velocity field is computed using an adaptive correlation method, which improves the correlation for larger displacements and velocity gradients. In the first incremental step an interrogation area size of pixels is used. The resulting displacements are used to preshift the interrogation areas in the next incremental step, in which the displacement field is computed using interrogation areas of pixels. After two refinement steps the final interrogation area size equals pixels. Furthermore, a 50% overlap of the interrogation areas is used to reduce loss-of-pairs. This also yields an oversampling of the data, which improves the accuracy of derived quantities (see chapter 3). Erroneous vectors, or outliers, are removed from the raw velocity field by range and moving average validation using the settings in table 4.3. In range validation, the maximum and minimum magnitude of the vectors is specified [25]. Since all vectors in the parent artery should be directed in the positive x-direction, the x-component of all vectors should be positive, while the smaller y-component may be both positive and negative. The exact values are determined by trial, which are chosen such that all obvious outliers are removed while all possibly correct vectors remain unaltered. The same procedure is used in the range validation 37

38 Table 4.3: The settings used in the range validation and moving average validation that are subsequently applied on the raw vector field. The first validation is used to remove outliers from the data, all vectors within the selected range are accepted. The second validation compares each vector to its surrounding vectors and adapts the vector if the deviation is larger than the allowed deviation specified by the acceptance factor. See the Dantec FlowManager manual for more information [25]. The values used in the range validation do not represent a velocity range since the Dantec Software introduces some scaling factor. This scaling factor is retrieved from the well-defined interrogation area size. Range validation Parent artery 0.05 < u < < u x < < u y < 1 Aneurysm < u < < u x < < u y < 0.5 Moving average validation Averaging area [IA] 3 3 Acceptance factor 0.1 Iterations 3 of intra-aneurysmal vector field. After the removal of most outliers moving average validation is used to smoothen the velocity field [25]. Each vector is compared to its neighboring vectors and adjusted if the difference exceeds the deviation defined by the acceptance factor. Only directly adjacent vectors are taken into account, as is specified by the averaging area of 3 3 interrogation areas. This process is executed three times. The effect of these validation procedures is visualized in figure D.4. A detailed description of postprocessing protocol is provided in appendix D.5. The data from the ultrasonic flow meter are obtained with a sample frequency of 1000 Hz. The signal is filtered using a moving average over 5 data points. There is no link between the time in the flow measurement and the time in the PIV measurement. In order to characterize the flow in the aneurysm, the intra-aneurysmal vorticity Ω z, which is mathematically expressed as the z-component of u, is determined for all vector fields. Counterclockwise rotation of particles results in a positive vorticity. The circulation Γ is derived from the vorticity using Γ = A ( u ) n da (4.1) with n the normal of the measured plane. Since the circulation represents the vortex strength, this enables quantitative analysis of the influence of the injection on the vortex strength in the aneurysm. The area over which the circulation is determined is the same for all measurements. 38

39 4.2 Results Stationary flow The flow equals 2.84 ± 0.04 ml s 1 and 2.86 ± 0.05 ml s 1 (mean ± SD) while recording the parent artery and aneurysm, respectively (figure 4.6(a)). The velocity at one point in the parent artery V p (x = 0 mm and y = 5.5 mm as indicated by the dot in figure 4.7) is 0.22±0.006 m s 1 (figure 4.6(b)). The velocity fluctuations show no unambiguous agreement with the measured flow (figures 4.6(a) and 4.6(b)). Figure 4.7 shows the stationary vector field averaged over 30 measurements. Since there is a significant difference in velocity in the aneurysm and parent artery, those regions are scaled separately. All results have been interpolated onto a uniform grid Parent artery Aneurysm V p (a) Time [s] (b) Frame Figure 4.6: (a) The flow measured while recording the parent artery and aneurysm. (b) The velocity at one point in the parent artery, indicated by figure 4.7, while recording the parent artery. 39

40 Figure 4.7: The vector field with stationary main flow averaged over 30 measurements. The vectors in the aneurysm and parent artery are scaled separately. Outliers have been removed by the validation routines described previously. The dot represents the position in the parent artery from which the velocity in time is retrieved and compared to the measured flow in figure 4.6. The contours in figure 4.8 represent the magnitude of the in-plane velocity defined as u 2 x + u 2 y. The in-plane velocity distribution in the parent artery shows higher velocities and velocity gradients near the outer wall. The distal side of intra-aneurysmal vortex shows the highest velocities. Furthermore, the center of the vortex is located distal to the aneurysmal center. These features are confirmed by the velocity profile at x 0 and y 0, which is presented in figure

41 Figure 4.8: The in-plane velocity distribution averaged over 30 measurements. The contours represent the magnitude of the velocity in m s 1. Figure 4.9: The averaged velocity profiles at x 0 and y 0 clearly show the slanted profile in the curved parent artery. The vortex center is situated at the distal side of the aneurysm. Note that the velocities in the parent artery and aneurysm are scaled differently. 41

42 The time averaged out-of-plane velocity, plotted in figure 4.10, shows no clear pattern. The average out-of-plane component equals ± m s 1 and ± m s 1 in the parent artery and aneurysm, respectively. The histograms of the outof-plane velocity shown in figure 4.11 reveal that most velocities are close to zero. Since the standard deviation is much larger than the measured velocities and no clear patterns can be distinguished, the out-of-plane component measurements are ignored. Figure 4.10: The out-of-plane velocity averaged over 30 measurements in m s (a) Parent artery u z [m s 1 ] (b) Aneurysm u z [m s 1 ] Figure 4.11: aneurysm. Histogram of the out-of-plane velocity in (a) the parent artery and (b) the 42

43 Figure 4.12 shows the vorticity in the parent artery and the aneurysm, again averaged over 30 measurements. The vorticity in the parent artery is higher near the outer wall due to the slanted velocity profile, with Ω z > 0 at the outer wall and Ω z < 0 at the inner wall. On the proximal side of the aneurysm the negative vorticity along the wall is clearly visible. On the distal side, the maximum velocity is reached close to the wall (figure 4.9), leaving only a thin layer with negative vorticity. Between this layer and the vortex center, the high velocity gradients result in a high vorticity. The intra-aneurysmal circulation equals ± m 2 s 1. Fluctuations in the circulation ( 10%) are only partly caused by the fluctuation in flow as observed in figure 4.6 (< 2%). Since the velocity field in the aneurysm and parent artery are measured in separate experiments, it is not possible to link the aneurysmal circulation to the velocity in the parent artery Figure 4.12: The vorticity in the parent artery and the aneurysm averaged over 30 measurements in s 1. 43

44 Frame [-] Figure 4.13: The intra-aneurysmal circulation equals ± m 2 s Injection into stationary flow The absolute in-plane velocity, out of plane velocity and vorticity throughout the aneurysm are discussed using the reference injection of 1.5 ml s 1 over 2.0 s as example. The flow measured during the reference injection is shown in figure Prior to injection the flow equals 2.7±0.04 ml s 1. Figure 4.15 shows that most peaks in the velocity at one point in the parent artery (defined in figure 4.7) also appear in the measured flow, which enables linking of the time in the measured flow to the time in the PIV measurement. The PIV measurement started at approximately t = 2.7 s in the flow measurement, whereas the injection started at t = 3.4 s. The in-plane velocity prior to injection, shown in figure 4.16(a), is similar to the inplane velocity measured in the stationary experiment described previously (figure 4.8). The increasing velocity in the parent artery during the injection results in an increase in intraaneurysmal velocity, as observed in figures 4.16(c) and 4.16(d). As the velocity in the parent artery decreases the influence of the injection on the intra-aneurysmal velocity fades gradually. The intra-aneurysmal vorticity is increased during the injection, as can be seen in figure As the injection fades, the vorticity decreases to the levels prior to injection. Figure 4.18 shows the intra-aneurysmal circulation, which reflects the increase in vortex strength during injection. The circulation within the aneurysm appears to be related to the velocity in the parent artery, although inertia seems to influence the reaction of the vortex strength to fluctuations in the main flow. Most velocity peaks in the parent artery occur slightly delayed in the intra-aneurysmal circulation. The velocity in the parent artery is measured at one point, which increases the chance of errors due to erroneous vectors. This could be avoided by comparing the flow to the circulation. However, in this approach delays can not be revealed since the time in the flow measurement is not linked to the time in the PIV measurement. 44

45 Time [s] Figure 4.14: The flow measured during the reference injection. At t = 3.4 s the injection becomes visible in the measured flow Normalized flow [ ] Normalized flow [ ] V p Time [s] (a) PIV Time [s] (b) Frame Figure0 4.15: 1 (a)the 2 measured 3 flow 4 and 5 (b)magnitude 6 7 of 8the velocity 9 10 V Time [s] p in m s 1 at one point in the parent artery (defined in figure 4.7). The fluctuations in the flow also appear in the measured velocity. The numbered peaks are 1.1used to estimate time at which the PIV measurement started. The PIV measurements started 1.05 at approximately s1.1 and1.1 ended at approximately 8.7 s, since the measurement time equals 6 s. 1 1 Normalized flow [ ] Normalized flow [ ] Normalized flow [ ] 1.25 Normalized flow [ ] 1.25 Normalized flow [ ] Normalized flow [ ] Normalized flow [ ] Time [s] Tim Time [s] 6

46 (a) Frame 1: t 2.7 s 0 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s 0 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s 0 (f) Frame 26: t 7.7 s Figure 4.16: The contours represent the magnitude of the in-plane velocity (in m s 1 ) in frame 1, 6, 11, 16, 21 and 26. For each frame, the corresponding flow is indicated by the flow pulse in the upper right corner. 46

47 (a) Frame 1: t 2.7 s -40 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s -40 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s -40 (f) Frame 26: t 7.7 s Figure 4.17: The contours represent the magnitude of the vorticity in s 1 in frame 1, 6, 11, 16, 21 and 26. For each frame, the corresponding flow is indicated by the flow pulse in the upper right corner. 47

48 Frame Figure 4.18: The normalized velocity at one point and the normalized circulation show a similar increase during injection. The numbering of the peaks corresponds to figure

49 4.3 Discussion Using PIV, velocities were measured in the major part of the model. The velocity field in the neck of the aneurysm and near the wall could not be measured due to the mismatch in refractive index and high curvature in the in vitro model. Since the layer along the aneurysmal wall is not taken into account as much as it should be the computed circulation is higher than the actual circulation. Furthermore, the distortion in the neck leads to problems in the calibration procedure, thereby introducing the need to process the aneurysm and its parent artery separately. The velocity field can be recombined after the stereo PIV computation is finished. Since this procedure significantly increases the time needed for postprocessing, it is strongly recommended to select a working fluid and in vitro model of which the refractive indices match closely. Another problem with PIV measurements in this particular model is scattering. Firstly, the scattering is introduced when the light sheet is directed at the model s plane of symmetry. This is caused by the slightly rounded edges of the aneurysm. Secondly, the seeding sticks to the wall resulting in an increase in scattering. Furthermore, the sticking seeding particles cause zero velocity biasing. In an attempt to reduce fouling of the wall, the wall was coated with copper polish (Brasso), which at first seemed to prevent, or at least significantly reduce, the fouling process. However, in later experiments the problem re-occurred and this time the copper polish did not help at all. Another factor that seemed to be of influence was the age of the seeding-paraffin mixture. Since PIV measurements are impossible under these circumstances, the chemical features that are important in this process should be reviewed. The phantom repositioning system enables calibration of the system, which is required in stereo PIV. Even if one camera is used, the calibration should be performed in order to reduce distortion effects due to the curvature of the wall. The slanted profile in the parent artery, as observed in figures 4.8 and 4.9, can be attributed to the curvature of the parent artery. As long as the boundary layer has not yet developed the viscous forces are restricted to a very thin layer along the wall. In the core the flow is inviscid and the pressure gradient and centrifugal forces are in equilibrium. As the boundary layer develops further down the tube, viscous forces will diminish the axial velocity thereby disturbing the equilibrium. A secondary flow develops resulting in an acceleration of particles in the central core towards the outer wall, while particles in the boundary layer will accelerate towards the inner wall. Since the particles in the central core have a relatively high velocity this secondary flow will cause a shift of the maximum axial velocity towards the outer wall [32, 33]. Since the plane of measurement is located below the plane of symmetry the secondary flow should induce an out-of-plane velocity which is directed away from the plane of symmetry near the outer wall, and towards the plane of symmetry near the inner wall of the parent artery. However, this is not observed in figure This might be caused by the fact that the out-of-plane velocity component is derived from the two in-plane components, resulting in an accumulated error as observed in the previous chapter. Since the standard deviation on the out-of-plane velocity was large compared to its average value and no clear distribution is observed, these measurements are considered not to be reliable. The intra-aneurysmal velocity fields show a single counterclockwise vortex, which is consistent with the findings of Liou et al.(1999) [21]. The in-plane velocity depicts a flow out of the aneurysmal sac, while Liou et al.(1999) reported that the inflow proceeds around the 49

50 distal lip of the orifice close to the plane of symmetry. This difference might be caused by the fact that the plane of measurement is localized below the plane of symmetry. The standard deviation of the intra-aneurysmal circulation is approximately 10%. This can only partly be explained by fluctuations in flow, which has a standard deviation of approximately 2%. Erroneous vectors and the fact that the vorticity is obtained through spatial differentiation also contribute to the standard deviation of the circulation. During injection an increase in intra-aneurysmal velocity is observed (figure 4.16). Obviously this results in an increased vorticity, as shown in figure Prior to injection the intra-aneurysmal vorticity is similar to the vorticity observed during stationary inflow (figure 4.12). The two extremes in the vortex center in figure 4.17 (a) and (e) are considered to be caused by erroneous vectors and are therefore not considered to be relevant. The increase in intra-aneurysmal vorticity is reflected in the increase in circulation. Figure 4.18 shows that the circulation follows the increase in velocity in the parent artery. Some peaks do not match, which is probably caused by inaccuracies in the velocity since this is the velocity at one point. This is confirmed by the fact that the all peaks but the ones that do not match are also visible in the flow measurement (figure 4.15). No correlations between the injection rate, duration and circulation are found based on the results of the different injection experiments. More data will be needed to reveal the influence of the injection on the vortex strength. In conclusion, both in the aneurysm and its parent artery the in-plane velocity field is successfully measured using stereo PIV. Only the out-of-plane velocity is not considered to be reliable. Therefore, the velocity field could be determined using only one camera in future experiments. This would significantly reduce the time needed for retrieving the velocity fields from the PIV images. A stationary flow in the parent results in a single vortex in the aneurysm. During injection the vortex pattern does not change, although the vortex strength follows the increased flow in the parent artery with delay. 50

51 Chapter 5 Computational Fluid Dynamics 51

52 In this chapter, the velocity field in the aneurysm and its parent artery is determined using finite element modeling. Finite element modeling is a powerful tool to examine the influence of parameters that are not easily varied in the experimental setup, such as the geometry. Furthermore, the velocity field in areas that can not be measured in the experimental model can be determined with the numerical model. In the experiments described in the previous chapter parameters like the laser sheet position relative to the in vitro model and the exact orientation of the sheet relative to the model influence the measured velocity field. The velocity field in the orifice and along the wall can not be measured due to distortion. Furthermore, the in vitro does not allow PIV measurement within the plane of symmetry. First, the stationary 3D velocity field is determined. The velocity field in the cross sections at the plane of symmetry and 1 mm below the plane of symmetry is examined in order to determine the influence of the laser sheet position on the experimental results. A qualitative comparison of the numerical and experimental results reveals whether important information misses in the experimental data (e.g. the velocity field in the neck of the aneurysm). Furthermore, a comparison of the in-plane and out of plane velocity distributions, as well as the vorticity and circulation, yields a qualitative analysis of the differences between the experimental and computational results. Next, an injection is simulated using the measured flow in the injection experiment. Again the results are compared both qualitatively and quantitatively to the experimental results. 5.1 Method and materials Incompressible Newtonian flow is described by the Navier-Stokes equations. Neglecting the influence of body forces like gravity, the Navier-Stokes equations read: ρ v t + ρ(v )v = p + ρν 2 v (5.1) v = 0 (5.2) which are solved for the geometry shown in figure 2.7. Due to the no-slip condition at the rigid impermeable wall, all velocities at the wall equal zero. At the inlet the normal velocity component is prescribed, while all other velocity components are set to zero. At the outflow all in-plane velocity component equal zero, whereas zero pressure is prescribed for the normal component. The density and viscosity of paraffin are ρ paraffin = 800kg m 3 and ν p = m 2 s 1, respectively. This model is implemented in Sepran. Figure 5.1 shows the 3D mesh generated with Patran (Hemolab), which consist of quadratic Crouzeix-Raviart type tetrahedron elements with discontinuous pressure interpolation (15 nodes per element). Temporal discretization of the Navier-Stokes equation is achieved using an implicit Euler scheme, while Newtons method is used for the linearization of the convective terms. The iterative method used to solve the linearized set of equations is Bi-CGStab with a incomplete LU decomposition pre-conditioner. The integrated method, or coupled approach, is used on the continuity equation. 52

53 Γ wall Γ inlet Γ outlet Figure 5.1: The 3D mesh generated with Patran consists of tetrahedron elements. Al velocities along the wall, denoted by Γ wall, equal zero. At the inlet Γ inlet as well as outlet Γ outlet both u x and u z are set to zero. Furthermore, the pressure is set to zero at Γ outlet and the magnitude of the velocity profile normal to Γ inlet varies per simulation: Problem 1: Stationary flow Poiseuille profile with flow resembling flow in experiments v z (r) = V max (1 r2 R 2 ) (5.3) with R the radius of the inlet, r the radius at which the velocity is computed and V max = 2q. The flow q = 2.5 ml s 1 equals the stationary flow as derived in chapter πr 2 4. Problem 2: Injection Again a Poiseuille profile is used, now with a time dependent V max. The flow measured during the reference injection is normalized and a fifth order approximation as displayed in figure 5.2 is used to compute V max (t). Prior to the injection the normalized flow is assumed to equal 1, resulting in the same V max as used in problem 1. 53

54 Normalized flow [ ] Time [s] Figure 5.2: The normalized flow measured during the reference injection. At t = 3.4 s the injection becomes visible in the flow signal. The peak in flow measured during the injection experiment is approximated using a fifth order polynomial. Prior to the injection the normalized flow is assumed to equal Results Time [s] In order to examine the velocity and vorticity within the plane of symmetry and 1 mm below the plane of symmetry all velocities within thin layer (0.5 and 0.1 mm respectively) are selected and interpolated onto a uniform grid Problem 1: Stationary inflow condition Plane of Symmetry Figure 5.3 shows the velocity field in the plane of symmetry. The x-range is chosen such that it contains the area measured in the PIV experiments described in the previous chapter. The velocity profile at x = 0 and y 0 shown in figure 5.4reveals the slanted profile in the parent artery. The aneurysmal neck shows a high velocity gradient where the aneurysmal vortex and the flow in the parent artery meet. Most vectors in the orifice are directed parallel to the main flow, except for two small regions adjacent to the orifice wall. The center of the intra-aneurysmal vortex is located distal to the center of the aneurysm. 54

55 0.2 m/s 0.1 m/s 0.2 m/s 1 m/s Figure 5.3: The velocity field in the plane of symmetry, scaled as depicted by the arrows. x m/s x m/s y 26 y 26 z[m] 24 z[m] m/s m/s x[m] x 10 (a) x [mm] 3 (b) x [mm] x[m] x 10 3 Figure 5.4: The velocity profile at x 0 and y 0 within the plane of symmetry, with the velocities in the aneurysm and parent artery scaled (a) equally and (b) differently, as depicted by the arrows. 55

56 The magnitude of the in plane velocity clearly shows the slanted profile in the curved parent artery, with higher velocities and velocity gradients near the outer wall (figure 5.5). Furthermore, it depicts the acceleration over the orifice and the high velocities near the distal wall of the aneurysm. At the proximal wall the velocities and velocity gradients are much lower. The out-of-plane velocity in the plane of symmetry shows no clear pattern (figure 5.6). Furthermore, the histogram in figure 5.7 that, although existent, the out-of-plane velocities are small compared to the in-plane velocities in both the aneurysm and it parent artery. Figure 5.8 shows positive vorticity near the outer wall of the parent artery, whereas negative vorticity is observed near the inner wall. Along the aneurysm wall the vorticity is negative. Furthermore, the vorticity on the distal side of the aneurysm is high due to the high velocity gradients in this region. The intra-aneurysmal circulation (equation 4.1) equals m 2 s 1. 56

57 Figure 5.5: The magnitude of the in-plane velocity within the plane of symmetry in m s Figure 5.6: The out-of-plane velocity in the plane of symmetry in m s 1. 57

58 (a) Parent artery u z [m s 1 ] (b) Aneurysm u z [m s 1 ] Figure 5.7: Histogram of the out-of-plane velocity in the plane of symmetry in (a) the parent artery and (b) the aneurysm Figure 5.8: The vorticity field within the plane of symmetry in s 1. 58

59 Below the plane of symmetry Figure 5.9 and 5.10 show the velocity field 1 mm below the plane of symmetry. Again the parent artery shows a slanted profile due to its curvature, although the effect is less profound than in the plane of symmetry (figure 5.10). Furthermore, the velocity gradient in the orifice is lower and the direction of the vectors in the orifice suggest a flow out of the aneurysm. When comparing the magnitude of the in-plane velocity (figure 5.5 and 5.11) it is evident that the velocities in the plane of symmetry are higher. Furthermore, the velocity at the distal lip of the orifice suggest that the flow into the aneurysm occurs near the plane of symmetry. 0.2 m/s 0.1 m/s 0.2 m/s 1 m/s Figure 5.9: The velocity field 1 mm below the plane of symmetry, scaled as depicted by the arrows. Proximal to the aneurysm, the out-of-plane velocity is directed away from the plane of symmetry (negative velocity) near the outer wall and towards the plane of symmetry (positive velocity) near the inner wall (figure 5.12). This phenomenon is caused by the secondary flow present in flow through a curved tube. The effect is reduced at the orifice where main flow and the intra-aneurysmal vortex meet. The negative velocity along the aneurysmal wall is induced by the inflow in the plane of symmetry, which spreads out over the distal wall. The central area of the aneurysm displays a positive out-of-plane velocity. Directly distal to the orifice an increase in the magnitude of the out-of plane velocities is observed. A comparison of the histograms in figures 5.7 and 5.13 reveals that both the deviation and number of vectors that differ from zero are larger in the plane 1 mm below the plane of symmetry. 59

60 0.2 m/s 0.02 m/s y y 0.2 m/s 0.2 m/s x [mm] x [mm] Figure 5.10: The velocity profile at x 0 and y 0 1 mm below the plane of symmetry Figure 5.11: The magnitude of the in-plane velocity 1 mm below the plane of symmetry in m s 1. 60

61 Figure 5.12: The out of plane velocity 1 mm below the plane of symmetry in17500 m s (a) Parent artery u z [m s 1 ] (b) Aneurysm u z [m s 1 ] Figure 5.13: Histogram of the out-of-plane velocity 1 mm below the plane of symmetry in (a) the parent artery and (b) the aneurysm. Even though the vorticity distribution in figure 5.14 does not differ much from the vorticity distribution in the plane of symmetry (figure 5.8), the intra-aneurysmal circulation does. The circulation equals m 2 s 1, whereas the circulation in the plane of symmetry is m 2 s 1. The vorticity distributions reveal that the vorticity at the orifice lip is higher in the plane of symmetry. Furthermore, the in-plane velocity displays is higher velocities at the distal wall and the distal orifice lip in the plane of symmetry. 61

62 Figure 5.14: The vorticity field 1 mm below the plane of symmetry in s 1. 62

63 5.2.2 Problem 2: Stationary main flow with injection The results are presented such that comparison to the experimental data presented in chapter 4 is possible. To this purpose both the time and the corresponding frame number are given. The first frame represents the situation prior to injection, the result of which corresponds to the stationary results described in Problem 1. Plane of Symmetry Figure 5.15(c) and (d) show an increase in in-plane velocity during injection. The vortex center does not seem to shift. In fact, the structure of the intra-aneurysmal vortex shows no evident changes, which suggests a quasi-static response the change in flow through the parent artery. As the injection fades, the in-plane velocity decreases to the levels observed in figure 5.15(b). This is consistent with the observation that the flow in the parent artery was still increased at the end of the measurement. The vorticity in 5.16 displays a similar response. Figure 5.17 shows that the circulation, which is normalized with the average circulation of m 2 s 1, follows the velocity in the parent artery closely. Below the plane of symmetry Throughout the injection, the intra-aneurysmal velocities shown in figure 5.18 are lower than the velocities within the plane of symmetry. An exception is observed near the proximal lip of the orifice when comparing figures 5.15(c) and 5.18(c), which might be caused by the fact that outflow mostly occurs through planes other than the plane of symmetry. The vorticity distribution in figure 5.16 resembles the distribution observed in figure 5.19, although the vorticity just below the vortex center is lower in the plane of symmetry. However, the average circulation equals m 2 s 1, which is lower than the average circulation within the plane of symmetry. Figure 5.20 shows that the circulation during injection follows the velocity in the parent artery with a slight delay, which is not observed in the plane of symmetry. 63

64 (a) Frame 1: t 2.7 s 0 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s 0 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s 0 (f) Frame 26: t 7.7 s Figure 5.15: The contours represent the magnitude of the in-plane velocity in m s 1 within the plane of symmetry. The corresponding flow is indicated by the flow pulse in the upper right corner. 64

65 (a) Frame 1: t 2.7 s -40 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s -40 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s -40 (f) Frame 26: t 4.7 s Figure 5.16: The contours represent the magnitude of the vorticity in s 1 within the plane of symmetry. For each frame, the corresponding flow is indicated by the flow pulse in the upper right corner. 65

66 Time [s] Figure 5.17: The normalized intra-aneurysmal circulation and velocity at one point in the parent artery (defined in figure 4.7) in the plane of symmetry. The time on the horizontal axis corresponds to the time in the PIV measurement described in the previous chapter, with t = 3.4 the time at which the injection appears in the measured flow. 66

67 (a) Frame 1: t 2.7 s 0 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s 0 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s 0 (f) Frame 26: t 7.7 s Figure 5.18: The contours represent the magnitude of the in-plane velocity in m s 1 1 mm below the plane of symmetry. For each frame, the corresponding flow is indicated by the flow pulse in the upper right corner. 67

68 (a) Frame 1: t 2.7 s -40 (b) Frame 6: t 3.7 s (c) Frame 11: t 4.7 s -40 (d) Frame 16: t 5.7 s (e) Frame 21: t 6.7 s -40 (f) Frame 26: t 7.7 s Figure 5.19: The contours represent the magnitude of the vorticity in s 1 1 mm below the plane of symmetry. For each frame, the corresponding flow is indicated by the flow pulse in the upper right corner. 68

69 Time [s] Figure 5.20: The normalized intra-aneurysmal circulation and velocity at one point in the parent artery (defined in figure 4.7) 1 mm below the plane of symmetry. The time on the horizontal axis corresponds to the time in the PIV measurement described in the previous chapter, with t = 3.4 the time at which the injection appears in the measured flow. 69

70 5.3 Discussion Overall, the velocity in the aneurysm and its parent artery seem to be computed correctly. However, the out-of-plane velocities observed within the plane of symmetry were not expected. They might depend on the mesh density and time step used in the simulation. Another factor that could introduce the out-of-plane velocities is the interpolation used to compute the velocity field within the plane of interest. The in-plane velocity fields within the plane of symmetry and 1 mm below the plane of symmetry show several differences (figures 5.3 to 5.5 versus 5.9 to 5.11). The slanted profile observed in the parent artery is more profound in the plane of symmetry. Furthermore, the outflow at the orifice depicted below the plane of symmetry is not observed within the plane of symmetry. This is consistent with the findings of Liou et al.(1999) [21]. The out-of-plane velocities within the plane of symmetry are small. Below the plane of symmetry however, a velocity towards the plane of symmetry is observed at the inner wall, while the velocity at the outer wall is directed away from the plane of symmetry (figure 5.12). These observations are consistent with the existence of a secondary flow in the curved parent artery. Although the intra-aneurysmal vorticity distributions show similar patterns (figure 5.8 and 5.14), the circulation within the plane of symmetry ( m 2 s 1 ) is significantly higher than the circulation below the plane of symmetry ( m 2 s 1 ). This is caused by the difference in in-plane velocity at the distal lip of the orifice and distal wall of the aneurysm. During injection, an increase in both the in-plane velocity and vorticity is observed while the vortex structure remains similar. This suggests a quasi-static response to the increased flow in the parent artery. Within the plane of symmetry, the intra-aneurysmal circulation follows the velocity in the parent artery closely. Below the plane of symmetry however, a delay of the increase in intra-aneurysmal circulation during injection is observed (figure 5.20). The numerical results were analyzed in a plane 1 mm below the plane of symmetry, to enable comparison with results from the PIV measurements described in the previous chapter which were obtained in the same plane. The in-plane velocity fields show similar characteristics, although the magnitude of the numerically obtained velocities in both the parent artery and aneurysm is larger in the numerical model than in the experiment (figures 4.7 to 4.9 versus 5.9 to 5.11). Both velocity fields depict an outflow at the orifice. Furthermore, the velocity profile in the parent artery is slightly slanted. Since the standard deviation in the measured out-of-plane velocity is large this result is not considered to be reliable. The numerically obtained out-of-plane velocity distribution, shown in figure 5.12, matches the theoretical features of flow in a curved tube. The measured intra-aneurysmal vorticity in figure 4.12 is lower than the numerically obtained vorticity shown in figure 5.14, which is reflected in the intra-aneurysmal circulations. The measured velocity field resulted in an intra-aneurysmal circulation of ± m 2 s 1, whereas the numerical circulation equals m 2 s 1. These results suggest that experimental velocity is measured even further below the plane of symmetry, which is not surprising considering the fact that the laser sheet thickness equals approximately 1 mm while the aneurysm is only 4 mm in diameter. The experimentally as well as the numerically obtained in-plane velocity and vorticity show an increase during injection. The intra-aneurysmal circulation in figure 4.18 appears to follow the velocity in the parent artery with a slight delay. This is also observed in the numerical data, as can be seen in figure Considering the similarities between the characteristics 70

71 of the measured and computed velocity field, it can be concluded that PIV experiments as presented in chapter 4 can be used to determine the velocity field in the in vitro model. 71

72 72

73 Chapter 6 General conclusion and recommendations 73

74 6.1 Experiment In the realistically dimensioned in vitro model, the in-plane velocity field in both the parent artery and aneurysm can be measured using PIV. The out-of-plane velocity component however, can not be measured accurately with the current setup. The in-plane velocity in the parent artery reveals a slanted profile, which is consistent with theoretical features of flow in a curved tube. The intra-aneurysmal velocity field shows a single vortex structure. Furthermore, an outflow at the orifice is depicted, which is caused by the fact that the plane of measurement is positioned below the plane of symmetry. During injection both the intra-aneurysmal velocity and vorticity increase, although the general flow pattern remains unaffected. The resulting increase in circulation follows the change in velocity in the parent artery with a delay. Although the in-plane velocity fields are successfully measured using PIV, some practical problems remain to be solved. The mismatch of the refractive index of the model and the fluid should be reduced to enable measurement in the aneurysms orifice and reduce the time needed for postprocessing. The added value of using two cameras for stereo PIV might be questioned since the measured out-of-plane velocity does not seem to be reliable. Using one camera rather than two would reduce the time needed for postprocessing. To reduce the sticking of the seeding to the inner walls of the model, it is recommended to review the chemical properties of the in vitro model, working fluid and seeding. 6.2 Computation fluid dynamics Overall, the CFD model presented in chapter 5 appears to describe the velocity field in the aneurysm and its parent artery accurately. Out-of-plane velocities were observed within the plane of symmetry. These might depend on the mesh density and time step used in the simulation, or on the interpolation used to compute the velocity field within the plane of interest. The velocity field obtained with the CFD model reveals that the inflow in the aneurysm occurs in the plane of symmetry, whereas below the plane of symmetry an outflow is observed. The slanted profile in the parent artery is more profound within the plane of symmetry. Furthermore, the out-of-plane velocity distribution below the plane of symmetry is consistent with the presence of a secondary flow. The circulation in the plane of symmetry is significantly higher than the circulation below the plane of symmetry, which is caused by the difference in velocity at the distal side of the aneurysm. During injection the magnitude of the intraaneurysmal velocity increases, while the pattern shows no evident changes. This suggests a quasi-static response, although a quantitative comparison of the velocity fields is needed to confirm this. In both planes, the circulation follows the changes in velocity within the parent artery. However, a delay is observed in the response of the circulation below the plane of symmetry. The velocity fields below the plane of symmetry correspond to the velocity fields obtained with PIV. The profile in the parent artery is slightly slanted and an outflow is observed in the aneurysmal neck. The experimentally obtained velocities and intra-aneurysmal circulation are lower than the results from the CFD model, which is caused by the thickness of the laser sheet. Both the experimentally and the numerically obtained circulation follow the increase in flow during injection with a slight delay. 74

75 6.3 Future work Since in the described experiments the injected fluid has the same properties as the fluid of which one wants to visualize the flow, the only differences will be caused by the injection itself. In the X-ray experiments the properties of a frequently used contrast agent, Ultravist, deviate from those of blood, causing an additional disturbance of the flow. Since both light and X-ray beams are able to pass through the in vitro model, the flow can be visualized using high-speed camera as well as X-ray systems. In order to apply the results obtained with PIV experiments, the injection speed should be scaled using the Reynolds number. To mimic the in vivo flow conditions, both in the in vitro and the numerical model a pulsatile inflow should be used. The timing of injection relative to the pulsatile flow might alter the influence of the injection on the intra-aneurysmal vortex. Hence, in the in vitro experiment the time of the flow measurement, PIV measurement and applied injection should be linked. The CFD model could be helpful in optimizing the injection protocol for flow visualization using X-ray. After implementation and validation of the pulsatile flow, the computational model could be expanded with the convection-diffusion equation in order to describe the distribution of the contrast agent throughout the geometry. Projection of the resulting contrast agent concentrations combined with the local depth yields a numerical X-ray image which can be validated with experimental X-ray images. This numerical model can be used to examine which parameters affect the X-ray image. The influence of the injection depends on the injection protocol, including parameters like injection rate and injected volume. However, other parameters, such as the distance of the catheter to the aneurysm and the nature of the catheter tip may be worth considering too. In X-ray, the distance of catheter to the aneurysm is an important parameter since the no slip boundary condition at the arterial wall forces diffusion of contrast agent. In the end, this should lead to a more accurate method to estimate the risk of rupture of cerebral aneurysms. When accurate in vivo measurement of the intra-aneurysmal flow becomes possible, the shear rate experienced by the endothelial cells covering the aneurysmal wall could be derived. The response of those endothelial cells lead to adaptation, or in aneurysms, degradation of the arterial wall. If models describing the relation of this degradation process to the shear rate are available, the flow visualization with X-ray will become a valuable tool in the risk of rupture assessment. 75

76 76

77 Appendix A Geometry in vitro model 77

78 Figure A.1: Geometry curved phantom 78

79 Appendix B Flow characterization 79

80 In general, incompressible Newtonian flow is described by the Navier-Stokes equations[32]: ρ v t + ρ(v )v = p + η 2 v, (B.1) v = 0, with ρ and η the density and dynamic viscosity of the fluid, v the velocity, p the pressure gradient and t the time. These equations are converted to a nondimensional form by introducing the following non-dimensional parameters: x = x R ; v = v V ; t = ωt; p = p ρv 2 ; with R, V and ω a characteristic length, velocity and frequency, respectively. After substitution of these nondimensional parameters and dropping the accent, equation B.1 read with α 2 v t + Re(v )v = Re p + 2 v, (B.2) ω α = R ν Re = RV ν Womersley number Reynolds number (B.3) (B.4) 80

81 Appendix C Phantom repositioning device: development and testing 81

82 C.1 Accuracy experimental setup The laser sheet enters the phantom at the side of the aneurysm, parallel and just below the upper half of the model. Since light scattered by particles in the laser sheet travels through the upper half of the phantom before entering the cameras, the calibration should be performed with the upper half of the phantom in exactly the same position as it was during the measurement. The device shown in figure C.1 enables reproducible positioning of the phantom relative to the cameras. C.1.1 Design repositioning device Reproducible positioning of the phantom within the container is accomplished using three springs. Each spring applies a force in one direction, thereby pushing beads on the phantom into slits in the container. Since all degrees of freedom are now constrained, the position of the phantom should be reproducible. The container rests on a base in three slits intersecting underneath the middle of the aneurysm, creating a thermal center. As a consequence, the position of the aneurysm will not change due to temperature fluctuations. Micro screws are used to tilt the device relatively to its base such that the aneurysm will be parallel to the cameras. The base is mounted on the same frame as the cameras. Figure C.1: Phantom repositioning device. The upper half of the phantom is reproducibly positioned using three springs. Three beads on the phantom are pressed into slits in the container, thereby imposing the position of the phantom. The same principle is used to attach the arm holding the calibration grid. A translation device enables vertical movement of the grid. The mirror is used for illumination of the grid during the calibration procedure. In flow measurements the arm holding the grid is removed and the whole phantom is placed into the container, again relying on the three beads and spring for reproducible positioning. A translation device is mounted perpendicular to the base plate of the container. This 82

83 Figure C.2: The round pits on either side of the aneurysm are clearly visible enabling accurate detection of their position. The standard deviation of the position in all images is determined, with the x- and y-direction in horizontal and vertical direction, respectively. device enables a well-defined translation of the calibration grid throughout the thickness of the laser sheet. This grid consists of a coated glass plate, the grid points being holes in this coating. The metal equilateral mirror underneath the grid allows illumination required for the grid points to become visible. During a measurement, both halves of the phantom are used. The two halves are connected using bolts and placed into the device as described above. The calibration grid has been removed. The tubes slide through the brass guiding tubes into the plug-in couplings in the phantom. The laser and cameras are aligned and focused. Filling and tilting of the container reduces background scattering. After setting the system all should remain untouched until both the measurements and calibration are finished. C.1.2 Method The successfulness of the measurement depends on the accuracy of repositioning the phantom. In order to test this two tiny pits were drilled in the upper plate of the phantom, on either side of the aneurysm. First, only the upper half of the phantom is placed into the container after which it is set down on the baseplate. An image is recorded with both cameras. This is repeated ten times. Subsequently, the two halves of the phantom are jointed and placed into the container. The tubes are fastened and the container is placed onto the base plate. Again this is repeated ten times. C.1.3 Results The round pits are clearly visible in figure C.2. The position of both dots is determined in all images and the standard deviation computed. The results are summarized in table C.1. 83

84 Table C.1: Testing of the accuracy with which the phantom is repositioned: the standard deviation over 10 repetitions for both the upper plate alone and the whole phantom. Upper plate Both plates Dot 1 Dot 2 Dot 1 Dot 2 Standard deviation x [pixel] Standard deviation y [pixel] The influence of the repositioning error is most significant in the neck of the aneurysm, near the edges of the image and near the edges of the lumen. However, these areas are either not used (the edges of the image) or not properly visible due to the mismatch in refractive indices (neck and edge of the lumen). Since all standard deviations are smaller than one pixel the effect of the repositioning on the quality of the calibration is assumed to be negligible. 84

85 Appendix D Protocol 85

86 D.1 Preparing a measurement D.1.1 Calibration flow probe Since electromagnetic flow probes rely on ions present in the flowing medium, salt is usually added. However, salt is not soluble in the apolar paraffin oil. Therefore, an ultrasonic flow probe is used to monitor the flow during injection. The ultrasonic flow probe was calibrated for water flowing through a silicon tube (4 mm in diameter). This calibration is not valid for the seeded paraffin. Since paraffin alters the properties silicon, the calibration of the flow probe was performed after using it for several hours. After this period no visually detectable changes of the silicon occurred. The pump was set at a certain value and the height difference between the tubes did not change during a measurement. The outflow was intercepted over 30 seconds, yielding the actual flow. The measured flow and tapped flow are plotted in figure D.1. The offset is not present for zero flow, indicating the calibration is only valid for the small range shown. D.1.2 Laser beam alignment The laser beams should overlap at the distance at which the measurement is performed. The beams are directed through a series of optical devices, as described in the laser manual [34]. The two beams are combined by one mirror, which is the mirror that needs adjustment for proper beam overlap. If you are not familiar with the laser alignment procedure, one should always ask for assistance. The procedure for checking and, if necessary, adjusting the beam overlap: Use the smallest camera diaphragm Put a folded black paper in the beam path within the cameras field of view Select a measurement map and run online Choose the continuous mode and adjust the paper till the beams are visible with the cameras Adjust the diaphragm and focus of the cameras Focus the light sheet by turning the middle part of the laser head Select stop in the run online window If the beams did not overlap properly one should adjust the mirror combining the beams. One should not be doing this alone for the first time. Remove the cover of the laser and tape the safety switch (always use goggles when the cover is removed) Select the continuous mode again Turn the screw in order to adjust the height of the beam till optimal overlap is achieved Select stop in the run online window 86

87 Figure D.1: Calibration data of the ultrasonic flow probe. The resulting trend line is used to compute the flow in the injection experiments. The offset is not observed when no flow is present, indicating these calibration data are only valid for the range shown here. D.1.3 Preparing the setup Build the flow and PIV setup as shown in figure 4.1 and 4.4. Build database in PIV software corresponding to measurement schedule. Make sure proper settings are selected for camera and laser. Use double frames for measurement and single frames for focussing and calibration images. For more information on the FlowManager software and PIV, read the manual accompanying the Dantec PIV system [25]. PIV system: aligning laser to setup Make sure the cameras are switched off and covered with their protection caps since scattering of laser light during this procedure will damage the CCD, Put the phantom (both plates) in the carrier with the phantom parallel to the field of view Switch the computer, processor and lasers on Open the database in FlowManager and initiate the processor Go to the measurement map and run online, select the continuous mode Adjust the height of the sheet till the sheet is positioned just below and parallel to the phantoms plane of symmetry Select stop in the run online window Flow circuit: connecting the aneurysm and mount the plug-in couplings Push the rubber rings into their chambers Put the brass tube guiders and rings around the tubes and push the tubes from outside the container towards the aneurysm Turn the tubes such that they can easily slide into the plug-in couplings (putting minimal veritcal pressure onto the phantom) 87

88 Gently tighten the brass cylinders Place the container on its base plate Ultrasonic flow meter Switch the flow meter on Put gel between the probe and the tube wall until the meter receives a strong signal (at least 4 bars). Pulsatile pump Switch the power supply on Switch the computer on and go to Measurements and Automations Choose the Devices and Interfaces tab and then go to PCI-7342(1) Press the initialize button in this program Switch the pulsatile pump on with the button on the small grey controller Create empty.txt files for the storage of the flow data the flow data Start the Labview application Set the values for the sample frequency, input file, number of cycles, amplitude (in encoder counts), storage yes/no and the DAQ-channels Stationary pump Injector Switch the pump on Get all air out of the flow circuit (aneurysm) Adjust the mean flow to the required value Switch the injector on Make sure the water in the injector is not heated Change the settings of injection PIV system: focussing the cameras Fill the container with paraffin and make sure there is no paraffin on top of the phantom Switch the cameras on, use the smallest diaphragm Use the continuous mode with low frame grabbing frequency Slowly increase the diaphragm and focus the cameras in the middle of the laser sheet height such that individual particles are visible Adjust the angle of the image plane and the focus of the camera till the whole field of field is focussed (Scheimpflug principle described in chapter 3) D.2 Performing a measurement Once everything is properly connected and set, the flow measurements can start. However, make sure the setup does not move prior to the calibration, or the measurements are lost. Select the map corresponding to the measurement and run online Check and initialize the injector Check the stationary pump 88

89 Start the pulsatile pump D.2.1 Start PIV in run online window Inject as soon as the laser starts As soon as injector is ready, get the actual flow rate and duration of the injection and initialize again Start new measurement Repeat till phantom is to dirty or new settings are needed. Calibration procedure After the measurements a calibration is performed in order to link the coordinates in the object plane and the coordinates in the image plane. Make sure the setup does not move at all during the measurements and calibration procedure. Handle the calibration set up with care since its functioning depends on its tuning. Switch off the pumps and drain the system Take the phantom out of the flow circuit Open the phantom and clean it thoroughly (prevent scratching) Attach the arm holding the calibration grid (the container should be partially filled with paraffin to prevent air under the grid) Clamp the upper half of the phantom (with the beads) in the setup (again all air should be removed) Add paraffin such that no paraffin is present on top of the phantom Adjust the height of the calibration grid till it is barely touching the phantom (the positioning of the arm carrying the grid fails when pressure is applied on the grid) Place a light source such that the illuminated grid is clearly visible with the cameras (enough contrast between grid points and its surroundings. A piece of paper can be placed in the beam path in order to prevent overexposure of the CCD, do not alter the diaphragm) Record the first images (z=+1 mm) Move the calibration grid 0.1 mm down and take the next image pair (z=+0.9 mm) Repeat the former step till the last image pair is obtained (z=-1 mm) 89

90 D.3 Processing the images After the measurements and calibration are finished, the images gathered in the FlowManager software are exported as bitmaps. This enables the processing of the data with more flexible non-commercially software. The processing steps are summarized in figure D.2. This section contains the processing protocol, including the settings used for the results reported in chapter 4. D.3.1 FlowManager Calibration images First, the calibration images are exported form FlowManager. Select all calibration images choose File-Export Select File - Export Choose a convenient base name, start numbering at 0 and export as separate.bmp files Annotate which image is from which camera (even from camera 0 and odd from camera 1) for the processing of the PIV images. Linux Convert all calibration images to.pgm and choose a name which contains the camera number. The.pgm image should have a 5-digit identification number. So if 10 calibration images were recorded with two cameras, one types for camera 0: do "convert cal %04d.bmp cal.0.%05d.pgm" Define a mask for both cameras using black for the regions to be masked (Gimp). Leave some room since the image will shift slightly in vertical translation. Convert the mask such that the areas to be masked are white in the masking image. convert -negate mask.0.pgm mask.0.pgm Apply the mask on every calibration image using fmask do "fmask cal.0.%05d.pgm mask.0.pgm cal.0.%05d.pgm" Refine the mask for every calibration image, removing all dots outside the lumen and all strongly deformed dots. (Gimp) Define one origin in the aneurysm and one origin in the tube as shown in figure D.3. The origin in the tube should placed at a certain constant number of grid points below the origin of the aneurysm. (Gimp) One dot defines the origin itself, a dot directly right from the origin defines the x-axis. To define the y-axis a dot is placed above the origin dot, skipping one grid point. After all origins masks are properly defined the lumen is split in two parts, masking either the parent artery or the lumen (fmask). Now the calibration is computed using fac. This routine needs the following input (between braces is the program with which the parameter is determined): 90

91 H L H L H L H L K K L L H L H L K L M + = A H =. =? + = E > H = J E E = C A I / H F E N A? E = J A I. E J A H? =? = E > H = J E + = E > H = J E + = A H =. =? + = E > H = J E E = C A I / H F E N A? E = J A I. E J A H? =? = E > H = J E + = A H =. H = A = >. K M = H F 7 M = H F B H = A = > = E > H = J E = A H =. H = A = >. K M = H F 7 M = H F B H = A = > Figure D.2: A schematic overview of the postprocessing steps. The upper diagram displays the calibration procedure, while the lower diagram contains the processing of the PIV images 91

92 MinBlobSize = number of pixels of smallest grid point (display) MaxBlobSize = number of pixels of largest grid point (display) Threshold = minimum gray value (xv) Pixelaspect = pixel aspect ratio, in general = 1 XGridSize = distance between grid points (physical coordinates) YGridSize = distance between grid points (physical coordinates) MinMaxXFilterSize = filter radius in x-direction MinMaxYFilterSize = filter radius in y-direction Image = the image of which the calibration is computed Every illumination larger than the filter size is ignored. Therefore, the filter radius should be somewhat larger then the radius of the largest grid point. In order to determine the proper parameter setting one could use fblobfind, showing which illuminations are defined as grid points and which are not. The distance between grid points equals 0.5 mm. However, it is more convenient to define everything in grid sizes and scale the final result, avoiding scaling errors. The output, the dot positions in both pixel and grid coordinates, should be written to a.cal file. All calibration files should have the same base name, in the case pa.0 and an.0. Due to diffraction in the neck of the aneurysm the parent artery (pa) and aneurysm (an) are processed separately and recombined after the computation of the velocity field. fac cal pgm > pa cal Another output of this routine is the file monitor.m, running this m-file results in a plot of the calibration dots on their pixel positions. The numbers represent the grid coordinate of the dote. This plot should be checked thoroughly in order to make sure the calibration is correctly computed. The z-calibration is computed using fintercal requiring the following input: num.calfiles = number of.cal files per camera dz = the z-range over which the calibration was performed BaseName = file name without identification number.cal XStart = the lowest x-coordinate of the region to be calibrated XEnd = the highest x-coordinate of the region to be calibrated YStart = the lowest y-coordinate of the region to be calibrated YEnd = the highest y-coordinate of the region to be calibrated z-value = the height at which the laser sheet is present. If GridSize=1 is used in fac one can simply count the grid points within the region of interest. If not, multiply the number of grid points with the grid size. Again the output is written to a.cal file. Plotting of the pixel coordinates and grid coordinates should result in two similar sawtooth shapes. fintercal pa > fipa.0.cal fintercal an > fian.0.cal In general only the part containing grid points is used in the calibration. In this case 92

93 Figure D.3: Two separate origins are defined in the aneurysm and parent artery. In each origin, the upper dot defines the direction of the y-axis while the right dot defines the x-axis. The third dot defines the origin itself. however, the parent artery and aneurysm are computed separately due to the diffraction in the neck of the aneurysm. Using the whole area prevents scaling differences, thereby enabling recombination of the data after the velocity field is computed. Repeat this process for the images from camera 1. D.4 Particle images After the calibration procedure is completed, it is applied on the images in order to reduce distortion effects. First export the PIV images as bitmaps (procedure equal to exporting calibration images). Linux If dysfunctional pixels are present its gray value should be interpolated from surrounding pixels as described in D.5(pixcor.m) Renumber all images such that the even images correspond to the first frame recorded and the odd images correspond to the second frame (renumber.m) Compute the background scattering (fand.m) Convert all images to.pgm Subtract the background scattering: do "fsub basename.0.%05d.pgm and.0.pgm basename.0.%05.pgm" 93