Atherosclerosis is a major cause of morbidity and mortality in the western world. The
focal depletion of oxygen and accumulation of macromolecules are believed to initiate,
accelerate and complicate the development of atherosclerosis. However, species concentrations
in vessel walls are difficult to measure in vivo non-invasively. Therefore, it
is essential to obtain detailed concentration profiles of atherogenic molecules to gain
further understanding of the mass transfer mechanisms within arterial walls.
In the present study, comprehensive mathematical models describing species
transport in large arteries are developed and presented. Existing mathematical models
are reviewed and reconciled. A fluid phase model, a single-layered and a multilayered
fluid-wall models are employed to simulate the mass transfer processes in proatherosclerotic
arteries. Since trans-endothelial transport is considered to be an important
sub-process in the system and is dependent on wall shear stress (WSS) imposed on
the endothelial surface, shear-dependent transport properties are derived from relevant
experimental data in the literature. A novel approach, which exploits the optimisation
theory, is proposed and used to determine model parameters based on the experimental
data. Furthermore, numerical schemes to accommodate the effects of pulsatile flow on
lipid transport in the arterial wall are presented in the thesis. Mathematical models and
numerical schemes are tested and compared using idealised computational geometries.
Then the models are applied to realistic geometries to investigate: 1) oxygen transport
in a normal human abdominal aorta and an abdominal aortic aneurysm (AAA)
with intralumenal thrombus (ILT); 2) macromolecular transport in a mildly stenosed
human right coronary artery (RCA). Based on the model predictions, mechanisms
inducing hypoxia and macromolecular accumulation are discussed in depth.