  Atherosclerosis is characterised by the growth of fatty plaques in the inner
(intimal) layer of the artery wall. In mature plaques, vascular smooth muscle
cells (SMCs) are recruited from the adjacent medial layer to deposit a cap of
fibrous collagen over the fatty plaque core. The fibrous cap isolates the
thrombogenic content of the plaque from the bloodstream and prevents the
formation of blood clots that cause myocardial infarction or stroke. Despite
the important protective role of the cap, the mechanisms that regulate cap
formation and maintenance are not well understood. It remains unclear why
certain caps become stable, while others become vulnerable to rupture. We
develop a multiphase PDE model with non-standard boundary conditions to
investigate collagen cap formation by SMCs in response to growth factor signals
from the endothelium. Diffusible platelet-derived growth factor (PDGF)
stimulates SMC migration, proliferation and collagen degradation, while
diffusible transforming growth factor (TGF)-$\beta$ stimulates SMC collagen
synthesis and inhibits collagen degradation. The model SMCs respond
haptotactically to gradients in the collagen phase and have reduced rates of
migration and proliferation in dense collagenous tissue. The model, which is
parameterised using a range of in vivo and in vitro experimental data,
reproduces several observations from studies of plaque growth in
atherosclerosis-prone mice. Numerical simulations and model analysis
demonstrate that a stable cap can be formed by a relatively small SMC
population and emphasise the critical role of TGF-$\beta$ in effective cap
formation and maintenance. These findings provide unique insight into the
cellular and biochemical mechanisms that may lead to plaque destabilisation and
rupture. This work represents an important step towards the development of a
comprehensive in silico plaque.
