Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

Influence of head position on carotid hemodynamics in young adults

Studies in adults have shown marked changes in geometry and relative positions of the carotid arteries when rotating the head. The aim of this study was to quantify the change in geometry and analyze its effect on carotid hemodynamics as a result of head rotation. The right carotid arteries of nine young adult subjects were investigated in supine position with straight and left turned head positions, respectively. The three-dimensional (3D) carotid geometry was reconstructed by using 3D ultrasound (3D US), and the carotid hemodynamics were calculated by combining 3D US with computational fluid dynamics. It was observed that cross-sectional areas and shapes did not change markedly with head rotation, but carotid vessel center lines altered with planarification of the common carotid artery as a main feature (P < 0.05). Measured common carotid flow rates changed significantly at the individual level when the head was turned, but on the average, the change in mean common carotid flow rate was relatively small (0.37 +/- 1.11 ml/s). The effect of the altered center lines and flow rates on the atherogenic nature of the carotid bifurcation was evaluated by using calculated hemodynamic wall parameters, such as wall shear stress (WSS) and oscillatory shear index (OSI). It was found that WSS and OSI patterns changed significantly with head rotation, but the variations were very subject dependent and could not have been predicted without assessing the altered geometry and flow of the carotid bifurcation for individual cases. This study suggests that there is a need for standardization of the choice of head position in the 3D US scan protocol, and that carotid stents and emboli diverters should be studied in different head positions.     

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.     

Coupled fluid–structure interaction hemodynamics in a zero-pressure state corrected arterial geometry

Hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall. A numerical procedure for solving the fluid–structure interaction problem encountered in cardiovascular flows is presented. We consider a patient-specific carotid bifurcation geometry, obtained from 3D reconstruction of in vivo acquired tomography images, which yields a geometrical representation of the artery corresponding to its pressurized state. To recover the geometry of the artery in its zero-pressure state which is required for a fluid–structure interaction simulation we utilize inverse finite elastostatics. Time-dependent flow simulations with in vivo measured inflow volume flow rate in the 3D undeformed artery are performed through the finite element method. The coupled-momentum method for fluid–structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain. To demonstrate the importance in recovering the zero-pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero-pressure state corrected geometric configurations of the carotid bifurcation. The most important resulting effects in the hemodynamic environment are evaluated. Our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions.     

A numerical study on hemodynamics in the left coronary bifurcation with normal and hypertension conditions

In this study, a three-dimensional analysis of the non-Newtonian blood flow was carried out in the left coronary bifurcation. The Casson model and hyperelastic and rigid models were used as the constitutive equation for blood flow and vessel wall model, respectively. Physiological conditions were considered first normal and then compliant with hypertension disease with the aim of evaluating hemodynamic parameters and a better understanding of the onset and progression of atherosclerosis plaques in the coronary artery bifurcation. Two-way fluid–structure interaction method applying a fully implicit second-order backward Euler differencing scheme has been used which is performed in the commercial code ANSYS and ANSYS CFX (version 15.0). When artery deformations and blood pressure are associated, arbitrary Lagrangian–Eulerian formulation is employed to calculate the artery domain response using the temporal blood response. As a result of bifurcation, noticeable velocity reduction and backflow formation decrease shear stress and made it oscillatory at the starting point of the LCx branch which caused the shear stress to be less than 1 and 2 Pa in the LCx and the LAD branches, respectively. Oscillatory shear index (OSI) as a hemodynamic parameter represents the increase in residence time and oscillatory wall shear stress. Because of using the ideal 3D geometry and realistic physiological conditions, the values obtained for shear stress are more accurate than the previous studies. Comparing the results of this study with previous clinical investigations shows that the regions with low wall shear stress less than 1.20 Pa and with high OSI value more than 0.3 are in more potential risk to the atherosclerosis plaque development, especially in the posterior after the bifurcation.     

Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model.

Numerical analysis of flow phenomena and wall shear stresses in the human carotid artery bifurcation has been carried out using a three-dimensional geometrical model. The primary aim of this study is the detailed discussion of non-Newtonian flow velocity and wall shear stress during the pulse cycle. A comparison of non-Newtonian and Newtonian results is also presented. The applied non-Newtonian behavior of blood is based on measured dynamic viscosity. In the foreground of discussion are the flow characteristics in the carotid sinus. The investigation shows complex flow patterns especially in the carotid sinus where flow separation occurs at the outer wall throughout the systolic deceleration phase. The changing sign of the velocity near the outer sinus wall results in oscillating shear stress during the pulse cycle. At the outer wall of the sinus at maximum diameter level the shear stress ranges from -1.92 N/m2 to 1.22 N/m2 with a time-averaged value of 0.04 N/m2. At the inner wall of the sinus at maximum diameter level the shear stress range is from 1.16 N/m2 to 4.18 N/m2 with a mean of 1.97 N/m2. The comparison of non-Newtonian and Newtonian results indicates unchanged flow phenomena and rather minor differences in the basic flow characteristics.     

Breaking symmetry in non-planar bifurcations: distribution of flow and wall shear stress

Non-planarity in blood vessels is known to influence arterial flows and wall shear stress. To gain insight, computational fluid dynamics (CFD) has been used to investigate effects of curvature and out-of-plane geometry on the distribution of fluid flows and wall shear stresses in a hypothetical non-planar bifurcation. Three-dimensional Navier-Stokes equations for a steady state Newtonian fluid were solved numerically using a finite element method. Non-planarity in one of the two daughter vessels is found to deflect flow from the inner wall of the vessel to the outer wall and to cause changes in the distribution of wall shear stresses. Results from this study agree to experimental observations and CFD simulations in the literature, and support the view that non-planarity in blood vessels is a factor with important haemodynamic significance and may play a key role in vascular biology and pathophysiology.     

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.     

Numerical simulation of local blood flow in the carotid and cerebral arteries under altered gravity

A computational fluid dynamics (CFD) approach was presented to model the blood flows in the carotid bifurcation and the brain arteries under altered gravity. Physical models required for CFD simulation were introduced including a model for arterial wall motion due to fluid-wall interactions, a shear thinning fluid model of blood, a vascular bed model for outflow boundary conditions, and a model for autoregulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models were solved iteratively using the pseudocompressibility method and dual time stepping. Gravity source terms were added to the Navier-Stokes equations to take the effect of gravity into account. For the treatment of complex geometry, a chimera overset grid technique was adopted to obtain connectivity between arterial branches. For code validation, computed results were compared with experimental data for both steady-state and time-dependent flows. This computational approach was then applied to blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other using an anatomical data set. A three-dimensional Circle of Willis configuration was reconstructed from subject-specific magnetic resonance images using an image segmentation method. Through the numerical simulation of blood flow in two model problems, namely, the carotid bifurcation and the brain arteries, it was observed that the altered gravity has considerable effects on arterial contraction/dilatation and consequent changes in flow conditions.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

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.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Dynamic curvature strongly affects wall shear rates in a coronary artery bifurcation model

This study was motivated by the need for a better understanding of coronary artery blood flow patterns and their possible role in atherosclerosis formation. Of particular interest in this study was the effects of the dynamic deformation due to myocardial contraction on wall shear rate patterns in the coronary arteries. A better understanding of these effects on wall shear rate in a bifurcation geometry and an evaluation of the importance of these effects was desired. A three-dimensional computer model of a bifurcation lying on the surface of a sphere with time-varying radius of curvature was employed to simulate the motion and deformation of the arteries. The results indicated low mean shear rates along the myocardial wall and very high shear rate variations (over 100% of the static mean shear rate) along the outer wall. The results obtained using a quasi-static analysis were found to underestimate the dynamic wall shear rate variation along the myocardial and outer walls. It was concluded that dynamic geometry effects are important in determining sites of low mean and oscillating wall shear that have been associated with atherogenesis in curved, bifurcating arteries.     

Flow patterns and wall shear stress distribution in human internal carotid arteries: the geometric effect on the risk for stenoses

It has been widely observed that atherosclerotic stenosis occurs at sites with complex hemodynamics, such as arteries with high curvature or bifurcations. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present study, 3D sinusoidally pulsatile blood flow through the models of internal carotid artery (ICA) with different geometries was investigated with computational simulation. Three preferred sites of stenoses were found along the carotid siphon with low and highly oscillatory WSS. The risk for stenoses at these sites was scaled with the values of time-averaged WSS and oscillating shear index (OSI). The local risk for stenoses at every preferred site of stenoses was found different between 3 types of ICA, indicating that the geometry of the blood vessel plays significant roles in the atherogenesis. Specifically, the large curvature and planarity of the vessel were found to increase the risk for stenoses, because they tend to lower WSS and elevate OSI. Therefore, the geometric study makes it possible to estimate the stenosis location in the ICA siphon as long as the shape of ICA was measured.     

Arterial adaptations to altered blood flow

Arterial remodeling in response to altered blood flow is believed to be critical to vascular adaptations to developmental, physiological, pathological, and therapeutically induced changes in blood flow. To assess this remodeling, we used left-to-right carotid anastomosis to increase blood flow in the right common carotid arteries of adult rabbits by 60%. After 2 months, these vessels exhibited no compensatory enlargement. In contrast, the same procedure performed in 5- to 6-week-old weanling rabbits resulted in accelerated growth of the vessels: diameters exceeded those of control arteries by 19% after 2 months. Common carotid arteries in adult rabbits remodeled to produce a diameter reduced by 23% when blood flow was reduced by 63% by external carotid ligation. This adaptation restored shear stress exerted on the vessel wall to control levels. The reduced diameter was not reversed when the vessels were maximally dilated with nitroprusside, adenosine, and forskolin; however, normal diameters were restored within 1 week when normal blood flows were reestablished. Thus, the adult arteries did not respond to increased blood flow produced by the anastomosis, but this procedure did reverse adaptations to decreased flow. In contrast, immature arteries were responsive to this increase in blood flow, even in the absence of prior flow modulation.     

Fundamental role of axial stress in compensatory adaptations by arteries

Arteries exhibit a remarkable ability to adapt to diverse genetic defects and sustained alterations in mechanical loading. For example, changes in blood flow induced wall shear stress tend to control arterial caliber and changes in blood pressure induced circumferential wall stress tend to control wall thickness. We submit, however, that the axial component of wall stress plays a similarly fundamental role in controlling arterial geometry, structure, and function, that is, compensatory adaptations. This observation comes from a review of findings reported in the literature and a comparison of four recent studies from our laboratory that quantified changes in the biaxial mechanical properties of mouse carotid arteries in cases of altered cell-matrix interactions, extracellular matrix composition, blood pressure, or axial extension. There is, therefore, a pressing need to include the fundamental role of axial wall stress in conceptual and theoretical models of arterial growth and remodeling and, consequently, there is a need for increased attention to evolving biaxial mechanical properties in cases of altered genetics and mechanical stimuli.     

Blood flow patterns in the proximal human coronary arteries: relationship to atherosclerotic plaque occurrence

Atherosclerotic plaques in human coronary arteries are focal manifestations of systemic disease, and biomechanical factors have been hypothesized to contribute to plaque genesis and localization. We developed a computational fluid dynamics (CFD) model of the ascending aorta and proximal sections of the right and left coronary arteries of a normal human subject using computed tomography (CT) and magnetic resonance imaging (MRI) and determined the pulsatile flow field. Results demonstrate that flow patterns in the ascending aorta contribute to a pro-atherosclerotic flow environment, specifically through localization of low and oscillatory wall shear stress in the neighborhood of coronary orifices. Furthermore, these patterns differ in their spatial distribution between right and left coronary arteries. Entrance effects of aortic flow diminish within two vessel diameters. We examined relationships between spatial distributions of wall shear stress and reports of plaque occurrence in the literature. Results indicate low wall shear stress is co-located with increased incidence of lesions, and higher wall shear stresses are associated with lesion-resistant areas. This investigation does not consider plaque progression or advanced lesions, inasmuch as the CFD model was developed from a normal individual and the clinical data used for comparisons were obtained from autopsy specimens of subjects who died from non-cardiovascular causes. The data reported are consistent with the hypothesis that low wall shear stress is associated with the localization of atherosclerotic lesions, and the results demonstrate the importance of aortic flow on flow patterns in the proximal segments of the coronary arteries.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.     

Fluid flow and plaque formation in an aortic bifurcation

Considering steady laminar flow in a two-dimensional symmetric branching channel with local occlusions, a finite element model has been developed to study velocity fields including reverse flow regions, pressure profiles and wall shear stress distributions for different Reynolds numbers, bifurcation angles and lumen reductions. The flow analysis has been extended to include a new submodel for the pseudo-transient formation of plaque at sites and deposition rates defined by the physical characteristics of the flow. Specifically, simulating the onset of atherosclerotic lesions, sinusoidal plaque layers have been placed in areas of critically low wall shear stresses, and simulating the growth of particle depositions, plaque layers have been added in a stepwise fashion in regions of critically high and low shear. Thus two somewhat conflicting hypothetical correlations between critical wall shear stress levels and atheroma have been tested and a solution has been postulated. The validated computer simulation model is a predictive tool for analyzing the effects of local changes in wall curvature due to surgical reconstruction and/or atherosclerotic lesions, and for investigating the design of aortic bifurcations which mitigate plaque formation.