Concentration polarization of atherogenic lipids in the arterial system

The transport of atherogenic lipids (LDL) in a straight segment of an artery with a semi-permeable wall was simulated numerically. The numerical analysis predicted that a mass transport phenomenon called ’concentration polarization’ of LDL might occur in the arterial system. Under normal physiological flow conditions, the luminal surface LDL concentration was 5%–14% greater than the bulk concentration in a straight segment of an artery. The luminal surface LDL concentration at the arterial wall was flow-dependent, varying linearly with the filtration rate across the arterial wall and inversely with wall shear rate. At low wall shear rate, the luminal surface LDL concentration was very sensitive to changes in flow conditions, decreasing sharply as wall shear rate increased. In order to verify the numerical analysis, the luminal surface concentration of bovine serum albumin (as a tracer macromolecule) in the canine carotid artery was measured in vitro by directly taking liquid samples from the luminal surface of the artery. The experimental result was in very good agreement with the numerical analysis. The authors believe that the mass transport phenomenon of ‘concentration polarization’ may indeed exist in the human circulation and play an important role in the localization of atherosclerosis.     

Theoretical study on flow-dependent concentration polarization of low density lipoproteins at the luminal surface of a straight artery

It is suspected that physical and fluid mechanical factors play important roles in the localization of atherosclerotic lesions and intimal hyperplasia in man by affecting the transport of cholesterol in flowing blood to arterial walls. Hence, we have studied theoretically the effects of various physical and fluid mechanical factors such as wall shear rate, diffusivity of low density lipoproteins (LDL), and filtration velocity of water at the vessel wall on surface concentration of LDL at an arterial wall by means of a computer simulation of convective and diffusive transport of LDL in flowing blood to the wall of a straight artery under conditions of a steady flow. It was found that under normal physiologic conditions prevailing in the human arterial system, due to the presence of a filtration flow of water at the vessel wall, flow-dependent concentration polarization (accumulation or depletion) of LDL occurs at a blood/endothelium boundary. The surface concentration of LDL at an arterial wall takes higher values than that in the bulk flow in that vessel, and it is affected by three major factors, that is, wall shear rate, gamma w, filtration velocity of water at the vessel wall, Vw, and the distance from the entrance of the artery, L. It increases with increasing Vw and L, and decreasing gamma w hence the flow rate. Thus, under certain circumstances, the surface concentration of LDL could rise locally to a value which is several times higher than that in the bulk flow, or drop locally to a value even lower than a critical concentration for the maintenance of normal functions and survival of cells forming the vessel wall. These results suggest the possibility that all the vascular phenomena such as the localization of atherosclerotic lesions and intimal hyperplasia, formation of cerebral aneurysms, and adaptive changes of lumen diameter and wall structure of arteries and veins to certain changes in hemodynamic conditions in the circulation are governed by this flow-dependent concentration polarization of LDL which carry cholesterol.     

The effect of the endothelial glycocalyx layer on concentration polarisation of low density lipoprotein in arteries

It has been postulated that a flow-dependent (and hence spatially varying) low density lipoprotein (LDL) concentration polarisation layer forms on the luminal surface of the vascular endothelium. Such a layer has the potential to cause heterogeneity in the distribution of atherosclerotic lesions by spatially modulating the rate of LDL transport into the arterial wall. Theoretical analysis suggests that a transmural water flux which is spatially heterogeneous at the cellular scale can act to enhance LDL concentration polarisation in a shear dependent fashion. However, such an effect is only observed if a relevant Peclet number (i.e. the ratio of LDL convection to LDL diffusion) is of order unity or greater. Based on the diffusivity of LDL in blood plasma, such a Peclet number is found to be far less than unity, implying that the aforementioned enhancement and shear dependence will not occur. However, this conclusion ignores the existence of the endothelial glycocalyx layer (EGL), which may inhibit the diffusion of LDL near the luminal surface of the endothelium, and hence raise any Peclet number associated with the transport of LDL. The present study numerically investigates the effect of the EGL, as well as a heterogeneous transmural water flux, on arterial LDL concentration polarisation. Particular attention is paid to measures of LDL concentration polarisation thought relevant to the rate of transendothelial LDL transport. It is demonstrated that an EGL is unlikely to cause any additional shear dependence of such measures directly, irrespective of whether or not LDL can penetrate into the EGL. However, it is found that such measures depend significantly on the nature of the interaction between LDL and the EGL (parameterised by the height of the EGL, the depth to which LDL penetrates into the EGL, and the diffusivity of LDL in the EGL). Various processes may regulate the interaction of LDL with the EGL, possibly in a flow dependent and hence spatially non-uniform fashion. It is concluded that any such processes may be as important as vascular scale flow features in terms of spatially modulating transendothelial LDL transport via an LDL concentration polarisation mechanism.     

Concentration polarization of macromolecules in canine carotid arteries and its implication for the localization of atherogenesis

To test the hypothesis that concentration polarization of atherogenic lipids may occur in the arterial system and play an important role in the localization of atherogenesis, we measured in vitro the luminal surface concentration of bovine serum albumin (as a tracer macromolecule) in the canine carotid artery by directly taking liquid samples from the luminal surface of the artery. The experimental results show that the luminal surface albumin concentration, c(w), was higher than the bulk concentration, c(0) as predicted by our theory. The relative luminal surface albumin concentration, c(w)/c(0), decreased very sharply at low wall shear rate, G, but gradually approached the value of 1.0 asymptotically as G was increased. The experiment shows that water flux rate across the vessel wall, v(w), has a profound impact on concentration polarization. For instance, at G = 0 and 185 s(-1), when v(w) = 8.9 +/- 1.7 x 10(-6) cm/s, c(w) was 65% and 15% higher than c(0), respectively, meanwhile when v(w) = 4.8 +/- 0.6 x 10(-6)cm/s, c(w) was only 42% and 5% higher than c(0), respectively. The experiment also revealed that concentration polarization occurred in a thin layer close to the luminal surface of the artery. The thickness of this layer was water flux rate-dependent. The higher the water flux rate, the thicker was the layer. The present study therefore confirms that concentration polarization can indeed occur in the arterial system and our theoretical analysis is accurate in predicting this mass transfer phenomenon.     

Comparative study of Newtonian and non-Newtonian simulations of drug transport in a model drug-eluting stent

To elucidate the difference between Newtonian and shear thinning non-Newtonian assumptions of blood in the analysis of DES drug delivery, we numerically simulated the local flow pattern and the concentration distribution of the drug at the lumen-tissue interface for a structurally simplified DES deployed in a curved segment of an artery under pulsatile blood flow conditions. The numerical results showed that when compared with the Newtonian model, the Carreau (shear thinning) model could lead to some differences in the luminal surface drug concentration in certain areas along the outer wall of the curved vessel. In most areas of the vessel, however, there were no significant differences between the 2 models. Particularly, no significant difference between the two models was found in terms of the area-averaged luminal surface drug concentration. Therefore, we believe that the shear thinning property of blood may play little roles in DES drug delivery. Nevertheless, before we draw the conclusion that Newtonian assumption of blood can be used to replace its non-Newtonian one for the numerical simulation of drug transport in the DES implanted coronary artery, other more complex mechanical properties of blood such as its thixotropic behavior should be tested.     

狭窄血管远心端低密度脂蛋白浓度极化促进动脉粥样硬化形成

低密度脂蛋白（low density lipoprotein,LDL）浓度极化可能是动脉粥样硬化局灶性的重要原因,本文以狭窄血管远心端为研究对象,探讨LDL浓度极化对动脉粥样硬化发生、发展的影响。用数值计算模拟狭窄血管远心端LDL的壁面浓度分布,用激光扫描共聚焦显微镜测定狭窄血管远心端LDL沿z轴的浓度分布;用外科手术方法建立颈总动脉局部狭窄的实验模型,从整体动物水平观察LDL浓度极化对动脉粥样硬化形成的影响。数值计算和激光扫描共聚焦显微镜测定的结果表明,狭窄血管远心端存在显著的LDL浓度极化现象,且LDL壁面浓度与入口液流速度和狭窄程度有关：在相同的速率下,LDL壁面浓度在狭窄度为40％的圆管内最大;在狭窄程度相同的情况下,雷诺数（Re）为250时测得的LDL壁面浓度高于Re为500时测得的壁面浓度。整体动物实验表明,在狭窄血管远心端LDL浓度极化显著的区域形成明显的动脉粥样硬化病变,并且有大量的脂质沉积。以上结果提示,LDL浓度极化可能是导致动脉粥样硬化局灶性的重要因素。     

Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model

Atherosclerosis localizes at a bend andor bifurcation of an artery, and low density lipoproteins (LDL) accumulate in the intima. Hemodynamic factors are known to affect this localization and LDL accumulation, but the details of the process remain unknown. It is thought that the LDL concentration will be affected by the filtration flow, and that the velocity of this flow will be affected by deformation of the arterial wall. Thus, a coupled model of a blood flow and a deformable arterial wall with filtration flow would be invaluable for simulation of the flow field and concentration field in sequence. However, this type of highly coupled interaction analysis has not yet been attempted. Therefore, we performed a coupled analysis of an artery with multiple bends in sequence. First, based on the theory of porous media, we modeled a deformable arterial wall using a porohyperelastic model (PHEM) that was able to express both the filtration flow and the viscoelastic behavior of the living tissue, and simulated a blood flow field in the arterial lumen, a filtration flow field and a displacement field in the arterial wall using a fluid-structure interaction (FSI) program code by the finite element method (FEM). Next, based on the obtained results, we further simulated LDL transport using a mass transfer analysis code by the FEM. We analyzed the PHEM in comparison with a rigid model. For the blood flow, stagnation was observed downward of the bends. The direction of the filtration flow was only from the lumen to the wall for the rigid model, while filtration flows from both the wall to the lumen and the lumen to the wall were observed for the PHEM. The LDL concentration was high at the lumenwall interface for both the PHEM and rigid model, and reached its maximum value at the stagnation area. For the PHEM, the maximum LDL concentration in the wall in the radial direction was observed at the position of 3% wall thickness from the lumenwall interface, while for the rigid model, it was observed just at the lumenwall interface. In addition, the peak LDL accumulation area of the PHEM moved about according to the pulsatile flow. These results demonstrate that the blood flow, arterial wall deformation, and filtration flow all affect the LDL concentration, and that LDL accumulation is due to stagnation and the presence of filtration flow. Thus, FSI analysis is indispensable.     

Effects of transmural pressure and wall shear stress on LDL accumulation in the arterial wall: a numerical study using a multilayered model

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.     

Large eddy simulation of LDL surface concentration in a subject specific human aorta

The development of atherosclerosis is correlated to the accumulation of lipids in the arterial wall, which, in turn, may be caused by the build-up of low-density lipoproteins (LDL) on the arterial surface. The goal of this study was to model blood flow within a subject specific human aorta, and to study how the LDL surface concentration changed during a cardiac cycle. With measured velocity profiles as boundary conditions, a scale-resolving technique (large eddy simulation, LES) was used to compute the pulsatile blood flow that was in the transitional regime. The relationship between wall shear stress (WSS) and LDL surface concentration was investigated, and it was found that the accumulation of LDL correlated well with WSS. In general, regions of low WSS corresponded to regions of increased LDL concentration and vice versa. The instantaneous LDL values changed significantly during a cardiac cycle; during systole the surface concentration was low due to increased convective fluid transport, while in diastole there was an increased accumulation of LDL on the surface. Therefore, the near-wall velocity was investigated at four representative locations, and it was concluded that in regions with disturbed flow the LDL concentration had significant temporal changes, indicating that LDL accumulation is sensitive to not only the WSS but also near-wall flow.     

Numerical simulation of the flow field and mass transport pattern within the coronary artery

In this study, the steady and pulsatile flow field with mass transport analysis in an anatomically correct model of coronary artery is simulated numerically using a specific patient data from a 64-multislice computed tomography scanner. It is assumed that the blood flow is laminar and that the Navier-Stokes equations of motion are applied. Downstream of the bifurcation, a strong skewing occurs towards the flow divider walls as a result of branching. For the low-density lipoprotein (LDL) transport analysis where a specific boundary condition at the arterial walls is applied, LDL is generally elevated at locations where shear stress distribution is low, but it does not co-locate at whole domain. This numerical simulation gives an insight, as well as detailed quantitative data, of haemodynamic conditions in the left coronary artery as well as mass transfer patterns for a specific patient.     

Effect of the endothelial glycocalyx layer on arterial LDL transport under normal and high pressure

To quantitatively investigate the role of the endothelial glycocalyx layer (EGL) in protecting the artery from excessive infiltration of atherogenic lipids such as low density lipoproteins (LDLs), a multilayer model with the EGL of an arterial segment was developed to numerically simulate the flow and the transport of LDLs under normal and high pressure. The transport parameters of the layers of the model were obtained from the hydrodynamic theory, the stochastic theory, and from the literature. The results showed that the increase in the thickness of the EGL could lead to a sharp drop in LDL accumulation in the intima. A partial damage to the EGL could compromise its barrier function, hence leading to enhanced infiltration/accumulation of LDLs within the wall of the arterial model. Without the EGL, hypertension could lead to a significantly enhanced LDL transport into the wall of the model. However, the intact EGL could protect the arterial wall from hypertension so that the LDL concentration in the intima layer was almost the same as that under normal pressure conditions. The results also showed that LDL concentration within the arterial wall increased with Φ (the fraction of leaky junctions) on the intima layer. The increase in LDL concentration with Φ was much more dramatic for the model without the EGL. For instance, without the EGL, a Φ of 0.0005 could lead LDL concentration within the arterial wall to be even higher than that predicted for the EGL intact model with a Φ of 0.002. In conclusion, an intact EGL with a sufficient thickness may act as a barrier to LDL infiltration into the arterial wall and has the potential to suppress the hypertension-driven hike of LDL infiltration/accumulation in the arterial wall.     

Effect of non-Newtonian and pulsatile blood flow on mass transport in the human aorta

To investigate the effects of both non-Newtonian behavior and the pulsation of blood flow on the distributions of luminal surface LDL concentration and oxygen flux along the wall of the human aorta, we numerically compared a non-Newtonian model with the Newtonian one under both steady flow and in vivo pulsatile flow conditions using a human aorta model constructed from MRI images. The results showed that under steady flow conditions, although the shear thinning non-Newtonian nature of blood could elevate wall shear stress (WSS) in most regions of the aorta, especially areas with low WSS, it had little effect on luminal surface LDL concentration (c(w)) in most regions of the aorta. Nevertheless, it could significantly enhance c(w) in areas with high luminal surface LDL concentration through the shear dependent diffusivity of LDLs. For oxygen transport, the shear thinning non-Newtonian nature of blood could slightly reduce oxygen flux in most regions of the aorta, but this effect became much more apparent in areas with already low oxygen flux. The pulsation of blood flow could significantly reduce c(w) and enhance oxygen flux in these disturbed places. In most other regions of the aorta, the oxygen flux was also significantly higher than that for the steady flow simulation. In conclusion, the shear shining non-Newtonian nature of blood has little effect on LDL and oxygen transport in most regions of the aorta, but in the atherogenic-prone areas where luminal surface LDL concentration is high and oxygen flux is low, its effect is apparent. Similar is for the effect of pulsatile flow on the transport of LDLs. But, the pulsation of blood flow can apparently affect oxygen flux in the aorta, especially in areas with low oxygen flux.     

The Effect of a Spatially Heterogeneous Transmural Water Flux on Concentration Polarization of Low Density Lipoprotein in Arteries

Uptake of low density lipoprotein (LDL) by the arterial wall is likely to play a key role in atherogenesis. A particular process that may cause vascular scale heterogeneity in the rate of transendothelial LDL transport is the formation of a flow-dependent LDL concentration polarization layer on the luminal surface of the arterial endothelium. In this study, the effect of a spatially heterogeneous transmural water flux (that traverses the endothelium only via interendothelial cell clefts) on such concentration polarization is investigated numerically. Unlike in previous investigations, realistic intercellular cleft dimensions are used here and several values of LDL diffusivity are considered. Particular attention is paid to the spatially averaged LDL concentration adjacent to different regions of the endothelial surface, as such measures may be relevant to the rate of transendothelial LDL transport. It is demonstrated in principle that a heterogeneous transmural water flux can act to enhance such measures, and cause them to develop a shear dependence (in addition to that caused by vascular scale flow features, affecting the overall degree of LDL concentration polarization). However, it is shown that this enhancement and additional shear dependence are likely to be negligible for a physiologically realistic transmural flux velocity of 0.0439 μm s⁻¹ and an LDL diffusivity (in blood plasma) of 28.67 μm² s⁻¹. Hence, the results imply that vascular scale studies of LDL concentration polarization are justified in ignoring the effect of a spatially heterogeneous transmural water flux.     

Coupled computational analysis of arterial LDL transport -- effects of hypertension

Hypertension, a risk factor for atherosclerosis, increases the uptake of low density lipoproteins (LDL) by the arterial wall. Our objective in this work was to use computational modeling to identify physical factors that could be partially responsible for this effect. Fluid flow and mass transfer patterns in the lumen and wall of an arterial model were computed in a coupled manner, replicating as closely as possible previous experimental studies in which LDL uptake into the artery wall was measured in straight, excised arterial segments. Under conditions of both flow and no-flow, simulations predicted an increase in concentration polarization of LDL at the artery wall when arterial pressure was increased from 120 to 160 mmHg. However, this led to only a slight increase in mean LDL concentration within the arterial wall. However, if the permeability of the endothelium to LDL was allowed to vary with intra-arterial pressure, then the simulations predicted that the uptake of LDL would be enhanced 1.9-2.6 fold at higher pressure. The magnitude of this increase was consistent with experimental data. We conclude that the concentration polarization effects, enhanced by elevated intra-arterial pressure, cannot explain the increase in LDL uptake seen under hypertensive conditions. Instead, the data are most consistent with a pressure-linked increase in endothelial permeability to LDL.     

Flow-dependent concentration polarization of plasma proteins at the luminal surface of a semipermeable membrane

The effect of steady shear flow on concentration polarization of plasma proteins and lipoproteins at the luminal surface of a semipermeable vessel wall was studied experimentally using suspensions of these molecules in a cell culture medium and a semipermeable membrane dialysis tube which served as a model of an implanted vascular graft or an artery. The study was carried out by flowing a cell culture medium containing fetal calf serum or bovine plasma lipoproteins or bovine albumin through a 7.5 mm diameter, 60 mm-long dialysis tube in steady flow under a physiologic mean arterial perfusion pressure of 100 mmHg, and measuring the filtration velocity of water (cell culture medium) at the vessel wall which varied as a consequence of the change in concentration of plasma protein particles at the luminal surface of the semipermeable membrane dialysis tube. It was found that for perfusates containing plasma proteins and/or lipoproteins, filtration velocity of water was the lowest in the absence of flow, and it increased or decreased as the flow rate (hence wall shear rate) increased or decreased from a certain non-zero value, indicating that surface concentration of protein particles varied reversibly as a direct function of flow rate. It was also found that at particle concentrations equivalent to those found in a culture medium containing serum at 5% by volume, plasma lipoproteins which were much smaller in number and lower in concentration but larger in size than albumin, had a much larger effect on the filtration velocity of water than albumin. These findings were very much the same as those previously obtained with a cultured endothelial cell monolayer, strongly suggesting that the flow-dependent variation in filtration velocity of water at a vessel wall results from a physical phenomenon, that is, flow-dependent concentration polarization of low density lipoproteins at the luminal surface of the endothelial cell monolayer.     

The accelerated atherogenesis of venous grafts might be attributed to aggravated concentration polarization of low density lipoproteins: A numerical study

We hypothesize that after implantation the much elevated water filtration rate of venous grafts may cause aggravated concentration polarization of low density lipoproteins (LDLs), in turn lead to the accelerated atherogenesis of the grafts. To verify the hypothesis, we numerically simulated the transport of LDLs in various models of arterial bypasses with different grafts (veins or arteries) and geometrical configurations. The results showed that the venous grafts might endure abnormally high lipid infiltration/accumulation within the vessel wall due to severely elevated luminal surface LDL concentration. When compared to the conventional bypass models, the S-type bypass had the lowest luminal surface LDL concentration along its host artery floor, but the highest degree of risk to develop atherosclerotic lesions in its venous graft. Among the three conventional bypass models, the one with 30° anastomosis had the lowest risk to develop atherosclerosis in the venous graft. In conclusion, when compared with the bypass models with arterial grafts, the venous bypass models had rather high levels of LDL concentration polarization (c_w) in the vein grafts, especially at the early stages of implantation. This might result in high infiltration/accumulation of LDLs within the walls of the venous grafts, leading to a fast genesis/development of atherosclerosis there.     

Computational analysis of coupled blood-wall arterial LDL transport

The transport of macromolecules, such as low density lipoproteins (LDLs), across the artery wall and their accumulation in the wall is a key step in atherogenesis. Our objective was to model fluid flow within both the lumen and wall of a constricted, axisymmetric tube simulating a stenosed artery, and to then use this flow pattern to study LDL mass transport from the blood to the artery wall. Coupled analysis of lumenal blood flow and transmural fluid flow was achieved through the solution of Brinkman's model, which is an extension of the Navier-Stokes equations for porous media. This coupled approach offers advantages over traditional analyses of this problem, which have used possibly unrealistic boundary conditions at the blood-wall interface; instead, we prescribe a more natural pressure boundary condition at the adventitial vasa vasorum, and allow variations in wall permeability due to the occurrence of plaque. Numerical complications due to the convection dominated mass transport process (low LDL diffusivity) are handled by the streamline upwind/Petrov-Galerkin (SUPG) finite element method. This new fluid-plus-porous-wall method was implemented for conditions typical of LDL transport in a stenosed artery with a 75 percent area reduction (Peclet number=2 x 10(8)). The results show an elevated LDL concentration at the downstream side of the stenosis. For the higher Darcian wall permeability thought to occur in regions containing atheromatous lesions, this leads to an increased transendothelial LDL flux downstream of the stenosis. Increased transmural filtration in such regions, when coupled with a concentration-dependent endothelial permeability to LDL, could be an important contributor to LDL infiltration into the arterial wall. Experimental work is needed to confirm these results.     

Low-density lipoprotein concentration in the normal left coronary artery tree

Background

The blood flow and transportation of molecules in the cardiovascular system plays a crucial role in the genesis and progression of atherosclerosis. This computational study elucidates the Low Density Lipoprotein (LDL) site concentration in the entire normal human 3D tree of the LCA.

Methods

A 3D geometry model of the normal human LCA tree is constructed. Angiographic data used for geometry construction correspond to end-diastole. The resulted model includes the LMCA, LAD, LCxA and their main branches. The numerical simulation couples the flow equations with the transport equation applying realistic boundary conditions at the wall.

Results

High concentration of LDL values appears at bifurcation opposite to the flow dividers in the proximal regions of the Left Coronary Artery (LCA) tree, where atherosclerosis frequently occurs. The area-averaged normalized luminal surface LDL concentrations over the entire LCA tree are, 1.0348, 1.054 and 1.23, for the low, median and high water infiltration velocities, respectively. For the high, median and low molecular diffusivities, the peak values of the normalized LDL luminal surface concentration at the LMCA bifurcation reach 1.065, 1.080 and 1.205, respectively. LCA tree walls are exposed to a cholesterolemic environment although the applied mass and flow conditions refer to normal human geometry and normal mass-flow conditions.

Conclusion

The relationship between WSS and luminal surface concentration of LDL indicates that LDL is elevated at locations where WSS is low. Concave sides of the LCA tree exhibit higher concentration of LDL than the convex sides. Decreased molecular diffusivity increases the LDL concentration. Increased water infiltration velocity increases the LDL concentration. The regional area of high luminal surface concentration is increased with increasing water infiltration velocity. Regions of high LDL luminal surface concentration do not necessarily co-locate to the sites of lowest WSS. The degree of elevation in luminal surface LDL concentration is mostly affected from the water infiltration velocity at the vessel wall. The paths of the velocities in proximity to the endothelium might be the most important factor for the elevated LDL concentration.