BSc Physics and Astronomy (Joint Degree)
Institutes:
University of Amsterdam (FNWI)
Vrije Universiteit Amsterdam (FEW)
Academisch Medisch Centrum (Radiology department)
Differences in healthy carotid pulse wave
velocity and wall shear stress for gender
and smoking history
Author:
Vera ˇ
Calukovi´
c
10773711
July 6, 2017
Report Bachelor Project Physics and Astronomy
size 15 EC
conducted between 03-04-2017 and 07-07-2017
Supervisor:
Examiners:
E.S.Peper
A.J. Nederveen
Abstract
One of the possible causes of cardiovascular diseases that involve atherosclerosis is smoking. Smoking can stimulate the production of atheromatous plaque, which thickens and narrows the blood vessels, causing stiffening and reduced elasticity. High pulse wave velocity (PWV), the velocity at which the arterial pulse propagates through the cardio-vascular system, is known to have a strong positive correlation with cardiocardio-vascular events and is clinically used as a measure of arterial stiffness. Wall shear stress (WSS), the mea-sure of the tangential force of the flowing blood on the vessel, is another haemodynamic parameter associated with wall stiffness. The objective of this study was to determine whether age, gender and smoking history could be strong indicative factors for the early development of cardiovascular diseases when observed through PWV and WSS. PWV and WSS were therefore calculated for 29 health volunteers (age = 30.5 ± 3.3, range 21-37, 13 male), of which 13 had a smoking history.
PWV was calculated using a compressed sensing algorithm, 2D flow phase-contrast magnetic resonance imaging (PC MRI) data of the common carotid artery and the internal carotid artery and manual segmentation. WSS was calculated using 4D flow PC MRI data, manual segmentation of the vessels and algorithms that were developed in MATLAB and were based on normalised probability distributions. Analysis of WSS was performed with the mean WSS at peak systole. Another algorithm was developed for comparison of PWV (n = 23) and mean WSS (n = 24) with each other and between the groups. Statistics performed consisted of a Wilcoxon signed-rank test and linear regression. For 18 volunteers both PWV and mean WSS were determined. Results showed PWV and age, expanding the group with another population of healthy volunteers (n = 10, age = 62.4 ± 10.3, range 53-77), measured with the same scan settings, into account, are positively correlated, p = 0.0003, R2 = 0.51. Whether gender and smoking history are
proper parameters for mean WSS and PWV comparisons cannot be affirmed yet. They showed no significant differences when compared. PWV had a p-value of 0.44 for gender comparisons. For smoking history this was 0.18. Comparisons between mean WSS and gender and mean WSS and smoking history resulted in p-values of 0.83. When comparing PWV and mean WSS for smoking history, those who have smoked consistently had, in the right carotid artery, a lower WSS for the same PWV than those who did not have a smoking history. Comparing PWV and mean WSS for the different sexes, men showed a positive and women a negative linear relation. As no solid conclusions, can be drawn yet further research is needed.
Populair wetenschappelijke samenvatting
Waarschijnlijk heb je het wel eens gehoord: roken is dodelijk. Het roken van sigaretten is ´e´en van de vele factoren die kan leiden tot hart- en vaatziekten (HVZ), doordat het de verkalking en vernauwing van bloedvaten stimuleert, waardoor de elasticiteit van de bloedvaten afneemt. Wanneer bloedvaten ver-kalken zullen deze meer moeite ervaren bij het pompen van het bloed door het gehele lichaam. Dit kan uiteindelijk leiden tot een vroege dood. Het is hierom belangrijk om in een vroeg ontwikkelingsstadium van de desbetreffende vorm van HVZ de ziekte te signaleren. Een hoge polsgolfsnelheid, in het Engels pulse wave velocity (PWV) genoemd, wordt geassocieerd met HVZ en is ´e´en van de klinisch gebruikte maatstaven voor het bepalen van de elasticiteit van de slagaderen. PWV kan met behulp van MRI-metingen bepaald worden en wordt beschreven als de snelheid waarmee een bloeddrukgolf zich door een slagader verplaatst. Hierbij spelen de afgelegde afstand van het bloed en de tijd waarin de bloeddrukgolf deze afstand afgelegd heeft een belangrijke rol.
Een andere factor die vaak met verkalking geassocieerd wordt is de schuifspanning, in het Engels ook wel wall shear stress (WSS) genoemd. De WSS kan ook met behulp van MRI bepaald worden en beschrijft de spanning die op elk punt van een vaatwand uitgeoefend wordt door het stromende bloed. Aangezien bloedvaten buigen en de stroomsnelheid van het bloed constant gehouden moet worden, zal de WSS op ieder punt binnen de vaatwand vari¨eren.
In dit project heb ik onderzoek gedaan naar de PWV in de rechter halsslagader en naar de WSS in beide halsslagaders bij 29 gezonde vrijwilligers. De waarden zijn bepaald met behulp van zowel commercieel verkrijgbare medische programma’s als zelfgeschreven scripts in de programmeertaal MATLAB. Na het bepalen van de waarden voor PWV en WSS werd tussen zowel mannen en vrouwen vergeleken als tussen mensen die wel eens gerookt hebben (rokers) en mensen die nooit gerookt hebben (niet-rokers). Aangezien van de elasticiteit van bloedvaten bekend is dat deze afneemt naar mate mensen ouder worden, is in dit project ook gekeken naar de hoogte van de PWV en WSS ten opzichte van de leeftijd. De gemiddelde PWV en WSS-waarden zouden in een klinische setting voor de verschillende parameters als richtlijn kunnen dienen. Hoe verder een gemeten waarde van de gezonde waarde afwijkt, des te groter de kans is dat iemand een vorm van HVZ is begonnen te ontwikkelen.
Voor het bepalen van de PWV en de WSS was het voor de gebruikte scripts in MATLAB belangrijk om de regio’s in de MRI-scans waarover gerekend moest worden, namelijk de halsslagaders, duidelijk aan te geven. Hierbij is de PWV bepaald tussen een punt binnen de gemeenschappelijke halsslagader en een punt binnen de binnenste slagader en de WSS rond de vertakking van de halsslagader. Uit de resultaten is gebleken dat met de jaren de PWV toeneemt en de WSS afneemt. Gemiddeld vertoonden mannen hogere PWV-waarden wanneer de WSS-waarden toenamen, terwijl bij vrouwen de PWV-waarden juist afnamen bij een hogere WSS. Wanneer de PWV en WSS-waarden tussen de niet-rokers en rokers vergeleken werden bleken de relaties afhankelijk van de ader waarin de WSS berekend was te verschillen. De analyse van de rechter halsslagader laat zien dat rokers steevast een lagere WSS hadden dan niet-rokers. Het is echter nog niet duidelijk of geslacht en het wel of niet gerookt hebben de beste parameters zijn om HVZ in een vroeg stadium te detecteren. Hiervoor zal verder onderzoek gedaan moeten worden met een grotere groep gezonde mensen. Verder zal ook vergeleken moeten worden met de waarden van HVZ-pati¨enten.
Contents
1 Introduction 2
2 Theory 2
2.1 Atherosclerosis . . . 2
2.1.1 Effect of age, gender and smoking on the arteries . . . 3
2.2 MRI measurements . . . 4
2.2.1 PC MRI: 2D and 4D flow MRI . . . 4
2.2.2 PWV . . . 5
2.2.3 WSS . . . 6
3 Setup and method 6 3.1 Study population . . . 6 3.2 Data acquisition . . . 6 3.3 PWV . . . 7 3.4 WSS . . . 10 3.5 Statistical analysis . . . 11 4 Results 12 4.1 PWV . . . 12 4.2 WSS . . . 14 4.3 PWV and mean WSS . . . 17 5 Discussion 20 5.1 PWV . . . 20 5.2 WSS . . . 23 5.3 PWV and mean WSS . . . 23
5.4 Suggestions for further research . . . 24
6 Conclusion 24
7 Acknowledgements 25
A Histograms and radar plots of the WSS data I
1
Introduction
Cardiovascular diseases are a leading cause of death worldwide (Laurent et al. 2001). Cardio-vascular diseases include, among stroke, peripheral arterial disease, heart failure, hypertensive heart disease and other forms, coronary artery diseases, or ischemic heart diseases, such as angina and myocardial infarctions. Ischemic heart disease, stroke and peripheral artery dis-eases involve atherosclerosis, which may be caused by, among others, high blood pressure, smoking, diabetes and high blood cholesterol. These factors can stimulate the production of atheromatous plaque, thickening and narrowing of the blood vessels and causing the vessels to become stiffer, reducing their elasticity. Most cardiovascular diseases happen in later stages of life (Blacher et al. 1999). High pulse wave velocity (PWV) is known to have a strong corre-lation with cardiovascular events and all-cause mortality, and is clinically used as a measure of arterial stiffness (Laurent et al. 2001). Another factor that might be a good predictor of cardiovascular events is wall shear stress (WSS), which is the tangential force, exerted by the blood flowing through the vessel, on the endothelial wall (Potters et al. 2014).
Im Cho et al. (2016) found that carotid WSS had a role as an index of atherosclerosis and served as a predictor of significant coronary atherosclerosis, as atheromatous plaque mainly develops in regions with a lower WSS.
In this study PWV and WSS have been calculated in the carotid arteries for 29 healthy volunteers, using velocity encoded magnetic resonance imaging. This was done in order to determine how PWV and WSS differ between the sexes, and how they differ between people who had never smoked and people who do have a history with smoking first-hand. The PWV was determined in the right carotid artery, while the WSS was determined in both the left and the right carotid artery. In order to calculate PWV and WSS, and in order to quantify those values in a way they could be compared between the different groups and with each other, several programs have been developed using MATLAB.
For future studies the average and the standard deviation of PWV and WSS values mea-sured in this study for gender and smoking history could be used as a reference of healthy PWV and WSS values. Deviation of PWV and WSS values from these averages could indicate early signs of a cardiovascular disease. This might help to detect cardiovascular diseases in even earlier stages than is currently possible.
As vessels become stiffer with age it is expected that PWV increases with age, while WSS decreases. Expected is also that, since men typically suffer of diseases several years earlier than women do, women would have, on average, a lower PWV and a higher WSS. The same is expected to be observed for people who have no smoking history compared to those who do have a smoking history.
2
Theory
2.1 Atherosclerosis
Atherosclerosis, which is the hardening of an artery specifically due to an atheromatous plaque, is a leading cause of death in developed countries (O’leary et al. 1999). An atheroma-tous plaque is an accumulation of degenerative material in the inner layer of an artery wall. The material consists of macrophage cells containing lipids, calcium and a variable amount of fibrous connective tissue. The accumulated material forms a swelling in the artery wall, narrowing and restricting the blood flow through the blocked artery. In atheromatous plaques
vascular smooth muscle cells (VSMC) migrate from the tunica media toward the tunica intima, where they undergo a phenotypic change and begin to proliferate. VSMC migration plays a major role in the formation of atherosclerosis plaques and as time progresses, the plaque will slowly increase in size, eventually leading to complete occlusion of smaller vessels downstream the restricted vessel (Yoshiyama et al. 2014). Depending on the location of the occlusion this could lead to myocardial infarction and ischemic strokes ( Loboz-Rudnicka et al. 2016). A valuable predictor of myocardial infarction and ischemic stroke is the carotid intima-media thickness (CIMT), which is oftentimes measured with carotid ultrasound, a noninvasive and effective screening tool for carotid atherosclerosis (Im Cho et al. 2016). CIMT is considered to be a marker of subclinical atherosclerosis. CIMT is defined as the thickness of the carotid media, between the outer layer and the muscular medium of the artery ( Loboz-Rudnicka et al. 2016).
2.1.1 Effect of age, gender and smoking on the arteries
It is found that CIMT is mostly determined by age. The older people become, the thicker the layer consisting of the inner and media layer becomes. This can happen without con-comitant formation of atheromatous plaques ( Loboz-Rudnicka et al. 2016). Loboz-Rudnicka et al. (2016) found that, in general, CIMT is, among men, mostly determined by age, while among women by age, pulse pressure and an increased waist circumference. They found that there was no significant difference between men and women below the age of 45, but that the differences became more notable when this age was exceeded. Over the age of 45 women showed to have lower CIMT values then men. The thicker the artery walls become, the more stiff, and thus less elastic, the arteries become (Kr¨oner et al. 2014). The vessel wall elasticity plays a central role in cardiovascular physiology. The less elastic a vessel wall becomes, the harder it becomes to dampen the systolic pressure wave, which could eventually result in damaging end-organs such as the brain by exposing it to excessive pulsatile energy.
Other than ageing, nicotine is another factor responsible for the formation of atheromatous plaques in the vascular intima (Yoshiyama et al. 2014). The results from Yoshiyama et al. (2014) indicate that nicotine has the effect of transforming VSMC from contractile type to synthetic-like type, an effect that occurs before the development of atheromatous plaque. The underlying mechanisms of increased arterial stiffness due to smoking, as explained by Doonan et al. (2010), is shown in figure 1.
Figure 1: The underlying mechanisms of smoking-induced increases in arterial stiffness. TG, triglycerides; LDL, low-density lipoprotein; HDL, high-density lipoprotein; GFR, glomerular filtration rate; ROS, reactive oxygen species; NO, nitric oxide; BP, blood pressure. Adapted from Doonan et al. (2010)
2.2 MRI measurements
Measurements of arteries are often performed using ultrasound. Another effective noninvasive tool that is often used in medical studies is phase contrast MRI (PC MRI).
PC MRI measures the blood flow in up to three spatial directions. This can be done for multiple time points along the cardiac cycle for both a 2 dimensional slice (2D flow MRI) and a 3 dimensional (3D) volume (4D flow MRI). The elasticity of the wall can be determined using PWV and 2D flow MRI, while vessel properties such as WSS can be determined using 4D flow PC MRI.
2.2.1 PC MRI: 2D and 4D flow MRI
Doppler ultrasonography (US) measures the blood flow direction away or toward the probe, as well as its relative velocity (Markl et al. 2011), but it tends to suffer more from aliasing than PC MRI. With MRI it is possible to take the variation of the blood flow velocity within the vessel into account, diminishing aliasing effects (Lotz et al. 2002).
PC MRI creates velocity encoded (VENC) images. The VENC, which is inversely re-lated to the area of the flow encoded gradients, has to be determined manually and specifies the highest and lowest velocity encoded by a phase-contrast sequence. The quality of the measurements depends on how closely the VENC matches the real velocity of the region of interest. Noise in velocity images increases with larger VENC values, but can be tolerated when the flow, and not the peak velocity, is the main interest of measurement.
Cardiac PC MRI data can be acquired with either prospective or retrospective gating. Both techniques require a trigger signal that can, for example, be provided by the heart rate measured with electrocardiography (ECG) or with a pulsoximeter. With prospective gating the cardiac MRI measurement is initiated by the trigger and is collected during several reg-istered cardiac cycles. Contrary to data acquisition with prospective gating, data acquisition with retrospective gating is done continuously throughout multiple cardiac cycles. Afterwards
the data is binned into a certain number of cardiac frames, thus providing full coverage of the whole cardiac cycle.
2D flow MRI planned perpendicular to a vessel allows the calculation of volume flow through a plane that transects the vessel. 4D flow MRI is a 3D acquisition method that can be used for 3D flow quantification and visualisation (Markl et al. 2011). The time dimension in these measurements represents the time course of an averaged heart cycle.
2.2.2 PWV
PWV, in m/s, is the velocity at which the arterial pulse propagates through the cardiovascular system, and can be related to wall stiffness using the Moens-Korteweg equation,
P W V = s
Einc· h
2rρ , (1)
where Einc, in Pa, is the incremental elastic modulus of the vessel wall, h, in m, the wall thickness, r, in m, the radius, and ρ, in kg/m3 the density of blood, given the ratio of h to r is constant.
From two slices measured with 2D flow MRI two flowcurves over time can be derived by averaging the flow within the vessel region for each timepoint. It can be seen in figure 2b that the two flowcurves at different positions along the vessel are slightly shifted in time. PWV can be calculated using equation 2, with ∆z being the distance, in meters, between the two observed points, travelled by the blood, and ∆t the time it took the pressure pulse to travel that distance, in seconds. The scans of such a measurement both have to be planned perpendicular to the slices, as shown in figure 2a.
P W V = ∆z
∆t (2)
Figure 2: Planning of the slices for the 2D flow scans when used for PWV calculations between two points within the carotid artery. The slices, in red, are placed perpendic-ular to the common carotid artery (CCA) and the internal carotid artery (ICA).
2.2.3 WSS
Using 4D flow data and the derived 3D velocity vector field, WSS, in Pa, can be calculated at each timepoint of the cardiac cycle at each point of the vessel surface. The WSS is the tangential force, exerted by the blood flowing through the vessel, on the endothelial wall, and is calculated as the product of the viscosity of the blood, η, and the spatial gradient of velocity perpendicular to the vessel wall, dvdn, as shown in equation 3 (Potters et al. 2014).
W SS = ηdv
dn (3)
3
Setup and method
3.1 Study population
29 healthy subjects, without familial hypercholesterolemia records, aged 30.5 ± 3.3 years (mean ± standard deviation, range 21-37 years, 13 male) were selected from an ongoing study using PC MRI techniques at the Academic Medical Centre of Amsterdam. Within this group of subjects 13 people (8 male) had a smoking history.
3.2 Data acquisition
MRI data was acquired with a 3.0 Tesla Ingenia MRI scanner (Philips Healthcare, Best, The Netherlands). For the scanning an eight channel carotid coil (Shanghai Chenguang Medical Technologies Co. Ltd, China) was placed around the neck of the subject. The scan procedure consisted of a 3D black blood scan with an isotropic resolution of 0.7 mm of the entire neck, two 2D flow scans focused on the right carotid artery for PWV analysis and one 4D flow scan of both carotid arteries for WSS analysis. For the PWV analysis two velocity encoded slices perpendicular to the right carotid artery were acquired, with a unidirectional VENC of 150 cm/s in food-head (FH) direction. This way the blood flowing away from the heart toward the head would be encoded positive and appear white, while the blood flowing back toward the heart would appear black, as can be seen in figures 3a and 3b. The first slice was placed perpendicular to the CCA, while the second slice was placed perpendicular to the ICA, as can be seen in figure 2.
The 2D flow datasets had, due to retrospective triggering and a compressed sensing recon-struction, a temporal resolution of 4 ms. The 2D flow scan had a repetition time (TR) of 8.0 ms, an echo time (TE) of 3.9 ms, a flip angle of 25◦, 250 cardiac frames after reconstruction of the initial 50 frames, a spatial resolution of 0.87 × 0.87 mm2, a field of view (FOV) of 139 × 139 mm2, and a VENC of 150 cm/s in FH. The scanning time was approximately 4 minutes. The 4D flow scan had a temporal resolution of 80 ms, a TR of 7.9 ms, a TE of 4.6 ms, a FA of 88◦, 12 cardiac frames, a spatial resolution of 0.8 × 0.8 × 0.8 mm3, a FOV of 24 × 160 × 160 mm3 and a VENC of 150 cm/s in FH, anterior-posterior (AP) and left-right (LR) direction. The scanning time was approximately 11 minutes due to a three times k-t PCA acceleration technique from Gyrotools (Z¨urich).
Figure 3: Magnitude (a) and velocity encoded (b) image of the axial view of both the left and right common carotid arteries, which appear white in (b). In (b) the vessel is white when the blood travels away from the heart toward the head, meaning the velocity is positive, and black when the velocity is negative, meaning the blood flows toward the heart.
3.3 PWV
The velocity encoded scans of the CCA and ICA were initially acquired at a low temporal resolution in order to obtain, after performing a compressed sensing reconstruction, a high quality image in a short scan time. Reconstruction of the scans was done at a higher temporal resolution than the temporal resolution the scans were initially acquired at. Rebinning the data to a higher number of cardiac frames lead to gaps in k-t space, which is also known as undersampling. By using a compressed sensing algorithm on the undersampled datathe images could be reconstructed at a higher temporal resolution without losing image quality due to undersampling artefacts. The compressed sensing reconstruction required three iterative steps, which depended on smoothing in order to calculate the missing data, and was performed using Berkely Advanced Reconstruction Tools (BART toolbox).
Once the PWV scans were reconstructed, a script for manual static segmentation of the vessels was used. A region of interest was defined for both the left and right CCA and ICA. Using these two regions within each 2D flow scan, the average velocity of the blood, in cm/s, could be calculated for all timeframes for each voxel. Multiplying the velocity in cm/s with the area of each vessel, which was equal to the number of segmented voxels multiplied with the spatial resolution of the image, the flow within the vessel is obtained in ml/s. In figure 4 the developed segmentation routine in shown. The flow in time is smoothed by performing a local regression using weighted linear least squares and a second degree polynomial model.
Figure 4: The segmentation routine as developed, shown for a common carotid artery. First the vessel of interest is selected in the magnitude image. Then the selected region, or mask, is laid over the velocity image. When observed that the mask envelops the positive blood velocities through the vessel, the blood flow is calculated at each timepoint within the cardiac cycle. The direction and velocity of the blood can be deducted from the colour bar.
After the flow quantifications of both slices PWV could be calculated using equation 2. The timeshift was calculated from the foot of the flowcurve, which is assumed to be reflection free and thus not influenced by the vessel geometry. However, the calculation of the timeshift remains sensitive to small changes in the individual flowcurve. Therefore it was estimated using four different methods; a cross correlation method, a Sigmoid curve function fitted to the cross correlation, a foot to foot method and a foot to foot method with a Sigmoid curve function fitted to it, each shown in figure 5. The average of these methods was taken to guarantee a robust and reliable result of the PWV calculation.
The foot to foot method calculates a linear function of the curve between 20% and 80% of the height of the systole peak. It further calculates the static mean flow at late diastole. The intersection of these two linear functions describes the foot of the flowcurve. The timeshift was then defined as the time difference between the two feet of the two flowcurves. For the correlation method both flowcurves were shifted in time until the correlation between them was maximal. This was done in a correlation window that only took the values in the reflection free range of the flowcurves into account. On both methods a sigmoid curve was fitted, resulting in two more timeshifts.
Figure 5: Overview of the four different methods used for calculating the timeshift and the PWV.
The distance between the two slices was determined using the program OsiriX Lite (Pixmeo SARL, Geneva, Switzerland), where the vessels were manually tracked using the 0.7 mm 3D black blood images. The centre of the vessel was tracked from the CCA coordi-nates to the ICA coordicoordi-nates in 3D Multi Planar Reformation (MPR) mode, shown in figure 6. The curved MPR path tool then calculated the displacement from the first to the last position.
Figure 6: The distance between two slices is determined using 3D black blood images and OsiriX.
The majority of the analysis was performed with MATLAB R2016a (Mathworks, Mas-sachusetts, USA). All MATLAB scripts were in-house written codes for previous projects or studies, and changes were made if required to be applicable for this PWV study.
3.4 WSS
In order to determine WSS, three times accelerated k-t PCA data was reconstructed using CRecon (Gyrotools, Z¨urich). The reconstructed data were exported as DICOM files which were used to create a PC magnetic resonance angiogram (PC-MRA). The angiogram visu-alises the anatomy of the vessels, which was required for the segmentation of the vessels. The carotid arteries were segmented in Mimics Medical (Materialise NV, Leuven, Belgium) to create a mask for the WSS analysis.
The left and right carotid arteries were segmented using a velocity threshold and manual detection. In order to make the data comparable for follow-up studies, the CCA was seg-mented 2 cm below the bifurcation. The ECA and ICA were, when possible, segseg-mented 2 cm long above the bifurcation. The binary masks were, for both the left and right artery separately, exported as DICOM files and used to calculate the velocity vector field, the mean and maximum velocity, peak systole and the WSS at 12 timepoints. The mask used for these calculations, velocity vector field and WSS distribution at peak systole were as shown in fig-ure 7 for a carotid artery located on the right side of the neck. The colour bars show the magnitude of the velocity vectors and the WSS measured at each point of the segmented area during peak systole.
Figure 7: A mask created during the segmentation of a carotid artery located on the right side of the neck. Using this mask the corresponding velocity vector field and the WSS were calculated. In this image the velocity vector field and WSS values are displayed at peak systole.
WSS was calculated for 12 timepoints per vessel. An analysis method was developed in which the WSS values were binned in histograms, considering either all timepoints, the first 4 timepoints or the timepoint at which peak systole occurred. The histograms were made not only for each individual vessel, but also for WSS values of respectively all right and all left vessels combined, and were normalised to the probability of the WSS data at each position in the vessels. Comparing the histograms of all subjects, it was decided to perform further
analysis of the WSS using properties of the histograms which only contained WSS data at peak systole. Those histograms were used since at peak systole the WSS distribution was more pronounced and high WSS values were perceived more often. In figure 8a the WSS distribution can be seen for all carotids on the right side of the neck for all timepoints during the cardiac cycle, in figure 8b during the first four timepoints and in figure 8c at peak systole.
Figure 8: In this figure the normalised probability distributions of WSS values for all carotids on the right side of the neck are shown for the WSS values during the entire cardiac cycle (a), the first third of the cardiac cycle (b) and at peak systole (c).
From histograms that contained the WSS values at peak systole the mean, median, stan-dard deviation, kurtosis and skewness were calculated, as described by Garcia et al. (2015). This was done both for all individuals separately and for each analysed group, considering the left and right artery independently of each other. The properties calculated from the histograms of all individuals separately are used in the statistical analysis. The properties calculated from the histograms which describe the different groups have been visualised in radar plots. Those radar plots and their histograms can be found in appendix A. The visual-isation of the properties was made for both gender and for the smoking history for both the left and right carotid artery, as for the average of the two carotids per subject. This was done in order to visualise which properties were most representative for both subgroups. Further analysis on WSS has been conducted using the mean WSS, as this property appeared to differ significantly between the different groups. The analysis was performed using MATLAB 2016a.
3.5 Statistical analysis
Averaging the PWV values calculated using the four different methods, the systematic error was minimised. The averaged PWV values have been plotted against age, and the relation
between PWV and age has been determined using a linear regression. The PWV values were then grouped and compared between the sexes and between those with a smoking history and those without a smoking history using a two-sided Wilcoxon signed-rank test.
Following the same procedure the mean WSS at peak systole has been related to age and compared between the sexes and between those with and without a smoking history.
Considering both the PWV and the mean WSS at peak systole, the averaged PWV values and mean WSS values have been plotted against each other for age, smoking status and gender. This has been done for mean WSS values of both the right carotid artery and the left carotid artery separately. The relations between PWV and mean WSS have been determined using a linear regressing.
4
Results
In this section the results are described for both the PWV, in section 4.1, and mean WSS, in section 4.2 values compared between age, sexes and smoking history. In section 4.3 the mean WSS values are compared with the PWV values.
4.1 PWV
Of the 29 datasets that were to be reconstructed, 28 qualified for further analysis of the PWV. For the omitted dataset there had been a problem with the 2D flow acquisition. Of those 28 datasets 5 more were omitted after the flow curve analysis, as the difference in steepness of the flow curves, and due to this the feet of the curves and thus the timeshifts, of the CCA and ICA proofed to be too small for detection. Due to this the PWV could be calculate for 23 of the initial 29 datasets.
The PWV values were plotted against age, and compared between the smoking histories and gender of the subjects. The 23 subjects were aged 30.1 ± 3.3 years (age ± standard deviation, range 21-36, 11 male). For 22 of these subjects the smoking history was known. Of these 22 subjects 10 had previously smoked.
In figure 9 the PWV values have been plotted against the age of the subjects. The average PWV was 4.73 ± 1.03 m/s ( mean ± standard deviation group), and ranged between 3.37 and 6.67 m/s. Linear regression analysis described the fit as −0.1151x + 8.195, with an R2 of 0.14 and a p-value of 0.08.
Figure 9: PWV in m/s against age in years (n=23). The average PWV was 4.73 ± 1.03 m/s. Linear regression analysis described the data with the fit −0.1151x + 8.195, with an R2 of 0.14 and a p-value of 0.08.
In figure 10 the PWV values have been plotted against gender. Men had on average a PWV of 4.47 ± 0.82 m/s, ranging between 3.38 and 6.01 m/s. Women had a PWV of 4.97 ± 1.17 m/s, ranging between 3.37 and 6.67 m/s. Comparing the two sexes, the p-value was 0.44, not rejecting the null hypothesis.
Figure 10: Boxplot of PWV, in m/s, grouped per gender. Women had an average PWV of 4.97 ± 1.17 m/s, ranging between 3.37 and 6.67 m/s, while men had an average PWV of 4.47 ± 0.82 m/s, ranging between 3.38 and 6.01 m/s. Doing a two-sided Wilcoxon signed-rank test to compare the two groups gave a p-value of 0.44.
In figure 11 the PWV values have been plotted against the smoking history. People who had never smoked before had a PWV of 4.97 ± 1.12 m/s, ranging between 3.37 and 6.67 m/s.
People who have at some point smoked had a PWV of 4.31 ± 0.78 m/s, ranging between 3.38 and 5.75 m/s. Comparing the two groups, the p-value was 0.18, not rejecting the null hypothesis.
Figure 11: Boxplot of PWV, in m/s, grouped per smoking history. People who had never smoked had a PWV of 4.97 ± 1.12 m/s, ranging between 3.37 and 6.67 m/s, while people who have smoked had a PWV of 4.31 ± 0.78 m/s, ranging between 3.38 and 5.75 m/s. Doing a two-sided Wilcoxon signed-rank test to compare the two groups gave a p-value of 0.18.
4.2 WSS
Of the 58 vessels (29 datasets, left and right carotid artery) that were reconstructed, 48 vessels (24 left arteries, 24 right arteries) qualified for further analysis of the WSS, of which some are shown in appendix B for further reference. This was due to the quality of the 4D flow images. Datasets were omitted when either the image quality was too low and too many artefacts were present for proper vessel detection, or when the ICA or ECA was cut off the image shortly after the bifurcation, leading to an insufficient amount of data of the vessel above the bifurcation. The 48 vessels that qualified belonged to 24 datasets, resulting in 24 complete sets. Of the 24 subjects, aged 30.4 ± 3.4 years (age ± standard deviation, range 21-37, 11 male), 11 had previously smoked.
In figure 12 the mean WSS has been plotted against age. The average mean WSS over all subjects, averaged over both carotid arteries, was equal to 1.66 ± 0.28 Pa, ranging between 1.10 and 2.21 Pa. The average mean WSS over all subjects in the left artery was 1.58 ± 0.34, ranging between 1.06 and 2.30. For the right artery this was 1.73 ± 0.33, ranging between 1.15 and 1.36. Linear regression analysis described the fit as −0.021561x + 2.2983, with an R2 of 0.07 and a p-value of 0.22.
Figure 12: The mean WSS, averaged over both carotid arteries, plotted against age in years. Age ranged between 21 and 37. The average mean WSS was 1.66 ± 0.28 Pa, ranging between 1.10 and 2.21 Pa. Linear regression analysis described the fit as −0.021561x + 2.2983, with an R2 of 0.07 and a p-value of 0.22.
The mean WSS has been plotted against gender in figure 13 and against smoking history in figure 14.
Women had a mean WSS of 1.59 ± 0.30 Pa on the left artery, ranging between 1.25 and 2.30 Pa, and a mean WSS of 1.71 ± 0.30 Pa on the right artery, ranging between 1.29 and 2.38 Pa, and were aged 29.3 ± 4.0 (age ± standard deviation, range 21-37). Men had a mean WSS of 1.58 ± 0.38 Pa on the left artery, ranging between 1.06 and 2.08 Pa, and a mean WSS of 1.76 ± 0.38 Pa on the right artery, ranging between 1.15 and 2.33 Pa, and were aged 31.5 ± 2.4 (age ± standard deviation, range 29-36). Comparing the two sexes while taking both arteries into account gave a p-value was 0.83, not rejecting the null hypothesis. Exclusively considering the mean WSS on the right artery the p-value was 0.79, while this was 1.0 when considering the left artery.
Figure 13: Boxplot of the mean WSS exerted on both carotid arteries, in Pa, grouped per gender. Women had, in total, an average WSS of 1.64 ± 0.31 Pa, ranging between 1.06 and 2.33 Pa. Men had, in total, an average WSS of 1.68 ± 0.38 Pa, ranging between 1.09 and 2.36 Pa. Doing a two-sided Wilcoxon signed-rank test the two groups gave a p-value of 0.83.
People who had never smoked before had a mean WSS of 1.71 ± 0.30 Pa on the right artery, ranging between 1.28 and 2.36 Pa, and a mean WSS of 1.59 ± 0.30 Pa on the left artery, ranging between 1.25 and 2.30 Pa, and were aged 29.3 ± 4.0 (age ± standard deviation, range 21-37). People who have at some point smoked had a mean WSS of 1.76 ± 0.38 Pa on the right artery, ranging between 1.15 and 2.33 Pa, and a mean WSS of 1.58 ± 0.38 Pa on the left artery, ranging between 1.06 and 2.08 Pa, and were aged 31.5 ± 2.4 (age ± standard deviation, range 29-36). Comparing the two groups while taking both arteries into account gave a p-value of 0.83, not rejecting the null hypothesis. Exclusively considering the mean WSS on the right artery the p-value was 0.82, while this was 1.0 when considering the left artery.
Figure 14: Boxplot of the mean WSS exerted on both arteries, in Pa, sorted by smoking history. People who had never smoked had a WSS of 1.65 ± 0.30 Pa, ranging between 1.25 and 2.36 Pa, while people who had smoked had a WSS of 1.67 ± 0.38 Pa, ranging between 1.06 and 2.33 Pa. Doing a two-sided Wilcoxon signed-rank test the two groups gave a p-value of 0.83.
4.3 PWV and mean WSS
In this section the PWV values acquired from the right carotid artery are compared with the mean WSS values acquired in both the right and left carotid artery. This has been done for both the age, the gender, and the smoking habits for those datasets that provided enough information for both the WSS and PWV. This was the case for 18 volunteers, with an average age of 29.9 ± 3.4, ranging between 21 and 36 years. Of these volunteers 8 smoked, and 8 were male.
For those datasets the PWV has been plotted against the mean WSS for both the right artery, in figure 15a, and the left artery, in figure 15b. Fitting the data in figure 15a gave the relation −0.05522x + 2.036, with an R2 of 0.03 and a p-value of 0.51, while for the data in figure 15b this relation was given by −0.3197x + 1.718, with an R2 of 0.01 and a p-value of 0.67.
(a) Right (b) Left Figure 15: In this figure the PWV and mean WSS have been plotted against each other for all subjects in the right artery, (a), and in the left artery, (b). For the artery artery a linear regression was done and gave the fit −0.05522x + 2.036, with an R2 of 0.03 and a p-value of 0.51. For the left artery this was given by −0.3197x + 1.718, with an R2 of 0.01 and a p-value of 0.67.
When comparing PWV and mean WSS values among men and women, plotted for the right artery in figure 16a and for the left artery in figure 17b. Fitting the data in figure 16a gave the relation 0.1939x + 0.947, with an R2 of 0.11 with a p-value of 0.42, for men, as shown in red. Doing the same for women, as shown in blue, resulted in the relation −0.1028x+2.244, with an R2 of 0.16 and a p-value of 0.25. Fitting the data in figure 17b gave the relation 0.3191x + 0.05273, with an R2 of 0.38 and a p-value of 0.10, and −0.1247x + 2.238, with an R2 of 0.33 and a p-value of 0.08, for men and women respectively.
(a) Right (b) Left Figure 16: In this figure the PWV and mean WSS have been plotted against each other for the different sexes in the right artery, (a), and in the left artery, (b). Women have been depicted in blue, while men in red. Fitting the data resulted in the following correlations in the right artery: for women this was given by −0.1028x + 2.244, with an R2 of 0.16 and a p-value of 0.25, while for men by 0.1939x + 0.947, with an R2 of
0.11 and a p-value of 0.42; in the left artery: for women given by −0.1247x + 2.238, with an R2 of 0.33 and a p-value of 0.08, and for men by 0.3191x + 0.05273, with an R2 of 0.38 and a p-value of 0.10.
When comparing the PWV and mean WSS values among those who have never smoked and those who have, plotted for the right artery in figure 17a and for the left artery in figure 17b. Fitting the data in figure 17a gave the relation −0.05163x + 2.074, with an R2 of 0.01 and a p-value of 0.78, for those who had smoked, in red, and the relation −0.04434x + 1.941, with an R2 of 0.02 and a p-value of 0.67, for those who had never smoked in blue. Doing the same for the data in figure 17b gave the relations 0.2186x + 0.596, with an R2 of 0.19 and a p-value of 0.28, and −0.1162x + 2.125, with an R2 of 0.36 and a p-value of 0.06, for those who had and those who had never smoked respectively.
(a) Right (b) Left Figure 17: In this figure the PWV and mean WSS have been plotted against each other for the different smoking habits in the right artery, (a), and in the left artery, (b). Those who had never smoked have been depicted in blue, while those who have smoked in red. Fitting the data resulted in the following linear regressions in the right artery: for those who never have this was given by −0.04434x + 1.941, with an R2 of
0.02 and a p-value of 0.67, while for those who have by −0.05163x + 2.074, with an R2
of 0.01 and a p-value of 0.78; in the left artery: for those who never have smoked this was given by −0.1162x + 2.125, with an R2of 0.36 and a p-value of 0.06, and for those who have smoked by 0.2186x + 0.596, with an R2 of 0.19 and a p-value of 0.28.
5
Discussion
From the initial 29 datasets 23 contained sufficient information for a PWV analysis, while 24 datasets contained sufficient information for WSS analysis. In total there were 18 datasets that contained the full information for both the PWV as for the WSS analysis. In section 5.1 the results on the PWV are discussed. The same is done in section 5.2 for the results on the mean WSS and in section 5.3 for the results on the compared PWV and mean WSS. In section 5.4 some final suggestions for further research are given.
5.1 PWV
To prevent data failure from happening in the future it would be recommended to rum the MATLAB program and the PWV calculations for each volunteer or patient during MR measurements. In doing so the person scanning will be certain the scans contain sufficient data for a proper PWV analysis, and the person being scanned will not need a re-scan for their current vessel elasticity. The data reconstruction of the two slices takes approximately 2 minutes per slice, and for the complete calculation, although with a dummy distance travelled, approximately 8 minutes in total. For this dummy distance travelled the distance could be set to the average length of the right carotid artery, which is approximately 80 cm.
process of the two slices, the masks were deemed optimal when the flow curves were smooth and comparable with literature images, as seen in articles by Dogui et al. (2011) and Lotz et al. (2002). The regions were selected with care and were examined over all timeframes during the cardiac cycle on both the magnitude and on the velocity images of the scans. Using OsiriX the distance travelled by the blood could be determined up to within 1 millimetre accurately, making the error of the distance negligible compared to the error of the timeshift. In order to determine the error of the timeshift, and thus the error of the PWV, the PWV has been calculated using four different statistical methods, as described in section 3.3. Averaging those values per volunteer resulted in the PWV values as shown in section 4.1. The error on those values is the standard deviation of the four different PWV values per volunteer.
When relating PWV values with age a soft negative correlation was found. However, when taking PWV data of a healthy population of elderly people (n = 10, age= 62.4 ± 10.3, range 53-77) from a different study, investigated with the same scan settings, into account, the relation between PWV and age became positive, with a p-value of 3.0000 · 10−4. This relation can be seen in figure 18, with the average PWV of the eldery population being 7.94 ± 1.36 m/s, ranging between 4.38 and 11.30 m/s and the average of the younger population (30.1 ± 3.3, range: 21-36) being 4.71 ± 1.03 m/s. Linear regression analysis described the data with the fit 0.09438x + 1.9442, with an R2 of 0.51 and a p-value of 3.37 · 10−6. These results are in agreement with PWV values reported by similar studies. In the PC MRI study of Kr¨oner et al. (2014) PWV was measured in a 20 cm segment of the carotid arteries, which resulted in a mean PWV of 6.9 ± 1.5 m/s for the older cohort (16 healthy volunteers older than 45, 8 male) and 5.7 ± 1.0 m/s for the younger cohort (16 younger volunteers younger than 30, 7 male). In Riley et al. (1992) the elastic modulus for the carotid arteries was measured using ultrasound for a healthy population of 3321 people. Using equation 1 PWV can be calculated from the reported elastic modulus, leading to an average PWV of 8.48 m/s for people older than 45 years. The incorrect negative correlation between age and PWV obtained with the 23 datasets was likely due to the small range of the ages. Other explanations might be that the increase of PWV becomes perceivable only after a certain age that was not included in the analysed datasets, or the fact that other factors that could increase the PWV, such as gender, blood pressure and smoking history, were not taken into account during the statistical analysis. Doing so in further research would be recommended.
Figure 18: PWV, in m/s, against age in years. Plotted for the initial subjects (n=23), combined with a group of healthy elderly people (n=10), whose PWV were investigated with the same scan settings. Fitting the data with a linear regression model, the relation was described as 0.09438x + 1.9442, with an R2of 0.51 and a p-value of 3.37 · 10−6.
When comparing the PWV values between the two sexes, women showed to have, on average, a higher PWV. This was confirmed when comparing the median value between the two groups. The result however was insignificant, as the p-value, when comparing the two groups, showed to be 0.44. This might have been due to the observed outlier and the high upper margin among the men, as two of the men showed to have a PWV value of 6.00 m/s and 5.75 m/s, while most of the men had a PWV value around 4.16 m/s. Nonetheless, when ignoring the outlier, and even when ignoring both the outlier and the second highest PWV, the result remained insignificant. Due to the sample sizes, however, none of the subject were ignored. In order to determine whether there is a correlation between PWV and gender, further research will have to be conducted, consisting of a larger sample size, including different factors such as blood pressure, smoking history and age into account during the statistical analysis. Chances are, however, that the relation between PWV and gender will remain insignificant even after corrections to other parameters are made, as Riley et al. (1992) found no significant differences between elastic moduli between sexes.
Finally, the PWV values have also been compared among those who had previously smoked or still did at the time of measurement, and those who had never smoked. People who had never smoked before showed to have a higher PWV than those who did have a smoking history. This was confirmed when comparing the median values of the two groups. When comparing the two groups using the Wilcoxon test, however, there was no significant difference observed, as the p-value was 0.18. The PWV values of those without a smoking history encompassed a larger range than those who did have a smoking history. This might be due to different factors that could increase the PWV, which were not taken into account during the analysis of this study. In order to determine whether there truly is a relation between smoking history and PWV further research will have to be conducted, consisting of a larger sample size, including different factors such as blood pressure, gender and age during the statistical analysis.
5.2 WSS
For WSS the image quality was too low for some of the PC MRA images to be used for segmentation with Mimics Medical. This was the case for 4 of the 29 datasets, and might be due to the movement artefacts combined with the k-t PCA acceleration. For a fifth dataset the scan was planned in such a way the FOV ended very short above the bifurcation, 1 cm indstead of 2 cm. This lead to an insufficient amount of datapoints of the WSS at the ICA and ECA for both arteries.
During the analysis it was assumed that the masks made for all arteries encompassed the vessels and properly represented the exerted WSS within the arteries. In order to verify the exactness of this assumption it is recommended to segment some of the analysed vessels again and perform intra- and inter-observer tests in the future.
From the properties that were calculated using the normalised histograms, the mean WSS was used as the parameter representing the WSS in the comparisons. This property was used as it differed significantly between those who had never smoked and those who had, while remaining relatively constant when compared between the sexes. This parameter was also used when relating the PWV to the WSS in section 4.3. Those results are further evaluated in 5.3. Whether this property represents the WSS best is yet to be determined. Other parameters, such as the kurtosis - which is another parameter that differed significantly between the different groups - could be considered in future studies.
When comparing the average men WSS on both arteries with the age a soft negative correlation was found. This agrees with the hypothesis that, as people become more prone to cardiovascular events when they get older, the WSS would decrease with age. The correlation is very soft, however, and future studies should be conducted with a larger sample size from more varied age categories.
Additionally to age, the mean WSS of both the left and right arteries has been compared among the sexes and smoking history. Both comparisons showed insignificant results, as the p-value was 0.83. Enlarging the sample sizes while keeping the ratios between groups constant might help provide more insight in the effect of those factors on the WSS. Another point to consider in further research is taking other factors that might have an effect on the WSS into account during the statistical analyses.
5.3 PWV and mean WSS
It was observed, when comparing the mean WSS on the left and right carotid artery, the mean WSS exerted on the right artery might be, on average, higher than the mean WSS exerted on the left artery. However, since the formation of possible atheromatous plaque in one of the vessels would result into the other vessel experiencing a different WSS, the mean WSS in both the left artery and in the right artery has been compared with the PWV as measured in the right artery. This was done in order to observe whether there might be a correlation between the height of the PWV and the mean WSS in either the same or the contra carotid artery, depending on the age, the smoking history or the gender of the subject. This combination might, in the future, proof to be a good early indicator of first-case cardiovascular diseases.
When comparing PWV and mean WSS among all subjects, taking only age into account, linear regression showed there was a soft negative correlation in both the left and right artery. This correlation was most pronounced in the right artery.
model, women showed a positive correlation between the mean WSS and PWV, while for men this was a negative correlation. These correlations were, for both men and women, most pronounced in the left artery. In both arteries men had a lower WSS when they had a low PWV and a higher WSS when they had a higher WSS.
Finally the PWV and mean WSS were compared between both those who did have a smoking history and those who did not. Considering only the right artery both those who have smoked and those who never had showed a soft negative correlation. Those who had smoked consistently had a higher mean WSS than those who never had. In the left artery however, those who had smoked showed a stronger positive correlation, while those who had never smoked showed a stronger negative correlation.
5.4 Suggestions for further research
During this study it was assumed that people who had reported to have a smoking history smoked nicotine cigarettes. The intensity of smoking and the time since smoking cessation have not been taken into account. For further research it is therefore recommended to take the duration and intensity of the smoking habit into account. With the duration is meant both the amount of years somebody has been smoking for and the amount of time that has passed since somebody has stopped smoking. It might therefore be appropriate to consider those who have stopped smoking as a separate group. With intensity is meant the amount of cigarettes smoked per week. For this third group, and for the people attempting smoking cessation, it is recommended to inform about the methods used during smoking cessation, as nicotine is not only contained in cigarettes, but also in nicotine patches and gums used for smoking cessation (Yoshiyama et al. 2014). These nicotine containing factors might also promote the formation of atheromatous plaques. Furthermore it is important to note that, as perceived among men by Doll et al. (2004), those who have stopped smoking before the age of 30 have almost as low a risk of death caused by cardiovascular diseases as those who never smoked.
Therefore it is, in order to determine the strength of anticipated or missed correlations, also highly recommended to correct for other factors, such as blood pressure, gender, age, and smoking history, when performing statistical analyses on either of the separate factors, while considering, ideally, a larger sample size.
6
Conclusion
In this study it was attempted to determine the relation for pulse wave velocity (PWV) and wall shear stress (WSS) for 29 healthy volunteers, with gender, age and smoking history. With this it was tested whether PWV and WSS, when combined, can function as an early indication of cardiovascular diseases, since both factors are related to the elasticity of vessels and are affected by the formation of atheromatous plaques. Hypothesised was that PWV would increase with age while WSS would decrease. The results showed that PWV and age are positively correlated, p = 0.0003, R2= 0.51. Whether gender and smoking history are proper parameters for mean WSS and PWV comparisons cannot be affirmed yet, as they showed no significant differences when compared. PWV had a p-value of 0.44 for gender comparisons and a p-value of 0.18 for smoking history comparisons. Mean WSS had a p-value of 0.83 for both gender and smoking history comparisons. When comparing PWV and mean WSS between smoking history those who have smoked consistently had a lower WSS for the same
PWV than those who did not have a smoking history when measured in the right carotid artery. Furthermore, when comparing PWV and mean WSS for the different sexes, men showed a positive linear relation, while women showed a negative linear relation. As no solid conclusions can be drawn yet further research is crucial. It would be recommended to consider a larger group of healthy volunteers of a wider age range. Additionally it is recommended to divide the group with a smoking history in two, namely in those who still smoke and those who have stopped, and to correct for blood pressure, age, gender and smoking history during further statistical analyses. Finally, other parameters than the mean WSS could be considered as the WSS characteristic that is used for comparison analyses.
7
Acknowledgements
I would like to thank the AMC, Radiology department and Cardiovascular department for providing me with the opportunity to conduct this study. For acquiring and providing the MRI data I thank I.K. Luirink and A.M. van den Berg-Faay. For advice on the analyses I thank P. van Ooij, G. Strijkers, A.J. Nederveen and E.S. Peper.
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A
Histograms and radar plots of the WSS data
In this appendix the histograms, which include all WSS data at each point in the vessels at peak systole, and the corresponding radar plots of the WSS data for both the left and right artery are shown. In figure 19a and 19b the mean, on axis x1, the median, on axis x2, the standard deviation (STD), on axis x3, the kurtosis, on axis x4, and the skewness, on axis x5, are given for respectively the right and left carotid artery for both men, in red, and women, in blue. In figure 20a and 20b the same is done for those with a smoking history, in red, and those without a smoking history, in blue. The values have been obtained from histograms normalised to the probability of WSS data, as shown in figure 21a and 21b for the different sexes and in figure 22a and 22b for the smoking history.
(a) In the right carotid artery the following val-ues have been found for women: mean = 1.62 Pa; median = 1.62 Pa; STD = 0.75 Pa; kurtosis = 2.36; skewness = 0.07. For men the following values have been found: mean = 1.71 Pa; me-dian = 1.66 Pa; STD = 0.98 Pa; kurtosis = 6.15; skewness = 0.96.
(b) In the left carotid artery the following values have been found for women: mean = 1.52 Pa; median = 1.48 Pa; STD = 0.77 Pa; kurtosis = 2.93; skewness = 0.41. For men the following values have been found: mean = 2.30 Pa; median = 2.17 Pa; STD = 1.25 Pa; kurtosis = 13.61; skewness = 2.05.
Figure 19: By normalising the histograms of the WSS data at peak systole the mean, median, standard deviation, kurtosis and the skewness have been determined and rep-resented in radar plots for both the right caroid artery, in a, and the left carotid artery, in b, and have been compared between men, in red, and women, in blue.
(a) In the right carotid artery the following val-ues have been found for those without a smoking history: mean = 1.65 Pa; median = 1.58 Pa; STD = 0.98 Pa; kurtosis = 6.17; skewness = 1.01. For those with a smoking history the following values have been found: mean = 2.04 Pa; median = 2.18 Pa; STD = 0.85 Pa; kurtosis = 3.09; skewness = 0.24.
(b) In the left carotid artery the following values have been found for those without a smoking his-tory: mean = 2.16 Pa; median = 2.01 Pa; STD = 1.23 Pa; kurtosis = 13.36; skewness = 2.02. For those with a smoking history the following values have been found: mean = 1.78 Pa; median = 1.75 Pa; STD = 0.82 Pa; kurtosis = 3.10; skewness = 0.29.
Figure 20: By normalising the histograms of the WSS data at peak systole the mean, median, standard deviation, kurtosis and the skewness have been determined and rep-resented in radar plots for both the right carotid artery, in a, and the left carotid artery, in b, and have been compared between those with a smoking history, in red, and those without a smoking history, in blue.
(a) Right arteries (b) Left arteries
Figure 21: Histograms of WSS values calculated in men and women in the right arter-ies (a) and the left arterarter-ies (b). From these histograms the mean, median, standard deviation, kurtosis and skewness have been calculated.
(a) Right arteries (b) Left arteries
Figure 22: Histograms of WSS values in the right arteries (a) and the left arteries (b) calculated for those who have never smoked and those who have smoked. From these histograms the mean, median, standard deviation, kurtosis and skewness have been calculated.
B
WSS maps
In figure 23 a small overview can be found of WSS maps as calculated for 14 subjects. In the first row the WSS maps of the right carotid artery in 7 men can be found, while in the second and third row the WSS maps of the right and left carotid artery in 7 women can be found.
Figure 23: Overview of WSS maps as calculated in 14 subjects. In the first row the WSS maps of the right carotid artery in 7 men can be found, while in the second and third row the WSS maps of the right and left carotid artery in 7 women can be found.
