Arteries are heterogeneous, composite structures that undergo large cyclic deformations
during blood transport. Presence, build-up and consequent rupture of blockages in blood
vessels, called atherosclerotic plaques, lead to disruption in the blood flow that can eventually
be fatal. Abnormal lipid profile and hypertension are the main risk factors for plaque
progression. Treatments span from pharmacological methods, to minimally invasive balloon
angioplasty and stent procedures, and finally to surgical alternatives. There is a need to
understand arterial disease progression and devise methods to detect, control, treat and
manage arterial disease through early intervention. Local delivery through drug eluting stents
also provide an attractive option for maintaining vessel integrity and restoring blood flow
while releasing controlled amount of drug to reduce and alleviate symptoms. Development of
drug eluting stents is hence interesting albeit challenging because it requires an integration of
knowledge of mechanical properties with material transport of drug through the arterial wall
to produce a desired biochemical effect. Although experimental models are useful in studying
such complex multivariate phenomena, numerical models of mass transport in the vessel have proved immensely useful to understand and delineate complex interactions between chemical species, physical parameters and biological variables. The goals of this review are to summarize literature based on studies of mass transport involving low density lipoproteins in the arterial wall. We also discuss numerical models of drug elution from stents in layered and porous arterial walls that provide a unique platform that can be exploited for the design of novel drug eluting stents