A fictitious domain formulation based on hierarchical model reduction applied to drug-eluting stents

05/2026

A fictitious domain formulation based on hierarchical model reduction applied to drug-eluting stents

Tuesday 13th January 2026

Ranno, A.; Ballarin, F.; Lespagnol, F.; Zunino, P.; Perotto, S.

This paper presents a novel combination of the Fictitious Domain (FD) approach with the Hierarchical Model (HiMod) reduction for the simulation of the hemodynamics in an artery with a drug-eluting stent. Classical finite element methods are computationally expensive due to the geometrical complexity of stented arteries. The FD approach merges stent and lumen domains into a single computational domain, weakly imposing boundary conditions on the stent-lumen interface via Lagrange multipliers. However, the FD technique can lead to inaccurate solutions when dealing with non-conforming grids. In contrast, a HiMod formulation offers flexibility in tuning accuracy and computational cost but struggles with non-smooth domains like stented arteries. To address these limitations, we combine the FD and HiMod approaches, using a reduced stent-lumen interface condition to simplify implementation while maintaining accuracy. This combined approach is tested on an advection-diffusion equation to model drug elution into the bloodstream. For proof-of-concept, we use a simplified axisymmetric geometry comprising an idealized artery segment and a ring-shaped stent. Finally, we extend our analysis to include more realistic blood flow conditions and conduct a sensitivity analysis of drug concentration with respect to ring spacing. The numerical results demonstrate the effectiveness of the proposed approach.