Biomedical Engineering Reference
In-Depth Information
the amount of drug eluted from the stent, the rate of drug release, accumulation of
drug and drug binding to cells in the arterial wall [
1
]. The local drug concentrations
achieved are directly correlated with the biological effects and local toxicity, and
establishing the optimum dose to be delivered to the tissue remains a challenge
in today's DES design and manufacturing [
2
,
3
]. The two most common drugs used
today are paclitaxel and derivatives of rapamycin (the so called limus drugs).
Although many studies of DES efficacy and optimal design have been carried out
using either experimental methods [
4
] or numerical simulations [
5
,
6
], many ques-
tions remain unanswered. Validated mathematical models for computing the drug
concentration in the arterial wall can provide a useful tool in the manufacturing and
development of new and more efficacious DES [
7
]. Such models should incorporate
the pharmacokinetics responsible for the drug release to study the effect of differ-
ent coating parameters and configurations on drug elution [
8
]. Hossainy and Prabhu
developed a mathematical model to predict the transport reaction of drug release
in biodurable materials and biodegradable polymers [
9
]. Although the polymer acts
as the drug reservoir and a strategic design of its characteristics would improve the
release performance, studies probing the drug elution process from the coating plat-
form are limited. In most studies, the coating is considered as a continuum where
the drug is incorporated directly into the liquid phase. However, at the microscopic
scale, the polymer is a porous medium where the solid and fluid phases coexist [
10
].
In particular, the solid matrix acts as a drug reservoir, where the drug is initially
bound to the solid phase. Subsequently, after stent insertion, expansion and contact
with vascular tissues, a part of the drug is first transferred to the fluid phase, at a
rate that depends on the porosity, permeability, and drug characteristics, and it then
diffuses into the surrounding tissues.
Drug transport depends on the properties of the “coating-wall” system, taken as
a whole and modeled as a coupled two-layered system. The multiphase release of
drug from the coated stent and its distribution in the arterial wall must be carefully
tailored to achieve the optimal therapeutic effect and to deliver the correct dose in
the required time [
11
,
12
]. The pharmacological effects of the drug as well as its
tissue accumulation, duration and distribution could potentially have an effect on the
drug's efficacy, and a delicate balance between adequate amount of drug delivered
over an extended period of time and minimal local toxicity needs to be struck [
13
].
Thus, the model also needs to properly describe the drug dynamics in the different
layers of the arterial wall. Although a large number of mathematical models are
available to describe drug transport in arterial tissue, only a few [
14
,
15
] consider the
dynamic nature of the interaction of the drug with the cells of the wall. The released
drug targets and binds to specific receptors on the surface of SMCs to block the
uncontrolled proliferation and migration of these cells. Similar to the process in the
coating, this entails a phase change of the mobile drug, which is transported through
the interstitial space of the arterial wall, to a state where the drug is bound to the
surface of the SMCs to exert its therapeutic effect.
In the present work, we model the coupled coating-wall system: we investigate
the effect of phase change in both layers (the coating and the wall) by combining
previous models, where a multi-layered porous wall model has been proposed and
