  Atherosclerotic plaque growth is characterised by chronic inflammation that
promotes accumulation of cellular debris and extracellular fat in the inner
artery wall. This material is highly thrombogenic, and plaque rupture can lead
to the formation of blood clots that occlude major arteries and cause
myocardial infarction or stroke. In advanced plaques, vascular smooth muscle
cells (SMCs) migrate from deeper in the artery wall to synthesise a cap of
fibrous tissue that stabilises the plaque and sequesters the thrombogenic
plaque content from the bloodstream. The fibrous cap provides crucial
protection against the clinical consequences of atherosclerosis, but the
mechanisms of cap formation are poorly understood. In particular, it is unclear
why certain plaques become stable and robust while others become fragile and
vulnerable to rupture.
  We develop a multiphase model with non-standard boundary conditions to
investigate early fibrous cap formation in the atherosclerotic plaque. The
model is parameterised using a range of in vitro and in vivo data, and includes
highly nonlinear mechanisms of SMC proliferation and migration in response to
an endothelium-derived chemical signal. We demonstrate that the model SMC
population naturally evolves towards a steady-state, and predict a rate of cap
formation and a final plaque SMC content consistent with experimental
observations in mice. Parameter sensitivity simulations show that SMC
proliferation makes a limited contribution to cap formation, and highlight that
stable cap formation relies on a critical balance between SMC recruitment to
the plaque, SMC migration within the plaque and SMC loss by apoptosis. The
model represents the first detailed in silico study of fibrous cap formation in
atherosclerosis, and establishes a multiphase modelling framework that can be
readily extended to investigate many other aspects of plaque development.
