5th International Conference on Nanosciences and Nanotechnologies (NN08) 12-18 July, 2008 Thessaloniki, GREECE

Arterial LDL Transport in the Normal Aortic Arch J.V. Soulis, G.D, Giannoglou, M.Demetrakopoulou, V.C. Papaioannou , S. Logothetidis Fluid Mechanics, Demokrition University of Thrace, AHEPA General Hospital Aristotle University of Thessaloniki, Physics Department, Aristotle University of Thessaloniki GREECE Thessaloniki, 2008

To understand the genesis and progression of atherosclerosis is essential to elucidate the blood flow and the transport of molecules in the cardiovascular system. Purpose of this computational study is to elucidate the relationship between low Wall Shear Stress (WSS)-high Low Density Lipoproteins (LDL) site concentration and atherosclerotic sites in the normal human 3D aortic arch under physiological flow and mass conditions.

The applied three-dimensional, numerical simulation couples the flow equations with transport equation using realistic boundary conditions at the aortic arch walls, in terms of blood-side concentration. The blood is considered to be non-Newtonian fluid obeying to the power law. We demonstrate that due to the semi-permeable nature of the arterial walls, high LDL concentration occurs at certain regions of the aortic arch endothelium. The variation is most noticeably at bifurcations and concave sides of the bend segments.

Computational Fluid Dynamics analysis of coronary flow Understanding the pathophysiology of coronry arteries Modelling the prognosis of coronoray artries Advancing the knowledge

Flow factors of great importance in atherosclerosis genesis and progression High or low oscillatory wall shear stress Flow recirculation Long residence time of atherogonous materials with the endothelium Wall shear stress gradients Local turbulence

Usual places where atherosclerosis occurs

Arrow in upper left figure Cell elongation and orientation parallel to flow direction, 3d proximal to stenosis Even intensified elongation at the throat of the stenosis Immediately distal to stenosis (cell disorientation due to flow disturbances) 2d distal to stenosis Arrow in upper left figure shows flow direction Levesque M et al, 1985

Normal arterial geometry

The descending aorta outlet diameter is 3.076 cm, The lumen diameter of the ascending aorta at entrance measures 3.477 cm. The descending aorta outlet diameter is 3.076 cm, while the corresponding outlet diameters of the brachiocephalic artery, left common carotid artery and left subclavian artery segments are 1.435 cm, 1.273 cm and 1.433 cm, respectively.

Details of the computational grid

The Navier-Stokes equations govern the blood flow

Shear stress

The convection-diffusion equation

The flux diffusion equation

Flow boundary conditions The blood velocity is assumed to be uniform at the orifice of the ascending aorta and equal 0.05 m/s (resting condition). Flow discharges are set analogous to the third power of the branching vessel inlet diameter according to Murray’s law

Mass boundary conditions For the mass transport solution a uniform constant concentration Co of LDL (=1.3 mg/ml) is applied at the orifice of the ascending aorta. At the descending aorta, brachiocephalic artery, left common carotid artery and left subclavian artery outlets, the gradient of LDL concentration along the vessels is set equal to zero (zero flux, Newmann condition) The boundary conditions at the semi-permeable aortic walls can be described as,

Results Wall shear stress (N/m2)

Results Normalized luminal surface LDL (Low Density Lipoprotein) concentarion (Cw/Co) Cw is the wall LDL concentration Co (=1.3 mg/ml) is the LDL at inlet

Cw/Co versus wall shear stress

Velocities (m/s) in the aorta

Velocities (m/s) in the aorta

Strain rate (1/s)

Conclusions WSS plays an important role in the wall concentration of the LDL. The luminal surface LDL concentration varies inversely with the WSS. Aortic arch walls are exposed to cholesterolemic environment although the applied mass and flow conditions refer to normal human geometry and normal mass-flow conditions. Nearly always, concave sides of the aortic arch exhibit relatively to the convex ones elevated concentration of the LDL.

The area averaged normalized LDL concentration over the entire normal aortic arch is 1.267. The net amount of LDL mass per second taken up by all luminal aortic arch surfaces is 1.189x10-11g/s. The maximum value of the normalized luminal surface LDL concentration at the outer wall of the aortic arch is 28.0 % higher than that at the entrance. At the inner wall, the maximum value of the normalized luminal surface LDL concentration is 17.0 %.

The daughter aortic arch vessels exhibit relatively to the ascending-descending aorta elevated LDL concentrations. Regions of high LDL luminal surface concentration do not necessarily co-locate to the sites of lowest WSS. The combined fluid and mass transport are the keys to understand the atherosclerosis phenomenon. The near to endothelium velocity paths might be the most important factor for the elevated LDL concentration at areas located either at the vicinity of bifurcations regions or at high curvature regions.

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