The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion–reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.

In the last decade, many computational mod-1 els have been developed to describe the transport of 2 drug eluted from stents and the subsequent uptake into 3 arterial tissue. Each of these models has its own set of 4 limitations: for example, models typically employ sim-5 plified stent and arterial geometries, some models as-6 sume a homogeneous arterial wall, and others neglect 7 the influence of blood flow and plasma filtration on the 8 drug transport process. In this study, we focus on two 9 common limitations. Specifically, we provide a compre-10 hensive investigation of the influence of arterial cur-11 vature and plaque composition on drug transport in 12 the arterial wall following drug-eluting stent implan-13

Stents have become the most successful device to treat advanced atherosclerotic lesions. However, one of the main issues with these interventions is the development of restenosis. The coating of stents with antiproliferative substances to reduce this effect is now standard, although such drugs can also delay re-endothelialization of the intima. The drug release strategy is therefore a key determinant of drug-eluting stent efficacy. Many mathematical models describing drug transport in arteries have developed and, usually separately, models describing the mechanics of arterial tissue have been devised. However, there the literature is lacking a comprehensive model that adequately takes into account both the mechanical deformation of the porous arterial wall and the resulting impact on drug transport properties. In this paper, we provide the most comprehensive study to date of the effect of stent mechanical expansion on the drug transport properties of a three-layer arterial wall. Our model incorporates the state-of-the art description of the mechanical properties of arterial tissue though an anisotropic, hyperelastic material model and includes a nonlinear saturable binding model to describe drug transport in the arterial wall. We establish relationships between mechanical force generated through device expansion and alteration in diffusion within the arterial wall and perform simulations to elucidate the impact of such alterations in spatio-temporal drug release and tissue uptake. Mechanical deformation of the arterial wall results in modified drug transport properties and tissue drug concentrations, highlighting the importance of coupling solid mechanics with drug transport.

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En el presente estudio se desarrolla un modelo numérico multicapa basado en una geometría 2D axisimétrica para describir el transporte convectivodifusivo de fármacos en el flujo sanguíneo y a través de la pared arterial.

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