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。     

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.     

Prediction of LDL concentration at the luminal surface of a vascular endothelium

To find out whether concentration polarization of low-density lipoprotein (LDL) occurs at the surface of a vascular endothelium or not, transport of LDL in flowing blood to an water-permeable endothelium was studied theoretically by means of CFD. Calculations were carried out for an endothelium exposed to a Couette flow by assuming that the surface geometry of the endothelium could be expressed by a cosine function. Two typical cases were considered for the permeability of endothelium to water; one was uniform permeability everywhere in the endothelium, and the other was uneven permeability which was augmented at the intercellular junction. It was found that, in both cases, the surface concentration of LDL increased in going distally from the entrance, taking locally high and low values at the valleys and hills of the endothelium, respectively, and the variation was larger in the case of endothelium with uneven permeability. These results clearly showed that concentration polarization of LDL which might affect the uptake of LDL by the arterial wall certainly occurs at the surface of the endothelium even if the flow is disturbed microscopically by the uneven surface of the endothelium.     

Concentration polarization of atherogenic lipids in the arterial system

Nomenclature c, Normalized LDL concentration (C*/C0); C0, incoming (bulk) LDL concentration (gr/cm3); Cw, LDL concentration on the luminal surface (gr/cm3); ,wC time average value of LDL concentration on the luminal surface (gr/cm3); D, diffusion coef-ficient of LDL (cm2/s); Q, blood flow rate (mL/s); 0R, average internal radius of the artery (cm); Re, Reynolds number (002/Run); Sc, Schmidt number (/Dn); t, normalized time (00*/tuR); u, normalized axial velocity (0*/uu); 0u, time a…     

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.     

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.     

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.     

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.     

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 arterial pressure on endothelial transport of macromolecules

The effects of variations in transmural pressure over a range of 0 to 200 mmHg on transendothelial transport of macromolecules were studied in the canine common carotid artery. The uptake of 125I-albumin per unit artery weight increased with rising pressure. There was no significant difference in albumin permeability per unit luminal surface area between 0 and 100 mmHg, but permeability nearly doubled when pressure was raised to 200 mmHg. The contribution of an increased rate of transendothelial vesicle diffusion, as evaluated from the experimental determination of the ratio of attached-to-free vesicles and theoretical modeling, was found to be negligible. The reduction in transendothelial vesicle diffusion distance due to pressure-induced thinning of the peripheral zone contributes to a 25% increase in permeability. With the use of colloidal Ag and Au of various sizes, vesicle loading of particles with diameters greater than or equal to 15 nm was found to be severely restricted at transmural pressure less than or equal to 100 mmHg, but it was significantly enhanced at 200 mmHg, when particles as large as 25 nm became detectable in endothelial vesicles and subendothelial space. This hypertension-induced increase in macromolecular transport across the endothelium may cause an overloading of the arterial wall with low-density lipoproteins and play a significant role in atherogenesis.     

Numerical simulation of LDL mass transfer in a common carotid artery under pulsatile flows

Symmetrical 30-60% stenosis in carotid artery with a semi-permeable wall under steady/unsteady flows for Newtonian/non-Newtonian fluids is investigated numerically. The results show that the unsteadiness of blood flow, blood pressure rise and LDL component size increase the luminal concentration, LC, of the surface. The maximum LC occurring immediately after the separation point and the non-Newtonian fluid predicts higher LDL accumulation. LC decreased as the recirculation length is increased and reaches maximum at 40% stenosis. This process is used to estimate the time-dependent growth of the arterial wall.     

Boundary layer considerations in a multi-layer model for LDL accumulation

Abstract

Boundary layer effects for Low-Density Lipoprotein (LDL) concentration problems in a multi-layer artery model are analyzed in this work. Both a straight artery and aorta-iliac bifurcation are analyzed. Mass, momentum and species governing equations are based on the porous media theory and solved with the commercial finite-element based code COMSOL Multiphysics. For the straight artery, various inlet velocities, arterial sizes and intramural pressure values are investigated. Results are presented in terms of concentration profiles close to the lumen/endothelium interface and boundary layer thickness. It is shown that the boundary layer is affected by all of the three analyzed parameters. The results in this work will further clarify the concentration polarization effects imposed by the arterial wall.     

Effects of arterial wall models and measurement uncertainties on cardiovascular model predictions

We developed a methodology to assess and compare the prediction quality of cardiovascular models for patient-specific simulations calibrated with uncertainty-hampered measurements. The methodology was applied in a one-dimensional blood flow model to estimate the impact of measurement uncertainty in wall model parameters on the predictions of pressure and flow in an arterial network. We assessed the prediction quality of three wall models that have been widely used in one-dimensional blood flow simulations. A 37-artery network, previously used in one experimental and several simulation studies, was adapted to patient-specific conditions with a set of three clinically measurable inputs: carotid–femoral wave speed, mean arterial pressure and area in the brachial artery. We quantified the uncertainty of the predicted pressure and flow waves in eight locations in the network and assessed the sensitivity of the model prediction with respect to the measurements of wave speed, pressure and cross-sectional area. Furthermore, we developed novel time-averaged sensitivity indices to assess the contribution of model parameters to the uncertainty of time-varying quantities (e.g., pressure and flow). The results from our patient-specific network model demonstrated that our novel indices allowed for a more accurate sensitivity analysis of time-varying quantities compared to conventional Sobol sensitivity indices.     

Reactive carbonyls from tobacco smoke increase arterial endothelial layer injury

We hypothesized that reactive carbonyls generated from smoke exposure cause increased arterial low-density lipoprotein (LDL) accumulation and endothelial layer permeability. In addition, we hypothesized that estrogen supplementation was protective against chronic environmental tobacco smoke (ETS) exposure to the artery wall. Quantitative fluorescence microscopy was used to determine artery injury after exposure. For our chronic studies, ovariectomized rats treated with subcutaneous placebo or 17beta-estradiol pellets were exposed to ETS or filtered air for 6 wk. ETS exposure increased carotid artery LDL accumulation more than fourfold compared with filtered air exposure, an effect largely mediated by increased permeability. No protective effect of estradiol was observed. Acute ETS exposure of a buffer solution containing LDL resulted in a more than sixfold increase in the highly reactive carbonyl glyoxal. Perfusion of this solution through carotid arteries resulted in a 105% increase in permeability. Moreover, perfusion of glyoxal alone caused a 50% increase in carotid artery permeability. This endothelial damage and changes in lipid accumulation may serve as an initiating event in atheroma formation in individuals exposed to ETS.     

Transarterial wall oxygen gradients at the deployment site of an intra-arterial stent in the rabbit

Intimal hyperplasia, common at the deployment site of an intra-arterial stent, may be caused by artery wall hypoxia. The purpose of this study was to determine the effect of an intra-arterial stent on artery wall oxygen concentrations. Transarterial wall oxygen gradients were measured by microelectrode at stent deployment sites in New Zealand White rabbits. Thinned artery walls and decreased oxygen tensions were noted throughout the artery wall immediately following stent deployment with a return toward control values at 28 days. Angioplasty alone had no acute effect on artery wall oxygen concentrations. Larger stent deployment diameters yielded acutely lower artery wall oxygen tensions. Using a linear one-dimensional model for the oxygen profile, we noted that stent deployment resulted in acute changes in oxygen consumption in the inner artery wall that rapidly returned to control values. Changes were noted without differences in blood pressure or arterial blood oxygen concentrations. Oxygen delivery to and consumption within the artery wall are altered by intra-arterial stent deployment. A role for artery wall hypoxia in artery wall pathology at the deployment site of an intra-arterial stent is supported by these findings.     

Visualization of the binding, endocytosis, and transcytosis of low- density lipoprotein in the arterial endothelium in situ

We investigated the interaction and transport of low-density lipoprotein (LDL) through the arterial endothelium in rat aorta and coronary artery, by perfusing in situ native, untagged human, and rat LDL. The latter was rendered electron-opaque after it interacted with the endothelial cell and was subsequently fixed within tissue. We achieved LDL electron-opacity by an improved fixation procedure using 3,3'-diaminobenzidine, and mordanting with tannic acid. The unequivocal identification of LDL was implemented by reacting immunocytochemically the perfused LDL with anti LDL-horseradish peroxidase conjugate. Results indicate that LDL is taken up and internalized through two parallel compartmented routes. (a) A relatively small amount of LDL is taken up by endocytosis via: (i) a receptor-mediated process (adsorptive endocytosis) that involved coated pits/vesicles, and endosomes, and, probably, (ii) a receptor-independent process (fluid endocytosis) carried out by a fraction of plasmalemmal vesicles. Both mechanisms bringing LDL to lysosomes supply cholesterol to the endothelial cell itself. (b) Most circulating LDL is transported across the endothelial cell by transcytosis via plasmalemmal vesicles which deliver LDL to the other cells of the vessel wall. Endocytosis is not enhanced by increasing LDL concentration, but the receptor-mediated internalization decreases at low temperature. Transcytosis is less modified by low temperature but is remarkably augmented at high concentration of LDL. While the endocytosis of homologous (rat) LDL is markedly more pronounced than that of heterologous (human) LDL, both types of LDL are similarly transported by transcytosis. These results indicate that the arterial endothelium possesses a dual mechanism for handling circulating LDL: by a high affinity process, endocytosis secures the endothelial cells' need for cholesterol; by a low-affinity nonsaturable uptake process, transcytosis supplies cholesterol to the other cells of the vascular wall, and can monitor an excessive accumulation of plasma LDL. Since in most of our experiments we used LDL concentrations above those found in normal rats, we presume that at low LDL concentrations saturable high-affinity uptake would be enhanced in relation to nonsaturable pathways.     

Effects of transmural pressure on the transport and distribution of low density lipoproteins in the arterial wall

In an attempt to investigate the effects of transmural pressure on LDL transport and distribution across the arterial wall, uptake of labeled LDL has been measured in excised rabbit thoracic aorta, held at in vivo length and pressurized to 70 or 160 mmHg. The transmural distribution of LDL concentration across the wall was determined by examining serial frozen sections cut parallel to the luminal surface at 20 microns intervals from the intima to adventitia. The LDL concentration observed in the first luminal section at 160 mmHg was 20-fold higher than that obtained at 70 mmHg. The LDL concentrations decreased in the subsequent sections of the first half of the media and became similar, in the outer half of the media, to the values observed under normal pressure. These results might provide an account of one of the mechanisms involved in the deleterious effects of hypertension in atherogenesis.     

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.     

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.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.