# A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

arXiv: https://arxiv.org/abs/2204.02301 · HTML: https://mlsanity.com/paper/2204.02301/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2022.

## Built on by (most cited first, 2 of 2)

- [Theory and implementation of inelastic Constitutive Artificial Neural Networks](https://mlsanity.com/paper/2311.06380/) (2023)
- [Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling](https://mlsanity.com/paper/2410.13645/) (2024)

## Abstract (arXiv)

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-β, 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.