Mahsa Dabagh

The transport of LDL across the deformable arterial wall: the effect of endothelial cell turnover and intimal deformation under hypertension

A multilayered model of the aortic wall is introduced to investigate the transport of low-density lipoprotein (LDL) under hypertension, taking into account the influences of increased endothelial cell turnover and deformation of the intima at higher pressure. Meanwhile, the thickness and properties of the endothelium, intima, internal elastic lamina (IEL), and media are affected by the transmural pressure. The LDL macromolecules enter the intima through leaky junctions over the endothelium, which are created by dying or dividing cells. Water molecules enter the intima via the paracellular pathway through breaks in tight junctions after passing the glycocalyx as well as through leaky junctions. The glycocalyx is modeled as a Brinkman porous medium to describe the fluid filtration associated with its structure. Combined Navier-Stokes and Brinkman equations are solved for the transmural flow, and the convective-diffusion equation is employed for LDL transport. The permeation of LDL over the surface of smooth muscle cells is modeled through a uniform reaction evenly distributed in the macroscopically homogeneous media layer. Simulations are performed in an axisymmetric plane centered at a leaky cell. The overriding issue addressed is that LDL fluxes across the leaky junction, the intima, fenestral pores in the IEL, and the media layer are highly affected by the transmural pressure, which affects the endothelial cell turnover rate and the compaction of intima. The present model, for the first time and with no adjustable parameters, is capable of making many realistic predictions including the proper magnitudes for the permeability of endothelium and intimal layers and the hydraulic conductivity of all layers as well as their trends with pressure. Results for the volume flux through the wall and the hydraulic conductivity of the entire arterial wall, the endothelium, and subendothelial layers at 70 and 180 mmHg are in good agreement with previous experimental studies.

Finite element modelling of pulsatile blood flow in idealized model of human aortic arch: study of hypotension and hypertension.

A three-dimensional computer model of human aortic arch with three branches is reproduced to study the pulsatile blood flow with Finite Element Method. In specific, the focus is on variation of wall shear stress, which plays an important role in the localization and development of atherosclerotic plaques. Pulsatile pressure pulse is used as boundary condition to avoid flow entry development, and the aorta walls are considered rigid. The aorta model along with boundary conditions is altered to study the effect of hypotension and hypertension. The results illustrated low and fluctuating shear stress at outer and inner wall of aortic arch, proximal wall of branches, and entry region. Despite the simplification of aorta model, rigid walls and other assumptions results displayed that hypertension causes lowered local wall shear stresses. It is the sign of an increased risk of atherosclerosis. The assessment of hemodynamics shows that under the flow regimes of hypotension and hypertension, the risk of atherosclerosis localization in human aorta may increase.

Shear-induced force transmission in a multicomponent, multicell model of the endothelium

Haemodynamic forces applied at the apical surface of vascular endothelial cells (ECs) provide the mechanical signals at intracellular organelles and through the inter-connected cellular network. The objective of this study is to quantify the intracellular and intercellular stresses in a confluent vascular EC monolayer. A novel three-dimensional, multiscale and multicomponent model of focally adhered ECs is developed to account for the role of potential mechanosensors (glycocalyx layer, actin cortical layer, nucleus, cytoskeleton, focal adhesions (FAs) and adherens junctions (ADJs)) in mechanotransmission and EC deformation. The overriding issue addressed is the stress amplification in these regions, which may play a role in subcellular localization of mechanotransmission. The model predicts that the stresses are amplified 250–600-fold over apical values at ADJs and 175–200-fold at FAs for ECs exposed to a mean shear stress of 10 dyne cm−2. Estimates of forces per molecule in the cell attachment points to the external cellular matrix and cell–cell adhesion points are of the order of 8 pN at FAs and as high as 3 pN at ADJs, suggesting that direct force-induced mechanotransmission by single molecules is possible in both. The maximum deformation of an EC in the monolayer is calculated as 400 nm in response to a mean shear stress of 1 Pa applied over the EC surface which is in accord with measurements. The model also predicts that the magnitude of the cell–cell junction inclination angle is independent of the cytoskeleton and glycocalyx. The inclination angle of the cell–cell junction is calculated to be 6.6° in an EC monolayer, which is somewhat below the measured value (9.9°) reported previously for ECs subjected to 1.6 Pa shear stress for 30 min. The present model is able, for the first time, to cross the boundaries between different length scales in order to provide a global view of potential locations of mechanotransmission.

The study of wall deformation and flow distribution with transmural pressure by three-dimensional model of thoracic aorta wall

The sensitivity of shear stress over smooth muscle cells (SMCs) to the deformability of media layer due to pressure is investigated in thoracic aorta wall using three-dimensional simulations. A biphasic, anisotropic model assuming the radius, thickness, and hydraulic conductivity of vessel wall as functions of transmural pressure is employed in numerical simulations. The leakage of interstitial fluid from intima to media layer is only possible through fenestral pores on the internal elastic lamina (IEL). The media layer is assumed a heterogeneous medium containing SMCs embedded in a porous extracellular matrix of elastin, proteoglycan, and collagen fibers. The applicable pressures for the deformation of media layer are varied from 0 to 180 mmHg. The SMCs are cylindrical objects of circular cross section at zero pressure. The cross sectional shape of SMCs changes from circle to ellipse as the media is compressed. The local shear stress over the nearest SMC to the IEL profoundly depends on pressure, SMCs configurations, and the corresponding distance to the IEL. The consideration of various SMC configurations, namely the staggered and square arrays, mimics various physiological conditions that can happen in positioning of an SMC. The results of our simulations show that even the second nearest SMCs to the IEL can significantly change their functions due to high shear stress levels. This is in contrast to earlier studies suggesting the highest vulnerability to shear stress for the innermost layer of SMCs at the intimal-medial interface.

Effect of the shape and configuration of smooth muscle cells on the diffusion of ATP through the arterial wall

In this study, the shape and the configuration of smooth muscle cells (SMCs) within the arterial wall are altered to investigate their influence on molecular transport across the media layer of the thoracic aorta wall. In a 2D geometry of the media layer containing SMCs, the finite-element method has been employed to simulate the diffusion of solutes through the media layer. The media is modeled as a heterogeneous system composed of SMCs having elliptic or circular cross sections embedded in a homogeneous porous medium made of proteoglycan and collagen fibers with an interstitial fluid filling the void. The arrangement of SMCs is in either ordered or disordered fashion for different volume fractions of SMCs. The interstitial fluid enters the media through fenestral pores, which are assumed to be distributed uniformly over the internal elastic lamina (IEL). Results revealed that in an ordered arrangement of SMCs, the concentration of adenosine 5′-triphosphate (ATP) over the surface of SMCs with an elliptic cross section is 5–8% more than those of circular SMCs in volume fractions of 0.4–0.7. The ATP concentration at the SMC surface decreases with volume fraction in the ordered configuration of SMCs. In a disordered configuration, the local ATP concentration at the SMC surface and in the bulk are strongly dependent on the distance between neighboring SMCs, as well as the minimum distance between SMCs and fenestral pores. Moreover, the SMCs in farther distances from the IEL are as important as those just beneath the IEL in disordered configurations. The results of this study lead us to better understanding of the role of SMCs in controlling the diffusion of important species such as ATP within the arterial wall.

Tissue prolapse and stresses in stented coronary arteries

Among the many factors influencing the effectiveness of cardiovascular stents, tissue prolapse indicates the potential of a stent to cause restenosis. The deflection of the arterial wall between the struts of the stent and the tissue is known as a prolapse or draping. The prolapse is associated with injury and damage to the vessel wall due to the high stresses generated around the stent when it expands. The current study investigates the impact of stenosis severity and plaque morphology on prolapse in stented coronary arteries. A finite element method is applied for the stent, plaque, and artery set to quantify the tissue prolapse and the corresponding stresses in stenosed coronary arteries. The variable size of atherosclerotic plaques is considered. A plaque is modelled as a multi-layered medium with different thicknesses attached to the single layer of an arterial wall. The results reveal that the tissue prolapse is influenced by the degree of stenosis severity and the thickness of the plaque layers. Stresses are observed to be significantly different between the plaque layers and the arterial wall tissue. Higher stresses are concentrated in fibrosis layer of the plaque (the harder core), while lower stresses are observed in necrotic core (the softer core) and the arterial wall layer. Moreover, the morphology of the plaque regulates the magnitude and distribution of the stress. The fibrous cap between the necrotic core and the endothelium constitutes the most influential layer to alter the stresses. In addition, the thickness of the necrotic core and the stenosis severity affect the stresses. This study reveals that the morphology of atherosclerotic plaques needs to be considered a key parameter in designing coronary stents.

Pulsatile Blood Flow Simulations in Aortic Arch: Effects of Blood Pressure and the Geometry of Arch on Wall Shear Stress

Pulsatile blood flow through human aortic arch is an unsteady flow with many complex features that could be analyzed by means of computational fluid dynamics (CFD) simulations by a certain degree of accuracy. In this work, a number of different geometric models have been created for the human aortic arch with branches included in the model to understand the effects of little geometric distortions in the arch on resulting wall shear stresses. Such distortions might be created due to injuries or diseases. On the other hand, the characteristics of the pressure pulse over the inlet section of the aortic arch have been varied, reflecting various normal or abnormal functions of heart, in order to calculate the associated effects on the wall shear stress distribution along the aortic arch. Here, we have used the computer package of Comsol Multiphysics, which performs the CFD simulations based on the finite element method (FEM). It also enables us for convenient coupling between solid deformation of arterial wall and the blood flow. Blood is assumed a homogeneous, incompressible liquid in our simulations.

Mechanotransmission in endothelial cells subjected to oscillatory and multi-directional shear flow

Local haemodynamics are linked to the non-uniform distribution of atherosclerosic lesions in arteries. Low and oscillatory (reversing in the axial flow direction) wall shear stress (WSS) induce inflammatory responses in endothelial cells (ECs) mediating disease localization. The objective of this study is to investigate computationally how the flow direction (reflected in WSS variation on the EC surface over time) influences the forces experienced by structural components of ECs that are believed to play important roles in mechanotransduction. A three-dimensional, multi-scale, multi-component, viscoelastic model of focally adhered ECs is developed, in which oscillatory WSS (reversing or non-reversing) parallel to the principal flow direction, or multi-directional oscillatory WSS with reversing axial and transverse components are applied over the EC surface. The computational model includes the glycocalyx layer, actin cortical layer, nucleus, cytoskeleton, focal adhesions (FAs), stress fibres and adherens junctions (ADJs). We show the distinct effects of atherogenic flow profiles (reversing unidirectional flow and reversing multi-directional flow) on subcellular structures relative to non-atherogenic flow (non-reversing flow). Reversing flow lowers stresses and strains due to viscoelastic effects, and multi-directional flow alters stress on the ADJs perpendicular to the axial flow direction. The simulations predict forces on integrins, ADJ filaments and other substructures in the range that activate mechanotransduction.

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.

Effect of Aortic Arch Geometry on Pulsatile Blood Flow: Flow Pattern and Wall Shear Stress

The aorta, with complex geometry is one of the most vulnerable arteries for creation and development of cardiovascular diseases, especially atherosclerosis. Because of the association of disease with region of altered fluid mechanics, the role of blood flow in the localization of atherosclerosis has been extensively studied recently. The diameter of aorta, its branches, and the geometry of branches are parameters which affect the blood flow significantly. However, much less attention has been focused on the effect of these parameters and their association with diseased regions. In the present study, three different geometries of human aorta with three branches are constructed and blood flow inside the arteries is simulated. Flow across longitudinal crosssections of all three geometries is analyzed. The disturbed velocity profiles are observed near branchiocephalic, left common artery and left subclavian artery. On the other hand, the wall shear stress profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The blood flow is considered as homogeneous, incompressible, and Newtonian fluid flow.