A biphasic, anisotropic model of the deformable aortic wall in combination with computational fluid dynamics is used to investigate the variation of shear stress over smooth muscle cells (SMCs) with transmural pressure. The media layer is modeled as a porous medium consisting of SMCs and a homogeneous porous medium of interstitial fluid and elastin, collagen and proteoglycans fibers. Interstitial fluid enters the media through fenestral pores, which are distributed over the internal elastic lamina (IEL). The IEL is considered as an impermeable barrier to fluid flow except at fenestral pores. The thickness and the radius of aortic wall vary with transmural pressure ranging from 10 to 180 mm Hg. It is assumed that SMCs are cylinders with a circular cross section at 0 mm Hg. As the transmural pressure increases, SMCs elongate with simultaneous change of cross sectional shape into ellipse according to the strain field in the media. Results demonstrate that the variation of shear stress within the media layer is significantly dependent on the configuration and cross sectional shape of SMCs. In the staggered array of SMCs, the shear stress over the first SMC nearest to the IEL is about 2.2 times lower than that of the square array. The shear stress even over the second nearest SMC to the IEL is considerably higher (about 15%) in the staggered array. In addition to configuration and cross sectional shape of SMCs, the variation of structural properties of the media layer with pressure and the sensitivity of the local shear stress to the minimum distance between SMCs and the IEL (reducing with transmural pressure) between SMCs and the IEL are studied. At 180 mm Hg, the ratio of the local shear stress of the nearest SMC to that of the second nearest SMC is 4.8 in the square array, whereas it reduces to about 1.8 in the staggered array. The importance of the fluid shear stress is associated with its role in the biomolecular state of smooth muscle cells bearing the shear stress.
"However, some of studies neglected the three major of branches of aortic arch. Towfiq  and Dabagh et al.  have shown that the aorta size is subjected to change with blood pressure. But no attention has been made on studying the corresponding influence on the blood flow features. "
[Show abstract][Hide abstract] ABSTRACT: 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.
Computational and Mathematical Methods in Medicine 02/2012; 2012(46):861837. DOI:10.1155/2012/861837 · 0.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: 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.
[Show abstract][Hide abstract] ABSTRACT: 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.
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