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

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.

A combined numerical and experimental framework for determining permeability properties of the arterial media

“…Direct measurement of medial permeability, and other regions of the arterial wall for that matter, is di cult, if not impossible; hence, modelling this layer can provide valuable information. In previous models, the medial structure has been treated as either an array of circles (Wang and Tarbell, 1995, Huang and Tarbell, 1997, Tada and Tarbell, 2000, Dabagh et al, 2009a or as a homogenous medium with an e↵ective permeability typically derived from the former approaches (Prosi et al, 2005, Ai and Vafai, 2006, Sun et al, 2009, Dabagh et al, 2009b. The array of circles, although useful, assumes that the media contains a regular arrangement of SMCs and neglects the influence of the elastic lamellae.…”

“…If the widely accepted view is in fact correct our methods would still be applicable; the relative permeabilities (and hence the detailed results) would be qualitatively similar but would di↵er in detail. Previous models of the media have reported the permeability of the GS to be around 6.09⇥10 19 m 2 (see for example Dabagh et al (2009b) ( 5 -8 ) of SMCs between the lamellae. The size of the blocks varied so they only contained GS and SMCs.…”

“…Transport of water and LDL in the arterial wall has received considerable attention both in studies utilising simple 2D & 3D models of the media (Wang and Tarbell, 1995, Huang and Tarbell, 1997, Tada and Tarbell, 2000, Dabagh et al, 2009a as well as in models of the whole arterial wall (Prosi et al, 2005, Ai and Vafai, 2006, Sun et al, 2009, Dabagh et al, 2009b. In the former studies, the medial layer was treated as an array of circles representing SMCs, embedded in the ground substance (GS).…”

Wall shear stress exposure time: a Lagrangian measure of near-wall stagnation and concentration in cardiovascular flows

“…The local transport of several substances near and at the vessel wall are known to influence atherosclerosis progression [56]. For example, previous studies have looked into transport of low density lipoproteins (LDL) [17,20,30,14], high density lipoproteins (HDL) [40,24], oxygen [16,27], nitric oxide (NO) [45,35], monocytes [12,14], and adenine triphosphate ATP and adenine diphosphate ADP [13,15,8] as important mass transport processes involved in atherosclerosis.Intravascular thrombosis is another compelling pathology associated with most cardiovascular diseases where near-wall transport becomes important [7,25]. The trajectories of individual platelets and the accumulation and residence time of chemical solutes including ADP, thrombin, and various blood factors control clot formation.…”

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

“…Note that the interfinger distance is 1 mm and the density of ADJs is 1 mm 22 [59 -61]. ADJs are located at 25% of the cleft depth or 250 nm from the apical surface [36,73]. The shape, location and distribution of ADJs in the cell -cell interface in this model are shown in figure 1d.…”