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.     

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.     

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.     

Geometric design improvements for femoral graft-artery junctions mitigating restenosis

The present study is based on the hypothesis that nonuniform hemodynamics, represented by large time-averaged wall shear stress gradients, trigger abnormal biological processes leading to rapid restenosis, i.e. excessive tissue overgrowth and renewed plaque formation, and hence early graft failure. It implies that this problem may be significantly mitigated by finding graft-artery bypass configurations for which the wall shear stress gradient is approximately zero and hence nearly uniform hemodynamics is achieved. These fluid flow and geometric design considerations are applied to four different end-to-side anastomoses for the distal end of a femoral artery bypass with an appropriate test input pulse and a typical 20–80 flow division. A validated finite-volume code has been used to compute the transient three-dimensional velocity vector fields, wall shear stress distributions and surface contours of the wall shear stress gradients. It is shown that large anastomotic flow areas, small continuously changing bifurcation angles, and smooth junction wall curvatures reduce local time-averaged wall shear stress gradients significantly and hence should mitigate restenosis.     

Common carotid wall shear stress and carotid atherosclerosis in end-stage renal disease patients

Decrease of arterial wall shear stress (WSS) is associated with higher probability of atherosclerotic plaque development in many disease conditions. End-stage renal diseases (ESRD) patients suffer from vascular disease frequently, but its nature differs from general population. This study was aimed at proving an association between common carotid wall shear stress and the presence of carotid bifurcation plaques in a group of ESRD patients. ESRD subjects, planned for the creation of a dialysis access and therapy were included. Wall shear rate (WSR) was used as a surrogate of WSS and was analyzed in the common carotid arteries by duplex ultrasonography. Intima media thickness (IMT) was measured at the same site. The presence/absence of carotid bifurcation plaques was recorded. The endothelial function was estimated by the levels of von Willebrand factor (vWf). 35 ESRD patients were included (19 females, 17 diabetics). Atherosclerotic plaque was present in 53 % of bifurcations. Wall shear rate was lower in arteries with plaques (349+/-148 vs. 506+/-206 s(-1), p=0.005) and was directly related to the height of IMT and inversely to the activity of vWf (r= -0.65, p=0.016). Lower wall shear rate in the common carotid arteries is linked to the endothelial dysfunction and to the presence of atherosclerotic plaques in carotid bifurcations in ESRD subjects. Faster arterial dilatation may facilitate this process in ESRD subjects.     

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.     

3D reconstruction techniques of human coronary bifurcations for shear stress computations

Background

Heterogeneity in plaque composition in human coronary artery bifurcations is associated with blood flow induced shear stress. Shear stress is generally determined by combing 3D lumen data and computational fluid dynamics (CFD). We investigated two new procedures to generate 3D lumen reconstructions of coronary artery bifurcations for shear stress computations.

Methods

We imaged 10 patients with multislice computer tomography (MSCT) and intravascular ultrasound (IVUS). The 3D reconstruction of the main branch was based on the fusion of MSCT and IVUS. The proximal part of side branch was reconstructed using IVUS data or MSCT data, resulting in two different reconstructions of the bifurcation region. The distal part of the side branch was based on MSCT data alone. The reconstructed lumen was combined with CFD to determine the shear stress. Low and high shear stress regions were defined and shear stress patterns in the bifurcation regions were investigated.

Results

The 3D coronary bifurcations were successfully generated with both reconstruction procedures. The geometrical features of the bifurcation region for the two reconstruction procedures did not reveal appreciable differences. The shear stress maps showed a qualitative agreement, and the low and high shear stress regions were similar in size and average shear stress values were identical. The low and high shear stress regions showed an overlap of approximately 75%.

Conclusion

Reconstruction of the side branch with MSCT data alone is an adequate technique to study shear stress and wall thickness in the bifurcation region. The reconstruction procedure can be applied to further investigate the effect of shear stress on atherosclerosis in coronary bifurcations.     

In Vitro Shear Stress Measurements Using Particle Image Velocimetry in a Family of Carotid Artery Models: Effect of Stenosis Severity,Plaque Eccentricity,and Ulceration

Atherosclerotic disease, and the subsequent complications of thrombosis and plaque rupture, has been associated with local shear stress. In the diseased carotid artery, local variations in shear stress are induced by various geometrical features of the stenotic plaque. Greater stenosis severity, plaque eccentricity (symmetry) and plaque ulceration have been associated with increased risk of cerebrovascular events based on clinical trial studies. Using particle image velocimetry, the levels and patterns of shear stress (derived from both laminar and turbulent phases) were studied for a family of eight matched-geometry models incorporating independently varied plaque features – i.e. stenosis severity up to 70%, one of two forms of plaque eccentricity, and the presence of plaque ulceration). The level of laminar (ensemble-averaged) shear stress increased with increasing stenosis severity resulting in 2–16 Pa for free shear stress (FSS) and approximately double (4–36 Pa) for wall shear stress (WSS). Independent of stenosis severity, marked differences were found in the distribution and extent of shear stress between the concentric and eccentric plaque formations. The maximum WSS, found at the apex of the stenosis, decayed significantly steeper along the outer wall of an eccentric model compared to the concentric counterpart, with a 70% eccentric stenosis having 249% steeper decay coinciding with the large outer-wall recirculation zone. The presence of ulceration (in a 50% eccentric plaque) resulted in both elevated FSS and WSS levels that were sustained longer (∼20 ms) through the systolic phase compared to the non-ulcerated counterpart model, among other notable differences. Reynolds (turbulent) shear stress, elevated around the point of distal jet detachment, became prominent during the systolic deceleration phase and was widely distributed over the large recirculation zone in the eccentric stenoses.     

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.     

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.     

Experimental determination of velocity profiles and wall shear rate along the rabbit aortoiliac bifurcation: relationship to vessel wall low-density lipoprotein (LDL) metabolism.

We have determined the velocity profiles and wall shear rates along the New Zealand White (NZW) rabbit aortoiliac bifurcation. A pulsatile perfusion apparatus was used to impose physiologic pressure and flow waveforms on nine freshly excised NZW bifurcation segments. Pulsed Doppler velocimetry (PDV) was utilized to construct velocity profiles at five measurement sites: within the infrarenal aorta; immediately distal to the apex of the bifurcation; and, more distally along the iliac arteries. Wall shear rate was derived from a numerical differentiation of the experimental velocity profiles. The results of this study indicate that the average shear rate was lower along the lateral (approximately 40 s-1) vs medial (approximately 240 s-1) wall of the proximal iliac branch. The degree of flow reversal along the proximal lateral walls (20 +/- 2%) exceeded that along the proximal flow divider wall (1 +/- 1%). Flow at the distal iliac measurement sites and within the infrarenal aorta was approximately symmetric. These findings complement our companion in vivo study [Berceli et al., Arteriosclerosis 10, 688-694 (1990)] wherein we determined the rates of low-density lipoprotein (LDL) incorporation and catabolism along this symmetrically bifurcating conduit. Taken together, these studies provide original information regarding the effects of hemodynamics on one presumed atherogenic risk factor, namely, LDL metabolism.     

Long time evolution of atherosclerotic plaques

The evolution of atherosclerosis in general, and the influence of wall shear stress on the growth of atherosclerotic plaques in particular, is an intricate phenomenon which is still only partly understood. We therefore propose a qualitative mathematical model which consists of a number of ordinary differential equations for the concentrations of the most relevant constituents of the atherosclerotic plaque. These equations were studied both for the case that the wall shear stress is a parameter (model A), and for the case in which the plaque evolution is coupled to the blood flow (model B) which results in a time dependent wall shear stress. We find that both models exhibit a class of marginally stable equilibria, all reflecting states in which the plaque only grows for a short period of time after a perturbation. The uncoupled model A, however, shows bi-stability between this class of equilibria and another equilibrium state in which the plaque experiences unlimited growth in time, if the LDL cholesterol intake exceeds a threshold value. In model B the bi-stability vanishes, but we find that there is still a critical value of the LDL cholesterol intake beyond which the lumen radius drastically decreases. We show that this decrease is quite sensitive to the value of the wall shear stress.     

Development of a general method for designing microvascular networks using distribution of wall shear stress

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.     

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.     

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.     

Branch angle and flow into a symmetric bifurcation

Arterial branches are found to be a major site for formation of arterial plaque. In this study, we investigate the role of the bifurcation angle on the flow into a symmetric bifurcation. Specially, how the changes in the bifurcation angle influences the distribution of axial wall shear in the bifurcation model. The flow in a range of branch opening half-angle of pi/25< or =theta< or =pi/4 are numerically simulated. The flow in the above models is calculated for the inlet flow Reynolds numbers of 250, 500, 1000, and 2000. It is found that at higher values of the opening angle of the bifurcation, the possibility and severity of flow separation at the appropriate wall location increases.     

Advanced human carotid plaque progression correlates positively with flow shear stress using follow-up scan data: An in vivo MRI multi-patient 3D FSI study

Although it has been well-accepted that atherosclerosis initiation and early progression correlate negatively with flow wall shear stresses (FSS), increasing evidence suggests mechanisms governing advanced plaque progression are not well understood. Fourteen patients were scanned 2–4 times at 18 month intervals using a histologically validated multi-contrast magnetic resonance imaging (MRI) protocol to acquire carotid plaque progression data. Thirty-two scan pairs (baseline and follow-up scans) were formed with slices matched for model construction and analysis. 3D fluid–structure interaction (FSI) models were constructed and plaque wall stress (PWS) and flow shear stress (FSS) were obtained from all matching lumen data points (400–1000 per plaque; 100 points per matched slice) to quantify correlations with plaque progression measured by vessel wall thickness increase (WTI). Using FSS and PWS data from follow-up scan, 21 out of 32 scan pairs showed a significant positive correlation between WTI and FSS (positive/negative/no significance ratio=21/8/3), and 26 out of 32 scan pairs showed a significant negative correlation between WTI and PWS (positive/negative/no significance ratio=2/26/4). The mean FSS value of lipid core nodes (n=5294) from all 47 plaque models was 63.5 dyn/cm², which was 45% higher than that from all normal vessel nodes (n=27553, p<0.00001). The results from this intensive FSI study indicate that flow shear stress from follow-up scan correlates positively with advanced plaque progression which is different from what has been observed in plaque initiation and early-stage progression. It should be noted that the correlation results do not automatically lead to any causality conclusions.     

Effects of varied lipid core volume and fibrous cap thickness on stress distribution in carotid arterial plaques

The rupture of atherosclerotic plaques is known to be associated with the stresses that act on or within the arterial wall. The extreme wall tensile stress is usually recognized as a primary trigger for the rupture of the plaque. The present study used one-way fluid-structure interaction simulation to investigate the impacts of fibrous cap thickness and lipid core volume to the wall tensile stress value and distributions on the fibrous cap. Von Mises stress was employed to represent the wall tensile stress (VWTS). A total of 13 carotid bifurcation cases were manipulated based on a base geometry in the study with varied combinations of fibrous cap thickness and lipid core volume in the plaque. Values of maximum VWTS and a stress value of VWTS_90, which represents the cut-off VWTS value of 90% in cumulative histogram of VWTS possessed at the computational nodes on the luminal surface of fibrous cap, were used to assess the risk of plaque rupture for each case. Both parameters are capable of separating the simulation cases into vulnerable and more stable plaque groups, while VWTS_90 is more robust for plaque rupture risk assessment. The results show that the stress level on the fibrous cap is much more sensitive to the changes in the fibrous cap thickness than the lipid core volume. A slight decrease of cap thickness can cause a significant increase of stress. For all simulation cases, high VWTS appears at the fibrous cap near the lipid core (plaque shoulder) regions.     

A new imaging technique to study 3-D plaque and shear stress distribution in human coronary artery bifurcations in vivo

OBJECTIVE: Bifurcations of coronary arteries are predilection sites for atherosclerosis and expansive remodeling, the latter being associated with plaque vulnerability. Both are related to blood flow-induced shear stress (SS). We present a new approach to generate 3-D reconstructions of coronary artery bifurcations in vivo and investigate the relationship between SS, wall thickness (WT) and remodeling. METHODS: The patient specific 3-D reconstruction of the main branch of the bifurcation was obtained by combining intravascular ultrasound and biplane angiography, and the 3-D lumen of the side branch was based on biplane angiography only. The two data sets were fused and computational methods were applied to determine the SS distribution, using patient derived flow and viscosity data. The intravascular ultrasound data allowed us to measure local WT and remodeling in the main branch. RESULTS: The lumen reconstruction procedure was successful and it was shown that the impact of the side branch on SS distribution in the main branch diminished within 3mm. Distal to the bifurcation, two continuous regions in the main branch were identified. In the proximal region, we observed lumen preservation, and expansive remodeling. Although a plaque was observed in the low SS region at the non-divider wall, no relationship between SS and WT was found. In the distal region, we observed lumen narrowing and a significant positive relationship between SS and WT. CONCLUSIONS: A new imaging technique was applied to generate a 3-D reconstruction of a human coronary artery bifurcation in vivo. The observed relationship between SS, WT and remodeling in this specific patient illustrates the spatial heterogeneity of the atherosclerosis in the vicinity of arterial bifurcations.