A Cellular Scale Study of Low Denisty Lipoprotein Concentration Polarisation in Arteries

Abstract

Uptake of Low Density Lipoprotein (LDL) by the arterial wall is likely to play a key role in the process of atherogenesis, which occurs non-uniformly within the ar- terial vasculature. A particular process that may cause vascular scale heterogeneity in the rate of transendothelial LDL transport is the formation of a flow-dependent LDL concentration polarisation layer adjacent to the luminal surface of the arte- rial endothelium. In this thesis the effects of cellular scale endothelial features on such LDL concentration polarisation are investigated using an idealised theoretical model. Specifically, the effect of a spatially heterogeneous transmural water flux is considered (flowing only through intercellular clefts), as well as the effect of the endothelial glycocalyx layer (EGL). The idealised model is implemented using both analytical techniques and the spectral/hp element method. A range of scenarios are considered, including those were no EGL is present, those where an EGL is present but LDL cannot penetrate into it, and finally those where an EGL is present and LDL can penetrate into it. For cases where no EGL is present, particular attention is paid to the spatially averaged LDL concentration adjacent to various regions of the endothelial surface, as such measures may be relevant to the rate of transendothelial LDL transport. It is demonstrated, in principle, that a heterogeneous transmural water flux alone can act to enhance such measures, and cause them to develop a shear dependence (in addition to that caused by vascular scale flow features affecting the overall degree of LDL concentration polarisation). However, it is shown that this enhancement and additional shear dependence are likely to be negligible for a physiologically realistictransmural flux velocity of 0.0439μms−1 and an LDL diffusivity in blood plasma of 28.67μm2 s−1 . For cases where an EGL is present, measures of LDL concentration polarisation relevant to the rate of transendothelial LDL transport can also be defined. It is demonstrated that an EGL is unlikely to cause any additional shear dependence of such measures directly, irrespective of whether or not LDL can penetrate into the EGL. However, it is found that such measures depend significantly on the nature of the interaction between LDL and the EGL (parameterised by the height of the EGL, the depth to which LDL penetrates into the EGL, and the diffusivity of LDL within the EGL). Various processes may regulate the interaction of LDL with the EGL, possibly in a flow dependent and hence spatially non-uniform fashion. It is concluded that any such processes may be as important as vascular scale flow features in terms of spatially modulating transendothelial LDL transport via an LDL concentration polarisation mechanism.