Modelling Time-dependent Release Kinetics in Stent-based Delivery

Abstract

IntroductionArterial stenting, acting as a supporting scaffold, has revolutionized the treatment of coronary artery disease, as it reopens the occluded vessel and restores the normal flow of blood. The bare metal stents (BMS s ), while revolutionary at the time, were soon rendered unsatisfactory due to their inability to prevent in-stent restenosis. The next wave of arterial stents coated by drug-the so-called drug-eluting stents (DES s ) raised all sorts of questions by releasing antiproliferative agents in a controlled manner into the injured site to reduce restenosis rates. 1-9 Drug-eluting stents are now the primary choice of percutaneous coronary interventions (PCI s ) in millions of patients, but questions regarding their longevity and safety still arise.Some experimental studies have been carried out in the recent past, with the aim of quantifying the capability of this device to reduce in-stent restenosis after stent implantation. 10-12 Lovich et al. 10 studied the behaviour of heparin in explanted arteries and concluded that the presence of binding sites changes along the transmural direction, being higher in the endothelium and lower in the adventitia. Lovich and Edelman studied the effects of specific binding sites inside the arterial wall on the drug uptake, 13 where the presence of specific binding site action was modelled using the reversible chemical reaction. Sakharov et al. 14 disregarded the convective effects on the transport of free drug. Hwang et al. 15 predicted the free as well as bound drug concentrations by solving for distribution of free drug and then using a multiplicative factor (partition approach) to predict the concentration of bound drug. Migliavacca et al. 16 studied the drug release pattern in vascular wall from drug-eluting stents using a single species approach along with a partition coefficient approach to relate the free and the Modelling Time-dependent Release Kinetics in Stent-based Delivery AbstractBackground and objective: The present study deals with a computational model of the transport and retention of drug within the arterial wall eluted from a drug-eluting stent, to enhance our understanding of the performance of this device. We considered a two-species model (free and bound) incorporating a reversible reaction to describe drug interactions with the constituents of the arterial wall. An axisymmetric model of drug delivery from a pair of stent struts has been developed, where the transport of free drug is modelled as an unsteady reaction-diffusion process, while the bound drug, assuming complete immobilization in the tissue, is modeled as an unsteady reaction process. The model also took into account a second-order binding process that describes a saturating reversible binding and time-dependent release kinetics of the drug-eluting stent. Considering that diffusion takes place over a tortuous path in a porous media, the effects of porosity and tortuosity on diffusion cannot be ruled out from this present investigation.

A Two-Species Finite Volume Scalar Model for Modeling the Diffusion of Poly(lactic-co-glycolic acid) into a Coronary Arterial Wall from a Single Half-Embedded Drug Eluting Stent Strut

“…The mathematical models for describing the drug delivery process are described in Sections 2.2 and 2.3. The model for describing drug transport and pharmacokinetics in the arterial wall was developed based on the works of Xiaoxiang and Braatz [36] and Saha and Mandal [35]. The next section describes the boundary conditions for the developed domain model.…”

“…The physiological and pharmacokinetic parameters modeled in Equations ( 1)-( 20) are listed in Table 2. These values were obtained from other relevant works [35,36]. For validation and verification of the developed finite volume scalar model, we compared the free drug concentration profiles in the arterial domain of the developed finite volume scalar model with a MATLAB finite difference code developed in our previous work [33].…”

“…The model described in this work is an improvement over previous works and considers the integrated process of the drug release in the PLGA coating, the free and bound drug diffusion profiles with varying polymer drug concentration (low and high), vascular diffusivities, tortuosity, porosity, and Peclet and Dahmokoler numbers over the course of 400 h (16.67 days) [33]. The mechanism of diffusion in the PLGA is adapted from the work of Zhu and Braatz [34] and couples the drug diffusion to degradation and erosion along with the drug pharmacokinetics taking place in the arterial wall from the work of Saha and Mandal [35]. The main contributions of the proposed work include:…”

A Computational Approach for Stent Elution Rate Determined Specific Drug Binding and Receptor-mediated Effects in Arterial Tissue

“…Steady state is achieved when the convergence criterion for concentration is 10 −6 for each drug form. Interested readers are referred to Saha et al 28 for the detailed numerical procedure.…”