  Development of in silico models are intrinsic in understanding disease
progression in soft biological tissues. Within this work, we propose a
fully-coupled Lagrangian finite element framework which replicates the process
of in-stent restenosis observed post stent implantation in a coronary artery.
Coupled advection-reaction-diffusion reactions are set up that track the
evolution of the concentrations of the platelet-derived growth factor, the
transforming growth factor-$\beta$, the extracellular matrix, and the density
of the smooth muscle cells. A continuum mechanical description of growth
incorporating the evolution of arterial wall constituents is developed, and a
suitable finite element implementation discussed. Qualitative validation of the
computational model are presented by emulating a stented artery.
Patient-specific data can be integrated into the model to predict the risk of
restenosis and thereby assist in tuning of stent implantation parameters to
mitigate the risk.

Computational Engineering, Finance, and Science