Numerical Study of Blood Flow and Anisotropic Drug Diffusion in Arterial Tissue with Stents

Resumo

The effectiveness of drug-eluting stents is directly associated with the interaction between blood flow in the arterial lumen and drug transport through the adjacent tissue. This tissue can be represented as a porous medium, where diffusive processes play a central role in the absorption and distribution of the active compound. However, most existing models assume blood as a Newtonian fluid and consider diffusion in the tissue to be isotropic, simplifications that may compromise prediction accuracy, especially in small diameter arteries, where non-Newtonian effects and porous medium anisotropy become relevant. Integrated modeling approaches that incorporate these characteristics remain scarce in the literature and lack robust numerical validation. In this work, we develop a unified computational model to describe fluid flow and drug transport in arteries with stents, using the Brinkman equation as a foundation to represent fluid behavior in both the lumen and the arterial tissue. In the lumen, the flow is treated as a limiting case of the Brinkman equation with effectively infinite permeability, which results in a model equivalent to the Navier–Stokes equations. In the arterial tissue, regarded as a porous medium with finite permeability, the Brinkman equation captures both viscous effects and the drag exerted by the porous matrix. Drug transport is modeled by an advection–diffusion equation in the lumen and by a modified diffusion equation in the tissue that incorporates an anisotropic dispersivity tensor, capable of representing distinct longitudinal and transverse dispersion mechanisms influenced by flow direction. For the numerical resolution of the coupled Brinkman and convective transport equations, we employ stabilized finite element methods, based on the SUPG (Streamline-Upwind Petrov–Galerkin) and PSPG (Pressure-Stabilizing Petrov–Galerkin) formulations, ensuring numerical stability and accuracy even in complex geometries and convection-dominated regimes. The numerical methodology is validated through comparisons with data available in the literature, analyzing the impact of blood rheology modeling, stabilization techniques, and anisotropic dispersivity formulation on drug concentration profiles within the tissue. In addition, different stent geometries are simulated to assess how structural variations influence flow and drug penetration in the porous medium.