Modelling and simulation of low-density lipoprotein transport through multi-layered wall of an anatomically realistic carotid artery bifurcation

A high concentration of low-density lipoprotein (LDL) is recognized as one of the principal risk factors for development of atherosclerosis. This paper reports on modelling and simulations of the coupled mass (LDL concentration) and momentum transport through the arterial lumen and the multi-layered arterial wall of an anatomically realistic carotid bifurcation. The mathematical model includes equations for conservation of mass, momentum and concentration, which take into account a porous layer structure, the biological membranes and reactive source/sink terms in different layers of the arterial wall, as proposed in Yang & Vafai (2006). A four-layer wall model of an arterial wall with constant thickness is introduced and initially tested on a simple cylinder geometry where realistic layer properties are specified. Comparative assessment with previously published results demonstrated proper implementation of the mathematical model. Excellent agreement for the velocity and LDL concentration distributions in the arterial lumen and in the artery wall are obtained. Then, an anatomically realistic carotid artery bifurcation is studied. This is the main novelty of the presented research. We find a strong dependence between underlying blood flow pattern (and consequently the wall shear stress distributions) and the uptake of the LDL concentration in the artery wall. The radial dependency of interactions between the diffusion, convection and chemical reactions within the multi-layered artery wall is crucial for accurate predictions of the LDL concentration in the media. It is shown that a four-layer wall model produced qualitatively good agreement with the experimental results of Meyer et al. (1996) in predicting levels of LDL within the media of a rabbit aorta under identical transmural pressure conditions. Finally, it is demonstrated that the adopted model represents a good initial platform for future numerical investigations of the initial stage of atherosclerosis for patient-specific geometries.