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

Abstract

In this article we investigate the role of anisotropic diffusion on the resulting arterial wall drug distribution following stent-based delivery. The arterial wall is known to exhibit anisotropic diffusive properties, yet many authors neglect this, and it is unclear what effect this simplification has on the resulting arterial wall drug concentrations. Firstly, we explore the justification for neglecting the curvature of the cylindrical arterial wall in favour of using a Cartesian coordinate system. We then proceed to consider three separate transport regimes (convection dominated, diffusion dominated, reaction dominated) based on the range of parameter values available in the literature. By comparing the results of a simple one-dimensional model with those of a fully three-dimensional numerical model, we demonstrate, perhaps surprisingly, that the anisotropic diffusion can promote the spatial uniformity of drug concentrations, and furthermore, that the simple analytical one-dimensional model is an excellent predictor of the three-dimensional numerical results. However, the level of uniformity and the time taken to reach a uniform concentration profile depends on the particular regime considered. Furthermore, the more uniform the profile, the better the agreement between the one-dimensional and three-dimensional models. We discuss the potential implications in clinical practice and in stent design

Multiscale Boundary Conditions for Non-Fickian Diffusion Applied to Drug-Eluting Stents

“…In what follows we calculate an analytical solution for a general non-Fickian desorption problem. We use Laplace transforms along with the residue theorem, following an approach similar to that in [25].…”

“…In this appendix we calculate the solution of the problem (25)-(28) presented in section 3. Letc 1 represent the Laplace transform of c 1 ; then from(25) and(26) we deduce∂ 2c 1 ∂x 2 (x, s) − λ 2 (s)c 1 (x, s) = − c 0 λ 2 (s) using the method of variation of parameters yields c 1 (x, s) = C 1 (s)e −λ(s)x + C 2 (s)e λ(s)x + c 0 s .From the boundary condition(27) we get thatc 1 (x, s) = C 1 (s) cosh (λ(s)x) + c 0 s ,(73)while from(28) it follows thatC 1 (s) = c out s − c 0 s 1 cosh (λ(s)L).Substituting the previous expression for C1 (s) into (73) gives c 1 (x, s) = c out cosh (λ(s)x) s cosh (λ(s)L) + c 0 (cosh (λ(s)L) − cosh (λ(s)x)) s cosh (λ(s)L) . (74)…”

Modeling of non‐Fickian diffusion and dissolution from a thin polymeric coating: An application to drug‐eluting stents

“…However, as shown in the work of McGinty and Pontrelli, a single‐phase bound model is well suited to study drug deposition in the arterial wall from a DES. According to the work of McGinty et al, the anisotropy can promote spatial uniformity in the drug delivery from a DES; thus, we consider the simplification of choosing the diffusion coefficients D i in Equation to be isotropic.…”

Computational Modelling of Three-phase Stent-based Delivery

“…1). 39, 40 At the strut surfaces, a time-dependent drug release kinetic in exponential manner has been accounted for McGinty et al 41 The governing equations together with their physiological realistic boundary conditions are solved numerically in an explicit manner.…”