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.     

MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.     

Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation

Finite element simulations of fluid-solid interactions were used to investigate inter-individual variations in flow dynamics and wall mechanics at the carotid artery bifurcation, and its effects on atherogenesis, in three healthy humans (normal volunteers: NV1, NV2, NV4). Subject-specific calculations were based on MR images of structural anatomy and ultrasound measurements of flow at domain boundaries. For all subjects, the largest contiguous region of low wall shear stress (WSS) occurred at the carotid bulb, WSS was high (6-10 Pa) at the apex, and a small localized region of WSS > 10 Pa occurred close to the inner wall of the external carotid artery (ECA). NV2 and NV4 had a "spot" of low WSS distal to the bifurcation at the inner wall of the ECA. Low WSS patches in the common carotid artery (CCA) were contiguous with the carotid bulb low WSS region in NV1 and NV2, but not in NV4. In all three subjects, areas of high oscillatory shear index (OSI) were confined to regions of low WSS. Only NV4 exhibited high levels of OSI on the external adjoining wall of the ECA and CCA. For all subjects, the maximum wall shear stress temporal gradient (WSSTG) was highest at the flow divider (reaching 1,000 Pa/s), exceeding 300 Pa/s at the walls connecting the ECA and CCA, but remaining below 250 Pa/s outside of the ECA. In all subjects, (maximum principle) cyclic strain (CS) was greatest at the apex (NV1: 14%; NV2: 11%; NV4: 6%), and a second high CS region occurred at the ECA-CCA adjoining wall (NV1: 11%, NV2: 9%, NV4: 5%). Wall deformability was included in one simulation (NV2) to verify that it had little influence on the parameters studied. Location and magnitude of low WSS were similar, except for the apex (differences of up to 25%). Wall distensibility also influenced OSI, doubling it in most of the CCA, separating the single high OSI region of the carotid bulb into two smaller regions, and shrinking the ECA internal and external walls' high OSI regions. These observations provide further evidence that significant intra-subject variability exists in those factors thought to impact atherosclerosis.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

Numerical analysis of flow through a severely stenotic carotid artery bifurcation

The results of computational simulations may supplement MR and other in vivo diagnostic techniques to provide an accurate picture of the hemodynamics in particular vessels, which may help demonstrate the risks of embolism or plaque rupture posed by particular plaque deposits. In this study, a model based on an endarterectomy specimen of the plaque in a carotid bifurcation was examined. The flow conditions include steady flow at Reynolds numbers of 300, 600, and 900 as well as unsteady pulsatile flow. Both dynamic pressure and wall shear stress are very high, with shear values up to 70 N/m2, proximal to the stenosis throat in the internal carotid artery, and both vary significantly through the flow cycle. The wall shear stress gradient is also strong along the throat. Vortex shedding is observed downstream of the most severe occlusion. Two turbulence models, the Chien and Goldberg varieties of k-epsilon, are tested and evaluated for their relevance in this geometry. The Chien model better captures phenomena such as vortex shedding. The flow distal to stenosis is likely transitional, so a model that captures both laminar and turbulent behavior is needed.     

Proton-induced X-ray emission analysis of atherosclerotic plaques of the carotid bifurcation

The trace elements of both calcified atherosclerotic plaques and plaque-free vessel walls of the carotid bifurcation from 31 autopsies were investigated using the proton-induced X-ray emission (PIXE) method. The trace elements studied were phosphorus (P), calcium (Ca), chrome (Cr), iron (Fe), copper (Cu), zinc (Zn), lead (Pb), selenium (Se), bromine (Br), strontium (Sr), and rubidium (Rb). All samples contained Fe and Zn. Mercury (Hg) was not detected in any of the samples studied. All plaque-free samples contained Cu and almost all Br and Ca, none Sr. All calcified atherosclerotic plaques contained Ca and almost all Br and Sr. The relative levels of Ca were higher in the calcified plaques than in the plaque-free vessel walls. The relative value of Ca in calcified and uncalcified samples was greatest in the group who had died because of cardiovascular disorders and smallest in the group who had died from other causes. There was a strong positive correlation between the Ca and Sr of the plaque samples and between the P and Br of the plaque-free samples.     

Flow pattern analysis in a highly stenotic patient-specific carotid bifurcation model using a turbulence model

The aim of this study is to investigate the blood flow pattern in carotid bifurcation with a high degree of luminal stenosis, combining in vivo magnetic resonance imaging (MRI) and computational fluid dynamics (CFD). A newly developed two-equation transitional model was employed to evaluate wall shear stress (WSS) distribution and pressure drop across the stenosis, which are closely related to plaque vulnerability. A patient with an 80% left carotid stenosis was imaged using high resolution MRI, from which a patient-specific geometry was reconstructed and flow boundary conditions were acquired for CFD simulation. A transitional model was implemented to investigate the flow velocity and WSS distribution in the patient-specific model. The peak time-averaged WSS value of approximately 73 Pa was predicted by the transitional flow model, and the regions of high WSS occurred at the throat of the stenosis. High oscillatory shear index values up to 0.50 were present in a helical flow pattern from the outer wall of the internal carotid artery immediately after the throat. This study shows the potential suitability of a transitional turbulent flow model in capturing the flow phenomena in severely stenosed carotid arteries using patient-specific MRI data and provides the basis for further investigation of the links between haemodynamic variables and plaque vulnerability. It may be useful in the future for risk assessment of patients with carotid disease.     

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.     

Stress-modulated collagen fiber remodeling in a human carotid bifurcation

This work concerns with the implementation of a new stress-driven remodeling model for simulating the overall structure and mechanical behavior of a human carotid bifurcation. By means of an iterative finite element based procedure collagen fiber direction and maximal principal stresses are computed. We find that the predicted fibers' architecture at the cylindrical branches and at the apex of the bifurcation correlates well with histological observations. Some insights about the mechanical response of the sinus bulb and the bifurcation apex are revealed and discussed. The results are compared with other, isotropic and orthotropic, models available in the literature.     

Pulsatile two-dimensional flow and plaque formation in a carotid artery bifurcation

Velocity and pressure fields, streamlines and wall shear stress distributions were numerically obtained for two-dimensional, steady and pulsatile flow in a carotid artery segment. Distinct regions of reverse flow near the bifurcation and wavy flow patterns in the branching channels were observed during portions of the pulse. These phenomena disappear at the end of the systolic phase of the cardiac cycle. A previously validated plaque formation model predicts that plaque sites and the local extent of atherosclerotic lesions are similar for those present on human angiograms.     

Numerical simulation of blood pulsatile flow in a stenosed carotid artery using different rheological models

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.     

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.     

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.     

Effect of common carotid artery inlet length on normal carotid bifurcation hemodynamics

Controversy exists regarding the suitability of fully developed versus measured inlet velocity profiles for image-based computational fluid dynamics (CFD) studies of carotid bifurcation hemodynamics. Here, we attempt to resolve this by investigating the impact of the reconstructed common carotid artery (CCA) inlet length on computed metrics of "disturbed" flow. Twelve normal carotid bifurcation geometries were reconstructed from contrast-enhanced angiograms acquired as part of the Vascular Aging--The Link That Bridges Age to Atherosclerosis study (VALIDATE). The right carotid artery lumen geometry was reconstructed from its brachiocephalic origin to well above the bifurcation, and the CCA was truncated objectively at locations one, three, five, and seven diameters proximal to where it flares into the bifurcation. Relative to the simulations carried out using the full CCA, models truncated at one CCA diameter strongly overestimated the amount of disturbed flow. Substantial improvement was offered by using three CCA diameters, with only minor further improvement using five CCA diameters. With seven CCA diameters, the amounts of disturbed flow agreed unambiguously with those predicted by the corresponding full-length models. Based on these findings, we recommend that image-based CFD models of the carotid bifurcation should incorporate at least three diameters of CCA length if fully developed velocity profiles are to be imposed at the inlet. The need for imposing measured inlet velocity profiles would seem to be relevant only for those cases where the CCA is severely truncated.     

Morphological age-dependent development of the human carotid bifurcation

The unique morphology of the adult human carotid bifurcation and its sinus has been investigated extensively, but its long-term, age-dependent development has not. It is important fundamentally and clinically to understand the hemodynamics and developmental forces that play a role in remodeling of the carotid bifurcation and maturation of the sinus in association with brain maturation. This understanding can lead to better prognostication and therapy of carotid disease. We analyzed the change of sinus morphology and the angle of the carotid bifurcation in four postnatal developmental stages (Group I: 0-2 years, Group II: 3-9 years, Group III: 10-19 years, and Group IV: 20-36 years, respectively) using multiprojection digital subtraction angiograms and image post-processing techniques. The most significant findings are the substantial growth of the internal carotid artery (ICA) with age and the development of a carotid sinus at the root of the ICA during late adolescence. The bifurcation angle remains virtually unchanged from infancy to adulthood. However, the angle split between the ICA and external carotid artery (ECA) relative to the common carotid artery (CCA) undergoes significant changes. Initially, the ICA appears to emanate as a side branch. Later in life, to reduce hydraulic resistance in response to increased flow demand by the brain, the bifurcation is remodeled to a construct in which both daughter vessels are a skewed continuation of the parent artery. This study provides a new analysis method to examine the development of the human carotid bifurcation over the developmental years, despite the small and sparse database. A larger database will enable in the future a more extensive analysis such as gender or racial differences.     

Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation

Hemodynamics at the human carotid bifurcation is important to the understanding of atherosclerotic plaque initiation and progression as well as to the diagnosis of clinically important disease. Laser Doppler anemometry was performed in a large scale model of an average human carotid. Pulsatile waveforms and physiologic flow divisions were incorporated. Disturbance levels and shear stresses were computed from ensemble averages of the velocity waveform measurements. Flow in the common carotid was laminar and symmetric. Flow patterns in the sinus, however, were complex and varied considerably during the cycle. Strong helical patterns and outer wall flow separation waxed and waned during each systole. The changing flow patterns resulted in an oscillatory shear stress at the outer wall ranging from -13 to 9 dyn cm-2 during systole with a time-averaged mean of only -0.5 dyn cm-2. This contrasts markedly with an inner wall shear stress range of 17-50, (mean 26) dyn cm-2. The region of transient separation was confined to the carotid sinus outer wall with no reverse velocities detected in the distal internal carotid. Notable disturbance velocities were also time-dependent, occurring only during the deceleration phase of systole and the beginning of diastole. The present pulsatile flow studies have aided in identifying hemodynamic conditions which correlate with early intimal thickening and predict the physiologic level of flow disturbances in the bulb of undiseased internal carotid arteries.     

Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation.

To analyse the pulsatile flow field and the mechanical stresses in a three-dimensional carotid artery bifurcation model, computer simulation is applied. The approximation of the Navier-Stokes equations uses a pressure correction finite element method. Numerical results are presented for axial and secondary flow velocity and wall shear stresses with special emphasis on the fluid dynamics in the carotid sinus. This region is of major interest because it is affected preferentially by lesions. Detailed local flow studies as carried out here should lead to a further insight into the mechanisms of atherogenesis. The flow conditions used in the study were chosen according to Ku et al. (Arteriosclerosis 5, 293-302, 1985). The results of this numerical analysis agree in the essential features with their experimental results.     

Turbulence detection in a stenosed artery bifurcation by numerical simulation of pulsatile blood flow using the low-Reynolds number turbulence model

The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.     

Hemodynamics and activation of mechanoreceptors in the human carotid sinus]

Investigation into consequences of the carotid sinus stimulation has revealed that the stimulation elicited a considerable decrease in arterial blood pressure because of a decrease in the cardiac output (often) or in peripheral vascular resistance (less frequently). The type of the response to the stimulation was found to depend on haemodynamic characteristics at rest.