Towards numerical simulations of atherosclerosis: Modelling of Low-Density-Lipoprotein (LDL) transport through multi-layered arterial wall

Abstract

The high concentration of the low-density-lipoprotein (LDL) is recognised as one of the principal risk factors for development of the atherosclerosis. The paper reports on modelling and simulations of the LDL transport through the multi-layered patient-specific arterial wall. The mathematical model includes conservative equations of mass, momentum and concentration that are specifically re-derived to include a porous layer structure, effects of the biological membranes and reactive source/sink terms in different layers of the arterial wall. Then, a four-layer wall model is introduced and firstly tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with results presented in Yang and Vafai [4] proved proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the artery lumen and in the artery wall are obtained. Then, a patient-specific carotid artery bifurcation is studied. We found a strong dependency between underlying blood flow pattern (and consequently the wall-shearstress (WSS) distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reaction within the multi-layered artery wall is crucial for accurate predictions of the LDL in the media. It is demonstrated that a four-layer wall model represents a good platform for the future numerical investigations of atherosclerosis for the patient-specific geometries. © 2013 Springer-Verlag.