Internal elastic lamina affects the distribution of macromolecules in the arterial wall: a computational study

The internal elastic lamina (IEL), which separates the arterial intima from the media, affects macromolecular transport across the medial layer. In the present study, we have developed a two-dimensional numerical simulation model to resolve the influence of the IEL on convective-diffusive transport of macromolecules in the media. The model considers interstitial flow in the medial layer that has a complex entrance condition because of the presence of leaky fenestral pores in the IEL. The IEL was modeled as an impermeable barrier to both water and solute except for the fenestral pores that were assumed to be uniformly distributed over the IEL. The media were modeled as a heterogeneous medium composed of an array of smooth muscle cells (SMCs) embedded in a continuous porous medium representing the interstitial proteoglycan and collagen fiber matrix. Results for ATP and low-density lipoprotein (LDL) demonstrate a range of interesting features of molecular transport and uptake in the media that are determined by considering the balance among convection, diffusion, and SMC surface reaction. The ATP concentration distribution depends strongly on the IEL pore structure because ATP fluid-phase transport is dominated by diffusion emanating from the fenestral pores. On the other hand, LDL fluid-phase transport is only weakly dependent on the IEL pore structure because convection spreads LDL laterally over very short distances in the media. In addition, we observe that transport of LDL to SMC surfaces is likely to be limited by the fluid phase (surface concentration less than bulk concentration), whereas ATP transport is limited by reaction on the SMC surface (surface concentration equals bulk concentration).     

The possible role of intimal convective transport in atherogenesis

The possibility of fluid flux within the thickened subendothelial intima is considered. Both the media and the endothelium were already shown to be major hydraulic barriers. It is hypothesized that if the hydraulic conductivity of the inbetween layer of the subendothelial intima is considerably higher, then fluid flux in the downstream (axial) direction is likely to occur within the intima as a result of the luminal blood pressure wave. Macromolecular species (as lipoproteins) would then be transported axially by the fluid. This convective transport may give rise to the formation of early atheromas. The proposed mechanism is in accord with several clinical and experimental observations.     

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.     

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.     

Computational study of LDL mass transport in the artery wall

A two-dimensional (2D) numerical simulation of convective–diffusive transport of LDL in the artery wall, coupled with the wall shear stress gradient (WSSG)-dependent LDL consumption of smooth muscle cells (SMCs) is presented. SMCs are modeled as an array of solid cylindrical pillars embedded in a continuous porous media which represents the interstitial proteoglycan and collagen fiber matrix. The internal elastic lamina (IEL), which separates the artery media from the intima, is modeled as an impermeable barrier to both water and LDL except for the fenestral pores that are assumed to be uniformly distributed over the IEL. The predictions demonstrate a range of interesting features of LDL transport and uptake in the media. For cells immediately below the fenestral pores, LDL uptake of SMCs is highly dependent on WSSG. Moreover, the rate of LDL consumption by SMCs is also affected by the diameter of the fenestral pore. This will be helpful in understanding the involvement of transmural transport processes in the initiation and development of atherosclerosis.     

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.     

Analysis of hemodynamic fluid phase mass transport in a separated flow region

The mass transfer behavior in the recirculation region downstream of an axisymmetric sudden expansion was examined. The Reynolds number, 500, and Schmidt number, 3200, were selected to model the mass transfer of molecules, such as ADP, in the arterial system. In a first step the transient mass transport applying zero diffusive flux at the wall was analyzed using experiments and two computational codes. The two codes were FLUENT, a commercially available finite volume method, and FTSP, a finite element code developed at Graz University of Technology. The comparison of the transient wall concentration values determined by the three methods was excellent and provides a measure of confidence for computational mass transfer calculations in convection dominated, separated flows. In a second step the effect of the flow separation on the stationary mass transport applying a permeability boundary condition at the water-permeable wall was analyzed using the finite element code FTSP. The results show an increase of luminal ADP surface concentration in the upstream and in the downstream tube of the sudden expansion geometry in the range of six and twelve percent of the bulk flow concentration. The effect of flow separation in the downstream tube on the wall concentration is a decrease of about ten percent of the difference between wall concentration and bulk concentration occurring at nearly fully developed flow at the downstream region at a distance of 66 downstream tube diameters from the expansion. The decrease of ADP flux into the wall is in the range of three percent of the flux at the downstream region.     

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.     

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.     

Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress

The work herein represents a novel approach for the modeling of low-density lipoprotein (LDL) transport from the artery lumen into the arterial wall, taking into account the effects of local wall shear stress (WSS) on the endothelial cell layer and its pathways of volume and solute flux. We have simulated LDL transport in an axisymmetric representation of a stenosed coronary artery, where the endothelium is represented by a three-pore model that takes into account the contributions of the vesicular pathway, normal junctions, and leaky junctions also employing the local WSS to yield the overall volume and solute flux. The fraction of leaky junctions is calculated as a function of the local WSS based on published experimental data and is used in conjunction with the pore theory to determine the transport properties of this pathway. We have found elevated levels of solute flux at low shear stress regions because of the presence of a larger number of leaky junctions compared with high shear stress regions. Accordingly, we were able to observe high LDL concentrations in the arterial wall in these low shear stress regions despite increased filtration velocity, indicating that the increase in filtration velocity is not sufficient for the convective removal of LDL.     

Influence of hypertension and of antihypertensive drugs on the arterial wall

This paper reviews some of the experimental data regarding the effects of hypertension and antihypertensive drugs on the arterial wall. Hypertension induces major changes in both the arterial media and intima. Experimental studies from our own and other laboratories have demonstrated that medial smooth muscle cells in several forms of hypertension in the rat undergo hypertrophy and nuclear polyploidy which contribute, along with connective tissue alterations, to a large increase in medial mass. Our studies in the deoxycorticosterone/salt-hypertensive rat indicate that such changes may be difficult to regress, despite prolonged control of the hypertension. In the arterial intima, major alterations in the endothelium are induced by hypertension in association with increase in arterial permeability. Marked enhancements of adherence of circulating white blood cells to the endothelium can also be demonstrated along with penetration of blood monocytes and their accumulation in the subendothelial space. Hypertension also appears to stimulate the migration and proliferation of smooth muscle cells in the intima, and evidence is beginning to accumulate that endogenous growth factors within the artery may be involved in this process. Essentially all of the intimal changes which we have observed as a result of arterial hypertension are also present with cholesterol feeding although intimal accumulation of lipid and formation of atherosclerotic plaques do not occur with hypertension alone. On the other hand, in hypercholesterolemic animals, hypertension appears to act as a promoter of atherogenesis. Several antihypertensive drugs may influence the atherosclerotic process. The experimental data regarding the effects of beta blockers and calcium antagonists in the cholesterol-fed rabbit are discussed. Though of considerable interest, the clinical relevance of the findings remains uncertain.     

Factors influencing arterial wall mass transport

Arterial wall mass transport has particularly attracted attention because it may be implicated in the development of arterial disease, including arteriosclerosis. A short review is presented of the structure of the arterial wall and of studies of mass transport within it. Recent findings confirm that mass transport occurs across the entire arterial wall apparently from the lumen to the adventitial lymphatics. Evidence has emerged of inhomogeneity of the distribution volume for extracellular tracers in different layers of the wall. An attempt is made to interpret results which indicate that distension per se of arteries and increase of medial smooth muscle tone tend to compact the medial interstitium whereas pressure driven convection across the wall tends to expand that tissue. These findings imply a potentially important role of endothelial permeability, smooth muscle tone and luminal pressure in influencing solute transport in the wall and wall transport properties.     

Flow-dependent concentration polarization and the endothelial glycocalyx layer: multi-scale aspects of arterial mass transport and their implications for atherosclerosis

Atherosclerosis is the underlying cause of most heart attacks and strokes. It is thereby the leading cause of death in the Western world, and it places a significant financial burden on health care systems. There is evidence that complex, multi-scale arterial mass transport processes play a key role in the development of atherosclerosis. Such processes can be controlled both by blood flow patterns and by properties of the arterial wall. This short review focuses on one vascular-scale, flow-regulated arterial mass transport process, namely concentration polarization of low density lipoprotein at the luminal surface of the arterial endothelium, and on one cellular-scale, structural determinant of arterial wall mass transport, namely the endothelial glycocalyx layer. Both have attracted significant attention in recent years. In addition to reviewing and appraising relevant literature, we propose various directions for future work.     

Nitric Oxide Transport in Normal Human Thoracic Aorta: Effects of Hemodynamics and Nitric Oxide Scavengers

Despite the crucial role of nitric oxide (NO) in the homeostasis of the vasculature, little quantitative information exists concerning NO transport and distribution in medium and large-sized arteries where atherosclerosis and aneurysm occur and hemodynamics is complex. We hypothesized that local hemodynamics in arteries may govern NO transport and affect the distribution of NO in the arteries, hence playing an important role in the localization of vascular diseases. To substantiate this hypothesis, we presented a lumen/wall model of the human aorta based on its MRI images to simulate the production, transport and consumption of NO in the arterial lumen and within the aortic wall. The results demonstrated that the distribution of NO in the aorta was quite uneven with remarkably reduced NO bioavailability in regions of disturbed flow, and local hemodynamics could affect NO distribution mainly via flow dependent NO production rate of endothelium. In addition, erythrocytes in the blood could moderately modulate NO concentration in the aorta, especially at the endothelial surface. However, the reaction of NO within the wall could only slightly affect NO concentration on the luminal surface, but strongly reduce NO concentration within the aortic wall. A strong positive correlation was revealed between wall shear stress and NO concentration, which was affected by local hemodynamics and NO reaction rate. In conclusion, the distribution of NO in the aorta may be determined by local hemodynamics and modulated differently by NO scavengers in the lumen and within the wall.     

Interstitial flow through the internal elastic lamina affects shear stress on arterial smooth muscle cells

Interstitial flow through the tunica media of an artery wall in the presence of the internal elastic lamina (IEL), which separates it from the subendothelial intima, has been studied numerically. A two-dimensional analysis applying the Brinkman model as the governing equation for the porous media flow field was performed. In the numerical simulation, the IEL was modeled as an impermeable barrier to water flux, except for the fenestral pores, which were uniformly distributed over the IEL. The tunica media was modeled as a heterogeneous medium composed of a periodic array of cylindrical smooth muscle cells (SMCs) embedded in a fiber matrix simulating the interstitial proteoglycan and collagen fibers. A series of calculations was conducted by varying the physical parameters describing the problem: the area fraction of the fenestral pore (0. 001-0.036), the diameter of the fenestral pore (0.4-4.0 microm), and the distance between the IEL and the nearest SMC (0.2-0.8 microm). The results indicate that the value of the average shear stress around the circumference of the SMC in the immediate vicinity of the fenestral pore could be as much as 100 times greater than that around an SMC in the fully developed interstitial flow region away from the IEL. These high shear stresses can affect SMC physiological function.     

Effects of diffusion coefficients and struts apposition using numerical simulations for drug eluting coronary stents

In the context of drug eluting stent, we present two-dimensional numerical models of mass transport of the drug in the wall and in the lumen to study the effect of the drug diffusion coefficients in the three principal media (blood, vascular wall, and polymer coating treated as a three-compartment problem) and the impact of different strut apposition configurations (fully embedded, half embedded, and not embedded). The different conditions were analyzed in terms of their consequence on the drug concentration distribution in the arterial wall. We apply the concept of the therapeutic window to the targeted vascular wall region and derive simple metrics to assess the efficiency of the various stent configurations. Although most of the drug is dispersed in the lumen, variations in the blood flow rate within the physiological range of coronary blood flow and the diffusivity of the drug molecule in the blood were shown to have a negligible effect on the amount of drug in the wall. Our results reveal that the amount of drug cumulated in the wall depends essentially on the relative values of the diffusion coefficients in the polymer coating and in the wall. Concerning the strut apposition, it is shown that the fully embedded strut configuration would provide a better concentration distribution.     

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.     

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.     

中华蟾蜍颈动脉腺的组织学结构

2005年10月～2006年5月,用组织学技术研究中华蟾蜍颈动脉腺结构。结果表明,颈动脉腺位于外颈动脉基部,圆球形,深红色至棕褐色。组织结构显示：颈动脉腺的外壁是动脉管壁的延续,包括外膜、中膜和内膜。整个外壁厚薄不均。颈动脉腺的最大特点是中膜和内膜并不像一般血管形成环圈状,而是从不同部位向管腔突出延伸、相互连接构成大小不一、形状各异、迂回曲折的网状血管。管腔大者,管壁厚,弹性纤维、平滑肌纤维多,内膜靠腔面内皮细胞多成立方状,细胞核端位近圆形;管腔小者,管壁薄,弹性纤维、平滑肌纤维少,内皮细胞扁平、排列稀疏,胞核长梭形;一些区域管径极小,管壁极薄,成为开放的血窦,只允许一个血细胞通过。网状管壁间有密集成团的大型类上皮细胞等细胞分布。据结构推测中华蟾蜍颈动脉腺有调节血压等功能。