Carotid geometry effects on blood flow and on risk for vascular disease

It has been widely observed that atherosclerotic diseases occur at sites with complex hemodynamics, such as artery bifurcations, junctions, and regions of high curvature. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present work, 3D pulsatile blood flow through a model of the carotid artery bifurcation was simulated using a finite volume numerical method. The goal was to quantify the risk of atherogenesis associated with different carotid artery geometries. A risk scale based on the average WSS on the sinus wall of the internal carotid artery was proposed-a scale that can be used to quantify the effect of the carotid geometry on the relative risk for developing vascular disease. It was found that the bifurcation angle and the out-of-plane angle of the internal carotid artery affect the formation of low stress regions on the carotid walls. The main conclusions are: (a) larger internal carotid artery angles (theta(IC)) generally increase the frequency and the area of blood recirculation and lower the WSS on the sinus wall, hence increasing the risk of plaque build-up; (b) off-plane angles were found to lower the WSS on the sinus for geometries with theta(IC)25 degrees . Larger off-plane angles generally increase the danger of plague build-up; (c) for theta(IC) < 25 degrees , the off-plane angle does not have an obvious effect on the hemodynamic WSS; (d) symmetric bifurcations were found to increase the WSS on the sinus wall and ease the risk of vascular disease.     

Sex differences in intracranial arterial bifurcations

Background: Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor—a local sex difference in the intracranial arteries.Objective: The aim of this study was to explore sex variation in the bifurcation anatomy of the middle cerebral artery (MCA) and internal carotid artery (ICA), and the subsequent hemodynamic impact.Methods: Vessel radii and bifurcation angles were measured in patients with MCA and ICA bifurcations. Data from a previously published study of 55 patients undergoing diagnostic cerebral digital subtraction angiography at Dalcross Private Hospital in Sydney, Australia, between 2002 and 2003, were available for analysis. The measurements were used to create idealized, averaged bifurcations of the MCA and ICA for females and males. Computational fluid dynamics simulations were performed to calculate hemodynamic forces in the models.Results: The vessel radii and bifurcation angles of 47 MCA and 52 ICA bifurcations in 49 patients (32 females, 17 males; mean age, 53 years; age range, 14–86 years) were measured. Statistically significant sex differences were found in vessel diameter (males larger than females; P < 0.05), but not in bifurcation angle. Computational fluid dynamics simulations revealed higher wall shear stress in the female MCA (19%) and ICA (50%) bifurcations compared with the male bifurcations.Conclusions: This study of MCA and ICA bifurcations in female and male patients suggests that sex differences in vessel size and blood flow velocity result in higher hemodynamic forces acting on the vessel wall in females. This new hypothesis may partly explain why intracranial aneurysms and SAH are more likely to occur in females than in males.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

大鼠局灶性脑缺血模型的有效制备

目的比较三种不同手术方法制作大鼠永久性脑缺血模型的效果,包括死亡率、神经功能评分、脑梗死体积、手术效率。方法将采用不同手术方法制备脑缺血模型的大鼠随机分为三组。1组在术中分别结扎颈总动脉（CCA）、颈外动脉（ECA）、枕动脉、翼腭动脉,并且用动脉夹对颈内动脉（ICA）进行临时夹闭;2组在术中分别结扎颈总动脉、颈外动脉,暴露枕动脉和翼腭动脉但不结扎,用丝线悬挂颈内动脉而不是用动脉夹夹闭,线栓在显微镜直视下插入颈内动脉越过翼腭动脉起始点至大脑中动脉分叉处;3组只暴露颈总动脉、颈外动脉和颈内动脉,结扎颈总动脉、颈外动脉,丝线悬挂颈内动脉,显微镜下将线栓盲插至颈内动脉大脑中动脉分叉处。分别检测三组模型的死亡率、神经功能评分、梗死体积、手术时间。结果第3组制作动物模型的方法所花费时间平均为17.5 min,死亡率较低,神经功能评分及梗死体积稳定。结论采用第3组手术方法可以缩短手术时间,提高手术效率,能够高效地制作出更加稳定的可用于临床实验的大鼠脑缺血模型。     

Wall stress of the cervical carotid artery in patients with carotid dissection: a case-control study

Spontaneous internal carotid artery (ICA) dissection (sICAD) results from an intimal tear located around the distal carotid sinus. The mechanisms causing the tear are unknown. This case-control study tested the hypotheses that head movements increase the wall stress in the cervical ICA and that the stress increase is greater in patients with sICAD than in controls. Five patients with unilateral, recanalized, left sICAD and five matched controls were investigated before and after maximal head rotation to the left and neck hyperextension after 45° head rotation to the left. The anatomy of the extracranial carotid arteries was assessed by magnetic resonance imaging and used to create finite element models of the right ICA. Wall stress increased after head movements. Increases above the 80th and 90th percentile were located at the intimal side of the artery wall from 7.4 mm below to 10 mm above the cranial edge of the carotid sinus, i.e., at the same location as histologically confirmed tears in patients with sICAD. Wall stress increase did not differ between patients and controls. The present findings suggest that wall stress increases at the intimal side of the artery wall surrounding the distal edge of the carotid bulb after head movements may be important for the development of carotid dissection. The lack of wall stress difference between the two groups indicates that the carotid arteries of patients with carotid dissection have either distinct functional or anatomical properties or endured unusually heavy wall stresses to initiate dissection.     

Carotid bifurcation position and branching angle in patients with atherosclerotic carotid disease

Carotid artery bifurcation (CB) is the preferred site for development of atherosclerosis (AS) in extracranial cerebral arteries; internal carotid artery stenosis is the most common cause of ischemic stroke. The frequent atherosclerotic disease of CB may best be explained by the hemodynamic influence of complex blood flow that results from the unique geometry of the bifurcation. Few papers analyze all possible geometric structural characteristics of this bifurcation. While performing many carotid endarterectomies, we noticed that a certain correlation between CB height in the neck and its angle existed, that a larger angle is accompanied with increased frequency of elongation and kinking and that CB shape influences distribution of atherosclerosis. The purpose of this paper is to quantify and evaluate these clinical observations. Radiogrametric analysis of 154 bi-plane orthogonal aortic arch arteriograms of patients with symptomatic atherosclerotic carotid artery disease was performed and a total of 289 CBs were analyzed. The CB height in relation to cervical spine segments was measured and real angles of each bifurcation were calculated. A positive linear correlation between CB height and angle exists: the CB angle increases /decreases 3.34 degrees for each third of the cervical vertebral body height or intervertebral space height. The CB is positioned a little higher on the left side. The proximal border of the atherosclerotic process is found at the level of intersection of the axes of the common carotid artery branches in 92.6% of examined CBs. In lower CBs (with smaller angles) the proximal border was located in the last segment of the common carotid artery, while in high bifurcations (wider angles) the proximal border of the AS process is more distally in the blood flow, in the beginning of the internal carotid artery, and the process was more extensive. High CBs are more suitable for eversion endarterectomy while normal and low CBs are more suitable for open (classic) carotid endarterectomy. The influence of the geometric risk factor demands further investigation.     

Numerical flow studies in human carotid artery bifurcations: basic discussion of the geometric factor in atherogenesis

In this study fluid dynamic variables are analysed numerically in different human carotid artery bifurcation models in order to clarify the geometric factor in carotid bifurcation atherogenesis. The geometric variations describe healthy human carotid bifurcation anatomy and concern the shape of the carotid sinus and the angle between the branches. The flow conditions remain unchanged. The governing Navier-Stokes equations describing incompressible, pulsatile, three-dimensional viscous flow are approximated using a pressure correction finite element procedure which has been developed for time-consuming, three-dimensional, time-dependent viscous flow problems. The study concentrates on flow velocity, on detailed analysis of flow separation and flow recirculation, and on wall shear stress distribution. The results show that the extension and the location of the recirculation zone in the sinus as well as the duration of separated flow during the pulse cycle are affected by the geometrical variations. In view of the significance of the reversed flow zones and of the accompanied low shear regions in atherogenesis the geometry-dependent flow separation characteristics in the sinus is of substantial interest.     

Modelling the circle of Willis to assess the effects of anatomical variations and occlusions on cerebral flows

Blood flow in the circle of Willis (CoW) is modelled using the 1-D equations of pressure and flow wave propagation in compliant vessels. The model starts at the left ventricle and includes the largest arteries that supply the CoW. Based on published physiological data, it is able to capture the main features of pulse wave propagation along the aorta, at the brachiocephalic bifurcation and throughout the cerebral arteries. The collateral ability of the complete CoW and its most frequent anatomical variations is studied in normal conditions and after occlusion of a carotid or vertebral artery (VA). Our results suggest that the system does not require collateral pathways through the communicating arteries to adequately perfuse the brain of normal subjects. The communicating arteries become important in cases of missing or occluded vessels, the anterior communicating artery (ACoA) being a more critical collateral pathway than the posterior communicating arteries (PCoAs) if an internal carotid artery (ICA) is occluded. Occlusions of the VAs proved to be far less critical than occlusions of the ICAs. The worst scenario in terms of reduction in the mean cerebral outflows is a CoW without the first segment of an anterior cerebral artery combined with an occlusion of the contralateral ICA. Furthermore, in patients without any severe occlusion of a carotid or VA, the direction of flow measured at the communicating arteries corresponds to the side of the CoW with an absent or occluded artery. Finally, we study the effect of partial occlusions of the communicating arteries on the cerebral flows, which again confirms that the ACoA is a more important collateral pathway than the PCoAs if an ICA is occluded.     

Direct numerical simulation of transitional flow in a stenosed carotid bifurcation

The blood flow dynamics of a stenosed, subject-specific, carotid bifurcation were numerically simulated using the spectral element method. Pulsatile inlet conditions were based on in vivo color Doppler ultrasound measurements of blood velocity. The results demonstrated the transitional or weakly turbulent state of the blood flow, which featured rapid velocity and pressure fluctuations in the post-stenotic region of the internal carotid artery (ICA) during systole and laminar flow during diastole. High-frequency vortex shedding was greatest downstream of the stenosis during the deceleration phase of systole. Velocity fluctuations had a frequency within the audible range of 100-300Hz. Instantaneous wall shear stress (WSS) within the stenosis was relatively high during systole ( approximately 25-45Pa) compared to that in a healthy carotid. In addition, high spatial gradients of WSS were present due to flow separation on the inner wall. Oscillatory flow reversal and low pressure were observed distal to the stenosis in the ICA. This study predicts the complex flow field, the turbulence levels and the distribution of the biomechanical stresses present in vivo within a stenosed carotid artery.     

A numerical and experimental analysis of the flow field in a two-dimensional model of the human carotid artery bifurcation

Axial velocities were measured in an enlarged, two-dimensional, rigid model of the carotid artery bifurcation by means of a laser-Doppler anemometer, under both steady and unsteady flow conditions. Also a numerical model was developed, based on the finite element approximation of the Navier-Stokes and continuity equations. From this study it appeared that the numerically predicted velocities agree well with the experimentally obtained values. Besides, the bifurcation hardly influenced the upstream flow in the main branch (common carotid artery), high velocity gradients were observed at the divider walls of the daughter branches (internal and external carotid arteries) and large zones with reversed flow were present near the nondivider walls of these branches. For steady flow the maximal diameter of this zone at the entrance of the internal carotid artery (carotid sinus) was about 25% of the local diameter of this branch. For unsteady flow this zone was absent during the initial phase of flow acceleration and maximal at the end of flow deceleration with a maximal diameter of about 50% of the local diameter of the carotid sinus.     

MRI-based quantification of outflow boundary conditions for computational fluid dynamics of stenosed human carotid arteries

Accurate assessment of wall shear stress (WSS) is vital for studies on the pathogenesis of atherosclerosis. WSS distributions can be obtained by computational fluid dynamics (CFD) using patient-specific geometries and flow measurements. If patient-specific flow measurements are unavailable, in- and outflow have to be estimated, for instance by using Murray’s Law. It is currently unknown to what extent this law holds for carotid bifurcations, especially in cases where stenoses are involved. We performed flow measurements in the carotid bifurcation using phase-contrast MRI in patients with varying degrees of stenosis. An empirical relation between outflow and degree of area stenosis was determined and the outflow measurements were compared to estimations based on Murray’s Law. Furthermore, the influence of outflow conditions on the WSS distribution was studied.For bifurcations with an area stenosis smaller than 65%, the outflow ratio of the internal carotid artery (ICA) to the common carotid artery (CCA) was 0.62±0.12 while the outflow ratio of the external carotid artery (ECA) was 0.35±0.13. If the area stenosis was larger than 65%, the flow to the ICA decreased linearly to zero at 100% area stenosis. The empirical relation fitted the flow data well (R²=0.69), whereas Murray’s Law overestimated the flow to the ICA substantially for larger stenosis, resulting in an overestimation of the WSS. If patient-specific flow measurements of the carotid bifurcation are unavailable, estimation of the outflow ratio by the presented empirical relation will result in a good approximation of calculated WSS using CFD.     

Targeted particle tracking in computational models of human carotid bifurcations

A significant and largely unsolved problem of computational fluid dynamics (CFD) simulation of flow in anatomically relevant geometries is that very few calculated pathlines pass through regions of complex flow. This in turn limits the ability of CFD-based simulations of imaging techniques (such as MRI) to correctly predict in vivo performance. In this work, I present two methods designed to overcome this filling problem, firstly, by releasing additional particles from areas of the flow inlet that lead directly to the complex flow region ("preferential seeding") and, secondly, by tracking particles both "downstream" and "upstream" from seed points within the complex flow region itself. I use the human carotid bifurcation as an example of complex blood flow that is of great clinical interest. Both idealized and healthy volunteer geometries are investigated. With uniform seeding in the inlet plane (in the common carotid artery (CCA)) of an idealized bifurcation geometry, approximately half the particles passed through the internal carotid artery (ICA) and half through the external carotid artery. However, of those particles entering the ICA, only 16% passed directly through the carotid bulb region. Preferential seeding from selected regions of the CCA was able to increase this figure to 47%. In the second method, seeding of particles within the carotid bulb region itself led to a very high proportion (97%) of pathlines running from CCA to ICA. Seeding of particles in the bulb plane of three healthy volunteer carotid bifurcation geometries led to much better filling of the bulb regions than by particles seeded at the inlet alone. In all cases, visualization of the origin and behavior of recirculating particles led to useful insights into the complex flow patterns. Both seeding methods produced significant improvements in filling the carotid bulb region with particle tracks compared with uniform seeding at the inlet and led to an improved understanding of the complex flow patterns. The methods described may be combined and are generally applicable to CFD studies of fluid and gas flow and are, therefore, of relevance in hemodynamics, respiratory mechanics, and medical imaging science.     

The role of the carotid sinus in the reduction of arterial wall stresses due to head movements—potential implications for cervical artery dissection

Spontaneous dissection of the cervical internal carotid artery (sICAD) is a major cause of stroke in young adults. A tear in the inner part of the vessel wall triggers sICAD as it allows the blood to enter the wall and develop a transmural hematoma. The etiology of the tear is unknown but many patients with sICAD report an initiating trivial trauma. We thus hypothesised that the site of the tear might correspond with the location of maximal stress in the carotid wall. Carotid artery geometries segmented from magnetic resonance images of a healthy subject at different static head positions were used to define a path of motion and deformation of the right cervical internal carotid artery (ICA). Maximum head rotation to the left and rotation to the left combined with hyperextension of the neck were investigated using a structural finite element model. A role of the carotid sinus as a geometrically compliant feature accommodating extension of the artery is shown. At the extreme range of the movements, the geometrical compliance of the carotid sinus is limited and significant stress concentrations appear just distal to the sinus with peak stresses at the internal wall on the posterior side of the vessel following maximum head rotation and on the anteromedial portion of the vessel wall following rotation and hyperextension. Clinically, the location of sICAD initiation is 10–30 mm distal to the origin of the cervical ICA, which corresponds with the peak stress locations observed in the model, thus supporting trivial trauma from natural head movements as a possible initiating factor in sICAD.     

Parametric geometry exploration of the human carotid artery bifurcation

A parametric computational model of the human carotid artery bifurcation is employed to demonstrate that it is only necessary to simulate approximately one-half of a single heart pulse when performing a global exploration of the relationships between shear stress and changes in geometry. Using design of experiments and surface fitting techniques, a landscape is generated that graphically depicts these multi-dimensional relationships. Consequently, whilst finely resolved, grid and pulse independent results are traditionally demanded by the computational fluid dynamics (CFD) community, this strategy demonstrates that it is possible to efficiently detect the relative impact of different geometry parameters, and to identify good and bad regions of the landscape by only simulating a fraction of a single pulse. Also, whereas in the past comparisons have been made between the distributions of appropriate shear stress metrics, such as average wall shear stress and oscillatory shear index, this strategy requires a figure of merit to compare different geometries. Here, an area-weighted integral of negative time-averaged shear stress, tau , is used as the principal objective function, although the discussion reveals that the extent as well as the intensity of reverse flow may be important. Five geometry parameters are considered: the sinus bulb width, the angles and the outflow diameters of the internal carotid artery (ICA) and external carotid artery (ECA). A survey of the landscape confirms that bulb shape has the dominant effect on tau with maximum tau occurring for large bulb widths. Also, it is shown that different sets of geometric parameters can produce low values of tau by either relatively small intense areas, or by larger areas of less intense reverse flow.     

Correlation Between the Rupture Risk and 3D Geometric Parameters of Saccular Intracranial Aneurysms

The purpose of this study is to evaluate the association of the location and geometric parameters of intracranial aneurysm with the risk of rupture. A retrospective study consisted of 284 patients diagnosed with saccular intracranial aneurysm between January 2009 and May 2013 at Wuxi Third People’s Hospital was conducted. 3D digital subtraction angiography images from all patients (240 ruptured, 44 unruptured) were obtained and analyzed. The location of the aneurysms and the 3D geometric parameters including the aneurysm depth, the neck size, diameter of the parent artery, aneurysm angle, aspect radio, size ratio, and the neck-to-parent-artery ratio (NPR) were compared between ruptured and unruptured groups. Results: In ruptured group, anterior communicating artery, posterior communicating artery (PCoA), and the bifurcation of internal carotid artery (ICA) were the top three locations for aneurysm occurrence, accounting for 40.00, 30.42, and 12.08 % respectively. While in the unruptured group, top three locations were PCoA (36.36 %), posterior cerebral circulation (18.18 %), and the bifurcation of the ICA (15.91 %). Distribution of aneurysm location is significantly different (p < 0.05) between ruptured and unruptured aneurysms. For the 3D geometric parameters characterizing aneurysm, aneurysm depth (p < 0.05), parent artery diameter (p < 0.05), aneurysm angle (p < 0.01), aspect ratio (p < 0.01), and size ratio (p < 0.01) all showed a significant difference between ruptured and unruptured group. No difference was found in the neck size and the NPR ratio between the two groups. 3D geometric parameters such as aneurysm depth, parent artery diameter, aneurysm angle, aspect ratio, and size ratio can be helpful in evaluating the rupture risk of saccular intracranial aneurysm for a better prevention and prognosis.     

Night sleep structure in the cases of disturbance of blood supply in the internal carotid artery pool

The study examines correlation between the degree of stenosis of the internal carotid artery (ICA) and the night sleep parameters. The possible neurophysiological mechanisms of sleep disorder in blood flow disturbances in the carotid system are also discussed. Twenty-four patients (19 men and 5 women) were examined, including 6 cases of 50% ICA stenosis, 7 cases of 50–70% ICA stenosis; and 11 cases of ICA occlusion. A polygraphic study of night sleep was conducted and the sleep stages were analyzed. The patients filled in the quality of sleep questionnaire with the presence of the somnolence scoring system. In order to assess brain perfusion, single-photon emission CT imaging of the brain was performed. The results of the study showed that the night sleep structure in the cases of 50% ICA stenosis was unchanged: all the sleep phases and stages whose quantitative parameters corresponded to the reference normal data were recorded, or only stage II sleep representation declined; in the cases of 50–70% ICA stenosis, predominantly stage II sleep and slow-wave sleep were compromised; in patients with ICA occlusion, slow-wave sleep and REM-sleep (45% of cases) were disturbed.     

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.     

On the atrophy of the internal carotid artery in capybara

Capybara might be a useful model for studying changes in cerebral circulation as the natural atrophy of the internal carotid artery (ICA) occurs in this animal at maturation. In this study, confocal and electron microscopy combined with immunohistochemical techniques were applied in order to reveal the changes in morphology and innervation to the proximal part of ICA in young (6-month-old) and mature (12-month-old) capybaras. Some features of the basilar artery (BA) were also revealed. The ICA of young animals degenerated to a ligamentous cord in mature animals. Immunolabelling positive for pan-neuronal marker protein gene product 9.5 but negative for tyrosine hydroxylase was observed in the proximal part of ICA at both ages examined. Axon varicosities positive for synaptophysin were present in the adventitia of ICA of young animals but were absent in the ligamentous cord of mature animals. In the ICA of young animals, adventitial connective tissue invaded the media suggesting that the process of regression of this artery began within the first 6 months of life. An increase in size of the BA was found in mature animals indicating increased blood flow in the vertebro-basilar system, possibly making capybara susceptible to cerebrovascular pathology (e.g. stroke). Capybara may therefore provide a natural model for studying adaptive responses to ICA regression/occlusion.The financial support of the Graduate Fund, UCL, London, UK (C. Steele) and the Brazilian Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) Brazil (200516/01-9; A.A.C.M. Ribeiro) is gratefully acknowledged.     

Three-dimensional geometry of the human carotid artery

Accurate characterization of carotid artery geometry is vital to our understanding of the pathogenesis of atherosclerosis. Three-dimensional computer reconstructions based on medical imaging are now ubiquitous; however, mean carotid artery geometry has not yet been comprehensively characterized. The goal of this work was to build and study such geometry based on data from 16 male patients with severe carotid artery disease. Results of computerized tomography angiography were used to analyze the cross-sectional images implementing a semiautomated segmentation algorithm. Extracted data were used to reconstruct the mean three-dimensional geometry and to determine average values and variability of bifurcation and planarity angles, diameters and cross-sectional areas. Contrary to simplified carotid geometry typically depicted and used, our mean artery was tortuous exhibiting nonplanarity and complex curvature and torsion variations. The bifurcation angle was 36 deg?±?11 deg if measured using arterial centerlines and 15 deg?±?14 deg if measured between the walls of the carotid bifurcation branches. The average planarity angle was 11 deg?±?10 deg. Both bifurcation and planarity angles were substantially smaller than values reported in most studies. Cross sections were elliptical, with an average ratio of semimajor to semiminor axes of 1.2. The cross-sectional area increased twofold in the bulb compared to the proximal common, but then decreased 1.5-fold for the combined area of distal internal and external carotid artery. Inter-patient variability was substantial, especially in the bulb region; however, some common geometrical features were observed in most patients. Obtained quantitative data on the mean carotid artery geometry and its variability among patients with severe carotid artery disease can be used by biomedical engineers and biomechanics vascular modelers in their studies of carotid pathophysiology, and by endovascular device and materials manufacturers interested in the mean geometrical features of the artery to target the broad patient population.     

Hemodynamics analysis of a stenosed carotid bifurcation and its plaque-mitigating design

Considering transient two-dimensional laminar flow in a diseased carotid artery segment with realistic inlet and outflow conditions, detailed velocity profiles, pressure fields, wall shear stress distributions and coupled, localized plaque formations have been simulated. The type of outflow boundary condition influences to a certain degree the extent of plaque build-up, which in turn reduces "disturbed flow" phenomena such as flow separations, recirculation zones, and wavy flow patterns in the artery branches during portions of the pulse. Based on computer experiments varying key geometric factors, a plaque-mitigating design of a carotid artery bifurcation has been proposed. Elimination of the carotid bulb, a smaller bifurcation angle, lower area ratios, and smooth wall curvatures generated a design with favorable hemodynamics parameters, leading to reduced plaque build-up by factors of 10 and 2 in the internal carotid and in the external carotid, respectively.