Simulating Drug-eluting Stents

Progress Made and the Way Forward

Sean McGinty

, Christopher McCormick

, Sean McKee

, Marcus Wheel

, Simon Kennedy

and Keith Oldroyd

Department of Mathematics and Statistics, University of Strathclyde, Glasgow, U.K.

Biomedical Engineering and Strathclyde Institute of Pharmacy and Biomedical Sciences, University of Strathclyde,

Glasgow, U.K.

Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, U.K.

Institute of Cardiovascular and Medical Sciences, University of Glasgow, Glasgow, U.K.

West of Scotland Regional Heart and Lung Centre, Golden Jubilee National Hospital, Glasgow, U.K.

Keywords:

Drug-eluting Stents, Mathematical Modelling, Drug Release, Binding.

Abstract:

Drug-eluting stents have signiﬁcantly improved the treatment of coronary artery disease. Compared with their

bare metal predecessors, they offer reduced rates of restenosis and thus represent the current gold standard

in percutaneous coronary interventions. Drug-eluting stents have been around for over a decade, and while

progress is continually being made, they are not suitable in all patients and lesion types. Furthermore there are

still real concerns over incomplete healing and late stent thrombosis. In this paper, some modelling approaches

are reviewed and the future of modelling and simulation in this ﬁeld is discussed.

1 INTRODUCTION

Coronary heart disease (CHD) is the main cause of

death in developed countries (Murray and Lopez,

1997). Such is the extent of the condition, CHD is

responsible for 18% of all deaths in the United States

annually (Lloyde-Jones, 2010). In simple terms, CHD

is caused by a blockage or interruption to blood ﬂow

and often results in heart attack. It is generally con-

sidered that this problem is the result of fatty deposits

accumulating and lining the arterial walls over a pe-

riod of many years (Beers, 2004). The fatty deposits

are called atheroma and the process during which the

atheroma accumulates is termed atherosclerosis (Lu-

sis, 2000). If left untreated, this leads to episodes

of angina. As well as restricting blood ﬂow, the

atherosclerotic plaque is also vulnerable to rupture,

ultimately resulting in a heart attack.

Traditionally, by-pass surgery was the only avail-

able treatment option. However, in the majority of

cases this has now been replaced by minimally in-

vasive procedures such as the insertion of a small

metallic cage called a stent into the occluded artery.

When a stent is implanted into an artery, the endothe-

lium is severely damaged. This provokes an inﬂam-

matory response which leads to excessive prolifera-

tion and migration of smooth muscle cells (SMCs)

towards the lumen. The result is restenosis - the re-

narrowing of the arterial wall. The introduction of

drug-eluting stents (DESs) has signiﬁcantly reduced

the occurrence of in-stent restenosis (ISR), by releas-

ing a drug to inhibit SMC proliferation.

Drug-eluting stents have undoubtedly signiﬁ-

cantly improved the treatment of coronary artery dis-

ease. Compared with their bare metal predecessors,

they offer reduced rates of restenosis and thus repre-

sent the current gold standard in percutaneous coro-

nary interventions. But despite being around for over

a decade, and while progress is continually being

made, they are still not suitable in all patients or lesion

types. Furthermore, there are still concerns over in-

complete healing of the artery and late stent thrombo-

sis (LST), resulting in anti-platelet therapy being rec-

ommended for at least 12 months after implantation

(Stefanini and Holmes, 2013). Substantial efforts are

now dedicated towards the development of enhanced

DESs and in this paper we summarise the modelling

approaches currently adopted and suggest important

considerations for future modelling and simulation in

this ﬁeld.

664

McGinty S., McCormick C., McKee S., Wheel M., Kennedy S. and Oldroyd K..

Simulating Drug-eluting Stents - Progress Made and the Way Forward.

DOI: 10.5220/0004622706640672

In Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (BIOMED-2013), pages

664-672

ISBN: 978-989-8565-69-3

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

2 THE CHICKEN OR THE EGG

DILEMMA

What is the logical sequence of events? Stent design

and then modelling of drug release and uptake into the

arterial wall? Or is it the other way round? Presently,

the stent manufacturers are predominantly concerned

with mechanical integrity of the device and as such

the stent design is usually the ﬁrst consideration. The

stent must be ﬂexible and expandable and stay in situ

after deployment. During the expansion process the

stent should undergo minimum shortening and after

implantation should conform to the natural geome-

try of the vessel without any unnatural straightening

(Khan et al., 2012). Radial strength is another key

component; without this the stent will collapse under

the strain of the artery. Furthermore, the materials

used must be biocompatible and must not fracture.

But it is no good having a stent which is mechan-

ically sound but does not elute drug in a favourable

fashion. The release of the drug must be controlled

so that it elutes over a deﬁned period of time and, fur-

thermore, the drug concentration in the arterial wall

should ideally be maintained between therapeutic and

toxic levels over and beyond the period of release.

Taking this into account, it would seem that the drug

release and uptake is intrinsically linked to the stent

design and so a fair argument could be made either

way.

Ideally the stent should be optimised, both in

terms of the mechanical design (material used, num-

ber and pattern of struts) as well as drug loading (type

and mass of drug, coating technique) so that the re-

quired clinical outcomes are realised. This optimisa-

tion is further complicated by the fact that every pa-

tient is different; the lesions vary in size and compo-

sition as well as location in the arterial tree. Further-

more, some patients have other complications such

as diabetes or hypertension. Thus a single optimised

stent design is simply unrealistic, but it may well be

possible to develop an optimised stent for a set of dif-

ferent situations.

Realising the importance of stent design, a num-

ber of authors have investigated various aspects. The

inﬂuence of stent geometry on restenosis was inves-

tigated (Garasic et al., 2000) while the distribution

of the stent struts has been experimentally studied

(Hwang et al., 2001), with the authors concluding

that the mere proximity of delivery device to tissue

does not ensure adequate drug targeting. The effect of

the number of struts and the ratio between the coated

area was researched by Delfour et al., and they at-

tempted to optimize the effect of the dose (Delfour et

al., 2005). A mathematical model for the study of the

mechanical properties of endovascular stents in their

expanded state has also been proposed (Tambaca et

al., 2010). Three-dimensional models of stent expan-

sion have been presented by, among others, (Zunino

et al., 2009) and (Horner et al., 2010).

3 THE EVOLUTION OF THE

DRUG-ELUTING STENT

Over the past decade DESs have evolved, and al-

ready third-generation DESs have been developed.

Despite their differences and improvements, these de-

vices typically all have three main components; the

stent platform, the coating and the drug.

3.1 First Generation DESs

The ﬁrst-generation DESs Cypher (sirolimus-eluting

stent; Cordis Corporation) and Taxus (paclitaxel-

eluting stent; Boston Scientiﬁc Corporation) com-

prised a stainless steel platform with a drug contain-

ing polymer coating attached to the stent struts ((Ste-

fanini and Holmes, 2013), (Tzafriri et al., 2012)). The

philosophy behind this design was to allow the drug

to be released gradually so as to avoid toxic levels

of drug initially, but also to permit sustained deliv-

ery over many weeks. The Cypher stent actually con-

sists of three distinct layers; a base coat, a drug-ﬁlled

middle layer and a drug-free topcoat. This design en-

hances the controlled nature of the release. While the

polymers used in these ﬁrst generation DESs are dif-

ferent, they are both non-erodible. The drugs used

(sirolimus and paclitaxel) are both lipophilic and are

able to inhibit SMC proliferation and migration.

3.2 Second Generation DESs

The second-generation DESs Endeavor (zotarolimus-

eluting; Medtronic), ZoMaxx (zotarolimus-eluting;

Abbott Laboratories), Promus (everolimus-eluting;

Boston Scientiﬁc Corporation) and Xience V

(everolimus eluting; Abbott Laboratories) attempted

to improve the biocompatibility and reduce the

incidence of thrombosis rate which was associ-

ated with ﬁrst-generation DES. These stents were

generally designed with thinner struts and utilised

cobalt-chromium and platinum chromium platforms.

A variety of multi-layer polymer combinations were

used on these stents to attempt to control the release.

Generally these stents have been shown to exhibit

lower thrombosis rates compared with ﬁrst generation

DES (Khan et al., 2012).

SimulatingDrug-elutingStents-ProgressMadeandtheWayForward

665

3.3 Third Generation DESs

Since the polymer coating in the earlier DES has been

associated with local vascular inﬂammatory reaction

and potentially inducing late stent thrombosis, newer

generation stents have focussed on biodegradable

polymers (BioMatrix, Biosensors Inc and NEVO,

Cordis Corporation, Johnson & Johnson), where the

polymer carries and controls the drug release and then

erodes or vanishes, and also coatings which do not

contain any polymer at all (Yukon, Translumina and

BioFreedom, Biosensors Inc), with the drug being

contained on a modiﬁed surface of the stent.

4 MODELLING THE RELEASE

OF DRUG FROM STENTS

Most of the modelling of drug release from stents in

the literature has thus far been concerned with ﬁrst

generation DESs. Drug release from these stents has

been modelled as a diffusion dominated process (see

for example (McGinty, 2011) and (Pontrelli and de

Monte, 2007)), with the drug concentration in the

polymer C

satisfying a diffusion equation with drug

diffusion coefﬁcient D

. In one dimension this is sim-

ply

∂C

∂t

= D

∂

∂x

. (1)

For the case of in-vitro drug release a zero ﬂux bound-

ary condition is normally assumed at the impermeable

stent and either an inﬁnite sink or Robin type bound-

ary condition at the interface with the release medium.

Models such as these can admit analytical solutions

and have shown favourable results when compared

with in-vitro experimental data. Figure 1 displays a

comparison between the model predicted cumulative

percentage of drug released and the average of four

experimental in-vitro release proﬁles from the Cypher

stent (for more details see Section 6). These analyti-

cal solutions also allow the drug diffusion coefﬁcient

to be estimated via a best ﬁtting process.

Several simplifying assumptions are usually

made. Firstly, it is assumed that the device geometry

is that of a thin ﬁlm with no edge effects so that the

modelling may be restricted to one dimension. The

diffusion of the drug in the polymer is thus consid-

ered to be isotropic and it is usually assumed that the

diffusion coefﬁcient is independent of time, space and

concentration. Furthermore, the initial drug concen-

tration is usually taken to be uniform. However, in

reality this is not always the case. For example, the

polymer coating on the Cypher stent consists of three

distinct layers; a base coat, a drug-ﬁlled middle layer

0 10 20 30 40 50 60

100

Cypher release under infinite sink conditions

Release Period (days)

Percentage of Rapamycin released

Model, Dp=6.3x10

−17

EXPT(Average)

Figure 1: Comparison between in-vitro experimental data

and model of Cypher release.

and a drug-free topcoat. However, the good ﬁt be-

tween the experimental data and the simple model de-

scribed above suggests that these modelling assump-

tions are reasonable and capture the release of drug

from the Cypher stent, albeit with a layer averaged, or

effective diffusion coefﬁcient. A tighter ﬁt is antici-

pated if the polymer is modelled as a tri-layer system

with the drug contained only within the middle layer

initially. Actually, it has been shown that the drug can

be found in the top coat prior to implantation, sug-

gesting that the intended drug-free top coat may not

always be realised. However it is less clear how the

in-vivo situation may be modelled. This is considered

in the following section.

Newer generation DESs which have focussed on

biodegradable polymers and polymer-free modiﬁed

surface designs have received less attention in the lit-

erature in terms of modelling their release. In the case

of biodegradable polymeric stents, the drug release

is likely governed by diffusion, erosion and possi-

bly dissolution and/or swelling ((Siepmann and Siep-

mann, 2008); (Fredenberg et al., 2011)). However, in

the case of polymer free stents, it is less clear how

the sustained release is obtained and how this may be

modelled. Furthermore, it even less clear how in-vivo

release may be modelled. Realising this, Tzafriri et

al. chose to write down a two-part equation to de-

scribe drug release from the Cypher and NEVO stents

and, using a best ﬁt process, found the values of the

parameters of the model (Tzafriri et al., 2012). Their

equation assumes that these stents contain two pools

of dispersed drug, one that is surface-connected and

elutes through a percolating network of drug ﬁlled

pores, and another that is embedded within the ma-

trix and diffuses more slowly through the percolating

polymer phase. Thus they utilised the following equa-

tion for the mass of drug released from the Cypher and

NEVO stents:

stent

(0) −M

stent

(t) = M



1 −e

−K



+ Q

sus

√

(2)

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where M

stent

(0), M

, K

and Q

sus

denote, respec-

tively, the initial load of drug, the initial pool of ﬁrst

order eluting drug, rate constant and Higuchi rate con-

stant. This equation, however, does not satisfy mass

conservation principles: the mass of drug released

eventually tends to inﬁnity as time increases. As a re-

sult, while their data is well-ﬁtted to this equation for

this set of experiments, it is unlikely that their model

may be used in a predictive capacity. A further warn-

ing must be issued when attempting to identify the re-

lease mechanism: it may be possible to ﬁt experimen-

tal data to a given model with a variety of different

parameter combinations, even if the values of some

of the parameters are unlikely (Sirianni et al., 2010).

5 MODELLING UPTAKE OF

DRUG INTO THE ARTERIAL

WALL

While the stent manufacturer may be primarily con-

cerned with stent design and the drug release proﬁle,

clinicians are more interested in the drug concentra-

tion proﬁle across the arterial wall, and in particular

in the target SMCs, as well as the therapeutic dura-

tion. Thus an understanding of what happens to the

drug in the arterial wall is essential. The arterial wall

is porous and plasma ﬂows through the extracellular

matrix as a result of the transmural pressure gradi-

ent. This pressure gradient induces convection so that

drug transport across the arterial wall is governed by

a combination of convection, molecular diffusion and

binding. A drug with anti-proliferative properties is

usually chosen so that when it is uptaken by SMCs it

suppresses their proliferation. Depending on the par-

ticular properties of the drug, it may also bind to sites

within the extracellular matrix.

5.1 One-dimensional Models

Early models of drug transport through the arterial

wall tended to include only convection and diffusion

((Pontrelli and de Monte, 2010), (Zunino, 2004)) and

neglected drug uptake/binding. Furthermore, they re-

stricted the number of dimensions and reduced the

problem to a single layer in the arterial wall. One of

the ﬁrst models which encompassed convection, dif-

fusion and uptake into SMC within the porous media

was presented by McGinty et al.:

∂C

∂t

+ v

∂C

∂x

= D

∂

∂x

−α



−



(3)

(1 −φ)

∂C

∂t

= α



−



, (4)

where C

and C

denote the volume averaged con-

centration of drug in the extracellular and cellular re-

gions, respectively (McGinty, 2011). The parameters

φ, v, D

, α and K denote the porosity, magnitude

of transmural convection, drug diffusion coefﬁcient

in the media, drug uptake rate constant and partition

coefﬁcient. Equation 4 expresses the rate of uptake

of drug by the cells: it is initially proportional to C

but that proportionality diminishes with increasing C

until the carrying capacity (or partition coefﬁcient) of

the drug is reached at which point the uptake becomes

zero. This system of equations allows for an exchange

of drug between the extracellular phase and the cells

which is dependent on the concentration in the ex-

tracellular phase. They considered the coupled poly-

mer/media system (equations 1,3 and 4) with continu-

ity of drug concentration and continuity of the relative

ﬂuxes expressed as boundary conditions at the inter-

face:

= C

(5)

−D

∂C

∂x

= −D

∂C

∂x

+ vC

. (6)

They assumed that the ﬂux of drug out of the media

was proportional to the concentration at the interface

between the media and adventitia to provide the ﬁnal

boundary condition. Their model was also extended

to include the adventitia region (where ﬁbroblast cells

were modelled in a similar way to SMCs), a topcoat

of polymer to slow the release of the drug, and one of

the ﬁrst models of atherosclerotic plaque (modelled

using an equilibrium model in the same way as SMCs

uptake).

McGinty et al. simulated the problem using a ﬁ-

nite difference scheme and conducted a thorough sen-

sitivity analysis which allowed them to infer the im-

portance of the parameters in their model. They found

that the results were particularly sensitive to ﬂuctua-

tions in the magnitude of the transmural velocity, and

to changes in the drug uptake rate and partition coef-

ﬁcient. Their simple model of plaque suggested that

the plaque could act as a reservoir for the drug, ensur-

ing that patients with a higher degree of atherosclero-

sis may receive therapeutic levels of drug for longer

than those with a lesser degree of plaque. This ﬁnd-

ing is in contrast to an experimental study in the litera-

ture (Tzafriri et al., 2010) where it was concluded that

drug concentration was inversely correlated to lipid

concentrations. The McGinty et al. model did, how-

ever, neglect the intimal region of the arterial wall and

the endothelium layer of cells. Their justiﬁcation for

this is that the endothelium is severely damaged when

a stent is inserted and in some cases is completely re-

moved; and indeed the properties of the intimal may

not be too different from those in the media.

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667

Despite considering two layers and accounting

for convection, diffusion and uptake/binding in each,

their model makes several simplifying assumptions.

Firstly, the geometry is restricted to one dimension

and as such cannot account for the anisotropic nature

of diffusion within the tissue ((Levin et al., 2004),

(Hwang et al., 2001)). Furthermore, the 1D model

clearly has its limitations in approximating 3D geom-

etry. The strut is considered to be in contact with

the arterial wall, when in reality it is likely embed-

ded within it. Finally, the ﬂow interaction problem

between the blood and the struts is not accounted for,

leading to the potential for under-prediction of drug

lost to the lumen, an aspect which has also been in-

vestigated in the literature (Zunino, 2004).

Pontrelli and de Monte (Pontrelli and de Monte,

2007) proposed a similar model to that of McGinty

et al. which allowed for a diffusion controlled re-

lease from the stent as well as convection-diffusion-

reaction in the arterial wall. Their most sophisticated

model has the beneﬁt of being multi-layered, but is

unable to model the drug concentration in the SMCs.

They do, however, model drug consumption via a lin-

ear reaction:

∂C

∂t

+ 2γ

∂C

∂x

= D

∂

∂x

−β

, (7)

where the subscript i indicates the ith layer and 2γ

represents a constant characteristic convection param-

eter. Pontrelli and de Monte’s model has the advan-

tage of admitting an analytical solution.

The convective and diffusive element of the drug

transport is well established, as evidenced by the

above models and countless others. However, the is-

sue of uptake/binding is more controversial. Some

authors have assumed equilibrium models ((McGinty,

2011), (Horner et al., 2010), (Abraham et al., 2013)),

while others have considered simple loss terms (Pon-

trelli and de Monte, 2007). More recently, a sec-

ond order reaction model which allows for saturable

reversible binding of sirolimus to speciﬁc receptors

and general extracellular matrix (ECM) sites has been

proposed (Tzafriri et al., 2012). The equations for the

rate of uptake of sirolimus to ECM sites and receptors

are:

∂b

ECM

∂t

= k

ECM

c(b

ECM,max

−b

ECM

)

−k

ECM

, (8)

∂b

REC

∂t

= k

REC

c(b

REC,max

−b

REC

)

−k

REC

. (9)

Here, c is the molar concentration of free drug per

unit tissue volume, b

ECM

and b

REC

are the molar con-

centrations of ECM-bound and receptor-bound drug,

respectively. The parameters b

ECM,max

and b

REC,max

denote the local molar concentration of ECM and re-

ceptor drug binding sites, k

ECM

and k

REC

are the re-

spective binding on-rate constants and k

ECM

and k

REC

are the respective equilibrium dissociation constants.

It is certainly true that the drug will bind to bind-

ing sites in the tissue and in the cells ((Levin et al.,

2005), (Tzafriri et al., 2012), (Bierer et al., 1990))

although the strength of the afﬁnity will likely vary

substantially with the particular drug under consider-

ation. Furthermore, it is not clear how the density of

the binding sites could easily be determined. Thus it

may be that this binding model is speciﬁc to a partic-

ular class of drugs and not suitable for more general

compounds. A greater understanding of the binding

process would undoubtedly assist with model devel-

opment.

5.2 Higher-dimensional Models

Despite providing useful, and in some cases, counter-

intuitive physiological insights, one-dimensional

models are inadequate for accurately resolving quan-

titative aspects. When the dimension of the model

is increased, numerical approaches are necessarily re-

quired.

Two-dimensional models in simpliﬁed geometries

were computed by (Hwang et al., 2001), (Grassi et

al., 2009) and (Zunino, 2004) among others. A num-

ber of three-dimensional models have also been de-

vised. (Weiler et al., 2012) provided a broad general-

ization of the works of (Mongrain, 2007), (Zunino et

al., 2009) and (Vairo et al., 2010); a three-dimensional

model of drug transport in the lumen and the arterial

wall. Laminar steady ﬂow was assumed in the lumen

and the steady diffusion equation (no convection) in

the arterial wall. Through numerical simulation using

commercial ﬁnite element software, they found that

the highest rates of mass transfer occurred at the for-

ward portion of the stent and the rate of drug delivery

to the lumen was greater than that to the tissue.

(Horner et al., 2010) appear to be one of the

ﬁrst authors to provide a three-dimensional reaction-

diffusion-convection model in a realistic geometry.

They stress the importance of considering two phases

of the drug (bound and unbound) and use a ﬁrst or-

der reaction kinetics model to describe the transfer of

drug between the two phases. They utilise ABAQUS

to obtain a realistic geometry of a deformed stent and

vessel wall and then utilise FLUENT to solve their

transport equations. Their three-dimensional setting

allows for the consideration of anisotropic diffusion

in the arterial wall. They do, however, make three

signiﬁcant simpliﬁcations. Firstly, they model the ar-

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terial wall as a linear homogeneous solid and do not

distinguish between the intima, media and adventi-

tia. Secondly, despite calculating the transmural ve-

locity ﬁeld, they assume this is ﬁxed when solving

the transport equations. Perhaps the most unrealistic

assumption is that the drug concentration on the stent

remains constant and does not deplete. They ﬁnd that

deposition patterns tend to follow the pattern of the

stent struts and that the drug is able to penetrate deep

into the arterial wall. The pattern of bound drug be-

comes less uniform as the Peclet number is increased,

eventually becoming restricted to areas adjacent to the

struts, as convection dominates over diffusion.

6 EXPERIMENTAL VALIDATION

An important aspect of modelling and simulation is

validation. The accuracy of the model results can

only ever be as good as the quality of the inputs, espe-

cially when the model is sensitive to changes in one

or more of the parameters. At present, before a DES

is approved for use in humans it must undergo in-vivo

testing in an animal model (for example porcine coro-

nary artery); this is a very costly exercise and also

raises ethical questions. However, a series of in-vitro

and ex-vivo experiments can be carried out at various

stages of the modelling process to verify certain as-

pects and to suggest improvements/modiﬁcations to

the model.

One such example of this is in the estimation of

the model parameters. In our laboratory we have

been performing in-vitro DES release experiments

which have allowed us to estimate the diffusion co-

efﬁcient of the drug in polymer-coated stents based

on a least squares analysis and utilising analytical so-

lutions (Figure 1). The experiments consisted of plac-

ing Cypher DESs in a sealed glass vial containing

physiological release medium (phosphate buffered

saline:ethanol (90:10)). At several time points up to

60 days, the stent was removed and placed in a sep-

arate vial containing fresh release medium, with the

mass of drug in the original solution subsequently

quantiﬁed using UV-spectroscopy. These simple ex-

periments give conﬁdence in the modelling and pro-

vide reliable estimates of the drug diffusion coefﬁ-

cient in the polymer, which can feed into more sophis-

ticated models. Alternatively, a diffusion cell contain-

ing a membrane made from the polymer under study

can be used. The diffusion coefﬁcients in each layer

of the arterial wall can be measured in a similar way.

The porosity of each layer of the arterial wall may be

measured from histological sections by quantitative

microscopy. Drug uptake/binding parameters, such

as the partition coefﬁcient K and uptake rate constant

α in equations (3-4) may be estimated by quantifying

drug uptaken by cells grown in culture plates at dif-

ferent time points. For estimation of the parameters

in the second order reaction model (equations 8-9),

the reader is referred to (Tzafriri et al., 2012) and ref-

erences therein.

But the use of experiments to inform the mod-

elling is not a one-way process. Indeed, our group

have utilised the modelling to design experiments

which in turn have fed back into the model. For ex-

ample, recognising that one of the important features

of in-vivo drug release from DESs is transport by con-

vection, in our laboratory we are developing ex-vivo

perfusion circuit experiments which will allow us to

control the intraluminal pressure (and thus vary con-

vection) across the arterial wall. Thus, experimental

validation should not be seen as the ﬁnal step, only to

be performed once the model has been built and the

results simulated. Instead, the modelling and exper-

imentation should go hand-in-hand, complementing

each other.

7 MODELLING

CONSIDERATIONS FOR THE

FUTURE

Whilst signiﬁcant progress has been made in simulat-

ing various aspects of drug-eluting stents, there is still

a need to better understand the drug elution process

and the drug transport in the lumen and arterial wall.

Here we indicate some possible modelling consider-

ations for future research in this ﬁeld so that the aim

of achieving an ‘optimal’ drug-eluting stent may be

realised.

7.1 Simulating Drug Release from New

Generation DESs

There is a real need for models to be developed

for drug release from newer generation biodegrad-

able polymer coated stents and polymer-free surface-

modiﬁed stents. It may be that the dominant release

mechanism in these stents is not diffusion and so

models which assume purely diffusion may not cap-

ture the release kinetics. Any new models should be

experimentally validated in-vitro to verify the phys-

ical processes governing the release have been cap-

tured. It is anticipated that for most DESs the in-vivo

release proﬁle may be signiﬁcantly different due to

the complex biological processes involved, but if the

in-vitro release can be well modelled then this should

SimulatingDrug-elutingStents-ProgressMadeandtheWayForward

669

shed some light as to how to model the in-vivo situa-

tion. Comparison of the in-vitro drug release proﬁle

of different stent platforms may indicate the release

mechanism(s) which give rise to the most favourable

release proﬁle. This, in turn, may allow for better de-

sign of DESs in the future.

7.2 Inclusion of the Endothelium,

Intima and Plaque

The inner layer of the the arterial wall, the intima, is a

thin layer comprising the endothelium as well as the

elastic lamina. It is well established that the endothe-

lium is damaged during the stent insertion process and

in some cases even removed. As a result, many cur-

rent models neglect the intima region.

A more complete model of the arterial wall should

include the intima region as well as the endothelium

and internal elastic lamina. The endothelium is im-

portant in vasoconstriction and vasodilation and reg-

ulates the uptake of plasma into the arterial wall.

While diseased endothelium is dysfunctional (this is

the starting point of atherosclerosis) it will neverthe-

less have an effect on the relative importance of con-

vection to diffusion in the arterial wall. It is antici-

pated that drug transport through the initma will oc-

cur via similar processes to that in the media, namely

diffusion (albeit with a different diffusion coefﬁcient

from the media), convection and possibly binding.

Another possible modelling consideration is

atherosclerotic plaque; the presence of the plaque

is the very reason that the stent is inserted and yet

it has received very little attention in the literature.

McGinty et al. seem to be the only authors who

have attempted to model the plaque to date, although

(Tzafriri et al., 2010) have experimentally examined

the effect of the plaque. The plaque is known to con-

tain a ﬁbrous cap of variable thickness as well as a

necrotic core made up of cellular debris, cholesterol

cleft and cell membranes. Furthermore, the plaque

also contains macrophages and SMCs as well as a

lipid pool containing lipid dispersed in a collagen

matrix. A More sophisticated model of plaque, tak-

ing into account its various components, may provide

more insight into the effect of plaque on tissue drug

concentrations.

7.3 Modelling Lumenal Blood Flow and

Stent Interaction

In simulations where the blood ﬂow is taken into ac-

count, it is common for the blood ﬂow to be modelled

as steady Poiseuille ﬂow. Of course, in reality blood

ﬂow near the heart is pulsatile and the artery is contin-

ually contracting and expanding. The presence of the

stent interrupts the ﬂow (Peacock et al., 1995) and the

effect this has on the drug transport should be simu-

lated.

In addition to simply considering some of the pa-

rameters to be time and space dependent, it may be

necessary to consider the proliferation of SMCs and

neointima growth as a wound healing problem.

7.4 Inclusion of Complex

Three-dimensional Geometry

While simpliﬁed one-dimensional models can pro-

vide useful insights into this problem, ultimately

three-dimensional models which capture the full com-

plex geometry of the stent and the arterial wall are

required. The idea of numerically simulating such a

complex problem may have seemed impossible not

so long ago, but with the accelerating advances in

computational power and numerical techniques it is

now possible. The existing three-dimensional models

in the literature all make certain simplifying assump-

tions, whether it be in idealising the stent geometry,

or in neglecting convection, diffusion or binding, or

in considering only single or bi-layer arterial walls.

Thus there is an opportunity to increase the sophisti-

cation of the three-dimensional models, whether it be

incrementally or in one fell swoop. However, caution

must be exercised to ensure that the results of the sim-

ulations are not subject to high uncertainty, in which

case the ﬁdelity of the results may be called into ques-

tion.

8 CONCLUSIONS

Drug-eluting stents have signiﬁcantly improved the

treatment of coronary artery disease. Despite real

progress being made in the past decade, a complete

understanding of DESs is still some way off. The

process of in-vitro drug release from newer genera-

tion DESs is still not fully understood, let alone the

complex in-vivo situation where ﬂowing blood, pul-

satility, wound healing, proliferation and migration

of SMCs and complex uptake/binding no doubt all

play some part. Future research should include the

modelling of drug release from biodegradable and

polymer-free modiﬁed surface stents, more accurately

modelling lumenal blood ﬂow and stent interaction,

including the endothelium, the intima and atheroscle-

rotic plaque. In order to be able to use simulations in a

predictive capacity, three-dimensional models which

encompass the full complex geometry are necessarily

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required. But care should be taken to verify the cor-

rectness of the numerical results. Finally, the mod-

elling should be complemented by appropriate exper-

iments to validate the resulting simulations and im-

prove on the model.

ACKNOWLEDGEMENTS

We would like to acknowledge the funding provided

by EPSRC under grant number EP/J007242/1. The

ﬁrst author would also like to acknowledge the receipt

of a Carnegie Scholarship.

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