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COBEM 2023
27th International Congress of Mechanical Engineering
Numerical simulation of drug transport from Drug-Eluting stents through the arterial wall with an atheroma plaque
Submission Author:
Rachel Manhães de Lucena , RJ
Co-Authors:
Haroldo Rosman Junior, Hyun Ho Shin, Rachel Manhães de Lucena, José da Rocha Miranda Pontes, Norberto Mangiavacchi, Sean McGinty
Presenter: Rachel Manhães de Lucena
doi://10.26678/ABCM.COBEM2023.COB2023-1671
Abstract
Drug-eluting stents (DES) are widely used for treating coronary artery disease, but there are cases where restenosis and late stent thrombosis occur. In this context, understanding the effects of the drugs used in DES and the transport through the arterial wall on the overall health of DES-treated arteries presents a complex challenge that could be addressed through the development of mathematical and computational models. Although experimental efforts have been made to determine fundamental physical and biophysical parameters, these parameter values are not always applicable in all circumstances, particularly when atheroma plaque is present. In this context, this study performs a sensitivity analysis of transport parameters associated with atheroma plaque in arterial walls treated with DES. The drug elution from the polymer coating and its transport using advection-diffusion-reaction equations in the arterial wall are simulated on a 2D-axisymmetric unstructured grid, representing a portion of a DES with the adjacent arterial wall, using the Finite Element Method. The polymer layer of the DES and the arterial wall are modeled as porous media with incompressible flow and a constant pressure Dirichlet condition. A nonlinear dissolution model is used for the drug dynamics in the polymer coating, and a nonlinear saturable binding model that includes both specific and non-specific binding as separate phases in the arterial wall. The transport of the drug in the arterial wall is modeled considering an anisotropic diffusion tensor, with principal directions re-oriented in the vicinity of the stent to properly account for the compression and realignment of tissue fibers. Finally, the atheroma plaque is represented by the variation of permeability from its value in the arterial wall, using a hyperbolic tangent function to define a smooth artery/atheroma interface. The sensitivity analysis is performed by considering two types of atheroma plaque: soft and firm, using the drug sirolimus represented by literature parameters. The velocity field in the case of a firm atheroma is lower in magnitude compared to the normal arterial wall, which also reduces the convective transport of eluted drug. On the other hand, in the case of a soft atheroma, velocities are higher than in the normal arterial wall, resulting in an increased convective flux and, eventually, the wash out of the drug. The presence of either firm or soft atheromas significantly modifies the concentration distribution, possibly leading to the need for modified dosages and polymer formulations to compensate for these effects.
Keywords
drug-eluting stents, atheroma plaque, Darcy’s law, convection-diffusion-reaction equations, Finite Element Method
