Modelling intravascular delivery from drug-eluting stents with biodurable coating: investigation of anisotropic vascular drug diffusivity and arterial drug distribution

Abstract

In-stent restenosis occurs in coronary arteries after implantation of drug-eluting stents with non-uniform restenosis thickness distribution in the artery cross-section. Knowledge of the spatiotemporal drug uptake in the arterial wall is useful for investigating restenosis growth but may often be very expensive/difficult to acquire experimentally. In this work, local delivery of a hydrophobic drug from a drug-eluting stent implanted in a coronary artery is mathematically modeled to investigate the drug release and spatiotemporal drug distribution in the arterial wall. The model integrates drug diffusion in the coating and drug diffusion with reversible binding in the arterial wall. The model is solved by the finite volume method for both high and low drug loadings relative to its solubility in the stent coating with varied isotropic/anisotropic vascular drug diffusivities. Drug release profiles in the coating are observed to depend not only on the coating drug diffusivity but also on the properties of the surrounding arterial wall. Time dependencies of the spatially-averaged free- and bound-drug levels in the arterial wall on the coating and vascular drug diffusivities are discussed. Anisotropic vascular drug diffusivities result in slightly different average drug levels in the arterial wall but very different spatial distributions. Higher circumferential vascular diffusivity results in more uniform drug loading in the upper layers and is potentially beneficial in reducing in-stent restenosis. An analytical expression is derived which can be used to determine regions in the arterial with higher free-drug concentration than bound-drug concentration.

Does anisotropy promote spatial uniformity of stent-delivered drug distribution in arterial tissue?

“…The focus of the work in [15] was on the difference in the transport properties of two commercially available drugs (paclitaxel and sirolimus) and how this can affect the distribution of drug in the arterial wall, while [16] focussed on the influence of strut compression on the drug transport properties of the arterial wall. Zhu et al [8], on the other hand, were more concerned with the effect of diffusion (in their two-dimensional model) on the resulting arterial wall drug levels. In each case, anisotropic diffusion coefficients were accounted for, with the diffusion coefficient in the radial direction chosen to be different from that in the circumferential direction.…”

“…Realising this, many authors have turned to higher dimensional models. For example, [15,8] both considered a two-dimensional model in a Cartesian geometry, and [16] proposed a twodimensional model in a cylindrical co-ordinate system. The focus of the work in [15] was on the difference in the transport properties of two commercially available drugs (paclitaxel and sirolimus) and how this can affect the distribution of drug in the arterial wall, while [16] focussed on the influence of strut compression on the drug transport properties of the arterial wall.…”

“…[3]), in the literature it is standard to neglect the curvature so that the resulting model may be written in a Cartesian coordinate framework (see e.g. [6][7][8]). However, this assumption is never justified mathematically.…”

Some design considerations for polymer-free drug-eluting stents: A mathematical approach

“…This problem is self-similar in the Boltzmann variable x= ffiffi t p , and we may write Dw 10 À11 À 10 À9 m 2 s À1 10 À10 m 2 s À1 [37,38] c 0 =cs 1:5 À 100 10 K 0:01…”

Analytical modeling of drug dynamics induced by eluting stents in the coronary multi-layered curved domain

“…In some cases drug transport due to the plasma filtration through the tissue (activated by physiological transmural pressure gradients) and chemical binding of drug with tissue proteins are also accounted for. Several computational approaches refer to simple one-dimensional formulations [18,19], as well as to more refined bi-dimensional [20][21][22][23][24][25] and threedimensional [26][27][28][29][30] models. In the context of one-dimensional models, a multi-layered computational approach has been proposed by Lovich and Edelman [18], with the aim of investigating the propagation of a hydrophilic drug, such as heparin.…”