MRI based quantification of outflow boundary conditions for wall shear stress calculations in stenosed human carotid bifurcations

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1 MRI based quantification of outflow boundary conditions for wall shear stress calculations in stenosed human carotid bifurcations Lenette Simons BME Master Thesis Medical Engineering (8Z170) 13 th October 2009 Student id: Graduation committee: Erasmus MC Department of Biomedical Engineering dr. ir. J.J. Wentzel Erasmus MC Department of Radiology dr. A. van der Lugt Eindhoven University of Technology Department of Biomedical Engineering prof. dr. ir. F.N. van de Vosse dr. ir. E.M.H. Bosboom dr. ir. G.J. Strijkers

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3 Abstract Introduction - Atherosclerosis is an inflammatory disease of the arteries. In an atherosclerotic artery a plaque forms in the intima. High wall shear stress (WSS) has been shown to promote the biological weakening of the plaque, which can ultimately lead to plaque rupture. Plaque rupture in the internal carotid artery (ICA) is associated with stroke. To assess WSS in patient-specific 3D geometries of the carotid bifurcation computational fluid dynamics (CFD) is often performed. For the calculation of WSS with CFD, it is important to know the outflow boundary conditions. When flow is not measured in the carotid bifurcation, the flow distribution from the common (CCA) over the external carotid artery (ECA) and ICA has to be estimated. In this study we investigated the influence of stenosis on the ICA/CCA and ECA/CCA flow ratio and the effect hereof on the WSS in the carotid bifurcation. Methods - To obtain flow, lumen radius and degree of stenosis, a 3D phase contrast MR measurement was performed in 65 carotid bifurcations of 33 subjects. First, the reproducibility and SNR of this measurement and the possible influence of aliasing due to the selected encoding velocity was determined with a volunteer study (n=4). Secondly, the relationship between the ICA/CCA and ECA/CCA flow ratio and the degree of area stenosis in the ICA was determined. Computational fluid dynamics (CFD) was used to calculate the WSS in five patient-specific 3D geometries of the carotid bifurcation with stenosis. For the determination of the outflow boundary conditions for the WSS calculations, the ICA/CCA flow ratio was determined with three methods: 1) the patient-specific MR flow measurements, 2) estimations with Murray s Law and 3) estimations from the generic relationship between flow ratio and degree of stenosis determined from the MR measurements. The differences between the WSS obtained with the measured flow ratio and obtained with the estimated flow ratios were investigated. Results- The protocol used for the flow measurements was a reproducible, easy to perform method to measure time-averaged flow in the carotid bifurcation. When the degree of stenosis was lower than 65, we found that the ICA/CCA and ECA/CCA flow ratio was constant (64 and 36%) based on non-linear regression analysis. Although Murray s Law gave a reasonable estimation of the mean flow ratios for bifurcations without stenosis (R 2 = 0.54), for bifurcations with a degree of stenosis lower than 65%, the estimations were not good (R 2 = 0.19). The differences between the WSS obtained with the measured and with the estimated flow ratios were small. When the degree of stenosis was higher than 65%, the ICA/CCA flow ratio decreased as function of degree of stenosis to zero, while the ECA/CCA flow ratio increases to 100%. Murray s Law overestimated the ICA/CCA flow ratio and underestimated the ECA/CCA flow ratio (R 2 = 0.05). The differences between the WSS obtained with the measured flow ratio and the flow ratio estimated with Murray s Law and the generic relationship increased when the degree of stenosis was higher than 65%. However, the differences between the measured flow ratio and the estimated flow ratio were larger when Murray s Law was used than when the generic relationship was used for 1

4 the estimation of the flow ratio. Especially at the site of the stenosis, this difference was large when Murray s Law was used (up to 4.7 Pa, and a relative difference of 250%). Discussion and conclusion- Although the 3D phase contrast measurement is a reproducible, easy to perform method to determine time-averaged flow, the venc should be chosen carefully to avoid aliasing in the measurement results. For carotid bifurcations with less than 65% stenosis, however, Murray s Law cannot be used for the estimation of the ICA/CCA and ECA/CCA flow ratios and therefore for the determination of outflow boundary conditions for WSS calculations. The best method to determine the flow ratios is a patient specific flow measurement. When this measurement is unavailable, the generic relationship between the degree of area stenosis and flow ratio derived in this study can be used instead. Although the WSS derived with the generic relationship also leads to local inaccuracies, these inaccuracies are smaller than the inaccuracies in the WSS derived with Murray s Law. Keywords: wall shear stress, flow, stenosis, Murray s Law, carotid bifurcation 2

5 Contents Abstract Introduction MRI protocol analysis - methods Aliasing in phase contrast measurements Flow measurement with non-triggered 3D phase contrast imaging Study group Measurement positions in the carotid bifurcation Image analysis Data analysis MRI protocol analysis - results Flow and signal to noise ratio Aliasing Reproducibility Flow measurements - methods Non-triggered 3D phase contrast flow measurements Study group Determination of the degree of area stenosis Generic relationship between stenosis and the ICA/CCA and ECA/CCA flow ratio Murray s Law Data analysis Flow measurements - results Study group Measured flow and flow ratios vs degree of stenosis Estimation of the flow ratio with Murray s Law and a general flow law Wall shear stress calculations - methods Navier-Stokes equations Volume mesh generation WSS calculations Geometries and prescribed flow Postprocessing Wall shear stress calculations - results Mean and maximum WSS obtained with the measured ICA/CCA flow ratio Differences between WSS obtained with different outflow boundary conditions

6 8 Discussion MRI protocol Influence of stenosis on the ICA/CCA and ECA/CCA flow ratio Wall shear stress calculations Conclusion References Appendix

7 1 Introduction Atherosclerosis is an important underlying cause of most cardiovascular diseases and the leading cause of death in the developed world [1]. It is a chronic, progressive, inflammatory disease of the arteries, which develops in the first layer of the arterial wall which is called the intima. In the healthy vessel wall, the intima consists of a layer of endothelial cells. In the process of atherosclerosis, cholesterol (LDL) particles from the blood pass through the endothelium and accumulate in the intima. As the LDLs accumulate, macrophages gather in the arterial wall and ingest the LDL particles. The macrophages with the ingested LDL particles form a fatty streak, which is the first precursor of atherosclerosis. At this point an inflammatory response can take place in the intima. As a result an atherosclerotic plaque will form in the arterial wall. Once a plaque is formed it can progress into a stable or a vulnerable plaque. A vulnerable plaque is distinguished from a stable plaque by the presence of a large lipid pool in the arterial wall, which is covered by a thin fibrous cap [2]. Inflammation weakens the fibrous cap, which causes cap thinning. This weakened, thin cap might rupture due to peaks in the blood pressure. Because of plaque rupture the contents of the plaque come into contact with the blood [1]. This leads to the formation of thrombus, a blood clot. Thrombus might occlude an artery and cause a cardiovascular event as the occlusion of an artery leads to a shortage of oxygen in the tissue. Stroke is often associated with rupture of a vulnerable plaque in the internal carotid artery (ICA) [3]. The ICA and the external carotid artery (ECA) arise from the common carotid artery (CCA) in the carotid bifurcation, which is positioned on the left and on the right side of the neck. The ICA is one of the arteries that provide the brain with blood, while the ECA supplies the other tissues of the head with blood. The thrombus that was formed in the ICA during the plaque rupture occludes an artery distal to the ICA and therefore disturbs the blood supply to the brain. In clinical practice, patients with plaque in the ICA are divided in symptomatic patients and asymptomatic patients. Symptomatic patients have demonstrated symptoms, like stroke and TIA, whereas asymptomatic patients do not. Removal of the plaque reduces the risk on a stroke [4]. Only symptomatic patients and asymptomatic patients with a high degree of stenosis qualify for removal of the stenosis. The plaque can be removed by balloon angioplasty, after which often a stent is placed at the site of the stenosis, or by surgical removal of the plaque with carotid endarterectomy. Blood flow induced wall shear stress (WSS) has been shown to influence the remodeling of the arterial wall. When the WSS deviates from its normal value the arterial wall remodels to bring the WSS back to its normal level by expansion or decrease of the lumen radius. This remodeling process is mediated by the endothelial cells, which register the WSS. The stabilization of the WSS therefore depends on the functioning of the endothelium. In regions of low WSS the functioning of the endothelial cells can be impaired [5]. Regions of low WSS are therefore more prone to atherosclerosis than others. Low WSS occurs when the blood flow is disturbed. The regions of disturbed flow in the arterial system are bifurcations or regions with high curvature of the artery [6]. 5

8 Atherosclerotic plaque usually expands outward to preserve the lumen of the artery and therefore the blood flow. However, lumen preservation is no longer possible when the plaque area is larger than 40% of the cross-sectional area of the arterial wall bounded by the media. The plaque then starts to intrude into the lumen and causes lumen narrowing [7]. This narrowed lumen area is called stenosis. The degree of stenosis is often used to predict if a patient with carotid artery stenosis will benefit from surgery [4]. Despite the criteria used in clinical practice for surgery in patients, the risk on plaque rupture of a vulnerable plaque does not necessarily depend on its degree of stenosis. This risk also depends on the composition of the plaque, which is influenced by WSS. Evidence is accumulating that exposure of the plaque to high WSS leads to thinning of the fibrous cap [8]. Eventually, this thinning of the fibrous cap can lead to cap rupture. To assess the vulnerability of a plaque WSS could therefore be a useful parameter. To test whether high WSS indeed causes weakening of the plaque and thereby rupture of the plaque it is important to know the WSS at the site of plaque rupture. An important tool for the assessment of WSS in patient-specific 3D geometries is computational fluid dynamics (CFD). With CFD, the velocity of the blood in the entire geometry is calculated and from these velocities the frictional force on the arterial wall, which is the WSS, is determined. For the calculation of WSS with CFD it is important to prescribe appropriate in- and outflow boundary conditions to the 3D geometries. In the carotid bifurcation, the flow distribution from the CCA over the ICA and the ECA (the ICA/CCA and ECA/CCA flow ratio) has a large influence on the WSS in the arteries. Unfortunately, it is not common practice to measure flow in carotid bifurcations suspected for plaque in the carotid artery. Mean flow in the carotid bifurcation has been measured for healthy volunteers [9], but the influence of stenosis on the flow is unknown. The mean flow in the CCA, ICA and ECA has never been measured in bifurcations with stenosis. When flow information in the carotid bifurcation is not available, the flow in the CCA and the distribution of the flow from the CCA over the ICA and ECA is estimated. The flow in the CCA can be chosen such that a physiological shear stress value is obtained at the CCA of 1.2 Pa [10, 11]. Murray s Law could be used to estimate the flow distribution from the CCA over the ICA and the ECA. Murray s Law relates the lumen radius of a mother branch in a bifurcation to the lumen radii of the daughter branches originating from the mother branch. It also relates the ratio of flow from the mother branch to each daughter branch to the ratio of the lumen radii to the third power. When Murray s Law is used for the estimation of outflow boundary conditions in the carotid bifurcation, the assumption is made that the shear rates in the mother and daughter branches are the same. It is unknown whether this assumption applies in the carotid artery with presence of stenosis in the ICA and therefore if Murray s Law gives a good estimation of the ICA/CCA and ECA/CCA flow ratio in the presence of a stenosis. Aim of this study was to investigate the influence of the degree of area stenosis on the ICA/CCA and ECA/CCA flow ratio, to estimate the flow ratios with different methods and to study the influence of the use of estimated instead of the measured flow ratios on the WSS calculations. First, the ICA/CCA and ECA/CCA flow ratio and degree of stenosis were determined with MR flow measurements in carotid bifurcations. Secondly, the ICA/CCA and ECA/CCA flow ratio was estimated with two methods. The first method uses Murray s Law to 6

9 estimate the ICA/CCA and ECA/CCA flow ratio. For the second method a generic relationship was determined between the measured ICA/CCA and ECA/CCA flow ratio and the measured degree of area stenosis in the ICA. Third, the WSS in carotid bifurcations was obtained with both the measured flow ratios and the estimated flow ratios with CFD. The differences between the WSS obtained with the measured and obtained with the estimated flow ratios were determined. A 3D time-averaged phase contrast MR scan was used to measure the flow and lumen radius in the CCA, ICA and ECA and the degree of area stenosis in the ICA. Since the time-averaged 3D phase contrast measurement used to determine flow in this study has not been used for flow measurements in the carotid bifurcation before, a volunteer study was performed to investigate the signal to noise ratio, reproducibility and possible influence of aliasing on the measurement results. The applied MR sequences and data analysis methods are discussed in Chapter 2. The results of the volunteer study and the comparison of the signal to noise ratio and reproducibility are presented in Chapter 3. The MR measurements were then performed in the carotid bifurcations of subjects suspected for stenosis in the right or left ICA and subjects without stenosis in the carotid bifurcation. The ICA/CCA and ECA/CCA flow ratio was determined for every bifurcation. A generic relationship between the degree of stenosis and the ICA/CCA and ECA/CCA flow ratio was fitted through the measured flow ratios as a function of the degree of stenosis. The measured ICA/CCA and ECA/CCA flow ratios were compared to the flow ratios estimated with Murray s Law. The MR measurement protocol, estimation methods for the ICA/CCA and ECA/CCA flow ratio and data analysis are discussed in Chapter 4. The results are presented in Chapter 5. WSS was calculated in patient specific 3D geometries with CFD. Three different methods were used to determine the prescribed ICA/CCA flow ratios. First the ICA/CCA flow ratio was determined from the MR flow measurements performed on the specific patient under study. The second method uses Murray s Law to estimate the ICA/CCA flow ratio. For the third method, the ICA/CCA flow ratio was estimated from the generic relationship between the ICA/CCA flow ratio and the degree of stenosis as determined in Chapter 5. The difference and relative difference between the WSS obtained with the measured ICA/CCA flow ratio and the WSS obtained using Murray s Law or the generic relationship between flow ratio and the degree of stenosis for the estimation of the ICA/CCA flow ratio was determined. The methods used to calculate the WSS with CFD are discussed in Chapter 6. The results of the WSS calculations are presented in Chapter 7. This report ends with a discussion and conclusion in Chapter 8. The limitations of the applied measurement protocol and the CFD calculations are discussed. Also, some recommendations for future studies are made. 7

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11 2 MRI protocol analysis - methods At the beginning of this study, MR flow measurements had already been performed on a CCA large number of subjects in the Rotterdam Study, a population based study. The biggest advantage of ICA the non-triggered 3D phase contrast MR sequence ECA (3D) used in this study for the measurement of flow in the carotid bifurcation was the large size of the venc image volume in which flow was measured in a relatively short image time. The planning of the scan was also easy. Abbreviations Common carotid artery Internal carotid artery External carotid artery Encoding velocity However, no information was available on the reproducibility of the non-triggered 3D phase contrast measurement and the possible influence of aliasing on the measurement data. Together with the SNR, the reproducibility and the possible influence of aliasing on the measurement data were investigated in this section. 2.1 Aliasing in phase contrast measurements For phase contrast measurements a bipolar gradient is applied to the image volume. Due to this gradient, the flowing blood gains a phase proportional to its velocity. Because a bipolar gradient is applied, stationary tissue will have no net change in phase[12]. During the velocity encoding, a phase shift of π is assigned to a maximum detectable velocity (v enc ) and a phase shift of π to a minimum detectable velocity (-v enc ). Aliasing occurs when the peak velocity in the artery exceeds the minimum or the maximum encoding velocity. This will lead to the wrapping around of the velocity information (Equation 2.1, Figure 2-1 ). A velocity higher than the venc and therefore the flow determined from a measurement with aliasing will be underestimated. v v : v v 2v enc enc v v : v v 2v enc enc (2.1) Figure 2-1: Phase image of a 2D time-dependent measurement with aliasing on the left and the same image without aliasing on the right [13]. 9

12 In time-dependent measurements, aliasing is obvious as can be observed in Figure 2-1. But if aliasing occurs in the 3D time-averaged measurement used in this study, no method is available to detect the aliasing, because the velocities in the phase images are timeaveraged [13]. A velocity encoding (venc) of 60 cm/s was used for the 3D measurements in the population study in which subjects older than 55 years of age were included. However, in the CCA, the mean peak systolic velocity (PSV) is expected to be around 64 cm/s in the age group of 50-59, as was measured with Doppler ultrasound in a study of Samijo, et al. (Figure 2-2) [14]. Therefore, aliasing could occur in the majority of the male and female subjects in the age of years. Figure 2-2: PSV (v max,sys ) as a function of age in male (blue) and female (magenta) subjects [14]. 2.2 Flow measurement with non-triggered 3D phase contrast imaging Time-averaged flow was determined with MRI measurements using a 1.5 T whole-body MR system (Signa Excite, GE Medical Systems, USA). A non-triggered 3D phase contrast measurement was used to measure time-averaged blood velocities in the carotid bifurcation with a bilateral 4-channel phased array surface coil. If the bilateral coil was unavailable because it was needed for other studies, a lateral 4-channel phased array surface coil was used. For the non-triggered 3D phase-contrast measurement a gradient echo spin sequence was used with velocity encoding in all spatial directions, TR/TE = 13/4.26 ms, 1.2 mm slice thickness, 256x256 acquisition matrix, FOV = 180x180 mm and the number of excitations, NEX = 1. NEX stands for the number of times the scan was repeated. The voxel size was 0.7x1.2x0.7 mm. The acquisition time was 5-6 minutes. The scan was performed in coronal direction. 10

13 2.3 Study group The study group consisted of four presumably healthy volunteers, three males and one female. They were years of age. An overview of the 3D time-averaged measurements is shown per volunteer in Table 2-1. On all four volunteers 3D measurements were performed to determine the flow and SNR from these measurements. In volunteer 1 and 2, flow measurements were only performed in the left carotid bifurcation, because the bilateral coil that measured also the right bifurcation was unavailable at the time of the measurement. In volunteer 3 and 4 the flow and SNR was determined in the left and the right carotid bifurcation. The flow measurements in volunteer 3 were performed on two different days: measurements with venc = 30, 60, 90 and 150 cm/s on one day and measurements with venc = 60 and 100 cm/s on the other day. In volunteer 1-3 the 3D flow measurements were performed with venc = 90 cm/s, but the peak systolic velocity in the CCA of these volunteers was only slightly lower than 90 cm/s. The venc of the 3D measurements of volunteer 3 and 4 was therefore increased to 100 cm/s. The difference in the venc between the measurements with the selected venc=90 cm/s and the selected venc=100 cm/s was assumed to have little influence on the measured flow. Table 2-1: Overview of the venc applied for the 3D phase contrast measurements performed on volunteer 1-4. v enc [cm/s] volunteer x 2 x 3 x x x x (n=3) x 4 x x (n=3) To investigate the possible effects of aliasing on the measured flow and SNR, 3D phase contrast measurements were performed on volunteer 3 in the left bifurcation (n=1). The venc was set to 30, 60, 90 and 150 cm/s. For each measurement, the flow was determined in the CCA to quantify the influence of aliasing on the measured flow. On volunteer 3 and 4 a measurement with a venc of 60 cm/s and three repeated 3D measurements with a venc of 100 cm/s were performed in the left and right bifurcation to investigate the possible influence of aliasing on the measured flow, velocities and the reproducibility of the measurements. The measurements with venc=60 cm/s and the first measurement with venc=100 cm/s (n=4) were used to investigate the possible influence of aliasing on the flow and maximum velocities in the left and right CCA in two volunteers. In the measurement with venc = 60 cm/s, which was used in patients included in this study, aliasing was expected and in the measurement with venc = 100 cm/s aliasing was not expected. The difference between the measured time-averaged flows obtained with both measurements gives information on the influence of aliasing on the measurement in the patient study. The possible influence of aliasing was only investigated in volunteers 3 and 4, because we had not considered the possibility of aliasing when the measurements on volunteer 1 and 2 were performed. 11

14 The reproducibility of the flow and maximum velocity was determined in the CCA from the three repeated measurements with venc=100 cm/s (n=12). The intra-observer reproducibility was determined in four bifurcations of patients (three female, one male) who were years of age. 2.4 Measurement positions in the carotid bifurcation The measurements were performed in both carotid bifurcations, which are positioned on the left and on the right side of the neck, just below the jaws (Figure 2-3). In the carotid bifurcation the CCA divides into the ICA and the ECA. The ICA is one of the arteries that provide the brain with blood and the ECA supplies most tissues of the head with blood except the brain [15]. Figure 2-3: Position of the carotid bifurcation in the neck [15]. The flow and lumen radius was determined 22 mm proximal to the apex of the carotid bifurcation in the CCA, 22 mm distal to the bifurcation in the ICA and 15 mm distal to the bifurcation in the ECA (Figure 2-4). The positions were based on a study of Long, et al. [16]. Due to the limited size of the image volume (approximately 5 cm in length), the measurement position in the CCA was 22 mm proximal to the apex of the bifurcation in contrast to the 35 mm used by Long, et al. The ECA often had side-braches close to the apex of the bifurcation. The measurement position was therefore chosen at 15 instead of 22 mm distal to the apex of the carotid bifurcation. If side branches were present closer than 15 mm to the carotid bifurcation in the ECA, flow was determined proximal to the first side branch. 12

15 Figure 2-4: Positions at which the flow and the lumen radius were determined in the carotid bifurcation. 2.5 Image analysis Four sets of images were reconstructed from the image volume of the 3D phase contrast measurement: magnitude images and phase images in the x, y, and z direction (S x, S y and S z ). Velocities (v) were calculated with a formula which was supplied by the manufacturer of the scanner from the ratio of the grayscale values of the phase images (S phase,lumen ) and the magnitude image (S mag,lumen ). The velocity scale factor (k) and the encoding velocity (v enc ) were scan parameters. The velocity encoding (venc) and the velocity were given in mm/s. The average signal intensity of the stationary tissue in the sternocleidomastoid muscle (S phase,stat ) was subtracted from the measurement data to correct for possible phase offset in the phase images. S v S v phase, lumen phase, stat enc S mag, lumen (2.2) k For the drawing of the lumen contours, 2D slices were reconstructed in the axial direction from the 3D image volume. To calculate the flow in an artery, lumen contours were drawn manually on nine consecutive magnitude images with ImageJ (rsbweb.nih.gov/ij). In order to obtain the cross sectional images perpendicular to the centerline, the centre of mass of each contour was determined. Then, a first order polynomial fit was made through these centers of mass to define a centerline. The direction vector of this centerline was assumed to be normal to the arterial cross-sections (Figure 2-5). The lumen area of the cross-sections was defined by the boundaries of the lumen contours. 13

16 Figure 2-5: Lumen contours were determined on magnitude images using ImageJ. The lumen crosssections perpendicular to the centerline of the artery were determined. Finally, the velocity profiles of the cross-sections were derived from the grayscale phase images with linear interpolation. Secondly, the velocities within the arterial cross-sections were calculated from the image volume by linear interpolation between the two neighbouring voxels in the z-direction. The total flow (Q) through the luminal area (A lumen ) with a voxel surface (ΔA) was determined from the inner product between the velocity in a voxel (v) and the normal (n) of the arterial cross-sections (Equation 2.3). Q ( v n) A (2.3) A lumen The flow was determined in three consecutive arterial cross-sections perpendicular to the centerline of the artery. The flows obtained in these cross-sections were averaged. 2.6 Data analysis Signal to noise ratio (SNR) The SNR (S/N) depends on several scan parameters like the venc and the image resolution. Generally, 3D images have a higher SNR than 2D images, because they have an additional phase encoding step in the z-direction (Equation 2.4) [12]. S N V voxel n n n ex y z f (2.4) Where n ex is the NEX, n y is the number of phase encoding steps in the y-direction, n z is the number of phase encoding steps in the z-direction, V voxel is the volume of a voxel and Δf is the bandwidth, which is the range of frequencies in the frequency encoding direction (the x direction). The SNR was determined for the 3D measurements. The SNR was determined from the signal intensity of a region of interest in the imaged object (S obj ) and the standard deviation of the signal of background noise (ς background ), which was measured in a region of interest outside the imaged object [17] (Equation 2.5). S S N object background (2.5) Reproducibility The precision with which flow can be measured with non-triggered 2D phase contrast measurements has been investigated and depends on the pulsatility of the flow [18]. If the 14

17 flow in an artery is highly pulsatile, the flow waveform has a large systolic peak and therefore a large difference between the systolic and diastolic flow. A large number of the waveform needs to be taken to determine the time-averaged flow. The effect of the pulsatility of the flow on the precision of the flow measured with the 3D measurements is unknown until now. The reproducibility of the 3D measurements gives some information about the precision of the measurement. Because the flow measurement was performed once in every subject, the reproducibility of the measurement itself could not be determined for the patient study. Therefore, the reproducibility of the MR sequence was determined using healthy volunteers. The healthy volunteers had a more pulsatile flow than the older subjects included in the study of the flow in the carotid bifurcation with stenosis. For volunteer 3 and 4 a 3D measurement (venc=100 cm/s) was repeated three times to investigate the reproducibility of the measurement. The absolute differences between the three measured flows and maximum velocities were determined for every measured CCA (n=4) and the absolute differences relative to the mean measured flow and velocities. All differences between the flow and velocities were combined (n=12) Effect of the intra-observer reproducibility and the measurement position on the measured flow and lumen area The flow was measured inside the lumen contours. The size and position of the lumen contours were therefore very important for the measured flow. The effect of the intraobserver reproducibility of the lumen contours on the flow, lumen area and velocities, was determined in the CCA and ICA of four bifurcations. First lumen contours were drawn twice in the CCA and ICA by the same observer. Then flow, maximum velocity and lumen area in bifurcations with stenosis was determined for both sets of lumen contours. Because the signal strength varies in the image volume, it was investigated to which degree the measurement position and the position along the z-axis influenced the measured flow, maximum velocity and lumen area. Lumen contours were drawn at two different positions by the same observer as far apart as possible in the image volume. The first set of lumen contours was drawn 22 mm below the apex of the bifurcation and the second set of lumen contours was drawn 12 mm below the apex of the bifurcation Statistics The Kolmogorov-Smirnov test was used to test whether the measurement data was normally distributed. Flow and maximum velocity measured to investigate the possible influence of aliasing, the intra-observer reproducibility and the measurement position were analyzed with paired t-tests with a 95% confidence interval. All data were presented as mean plus standard deviation. SPSS Statistics 17.0 was used for all statistical analysis and p<0.05 was considered to be statistically significant. 15

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19 3 MRI protocol analysis - results In this chapter the mean flow, signal to noise ratio (SNR) and reproducibility of the measurements on healthy volunteers are discussed. Also the errors in the determination of flow, maximum velocity, lumen area and degree of stenosis are reviewed. 3.1 Flow and signal to noise ratio The mean time-averaged flows were 7.6 ± 1.1, 4.8 ± 0.7 and 2.4 ± 0.9 ml/s in the CCA, ICA and ECA. The mean maximum velocities were 38 ± 4, 37 ± 9 and 22 ± 5 cm/s in the CCA, ICA and ECA. The mean SNR of the magnitude images (26 ± 13) was higher than the SNR of the phase images (4.7 ± 1.3). The SNR of the magnitude images of volunteer 3 did not change with increasing venc (Figure 3-1A, R 2 =0.02 and p=0.85). However, there was a strong correlation between the venc and the SNR of the phase images (Figure 3-1B, R 2 =0.85). The SNR of the phase images decreased with increasing venc. However, this decrease was not significant due to the small number of measurements (p=0.06). Thus, from Figure 3-1B can be concluded that it is important to set the venc of the sequence to a value just above the expected maximum blood velocity in the artery in order to obtain the highest possible SNR without aliasing. Magnitude Phase A Figure 3-1: The SNR of the A) magnitude images and B) phase images as a function of the venc in the 3D measurements performed on volunteer 3. B 17

20 3.2 Aliasing In Figure 3-2 the measured flows with a venc of 30, 60, 90 and 150 cm/s are shown for volunteer 3 in the CCA. The measured flows increased when the venc increased, indicating aliasing at low venc. When the venc was 150 cm/s, the measured flow decreased slightly which could be caused by a drop in the SNR of the phase images. Figure 3-2: Flow (q) measured with 3D measurements on volunteer 3 as a function of venc in the CCA. The mean measured flow in the left and right CCA of volunteer 3 and 4 (n=4) was 7.7 ± 0.9 ml/s when it was determined from the measurement with venc = 100 cm/s and 6.9 ± 0.5 ml/s determined from the measurement with venc = 60 cm/s. The flow measured with venc = 60 cm/s was 11% lower than the flow measured with venc = 100 cm/s (p<0.05, paired t-test). The mean measured maximum velocity in the CCA was 38 ± 2 cm/s when venc = 100 cm/s and 36 ± 3 cm/s when venc = 60 cm/s. The velocity measured with venc = 60 cm/s was, with an underestimation of 5 %, significantly lower than the measured velocity when venc = 100 cm/s was used (p<0.05, paired t-test). 3.3 Reproducibility The reproducibility of the 3D measurements was determined by performing the flow measurement three times in the CCA of four carotid bifurcations. The median of the absolute difference between the measured flows was 0.9 ml/s, which was a relative difference of 12%. The median of the absolute difference in the maximum velocity was 1.9 cm/s (a relative difference of 5%). The absolute differences in the measured flows varied with 0 to 20% and the maximum velocities with 1 to 17% Effect of the intra-observer reproducibility and the measurement position on the measured flow and lumen area The intra-observer reproducibility of the flow, maximum velocity and lumen area was determined in the CCA and ICA in four bifurcations. In Table 3-1, the mean difference and relative difference is shown between the flow, maximum velocity (v max ) and lumen area (A lumen ) determined from the lumen contours drawn twice by the same observer in the CCA. The difference in flow, v max and A lumen was not significant in the CCA. The relative difference was smaller than 10%. The in-plane resolution of the measurement (0.7 x 1.0 or 1.2 mm) was sufficient to satisfy the minimum amount of three pixels across the lumen diameter (4.1 18

21 mm) in three directions required for the determination of the velocity profile in an artery [13]. Table 3-1: Intra-observer reproducibility of the measured flow, maximum velocity and lumen area in the CCA Mean Difference Relative difference [%] p-value q 5.7 ± ± ± v max 21 ± ± ± A lumen 58 ± ± ± q = blood flow in ml/s; v max = maximum velocity in cm/s; A lumen = lumen area in mm 2 The same procedure was repeated for the ICA (Table 3-2). Although the differences were not significant, the relative difference in flow and v max were larger than in the CCA and larger than 10% of the mean. The relative difference in the lumen area of the CCA and ICA was comparable. The in-plane resolution of the measurement (0.7 x 1.0 or 1.2 mm) was sufficient to satisfy the minimum amount of three pixels across the lumen diameter (3.2 mm) in three directions. The difference in lumen area determined from the lumen contours drawn twice by the same observer was 7 % for the ICA. It is expected that this difference also influenced the intra-observer reproducibility of the degree of stenosis. Table 3-2: Intra-observer reproducibility of the measured flow, maximum velocity and lumen area in the ICA Mean Difference Relative difference [%] p-value q 3.1 ± ± ± v max 28 ± ± ± A lumen 46 ± ± ± q = blood flow in ml/s; v max = maximum velocity in cm/s; A lumen = lumen area in mm 2 At two different positions along the z-axis, the difference and relative difference between the flow, v max and A lumen was determined to investigate the influence of a difference in position along the z-axis on the measurement results (Table 3-3). None of these differences was significant. The lumen area is larger close to the bifurcation, which explains the larger difference in lumen area than observed for the analysis of the intra-observer reproducibility. However, the difference in the measured flow and v max was also higher than for the intraobserver reproducibility in the CCA. Table 3-3: Influence of the position on the z-axis on the flow, maximum velocity and lumen area in the CCA Mean Difference Relative difference [%] p-value q 5.7 ± ± ± v max 23 ± ± ± A lumen 58 ± ± ± q = blood flow in ml/s; v max = maximum velocity in cm/s; A lumen = lumen area in mm 2 19

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23 4 Flow measurements - methods To determine the outflow boundary conditions for CFD calculations in diseased carotid bifurcations, flow was measured in the common carotid (CCA), internal carotid (ICA) and external carotid artery (ECA) in a large group of volunteers with different degrees of area stenosis in the ICA. From these flow measurements the relationship between the ICA/CCA and ECA/CCA flow ratio and the degree of Abbreviations CCA ICA ECA venc Internal carotid artery External carotid artery Encoding velocity stenosis was determined. The flow ratios were also estimated with Murray s Law and a general flow law and compared to the measured flow ratios. Common carotid artery 4.1 Non-triggered 3D phase contrast flow measurements Time-averaged flow was determined with MRI measurements using a 1.5 T whole-body MR system (Signa Excite, GE Medical Systems, USA). A non-triggered 3D phase contrast measurement was used to measure time-averaged blood velocities in the carotid bifurcation with a bilateral 4-channel phased array surface coil. For the non-triggered 3D phase contrast measurement a gradient echo spin sequence was used with velocity encoding in all directions. The scan parameters were TR/TE = 13/4.26 ms, 256x256 matrix and NEX = 1. For the asymptomatic patients (Rotterdam Study) the voxel size was 0.7x1.0x0.7 mm with venc = 60 cm/s and for the symptomatic patients (Erasmus MC) the voxel size was 0.7x1.2x0.7 mm with venc = 90 cm/s. The scan was performed in coronal direction. More information on the MR sequences and positions of the flow measurements, the scan parameters and the determination of flow from the MR measurements was given in Chapter Study group For this study MRI measurements were performed on the left and right carotid bifurcation of a group of subjects. In total 33 (19 male, 14 female) subjects were included into the study. The mean age of the subjects was 76 ± 8 years. These subjects consisted of asymptomatic and symptomatic patients. The asymptomatic patients in the study group were recruited from the Rotterdam Study (n=21), a population based study on subjects aged 55 years and over. When the intima-media thickness (IMT) of the ICA of a subject was larger than 2 mm, a plaque in the carotid bifurcation was suspected and MRI measurements of the carotid bifurcation were performed. The mean age of the subjects recruited from the Rotterdam Study was 78 ± 6 years. The symptomatic patients were recruited from patients scheduled for carotid endarterectomy in the Erasmus MC Rotterdam (n=12). Since carotid endarterectomy is usually performed on patients with severe stenosis, the symptomatic patients were expected to have a high degree of stenosis. The mean age of these subjects was 71 ± 9 years. In the Rotterdam Study, the maximum velocity that could be measured with the used MR sequence (venc=60 cm/s) was possibly lower than the peak systolic velocity of the blood in the carotid bifurcation of the studied subjects. As patients with a higher age have a lower peak systolic velocity (see Chapter 2), only patients older than 70, the age at which the peak 21

24 systolic velocity was presumably lower than the venc of the used MR sequence, were included in this study (see Chapter 2 and 3). The difference between the flow in the CCA and the sum of flow in the ICA and ECA was also investigated. Although mass conservation requires that the flow in the CCA and the sum of flow in the ICA and ECA were equal, measurement errors caused a difference between them. We aimed at a difference between these flows of less than 10% to restrict the influence of measurement errors on the measured flow ratios. However, twelve bifurcations with a difference between 10 and 15% were also included in this study, because a difference of less than 10% could not be achieved. 4.3 Determination of the degree of area stenosis Due to the limited acquisition time in the MR protocol (see Chapters 2 and 3), an anatomical proton density weighted MR scan was only performed on the plaque in the ICA and not on the entire bifurcation. The degree of stenosis was therefore determined from the magnitude images of the MR phase contrast measurement. To determine the degree of area stenosis in the ICA, twenty contours were drawn in the 2D axial images distal to the bifurcation. The 2D axial magnitude slices were reconstructed from the 3D image volume. The centerline and arterial cross-sections of these slices were determined from these contours (Figure 4-1). The degree of area stenosis (x) was calculated from the minimum lumen area (A min ) of these cross-sections and the average lumen area of the three cross-sections most distal to the bifurcation (A 0 ) (Equation 4.1). A 1 min x 100% A0 (4.1) This average lumen area should be determined distal to the plaque in a plaque-free part of the artery. The cross-sections most distal to the bifurcation were assumed to be plaque-free when the lumen area was constant. The standard deviation of the mean lumen area of the three cross-sections distal to the plaque should therefore be smaller than 10%. If the crosssections were not plaque free, additional contours were drawn on additional slices distal to the stenosis until the standard deviation of the lumen area was smaller than 10%. A A 0 A A min Figure 4-1: Lumen cross-sections perpendicular to the centerline of the artery were determined. The degree of area stenosis was determined from the minimal lumen area (A min ) and the lumen area distal to the stenosis (A 0 ). 22

25 4.4 Generic relationship between stenosis and the ICA/CCA and ECA/CCA flow ratio The ICA/CCA and ECA/CCA flow ratio was determined from the measured flow in the CCA, ICA and ECA. With parameter estimation, a relationship was determined between the measured ICA/CCA and ECA/CCA flow ratio and the degree of stenosis in the ICA. This relationship was assumed to be linear. The relationship between the flow ratio and degree of area stenosis was expected to change above a certain degree of stenosis. A cut-off value was therefore determined for the degree of stenosis above which the relationship between degree of stenosis and the flow ratios changes. Equation 4.2 applies when the degree of stenosis is lower and Equation 4.3 applies when the degree of stenosis is higher than the cut-off value. q a x b b x b q when a1 a2 (4.2) q a x b b x b q when a1 a2 (4.3) Where x is the degree of area stenosis, q 1 is the flow through the daughter branch (the ICA or the ECA), q 0 is the flow through the mother branch (the CCA) and a 1, a 2, b 1 and b 2 are the estimated parameters that define the linear relationships. 4.5 Murray s Law Murray s physiological principle of minimum work is based on the assumption that the radii of blood vessels in the cardiovascular system are a trade-off between the power needed to pump the blood volume through the arterial system and the cost of maintaining the blood volume [19]. The heart provides the power needed to pump the blood through the cardiovascular system. This is the sum of the power needed to pump the blood through each individual artery. The power needed to pump blood through an artery is determined by the flow through the artery and its resistance (Equation 4.4) [19]. 8 Lq W 4 r L when W q R and R (4.4) 4 r Where W is the work done by the heart, q is the blood flow, R is the resistance of the artery, η is the viscosity of blood, L is the length of a blood vessel segment and r is the lumen radius. From Equation 4.4 can be concluded that energy can be saved by increasing the radius of an artery. However, energy is also needed to produce and maintain the total volume of blood in the circulation. This is also called the cost of blood volume and should be added to the total energy required for the circulation of blood (Equation 4.5). 8 Lq E 4 r 2 bl r 2 (4.5) 23

26 Where E is the sum of the energy needed to pump blood through an artery and the energy needed to produce and maintain the volume of blood. The constant b represents the cost of blood in the arterial system. The total energy is a minimum, which occurs when: 2 de 32 Lq 2bL r 0 5 dr r (4.6) The constant b can be derived from Equation 4.6 (Equation 4.7). 2 16q b 2 6 r (4.7) A relationship can be derived from Equation 4.7 between the blood flow through an artery and lumen radius (Equation 4.8). q kr 3 with k 2 b 16 (4.8) Where q is the blood flow, r is the lumen radius and k is a constant factor that depends on the viscosity η and b [J/(Ls)]. If blood is assumed to be an incompressible fluid, the principle of conservation of mass should apply to the mother vessel, the CCA, and the two daughter vessels, the ICA and ECA (Equation 4.9). qcca qica qeca (4.9) When the assumption is made that the artery is a circular, cylindrical tube and the flow in the artery is laminar, the ratio of the WSS (τ w ) in an artery and the viscosity of the blood, which is called the shear rate (γ ), is proportional to the flow (Equation 4.10). 3 r q w with 4 (4.10) If the shear rate is the same in all three arteries of the carotid bifurcation, k in Equation 4.8 is constant and Equation 4.11 can be derived from Equation 4.9 [20]. r r r (4.11) CCA ICA ECA To determine if Murray s Law (Equation 4.11) gives the best estimation of the lumen radius of the CCA a general law for the relationship between the radius in the CCA and the radii of the ICA and ECA was established by the estimation of the parameter x (Equation 4.12) [21]. The radii estimated with this general law were compared to the measurement results and the results of the estimations with Murray s Law. r r r (4.12) x x x CCA ICA ECA If the relationship between the radius in the mother and daughter branches as described in Equation 4.11 holds in the carotid bifurcation and k is indeed a constant, Equation 4.13 can 24

27 be derived from Equation 4.8. The ICA/CCA and ECA/CCA flow ratio can be estimated from the lumen radii in the ICA, ECA and CCA without flow measurements. q q ICA CCA r r ICA CCA 3 and q q ECA CCA r r ECA CCA 3 (4.13) The measured ICA/CCA and ECA/CCA flow ratios were compared to the flow ratios estimated with Murray s Law with Equation To determine if Murray s Law indeed gives the best estimation of the flow ratios, parameter estimation was used to determine a general flow law (Equation 4.14). q q ICA CCA r r ICA CCA x and q q ECA CCA r r ECA CCA x (4.14) Where x is the estimated parameter. This parameter x was compared to the parameter x = 3 in Murray s Law. The flow ratios estimated with this general flow law were also compared to the measurement results. The lumen radii were determined at the same position in the CCA, ICA and ECA as the flow (see Chapter 2.4). 4.6 Data analysis In every subject, the flow and degree of stenosis was measured in both the left and the right carotid bifurcation. Comparisons were made between subjects and bifurcations. If comparisons were made between subjects, it was determined whether the left or the right bifurcation had the major stenosis. The subjects were subdivided into four groups according to the degree of stenosis of the major stenosis. Group 1 consisted of subjects without stenosis in any bifurcation. The subjects in group 2 had a degree of stenosis lower than the cut-off value. The subjects with a degree of stenosis higher than the cut-off value were divided into two groups according to degree of stenosis (group 3 and 4). Group 3 and 4 were chosen such that they contained the same number of subjects. If comparisons were made between bifurcations, the bifurcations were subdivided into four groups with the same subdivisions according to degree of stenosis as the subjects. Non-linear regression analysis was used to estimate the relationship between the degree of stenosis and the measured ICA/CCA and ECA/CCA flow ratio and the cut-off value from which the relationship between the degree of stenosis and the flow ratio changes (Equation 4.1-2), the parameter x in the general law used to estimate the radius of the CCA and the parameter x in the general flow law (Equation ). The Kolmogorov-Smirnov test was used to test whether the measurement data was normally distributed. If the data was normally distributed, paired t-tests with a 95% confidence interval were used to compare estimated to measured flow ratios and to compare the measured flows in both bifurcations of a subject. The correlation between Murray s Law, the general laws and the measurement results was determined with linear regression analysis. The systematic and relative errors in the estimations with Murray s Law and the general flow law were determined from Bland-Altman plots. Mean flows and flow ratios between different groups of bifurcations or subjects were compared with a one-way 25

28 analysis test (ANOVA) with a 95% confidence interval and equal variances. All data were presented as mean plus standard deviation. SPSS Statistics 17.0 was used for all statistical analysis and p<0.05 was considered to be statistically significant. 26

29 5 Flow measurements - results In this section the results of the MRI flow measurements are reviewed. The results consist of the mean measured flows in the CCA, ICA and ECA per subject in the bifurcations with the major stenosis and the contralateral bifurcations, the measured ICA/CCA and ECA/CCA flow ratios in all bifurcations as a function of stenosis. The ICA/CCA and ECA/CCA flow ratios estimated with Murray s Law and the general flow law are presented and compared to the measured flow ratios. 5.1 Study group The mean degree of stenosis of the subjects included in the study (n=33) was 48 ± 30%. The total number of bifurcations included in this study was 65, because in one subject only one carotid bifurcation was included in the image volume. The mean degree of stenosis of the subjects recruited from the Rotterdam Study (n=21) was 35.4 ± 34.0 %. Seven subjects were without stenosis in both carotid bifurcations. The mean degree of stenosis of the patients scheduled for carotid endarterectomy in the Erasmus MC was 42.6 ± 33.4 %. No subjects were without stenosis in both carotid bifurcations; 5.2 Measured flow and flow ratios vs degree of stenosis MRI measurements were performed in the right and left carotid bifurcation. All measured flows, flow ratios and degrees of stenosis were normally distributed. The mean flow was 5.1 ± 2.0 ml/s for the CCA, 2.8 ± 1.6 ml/s for the ICA and 2.1 ± 0.9 ml/s for the ECA. There was a moderate correlation between the degree of stenosis and the ICA/CCA and ECA/CCA flow ratio (Figure 5-1). The ICA/CCA and ECA/CCA flow ratio was constant when the degree of stenosis was smaller than 64% and 66% (p = 0.63 and p = 0.98). If the degree of stenosis was higher than 64%, the ICA/CCA flow ratio decreased with to zero when the degree of stenosis increases to 100% (p<0.05). When the degree of stenosis was higher than 66%, the ECA/CCA flow ratio increased to 100% when the degree of stenosis was 100% (p<0.05). 27

30 ICA y 0.05x 63 x 64 y 1.52x 157 x 64 R ECA y 0.003x 36 x 66 y 1.76x 80 x 66 R A Figure 5-1: Generic relationship between the A) ICA/CCA and B) ECA/CCA flow ratio (q ICA /q CCA and q ECA /q CCA ) and the degree of stenosis (x) in the ICA. Thus, the cut-off values, for which the relationship between flow ratio and degree of stenosis changed, were determined at 64% in the ICA and 66% in the ECA (see Equations 4.1 and 4.2). The cut-off value for the degree of stenosis, for which the generic relationship between flow ratio and degree of stenosis changed, was determined at 65%. The subdivision of the subjects and bifurcations according to this cut-off value is shown in Table 5-1. Table 5-1: Number of subjects and bifurcations subdivided in each group according to degree of stenosis [%] Group No stenosis 0-65% 66-80% % Total Subjects Bifurcations B For every subject the bifurcation with the major stenosis was determined. One subject was excluded, because the flow measurements were performed in only one carotid bifurcation. For ten subjects, the major stenosis was situated in the left bifurcation and for fifteen subjects the major stenosis was situated in the right bifurcation. Seven subjects did not have any stenosis in the carotid bifurcation at all. To investigate if the flow in the bifurcation with the major stenosis was reduced and the flow in the contralateral bifurcation compensated for this reduced flow, the total flow through both bifurcations was determined. The total flow through both bifurcations, determined as the sum of flow through the CCA of the bifurcation with the major stenosis and the contralateral bifurcation, tended to decrease with increasing area stenosis (p=0.29, Figure 5-2A). Similarly, the total flow through the ICA decreased when the major stenosis was higher than 65% (p<0.05, Figure 5-2B). This decrease in total flow through the CCA and the ICA was caused by the decrease in flow through the artery with the major stenosis (p<0.05). The flow through the CCA and ICA of the contralateral bifurcation did not significantly change with 28

31 increasing degree of stenosis (p = 0.73 and p = 0.64). This suggests that the contralateral bifurcation did not compensate for the loss of flow in the ICA with the major stenosis. The flow through the ECA in the bifurcation with the major stenosis and the contralateral bifurcation did not change as a function of stenosis (p = 0.63 and p = 0.86). CCA ICA A Figure 5-2: Flow (q) through the A) CCA and B) ICA of the bifurcations with the major stenosis and the contralateral bifurcations as a function of the major stenosis. 5.3 Estimation of the flow ratio with Murray s Law and a general flow law To investigate whether Murray s Law was feasible for the estimation of the ICA/CCA and ECA/CCA flow ratio, we first investigated if the lumen radius of the CCA could be estimated either with Murray s Law or the general law. The mean measured lumen radius was 4.1 ± 0.6, 3.1 ± 0.9 and 2.9 ± 0.4 mm for the CCA, ICA and ECA in the bifurcations with stenosis (n=51). In the bifurcations without stenosis, the mean lumen radii were 3.9 ± 0.4, 3.2 ± 0.3 and 2.7 ± 0.3 mm for the CCA, ICA and ECA (n=14). For the bifurcations in subjects without stenosis (n=14), the lumen radius of the CCA could be estimated from the lumen radius of the ICA and the ECA with Murray s Law ( r CCA =r ICA +r ECA, R 2 x x = 0.81, p<0.05) or a general law ( r CCA =r ICA +r x ECA, x=2.7 ± 0.1, R 2 =0.81, p<0.05). For bifurcations with stenosis (n=51), the correlation between the measured lumen radius of the CCA and the lumen radius estimated with Murray s Law or a general law (x=2.5 ± 0.1) was moderate (respectively R 2 =0.57 and R 2 =0.55, p<0.05). The regression and Bland- Altman plots of the estimation of the radius of the CCA with Murray s Law and a general law can be found in Appendix A. For the estimation of the flow ratios with Murray s Law and a general flow law, the ICA/CCA and ECA/CCA flow ratios were combined (n=130). For the group of bifurcations without stenosis an exponent 2.8 ± 0.2 was estimated for the general flow law. The exponent x was not different from the exponent 3 in Murray s Law (p = 0.86). A moderate correlation existed between the measured flow ratios and the flow ratios estimated with Murray s Law and with the general flow law (Figure 5-3). The slope of the regression line coefficient differed from zero in both cases (p<0.05). The ICA/CCA and ECA/CCA flow ratio with Murray s Law and B 29

32 with the general flow law did not have a significant systematic (p = 0.36 and p = 0.90) or relative error (p = 0.26 and p = 0.18). The Bland-Altman plots from which the systematic and relative error was estimated are shown in Appendix B. Flow ratios in bifurcations without stenosis (n=28) Murray s Law General flow law A Figure 5-3: The ICA/CCA and ECA/CCA flow ratios (q 1 /q 0 ) estimated from the lumen radius in the CCA and the ICA or ECA (r 1 and r 0 ) with A) Murray s Law and B) a general flow law (x=2.8) in bifurcations without stenosis. The group of bifurcations with stenosis had an estimated exponent x = 2.6 ± 0.2 for the general flow law. The exponent x in the general flow law was significantly different from the exponent x=3 in Murray s Law (p<0.05). Contrary to the ICA/CCA and ECA/CCA flow ratio for bifurcations without stenosis, in bifurcations with stenosis the ICA/CCA and ECA/CCA flow ratio estimated with Murray s Law and with the general flow law were not correlated with the measured flow ratios (Figure 5-4). Both estimation methods also had significant relative errors (p<0.05, Appendix B) and the estimations with Murray s Law also had a significant systematic error. B 30

33 Flow ratios in bifurcations with stenosis (n=102) Murray s Law General flow law A Figure 5-4: The ICA/CCA and ECA/CCA flow ratios (q 1 /q 0 ) estimated from the lumen radius in the CCA and the ICA or ECA (r 1 and r 0 ) with A) Murray s Law and B) a general flow law (x=2.6) in bifurcations with stenosis. Because there was no correlation between the measured and the estimated flow ratios for bifurcations with stenosis, the ICA/CCA and ECA/CCA flow ratio was also investigated for the group of bifurcations with a degree of stenosis smaller than 65%. For this group of bifurcations the ICA/CCA and ECA/CCA flow ratio was constant (see Figure 5-1) and Murray s Law and the general flow law were expected to give better estimations for the flow ratios than for the bifurcations with more than 80% stenosis. Non-linear regression analysis gave a parameter x=2.5 ± 0.2, which is significantly different from x=3 in Murray s Law (p<0.05). The regression coefficient was only slightly better in the group of bifurcations with stenosis 0-65% than in the group with stenosis 0-100% (R 2 =0.19 and R 2 =0.20, Figure 5-5). The correlation between the measured flow ratios and the flow ratios estimated with Murray s Law and the general flow law was weak for this group of bifurcations. There was no relative error in the flow ratios estimated with Murray s Law and the general flow law for the group of bifurcations with a degree of stenosis smaller than 65%. However, there was a significant systematic error in the estimations with Murray s Law (p<0.05, Appendix B). B 31

34 Flow ratios in bifurcations with stenosis<65% (n=74) Murray s Law General flow law A Figure 5-5: The ICA/CCA and ECA/CCA flow ratios (q 1 /q 0 ) estimated from the lumen radius in the CCA and the ICA or ECA (r 1 and r 0 ) with A) Murray s Law and B) a general flow law (x=2.5) in bifurcations with a degree of stenosis<65%. In Figure 5-6 the mean ICA/CCA and ECA/CCA flow ratio in the groups of bifurcations without stenosis, with a degree of stenosis of 0-65%, 66-80% and % are shown. Both in the measured and in the estimated flow ratios, the variation between the bifurcations within each group in the measured and estimated ICA/CCA and ECA/CCA flow ratios was very large. Similarly to the flow ratios in Figure 5-1, the measured ICA/CCA flow ratio in the group of bifurcations decreased when the degree of stenosis was higher than 65% (p<0.05). The ICA/CCA flow ratio estimated with Murray s Law and the general flow law was constant in all groups of bifurcations (p = 0.27 and p = 0.44). The measured ECA/CCA flow ratio increased when the degree of stenosis was higher than 65% (p<0.05). The flow ratio estimated with Murray s Law and the general flow law did not significantly change with increasing degree of stenosis (p = 0.12 and p = 0.07). B ICA * * * * * ECA * * * * * A Figure 5-6: The mean and standard deviation of the measured and estimated A) ICA/CCA and B) ECA/CCA flow ratios with Murray s Law and the general flow law as a function of stenosis. Significant differences p<0.05 (*) between the measured and the estimated flow ratio were determined with a paired t-test. B 32

35 The ICA/CCA flow ratio estimated with Murray s Law and the general flow law was higher than the measured flow ratio and the ECA/CCA flow ratio estimated with Murray s Law and the general flow law was lower than the measured flow ratio when the degree of stenosis was higher than 80% (p<0.05). In bifurcations with less than 80% stenosis, the measured ICA/CCA and ECA/CCA flow ratio and the flow ratio estimated with Murray s Law and the general flow law was not significantly different. However, the ICA/CCA flow ratio estimated with Murray s Law was significantly lower than the measured flow ratio and the general flow law was significantly higher than the measured flow ratio in the group of bifurcations with a degree of stenosis lower than 65%. 33

36 34

37 6 Wall shear stress calculations - methods In this chapter the method that was used to calculate the WSS in a 3D patient-specific geometry with computational fluid dynamics (CFD) is described. Three methods were used to determine the ICA/CCA flow ratio used in the WSS calculations. The first method used the flow measurements to estimate the ICA/CCA flow ratio, the second and third method applied Murray s Law and the generic relationship between the ICA/CCA flow ratio and the degree of stenosis, as determined in Chapter Navier-Stokes equations The Navier-Stokes equations governing the CFD calculations follow from the momentum balance and mass conservation (Equation 6.1-2). v t 2 ( v ) v f p v (6.1) v 0 (6.2) Where v is the velocity of the blood, p is the pressure, ρ is the density of blood, f are body forces and η is the viscosity of blood. 6.2 Volume mesh generation Five bifurcations were selected from the different groups of bifurcations with stenosis determined in Chapter 5. Two geometries were selected from the group of bifurcations with a degree of stenosis lower than 65%, one geometry from the group with a degree of stenosis between 65 and 80% and two geometries from the group of bifurcations with a degree of stenosis higher than 80% (Figure 6-1). The geometries were selected on the quality of the MR images of the carotid bifurcation, because the lumen contours for these geometries could be more easily drawn. Geometry 1 <65% stenosis Geometry 2 <65% stenosis Geometry 3 65%<stenosis<80% Geometry 4 >80% stenosis Geometry 5 >80% stenosis Figure 6-1: The five geometries that were selected for the WSS calculations and the group of bifurcations they were selected from Contours of the lumen of the carotid bifurcation were manually drawn on the magnitude images of the 3D MR phase contrast sequence in order to obtain 3D patient specific geometries of carotid bifurcations. These contours were drawn in MeVisLab (MeVis Research GmbH, Germany), a development environment for medical image processing. The 35

38 contours were drawn from 22 mm proximal to the bifurcation in the CCA until 22 and 15 mm distal to the bifurcation in the ICA and ECA. An isosurface of the bifurcation was determined from these contours and exported to the Vascular Modeling ToolKit (VMTK, VMTK is a software tool designed for the reconstruction, geometric analysis, mesh generation and surface data analysis of 3D geometries for CFD. In VMTK a surface mesh was created from the isosurface of the bifurcation. The VMTK script used for the creation of the surface mesh is described in Appendix C. The process consists of three steps: Clipping: The closed isosurface was opened at the inflow and the outflow surfaces of the bifurcation to enable the creation of flow extensions. The branches of the bifurcation were clipped in the direction perpendicular to the arterial centerline. Flow extensions: Flow extensions were added to the inlet and outlets of the clipped surface mesh. The flow extensions were straight tubes in the direction of the arterial centerline. The shape of these straight tubes gradually changed from a circular inlet surface to the shape of the outlet surface of the artery at the site where the flow extension was attached to the artery. A longer inlet or outlet flow extension provided a smoother attachment to the inlet or outlet of the artery. When the length of the inlet flow extensions was four times the lumen radius the attachment was considered to be smooth. At the outlet the smoothness of the attachment was less important, the length of the flow extension was therefore shorter (equal to the lumen radius) to reduce the mesh size and thereby the computation time. The length of the inlet flow extensions was shorter than the length that is needed for a plug flow to develop to a Womersley flow profile, which is called the entrance length of the flow. The assumption was made that the influence of the inlet velocity profile on the calculated WSS was much smaller than the influence of geometric variation [22]. The influence of the use of longer flow extensions would therefore be small, but extend the computation time due to the larger volume mesh size. Surface smoothing and capping: Finally, the surface mesh with the flow extensions was smoothed with a low pass filter to remove local irregularities in the mesh. The open inlet and outlet surfaces were closed with flat circular caps. This was required for the mesh generator that was used for the creation of the volume mesh. The volume mesh was created and discretized into continuous tetrahedral volume elements using the mesh generator Netgen (RWTH Aachen University/ Johannes Kepler University Linz). In Appendix D a protocol for the mesh generation with Netgen is described. High gradients in WSS were expected at locations of the geometry with high curvature or a reduced diameter due to stenosis. A dense mesh is more accurate to calculate these high gradients in WSS. In Netgen the edge size of the elements is related to the curvature of the geometry. Curved locations of the geometry will have a more dense volume mesh than straight locations. At locations of the geometry with a smaller radius, the curvature of the geometry is also higher and the surface mesh is denser. The method used by Netgen to determine the curvature of the mesh is also described in Appendix D. Linear tetrahedral volume elements with continuous pressure interpolation were used. To ensure mesh independent CFD calculations, the mean edge size of the surface elements was smaller than 0.17 mm, which was derived from earlier studies performed at the Biomechanics Lab. 36

39 6.3 WSS calculations Medium Blood behaves as an incompressible non-newtonian fluid with a density of 1060 kg m -3. The Carreau model describes the shear rate dependent viscosity of blood in the CFD calculation (Equation 6.3). [1 ( ) ] n 0 2 ( 1)/2 (6.3) Where η 0 is the viscosity at low shear rate, 0.25 Pa s, η is the viscosity at high shear rate, Pa s, λ is a time constant, 25, n is the power law constant, 0.25, and γ is the rate of strain tensor [23]. The shear rate (γ ) was determined from the rate of deformation tensor (D) (Equation 6.4). 1 ( 2 ) 2 tr D with the rate of deformation tensor 1 ( ( ) T D v v ) (6.4) Boundary conditions The arterial wall of the bifurcation was assumed to be rigid. In reality, the arterial wall is distensible and moves as a function of the pressure waveform. However, the assumption was made that the influence of the movement of the arterial wall during the heart cycle on the development of atherosclerosis was negligible [24]. At the inlet a static parabolic velocity profile was prescribed. The maximum velocity (v max ) of the parabolic profile has been chosen such that the prescribed flow was equal to the flow measured in the CCA with the MR flow measurements. Although a stationary solution was determined from the CFD calculation, the flow in the geometry was gradually increased with time-steps to obtain a converged solution. With every time-step the v in the prescribed parabolic profile increased from zero to the prescribed v max following an exponential function (Figure 6-2). If the v max was prescribed at the first time-step, the solution of the calculation would not converge. For the time integration, the implicit, backward Euler method was used. The initial magnitude of the time-step used in the calculations was dt = 0.01 s. As the calculation time progressed the solver optimized the size of the time-step to obtain the shortest possible calculation time and to obtain a converged solution at the same time. 37

40 Figure 6-2: Stepwise increase of the velocity with an exponential function from v=0 m/s at t=0 s to v=v max m/s at t=1 s. Three different methods were used to determine the ICA/CCA flow ratio for the five patientspecific 3D geometries: 1. The ICA/CCA flow ratio was determined from the MR flow measurements; 2. Murray s Law was used to estimate the ICA/CCA flow ratio from the lumen radii of the CCA and the ICA (Equation 6.5); q q ICA CCA r r ICA CCA 3 (6.5) 3. The generic relationship between the degree of stenosis (x) and the ICA/CCA flow ratio, which was determined in Chapter 5, was used (Equation 6.6). qica 0.05x 63 x 65% qcca qica 1.52x 157 x 65% qcca In order to calculate the WSS with the measured or estimated ICA/CCA flow ratio, outflow boundary conditions need to be prescribed. Unfortunately, the flow ratio could not be prescribed. Instead, the velocity profile had to be prescribed. The velocity profile, however, was not available for the estimated ICA/CCA flow ratios and a different method to prescribe the outflow boundary conditions needed to be found. A tension normal to the outflow surface of the ICA was therefore used to determine the ICA/CCA flow ratio. To the outflow surface area of the ECA free outflow (a tension equal to zero) was always prescribed. In earlier studies in the Biomechanics Lab was determined that the relationship between the ICA/CCA flow ratio and the tension normal to the outflow surface of the ICA was linear (Figure 6-3). This relationship was used to estimate the normal tension that should be prescribed to obtain the measured or estimated ICA/CCA flow ratio. All geometries had a different slope and offset of this linear relationship. To obtain the slope and offset of the linear relationship, the CFD calculations were performed twice with a prescribed pressure of 0 and 50 Pa. (6.6) 38

41 Figure 6-3: The linear relationship between the ICA/CCA flow ratio (q ICA /q CCA ) and the prescribed normal tension (p) to the ICA outflow surface. For the CFD calculations, the finite element software package FIDAP (Fluent Inc) was used. The Navier-Stokes equations were solved for every node in the geometry. For every node velocities in the x, y and z direction (v x, v y and v z ) and the pressure (p) were calculated. For the surface elements the WSS was derived from the velocities. The convergation criteria were met when the relative error in the v x, v y, v z and p was smaller than Geometries and prescribed flow In Table 6-1 some geometric parameters of the bifurcations and the prescribed inflow and outflow boundary conditions for the computational fluid dynamics are shown. As expected, the inflow in the CCA and the measured ICA/CCA flow ratio decreased with increasing degree of stenosis. The differences between the measured and estimated ICA/CCA flow ratios were large. Especially, the ICA/CCA flow ratios estimated with Murray s Law were substantially different from the measured flow ratios. The difference varied from an underestimation of 20% to an overestimation of 29%, resulting in a relative difference ranging from -21% to 113% relative to the measured ICA/CCA flow ratio. The difference between the measured ICA/CCA flow ratio and the flow ratio obtained from the generic relationship between the degree of stenosis and the ICA/CCA flow ratio were much smaller, ranging from -15 to 7%, resulting in a relative difference of -48% to 13%. For geometries 2-5, the ICA/CCA flow ratio estimated with the fit resembled the measured ICA/CCA flow ratio better than the flow ratio estimated with Murray s Law. For geometry 1, the geometry with the lowest degree of stenosis, the flow ratio estimated with Murray s Law was a better approximation than the flow ratio estimated with the fit. 39

42 Table 6-1: The degree of stenosis, flow in the CCA and ICA/CCA flow ratios of geometry 1-5. Geometry Degree of r CCA q CCA q ICA /q CCA [%] stenosis [%] Measurement Murray s Law Fit r CCA = lumen area of the CCA [mm]; q CCA = flow in the CCA [ml/s]; q ICA/CCA = ICA/CCA flow ratio [%] 6.5 Postprocessing Mean and maximum WSS of the CCA, ICA and ECA of all geometries were calculated. The WSS was calculated from the shear rate and the viscosity as determined with the Carreau model (Equation 6.7). () (6.7) w The resulting WSS in an artery was shown as a 2D map of the opened surface of the artery. To obtain these 2D maps, the surface mesh of the wall was analyzed in VMTK. First, for every node on this surface, it was determined to which artery it belongs. Second, a local cylindrical coordinate system was defined with the centerline of the artery on one axis and the angle of the artery on the other. For every node its position on the centerline of the bifurcation (abscissa metric) and its angle (angular metric) between π and π was determined. Subsequently, the 2D map was mapped on a grid for which the angular metric was divided into thirty discrete steps of π/15 and the abscissa metric was divided into discrete steps of 0.5 mm (Figure 6-4). For every surface element the centre of mass was determined. This centre of mass determined the position of the element in the grid. A grid element consists of all surface elements of which the center of mass is positioned inside the grid element. Figure 6-4: Assignment of the surface elements to the grid elements with the abscissa [mm] plotted versus the angle. The WSS averaged over the nodes of every surface element was multiplied with its surface area to determine the shear force on the element. The shear force on an element in the grid was determined as the sum of shear forces of all surface elements inside the grid element. 40

43 The WSS of every grid element was determined as the sum of shear forces of all surface elements divided by the surface area of the grid (Equation 6.8). n F i i 1 i 1 w n n A n i i 1 i 1 ( w, i w, i w, i ) Ai 3 A i (6.8) Where τ w is the WSS on a grid element, F i, the shear force on the surface element i, A i, the area of surface element i and τ w,i1, τ w,i2 and τ w,i3, the WSS on nodes 1, 2 and 3 of surface element i. The 2D maps were determined for the WSS obtained with the measured ICA/CCA ratio. For visualization purposes, the grid elements were color coded with the WSS as obtained using Equation 6.8. The differences in WSS between the 2D maps of the WSS obtained with the measured ICA/CCA ratio and obtained with the estimated ICA/CCA flow ratios were also determined. Finally, the relative differences between the WSS obtained with the measured ICA/CCA flow ratio and obtained with the estimated ECA/CCA flow ratio were determined. The differences and relative differences between WSS obtained with measured and estimated ICA/CCA flow ratio were also shown in 2D maps. Because high WSS can influence the biological weakening of the fibrous cap of the plaque and the stenosis is situated in the ICA, an accurate WSS calculation is more important in the ICA than in the CCA and the ECA. The difference between the WSS obtained with the measured and obtained with the estimated flow ratio was therefore only studied in the ICA. The results of the WSS calculation in the CCA and ECA can be found in Appendix E. 41

44 42

45 7 Wall shear stress calculations - results In this chapter the results of the WSS calculations in five patient-specific geometries with stenosis are described. For these calculations different ICA/CCA flow ratios were used. The differences between the WSS obtained with the measured ICA/CCA flow ratio and the WSS obtained with an estimated ICA/CCA flow ratio will be presented. 7.1 Mean and maximum WSS obtained with the measured ICA/CCA flow ratio In Table 7-1 the maximum and minimum WSS in every artery obtained with the measured ICA/CCA flow ratio is shown. No relationship was observed between the degree of stenosis and the maximum or mean WSS in the CCA, ICA and ECA of a geometry. Although the prescribed flow in the CCA and therefore the velocity of the blood in the artery decreased with increasing degree of stenosis, the mean WSS did not decrease. Table 7-1: Maximum and mean WSS [Pa] in the CCA, ICA and ECA of geometry 1-5. The ICA/CCA flow ratio was determined from the measurements. Geometry Degree of stenosis [%] CCA ICA ECA Max WSS Mean WSS Max WSS Mean WSS Max WSS Mean WSS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 0.2 WSS = wall shear stress [Pa] In Figure 7-1:, the 3D representations of the WSS in the geometries are shown. In geometry 4 and 5, the maximum WSS as presented in Table 7-1 was measured at the site of the stenosis whereas it was measured near the apex of the bifurcation in geometry 1-3. When the apex was excluded from the determination of the maximum WSS in the ICA, the maximum WSS in the ICA was found at the site of the stenosis in all bifurcations and was related to the degree of stenosis. In geometry 1 and 2, the geometries with a degree of stenosis lower than 65%, no WSS elevation was observed in the ICA at the site of the stenosis. The highest maximum and mean WSS for every artery was observed in the CCA, ICA and ECA of geometry 3. The high maximum WSS was observed at the site of the apex of the bifurcation. However, the high mean WSS was due to the curvature of geometry 3 and an extra stenosis in the ICA, which led to more regions of elevated WSS in the ICA. Geometry 3 also had a low arterial radius when compared to the prescribed flow in the CCA. 43

46 Geometry 1 Geometry 2 Geometry Geometry 4 Geometry 5 Figure 7-1: WSS [Pa] in the geometries 1-5. The ICA/CCA flow ratio was obtained from the flow measurements. 44

47 7.2 Differences between WSS obtained with different outflow boundary conditions In Figure 7-2-Figure 7-6:, the 2D maps of the WSS in the ICA are shown for geometry 1-5. Also, the differences and the relative differences between the WSS obtained with the measured ICA/CCA flow ratio and the estimated ICA/CCA flow ratios are shown in these figures. The differences between the WSS with the measured and estimated ICA/CCA flow ratio were small in the CCA (<1.0 Pa), but had influence on the WSS in the ICA and the ECA. The differences in WSS as obtained with the different outflow boundary conditions was only studied in the ICA, the results of the WSS calculations in the CCA and ECA can be found in Appendix E. 45

48 The WSS in the ICA of geometry 1 with a degree of stenosis of 1% was low (<1 Pa, relative difference <10%, Figure 7-2). If no surface element lies inside a grid element, the element has no WSS value and is therefore coloured white. The maximum difference between WSS obtained with the estimated and the measured ICA/CCA flow ratio was small in geometry 1 (<0.2 Pa). The differences were observed near the apex of the bifurcation. The maximum relative difference between the WSS obtained with the measured and with the estimated ICA/CCA flow ratio was smaller when Murray s Law was used for the estimation of the flow ratio than when the generic relationship was used (-16% and 32%). Measurement vs. Murray s Law Measurement vs. generic relationship Figure 7-2: Geometry 1: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and difference and relative difference between WSS (dwss in Pa or percentage) obtained with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ICA. 46

49 In Figure 7-3 the WSS in the ICA of geometry 2 with a degree of stenosis of 22% is shown. The WSS was elevated to approximately 2 Pa near the apex of the bifurcation and at a site where the lumen radius decreased (see Figure 7-1:). The maximum differences and maximum relative differences between the WSS obtained with the measured ICA/CCA flow ratio and with the estimated ICA/CCA flow ratio were higher when Murray s Law was used than when the generic relationship was used (-0.7 or -49% vs -0.4 Pa or -45%). Measurement vs. Murray s Law Measurement vs. generic relationship Figure 7-3: Geometry 2: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and difference and relative difference between WSS (dwss in Pa or percentage) obtained with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ICA. 47

50 In Figure 7-4 the 2D WSS maps of geometry 3 with 69% stenosis are shown. In geometry 3 the highest WSS in the ICA was observed near the apex and at the site of the stenosis. In Figure 7-1: two stenoses in the ICA are visible. The largest differences in WSS between the calculation with the measured and the estimated flow ratio were also observed at the site of the stenosis when Murray s Law was used and when the generic relationship was used. At the site of the stenoses, both the differences and relative differences in the WSS were slightly larger when Murray s Law was used for the estimation of the ICA/CCA flow ratio at the site of the stenosis (1.5 Pa or 70% vs 1.0 Pa or 40%). Measurement vs. Murray s Law Measurement vs. generic relationship Figure 7-4: Geometry 3: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and difference and relative difference between WSS (dwss in Pa or percentage) obtained with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ICA. 48

51 The WSS was elevated at the site of the stenosis in geometry 4 with a degree of stenosis of 87% (Figure 7-5). Behind the stenosis was a region of low WSS. The largest differences in WSS were observed at the location of the stenosis in the ICA. The differences between the WSS obtained with the measured and obtained with the estimated ICA/CCA flow ratio was 1.1 Pa at the site of the stenosis with Murray s Law and -0.6 Pa with the generic relationship. The largest relative differences were not observed at the site of the stenosis, but at the site of low WSS. At this site, the relative differences were much higher for the calculations using Murray s Law than for the calculations using the generic relationship for the estimation of the ICA/CCA flow ratio (250% vs -85%). Measurement vs. Murray s Law Measurement vs. generic relationship Figure 7-5: Geometry 4: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and difference and relative difference between WSS (dwss in Pa or percentage) obtained with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ICA. 49

52 In Figure 7-6 the 2D WSS maps of geometry 5 with 93% stenosis are shown. The WSS was elevated to 5.1 Pa at the site of the stenosis. The largest differences between WSS calculated with Murray s Law and with the generic relationship were observed at the site of the stenosis in the ICA. The relative differences, however, were high in the region distal to the stenosis with low WSS leading to an overestimation of 289% for Murray s Law and an underestimation of 88% for the generic relationship. The differences between the WSS obtained with a measured and estimated ICA/CCA flow ratio were larger when Murray s Law was used than when the generic relationship was used (with an overestimation in WSS of 4.7 Pa vs. an underestimation of 1.9 and a relative difference of 81% vs -32%) at the site of the stenosis. Measurement vs. Murray s Law Measurement vs. generic relationship Figure 7-6: Geometry 5: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and difference and relative difference between WSS (dwss in Pa or percentage) obtained with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ICA. 50

53 In the geometries with a degree of stenosis lower than 65% (geometry 1 and 2), the difference between WSS obtained with the measured and the WSS obtained with the estimated ICA/CCA flow ratio was very small. The choice for Murray s Law or the generic relationship for the estimation of the ICA/CCA flow ratio did not make much difference. In the geometries with a degree of stenosis higher than 65 % (geometries 3-5), the WSS at the location of the stenosis as obtained using the measured flow ratio was best approximated using the generic relationship for the estimation of the ICA/CCA flow ratio for the WSS calculations. When Murray s Law was used the WSS was overestimated at the site of the stenosis. Although the difference in the WSS was larger when Murray s Law was used, the underestimation of the WSS was still substantial when the generic relationship was used. The relative differences in WSS were especially large in areas with low WSS, but also large at the site of the stenosis. 51

54 52

55 8 Discussion 8.1 MRI protocol In the 3D flow measurements aliasing could occur when the venc was lower than the peak systolic velocity. The influence of aliasing on the measured flow and maximum velocity was unknown for time-averaged 3D phase contrast measurements and was therefore investigated in both bifurcations of two presumably healthy volunteers of 28 years. Because the peak systolic velocity was expected to be 85 cm/s for males and 75 cm/s for females [14], aliasing was expected to occur when the venc was set to 60 cm/s. When the venc for the flow measurements in a healthy volunteer was set to 30, 60, 90 and 150 cm/s, a large underestimation in the measured flow was observed when the venc was lower than 90 cm/s (see Figure 3.2). Flow measurements with venc = 60 cm/s and venc = 100 cm/s were therefore performed on two healthy volunteers. For these volunteers, the flow and maximum velocity were significantly lower when venc = 60 cm/s than when venc = 100 cm/s. The difference was 0.77 ml/s for the flow and 2.5 cm/s for the maximum velocity. The underestimation of the flow and velocity was therefore 10% at the most in these measurements. Since the peak systolic velocity in the CCA decreases with age, the influence of aliasing on the measured flow would be even smaller when older patients are studied. However, the number of bifurcations (n=4) for which the influence of aliasing was determined was rather small to draw final conclusions on the influence of aliasing. Since the measurements in the Rotterdam Study had already been performed before the influence of aliasing was investigated, the results of the volunteer study were only used to decide on the inclusion criteria for subjects of this study. In this study, only patients older than seventy were therefore included from the Rotterdam Study. Based on the results of the volunteer study, the venc for the flow measurements in the Erasmus MC was set to 90 cm/s to exclude the possibility of aliasing. From the volunteer measurements can be concluded that it is important to set the venc of the sequence to a value just above the expected maximum velocity in the artery in order to obtain the highest possible SNR without aliasing. Although the SNR of the phase images was lower when the venc was set to 90 cm/s than when the venc was set to 60 cm/s, the signal was still much higher than the noise. The reproducibility of the flow and maximum velocity of the measurement was good, because the three mean flows measured in the same bifurcation were not significantly different. However, the maximum relative differences between the measured flows and maximum velocities measured in the same bifurcations were 20% and 17%, which is rather high. The intra-observer reproducibility of the flow and maximum velocity, however, was good. The measurement position in the image volume did also not have a large influence on the measured flow and maximum velocity. Significant partial volume effects are expected if the pixel size exceeds one-third of the vessel diameter in two directions. At least three pixels were therefore needed across the arterial diameter to have sufficient accuracy [13]. The mean measured lumen radius was 4.1 ± 0.6, 3.2 ± 0.5 and 2.9 ± 0.4 mm for the CCA, ICA and ECA. The in-plane resolution of the flow measurements of 1.0 x 0.7 mm in the Rotterdam Study and 1.2 x 0.7 mm in the Erasmus MC therefore satisfied the requirement of three pixels across the lumen diameter for the mean lumen diameter of the CCA, ICA and ECA. However, partial volume effects had 53

56 influence on the measurement of the flow and lumen radius of the measured ICA and ECA when the diameter was smaller than the mean diameter. A disadvantage of the non-triggered 3D measurement is the lack of information on the pulsatility of the flow. Keeping in mind that in the future model studies are planned to estimate the peripheral resistance and resistance due to the stenosis, triggered phase contrast measurements should be performed to determine the flow waveform in the carotid arteries. However, due to the longer acquisition time, difficulties 2D triggered measurement measurement in patients with a high degree of stenosis with the slice planning and the triggering and the lower signal to noise ratio of the 2D, the 3D measurement was considered more suitable than the triggered 2D measurement for flow assessment in large population studies like the Rotterdam Study. In appendix F, the application of a 2D triggered measurement is described. The application of the MR sequence was easy, the measured flow reproducible. Although the measured flow was found reproducible in the volunteer study, the reproducibility of the measurement should be investigated in a larger number of bifurcations than the four bifurcations in this study and in patients with stenosis in the ICA. To avoid aliasing in the measurement results, the venc should be set to 90 cm/s like in the Erasmus MC. The best method, however, to determine the venc would be to determine the peak systolic velocity with a 2D triggered measurement, but this cannot be done due to the limitations to the acquisition time. An alternative method to determine the venc would be to use the relationship between age, gender and peak systolic velocity in the CCA determined by Samijo et al. [14]. 8.2 Influence of stenosis on the ICA/CCA and ECA/CCA flow ratio The mean flow measured in this study was 5.1 ± 2.0, 2.8 ± 1.6 and 2.1 ± 0.9 ml/s for the CCA, ICA and ECA. The flow in the CCA and ICA was smaller than the flow in healthy bifurcations, 6.2 and 4.1 ml/s, measured by Marshall et al. Our study showed that the flow through the CCA and the ICA decreased when the degree of stenosis was higher than 65%. Because a large number of the studied group of bifurcations had a higher degree of stenosis than 65%, the flow in the CCA and ICA in this group was expected to be lower than in healthy volunteers as described by Marshall et al. [9]. The measured flow in the ECA in bifurcations with stenosis was 22% higher than in the study on healthy subjects by Marshall et al. (2.1 vs 1.6 ml/s). Because the flow in the ECA did not change with increasing degree of stenosis, this difference could not be explained by the presence of stenosis in the ICA. Because the 95% confidence interval of the flow measurements was ml/s in the ECA and since the flow in the ECA did not change due to stenosis in the ICA, this difference can be explained by the large measurement error (see Chapter 8.1) on the flow measurements. Because of the large biological variation and the measurement errors on the flows in the carotid bifurcation, it was difficult to derive a generic relationship for the ICA/CCA and ECA/CCA flow ratio. When the degree of stenosis was lower than 65%, the ICA/CCA and ECA/CCA flow ratio remained constant at 63/36%, which was similar to the ICA/CCA and ECA/CCA flow ratios determined by Marshall et al. [9]. However, when the degree of stenosis was higher than 65% the ICA/CCA flow ratio decreased from 63% to zero and the ECA/CCA flow ratio increased from 36% to 100%. 54

57 The flow in the ICA was reduced when the degree of stenosis was higher than 65%. The contralateral bifurcation did not compensate for the reduction in flow through the bifurcation with the major stenosis. This can be explained by the fact that the blood supply of the brain was not only provided for by the internal carotid arteries, but also by six other arteries that are connected in the circle of Willis. These arteries can also compensate for the loss of flow in the ICA with more than 65% diameter stenosis. Several studies were performed to determine from which cut-off value in degree of stenosis, surgical intervention with carotid endarterectomy would be beneficial. From these studies was concluded that surgical intervention was beneficial in symptomatic patients when the degree of diameter stenosis was higher than 70% [4]. The 65% area stenosis found in the present study for which the flow in the ICA was decreased corresponds with 41% diameter stenosis, which is far less than the 70% diameter stenosis used as a criterion for surgical intervention. This criterion however was based entirely on the incidence of complications and the prevention of stroke and was not based on reduced flow in the ICA. Apparently, reduced flow in the ICA does not cause any symptoms. Murray s Law gives good estimations for the ICA/CCA and ECA/CCA flow ratio in bifurcations without stenosis. Therefore the assumption that Murray s Law applies to the carotid bifurcations seemed feasible when both lumen radius and flow are unaffected by stenosis in the ICA. For the estimation of the ICA/CCA and ECA/CCA flow ratio with Murray s Law for bifurcations with stenosis an additional assumption had to be made, namely that the lumen radius in the ICA distal to the plaque was unaffected by atherosclerosis. While the estimation of the lumen radius with Murray s Law was still rather good for bifurcations with stenosis, the estimation of the ICA/CCA and ECA/CCA flow ratio in bifurcations with stenosis with Murray s Law were poor. These poor estimations were expected, because earlier in the study we determined that the ICA/CCA flow ratio decreased and the ECA/CCA flow ratio increased when the degree of stenosis was higher than 65%. Murray s Law does not take into account the stenosis and the change in the flow ratios due to this stenosis. Therefore, when Murray s Law was used to estimate the flow ratios when the degree of stenosis was higher than 65%, the ICA/CCA was overestimated and the ECA/CCA flow ratio was underestimated. For carotid bifurcations with a degree of stenosis higher than 65% it is therefore better to use the generic relationship between the degree of stenosis and the flow ratio determined from the measurements for the estimation of the ICA/CCA and the ECA/CCA flow ratio rather than Murray s Law. The general law did not give better estimations of the ICA/CCA and ECA/CCA flow ratio than Murray s Law. In bifurcations without stenosis, the general law was not different from Murray s Law. In bifurcations with stenosis, the general law was different from Murray s Law, but both methods gave poor estimations for the flow ratios. When the flow ratios were estimated for bifurcations with a degree of stenosis smaller than 65%, there was still only a weak correlation between the measured flow ratios and the flow ratios estimated with Murray s Law and the general flow law. Because the flow was still unaffected by the stenosis in this group of bifurcations, this is an indicator that the lumen radius of the ICA distal to the stenosis and possibly the lumen radii of the CCA and the ECA in bifurcations with stenosis were influenced by atherosclerosis. The assumption made for the 55

58 estimation of the lumen radius of the CCA with Murray s Law that the lumen radii in the carotid bifurcation were unaffected by biological changes due to atherosclerosis seems not valid, but other measurements are needed to confirm that atherosclerosis affects the lumen radius in the CCA, ICA and ECA. In this study, only a limited number of bifurcations (n=14, 22%) had a degree of stenosis higher than 65%. Based on this small number of bifurcations, the relationship between the ICA/CCA and ECA/CCA flow ratio was established. Although the relationship had a small confidence interval, the relationship between the degree of stenosis and flow ratio should be confirmed with a larger number of bifurcations with a degree of stenosis higher than 65%. 8.3 Wall shear stress calculations If the measured ICA/CCA and ECA/CCA flow ratio was used to calculate the mean and maximum WSS in the carotid bifurcation, the WSS did not depend on the degree of stenosis in the group of five geometries for which the CFD calculations were performed. The calculated mean WSS in the CCA and ICA were 69% lower and 57% higher than reported in literature for healthy subjects (0.36 and 0.88 Pa vs 1.15 and 0.56 Pa) [11, 25]. This difference can be partly explained by the fact that the flow and therefore the velocities of the blood in the carotid bifurcation of four out of five geometries was lower than the flow measured in the CCA of healthy subjects by Marshall et al. [9]. The lower velocities of the blood lead to a lower WSS. Furthermore, the lumen radius of the CCA measured in all five bifurcations was larger than the mean lumen radius of 3.14 mm reported in literature, which also leads to a lower WSS [26]. Because high WSS at the site of the stenosis can influence the biological weakening of the plaque [8], the accurate estimation of the WSS at the site of the stenosis in the ICA is very important. This study showed that a change in the flow through the ICA and therefore the ICA/CCA flow ratio mostly influences the WSS at the site of the stenosis. Two methods were used to estimate the ICA/CCA flow ratio. The first method used the generic relationship between degree of stenosis and flow ratio determined from the flow ratios measured in this study. The second method used Murray s Law. When the degree of stenosis was smaller than 65% in a geometry, it made no difference in the calculated WSS whether Murray s Law or the generic relationship between stenosis degree and flow ratio was used for the estimation of the ICA/CCA flow ratio. For the geometries with a degree of stenosis higher than 65%, the WSS obtained with the ICA/CCA flow ratio derived from the generic relationship more closely approximated the WSS obtained with the measured flow ratio than when Murray s Law was used for the estimation of the flow ratio. The latter was expected since the generic relationship already gave a better estimation of the ICA/CCA flow ratio than Murray s Law. Because the difference between WSS obtained with the measured and estimated ICA/CCA flow ratios can be very large, the best method to determine outflow boundary conditions for the WSS calculations is to measure the ICA/CCA flow ratio with MRI. Because the measurement of flow in the carotid bifurcation is not common practice in the clinic, a large set of bifurcations is available without any flow information. For these bifurcations, the best 56

59 results for the WSS are obtained when the ICA/CCA flow ratio is estimated from the generic relationship between the degree of stenosis and the ICA/CCA flow ratio described in this study. If Murray s Law holds for the estimation of the ICA/CCA flow ratio, the shear rate was the same in the CCA, ICA and ECA [20]. However, the shear rates which were determined from the WSS calculations in the CCA, ICA and ECA were not constant in any of the geometries and therefore Murray s Law does not hold in the carotid bifurcations used for the WSS calculations in this study. The CFD calculations had some limitations. The arterial wall was assumed to be rigid and the flow to be stationary. In reality, the arterial wall is distensible and the flow pulsatile. The inclusion of the time-dependency of the flow and wall distensibility into the CFD model would be computationally expensive. As atherosclerosis progresses over a long time course, it is questionable whether changes in WSS during the cardiac cycle have a large influence on the development of a plaque. A study of Younis et al. showed that a distensible wall has no significant influence on the WSS distribution [24]. Furthermore, an atherosclerotic wall is stiff and rigid and the time-averaged WSS is correlated to the oscillatory shear index [27]. All these arguments justify the use of a stationary flow. The geometries in this study were also included in the set of bifurcations from which the generic relationship between the degree of stenosis and the flow ratio was determined. It would be better to perform the WSS calculations on five other geometries that were not included in the set of bifurcations for which the generic relationship between the degree of stenosis and the flow ratio was determined. Unfortunately, these bifurcations were not available. Also, the WSS calculations were performed on only five geometries. To draw any final conclusions on the influence of the ICA/CCA flow ratio on the WSS in the carotid bifurcation, the WSS should be calculated in a larger number of geometries that were also not included in the set of bifurcations from which the generic relationship was determined. Inflow boundary conditions were not determined in this study. When flow measurements in the CCA are not available, the flow can be chosen such that a physiological shear stress value was obtained at the CCA. Also a generic relationship between the flow in the CCA and degree of stenosis can be determined. 8.4 Conclusion Although it would be preferable to perform time-dependent flow measurements for certain research goals, the 3D phase contrast measurement is a reproducible, easy to perform method to determine time-averaged flow in the carotid bifurcation. Especially in the protocol used for the Rotterdam Study, which sets strict limitations to the acquisition time, a time-averaged flow measurement is more suitable than a 2D triggered measurement. If no additional measurement can be performed to estimate the encoding velocity, it can be estimated from the relationship between age, gender and peak systolic velocity in the CCA determined by Samijo et al. [14]. In the study described in this report, the measurements from the Rotterdam Study had already been performed with a venc of 60 cm/s. Subjects in 57

60 the present study were older than seventy years of age, to minimize the errors related to aliasing. The flow and the ICA/CCA and ECA/CCA flow ratio was determined for 65 bifurcations suspected for stenosis. Based on the flow measurements a generic relationship was derived between the flow ratio and the degree of stenosis. In carotid bifurcations with a degree of stenosis higher than 65%, Murray s Law cannot be used for the determination of the ICA/CCA and ECA/CCA flow ratio conditions. For bifurcations with a degree of stenosis smaller than 65%, the differences between the WSS obtained with the measured ICA/CCA flow ratio and the estimated flow ratio were small. The outflow boundary conditions for WSS calculations could be estimated with either Murray s Law or the generic relationship. For bifurcations with a degree of stenosis higher than 65%, the differences between the WSS obtained with the measured and the estimated flow ratios were larger. When the generic relationship was used for the estimation of the flow ratio, the WSS more closely approximated the WSS obtained with the measured flow ratio than when Murray s Law was used for the estimation of the flow ratio. The differences in WSS were especially large at the site of the stenosis. Since high WSS at the site of the stenosis causes biological weakening of the cap [8], accurate estimation of the WSS is important in this area. Because the biological variation in the measured ICA/CCA flow ratios and therefore in the WSS at the site of the plaque was high, the best method to determine the outflow boundary conditions for CFD would be to measure the ICA/CCA and ECA/CCA flow ratio. When flow measurements are unavailable anyway, the generic relationship between the degree of area stenosis and the flow ratio determined in this study could be used instead. Although the WSS derived with the generic relationship also leads to local inaccuracies, these inaccuracies are smaller than the inaccuracies in the WSS derived with Murray s Law. 58

61 9 References 1. Libby P: Atherosclerosis: the new view. Sci Am 2002, 286: Nakamura M, Lee DP, Yeung AC: Identification and treatment of vulnerable plaque. Rev Cardiovasc Med 2004, 5 Suppl 2:S Hademenos GJ, Massoud TF: Biophysical mechanisms of stroke. Stroke 1997, 28: Goldstein LB: Extracranial carotid artery stenosis. Stroke 2003, 34: Malek AM, Alper SL, Izumo S: Hemodynamic shear stress and its role in atherosclerosis. JAMA 1999, 282: VanderLaan PA, Reardon CA, Getz GS: Site specificity of atherosclerosis: siteselective responses to atherosclerotic modulators. Arterioscler Thromb Vasc Biol 2004, 24: Glagov S, Weisenberg E, Zarins CK, Stankunavicius R, Kolettis GJ: Compensatory enlargement of human atherosclerotic coronary arteries. N Engl J Med 1987, 316: Gijsen FJ, Wentzel JJ, Thury A, Mastik F, Schaar JA, Schuurbiers JC, Slager CJ, van der Giessen WJ, de Feyter PJ, van der Steen AF, Serruys PW: Strain distribution over plaques in human coronary arteries relates to shear stress. Am J Physiol Heart Circ Physiol 2008, 295:H Marshall I, Papathanasopoulou P, Wartolowska K: Carotid flow rates and flow division at the bifurcation in healthy volunteers. Physiol Meas 2004, 25: Groen HC, Gijsen FJ, van der Lugt A, Ferguson MS, Hatsukami TS, van der Steen AF, Yuan C, Wentzel JJ: Plaque rupture in the carotid artery is localized at the high shear stress region: a case report. Stroke 2007, 38: Cheng C, Helderman F, Tempel D, Segers D, Hierck B, Poelmann R, van Tol A, Duncker DJ, Robbers-Visser D, Ursem NT, et al: Large variations in absolute wall shear stress levels within one species and between species. Atherosclerosis 2007, 195: Hashemi RH, Bradley WG: MRI: the basics. Lippincott Williams & Wilkins; Lotz J, Meier C, Leppert A, Galanski M: Cardiovascular flow measurement with phase-contrast MR imaging: basic facts and implementation. Radiographics 2002, 22: Samijo SK, Willigers JM, Barkhuysen R, Kitslaar PJ, Reneman RS, Brands PJ, Hoeks AP: Wall shear stress in the human common carotid artery as function of age and gender. Cardiovasc Res 1998, 39: Marieb EN: Human anatomy and physiology. 5th edn: Addison Wesley Longman, Inc; Long Q, Xu XY, Ariff B, Thom SA, Hughes AD, Stanton AV: Reconstruction of blood flow patterns in a human carotid bifurcation: a combined CFD and MRI study. J Magn Reson Imaging 2000, 11: The basics of MRI [ 18. Bakker CJ, Kouwenhoven M, Hartkamp MJ, Hoogeveen RM, Mali WP: Accuracy and precision of time-averaged flow as measured by nontriggered 2D phase-contrast MR angiography, a phantom evaluation. Magn Reson Imaging 1995, 13: Murray CD: The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume. Proc Natl Acad Sci U S A 1926, 12: Kassab GS, Fung YC: The pattern of coronary arteriolar bifurcations and the uniform shear hypothesis. Ann Biomed Eng 1995, 23: Taber LA, Ng S, Quesnel AM, Whatman J, Carmen CJ: Investigating Murray's law in the chick embryo. J Biomech 2001, 34:

62 22. Moyle KR, Antiga L, Steinman DA: Inlet conditions for image-based CFD models of the carotid bifurcation: is it reasonable to assume fully developed flow? J Biomech Eng 2006, 128: Seo T, Schachter LG, Barakat AI: Computational study of fluid mechanical disturbance induced by endovascular stents. Ann Biomed Eng 2005, 33: Younis HF, Kaazempur-Mofrad MR, Chan RC, Isasi AG, Hinton DP, Chau AH, Kim LA, Kamm RD: Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation. Biomech Model Mechanobiol 2004, 3: Sui B, Gao P, Lin Y, Gao B, Liu L, An J: Blood flow pattern and wall shear stress in the internal carotid arteries of healthy subjects. Acta Radiol 2008, 49: Riley WA, Barnes RW, Evans GW, Burke GL: Ultrasonic measurement of the elastic modulus of the common carotid artery. The Atherosclerosis Risk in Communities (ARIC) Study. Stroke 1992, 23: Lee SW, Antiga L, Steinman DA: Correlations among indicators of disturbed flow at the normal carotid bifurcation. J Biomech Eng 2009, 131:

63 Appendix A Estimation of lumen radius of the CCA with Murray s Law and the general law. The lumen radius in the CCA was estimated from the lumen radii of the ICA and the ECA with Murray s Law and with a general law. The exponent x in the general law was estimated with non-linear regression analysis. Linear regression analysis and Bland-Altman plots are shown in Figures A1-6. A.1 Bifurcations without stenosis (n=14) Murray s Law General law A Figure A- 1: Correlation between the measured lumen radius of the CCA obtained with measurements and estimated with A) Murray s Law and B) the general law (x=2.7 ± 0.1). B Murray s Law General law A Figure A- 2: Bland-Altman plot of the lumen radius of the CCA estimated with A) Murray s Law and B) the general law. B 61

64 A.2 Bifurcations with stenosis (n=51) Murray s Law General law A Figure A- 3: Correlation between the measured lumen radius of the CCA obtained with measurements and estimated with A) Murray s Law and B) the general law (x=2.5 ± 0.1). B Murray s Law General law A Figure A- 4: Bland-Altman plot of the lumen radius of the CCA estimated with A) Murray s Law and B) the general law. B 62

65 A.3 Bifurcations with stenosis 0-65% (n=37) Murray s Law General law A Figure A- 5: Correlation between the measured lumen radius of the CCA obtained with measurements and estimated with A) Murray s Law and B) the general law (x=2.4 ± 0.2). B Murray s Law General Law A Figure A- 6: Bland-Altman plot of the lumen radius of the CCA estimated with A) Murray s Law and B) the general law. B 63

66 B Estimation of ICA/CCA and ECA/CCA flow ratio with Murray s Law and the general law Bland Altman plots Murray s Law General flow law A Figure B- 1: Bland-Altman plot of the relationship between the measured ICA/CCA and ECA/CCA flow ratios and the flow ratios estimated with A) Murray s Law and B) the flow general law in bifurcations without stenosis. B Murray s Law General flow law A Figure B- 2: Bland-Altman plot of the relationship between the measured ICA/CCA and ECA/CCA flow ratios and the flow ratios estimated with A) Murray s Law and B) the flow general law in bifurcations with stenosis. B Murray s Law General flow law A Figure B- 3: Bland-Altman plot of the relationship between the measured ICA/CCA and ECA/CCA flow ratio and the flow ratios estimated with A) Murray s Law and B) the flow general law in bifurcations with a degree of stenosis<65%. B 64

67 C VMTK protocol to create a surface mesh The surfacemesh created in MeVisLab is loaded. The surface mesh is closed at the in- and outlets of the bifurcation. First, the in- and outflow surfaces have to be opened. The arterial centerline from the CCA to the ICA and from the CCA to the ECA is determined and used to clip the bifurcation in a direction perpendicular to the centerline. vmtksurfacereader -ifile surfacemesh.vtk --pipe vmtkcenterlines \ --pipe vmtkendpointextractor -numberofendpointspheres 1\ --pipe vmtkbranchclipper \ --pipe vmtksurfaceconnectivity -cleanoutput 1 \ The centerline of the opened bifurcation is determined and used to add a flow extension with the length of four times the radius to the inlet and flow extensions with the length of the radius to the outlets of the surface mesh with the option extensionratio. The coordinates of the arterial centerline are stored in the file centerline.dat and the position of and normal to the in- and outlet surfaces in ref_boundary.dat. --pipe vmtkcenterlines -seedselector openprofiles \ --pipe vmtkflowextensions -adaptivelength 1 -extensionratio 4 - normalestimationratio 1.0 -interactive 1 -ofile centerline.dat \ --pipe vmtkflowextensions -adaptivelength 1 -extensionratio 1 - normalestimationratio 0.0 -interactive 1 \ --pipe vmtkboundaryreferencesystems -ofile ref_boundary.dat \ The surface is smoothed, which can be controlled with the iterations and passband values. vmtksurfacesmoothing -passband 0.1 -iterations 30 \ The number of surface elements is increased. The option subdivision is set to two, which divides every surface element in two. The method butterfly preserves the original nodes of the surface mesh and adds new ones to increase the number of surface elements. --pipe vmtksurfacesubdivision -method butterfly -subdivisions 2 \ The open extension of the surface mesh is closed again with flat caps. This is required by Netgen. The surfacemesh is exported as a STL file which is recognized by Netgen. --pipe vmtksurfacecapper -interactive 0 --pipe vmtksurfacewriter - ofile surfacemesh.stl The results can be viewed with the function vmtksurfaceviewer. 65

68 D Creating a volume mesh in Netgen The STL file of the surface mesh is imported into Netgen by clicking File -> Load Geometry. Next, the edges of the surface inlet and outlet have to be determined. Click Geometry -> STL Doctor and select the Edit Edges tab. Move the slider build edges with yellow angle towards 90 degrees until only the edges of the inlet and outlet planes are selected. When the edges are properly selected, the volume mesh can be created. Click on Mesh -> Meshing Options and select the density of the mesh by selecting the option Very Fine in Mesh granularity. The parameters in the Mesh Size tab are determined by the choice for Mesh Granularity. The mesh-size grading parameter determines the ratio of the maximum size difference between adjacent elements. By changing this value especially the mesh size in more curved areas of the mesh is influenced. In Netgen, the local density of elements is determined by the local curvature of the geometry. Netgen divides the surface mesh in several subsurfaces, which are called charts. Every surface element has a normal n 0. All adjacent surface elements for which the angle between the normal n 0 and the normal n i of that element is smaller than 15 degrees, are part of the same inner chart (Figure D- 1:). Every surface element belongs to only one inner chart area. The adjacent surface elements for which the angle between the n i and n 0 is smaller than 70 degrees are part of the same outer chart. The distance between the inner and outer chart is a measure for the curvature of the geometry. The curvature of the geometry increases when the distance between the inner and outer chart decreases. Figure D- 1: The inner and outer chart area shown on the surface mesh of a cylinder and a sphere. The dependency of the density of the mesh on the curvature of the geometry is mostly influenced by two parameters. The parameter STL-chart distance determines the influence of the curvature on the density of the mesh. If this parameter increases, the influence of the curvature on the mesh density is larger. By changing the outer chart angle from 70 degrees to a lower value, the distance between the inner and outer chart decreases and therefore mesh becomes denser. 66

69 When the meshing options are determined, click Generate Mesh. If the mesh is not dense enough it can by uniformly refined by clicking Refine uniform until the desired number of elements is reached. This refinement of the mesh is not influenced by the curvature of the mesh. 67

70 E WSS in the CCA and ECA E.1 2D WSS maps of geometry 1 (degree of stenosis 1%) in the CCA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 1: Geometry 1: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the CCA. 68

71 E.2 2D WSS maps of geometry 1 (degree of stenosis 1%) in the ECA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 2: Geometry 1: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ECA. 69

72 E.3 2D WSS maps of geometry 2 (22% stenosis) in the CCA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 3: Geometry 2: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the CCA. 70

73 E.4 2D WSS maps of geometry 2 (22% stenosis) in the ECA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 4: Geometry 2: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ECA. 71

74 E.5 2D WSS maps of geometry 3 (69% stenosis) in the CCA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 5: Geometry 3: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the CCA. 72

75 E.6 2D WSS maps of geometry 3 (69% stenosis) in the ECA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 6: Geometry 3: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ECA. 73

76 E.7 2D WSS maps of geometry 4 (87% stenosis) in the CCA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 7: Geometry 4: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the CCA. 74

77 E.8 2D WSS maps of geometry 4 (87% stenosis) in the ECA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 8: Geometry 4: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ECA. 75

78 E.9 2D WSS maps of geometry 5 (93% stenosis) in the CCA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 9: Geometry 5: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the CCA. 76

79 E.10 2D WSS maps of geometry 5 (93% stenosis) in the ECA Measurement vs. Murray s Law Measurement vs. generic relationship Figure E- 10: Geometry 5: 2D Maps of the calculated WSS in the ICA with the measured ICA /CCA ratio and the difference and relative difference in WSS (dwss, in Pa or percentage) between the CFD calculations with the measured and with an estimated ICA/CCA flow ratio, with the ICA/CCA flow ratio estimated with Murray s Law (left) and the generic relationship (right) in the ECA. 77

80 F MRI protocol optimization The biggest advantage of a non-triggered 3D phase contrast (PC) measurement (3D) of the carotid bifurcation is the large size of the image volume in which flow is measured in a relatively short image time. The planning of the scan is also easy. A disadvantage of the non-triggered 3D phase contrast measurement is the lack of information on the pulsatility of the flow. When a model of the carotid bifurcation would be used to estimate peripheral resistance and resistance of the stenosis, triggered phase contrast measurements should be added to the scan protocol to determine the flow waveform in the carotid arteries. Abbreviations MRI sequences 3D 2Dv (t) 2D v x,y,z (t) Nontriggered time-averaged phase contrast (PC) measurement with multi velocity encoding and coronal slice select direction Triggered, time dependent 2D PC measurement with velocity encoding the perpendicular to slice select direction Triggered time dependent PC measurement with multi velocity encoding Our goal was to find an optimal scan protocol to measure the flow waveform given the limitations as are present for large scale population studies. One of the major limitations was the available acquisition time. The triggered measurements have to be added to an existing scan protocol for which the study coordinators determined that the maximum duration is thirty minutes. The acquisition time of the triggered scan was therefore limited to two minutes per scan. Because a 3D triggered scan would take much longer, triggered, time-dependent 2D phase contrast measurements were investigated with velocity encoding perpendicular to the slice select direction on a group of healthy subjects. A trade-off between acquisition time and signal to noise ratio (SNR) had to be made. The SNR and flow of the 2D and 3D measurements were compared. To optimize the scan protocol, the measurements were performed on healthy volunteers and the scan parameters of the 2D measurements were changed. F.1 Study group Both 2D triggered and 3D non-triggered MRI measurements were performed on four presumably healthy volunteers (4 male, 1 female, years old). The 3D non-triggered measurements were discussed in Chapters 2 and 3. Two 2D measurements were performed on the healthy volunteers: 1. A triggered, time-dependent 2D PC (2Dv (t)) measurement with velocity encoding in one direction, which was perpendicular to the slice select direction; 2. A triggered time-dependent 2D PC (2D v x,y,z (t)) measurement with multi velocity encoding, for which the first direction was perpendicular to the slice select direction and the second and third direction were in-plane with the slice. On the first two volunteers 2Dv (t) and 3D scans (see Chapter 2) were performed on the left carotid bifurcation to compare the flow and SNR from these measurements. To test the influence of the slice positioning in the 2Dv (t) measurement, this measurements and a 2Dv x,y,z (t) measurement were performed on the left and right carotid bifurcation of volunteers 3 and 4. 78

81 Triggered 2Dv (t) measurements in the CCA were performed on all volunteers, in the ICA on volunteers 1-3 and in the ECA on volunteers 1 and 2 (Table F- 1). For volunteers 1 and 2, the measurements were only performed in the left carotid bifurcation, because the coil for both bifurcations was unavailable at the time of the measurements. The flow was not measured in the ECA and right ICA of volunteer 3 and the ECA and ICA of volunteer 4, because these measurements could not be performed within the time during which the MR scanner was available. Table F- 1: Overview of the measurement positions in the carotid bifurcation for the 2Dv (t) phase contrast measurements performed on volunteer 1-4. subject Left CCA Right CCA Left ICA Right ICA Left ECA Right ECA 1 x x x 2 x x x 3 x x x 4 x x As the 2Dv (t) measurement would serve the research on peripheral resistance in patients with stenosis in the ICA, we investigated the feasibility of the application of this sequence in a group of patients with plaque in the ICA. The 2Dv (t) measurements were performed in the CCA and ICA of one bifurcation in a group of nine subjects recruited from a group of symptomatic patients scheduled for carotid endarterectomy in the Erasmus MC Rotterdam. In this group the applicability of the 2Dv (t) sequence for flow measurements in bifurcations with stenosis was determined. F.2 Methods F.2.1 Triggered 2D phase contrast imaging Flow was measured in one slice, which was positioned, perpendicular to the centerline of the artery in the CCA (22 mm proximal to the bifurcation), ICA (22 mm distal to the bifurcation) and ECA (15 mm distal to the bifurcation) in the left and right carotid bifurcation. The position of the carina of the carotid bifurcation is determined as the position at which the ICA and ECA can be observed separately in the 3D images. Scan parameters, views per segment (VPS), bandwidth and cardiac number of phases (CNF)) were changed to obtain the best possible trade off between SNR and scan time, which should be less than two minutes per scan. In the 2Dv (t) measurement every slice contains the velocity profile at a certain moment in the cardiac cycle. Within each heartbeat, a certain number of lines in k-space are sampled for every slice. This number of lines is called views per segment. Decreasing the views per segment and the bandwidth increases the temporal resolution of the measurement and therefore the SNR, but also increases the acquisition time. The cardiac number of phases represents the number of slices within a cardiac cycle that is reconstructed from the images. When the number of cardiac phases exceeds the number of slices that was initially reconstructed, extra slices are reconstructed by linear interpolation of adjacent slices. For a high number of cardiac phases, a high temporal resolution and therefore a long acquisition time is needed. Changing the number of cardiac phases has no direct influence on the SNR, but a low number of cardiac phases may lead to the underestimation of the peak systolic velocity and flow. A lower flow leads to a decrease 79

82 in the SNR of the phase images. The bandwidth is the range of frequencies in the frequency encoding direction, an increase in bandwidth means a decrease in SNR and a longer acquisition time. Other scan parameters were venc = 120 cm/s in the slice-select direction, 4 mm slice thickness, 256x256 acquisition matrix, FOV = 130x130 mm, a time resolution of 29.6 ms and NEX = 1. The scans were triggered with a finger pressure sensor. Because the scan was triggered, the acquisition time depended on the heart rate of the subject. The reconstructed images consisted of magnitude images and phase images in the slice select direction. The grayscale in the phase images was equal to the velocity in the slice select direction in mm/s. Lumen contours were drawn manually on each magnitude image in the cardiac cycle in ImageJ. Flow over time could be determined from the velocity image by summation of the velocity field over the arterial cross-section. To compare the results of the 2D v (t) to the 3D measurements the resulting flow waveform was time-averaged. 2Dv (t) phase contrast measurement protocol applied to patients Based on the results of the volunteer measurements above was decided on a protocol with 4 VPS and sixty cardiac phases. The 2Dv (t) flow measurement was tested for applicability in carotid bifurcations with stenosis. 2Dv (t) measurements were performed in the ICA and CCA in one bifurcation in a group of patients suspected for stenosis. F.2.2 Slice planning Slice planning was performed on a maximum intensity projection (MIP) image of the carotid bifurcation. This MIP image was noisy and the direction of the carotid arteries difficult to observe. Therefore, the planning of the slices perpendicular to the centerline of the artery before the 2Dv (t) measurement was difficult and sensitive to errors. The slice placement is especially difficult in patients with a high degree of stenosis and reduced flow in the carotid arteries. The intensity of the MIP image in the stenosed artery is lower than in healthy volunteers. To investigate the influence of slice planning on the measured flow in two healthy volunteers a triggered, time dependent PC measurement with multi velocity encoding (2D v x,y,z (t)) was performed with venc =120 cm/s, 4 mm slice thickness, 256x256 acquisition matrix, FOV = 130x130 mm, NEX = 1 and a time resolution of 59.2 ms. The scans were triggered with a finger pressure sensor. The slice was positioned 22 mm below the bifurcation in the CCA perpendicular to the centerline of the artery. The velocities in the directions normal to the arterial centerline will tell something about the error in the measured flow caused by the planning of the slices. The possible influence of in-plane velocities in the CCA was neglected. Because the CCA is a straight artery and no stenosis is expected, the magnitudes of in-plane velocities are expected to be small. F.2.3 Data analysis Flow and maximum velocity measured with the measurements to investigate the reproducibility of the scans were both compared with paired t-tests with a 95% confidence interval. 80

83 Signal to noise ratio (SNR) SNR (S/N) was determined in the phase images and in the magnitude images from a region of interest in the signal intensity of the imaged object (S object ) and the standard deviation of the signal of background noise (ς background ) (Equation F.4), which was measured in a ROI outside the imaged object [17]. S S N object background (F.4) Reproducibility The reproducibility of the 2Dv (t) measurements was determined. The flow and the peak systolic velocity was determined from repeated measurements in the CCA, ICA and ECA in volunteers 1 and 2 and compared. The measured flow, SNR and time-averaged maximum velocity were of the 2Dv (t) measurements were also compared to the 3D measurements of Chapter 2. F.3 Measurement results of the 2D measurements F.3.1 SNR, flow and velocity in the 2Dv (t) measurements in healthy volunteers The mean time-averaged flow, systolic flow, peak systolic velocity and time-averaged maximum velocity measured in the CCA, ICA and ECA are shown in Table F- 2. The difference between the mean time-averaged flow in the CCA and the sum of flow in the ICA and ECA was 22% of the flow measured in the CCA. The mean systolic maximum velocity was higher in the ECA than in the ICA. Table F- 2: Mean and standard deviation of the flow and velocity in the CCA, ICA and ECA assessed with 2Dv (t) measurements. q mean [ml/s] q sys [ml/s] v max,sys [cm/s] v max [cm/s] CCA 7.4 ± ± 4 86 ± ± 3 ICA 4.2 ± ± 2 50 ± 9 28 ± 7 ECA 1.6 ± ± 1 67 ± 3 23 ± 2 q mean = time-averaged flow; q sys = systolic flow; v max,sys = peak systolic velocity; v max = time-averaged maximum velocity For volunteer 1 and 2 six 2Dv (t) measurements with different scan parameters were performed in the left CCA. The measured flow waveforms are shown in Figure F- 1. Systolic and diastolic flow was comparable in all waveforms. Some measurement noise in the measurement was visible in the diastolic part of the waveform when the flow and therefore the signal intensity of the phase images was low. Especially the flow in the ECA was almost zero during diastole. 81

84 A B Figure F- 1: Flow (Q) as a function of time for A) volunteer 1 and B) volunteer 2 determined from all measurements with different scan parameters. Waveforms were measured in the CCA (blue), ICA (red) and ECA (green). Signal to noise ratio (SNR) The mean SNR of the 2Dv (t) measurements of all volunteers was 27 ± 5 in the magnitude images and 0.37 ± 0.06 in the phase images. The SNR of the phase images was lower than one, which means that the signal of the phase images was lower than the noise. To determine which scan parameters gave the best SNR, 2Dv (t) measurements were performed in the CCA with different views per segment (VPS 1, 2 or 4), bandwidth (11 and 33 MHz) and cardiac number of phases (30 or 60). All combinations of these scan parameters were investigated to obtain the best possible measurement results. Because the acquisition time should be limited to two minutes per scan, sequences with an acquisition time longer than two minutes were not investigated. Figure F- 2 shows all 2Dv (t) measurements sorted on the scan parameters VPS and cardiac number of phases. For all 2Dv (t) measurements, the signal intensity was smaller than the measurement noise. Mean SNR changed very little when the VPS and cardiac number of phases were changed. After the bandwidth was decreased to 11 MHz the SNR increased in the magnitude images to 38 for volunteer 1 and to 51 for volunteer 2, but did not increase in the phase images. Possibly NEX has a larger influence on the SNR of the 2D measurements than the parameters mentioned above. Future measurements should include scans with a NEX > 1. However, an increase of the NEX will increase the acquisition time well above two minutes. 82

85 Magnitude Phase Figure F- 2: Mean SNR of the 2Dv (t) measurements as a function of the scanning parameters views per segment and cardiac number of phases. On the left the SNR of the magnitude images (SNR mag ) and on the right of the SNR of the phase images (SNR phase ). Reproducibility The time-averaged flow and systolic flow determined with the 2Dv (t) measurements of volunteer 1 and 2 already looked reproducible in the waveforms in Figure F- 1. The standard deviation of the time-averaged flow, systolic flow and time-averaged v max were indeed smaller than 10% of the mean in volunteer 1 and 2. 83

86 A B C Figure F- 3: Mean and standard deviation of the A) time-averaged flow (q), B) systolic flow (q sys ), C) time-averaged maximum velocity (v max ) and D) peak systolic velocity (v max,sys ) in the CCA and ICA in volunteer 1 and 2. F.3.2 2Dv (t) phase contrast measurements applied to patients For the measurements in the symptomatic patients a 2Dv (t) sequence with a bandwidth of 33 MHz, 2 views per segment and 60 cardiac phases was used. Out of eighteen 2Dv (t) measurements, eight flow waveforms resulted from the measurements, but for ten measurements, the data seemed to contain only noise. Some examples of the flow waveforms are shown in Figure F- 4. D 84

87 CCA ICA good bad Figure F- 4: Examples of flow waveforms resulting from good and bad measurements in the CCA and ICA with 2Dv (t) measurements in symptomatic patients. The bad 2Dv (t) measurements of the flow waveforms in symptomatic patients had a number of causes: Stenosis in the ICA reduced the flow through the CCA and ICA. The SNR of the phase images of patients was therefore lower than in healthy volunteers; The heart rate of the patients was not stable, which disturbed the triggering of the measurement; The planning of the slices for the 2Dv (t) measurements was done on a maximum intensity projection (MIP) image. The SNR of this image was low due to the reduced flow through the carotid bifurcation. The ICA was therefore sometimes hardly visible on the MIP image, which complicated the planning of the slices. F.3.3 Error analysis of the slice planning in healthy volunteers with 2Dv x,y,z(t) and 2Dv (t) measurements In Figure F- 5 the results of the 2Dv x,y,z (t) and the 2Dv (t) measurements in volunteer 3 and 4 are shown. Both measurements had an acquisition time of four minutes, the number of cardiac phases was 40 in the 2Dv x,y,z (t) and 90 in the 2Dv (t) measurement. The slices were planned perpendicular to the centerline of the artery. The difference between the time-averaged flow and time-averaged v max in both measurements was less than 10% for both volunteers. The difference between the systolic flow and between the peak systolic velocity in the 2Dv (t) and the 2Dv x,y,z (t) measurement 85

88 were 2.4 ml/s and 1.8 ml/s in the left and the right carotid bifurcation of volunteer 4, which was more than 10% of the mean systolic flow of both measurements. The mean flow in the in-plane directions in the 2Dv x,y,z (t) measurements was 0.4 ml/s for volunteer 3 and 0.5 ml/s for volunteer 4. The measurement error due to an error in the planning of the slices was therefore less than 10% of the mean flow (6.8 ml/s). A B C Figure F- 5: A) Time-averaged flow (q mean ), B) systolic flow (q sys ), C) peak systolic velocity (v max,sys ) and D) time-averaged maximum velocity (v max ) in the CCA measured with 2Dv (t) (2D perp) and 2Dv x,y,z (t) measurements in volunteer 3 and 4. The shape of the waveform was comparable in both measurements, especially in the diastolic part of the waveform (Figure F- 6). However, the systolic peaks in the 2Dv x,y,z (t) measurements in volunteer 4 were lower than in the 2Dv (t) measurements, which could be due to the lower time resolution of the 2Dv x,y,z (t) measurements, which was two times lower due to the velocity encoding in the in-plane directions (59.2 vs 29.6 ms). D 86

89 Volunteer 3, left CCA Volunteer 3, right CCA Volunteer 4, left CCA Volunteer 4, right CCA Figure F- 6: The flow (q) waveform measured in the left and right CCA with 2Dv x,y,z (t) (red) and 2Dv (t) (blue,- -) measurements in volunteer 3 and 4 F.4 2Dv (t) vs 3D nontriggered phase contrast measurements Flow was determined with 3D and 2Dv (t) measurements in the left CCA for volunteers 1-4 and in the right CCA for volunteers 3 and 4. In the left ICA flow was determined for volunteers 1-3 and in the left ECA for volunteers 1 and 2. In total the flow was measured in six bifurcations in the CCA, three in the ICA and two in the ECA. The differences in the measured time-averaged flow and maximum velocity between the 3D and the 2Dv (t) measurements are shown for all measured bifurcations in Figure F- 7. The mean measured flow in the CCA was 7.5 ± 1.2 and 7.1 ± 0.8 ml/s in the 3D and the 2Dv (t) measurements. The difference between these flows was not significant (p=0.25). However, the difference in the measured maximum velocity (37 ± 4 and 42 ± 3 cm/s) was significant (p<0.05). The mean measured flow in the ICA was 4.8 ± 1.2 and 3.7 ± 2.3 ml/s in the 3D and 2Dv (t) measurements. This difference was mostly caused by the large difference in measured flow between both 2D measurements in bifurcation 2. The difference in the measured flow in the ECA was large for volunteers 1 and 2, but the mean difference is smaller than 10% of the mean flow (2.1 ± 0.1 and 2.3 ± 0.6 ml/s). The measured v max in the ECA was 17 ± 4 and 22 ± 2 cm/s. The mean difference between the flow through the CCA and the sum of flow through 87

90 the ICA and ECA was almost the same (22% in the 2Dv (t) and 24% in the 3D measurements). CCA CCA ICA ICA ECA ECA Figure F- 7: Mean time-averaged flow (q) of the CCA, ICA and ECA and mean time-averaged maximum velocity (v max ) of the CCA, ICA and ECA derived from the 2D and the 3D MR measurements. The mean flow measured in the symptomatic patient group was 6.3 ± 2.2 and 6.4 ± 2.4 ml/s in the CCA and 3.1 ± 1.8 and 3.1 ± 1.8 ml/s in the ICA determined with the 3D and the 2D v (t) measurements. These differences between the mean measured flows in the CCA and the ICA were not significant (p=0.67 and p=0.99). Signal to noise ratio (SNR) 2D v (t) measurements offer the opportunity to measure the flow over time in the carotid bifurcation. However, the SNR of these measurements was expected to be lower than the SNR of the 3D measurements, because the imaging volume in the direction of the flow was 88

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