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.     

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.     

Factors that affect mass transport from drug eluting stents into the artery wall

Coronary artery disease can be treated by implanting a stent into the blocked region of an artery, thus enabling blood perfusion to distal vessels. Minimally invasive procedures of this nature often result in damage to the arterial tissue culminating in the re-blocking of the vessel. In an effort to alleviate this phenomenon, known as restenosis, drug eluting stents were developed. They are similar in composition to a bare metal stent but encompass a coating with therapeutic agents designed to reduce the overly aggressive healing response that contributes to restenosis. There are many variables that can influence the effectiveness of these therapeutic drugs being transported from the stent coating to and within the artery wall, many of which have been analysed and documented by researchers. However, the physical deformation of the artery substructure due to stent expansion, and its influence on a drugs ability to diffuse evenly within the artery wall have been lacking in published work to date. The paper highlights previous approaches adopted by researchers and proposes the addition of porous artery wall deformation to increase model accuracy.     

17beta-estradiol acts separately on the LDL particle and artery wall to reduce LDL accumulation

Estrogen replacement therapy has been shown to attenuate atherogenesis, although the mechanisms for this effect are incompletely defined. Previously, we showed that 17-beta estradiol (estradiol) attenuated oxidant stress-induced increases in vascular low density lipoprotein (LDL) accumulation. It was unclear whether estradiol's effect was imparted on the lipoprotein particle or the artery wall. To examine this, we chronically treated rats with the following sex hormones: low estradiol, high estradiol, progesterone, low estradiol + progesterone, placebo, or control. Carotid arteries (n = 8/group) were isolated and perfused with fluorescently labeled LDL. Rates of LDL accumulation were measured before and after treatment with 10 ng/ml tumor necrosis factor-alpha (TNF) using quantitative fluorescence microscopy. We observed a 50% decrease in basal LDL accumulation rates (P < 0.01) and a 25% decrease in endothelial layer permeability (P < 0.01) in arteries from estradiol-treated animals. There was no effect of hormone replacement on rate of TNF-induced LDL accumulation (P = 0.451), while incubation of LDL with 65 pg/ml estradiol attenuated the TNF effect (P < 0.01). These experiments suggest two independent mechanisms of anti-atherogenic protection by estradiol: 1) decreased endothelial layer permeability; and 2) incorporation of estradiol into the LDL particle and prevention of LDL binding to the artery wall.     

17beta-estradiol reduces tumor necrosis factor-alpha-mediated LDL accumulation in the artery wall

Estrogens have direct effects on the vascular wall that may prevent the development of atherosclerosis. In particular, estrogens, such as 17beta-estradiol (estradiol), are known to have potent antioxidant activity. Tumor necrosis factor-alpha (TNF) is found in human atheroma and produces oxygen-derived free radicals. These oxygen-derived free radicals may modify low density lipoproteins (LDL) and increase LDL binding in the artery wall. We asked: 1) does TNF increase LDL accumulation in the artery wall and 2) can the TNF-mediated increase in LDL accumulation be prevented by the antioxidant activity of estradiol? Carotid arteries from ovariectomized 3-month-old rats were removed and perfused with fluorescently labeled LDL and arterial LDL flux was measured using quantitative fluorescence microscopy. In six arteries, addition of TNF (10 ng/ml) to the perfusate resulted in a 2.3-fold increase in the rate of LDL accumulation (1.50 +/- 0.37 ng/min per cm2 vs. 3.38 +/- 0.48 ng/min per cm2; P < 0.01). Estradiol (65 pg/ml) and alpha-tocopherol (6 mg/L) both attenuated TNF-mediated LDL accumulation (P < 0.05), indicating that TNF may exert its effects on LDL accumulation through cellular production of oxygen-derived free radicals. These results support an antioxidant role for estradiol in the protection against LDL accumulation in the artery wall and subsequent progression of atherosclerosis.     

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.     

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.     

Numerical modelling of mass transport in an arterial wall with anisotropic transport properties

Coronary artery disease results in blockages or narrowing of the artery lumen. Drug eluting stents (DES) were developed to replace bare metal stents in an effort to combat re-blocking of the diseased artery following treatment. The numerical models developed within this study focus on representing the changing trends of drug delivery from an idealised DES in an arterial wall with an anisotropic ultra-structure. To reduce the computational burden of solving coupled physics problems, a model reduction strategy was adopted. Particular focus has been placed upon adequately modelling the influence of strut compression as there is a paucity of numerical studies that account for changes in transport properties in compressed regions of the arterial wall due to stent deployment. This study developed an idealised numerical modelling framework to account for the changes in the directionally dependent porosity and tortuosities of the arterial wall as a result of radial strut compression. The results show that depending on the degree of strut compression, trends in therapeutic drug delivery within the arterial wall can be either increased or decreased. The study highlights the importance of incorporating compression into numerical models to better represent transport within the arterial wall and suggests an appropriate numerical modelling framework that could be utilised in more realistic patient specific arterial geometries.     

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.     

Coupled oxygen transport analysis in the avascular wall of a post-angioplasty coronary artery stenosis

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied by numerically solving the convection-diffusion equations. Geometry, replicating residual stenosis after percutaneous transluminal coronary angioplasty (PTCA), is used for the analysis. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. Mean blood flow rate in the lumen is varied from basal to hyperemic conditions. The results show that the P(O2) in the medial region of the arterial wall is approximately 10 mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation there is a small rise and a sharp fall in the oxygen flux. The minimum P(O2) in the avascular wall, P(O2, min ), at the point of flow reattachment reduces to approximately 6 mmHg for a 300 micron wall thickness. For a thinner wall of 200 micron, the P(O2, min ) at the location of flow reattachment increases to 6 times that of a 300 micron wall. The P(O2, min ) in the wall decreases by 60% when volumetric oxygen consumption is increased by 30% for the same avascular wall thickness.     

Computational analysis of confined jet flow and mass transport in a blind tube.

A computational analysis of confined nonimpinging jet flow in a blind tube is performed as an initial investigation of the underlying fluid and mass transport mechanics of tracheal gas insufflation. A two-dimensional axisymmetric model of a laminar steady jet flow into a concentric blind-end tube is put forth and the governing continuity, momentum, and convection-diffusion equations are solved with a finite element code. The effects of the jet diameter based Reynolds number (Re(j)), the ratio of the jet-to-outer tube diameters (epsilon), and the Schmidt number (Sc) are evaluated with the determined velocity and contaminant concentration fields. The normalized penetration depth of the jet is found to increase linearly with increasing Re(j) for epsilon = O(0.1). For a given epsilon, a ring vortex that develops is observed to be displaced downstream and radially outward from the jet tip for increasing Re(j). The axial shear stress profile along the inside wall of the outer tube possesses regions of fixed shear stress in addition to a local minimum and maximum in the vicinity of the jet tip. Corresponding regions of axial shear stress gradients exist between the fixed shear stress regions and the local extrema. Contaminant concentration gradients develop across the ring vortex indicating the inward diffusion of contaminant into the jet flow. For fixed epsilon and Sc and Re(j) approximately 900, normalized contaminant flow rate is observed to be approximately twice that of simple diffusion. This model predicts modest net axial contaminant transport enhancement due to convection-diffusion interaction in the region of the ring vortex.     

Computational modeling of blood component transport related to coronary artery thrombosis in Kawasaki disease

Coronary artery thrombosis is the major risk associated with Kawasaki disease (KD). Long-term management of KD patients with persistent aneurysms requires a thrombotic risk assessment and clinical decisions regarding the administration of anticoagulation therapy. Computational fluid dynamics has demonstrated that abnormal KD coronary artery hemodynamics can be associated with thrombosis. However, the underlying mechanisms of clot formation are not yet fully understood. Here we present a new model incorporating data from patient-specific simulated velocity fields to track platelet activation and accumulation. We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite element method to describe the evolution of non-activated platelets and activated platelet concentrations [AP], local concentrations of adenosine diphosphate (ADP) and poly-phosphate (PolyP). The activation of platelets is modeled as a function of shear-rate exposure and local concentration of agonists. We compared the distribution of activated platelets in a healthy coronary case and six cases with coronary artery aneurysms caused by KD, including three with confirmed thrombosis. Results show spatial correlation between regions of higher concentration of activated platelets and the reported location of the clot, suggesting predictive capabilities of this model towards identifying regions at high risk for thrombosis. Also, the concentration levels of ADP and PolyP in cases with confirmed thrombosis are higher than the reported critical values associated with platelet aggregation (ADP) and activation of the intrinsic coagulation pathway (PolyP). These findings suggest the potential initiation of a coagulation pathway even in the absence of an extrinsic factor. Finally, computational simulations show that in regions of flow stagnation, biochemical activation, as a result of local agonist concentration, is dominant. Identifying the leading factors to a pro-coagulant environment in each case—mechanical or biochemical—could help define improved strategies for thrombosis prevention tailored for each patient.     

Coupled oxygen transport analysis in the avascular wall of a coronary artery stenosis during angioplasty

The coupled oxygen transport in the avascular wall of a coronary artery stenosis is studied numerically by solving the convection-diffusion equations. Two geometries replicating stenosis before and after percutaneous transluminal coronary angioplasty (PTCA) are used for the analysis. The results are compared to evaluate the effect of the degree of stenosis on oxygen transport. Important physiological aspects, such as oxygen consumption in the wall, oxygen carried by the hemoglobin, non-Newtonian viscosity of the blood, and supply of oxygen from the vasa vasorum are included. The results show that the PO2 in the medial region of the arterial wall is approximately 10mmHg. The oxygen flux to the wall increases in the flow acceleration region, whereas it decreases at the flow reattachment zone. Near the location of flow separation, there is a small rise followed by a sharp fall in the oxygen flux. The drop in the oxygen flux to the wall at the point of flow reattachment for pre-PTCA stenosis is four times that for post-PTCA stenosis. The minimum PO2 in the avascular wall, PO2,min, at this location decreases to approximately 6.0 and 4.2mmHg for post- and pre-PTCA stenosis, respectively. The drop in PO2,w and PO2,min at the point of flow reattachment for pre-PTCA is approximately 2 times that for post-PTCA stenosis. Thus, the present study quantifies the oxygen transport to the arterial wall before and after cardiovascular intervention.     

Computational fluid dynamics modeling of momentum transport in rotating wall perfused bioreactor for cartilage tissue engineering

In this study, computational fluid dynamics (CFD) analysis of a rotating-wall perfused-vessel (RWPV) bioreactor is performed to characterize the complex hydrodynamic environment for the simulation of cartilage development in RWPV bioreactor in the presence of tissue-engineered cartilage constructs, i.e., cell-chitosan scaffolds. Shear stress exerted on chitosan scaffolds in bioreactor was calculated for different rotational velocities in the range of 33-38 rpm. According to the calculations, the lateral and lower surfaces were exposed to 0.07926-0.11069 dyne/cm(2) and 0.05974-0.08345 dyne/cm(2), respectively, while upper surfaces of constructs were exposed to 0.09196-0.12847 dyne/cm(2). Results validate adequate hydrodynamic environment for scaffolds in RWPV bioreactor for cartilage tissue development which concludes the suitability of operational conditions of RWPV bioreactor.     

In vitro study of LDL transport under pressurized (convective) conditions

It is difficult to assess the transport pathways that carry low-density lipoprotein (LDL) into the artery wall in vivo, and there has been no previous in vitro study that has examined transendothelial transport under physiologically relevant pressurized (convective) conditions. Therefore, we measured water, albumin, and LDL fluxes across bovine aortic endothelial cell (BAEC) monolayers in vitro and determined the relative contributions of vesicles, paracellular transport through "breaks" in the tight junction, and "leaky" junctions associated with dying or dividing cells. Our results show that leaky junctions are the dominant pathway for LDL transport (>90%) under convective conditions and that albumin also has a significant component of transport through leaky junctions (44%). Transcellular transport of LDL by receptor-mediated processes makes a minor contribution (<10%) to overall transport under convective conditions.     

Topological analysis of wall mass transport using a luminescent immobilized enzymatic system

A new technique of visualization of diffusion-convection phenomena at a solid-liquid interface using the luminol chemiluminescent reaction catalyzed by immobilized peroxidase has been previously described (Dimicoli, J.L., M. Nakache, and P. Peronneau, 1982, Biorheology, 19:281-300). We propose now a theoretical model that predicts quantitatively the light fluxes, JL, corresponding to the transfer J of the hydrogen peroxide substrate at the liquid-solid interface in a cylindrical tube for continuous flow experiments. A simple phenomenological relation, J alpha J1/mL (1 less than m less than 3) was first established for each point of the wall. Then, numerical integration showed that, independent of the laminar or turbulent character of the flow, J1/mL was proportional to (S1 Kideal)/(1 + Kideal/ET), where S1 is the bulk substrate concentration, Kideal is the ideal transport coefficient, and ET (in cm.S-1) a phenomenological first-order enzymatic rate constant per unit of wall surface. This relation proved to be satisfactory for all experimental conditions since a single mean value of ET takes into account the experimental data collected for a given enzymated tube in a large range of Reynolds number values (Re) (500 less than Re less than 9,000) and of distances from the entrance of the tube (chi greater than 0.3 cm). This quantitative analysis using a pseudo-first-order approximation interprets the observed great dependence of JL on Re(JL alpha Ren', with n' usually greater than 1/3 for laminar flows) and on S1 (JL alpha S1m). It predicts also that the laminar-to-turbulent transition can be evidenced for interfacial enzymatic activity, ET greater than 2.10(-4) cm.S-1, as observed with most of the tubes prepared by covalent binding of peroxidase on the acrylamide gel wall. The experiment had to be carried out at a pH value of 8, which corresponds to the fastest rate of the chemiluminescent reaction. The predicted entrance effects were also observed experimentally for the first time in an immobilized enzyme system. This technique appears therefore to be a valuable tool for the quantitative analysis of diffusion-convection phenomena at a liquid-solid interface with a good spatial resolution with a great range of flow rate.     

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.     

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.