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

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

Atherosclerosis, due to the permeation of low-density lipoprotein (LDL) particles into the arterial wall, is one of the most common and deadly diseases in today's world. Due to its importance, numerous studies have been conducted on the factors affecting this disease. In this study, using numerical simulation, the effects of Wall Shear Stress (WSS), non-Newtonian behavior of blood, different values of hematocrit and blood pressure on LDL permeation into the arterial wall layers are investigated in a 4-layer wall model of a coronary bifurcation. To obtain the velocity and concentration fields in the fluid domain, the Navier-Stokes, Brinkman, and mass transfer equations are numerically solved in the lumen and wall layers. Results show that it is important to consider the effects of WSS on transport properties of endothelium layer in bifurcations and this leads to completely different concentration profiles compared to the constant properties model. Our computations show that a giant accumulation of LDL in the intima layer of the outer wall of the left anterior descending artery, especially in low WSS regions, may lead to atherosclerosis. It is also, necessary to consider the non-Newtonian behavior of blood in bifurcations due to its direct effect on WSS. A pressure-induced increase in the half-width of leaky junctions may be responsible for the higher risk of atherosclerosis in hypertension. In addition, it is shown that the dominant mechanism in LDL permeation into the wall is convection, and also, hypertension increases the effect of mass transfer by convection mechanism more than the diffusion mechanism. Furthermore, our results are consistent with various clinical studies.

Effect of Extended Lipid Core on the Hemodynamic Parameters: A Fluid-Structure Interaction Approach

Myocardial infarction is one of the leading causes of death in the developed countries. A majority of myocardial infarctions are caused by the rupture of coronary artery plaques. In order to achieve a better understanding of the effect of the extension of the lipid core into the artery wall on the change of flow field and its effect on plaque vulnerability, we have studied the hemodynamic parameters by utilizing a finite element method and taking into account the fluid-structure interaction (FSI). Four groups of stenosis models with different sizes of lipid core were used in the study. The fully developed pulsatile velocity profile of the right coronary artery was used as the inlet boundary condition, and the pressure pulse was applied as the outlet boundary condition. The non-Newtonian Carreau model was used to simulate the non-Newtonian behavior of blood. Results indicate that the extension of the lipid core into the artery wall influences the flow field; subsequently, creates favorable conditions for additional development of the lipid core which can lead to a higher risk of plaque rupture.

Numerical simulation of pulsatile blood flow characteristics in a multi stenosed coronary artery

BACKGROUND

Coronary artery disease is reported as one of the most common sources of death all over the world. The presence of stenosis (plaque) in the coronary arteries results in the restriction of blood supply, which leads to myocardial infarction.

OBJECTIVE

The aim of this study was to investigate the effect of multi stenosis on hemodynamics parameters in idealized coronary artery models with varying degrees of stenosis and interspace distance between the stenosis.

METHODS

A finite volume-based software package (Ansys CFX version 17.2) was employed to model the blood flow. The hemodynamic stenosis parameters of blood, such as the pressure, velocity, and wall shear stress were obtained.

RESULTS

The computed results showed that the pressure drop is maximum across the 90% area stenosis (AS). The pressure drop is increased as the distance between the proximal and distal stenosis is decreased across the proximal stenosis for the model P70_D70 during the systolic period of the cardiac cycle. A recirculation zone is formed behind the stenosis and is restricted by the occurrence of distal stenosis as the interspacing distance decreases, which could lead to further progression of stenosis in the flow-disturbed area. The wall shear stress was found to increase as the distance between the proximal and distal stenosis is increased across the distal stenosis. The maximum wall shear stress was found at 90% AS.

CONCLUSIONS

In the clinical diagnosis, an overestimation of distal stenosis severity could be possible. Furthermore, the low wall shear stress zone in between the proximal and distal stenosis may help atherosclerotic growth or merge adjacent stenosis.

A study on the transport and interaction between blood flow and low-density-lipoprotein in near-wall regions of blood vessels

Differences in the dynamics and transport of blood make certain regions of the arterial network the preferred sites for initiation and formation of arterial diseases like stenosis and aneurysms. Understanding of such arterial diseases is directly linked to critical hemodynamic parameters such as the wall shear stress (WSS). The present work generalises the influence of WSS on the concentration of LDL that was observed in an earlier study. To this end, a wide variety of simplified flow domain, inspired by the near-wall regions of aneurysms and stenosis, are constructed and analyzed. The effects of pulsatile inflow condition, rheology of blood and curvature of the wall on the correlation between WSS and LDL concentration are investigated. It is demonstrated that the time-scale of variation of lumen-surface-concentration (LSC) of LDL is larger than a single cardiac cycle. As a consequence, the time-average values of WSS are sufficient to locate the regions of higher LSC. This idea is strengthened by making use of simplified flow domain that generates moving stagnation point. Further, it was observed that the rheology of the blood and curvature of the wall does not affect the observed correlation between the WSS and LDL concentration.

The Story of Wall Shear Stress in Coronary Artery Atherosclerosis: Biochemical Transport and Mechanotransduction

Coronary artery atherosclerosis is a local, multifactorial, complex disease, and the leading cause of death in the US. Complex interactions between biochemical transport and biomechanical forces influence disease growth. Wall shear stress (WSS) affects coronary artery atherosclerosis by inducing endothelial cell mechanotransduction and by controlling the near-wall transport processes involved in atherosclerosis. Each of these processes is controlled by WSS differently and therefore has complicated the interpretation of WSS in atherosclerosis. In this paper, we present a comprehensive theory for WSS in atherosclerosis. First, a short review of shear stress-mediated mechanotransduction in atherosclerosis was presented. Next, subject-specific computational fluid dynamics (CFD) simulations were performed in ten coronary artery models of diseased and healthy subjects. Biochemical-specific mass transport models were developed to study low-density lipoprotein, nitric oxide, adenosine triphosphate, oxygen, monocyte chemoattractant protein-1, and monocyte transport. The transport results were compared with WSS vectors and WSS Lagrangian coherent structures (WSS LCS). High WSS magnitude protected against atherosclerosis by increasing the production or flux of atheroprotective biochemicals and decreasing the near-wall localization of atherogenic biochemicals. Low WSS magnitude promoted atherosclerosis by increasing atherogenic biochemical localization. Finally, the attracting WSS LCS's role was more complex where it promoted or prevented atherosclerosis based on different biochemicals. We present a summary of the different pathways by which WSS influences coronary artery atherosclerosis and compare different mechanotransduction and biotransport mechanisms.

The Effect of Hematocrit and Nanoparticles Diameter on Hemodynamic Parameters and Drug Delivery in Abdominal Aortic Aneurysm with Consideration of Blood Pulsatile Flow

BACKGROUND AND OBJECTIVE

The present article has simulated to investigate the efficient hemodynamic parameters, the drug persistence, and drug distribution on an abdominal aortic aneurysm.

METHODS

Blood as a non-Newtonian fluid enters the artery acting as a real pulse waveform; its behavior is dependent on hematocrit and strain rate. In this simulation of computational fluid dynamic, magnetic nanoparticles of iron oxide which were in advance coated with the drug, are injected into the artery during a cardiac cycle. A two-phase model was applied to investigate the distribution of these carriers.

RESULTS

The results are presented for different hematocrits and the nanoparticle diameter. It is observed that hematocrit significantly affects drug persistence, so that lower hematocrit incites more accumulation of the drug in the dilatation part of the artery. The better drug accumulation is noticed, at the higher wall shear stress. Although no considerable impact on the flow pattern and wall shear stress was found with various nanoparticle diameters, the smaller size of the nanoparticles results in a greater amount of drug augmentation in the aneurysm wall output.

CONCLUSIONS

At the higher hematocrit levels, the blood resistance to drug delivery increases throughout the artery. Also, the drug accumulates less on the aneurysm wall and stays longer on the aneurysm wall. On the contrary, the drug accumulates more by decreasing hematocrit level and stays shorter on the aneurysm wall. Moreover, the maximum drug concentration is observed at the lowest hematocrit level and nanoparticle diameter; also, the diameter of nanoparticles imposes no significant effect on the vorticity and wall shear stress. It is seen that the increment of the hematocrit level reduces the strength of vorticity and increases the amount of wall shear stress in the dilatation segment of the artery. The shear stress at three points of the dilatation wall is extreme, where the maximum density of nanoparticles occurs.

Coronary artery plaque growth: A two-way coupled shear stress-driven model

Atherosclerosis in coronary arteries can lead to plaque growth, stenosis formation, and blockage of the blood flow supplying the heart tissue. Several studies have shown that hemodynamics play an important role in the growth of coronary artery plaques. Specifically, low wall shear stress (WSS) appears to be the leading hemodynamic parameter promoting atherosclerotic plaque growth, which in turn influences the blood flow and WSS distribution. Therefore, a two-way coupled interaction exists between WSS and atherosclerosis growth. In this work, a computational framework was developed to study the coupling between WSS and plaque growth in coronary arteries. Computational fluid dynamics (CFD) was used to quantify WSS distribution. Surface mesh nodes were moved in the inward normal direction according to a growth model based on WSS. After each growth stage, the geometry was updated and the CFD simulation repeated to find updated WSS values for the next growth stage. One hundred twenty growth stages were simulated in an idealized tube and an image-based left anterior descending artery. An automated framework was developed using open-source software to couple CFD simulations with growth. Changes in plaque morphology and hemodynamic patterns during different growth stages are presented. The results show larger plaque growth towards the downstream segment of the plaque, agreeing with the reported clinical observations. The developed framework could be used to establish hemodynamic-driven growth models and study the interaction between these processes.

Effect of arterial curvature on hemodynamics and mass transport

BACKGROUND

Atherosclerotic lesions develop preferentially at certain sites in the human arterial system, such as the inner wall of curved segments and the outer wall of bifurcations. Local wall shear stress (WSS) and concentration of low density lipoprotein (LDL) have been identified as two important factors contributing to these lesions.

OBJECTIVE

To determine if a connection exists between arterial curvature and the formation of atherosclerosis.

METHODS

A set of 3-D vessel models with different bend angles was constructed. By comparing blood flow, WSS, and LDL aggregation, the influence of bend curvature on atherosclerotic lesions was assessed.

RESULTS

Upon increasing arterial bending, low WSS regions were formed at the outer wall of the junction between straight and curved segments, as well as the inner wall of curved segments. However, high LDL concentrations only appeared at the inner wall of the bend region. A connection between secondary flow and LDL concentration was observed; high LDL concentration regions had stronger secondary flow. Higher water infiltration velocity could enhance LDL aggregation, while blood non-Newtonian properties, by easing secondary flow, diminished its aggregation.

CONCLUSIONS

Under the same flow rate, a larger bend angle increased flow resistance, lowered WSS, and increased LDL surface concentrations, thus indicating an increased risk of atherosclerosis.

Mathematical Modelling and Simulation of Atherosclerosis Formation and Progress: A Review

Cardiovascular disease (CVD) is a major threat to human health since it is the leading cause of death in western countries. Atherosclerosis is a type of CVD related to hypertension, diabetes, high levels of cholesterol, smoking, oxidative stress, and age. Atherosclerosis primarily occurs in medium and large arteries, such as coronary and the carotid artery and, in particular, at bifurcations and curvatures. Atherosclerosis is compared to an inflammatory disease where a thick, porous material comprising cholesterol fat, saturated sterols, proteins, fatty acids, calcium etc., is covered by an endothelial membrane and a fragile fibrous tissue which makes atheromatic plaque prone to rupture that could lead to the blockage of the artery due to the released plaque material. Despite the great progress achieved, the nature of the disease is not fully understood. This paper reviews the current state of modelling of all levels of atherosclerosis formation and progress and discusses further challenges in atherosclerosis modelling. The objective is to pave a way towards more precise computational tools to predict and eventually reengineer the fate of atherosclerosis.

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

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.

Numerical simulation of low-density lipoprotein mass transport in human arterial stenosis - Calculation of the filtration velocity

Accumulation of cholesterol and other atherogenic lipids such as low-density lipoprotein (LDL) in artery wall causes reduction of vessel diameter and artery stenosis. The study of the mass transfer of these large molecules in the wall with considering effective factors on lumen flow and different physiological factors is the subject considered nowadays. In this paper, results of two dimensional and axi-symmetric simulations of three different models of the artery with 60% stenosis under pulsatile blood flow are presented. Filtration velocity of LDL mass transport in the permeable artery wall and shear stress of blood flow are investigated using ADINA software Three different flow models are considered. In the first and second models, the filtration velocity considered as a given parameter and constant in arterial wall boundary, while in third model arterial wall considered as porous wall, the filtration velocity is calculated from pressure difference as an input parameter of the model. The results show that filtration velocity is strongly depend on geometry and it is not constant along the wall, contrary to simplified models. The results of concentration variations in lumen and wall illustrate the increase in near wall LDL concentration or concentration polarization.

Analysis of non-Newtonian effects on Low-Density Lipoprotein accumulation in an artery

In this work, non-Newtonian effects on Low-Density Lipoprotein (LDL) transport across an artery are analyzed with a multi-layer model. Four rheological models (Carreau, Carreau-Yasuda, power-law and Newtonian) are used for the blood flow through the lumen. For the non-Newtonian cases, the arterial wall is modeled with a generalized momentum equation. Convection-diffusion equation is used for the LDL transport through the lumen, while Staverman-Kedem-Katchalsky, combined with porous media equations, are used for the LDL transport through the wall. Results are presented in terms of filtration velocity, Wall Shear Stresses (WSS) and concentration profiles. It is shown that non-Newtonian effects on mass transport are negligible for a healthy intramural pressure value. Non-Newtonian effects increase slightly with intramural pressure, but Newtonian assumption can still be considered reliable. Effects of arterial size are also analyzed, showing that Newtonian assumption can be considered valid for both medium and large arteries, in predicting LDL deposition. Finally, non-Newtonian effects are also analyzed for an aorta-common iliac bifurcation, showing that Newtonian assumption is valid for mass transport at low Reynolds numbers. At a high Reynolds number, it has been shown that a non-Newtonian fluid model can have more impact due to the presence of flow recirculation.

A reduced-dimensional model for near-wall transport in cardiovascular flows

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow.

Low-density lipoprotein accumulation within a carotid artery with multilayer elastic porous wall: fluid-structure interaction and non-Newtonian considerations

Low-density lipoprotein (LDL), which is recognized as bad cholesterol, typically has been regarded as a main cause of atherosclerosis. LDL infiltration across arterial wall and subsequent formation of Ox-LDL could lead to atherogenesis. In the present study, combined effects of non-Newtonian fluid behavior and fluid-structure interaction (FSI) on LDL mass transfer inside an artery and through its multilayer arterial wall are examined numerically. Navier-Stokes equations for the blood flow inside the lumen and modified Darcy's model for the power-law fluid through the porous arterial wall are coupled with the equations of mass transfer to describe LDL distributions in various segments of the artery. In addition, the arterial wall is considered as a heterogeneous permeable elastic medium. Thus, elastodynamics equation is invoked to examine effects of different wall elasticity on LDL distribution in the artery. Findings suggest that non-Newtonian behavior of filtrated plasma within the wall enhances LDL accumulation meaningfully. Moreover, results demonstrate that at high blood pressure and due to the wall elasticity, endothelium pores expand, which cause significant variations on endothelium physiological properties in a way that lead to higher LDL accumulation. Additionally, results describe that under hypertension, by increasing angular strain, endothelial junctions especially at leaky sites expand more dramatic for the high elastic model, which in turn causes higher LDL accumulation across the intima layer and elevates atherogenesis risk.

Analysis of flow and LDL concentration polarization in siphon of internal carotid artery: Non-Newtonian effects

Carotid siphon is known as one of the risky sites among the human intracranial arteries, which is prone to formation of atherosclerotic lesions. Indeed, scientists believe that accumulation of low density lipoprotein (LDL) inside the lumen is the major cause of atherosclerosis. To this aim, three types of internal carotid artery (ICA) siphon have been constructed to examine variations of hemodynamic parameters in different regions of the arteries. Providing real physiological conditions, blood considered as non-Newtonian fluid and real velocity and pressure waveforms have been employed as flow boundary conditions. Moreover, to have a better estimation of risky sites, the accumulation of LDL particles has been considered, which has been usually ignored in previous relevant studies. Governing equations have been discretized and solved via open source OpenFOAM software. A new solver has been built to meet essential parameters related to the flow and mass transfer phenomena. In contrast to the common belief regarding negligible effect of blood non-Newtonian behavior inside large arteries, current study suggests that the non-Newtonian blood behavior is notable, especially on the velocity field of the U-type model. In addition, it is concluded that neglecting non-Newtonian effects underestimates the LDL accumulation up to 3% in the U-type model at the inner side of both its bends. However, in the V and C type models, non-Newtonian effects become relatively small. Results also emphasize that the outer part of the second bend at the downstream is also at risk similar to the inner part of the carotid bends. Furthermore, from findings it can be implied that the risky sites strongly depend on the ICA shape since the extension of the risky sites are relatively larger for the V-type model, while the LDL concentrations are higher for the C-type model.

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

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

SIMULATION OF PULSATILE BLOOD FLOW THROUGH STENOTIC ARTERY CONSIDERING DIFFERENT BLOOD RHEOLOGIES: COMPARISON OF 3D AND 2D-AXISYMMETRIC MODELS

Hemodynamic factors such as velocity distribution, pressure gradient and wall shear stress are thought to play an important role in the prognosis of symptomatic carotid occlusion. Although there are many studies about modeling the blood flow behavior in carotid, hemodynamic characteristics of blood flow in a stenosed carotid artery is still debatable. In this study a three-dimensional (3D) model of a symmetric stenosed common carotid artery (CCA) is developed and the simulation results of it are compared to the experimental data where subsequent agreement is confirmed. To study the accuracy of two-dimensional (2D) axisymmetric model, the result of it is compared to the result of the 3D model. Two non-Newtonian rheological models, namely Carreau and modified Power-law, as well as Newtonian model are used to realize the hemodynamical differences of 2D-axisymmetric and 3D models in pulsatile blood flow. Comparing the 3D simulated results with 2D-axisymmetric modeling results that were published in recent years indicates that the assumption of 2D-axisymmetric model cannot adequately predict the velocity profiles even for a symmetric stenotic artery. Although a symmetric stenotic artery is considered, the results indicate a nonsymmetric flow in poststenosis region that is detected by the presence of extensive secondary flows particularly at diastole. The existence of secondary flows that can only be detected in 3D modeling is the main reason for the differences in hemodynamic factors in 3D and 2D results.