Effect of the fluid-structure interactions on low-density lipoprotein transport within a multi-layered arterial wall

The effects of fluid-structure interactions (FSI) and pulsation on the transport of low-density lipoprotein (LDL) through an arterial wall are analyzed in this work. To this end, a comprehensive multi-layer model for both LDL transport as well as fluid-structure interaction (FSI) is introduced. The constructed model is analyzed and compared with the existing results in the limiting cases. Excellent agreement is found between the presented model and the existing results in the limiting cases. The presented model takes into account the complete multi-layered LDL transport while incorporating the FSI aspects to enable a comprehensive study of the deformation effect on the pertinent parameters of the transport processes within an artery. Since the flow inside an artery is time-dependent, the impact of pulsatile flow is also analyzed with and without FSI. A detailed analysis is presented to illustrate the consequence of different factors on the LDL transport in an artery.     

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.     

Impedance-based outflow boundary conditions for human carotid haemodynamics

In this study, we develop structured tree outflow boundary conditions for modelling the human carotid haemodynamics. The model geometry was reconstructed through computerised tomography scan. Unsteady-state computational fluid dynamic analyses were performed under different conditions using a commercial software package ADINA R&D, Inc., (Watertown, MA, USA) in order to assess the impact of the boundary conditions on the flow variables. In particular, the results showed that the peripheral vessels massively impact the pressure while the flow is relatively unaffected. As an example of application of these outflow conditions, an unsteady fluid-structure interaction (FSI) simulation was carried out and the dependence of the wall shear stress (WSS) on the arterial wall compliance in the carotid bifurcation was studied. In particular, a comparison between FSI and rigid-wall models was conducted. Results showed that the WSS distributions were substantially affected by the diameter variation of the arterial wall. In particular, even similar WSS distributions were found for both cases, and differences in the computed WSS values were also found.     

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.     

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.     

Simulation of LDL permeation into multilayer wall of a coronary bifurcation using WSS-dependent model: effects of hemorheology

Biomechanics and Modeling in Mechanobiology - Atherosclerosis, due to the permeation of low-density lipoprotein (LDL) particles into the arterial wall, is one of the most common and deadly diseases...     

Influence of non-Newtonian properties of blood on the wall shear stress in human atherosclerotic right coronary arteries

The objective of this work is to investigate the effect of non-Newtonian properties of blood on the wall shear stress (WSS) in atherosclerotic coronary arteries using both Newtonian and non-Newtonian models. Numerical simulations were performed to examine how the spatial and temporal WSS distributions are influenced by the stenosis size, blood viscosity, and flow rate. The computational results demonstrated that blood viscosity properties had considerable effect on the magnitude of the WSS, especially where disturbed flow was observed. The WSS distribution is highly non-uniform both temporally and spatially, especially in the stenotic region. The maximum WSS occurred at the proximal side of the stenosis, near the outer wall in the curved artery with no stenosis. The lumen area near the inner wall distal to the stenosis region experienced a lower WSS during the entire cardiac cycle. Among the factors of stenosis size, blood viscosity, and flow rate, the size of the stenosis has the most significant effect on the spatial and temporal WSS distributions qualitatively and quantitatively.     

Mechanobiology of low-density lipoprotein transport within an arterial wall—Impact of hyperthermia and coupling effects

The effects of hyperthermia, coupling attributes and property variations on Low-density lipoprotein (LDL) transport within a multi-layered wall while accounting for the fluid structure interaction (FSI) is analyzed in this work. To understand the potential impact of the hyperthermia process, thermo-induced attributes are incorporated, accounting for the plasma flow, mass transfer, as well as the elastic wall structure. The coupling effect of osmotic pressure, Soret and Dufour diffusion is discussed and their influence on LDL transport is examined, demonstrating that only the Soret effect needs to be accounted for. The effect of thermal expansion on changing the behavior of flow, mass transport, and elastic structure is illustrated and analyzed while incorporating the variations in the effective LDL diffusivity and consumption rate, as well as other dominating parameters. It is shown that hyperthermia results in an enhancement in LDL transport by increasing the concentration levels within the arterial wall.     

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.     

Haemodynamic assessment of human coronary arteries is affected by degree of freedom of artery movement

Abnormal haemodynamic parameters are associated with atheroma plaque progression and instability in coronary arteries. Flow recirculation, shear stress and pressure gradient are understood to be important pathogenic mediators in coronary disease. The effect of freedom of coronary artery movement on these parameters is still unknown. Fluid–structure interaction (FSI) simulations were carried out in 25 coronary artery models derived from authentic human coronaries in order to investigate the effect of degree of freedom of movement of the coronary arteries on flow recirculation, wall shear stress (WSS) and wall pressure gradient (WPG). Each FSI model had distinctive supports placed upon it. The quantitative and qualitative differences in flow recirculation, maximum wall shear stress (MWSS), areas of low wall shear stress (ALWSS) and maximum wall pressure gradient (MWPG) for each model were determined. The results showed that greater freedom of movement was associated with lower MWSS, smaller ALWSS, smaller flow recirculation zones and lower MWPG. With increasing percentage diameter stenosis (%DS), the effect of degree of freedom on flow recirculation and WSS diminished. Freedom of movement is an important variable to be considered for computational modelling of human coronary arteries, especially in the setting of mild to moderate stenosis.

Abbreviations: 3D: Three-dimensional; 3DR: Three-dimensional Reconstruction; 3D-QCA: Three-dimensional quantitative coronary angiography; ALWSS: Areas of low wall shear stress; CAD: Coronary artery disease; CFD: Computational fluid dynamics; %DS: Diameter stenosis percentage; EPCS: End point of counter-rotating streamlines; FSI: Fluid–structure interaction; IVUS: Intravascular ultrasound; LAD: Left anterior descending; MWSS: Maximum wall shear stress; SST: Shear stress transport; TAWSS: Time-averaged wall shear stress; WSS: wall shear stress; WPG: Wall pressure gradient; MWPG: Maximum wall pressure gradient; FFR: Fractional flow reserve; iFR: Instantaneous wave-free ratio     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

The influence of aortic dimensions on calculated wall shear stress in the mouse aortic arch

In this paper, the influence of the aortic dimensions of an investigated mouse on its resulting wall shear stress (WSS) was studied. A numerical model of a mouse aortic arch was created based on a micro-CT scan of a vascular corrosion cast of an 8-week-old wild type mouse. This model was then rescaled to obtain five models with aortic root diameters corresponding to five different stages in the mouse life cycle varying from late fetal (0.7 mm) to old adult (1.5 mm). Consistent with literature, WSS values much higher than those normally encountered in humans were found. WSS was found to decrease rapidly in early life stages and to reach a plateau in adulthood, thus supporting a mediating role for WSS in arterial growth. Our results show that WSS values for mice should be interpreted very cautiously, and if possible an animal-specific geometry with animal-specific boundary conditions should be used.     

壁剪应力变化对动脉重建影响的在体研究

为探讨动脉血流受阻后壁剪应力（Wall shear stress,WSS)变化对动脉适应性重建的影响,在60只实验兔建立动脉血流减小模型,术后0－30天8个不同时相点,检测动脉样本的壁厚及内径,单位面积（mm^2),动脉内皮细胞（Artereial endothelial cell,AEC）核数目和平滑肌细胞核数目。结果显示WSS变化通过调节动脉的舒缩而致使动脉管径适应性缩减,动脉壁腔比（WT／LD）保持恒定。动脉壁细胞成分中AEC受WSS变化的影响,而平滑肌细胞则不受影响。在术后3天、7天、AEC密度较正常对照显著降低（P＜0．01）;而在术后14天、30天,AEC密度显著增高（P＜0．01）。说明WSS对动脉适应性重建的影响,是通过调节动脉的舒缩所致,而非壁腔比的改变,WSS的变化在AEC的适应性重建过程中可能起着重要调节作用。     

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.     

Opposing effects of estrogen and progestins on LDL oxidation and vascular wall cytotoxicity: implications for atherogenesis

Estrogens are widely regarded as beneficial to arterial wall health. Among the mechanisms of this benefit are antioxidant effects on LDL and the arterial wall. Because progestins oppose the effect of estrogen in several systems, we asked if progestins oppose the antioxidant effect of estrogen. To study this question, LDL and various female sex hormones were incubated alone and combined in the absence or presence of bovine aortic endothelial cells, placental trophoblast, or macrophages, and LDL oxidation and cytotoxicity were quantitated. In the absence of cells, LDL incubated with copper in phosphate-buffered saline enhanced the oxidation of LDL. When 17beta-estradiol was added to this system, an antioxidant effect was observed. Progestins inhibited this protective estrogenic effect. In endothelial cell culture, progestins also opposed the antioxidant effect of estrogen, with the strongest antiestrogenic effect seen with the synthetic progestins, levonorgestrel and medroxyprogesterone acetate (MPA). Endothelial cell cytotoxicity was proportional to the enhanced lipid peroxide formation observed with progestins or estrogen. Similar opposing effects were seen when estrogen and progesterone were added to primary cultures of placental trophoblast or macrophages. Thus, three cell culture systems modeling circulating arterial blood contact with cell surfaces demonstrated opposing effects of estrogens and progestins on LDL oxidation and cell cytotoxicity. These studies are in keeping with published reports that female sex steroids influence LDL oxidation in vivo and consequent arterial wall injury.     

Lipid retention in the arterial wall of two mouse strains with different atherosclerosis susceptibility

LDL deposition in the subendothelium of arterial walls is the initial event in the development of atherosclerosis. The deposited LDL undergoes oxidative modification by arterial wall cells to become oxidized LDL and consequently contributes to atherosclerotic formation. Using mouse strains C57BL/6J (B6) and C3H/HeJ (C3H), which differ markedly in susceptibility to atherosclerosis, we determined whether variation in subendothelial retention of apolipoprotein B (apoB)-containing lipoproteins constitutes a genetic component in atherosclerosis. Lipoprotein retention was quantitated by Western blot analysis to detect the presence of apoB in aortic walls before foam cells developed. In both dietary and apoE-deficient models, B6 mice exhibited up to a 2-fold increase of apoB in the aortic wall compared with C3H mice. This increase could not be attributed to differences in plasma lipid levels of the two strains. In vitro, endothelial cells from C3H mice took up more acetylated and oxidized LDL but not native LDL and converted more native LDL to oxidized LDL than did endothelial cells from B6 mice. C3H mice expressed more scavenger receptor A in their aortic wall than B6 mice. Thus, variation in the subendothelial retention of apoB-containing lipoproteins cannot explain the dramatic difference in atherosclerosis susceptibility between B6 and C3H mice, and endothelial cells may play a role in alleviating lipid accumulation in arterial walls.     

Alterations in wall shear stress predict sites of neointimal hyperplasia after stent implantation in rabbit iliac arteries

Restenosis resulting from neointimal hyperplasia (NH) limits the effectiveness of intravascular stents. Rates of restenosis vary with stent geometry, but whether stents affect spatial and temporal distributions of wall shear stress (WSS) in vivo is unknown. We tested the hypothesis that alterations in spatial WSS after stent implantation predict sites of NH in rabbit iliac arteries. Antegrade iliac artery stent implantation was performed under angiography, and blood flow was measured before casting 14 or 21 days after implantation. Iliac artery blood flow domains were obtained from three-dimensional microfocal X-ray computed tomography imaging and reconstruction of the arterial casts. Indexes of WSS were determined using three-dimensional computational fluid dynamics. Vascular histology was unchanged proximal and distal to the stent. Time-dependent NH was localized within the stented region and was greatest in regions exposed to low WSS and acute elevations in spatial WSS gradients. The lowest values of WSS spatially localized to the stented area of a theoretical artery progressively increased after 14 and 21 days as NH occurred within these regions. This NH abolished spatial disparity in distributions of WSS. The results suggest that stents may introduce spatial alterations in WSS that modulate NH in vivo.     

Impact of plaques in the left coronary artery on wall shear stress and pressure gradient in coronary side branches

In this study, we investigate plaques located at the left coronary bifurcation. We focus on the effect that the resulting changes in wall shear stress (WSS) and wall pressure stress gradient (WPSG) have on atherosclerotic progress in coronary artery disease. Coronary plaques were simulated and placed at the left main stem and the left anterior descending to produce >50% narrowing of the coronary lumen. Computational fluid dynamics analysis was carried out, simulating realistic physiological conditions that show the in vivo cardiac haemodynamic. WSS and WPSG in the left coronary artery were calculated and compared in the left coronary models, with and without the presence of plaques during cardiac cycles. Our results showed that WSS decreased while WPSG was increased in coronary side branches due to the presence of plaques. There is a direct correlation between coronary plaques and subsequent WSS and WPSG variations based on the bifurcation plaques simulated in the realistic coronary models.     

Understanding the fluid mechanics behind transverse wall shear stress

The patchy distribution of atherosclerosis within arteries is widely attributed to local variation in haemodynamic wall shear stress (WSS). A recently-introduced metric, the transverse wall shear stress (transWSS), which is the average over the cardiac cycle of WSS components perpendicular to the temporal mean WSS vector, correlates particularly well with the pattern of lesions around aortic branch ostia. Here we use numerical methods to investigate the nature of the arterial flows captured by transWSS and the sensitivity of transWSS to inflow waveform and aortic geometry. TransWSS developed chiefly in the acceleration, peak systolic and deceleration phases of the cardiac cycle; the reverse flow phase was too short, and WSS in diastole was too low, for these periods to have a significant influence. Most of the spatial variation in transWSS arose from variation in the angle by which instantaneous WSS vectors deviated from the mean WSS vector rather than from variation in the magnitude of the vectors. The pattern of transWSS was insensitive to inflow waveform; only unphysiologically high Womersley numbers produced substantial changes. However, transWSS was sensitive to changes in geometry. The curvature of the arch and proximal descending aorta were responsible for the principal features, the non-planar nature of the aorta produced asymmetries in the location and position of streaks of high transWSS, and taper determined the persistence of the streaks down the aorta. These results reflect the importance of the fluctuating strength of Dean vortices in generating transWSS.