Oscillating LDL accumulation in normal human aortic arch - shear dependent endothelium

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/51160447 Oscillating LDL accumulation in normal human aortic arch - shear dependent endothelium ArticleinHippokratia · March 2011 Source: PubMed CITATIONS 8 READS 599 5 authors, including: Johannes Vassiliou Soulis Democritus University of Thrace 120 PUBLICATIONS1,672 CITATIONS SEE PROFILE Dimitrios K. Fytanidis Argonne National Laboratory 50 PUBLICATIONS597 CITATIONS SEE PROFILE Vassilios Papaioannou Centre for Research and Technology Hellas 36 PUBLICATIONS193 CITATIONS SEE PROFILE Charis Styliadis Aristotle University of Thessaloniki 62 PUBLICATIONS1,853 CITATIONS SEE PROFILE All content following this page was uploaded by Dimitrios K. Fytanidis on 31 May 2014. The user has requested enhancement of the downloaded file. 22 PASCHOS KA HIPPOKRATIA 2011, 15, 1: 22-25 ORIGINAL ARTICLE Oscillating LDL accumulation in normal human aortic arch - shear dependent endothelium Soulis JV1, Fytanidis DK1, Papaioannou VC1, Styliadis H2, Giannoglou GD2 1Fluid Mechanics Division, Faculty of Engineering, Demokrition University of Thrace, Xanthi, Greece 2Cardiovascular Engineering and Atherosclerosis Laboratory, 1st Cardiology Department, AHEPA Hospital, Aristotle University of Thessaloniki, Thessaloniki, Greece Abstract Objective: Abnormal mass transfer of blood components to the arterial walls initiates atherosclerosis. Understating the role of mass transfer within the arterial walls requires quantitative analysis. The oscillating lipid accumulation in the aortic wall is examined in the normal human aortic arch with shear dependent endothelium properties. Methods: A semi-permeable nature of the arterial wall computational model, applied in the normal human aortic arch under unsteady normal flow and mass conditions, is incorporated with hydraulic conductivity and permeability treated as wall shear stress dependent. The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky equation. A typical aortic arch blood flow waveform at resting conditions and lasting 800 msec is applied. Results: With constant values of water infiltration and endothelial permeability the surface vertex average normalized luminal concentration is 4.25 % higher than that at the entrance. With shear dependent values the surface vertex average normalized luminal concentration is 7.3 % higher than at the entrance. The luminal surface concentration at the arterial wall is flow-dependent with local variations due to geometric features. Concave sides of the aortic arch exhibit, relatively to the convex ones, elevated low density lipoprotein at all time steps. Conclusions: The degree of elevation in luminal surface LDL concentration is mostly affected from the water infiltration velocity at the vessel wall. Shear dependent endothelial values must be taken into account whenever fluid and mass flow within the arterial system is incorporated. Hippokratia 2011; 15 (1): 22-25 Key Words: oscillating LDL transport, shear dependent endothelium, aortic arch Corresponding author: Johannes V. Soulis, Fluid Mechanics Division, Faculty of Engineering, Demokrition University of Thrace, Vas. Sofias 12, 67100 Xanthi, Greece Tel: ++302310260011, ++302541079617, e-mail: [email protected] Abnormal mass transfer of blood components to the arterial walls initiates atherosclerosis. Understating the role of mass transfer within the arterial walls requires quantitative analysis. Regional variations in the permeability of arterial endothelium may contribute to the localization of atherosclerosis1. Lipids and inflammatory cells infiltrate into the artery wall eventually forming plaques and subsequently artery stenosis. Wall Shear Stress (WSS)-induced biological responses of endothelial cells and transmural filtration flow play important roles in localized Low Density Lipoprotein (LDL) accumulation in vascular walls2. The effects of local WSS on the endothelial cell layer were numerically analyzed in a coupled blood-wall mass transport of LDL model3 observing high luminal surface LDL concentrations in low WSS regions. An increased permeability to LDL, as it is the case of increased plasma LDL concentration, increases atherosclerosis4. In vitro tests have shown that vascular permeability is acutely sensitive to WSS5. A fluid-wall model with shear-dependent transport parameters was used to investigate the LDL transport in a human right coronary artery6. Higher permeability of the endothelium caused excessive influx of LDL to the subendothelial layer. In the current research work a homogeneous and semi-permeable nature of the arterial wall computational model using non-Newtonian blood flow is incorporated to study oscillating mass transport patterns in normal human aortic arch using shear dependent endothelial properties namely hydraulic conductivity and endothelial permeability. Methods Firstly, the aortic arch centerline is generated. Thereafter, the daughter vessels centerlines are generated and placed at the appropriate aortic arch centerline locations. Various vessel cross-sections, taken every 1.0 mm, are set perpendicular to ascending-descending aortic arch and daughter vessel centerlines at appropriate locations. The grid size was comprised of 796647 cells, 1876198 faces and 317914 nodes, Figure 1. The numerical code solves the governing Navier-Stokes flow equations and the mass transport of LDL equation. The assumptions made about the nature of the blood flow are, 3D, unsteady, laminar and isothermal. The arterial wall is comprised from homogeneous, non-elastic and permeable material7. We assume the molecular diffusivity to be isotropic8 (=50.0x10-12 m2/ HIPPOKRATIA 2011, 15, 1 23 s). The coupling of fluid dynamics and solute dynamics at the endothelium was achieved by the Kedem-Katchalsky9 equation. The shear dependent water infiltration velocity Vw (m/s) is calculated10-12, Vw(τw=[0.392x10-12 ln(|τw|+0.015) + 2.7931χ10-12] 5933.33 (Equation 1) Low WSS (N/m2) or τw results into decreased Vw and vice versa. For the shear dependent endothelial permeability coefficient K the following equation is used12, Κ(Cw,τw)=Κconst(0.037e2.75CwCo) (0.537|τw|0.27) (Equation 2) Kconst is the constant permeability coefficient of 2.0Χ10-10 m/s, Cw (mg/ml) the luminal surface LDL concentration and Co (=1.3 mg/ml) the uniform constant LDL concentration at aortic arch inlet. The flow discharges were set according to Murray’s law. A typical aortic arch blood flow waveform (resting condition) lasting 800 msec and shown in Figure 2 is applied over the entire ascending aorta entrance cross-section. Two characteristic time-points are selected for analysis; at 53.3 msec and refers to 0.17 m/s and at 336.7 msec with 0.05 m/s. The boundary conditions at the wall (endothelium), where n is the direction normal to the wall, can be described2 as, ∂C (Cw,Vw)-D______=KCw ∂n (Equation 3) Results Normalized luminal surface LDL concentration Cw/Co contours at 0.05 m/s and 0.17 m/s are shown in Figures 3 and 4, respectively. In comparison to constant value model, shear dependent hydraulic conductivity exhibits increased LDL concentration. Table 1 shows the surface vertex average Cw/Co for various endothelial property scenarios. Using Vw=0.6x10-8 m/s, K=2.0x10-10 m/s the surface vertex average Cw/Co is 1.0425. The surface vertex average Cw/Co is 1.0726 and 1.0848, at 336.7 msec and 53.3 msec time instants, respectively, for the shear dependent model. Peak Cw/Co are 1.20 and 1.22 at 336.7 msec and 53.3 msec time instants, respectively. The concave side, compared to the convex one exhibits high LDL concentration. At the same time instant, the surface vertex average Cw/Co over the entire normal aortic arch are 1.072 and 1.128 for the high (=50.0x10-12 m2/s) and low molecular diffusivity (=25x10-12 m2/s) values, respectively. Increased inlet blood flow yields elevated endothelial permeability. Peak endothelial permeability, using constant Vw for low and high inlet blood flow velocities, reaches 4.97x10-10 m/s and 5.74x10-10 m/s, respectively. For shear dependent Vw, the corresponding peak endothelial permeability values are 9.17x10-10 m/s and 12.9x10-10 m/s for low and high inlet blood flow velocities, respectively. High inlet blood flow velocity results into elevated Vw. As expected high Vw give rise to high WSS. Convex aortic arch regions expose high Vw and vice versa for the concave regions. Peak Vw for low and high inlet blood flow velocities reaches 1.71x10-8 m/s and 1.94x10-8 m/s, respectively. Discussion In the present research work experimental data of shear-dependent models for hydraulic conductivity and albumin permeability are used to numerically investigate the WSS influence on macromolecular accumulation in the aortic arch wall under oscillating flow conditions at rest. The amount of LDL transported to the arterial wall is a function of the luminal surface LDL elevation. High luminal surface concentration does not necessarily denote that all the LDL molecules will be transported through Table 1. Statistics of surface vertex average Cw/Co at cardiac cycle specific instants. Time (msec) Average inlet flow velocity (m/s) Vw=0.6x10-8 K=2.0x10-10 (m/s) Vw=0.6x10-8 shear dependent Κ (Εquation 2) (m/s) Shear dependent Vw (Εquation1) K=2.0x10-10 (m/s) Shear dependent Vw (Εquation1), K (Εquation2) (m/s) 53.3 0.17 1.04249 1.04158 1.08658 1.08485 336.7 0.05 1.04257 1.04217 1.07336 1.07259 Figure 1: Computational grid details of the human aortic arch. The tested grid is comprised from 317914 nodes. 24 the vessel wall. It is generally considered that low WSS regions exhibit elevated LDL concentrations. The amount of LDL which finally passes is determined from the difference of the mass flow carried to the vessel wall by infiltration flow and the amount of flow which diffuses back to the main vessel flow13, Εquation 3. It is apparent that increased Vw results into elevated LDL concentration. This does not contradict the fact that reduced WSS values exhibit reduced Vw, yielding lower LDL concentration. The WSS is a predominant factor in determining the LDL concentration. Cells try to minimize the side effects of increased LDL by reducing Vw wherever and whenever low WSS is encountered. The luminal surface LDL concentration is altered in the case of shear dependent Vw. Thus, the mass flow carried to the endothelium is higher. Infiltration flow increases LDL accumulation under low WSS2 and reduces LDL under high WSS. Surface vertex average Cw/Co using constant Vw and endothelial permeability is of 4.2 % order higher than that at the entrance. In case of shear dependent Vw, the surface vertex average Cw/Co is 7.3 % higher than that at the entrance for low velocity inlet. At increased inlet velocity the above value reaches 8.5 %. Current results show that increased LDL diffusivity reduces the endothelial surface lipid concentration. Arterial wall deformation needs to be taken into consideration, since the flow pattern-mass transport is largely determined by the geometrical configuration of the artery. Hypolipidaemic and antihypertensive agents may affect the localization of aortic arch atherosclerotic regions; this possibility should be investigated. The percentage of LDL deposition at the surface of the endothelium, in terms of the circulating LDL quantity, needs to be analyzed. Conclusion The luminal surface LDL concentration at the arterial wall increases with the Vw rate through the vessel wall and decreases with increasing WSS rate. Concave sides of the aortic arch exhibit, relatively to the convex ones, elevated LDL at all time steps. At any instant of the cardiac cycle, the surface vertex average Cw/Co is 4.25 % higher than that at the entrance (constant value model). With shear dependent Vw and endothelial permeability the surface vertex average Cw/Co is 7.3 % higher than at the entrance (low inlet velocity). At the increased inlet velocity the above value reaches 8.5 %. The degree of Figure 2: Average physiological human aortic arch velocity waveform. Computational analysis results refer to inlet flow velocities of 0.17 m/s and 0.05 m/s corresponding to waveform instants of 53.3 msec and 336.7 msec, respectively. Figure 3: Normalized luminal surface LDL concentration Cw/Co contours of the normal human aortic arch with shear dependent water infiltration and endothelial permeability, at 336.7 msec. Figure 4: Normalized luminal surface LDL concentration Cw/Co contours of the normal human aortic arch with shear dependent water infiltration and endothelial permeability, at 53.3 msec. SOULIS JV HIPPOKRATIA 2011, 15, 1 25 elevation in luminal surface LDL concentration is mostly affected from the Vw at vessel wall. 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