Thesis Final (3 files merged)

I

Modelling and Design

Optimisation of Arterial Stents

Carl McEncroe

School of Aerospace, Mechanical and Mechatronic Engineering

University of Sydney

2012 Honours Thesis

Modelling and Design Optimisation of Arterial Stents Carl McEncroe

V

Table of Contents

Statement of Contribution………………………………………………………………………………… II

Abstract……………………………………………………………………………………………………………. III

Acknowledgements…………………………………………………………………………………………... IV

Table of Figures………………………………………………………………………………………………… VII

Abbreviations and Acronyms……………………………………………………………………………. X

1. Introduction ................................................................................................................................. 1

2. Literature Review ....................................................................................................................... 3

2.1. Indications for Revascularisation ...................................................................................................... 3

2.1.1. Coronary Artery Disease .................................................................................................................................. 3

2.1.2. Peripheral Artery Disease ................................................................................................................................ 4

2.1.3. Renovascular Hypertension ............................................................................................................................ 4

2.1.4. Carotid Artery Disease ...................................................................................................................................... 4

2.2. Balloon Angioplasty ................................................................................................................................ 5

2.3. Stents ............................................................................................................................................................ 6

2.3.1. Surgical Procedure .............................................................................................................................................. 7

2.4. Arterial Anatomy ..................................................................................................................................... 9

2.5. Existing Stent Designs ......................................................................................................................... 10

2.5.1. Slotted‐Tube ....................................................................................................................................................... 11

2.5.2. Coil .......................................................................................................................................................................... 12

2.6. Acumen for an Ideal Stent .................................................................................................................. 15

2.6.1. Difficulty of Delivery ....................................................................................................................................... 15

2.6.2. Scaffolding ........................................................................................................................................................... 15

2.6.3. Dog‐Boning .......................................................................................................................................................... 16

2.6.4. Foreshortening .................................................................................................................................................. 18

2.6.5. Acute Stent Thrombosis ................................................................................................................................ 18

2.6.6. Restenosis ............................................................................................................................................................ 18

2.7. Clinical Indications for Stent Choice: ............................................................................................. 19

2.7.1. Coronary Arteries ............................................................................................................................................. 19

2.7.2. Treating Carotid Arteries .............................................................................................................................. 22

2.7.3. Treating Peripheral Artery Disease (PAD) ............................................................................................ 23

2.8. The Finite Element Method ............................................................................................................... 23

2.9. Finite Element Analysis Software .................................................................................................... 24

2.10. Design Optimisation .......................................................................................................................... 24

2.11. Summary ................................................................................................................................................ 25


VI

3. Methods ........................................................................................................................................ 26

3.1. Material Properties and Characteristics ....................................................................................... 26

3.1.1. Stent ....................................................................................................................................................................... 26

3.1.2. Coronary Artery ................................................................................................................................................ 28

3.1.3. Balloon .................................................................................................................................................................. 32

3.2. Simulation of Stent Deployment ...................................................................................................... 33

3.2.1. Boundary and Contact Conditions ............................................................................................................ 34

3.2.2. Loading ................................................................................................................................................................. 35

4. Preliminary Results ................................................................................................................. 41

4.1. Expansion within Realistic Coronary Artery ............................................................................... 41

4.2. Stent Free Expansion ........................................................................................................................... 46

5. Results and Discussion ........................................................................................................... 48

5.1. Original Palmaz Schatz PS 154 ......................................................................................................... 48

5.1.1. Stress Distribution ........................................................................................................................................... 49

5.1.2. Luminal Gain ....................................................................................................................................................... 50

5.1.3. Vessel Straightening ........................................................................................................................................ 51

5.1.4. Elastic Recoil ....................................................................................................................................................... 51

5.1.5. Stent Foreshortening ...................................................................................................................................... 52

5.1.6. Dog‐boning .......................................................................................................................................................... 52

5.1.7. Ratio of Kinetic and Internal Energy ........................................................................................................ 53

5.2. Modified Geometry – PS 154 ............................................................................................................. 54

5.2.1. Eight Circumferential Slots .......................................................................................................................... 54

5.2.2. Sixteen Circumferential Slots ...................................................................................................................... 60

5.2.3. Curved End PS 154 .......................................................................................................................................... 66

5.2.4. Altering the width of PS 154 distal strut ................................................................................................ 70

5.3. Optimised Stent Design ....................................................................................................................... 71

6. Conclusion and Recommendations..................................................................................... 73

7. References ................................................................................................................................... 75

8. Appendix ...................................................................................................................................... 79

8.1. Consistent unit requirement in Abaqus ........................................................................................ 79


VII

Table of Figures

Figure 1 ‐ Different types of vulnerable plaque as underlying cause of acute coronary

events (ACS) and sudden cardiac death (SCD). A, Rupture‐prone plaque with large

lipid core and thin fibrous cap infiltrated by macrophages. B, Ruptured plaque with

subocclusive thrombus and early organization. C, Erosion‐prone plaque with

proteoglycan matrix in a smooth muscle cell‐rich plaque. D, Eroded plaque with

subocclusive thrombus. E, Intraplaque hemorrhage secondary to leaking vasa

vasorum. F, Calcific nodule protruding into the vessel lumen. G, Chronically stenotic

plaque with severe calcification, old thrombus, and eccentric lumen [8] ............................. 4

Figure 2 ‐ Carotid artery disease and stenting of the carotid arteries [12] .................................... 5

Figure 3 ‐ Percutaneous transluminal coronary angioplasty (PTCA) procedure

demonstrating the improved lumen area after plaque is compressed against the walls

of the coronary arteries [13]. .................................................................................................................... 6

Figure 5 ‐ Coronary angiography before and after angioplasty [18] ................................................. 8

Figure 6 ‐ Layers of the arterial wall ................................................................................................................ 9

Figure 7 ‐ Typical stent constructions: (A) closed cell, peak‐peak, flex connector, (B) open

cell, nonflex connector, peak‐peak, (C) open cell, nonflex connector, peak‐peak, (D)

open cell, flex connector, peak‐peak, (E) open cell, nonflex connector, peak‐valley, and

(F) open cell, nonflex connector, midstrut [20] ............................................................................. 11

Figure 8 ‐ Strut progression toward circumferential orientation in two tubular stent

designs [22] .................................................................................................................................................... 12

Figure 9 ‐ Typical structure of coil stents [22]. ........................................................................................ 12

Figure 10 ‐ pattern of transient non‐uniform balloon‐stent expansion at different stages

during expansion process [24] .............................................................................................................. 17

Figure 11 ‐ Lefevre classification of plaque burden at bifurcation [31] ........................................ 20

Figure 13 ‐ Photograph of the Palmaz Schatz PS 154 balloon‐expandable stent in its

constricted pre‐deployment phase [46]. ........................................................................................... 26

Figure 14 ‐ The isometric view of the resulting Solidworks of the PS 154 stent ....................... 27

Figure 16 ‐ Screenshots of the branched coronary artery model created in ScanIP with

hollowed body to define the arterial wall ......................................................................................... 29

Figure 18 ‐ Screenshots taken from Simpleware ScanIP of the segmentation procedure to

procure a straight coronary artery section ...................................................................................... 30

Figure 19 ‐ Hollow cylindrical model of the artery modelled in Abaqus ...................................... 31

Figure 20 ‐ Sketch in Abaqus of the three‐fold balloon to be extruded including parameters

............................................................................................................................................................................. 32

Figure 21 ‐ Compliance data from the manufacturers of duralyn with the line of best fit

representing the linear relationship of the material [52] .......................................................... 33

Figure 22 ‐ The resulting thin shell membrane model of the tri‐fold balloon modelled in

Abaqus .............................................................................................................................................................. 33

Figure 23 ‐ Screenshot of the setup within Abaqus of the realistic coronary artery model

illustrating the application of a uniform pressure load to the already meshed inner

surface of the stent. The green section represents the artery, the white part is the PS

154 stent, and the pink arrows represent the selected faces of the finite elements on

the inner surface of the stent that are to be assigned a pressure loading. ......................... 38

Figure 24 ‐ Screenshot of a preliminary simulation of the PS 154 stent by the method of

applying a uniform pressure to the inner surface of the stent. Excessive dog‐boning

caused the distal ends of the stent to perforate the arterial wall, an example of deep

nodal penetration. The perforations have been circled in red. ............................................... 39


VIII

Figure 25 ‐ Pressure Ramping Profile. The profile represents the amplitude of the

application of loading and unloading for all simulations. The dotted red line depicts the

transition point between the loading and unloading steps....................................................... 40

Figure 26 ‐ Segment cut view of initial setup for realistic coronary artery simulation. ......... 41

Figure 27 – YZ‐plane cut view of initial setup for realistic coronary artery model ................. 41

Figure 28 – YZ‐plane cut view of final phase of the simulation ........................................................ 42

Figure 29 ‐ Ratio of Kinetic Energy to Internal Energy throughout the simulation for the

realistic coronary artery model ............................................................................................................. 42

Figure 30 ‐ Residual stress distribution contour on the arterial wall (without and with the

stent). ................................................................................................................................................................ 43

Figure 31 ‐ Radial Displacement of three nodes on the outer surface of the stent (the two

distal ends and in the centre) and their corresponding values of dog‐boning

percentage. ..................................................................................................................................................... 43

Figure 32 ‐ Superimposed image of the initial pre‐deployment phase of the stent (dark

green) and the final post‐deployment inflated geometry (light green) ............................... 44

Figure 33 ‐ Foreshortening of the stent vs the applied pressure loading for the realistic

artery model. ................................................................................................................................................. 45

Figure 34 – Deformed end‐phase of free expansion of stent in Abaqus by applying a

uniform pressure load to the inner surface of the stent. Note the over‐expansion of the

distal ends of the stent beyond the maximum inflated body section of the stent

(~3.5mm). ....................................................................................................................................................... 46

Figure 35 ‐ The original PS 154 stent with the inclusion of wire connector elements. The

connector elements must be restrained from expanding larger than the maximum

inflated size of the balloon. ...................................................................................................................... 47

Figure 36 ‐ Initial setup of model including the artery (green), stent (red) and balloon

(white) in Abaqus. ....................................................................................................................................... 48

Figure 37 ‐ Side transparent view of the expansion stages. The tip image depicts the initial

setup of the model, and the bottom image depicts the final expanded phase. ................. 49

Figure 38 – Contour plot of the stress distribution in the arterial wall at first impact of the

distal ends of the stent with the arterial wall. ................................................................................. 49

Figure 39 ‐ Contour plot of the residual stress distribution in the arterial wall after the

balloon has been deflated and removed from the artery. .......................................................... 50

Figure 40 ‐ Superposition of the initial and final geometry of the stent from the side and

front views. ..................................................................................................................................................... 50

Figure 41 ‐ Graph of the radial displacement of the arterial wall and the corresponding

luminal gain in area of the vessel compared to the expansion pressure loading. ........... 51

Figure 42 ‐ Graph of the percentage foreshortening of the stent vs the pressure loading. .. 52

Figure 43 ‐ Graph of the radial displacement of nodes at the centre and at the distal end of

the stent as well as the corresponding % dog‐boning. ................................................................ 52

Figure 44 ‐ Ratio of Kinetic Energy to Internal Energy throughout the simulation of the

expansion of the original PS 154 stent ............................................................................................... 53

Figure 46 ‐ Side transparent view of the expansion process. The top image depicts the point

of first impact between the stent and the artery, and the bottom image depicts the final

stage of the simulation. ............................................................................................................................. 55

Figure 47 – Contour plot of the stress distribution of the artery when distal ends of stent

make first contact ........................................................................................................................................ 56

Figure 48 ‐ Superposition of original pre‐deployment phase of stent (dark green) and the

geometry of the stent when fist making contact with the arterial wall (light blue). ...... 56

Figure 49 ‐ Residual stress distribution of the arterial wall once the balloon has been

deflated. ........................................................................................................................................................... 57

Figure 50 ‐ Symbol plot depicting the magnitude and direction of residual principle stresses

in the arterial wall at the end of the simulation. ............................................................................ 57


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Figure 51 ‐ Graph of the Luminal Gain achieved vs. the applied pressure loading. ................. 58

Figure 52 ‐ Graph of the percentage foreshortening of the stent vs. the pressure loading. . 58



Figure 54 ‐ Graph of the ratio of kinetic energy to internal energy throughout the expansion

simulation. ...................................................................................................................................................... 60

Figure 55 ‐ Isometric view of the Solidworks model of the PS 154 stent modified to include

16 circumferential slot sites. .................................................................................................................. 60

Figure 56 ‐ Side transparent view of the expansion process. The top image depicts the

initial setup of the stent, balloon and artery, the second image depicts point of first

impact between the stent and the artery, and the bottom image depicts the final stage

of the simulation. ......................................................................................................................................... 61

Figure 57 ‐ Contour plot of the stress distribution of the artery when distal ends of stent

make first contact. ....................................................................................................................................... 62

Figure 58 ‐ Superposition of the initial and final geometry of the stent from the side view.62


deflated. ........................................................................................................................................................... 63


Figure 62 ‐ Graph of the ratio of kinetic energy to internal energy throughout the expansion

simulation. ...................................................................................................................................................... 64



Figure 65 ‐ Side transparent view of the expansion process. The top image depicts the

initial setup of the stent, balloon and artery, the second image depicts point of first

impact between the stent and the artery, and the bottom image depicts the final stage

of the simulation. ......................................................................................................................................... 66

Figure 66 ‐ Contour plot of the stress distribution of the artery when distal ends of stent

make first contact. ....................................................................................................................................... 67


deflated. ........................................................................................................................................................... 67

Figure 68 ‐ Symbol plot depicting the magnitude and direction of residual principle stresses

in the arterial wall at the end of the simulation. ............................................................................ 68


Figure 70 ‐ Graph of the percentage foreshortening of the stent vs. the pressure loading. . 69



Figure 72 ‐ Screenshots of the three modified stents in terms of width of the distal strut.

From left to right, the distal strut width is 0.25mm, 0.30mm (original stent parameter),

0.35mm and 0.40mm. ................................................................................................................................ 70


X

Abbreviations and Acronyms

BMS: Bare Metal Stent

CAD: Coronary Artery Disease

CTO: Chronic Total Occlusion

DES: Drug Eluting Stent

FDA: Food and Drug Administration

FEA: Finite Element Analysis

FEM: Finite Element Method

ISR: In-stent restenosis

PAD: Peripheral Artery Disease

PCI: Percutaneous Coronary Intervention

SVG: Saphenous Vein Graft


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1. Introduction

The era of interventional cardiology had its grounds in 1964 when Charles Theodore

Dotter and Melvin P. Judkins used a balloon-tipped catheter to treat a case of atherosclerotic

disease in a femoral artery [1]. In wasn’t until 1977 when Andreas Gruentzig went on to perform

the first percutaneous transluminal coronary angioplasty (PTCA) on a human [2]. Angioplasty

was a revolutionary procedure to improve blood flow through vessels throughout the body by

inflating and then deflating a balloon within the diseased segment of the vessel. The procedure

had the effect of dilating areas of blood vessels that had experienced narrowing from blockages

to improve the blood flow through the vessel. The development of stents was prompted due to

the two main shortcomings of angioplasty; acute occlusion and long-term restenosis [3]. The

stent is a tubular metallic structure that is implanted and left within the vessel during an

angioplasty procedure to give on-going support in the form of scaffolding to maintain vessel

patency [4].

Angioplasty and stenting is a minimally invasive and relatively low risk procedure that

has revolutionised the treatment of coronary artery disease (CAD). Although stenting is used

predominantly to treat CAD within the coronary arteries, stents are also used to treat numerous

diseases that cause narrowing or blockage of arteries throughout the body. Stent design has

evolved to improve its performance and reduce the risks involved with their use as well as being

considered for more complex situations.

There are many different designs for arterial stents and each different design varies the

mechanical characteristics of the stents and therefore varies their suitability for different types

and anatomical sites of arterial lesions. The favourable stent characteristics include flexibility,

trackability, low profile, radio-opacity, thromboresistancy, biocompatibility, reliable

expandability, high radial strength, circumferential coverage and a low surface area. There does

not yet exist a stent that has these ideal properties that would make its use optimal for all cases,

therefore interventional cardiologists are required to understand the differences in the different

types of stents to determine the best candidate for different lesion types and anatomical sites.

In 2003 the Food and Drug Administration (FDA) approved the first drug-eluting stent

(DES) in the United States. These stents slowly release medication that inhibit cell proliferation

and has consequently caused a drastic reduction in restenosis rates compared to bare metal stents


2

(BMS). The improved outcomes associated with DES has expanded stent usage to include

diabetic patients and to treat lesions that were previously believed to be too complex [2]. DES

are now used in 70-80% of all stent procedures worldwide [5].

Persisting concerns of in-stent restenosis and thrombosis keep the design evolution

process alive. As no ideal arterial stent yet exists, the on-going design optimisation of arterial

stents continues. This thesis aims to identify potential design optimisation of a commercially

available stent by finite element analysis focusing on residual stress distribution in the artery,

stent dog-boning, foreshortening, elastic recoil and luminal gain.


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2. Literature Review

2.1. Indications for Revascularisation

Angioplasty is a procedure used to treat conditions that cause the narrowing and blockage

of vessels throughout the body. The implanting of a stent is now involved in more than 70% of

angioplasties performed worldwide to assist the vessel to remain open [6]. The most common

conditions that require revascularisation procedures are Coronary Artery Disease (CAD),

Peripheral Artery Disease (PAD), Renovascular Hypertension, and Carotid Artery Disease.

2.1.1. Coronary Artery Disease

CAD is the single leading cause of mortality worldwide with greater than 19 million

deaths annually [7, 8]. The three main coronary arteries (left anterior descending, circumflex and

the right coronary artery) and their respective branches supply different sections of the heart

muscle with oxygen-rich blood. CAD is caused by atherosclerosis of the coronary arteries, which

is a build-up of plaque on the walls of arteries. Plaque is composed of cells, lipids, calcium,

collagen, and inflammatory infiltrates [9]. Atherosclerosis of arteries can vary in severity

depending on the amount of plaque build up as well as the composition of the plaque build-up.

The varying levels of severity are depicted in Figure 1 on the following page.

The coronary arteries supply the heart’s muscle tissue with its oxygen and nutrient

requirements and when the coronary arteries experience such atherosclerosis they are not able to

supply the heart with the blood that it demands. An imbalance between blood demand and

supply to the heart muscle cause chest pain for the patient called angina pectoris. Vulnerable

atherosclerotic plaques can rupture which trigger a repair response from the body, producing a

blood clot at the site of the superficial crack to seal it. If the clot completely obstructs the already

narrowed artery then the blood supply to the heart muscle is cut off, known as ischemia –

without oxygen and nutrients the patient suffers myocardial infarction and possible death if not

immediately treated. 70-85% of all myocardial infarctions occur with <30% stenosis of the

coronary arteries [7].

4

Figure 1 - Different types of vulnerable plaque as underlying cause of acute coronary events (ACS) and sudden

cardiac death (SCD). A, Rupture-prone plaque with large lipid core and thin fibrous cap infiltrated by

macrophages. B, Ruptured plaque with subocclusive thrombus and early organization. C, Erosion-prone plaque

with proteoglycan matrix in a smooth muscle cell-rich plaque. D, Eroded plaque with subocclusive thrombus. E,

Intraplaque hemorrhage secondary to leaking vasa vasorum. F, Calcific nodule protruding into the vessel lumen.

G, Chronically stenotic plaque with severe calcification, old thrombus, and eccentric lumen [8]

2.1.2. Peripheral Artery Disease

PAD is caused by atherosclerotic plaque build-up in the peripheral arteries of the

body. PAD usually affects the arteries supplying the legs but can also affect the arteries to the

stomach, kidneys, arms and the head. The reduction or cessation of blood flow to these

regions can cause pain and numbing and if severe enough it can cause tissue death such as

gangrene. A patient that suffers from PAD also has an increased chance of coronary and

carotid artery disease [10].

2.1.3. Renovascular Hypertension

Renovascular hypertension is a condition whereby narrowing of the renal arteries

causes a decreased blood flow to the kidneys and in turn the kidneys release hormones to

retain salts and water. This has the effect of increasing the patient’s blood pressure.

Atherosclerosis of the renal arteries is the most common cause of renovascular hypertension.

2.1.4. Carotid Artery Disease

Carotid Artery Disease is a narrowing of the carotid arteries in the neck that supply the

head and brain with oxygen-rich blood. The narrowing is also a result of atherosclerosis and

the patient can suffer a stroke if the blood supply is restricted to the brain, in the same respect

as myocardial infarction for the heart. Carotid Artery Disease is the cause of 20% of all

ischemic strokes and transient ischemic attacks [11]. A stroke can cause lasting brain damage,


5

paralysis or death if the blood supply to the brain is cut off for too long. Carotid artery disease

and stenting of the bifurcation of the carotid arteries is depicted in Figure 2.

Figure 2 - Carotid artery disease and stenting of the carotid arteries [12]

2.2. Balloon Angioplasty

Balloon angioplasty is a procedure performed to treat patients that have stenosed

blood vessels by compressing atherosclerotic plaques against the arterial wall and dilating the

lumen for improved blood flow. The procedure involves passing a balloon-tipped catheter to

the diseased segment of a vessel, inflating the balloon to a set diameter for roughly a minute

and then deflating and removing the balloon-tipped catheter from the patient.

Balloon angioplasty performed on the coronary arteries is known as percutaneous

transluminal coronary angioplasty (PTCA) as depicted in Figure 3.

Angioplasty as a treatment alone had several shortcomings that prompted the

development of the stent. The two main shortcomings were acute occlusion and long-term

restenosis. Some of the compressed material tends to spring back, or recoil, after balloon

angioplasty. The procedure damages the arterial wall to some degree, which causes

physiological mechanisms to repair the damage. Further cell proliferation of the intima,

known as neointimal hyperplasia, occurs 3-6 months after the procedure. The combined effect

of these factors causes the luminal area to re-narrow, called restenosis. The Belgium

Netherlands Stent Study (Benestent) and the Stent Restenosis Study (STRESS) were two

major randomised trials that popularised stent usage by confirming that stenting caused a

reduction in angiographic restenosis and clinical events post-procedure [3].


6

Figure 3 - Percutaneous transluminal coronary angioplasty (PTCA) procedure demonstrating the improved

lumen area after plaque is compressed against the walls of the coronary arteries [13].

As stenting is now involved in the majority of percutaneous coronary intervention

(PCI) procedures the role of balloon angioplasty is to initially prepare the passage-way and

site of the stent prior to its deployment, and then to inflate the stent against the arterial wall if

the stent is not self-expanding, and then for further expansion of the stent to ensure complete

dilation, if necessary.

2.3. Stents

A stent is a metallic tubular structure implanted and left in the diseased section of a

vessel to restore blood flow. Stents vary greatly in their design however the main purpose is to

give on-going assistance in holding a blood vessel open and preventing vessel recoil. Stents

do this by providing a scaffolding feature for the arterial wall, mechanically enforcing it and

resetting an improved luminal area, having the effect of decreasing the incidence of

restenosis. The atherosclerotic plaques are compressed against the arterial walls, dilating the

luminal area and maintaining vessel patency [14]. Stents can also be used after unsuccessful

balloon angioplasty to hold back intimal flaps, close off vessel dissections and prevent plaque

prolapse into the vascular lumen to treat threatened vessel closure [3, 4].

In 2003 the Food and Drug Administration (FDA) approved the first drug-eluting stent

(DES) in the United States. These stents slowly release medication that inhibit cell

proliferation and has consequently caused a drastic reduction in restenosis rates compared to


7

bare metal stents (BMS). The improved outcomes associated with DES has expanded stent

usage to include diabetic patients and to treat specific lesion types that were previously

believed to be too complex [2]. As of 2009, DES are used in 70-80% of all stent procedures

worldwide [5]. Despite the dominance of DES usage, bare metal stents (BMS) still have a role

in contemporary practice. The decision for usage of a BMS or DES comes down to both

clinical and economic factors. DES are considerably more expensive than BMS, they require

the patient to be on long-term dual antiplatelet therapy (DAPT) and they have been shown to

increase the risk of late stent thrombosis. However, they significantly reduce restenosis rates

(and therefore repeat vascularisation procedures) with no additional risk of mortality.

Ultimately it depends on a patient-specific basis but DES are currently believed to be the

superior choice in the majority of cases [2].

As can be seen in Figure 4, the procedure for implanting a stent is effectively the same

as balloon angioplasty, however, the stent remains in the diseased section of the vessel. Stents

can be both self-expanding or balloon expandable, whereby the stent is crimped and mounted

on a balloon-tipped catheter and expanded at the target site by balloon angioplasty. Self-

expandable are easily deployed however they may require additional expansion by balloon

angioplasty to ensure satisfactory dilation of the vessel [15].

There are many different designs for arterial stents,

the main types being mesh, slotted tube, tubular, coil, ring

and multi-design. Each different design varies the

mechanical characteristics of the stents and therefore varies

their suitability for different types and anatomical sites of

arterial lesions. The favourable stent characteristics include

flexibility, trackability, low profile, radio-opacity,

thromboresistancy, biocompatibility, reliable

expandability, high radial strength, circumferential

coverage and a low surface area [16]. There does not yet

exist a stent that has these ideal properties that would make

its use optimal for all cases, therefore interventional

cardiologists are required to understand the differences in

the different types of stents to determine the best candidate

for different lesion types and anatomical sites [17].

2.3.1. Surgical Procedure

Balloon angioplasty and stenting is a minimally

Figure 4 - Deployment of a balloon-expandable

stent in the coronary artery [13].


8

invasive procedure that takes between 30 and 60 minutes to complete. At least one week prior

to the procedure, the patient will commence an anticoagulant drug regimen to thin their blood

to ensure no blood clots occur during the operation. The patient is administered a local

anaesthetic and an incision is made in an access artery, usually in the groin or the arm, as an

entrance point to the body’s circulatory system. The patient is injected with a radio-opaque

contrast material to circulate through the circulatory system that block x-rays, enabling the

circulatory system to be visualised by an angiogram.

The interventional cardiologist is able to navigate a guide wire of the diagnostic

catheter through the circulatory system under angiogram image guidance to the target site.

Using angiography and intravascular ultrasound (IVUS) the interventional cardiologist is then

able to determine the length, diameter and type of balloon and stent required for each patient.

Balloon angioplasty alone is performed before the stent is deployed to prepare the site

of deployment and to help deliver the stent, this is known as pre-dilation. The stent is then

advanced to the site, positioned to fully cover the lesion, and then expanded (either by balloon

angioplasty or self-expanded). A hand-held syringe pump controls inflation of the balloon

whereby the interventional cardiologist can monitor the inflationary pressure to ensure ideal

dilation of the balloon and the stent. The balloon is left inflated for 30-60 seconds before

being deflated. Once the interventional cardiologist believes the stent is satisfactorily

expanded appositional to the arterial wall the balloon and catheters are removed from the

body, leaving the stent behind. Figure 5 depicts coronary angiography images before and after

an angioplasty procedure illustrating the improvement in blood flow after the deployment of a

stent.

Figure 5 - Coronary angiography before and after angioplasty [18]


9

The operator technique for the deployment of stents is vitally important – sub-optimal

expansion is associated with increased rates of restenosis and stent thrombosis.

Underestimating the size of stent required is the main cause of sub-optimal expansion.

Intravascular ultrasound has been shown to improve optimal stent size selection as it is more

accurate than angiography to determine stent length and diameter required, as well as

identifying if stent-edge dissections occur and if the there is incomplete stent apposition [2].

2.4. Arterial Anatomy

The artery is a blood vessel that carries oxygen and nutrient-rich blood away from the

heart throughout the body (with the exception of the pulmonary artery). An artery has three

distinct layers that make up the arterial wall. The three layers of an artery are the tunica

intima, tunica media and tunica externa (previously tunica adventitia) [19]. The hollow cavity

in the middle of the artery through which the blood flows is known as the lumen. The three

layers of the artery can be seen in Figure 6 and will be further discussed.

Figure 6 - Layers of the arterial wall

The arteries that are most commonly stented are the coronary arteries, carotid arteries,

renal arteries, and the peripheral arteries such as the superficial femoral arteries.

The tunica intima is the innermost layer of the artery and it is made up of connective

tissue and endothelial cells that are in contact with the blood that flows through the artery.

The endothelial cells make up a thin layer called the endothelium that acts as the scaffold for


10

atherosclerotic plaques to build on. Several months after the deployment of a stent, the

endothelium will grow over the top of the stent. The connective tissue consists of collagenous

and elastic fibers that provide structural support for the artery.

The tunica media is the middle layer of the artery and it is made up of smooth muscle

cells and elastic tissue. The overall thickness of an artery is completely dependant on the

thickness of the tunica media layer. Depending on the volume of blood that is flowing through

the artery and the force that blood exerts on the artery due to the blood pressure dictates the

amount of smooth muscle and elastic tissue required for the artery to maintain its structure

without rupturing. The larger arteries, such as the aorta, require significantly more smooth

muscle cells and elastic tissue than the smaller coronary or carotid arteries that accounts for

the difference in thickness. The pressure in the artery varies between its peak (systolic

pressure) and its minimum (diastolic pressure). The smooth muscle cells and elastic

connective tissue allows the artery to resist and adapt to the varying pressure that it

experiences between heart contractions. The tunica media is of utmost importance for this

thesis as it is this layer that causes recoil of the vessel during and after stent deployment, as

well as the source of resistance that the stent experiences over its lifetime.

The tunica externa (formerly tunica adventitia) is the outer layer of the artery and it is

made up of irregular connective tissue, both collagenous and elastic fibers. The function of

the tunica externa is simply to connect the vessel to the area it is running through. The

connective tissue of the tunica externa will connect to adjacent tissues to hold it in place and

provide the artery with some support. Although the tunica externa provides the artery stability

and allows it to stay in place, it does not have a significant role in maintaining vessel patency.

The lumen of the artery is the cavity through which the blood flows. When the arteries

experience atherosclerosis of the artery wall, the lumen size through which the blood can flow

is reduced. The obstruction to normal blood flow that atherosclerotic plaques cause means

that the oxygen demands of the body are not met.

2.5. Existing Stent Designs

There are various commercially available stents currently and they can be classified on

the basis of their mode of expansion, their geometry design, and whether they are drug-eluting

or bare-metal. Stents can be either self-expandable or balloon-expandable, with the latter

being the major focus of this thesis. The materials used are plastically deformed during

expansion by balloon angioplasty so that they retain their expanded form when the balloon is

deflated and removed. The material has slight recoil that is related to the elastic deformation


11

being reversed by relaxation. The ideal material would have a low yield so that the stent can

be plastically deformed at manageable balloon pressures, and low intrinsic elastic recoil. 316

L stainless steel is the material of choice in the majority of balloon-expandable stents. The

two main types of stent geometry design for vascular means are slotted-tube and the coil

designs and they all differ in length, percentage metal coverage, number of struts, strut

thickness, and cross section [14].

The two main constituents of stent design are expandable ring elements and

connecting bridge elements. The expandable rings are generally of zig-zag patterns that make

up the longitudinal struts of the stent. These expandable rings are positioned adjacent to each

other and connected via the bridge elements. The bridge elements can be described as either

flex or non-flex, which is dependant upon their shape. The designs vary where the bridges

occur and how many there are. Stents that have all struts connected to the adjacent ring’s

struts are called closed-cell, whereas when only some of the struts are the bridge connection

points they are called open-celled. A few examples of different open and closed-cell designs

with different combinations of connection points can be seen in Figure 7.

Figure 7 - Typical stent constructions: (A) closed cell, peak-peak, flex connector, (B) open cell, nonflex

connector, peak-peak, (C) open cell, nonflex connector, peak-peak, (D) open cell, flex connector, peak-peak, (E)

open cell, nonflex connector, peak-valley, and (F) open cell, nonflex connector, midstrut [20]

2.5.1. Slotted-Tube

Slotted-tube design stents make up roughly 75% of all commercially available

vascular stents [20]. The slotted-tube design is made up of a series of expandable “Z” shaped

elements called struts that are connected by bridge elements as described and illustrated

above. In general, slotted-tube stents have excellent radial strength but lack longitudinal

flexibility compared to coil designs [21].

As is demonstrated in Figure 8, the struts that are in the longitudinal direction rotate

outwards to become the circumferential struts [22].


12

Figure 8 - Strut progression toward circumferential orientation in two tubular stent designs [22]

2.5.2. Coil

Coil stents exhibit the highest longitudinal flexibility of all the stents as they have no

longitudinal shaft [22]. However, the strength of coil stents is somewhat lacking. The mode of

expansion for coil stents is by stretching of the circumferential struts until the desired

diameter is achieved – as the diameter of the stent is dilated the space between the struts

increases which increases the chance of tissue prolapsing through the gaps. The most readily

used coil stent is the Freedom stent made by Global Therapeutics Inc. [23]. A typical coil

stent structure is illustrated in Figure 9, depicting in particular the increase in gap size

between the struts as the stent is expanded.

Figure 9 - Typical structure of coil stents [22].

Stent Manufacturer Geometry and design Drug-

Eluting? Material Deployment

Diameter

(mm)

Length

(mm) Clinical Use Notes Picture

Acculink Guidant

comes in both a classical

tube and a conical

configuration

- nitinol Self-

expandable 6.0-10.0 20-40 Carotid

The conical configuration manufactured so that

when expanded the distal diameter is smaller than

the proximal diameter (for being in apportioned in

the internal carotid artery and the common carotid

artery, respectively)

beStent Medtronic AVE

Slotted tube - sinusoidal

ring modules linked via

sigmoidal link elements.

Radiopaque gold markers

at both ends

- 316 L stainless

steel

Balloon-

expandable 2.5-5.5 8-25

Regular, ostial,

bifurcation lesions

Large/open cell design that facilitates access to side

branches, virtually no shortening, low elastic recoil

beStent 2 Medtronic AVE

Slotted tube - flexible

radial "S" crowns and

longitudinal "V" crowns

crossing at a junction that

rotates during expansion.

Gold markers at both ends

- 316 L stainless

steel

Balloon-


Regular coronary

stent

Closer strut design than beStent so not suitable for

ostial or bifurcational lesions

Biodivysio Biocompatibles

Slotted tube - alternating

sinusoidal rings with

rectangular and rounded

edges. Rings linked by S

articulations

-

316 L stainless

steel coated with

phosphorylcholine

Balloon-


Regular, ostial,

bifurcational

lesions

Good scaffolding and open cell design that

facilitates access to side branches. The

phosphorylcholine coating is designed to reduce

thrombosis

CYPER

system (Bx

Velocity

stent)

Cordis


ring strut modules linked

by "N" shaped flex

segments

Simolimus 316 L stainless

steel

Balloon-


Ostial lesions

(aorto-ostial),

regular lesions,

calcified

The CYPHER system is the popular Bx Velocity

slotted tube stent that has been treated to be drug-

eluting with Simolimus to decrease the incidence of

thrombosis

NIR (9 cell) Medinol


ring modules linked via

curved link elements

- 316 L stainless

steel

Balloon-


Ostial lesions

(aorto-ostial),

calcified lesions,

not good for

Designed to be a stiff stent compared to others


14

configuration designed to

improve the stent's

scaffolding properties

crossed vessels

Carbostent

Sirius

Sorin

Biomedica

Cardio

Slotted tube - with

platinum end markers -

316 L stainless

steel covered with

thin layer of

turbostratic

carbon

Balloon-


Regular and

difficult

anatomies/lesions

Turbostratic carbon with the intent to decrease its

interaction with platelets

Multi-Link

RX

ULTRA

Guidant

Slotted tube - corrugated

multi-link five crown

rounded corner zigzag ring

module design linked with

straight link elements

- 316 L stainless

steel

Balloon-


Ostial lesions

(aorto-ostial)

Excellent longitudinal flexibility and traceability.

Lacks in radial strength.

PS 154 Palmaz Schatz

Laser cute slotted tube

microstent with 12

circumferential slot sites

and no bridge connectors

- 316L Stainless

Steel

Balloon-

expandable 3.5 8.06

Regular coronary

stent. Small

arterial lesions

Excellent radial strength but lacks in flexibility and

has unfavourable levels of dog-boning

15

2.6. Acumen for an Ideal Stent

An ideal stent can be judged on the outcomes of difficulty of delivery, scaffolding

capability, degree of dog-boning and foreshortening, and the occurrence of acute stent

thrombosis and restenosis.

2.6.1. Difficulty of Delivery

The ideal stent should be easy to deliver to the diseased site of the vessel. The two

characteristics of stent design that are of great importance when considering the ease of

delivery are having high longitudinal flexibility in its unexpanded state and having a low

profile [22]. The flexibility of the stent can be described by the bending stiffness of the stent.

Evaluating the stiffness of stents can be achieved by using the bending equation of a simple

cantilever beam [24]:

!" =!"

!

3!

(EI = Bending Stiffness, P = Pressure, L = Length of stent, ! = Deflection)

High longitudinal flexibility is important so that the stent can be easily advanced to the

target through tortuous anatomical curves and bends with minimum effort, without injuring

the intima of the arterial wall and without eliciting spasm. Smooth delivery is also termed

high trackability.

2.6.2. Scaffolding

For ideal scaffolding the stent is required to have sufficient radial strength to be able to

hold the artery open to the desired luminal area, resisting the elastic recoil of the tunica media.

The stent must be able to cover the diseased segment of the artery in a uniform manner so that

there is no tissue or plaque prolapse through gaps in the stent. It is also required that the stent

have to strength to be able to tack back intimal flaps and seal off vessel dissections. Once the

stent is deployed at the target site, the stent should be able to mould to the natural contour of

the vessel. This is especially important if the stent is to be deployed in the curvature of a

vessel or in a complex anatomical region such as a bifurcation. The stent must have high

longitudinal flexibility in its expanded stage so that it doesn’t tend to straighten out the vessel

but rather have a smooth transition between the stented and adjacent arterial wall areas. The

first Palmaz-Schatz stent had low longitudinal flexibility and it was found to straighten the

target site if deployed at a bend – this would induce stress concentrations at the ends of the

stent and injure the arterial wall increases the incidence of restenosis and acute stent


16

thrombosis. High longitudinal flexibility is found in the multi-design stents and the more

flexible coil stents that have no longitudinal shaft or only a single longitudinal shaft such as

the Bart XT stent [22].

2.6.2.1. Radial Strength

Radial strength is the resistance that the circumferential struts provide against the

elastic recoil response of the vessel’s media [22]. The hyperelastic media induces a

compressing pressure on the circumferential struts of the stent. The stent tends to recoil after

the balloon is deflated and removed due to the relaxation of the elastic media but also due to

the internal stresses within the stent [25]. In general, a stent will have higher radial strength if

it has wide, thick longitudinal struts that during expansion rotate circumferentially [22].

Generally, there is an inverse relationship between the radial strength of a stent and its

longitudinal flexibility.

2.6.2.2. Recoil

Recoil of the stent occurs in both the longitudinal and radial directions, they represent

the amount of contraction of the stent after the removal of the balloon catheter [24]. The

following equations describe both longitudinal and radial recoil:

!"#$%&'(%#)* !"#$%& =!!"#$ − !!"#$%&

!!"#$

!"#$"% !"#$%& =!!"#$ − !!"#$%&

!!"#$

Where L and R are the length and radius of the stent before removing the balloon

catheter and after removing the balloon catheter. Radial recoil of the stent after the stent is

deployed is a serious engineering concern as it decreases the luminal area of the vessel and

affects the stability of the stent. Stents that exhibit high recoil due to their material, design and

geometry require the operator to over-dilate the stent with respects to the desired luminal area

so allow for the recoil – this can damage the arterial wall tissue and cause intimal

proliferation. The elastic recoil of tubular stents is greater than coil or hybrid stents [25].

2.6.3. Dog-Boning

Dog-boning is the phenomenon that takes place during the expansion of a stent by a

balloon catheter whereby the distal ends of the stent are the first places to expand, resembling

a dog-bone shape. Dog-boning causes unnecessary trauma and damage to the arterial wall


17

during the expansion phase which can increase the risk of restenosis of the artery [26]. Four

stages of the expansion of a stent can be seen below in Figure 10, with the dog-boning

phenomenon very obvious in the second and third stages.

Figure 10 - pattern of transient non-uniform balloon-stent expansion at different stages during expansion process

[24]

Dog-boning can be described by the following equation:

!"#$"%&%# = !!"#$%&!"#$

−!!"#$%&'

!"#$

!!"#$%&

!"#$

(!!"#$%&!"#$ = the distal radius of the stent, !

!"#$%&'

!"#$ = the central radius of the stent [24])

Several finite element analysis studies have been completed to determine whether

altering the geometrical design at the distal ends of the stent would result in decreased dog-

boning, however Wang et al demonstrated that dog-boning can be drastically reduced by

using shorter balloons so that the overhang at either end of the stent is not as pronounced [27].

Wang also found that increasing the width of the distal struts had beneficial results in

decreasing dog-boning.


18

2.6.4. Foreshortening

Foreshortening is the deformation of the stent in the longitudinal direction when the

stent is expanded [24].

!"#$%ℎ!"#$%&%' = ! − !!"#$%&

!

(L = the pre-expansion length of the stent, !!"#$%& = the length of the stent after expansion)

Foreshortening is an important issue that needs to be considered when evaluating stent

design. If the stent exhibits a large amount of foreshortening then when it is expanded there is

a possibility that it is not covering all of the atherosclerotic plaque anymore. Simply

overestimating the length of the stent required to avoid this problem can also damage the

arterial wall at the ends of the stent. Foreshortening of the stent can cause damage to the

arterial wall as the contact between the stent and the arterial wall exhibit a shearing force that

can increase the chance of restenosis of the artery.

2.6.5. Acute Stent Thrombosis

The ideal stent would have a low incidence rate of acute stent thrombosis. The design

and material of the stent are extremely important as well as correct apposition of the stent’s

struts to the arterial wall. Malapposition of the struts leave gaps between the stent and the

artery wall where thrombus is able to form. For the struts that are not well embedded into the

vessel wall, they tend to have much friction with the wall during ventricular contraction and

relaxation that increases the risk of acute stent thrombosis. The surface of stent should be

smooth and burr-free by being polished or electroplated [22]. The material used by the stent

also has a major effect on the thromboresistancy of the stent.

2.6.6. Restenosis

Restenosis is a condition where a vessel that has already been revascularised begins to

narrow again. It is caused by the early recoil and late arterial remodelling already mentioned,

but the major cause of restenosis is neointimal hyperplasia [22]. Neointimal hyperplasia is a

result of the initial arterial tissue damage that occurs during stent implantation and the

persistent frictional stimulation by the stent. The design of the stent must ensure full

apposition of the struts to the arterial wall and with the least injury to the arterial wall as

possible. As discussed earlier, drug-eluting stents have greatly reduced the incidence rate of

in-stent restenosis compared to bare-metal stents.


19

2.7. Clinical Indications for Stent Choice:

Interventional cardiologists are faced with a very large and varied assortment of stent

types and it is up to their decision-making process and their experience to select the most

appropriate stent for all cases. The choice depends on the patient, the size and composition of

the lesion, and the artery that the lesion is located in. The different characteristics of stents to

match different clinical issues will assist in making a judicious selection of stents. The

following discussion will outline some features that will make a stent more or less appropriate

for certain anatomical sites and lesion types.

2.7.1. Coronary Arteries

2.7.1.1. Regular Coronary Lesion

The regular coronary lesion is characterized by being a proximal and non-angulated

lesion [28]. It is understood that procedural success in these straightforward cases can be

achieved with almost any stent [22]. Stents recommended for use in the regular coronary

artery are the tubular, slotted-tube and ring geometries [28]. All of the design characteristics

such as deliverability and lesion coverage need to be determined for the specific case.

2.7.1.2. Lesions located in curvature of vessel

As has already been discussed, it is essential that a stent have very high longitudinal

flexibility when treating lesions in curvature of a vessel. If the flexibility is low then the stent

will tend to straighten the vessel and exert unwanted stresses at the ends damaging the arterial

tissue. Stents with no longitudinal shaft have the highest flexibility such as the multi-design

and coil stents [22].

2.7.1.3. Ostial Lesions

An ostial lesion is an atherosclerotic plaque that occurs at an ostium of a vessel –

where the origin of a vessel branches off from a larger parent conduit vessel. The main

concerns when stenting ostial lesions is the difficulty involved localising the ostium

angiographically and then optimally positioning and deploying the stent without having

excess metal protruding in to the parent vessel [29]. It is paramount that the stent chosen for

ostial lesions has excellent radiologic visibility – several stents incorporate end markers that

assist optimal positioning of the stent to the ostium. The elastic recoil of the parent vessel is

generally much stronger than that of the artery being stenting, such as with the aorta and the

coronary arteries. The chosen stent should have high radial strength and low elastic recoil to

allow for the increased recoil response at the ostial end. Three slotted tube stents that have


20

been shown to be effective for aorto-ostial lesions are the BxVelocity, the NIR, and the Ultra

[28].

2.7.1.4. Bifurcational Lesions

Bifurcational lesions are atherosclerotic plaques that are found at a bifurcation of an

artery – where the artery separates in to two parts. They are a very complex subset of lesions

and there are many different forms of plaque burden at a bifurcation that all require different

stent choice and deployment technique. The six main types of plaque burden are described by

the Lefevre classification in Figure 7. The main concerns with stenting a bifurcational lesion

is the risk of excess metal protruding into the side branch and not being able to have sufficient

coverage of the lesion in complex areas. Bifurcational lesions also have a risk of side branch

occlusion as the plaque tends to shift and this is what prompted the development of the

“kissing” balloon technique which corrects distortion of the side branch that occurs during

deployment [30].

Figure 11 - Lefevre classification of plaque burden at bifurcation [31]


21

Stents for bifurcational lesions should have excellent radiologic visibility for optimal

positioning and have large side openings between the struts for passage of further stenting of

the side branch using the modified T-technique for lesions proximal to the bifurcation [31].

The slotted tube stents are found to have the greatest side opening between struts and are the

best choice for stenting bifurcational lesions [28].

2.7.1.5. Calcified Lesions

As discussed previously, atherosclerotic plaques can vary greatly in composition.

Expanding a stent at a calcified lesion will result in a less than desired luminal size compared

to non-calcified lesions [28]. Stents for calcified lesions must have high radial strength to

resist the elastic recoil and to maintain vessel stabilisation. Preparing the site prior to stent

deployment by using rotational atherectomy is advised with highly calcified lesions. Highly

calcified lesions have been shown to hinder optimal expansion of stents, especially self-

expandable stents. The NIR, BxVelocity and Ultra are considered sound choices for calcified

lesions [28].

2.7.1.6. Chronic Total Occlusions

Chronic total occlusion (CTO) is defined as an older than 3 month old total

obstruction of an artery. They are a still a very difficult condition to treat effectively and

recanalisation is performed prior to stent deployment to allow passage for the balloon and

stent. A stent for treating CTO should have high radial strength to hold back the remaining

plaque, and have good coverage with a closed-cell design so that there is no plaque prolapse

in to the lumen. More recently drug-eluting stents have also been shown to be superior to

bare-metal stents in the treatment of CTO.

2.7.1.7. Small Vessels

Stents were not initially developed for very small vessels, however there is now a

modest range of stents available to treat vessels less than three millimetres in diameter. They

have improved flexibility, capacity to reach distal lesions, and thin strut structure which are

all very important attributes when the navigating through and deploying in very small vessels.

2.7.1.8. Saphenous Vein Grafts

A saphenous vein graft (SVG) is a cardiac intervention to treat vascular occlusions in

the coronary arteries by removing the diseased segment and grafting in a saphenous vein to

improve the blood flow. Saphenous vein grafts are susceptible to atherosclerotic plaque build-

up and stenosis also once they take the place of the coronary artery. Stenting of the SVG is

different to a regular coronary artery stenting procedure because it involves a larger vessel


22

diameter and there is significant risk of distal embolization. The lesions in SVG tend to be

considerably longer than regular lesions so the stent has to be available in longer lengths.

Self-expanding stents such as the Wallstent or the nitinol NIR are a good choice for SVG

lesions as they minimise trauma and damage to the arterial wall lowering the risk of distal

embolization [32].

Despite all of the theoretic and practical considerations provided for selecting a

particular stent to treat a specific lesion, the individual experience and confidence of the

operator are paramount. No rationale for choosing a specific stent for a specific lesion is yet

supported by randomized trials.

Except for the use of a stent to prevent threatened occlusion, stents are implanted with

the intent to prevent restenosis. The operator should strive to reach this goal while

maximizing the patient’s safety. Judicious stent selection, balloon sizing, and lesion

preparation to achieve an optimal final lumen dimension remain the most important goals in

percutaneous coronary interventions [28].

2.7.2. Treating Carotid Arteries

Stents used to treat carotid artery disease improve the blood flow to the head and

brain. If the carotid arteries become completely blocked, or if some of the atherosclerotic

plaque becomes dislodged and carries to the brain then the patient can suffer a life-threatening

stroke. Carotid endarterectomy had been the general procedure for the treatment of

atherosclerotic carotid arteries however stenting of the carotid arteries is recently being

acknowledged as a safe and cost-effective alternative to carotid endarterectomy [11]. Stenting

is the preferred treatment compared to

angioplasty alone as stenting largely avoids

plaque dislodgment, intimal dissection,

elastic recoil and late restenosis [33].

Stenting for the treatment of carotid artery

disease has been shown to be an effective

and relatively safe treatment [34].

Atherosclerosis of the bifurcation of the

common and internal carotid arteries is

responsible for the majority of strokes [33].

Intrathoracic, ostial common carotid and

intracerebral lesions are also associated with

Figure 12 - Acculink stent: both cylinder and conical designs

are available


23

stroke events too. The differing anatomies and size of these lesions warrants different stents.

Much of the discussion of different stent usage for coronary arteries carries over in the

concerns for the carotid arteries. Ostial lesions require high radial strength and precise

positioning. Carotid bifurcation lesions may require stents of varying diameters as the lumen

area of the common carotid and the internal carotid artery vary greatly. The Guidant Acculink

stent comes in both a classic cylinder but also a conical design as seen in Figure 12. The

conical configuration is designed so that the smaller distal end is placed in the internal carotid

artery whereas the larger proximal end is appositioned within the common carotid artery. The

intracerebral arteries have a much smaller diameter and have tortuous curvature. These

arteries require extremely small diameter stents that have high longitudinal flexibility as the

intracranial arteries are very sensitive to spasm [33].

2.7.3. Treating Peripheral Artery Disease (PAD)

There are several stents that have now been designed specifically for peripheral artery

disease to treat pain, numbness and tissue death in the extremities. The legs are the most

commonly affected area of the body as the femoral arteries that supply the legs with blood

become stenosed. Patients with severe cases of PAD are at the risk of limb amputation,

however as PAD is a major risk factor for coronary artery disease, their associated risks often

overshadow those of PAD [10]. This is due to PAD being a marker for systemic

atherosclerosis, so the risks to limbs are low compared to the risk to life of the patient [35].

Because of this patients are often stented in the coronary and peripheral arteries in the same

procedure.

The main arteries that are stented to treat PAD are the aorta, iliac, femoral, popliteal,

tibial and peroneal arteries. Each of these arteries varies greatly in size, elastic recoil and

blood flow conditions. Stents are chosen on a case specific basis for much of the reasons

already discussed.

2.8. The Finite Element Method

The finite element method is a numerical technique that provides approximate

solutions to a series of differential equations that describe a range of physical and non-

physical problems. It can be applied in structural analysis to determine stresses and

deformations of a model. The finite element method discretises a large complex model into

many simple finite elements. Shared nodes connect each of the finite elements. The collection

of all of the finite elements and the nodes creates the mesh of a model. The fundamental

variable of a stress analysis is the displacements of the nodes. Once these displacements are


24

calculated the stresses and strains of all finite elements can be determined. The quality of the

mesh can be described by the average size of the finite elements that make up the model.

Finer mesh qualities include more elements and nodes in the mesh and should converge upon

an approximate solution closer to the realistic solution. A finer mesh quality involves

increased degrees of freedom of the nodes in the model thus the solution more accurately

describes the stresses and deformation of the whole model. Increasing the quality of the mesh

involves increasing the number of differential equations that need to be solved to determine

the approximate solution.

One must consider the weigh-off between accuracy of the solution and the

computational time required to come to the solution. A convergence test can run to determine

the ideal mesh quality of the model to ensure a balance between an accurate solution and a

reasonable simulation time.

2.9. Finite Element Analysis Software

After reviewing the methodology and practices of several stent optimisation papers it

was concluded that Abaqus and ANSYS were the two main finite element analysis (FEA)

software packages used for similar simulations [14, 23, 24, 27, 36-42]. It was decided that

Abaqus would be the best choice for the FEA simulation in this thesis as Abaqus is a more

robust package compared to ANSYS when considering non-linear and dynamic models. The

numerical analysis required in this thesis involves large levels of deformation and contact

making the Abaqus code a clear choice as it provides a stable general contact algorithm [11].

Abaqus is a powerful engineering simulation program that can has the capability of modelling

and running finite element analysis of very complex models. As much of the analysis that will

be done in this thesis will involve complex geometries of artery models and of the stents

themselves, Abaqus is the best choice for a finite element method program.

Abaqus has the ability of studying more that simply structural problems – it is also

able to simulate problems relating to acoustics, mass diffusion, thermal management of

electrical components, soil mechanics, piezoelectric analysis and heat transfer. This thesis

however will only be using structural (stress/displacement) component of the software.

2.10. Design Optimisation

This thesis aims to optimise the design of a commercially available coronary stent in

order to reduce the incidence of restenosis and thrombosis. Reklaitis et al [43] describe

optimisation succinctly in the following quote: “In general terms, optimisation theory is a


25

body of mathematical results and numerical methods for finding and identifying the best

candidate from a collection of alternatives without having to explicitly enumerate and

evaluate all possible alternatives”.

The design optimisation procedure that this thesis undertakes is a qualitative approach

whereby finite element method software is utilised to observe improvements in results from

simulations of several stent designs to select the best candidate. FEM is a major tool of the

design optimisation process as it is an inexpensive and fast way to evaluate changes in design

geometry and material properties without having to manufacture and implant first.

Experimental measurement would be very expensive and time consuming. FEM software is

utilised to determine if stress can be minimised as well as improving on other expansion

outcomes such as dog-boning, foreshortening and elastic recoil.

2.11. Summary

Stenting has become a very common and relied upon technique employed in

interventional cardiology and increasingly in other blood vessels also. With persisting

concerns of in-stent restenosis and thrombosis, stents are not yet a perfect treatment of

atherosclerotic arteries. The ongoing mechanical design evolution of the stent has seen

improvements in clinical outcomes over the past decades, in addition to the introduction of

drug-eluting stents in recent years. However as the ideal arterial stent does not yet exist, there

is potential for further design optimisation so that the stent can become a safe, effective, and

reliable device to restore vessel patency for the patient’s lifetime.

This thesis will focus on the design optimisation of a balloon-expandable slotted tube

stent utilising finite element analysis software. Many studies have previously been conducted

on this topic and this thesis will attempt to validate and build upon this work by determining

mechanical factors of the stent that can be altered to improve the long-term performance of

arterial stents.


26

3. Methods

The remainder of this thesis will focus on the Palmaz Schatz PS 154 balloon-

expandable coronary artery stent (Johnson & Johnson, Warren, NJ, USA) in particular. The

PS 154 will be the subject of finite element method (FEM) simulation and analysis to propose

recommendations on design optimisation of the original stent design.

One of the main challenges of this thesis is to develop a general and easily repeatable

finite element procedure to model the mechanical characteristics of the stent and the arterial

wall. This thesis initially considered simulation of stent deployment in a realistic coronary

artery. Modelling and simulating the deployment of a stent in a realistic coronary artery has

been achieved by Zahedmanesh & Gijsen et al [44, 45] but not attempted by many others.

Modelling of a realistic coronary artery comes with the complexity of producing the model,

the complications associated with the complex non-linearity of the geometry and the difficulty

in producing an easily repeatable FEM procedure.

Initially a model for the arterial wall was created using the Simpleware software,

ScanIP. It was found that continuing to use the ScanIP generated artery would not be a wise

choice as it was not completely compatible with the FEM software being used. The final

decision was to create the artery natively within Abaqus CAE in the form of a perfect hollow

cylinder, which was also the chosen finite element method software package for analysis in

this thesis. This was deemed necessary to reduce the computational workload in completing

the simulations, and also to ensure consistent placement and fixing of the several stent

expansion simulations that were analysed. The assumption of the artery being a straight,

hollow cylindrical tube is the basis of the mast majority of literature on modelling and design

optimisation of arterial stents.

3.1. Material Properties and Characteristics

3.1.1. Stent

Figure 13 - Photograph of the Palmaz Schatz PS 154 balloon-expandable stent in its constricted pre-deployment

phase [46].


27

The Palmaz Schatz PS 154 stent is a laser-cut slotted tube stent (see Figure 13). The

PS 154 stent was created in Solidworks under parameters set out in Gu et al [46] and can be

viewed in the following table.

PS 154 Stent Parameters

Outer Diameter 1.47mm

Length 8.06mm

Thickness 0.10mm

Direction Number of Slots

Longitudinal 2

Circumferential 12

Slot Dimensions

Length 3.62mm

Width 0.22mm

Distal Strut Length 0.30mm

Inner Strut Length 0.22mm

Metal Strut Width 0.14mm

Figure 14 - The isometric view of the resulting Solidworks of the PS 154 stent

As the elastic strain of the stent is very small in comparison to the plastic strain it can

be assumed that the stent material exhibits isotropic elasticity [47]. The plastic properties of

the PS 154 stent were not made available by the manufacturer so the guidelines set out in


28

Migliavacca et al [41] were adopted and are detailed below. The plastic behaviour of the

model assumed a piece-wise linear isotropic hardening between the yield and ultimate stress

to mimic the plastic region [46].

3.1.2. Coronary Artery

The initial intentions of the thesis were to model the expansion of a balloon-

expandable stent within a realistic coronary artery. A realistic coronary artery was generated

with the use of ScanIP. As complications in producing repeatable results due to the

complexity and non-linearity of the realistic coronary artery became apparent it was deemed

necessary for the thesis to consider the a simpler artery model. Subsequent simulations were

performed with a hollow cylindrical artery model created natively within Abaqus CAE for its

comparative simplicity in setting up simulations and producing repeatable results with

multiple stent designs.

3.1.2.1. Modelling artery with Simpleware software

The realistic coronary artery model created for

analysis was produced using the Simpleware ScanIP

software. The input data used to create the model came in

the form of a DICOM (Digital Imaging and

Communications in Medicine) set that accompanied the

Simpleware software. DICOM is a data set that a variety of

medical imaging outputs (including Magnetic Resonance

Imaging and X-Ray Computed Tomography) can be saved

to for storing, transmitting, printing or for post-processing.

ScanIP is able to import DICOM data sets and assist the

user in creating 3D models from the data set.

PS 154 Stent Material Properties

Material Stainless Steel 316L

Young's Modulus, E 196GPa

Poisson Ratio, ν 0.3

Yield Stress, σY 205MPa

Ultimate Stress, σM 515MPa

Ultimate Strain, εM 0.6

Density, ρ 7850 kg/m3 = 7.85 x 10

-9 tonne / mm

3

Figure 15 – Realistic branched coronary

artery model created in ScanIP


29

The DICOM set used to create the model was of the heart and the coronary arteries

from a computed tomography angiography (CTA) data set. The blood that was present inside

of the arteries could be selected by using the threshold floodfill tool. The section of the

coronary artery to be modelled was then created in to a new mask and the excess data was

cropped from the segment. The threshold floodfill feature is not perfect and it usually requires

the user to make manual fixes to the mask. The use of a smoothing and Gaussian filter tool

enables the user to refine the smoothness and continuity of the model surface.

The branched coronary artery blood flow mask can be seen in Figure 15. The DICOM

data set was not of a high enough quality to be able to distinguish the arterial wall from other

tissues in the CT images so the arterial wall needed to be created by exporting the blood mask

to ScanCAD and then use an offset tool to create the arterial wall at a fixed distance from the

blood mask. The thickness assigned to the ScanIP mask was set at 0.7mm which equates to a

typical coronary artery thickness [48]. One issue with this method of creating the arterial wall

is that the thickness of the arterial wall varies greatly at all points along the length of arteries

and it has been found to be directly related to the luminal area of the artery. As can be seen in

Figure 15 the thickness of the branched arteries varies greatly and strictly would have varying

corresponding arterial wall thicknesses. An assumption of a fixed arterial wall thickness can

be justified for this model as the artery segment that will be eventually analysed will be

cropped from the remainder of the branched artery model. The final model mask for the

arterial wall branched network can be seen below in Figure 16.

Figure 16 - Screenshots of the branched coronary artery model created in ScanIP with hollowed body to define

the arterial wall

A benefit of using a realistic coronary artery model is to evaluate the vessel

straightening that occurs during the deployment of a stent as no realistic artery is ever


30

perfectly straight. Analysis of the flexibility of the stent plays a major role when simulating

deployment in an artery that exhibits non-linearity.

Once the arterial wall thickness was defined within ScanCAD it was also possible to

position the stent within the artery in preparation

for expansion in FEM software. ScanCAD allows

for .sat files to be easily imported and effortlessly

positioned within ScanIP generated models. Figure

17 shows the positioning of the stent within the

branched artery model within ScanCAD.

Once the stent is positioned within the

artery the whole model can then be exported to

Abaqus for finite element analysis and simulation

of the expansion of the stent. As the entire

branched coronary artery network model is not

necessary for the finite element method expansion

simulation it is wise to cut down the size of the

model to a small segment of one of the coronary

arteries. The Saint-Venant’s Principle states that

the impact of local displacements and stresses

diminish with distance from the local area [49] –

thus it is not necessary to run a finite element

method simulation of the entire branched model when it is only the site of the stent

deployment that is of concern for finite element analysis. The chosen segment of the coronary

artery can be seen in Figure 18.

Figure 18 - Screenshots taken from Simpleware ScanIP of the segmentation procedure to procure a straight

coronary artery section

Figure 17 - Screenshots of the placement of the

PS 154 stent model within the branched coronary

artery model within Simpleware ScanCAD


31

A downside to using ScanIP to produce an artery model is that it is a requirement that

ScanIP meshes all models through its +FE module before exporting to FEM software. FEM

software such as Abaqus that are dedicated finite element software with very powerful built-in

meshing engines ideally would be used to mesh the entire model, however Simpleware does

not enable this. The meshing capability of the Simpleware +FE module is quite

computationally expensive. There are further issues that the +FE module causes regarding

selecting the inner surface of the stent that will be discussed later.

3.1.2.2. Modelling artery with Abaqus

Several papers have run stent expansion simulations modelling the artery as three

separate concentric layers representing the tunica intima, tunica media, and tunica adventitia

all with different corresponding mechanical properties [36]. It is the decision of this thesis to

model the artery as one hollow cylindrical layer, a procedure adopted by Pant et al [50]. The

single layer artery model is assumed to have the material characteristics of the tunica media

layer of the artery as this is the largest layer by volume and is the location of the smooth

muscle cells and elastic tissue. It is these tissue types that give the artery its hyperelastic

characteristics and their mechanical responses are the subject of stent expansion research. For

these reasons it is justifiable to model the artery as one hollow cylindrical layer with the

material properties of the tunica media layer.

The coronary artery was modelled as a hollow cylindrical tube of length 10.00mm,

outer diameter of 4.40mm and an internal diameter of 3.00mm. These artery parameters are

adopted from Pant et al [50] and are considered typical coronary artery proportions. The

coronary artery was made to these parameters within Abaqus CAE and the final model is

depicted in Figure 19.

Figure 19 - Hollow cylindrical model of the artery modelled in Abaqus

The method for modelling the mechanical behaviour of the arterial wall will be

isotropic hyperelastic behaviour following a reduced polynomial strain energy density


32

function of the sixth order (U) and the material density of the artery is assumed to be 1 g/cm3

[36].

! = !!" !! − 3 + !!" !! − 3!+ !!" !! − 3

!+ !!" !! − 3

!+ !!" !! − 3

!+ !!" !! − 3

!

(where I!is the first invariant of the deviatoric Cauchy-Green tensor [50])

Experimental data from the analysis of the coronary artery to the reduced polynomial

strain energy density function model produced the following coefficients for the three layers

of the artery. This work is adopted from Gervaso et al [42].

Alternative strain energy density functions used in prior studies to model the

hyperelastic nature of the artery include the polynomial and Mooney-Rivlin [51] form.

3.1.3. Balloon

The balloon was created within Abaqus and modelled as a tri-fold balloon. The simple

tri-fold sketch was extruded to create the thin-shell membrane part. The sketch was extruded

to a length of 15mm and the membrane of the balloon was assigned a thickness of 0.02mm.

Figure 20 - Sketch in Abaqus of the three-fold balloon to be extruded including parameters

The balloon was assumed to have been made of the material, duralyn. Based on thin

shell membrane theory the balloon’s material behaviour can be derived from the compliance

Arterial Layer C10 C20 C30 C40 C50 C60

Intima 6.70E-03

0.54 -1.11 10.65 -7.27 1.63

Media 6.52E-03

4.89E-02

9.26E-03

7.60E-01

-4.30E-01

8.69E-02

Adventitia 8.27E-03

1.20E-02

0.52 -5.63 21.44 0


33

data of the true stress and strain of the material. This compliance data is provided from the

manufacturer of duralyn in Figure 21. The balloon material was derived from the line of best

fit for the compliance data for duralyn representing the elastic line corresponding to a

Young’s modulus of 920MPa and a Poisson’s ratio of 0.4. The material behaviour of the

balloon is modelled as having linear isotropic elasticity. The density of the balloon was

assumed to be 1.1 gram/cm3. The material properties for the balloon was adopted from De

Beule et al [52].

Figure 21 - Compliance data from the manufacturers of duralyn with the line of best fit representing the linear

relationship of the material [52]

Figure 22 - The resulting thin shell membrane model of the tri-fold balloon modelled in Abaqus

3.2. Simulation of Stent Deployment

The expansion of the stents within the artery was simulated by quasi-static dynamic

analysis with the use of the commercial Abaqus code based on the finite element method. The

finite element method is a widely used and reliable engineering tool for testing of product

design and product development.


34

The deployment of a stent is considered a quasi-static phenomenon where inertial

forces are small [11]. A quasi-static process is a thermodynamic process that occurs infinitely

slowly and thus the way to approximate the process is to perform them infinitesimally slowly.

Abaqus approximates the quasi-static process of stent deployment by performing the

deployment at infinitesimal increments.

It should be noted that Abaqus does not use a built-in unit system and it is the user’s

responsibility to keep consistency in the use of units. As the models that have been created for

this thesis have been created in terms of millimetres it is necessary for all other unit inputs to

be scaled to be consistent with this. For instance, if entering an input for mass of the stent it

would need to be entered in tonnes (103 kg) rather than kilograms. A full conversion table is

included in the appendix of the thesis for reference.

3.2.1. Boundary and Contact Conditions

A local cylindrical coordinate system needs to be created through the medial cross-

section of the stent so that three nodes on the stent (in an equilateral triangle shape) can be

identified. These three nodes on the stent must be free to expand radially but be restricted

from rotating circumferentially or migrating longitudinally [36].

This method will ensure that the stent is ideally fixed within the artery and will ensure

that the stent does not shift out of the artery when the simulation brings the artery and stent in

contact with each other. This restriction must only be applied to nodes in the medial plane of

the stent so the effects of dog-boning and foreshortening can be observed. The distal ends of

the stent should be free from any constraints to allow for the observation of these phenomena

during the simulations. This boundary condition should be repeated for three nodes on the

artery part to keep the expansion of the artery constrained to the radial direction.

The distal ends of the artery and balloon must be pinned in all directions of the

coordinate system, as it is essential the whole artery and the balloon to be fixed at its ends.

The ends should be fixed with respect to displacement and rotation about all three axes of the

coordinated system. The fixed boundary conditions on the distal ends of the artery are

necessary to mimic the continuation of the artery longitudinally down the remainder of its

length.

Although it would have been possible to model the simulation using only one-twelfth

of the full model this thesis chose to consider the full model simulation for ease of

interpretation of the results at the sacrifice of a shorter computational processing time. This

would have been possible due to the symmetrical boundary conditions of the circular

geometry of the stent and artery assembly.


35

When the method of expansion for the stent was by applying a pressure to the inside

surface of the stent it was necessary to include restraints on connector elements in the model

[44]. This was necessary to ensure that the stent would not expand beyond the maximum

diameter of a balloon. If these connector element restraints were not utilised then the distal

ends of the stent will expand quicker than the body of the stent. The ends would also begin to

deform beyond the maximum diameter of a balloon as the applied pressure is uniform

throughout the step.

The Abaqus General Contact algorithm defined the contact conditions of the

simulations between the stent, balloon and the artery. The tangential contact was assumed to

be frictionless and the normal contact was set to default “hard” contact while being able to

separate after contact

3.2.2. Loading

For the stent expansion simulation in Abaqus it is necessary to first decide on the

method of expansion for Abaqus to execute. Once the method has been chosen, it is necessary

to set up time steps and to assign loads within each step period in accordance with the chosen

expansion method. Following is an in-depth overview of the steps involved in assigning loads

to expand the stent.

3.2.2.1. Method of Stent Inflation

There are three commonly used methods to simulate the expansion of the stent within

the artery and they will be discussed below.

Displacement of Stent

The simplest approach for the expansion of the stent is by applying a displacement

condition on the inner surface of the stent. The inner surface of the stent is increased until the

diameter of a fully inflated balloon is achieved. For the case of the PS 154 this is 3.5mm. This

is not an ideal method for simulating the stent deployment as a realistic expansion would

exhibit dog-boning where the distal ends of the stent expand first and at a greater rate than the

middle of the stent. This method would not be effective at simulating this expected

phenomenon.

Pressure applied to Stent

The stent expansion can be simulated by applying a uniform pressure to the inner

surface of the stent, mimicking the pressure that the balloon induces on the stent during


36

expansion [15, 37, 51, 53, 54]. This method is far superior to the displacement method as it

allows for the simulation of dog-boning at the distal ends of the stent as the ends are the

weakest part of the geometry and thus deform first and at the highest rate.

This method however does not account for the maximum deformation that should

ideally occur. As the increasing pressure on the inner surface continues to expand and deform

the stent it can tend to over-expand the distal ends to a point where they would not even be in

contact with an expanding balloon anymore in a realistic situation.

Therefore for this method it is important to restrain connector elements on nodes of

the stent to ensure that it does not deform beyond the maximum inflated size of a balloon.

Zahedmanesh et al [44] shows that this method is inaccurate at describing the stress-strain

field and the deformation experienced in the vessel wall and the stent. However, utilising

restrained connector elements to restrict the maximum deformation of the distal ends of the

stent is a computationally efficient and accurate method for predicting the stress-strain field

and the deformation experienced in the arterial wall and the stent.

Pressure applied to Balloon

This method has the inclusion of an expandable balloon to the model positioned within

the stent part [40, 42]. The method of expansion is by applying a uniform pressure on the

inner surface of the balloon, expanding the balloon until it makes contact with the stent and

then continuing to expand the stent into the artery. This method would be considered a

transient non-uniform balloon-stent expansion. Although the second method is quite

reasonable, realistically the balloon does not apply a uniform pressure to the inner surface of

the stent. The balloon tends to be marginally longer than stent therefore there is some excess

balloon on either side of the stent. When the balloon starts to expand it tends to expand the

distal ends of the balloon that are free from the stent’s resistance. The pressure induced on the

inner surface of the stent is actually greater initially at the distal ends of the stent. When the

balloon is fully expanded at the distal ends of the stent, the pressure distribution then reduces

to zero at the ends and increasing in the middle of the balloon until the whole stent is fully

expanded. Refer back to Figure 10 for the demonstration of dog-boning throughout the

expansion period. This method simulates the true expansion of the stent and exhibits realistic

dog-boning.

This method however introduces a new model part in to the simulation and with it includes

additional computational workload and the potential of more contact errors throughout the

simulation. In the prior methods the only contact involved is between the stent and artery.


37

With the inclusion of the balloon there is contact between the stent and artery, the balloon and

the stent, the balloon and the artery, as well the balloon self contact

It was decided that for this thesis the second and third method of expansion would be

employed. The second method was chosen to reduce the computational cost and

contact complications associated with including an expandable balloon in the

simulation. Auricchio et al [55] justifies the use of the second method as the balloon is

made of a much more flexible material compared to the stent. Accordingly, the

stiffness of the balloon could be considered negligible compared to the stiffness of the

stent hence justifying the possibility of discarding the balloon from the analysis. The

third method will also be employed to return clinically realistic results.

3.2.2.2. Mass Scaling

Mass scaling was utilised for all simulations to decrease the computational workload

involved. Mass scaling is a tool within Abaqus that increases the minimum stable time

increment considered in the simulation. However the usage of mass scaling makes it

important to monitor the ratio of the kinetic energy (KE) to internal energy (IE) of the model

throughout the time of the simulation. It is recommended that the ratio remain below 5%

throughout the simulation [36, 40] for a quasi-static analysis. Keeping the ratio below 5%

ensures a quasi-static process in accordance with guidelines from the developers of Abaqus.

In order to achieve this the models must toggle the step times of the simulation and the degree

of mass scaling utilised as the material properties of the model are not time dependant.

3.2.2.3. Defining the inner surface of the stent

When expanding the stent by the method of applying a uniform pressure load to the

inner surface of the stent it is necessary to be able to distinguish the inner surface of the stent.

ScanIP generated model

As was previously mentioned, the +FE module of ScanIP requires that all models be

meshed within ScanIP before being exported to FEM software such as Abaqus. This poses an

issue for this step of the process, as the previously continuous inner surface of the stent was

discretised by the +FE model to a relatively coarse quadratic tetrahedral surface. The

consequence of this is that the inner surface of the stent cannot be easily defined once in

Abaqus in order to apply the uniform pressure load.

It is necessary to use a tool that creates a surface by picking the face of one of the

finite elements sitting on the inner surface of the stent and then getting it to create a surface


38

based on adjacent finite element surfaces where they are included if they are within a certain

angle difference of the selected face. Realistically, unless the mesh quality was very fine it is

very difficult to fully define the inner surface of the stent by this method. This tool requires

the user to experiment by trial and error with the chosen angle difference and the initial finite

element face in order to produce a close to all-encompassing surface. It can be seen in Figure

23 that the surface may not include all the finite element faces and therefore will not result in

a perfectly uniform pressure load on the inner surface of the stent.

Figure 23 - Screenshot of the setup within Abaqus of the realistic coronary artery model illustrating the

application of a uniform pressure load to the already meshed inner surface of the stent. The green section

represents the artery, the white part is the PS 154 stent, and the pink arrows represent the selected faces of the

finite elements on the inner surface of the stent that are to be assigned a pressure loading.

3.2.2.4. Steps

Within Abaqus steps are a period of time in which loads can be assigned for the

simulation. For the expansion of a stent there are three distinct phases over which the

procedure occurs. These three phases are the loading phase, holding phase and the unloading

phase. Each of these phases must have an assigned step in which their corresponding pressure

loadings can be assigned.

Loading Phase

For this thesis a loading phase was created with a length of 10 seconds. This thesis has

chosen to simulate the deployment of the stent with both a uniform pressure load applied to

the inner surface of the stent to mimic the pressure induced on a stent from an expanding

balloon, and comparing this with expansion with a balloon model.


39

For the method of expansion by balloon, a uniform pressure of 0.7 MPa is applied to

the inner surface of the balloon, which is a clinically accurate magnitude in accordance with

true angioplasty procedure.

For the method of expansion by applying a uniform pressure on the inner surface of

the stent a maximum pressure of 1.2 MPa was adopted from Gu et al [46]. Zahedmanesh et al

[44] argues that the applied pressure loading is clinically meaningless as this method does not

include the presence of an expanding balloon. Zahedmanesh stresses the importance of

restraining connector elements if this method is used to ensure that the stent does not expand

to a larger diameter than the balloon.

The amplitude of the ramping up of the pressure from zero to 1.2 MPa was initially

simulated as linear over the whole period of expansion. Several problems can arise during

simulation in Abaqus if expansion of the stent occurs too quickly. If the stent comes in to

contact with the artery with excessive velocity then deep penetration contact issues occur

where the distal ends of the stent can perforate the meshed artery as can be seen in Figure 24.

Figure 24 - Screenshot of a preliminary simulation of the PS 154 stent by the method of applying a uniform

pressure to the inner surface of the stent. Excessive dog-boning caused the distal ends of the stent to perforate the

arterial wall, an example of deep nodal penetration. The perforations have been circled in red.

This situation also causes a large spike in the ratio of kinetic energy to internal energy,

which disobeys Abaqus guidelines for maintaining a quasi-static process. This situation can

be mitigated by altering the amplitude of the ramping up of the pressure load; the pressure

should increase from zero very slowly in a linear fashion until the stent has come in to contact


40

with the artery, then after contact has been initiated the remainder of the pressure increase can

occur. The ramping up profile adopted for simulations in this thesis can be seen in Figure 25.

Holding Phase

Literature differs in its opinion on the inclusion of a holding period whereby the

maximum pressure is held for a short period of time before decreasing the pressure in the

balloon. In clinical practice, the balloon is kept fully expanded for roughly 30 seconds before

being deflate and removed from the vessel.

As the simulations in this thesis are quasi-static it can be justified that the holding

phase would not be a necessary step in the simulation as the elastic mechanical properties of

the artery and stent are time independent.

Unloading Phase

The pressure must be unloaded from the inner surface of the balloon uniformly in

order to study the elastic recoil of the stent and artery. For this thesis, the length of the

unloading phase was set at 0.5 seconds. When simulating the expansion of the stent by

balloon inflation, it is important to decrease the pressure loading throughout the step until

there is slight negative pressure acting on the inner surface of the balloon at the end of the

simulation. This is important when wanting to analyse the stress distribution contours of the

artery and stent at the end of the simulation, as the negative pressure causes the balloon to

deflate slightly and no longer be in contact with the stent or the arterial wall, thus having no

influence on the final stress distribution in the stent and artery.

Figure 25 - Pressure Ramping Profile. The profile represents the amplitude of the application of loading and

unloading for all simulations. The dotted red line depicts the transition point between the loading and unloading

steps.

Step Transition

‐0.15 ‐0.10 ‐0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0

Pressure (MPa)

Step Time (seconds)

Pressure Ramping Pro7ile


41

4. Preliminary Results

4.1. Expansion within Realistic Coronary Artery

The realistic coronary artery model that was created in ScanIP was revascularised by

the method of applying a uniform pressure to the inner surface of the stent. The initial setup of

the model can be seen in Figure 26 and 27.

Figure 26 - Segment cut view of initial setup for realistic coronary artery simulation.

Figure 27 – YZ-plane cut view of initial setup for realistic coronary artery model

The stent was positioned within the realistic coronary artery in relatively straight section to

minimise the bending of the stent and the straightening of the vessel. The final expanded stage

of the simulation can be seen in Figure 28. The expansion of the stent resulted in a large

degree of luminal gain for the artery. The magnitude of luminal gain displayed is an

indication that the PS 154 stent was of a greater than necessary diameter for this artery. A

stent with a smaller expansion diameter would be better suited in this realistic coronary artery

model.


42

Figure 28 – YZ-plane cut view of final phase of the simulation

Figure 29 - Ratio of Kinetic Energy to Internal Energy throughout the simulation for the realistic coronary artery

model

The graph of the ratio of the kinetic energy to the internal energy shows a significant

jump mid way through the simulation. This spike is associated with the speed at which the

stent expanded and the corresponding velocity of expansion of the arterial wall when the stent

initially makes contact with it. As has been discussed earlier, Abaqus recommends

maintaining a ratio below 5% throughout the simulation to ensure a quasi-static process. The

ratio for this simulation peaked at 18% suggesting that a quasi-static process was not achieved

in this simulation. The simulation could have been adjusted to reduce the degree of mass

scaling utilised and to spread the expansion over a greater step period in order to avoid

breaching the 5% threshold. As further simulations dismissed the inclusion of the realistic


43

artery model in favour of expansion of a stent within a hollow cylindrical artery it was not

deemed necessary to achieve a quasi-static process for this simulation.

Figure 30 - Residual stress distribution contour on the arterial wall (without and with the stent).

Figure 30 displays the residual stress distribution contour of the arterial wall with and

without the implanted stent. As can be seen, the residual stress distribution is quite uniform

throughout the section of artery appositional to the implanted stent with the exception of four

localised high stress areas. These high stress areas are caused by the slight pinching of the

arterial wall by some of the corners of the distal struts. Regardless of the somewhat

uniformity of the stress distribution there still exists an unacceptable magnitude of residual

stress on the artery due to the incorrect sizing of the stent for the artery model and over-

dilation of the artery.

Figure 31 - Radial Displacement of three nodes on the outer surface of the stent (the two distal ends and in the

centre) and their corresponding values of dog-boning percentage.


44

The unusual negative dog-boning values seen if Figure 31 can be explained by the fact

that the stent was deployed in to an artery that was too small for the chosen stent. As can be

seen in Figure 28, the initial pre-stent deployment diameter of the artery is significantly less

than the final expanded stent diameter.

Usually dog-boning occurs because the ends of the stent deform first and fastest under

an internal pressure as they are the weakest parts of the structure. However in the case of this

simulation, the artery was too small for the stent and therefore the artery produced large

reaction forces on to the distal ends of the stent. The arterial reaction forces are strongest at

the distal ends of the stent because these areas exhibit the highest stress gradient as the

adjacent unexpanded artery experiences low stress. These strong reaction forces from the

artery tend to cause this negative dog-boning.

Another interesting result is the difference in magnitude of the dog-boning between

two distal nodes on opposite ends of the stent to each other. One end of the stent achieves a

minimum dog-boning around -10%, and the opposite end has a minimum close to -30%. This

shows that the dilation of the stent was not only non-uniform throughout its length but also

asymmetrical. This asymmetry is made quite obvious in Figure 32 that displays the initial

undeformed stent and the final deformed stent superimposed on each other.

Figure 32 - Superimposed image of the initial pre-deployment phase of the stent (dark green) and the final post-

deployment inflated geometry (light green)

In this image it can be seen that the stent has deformed to the natural contours of the

artery to some degree whereby the uniform internal pressure applied to the inner surface of

the stent has not resulted in a uniform dilation of the stent. The right half of the stent does not


45

appear to be fully expanded as the artery was slightly narrower on that end, therefore the stent

experienced higher resistance to expansion from the reaction forces of the artery.

The right half of the stent may not have achieved full expansion either due to the

inability to fully define the inner surface of the stent to apply the uniform pressure load.

Figure 33 - Foreshortening of the stent vs the applied pressure loading for the realistic artery model.

The results of foreshortening of the PS 154 stent throughout expansion can be seen in

Figure 33. At the end of the expansion phase the foreshortening of the stent had reached -11%

that is much greater than the recommended range listed in literature of -5% to -9%. This large

value of foreshortening can be explained by the irregular final geometry of the stent whereby

the central body of the stent was found to deform outwards in a convex fashion (see Figure

32). This convex bulging of the central body and incomplete expansion of the distal ends

increased the degree of foreshortening. The stent exhibited longitudinal recoil of 1.2% after

the end of the unloading phase for a final stent foreshortening of -9.8%.

It was decided that it would be best for the consistency of results and repeatability of

the finite element method of several stent simulations if the hollow cylinder artery were

modelled instead of the realistic coronary artery. The large degree of complexity of the model

and difficulty of positioning the stent part in the model made the process of producing a

repeatable and reliable finite element method simulation very difficult. It is believed that the

results from the simulation suffered as complications such as the inability to fully define the


46

inner surface of the stent and the incorrect sizing of the chosen artery affected the complete

expansion of the stent and hence the validity of the results. The analysis of the ratio of kinetic

energy to internal energy throughout the simulations suggests the process was not quasi-static

throughout all phases.

4.2. Stent Free Expansion

It was deemed necessary to analyse the effects of expanding a stent without the artery

model to decide which method of expansion should be utilised.

A simulation of the expansion of the PS 154 stent by the method of applying a

uniform pressure to the inner surface of the stent was run without the presence of the artery

part. A uniform internal pressure of was applied to the inner surface of the stent, ramping up

the load from 0 MPa at the start to 1 MPa at 3 seconds (tabular fashion). Figure 34 depicts the

deformed stent at the end of the expansion phase. As can be seen, the distal ends of the stent

exhibit a large degree of flaring and dog-boning compared to the fully expanded body of the

stent. The stent is designed to be fully expanded when an inner diameter of 3.5mm is

achieved. This is why the balloons are designed to have a maximum inflated diameter of

3.5mm. The consequence of the additional dog-boning of the distal ends is that this method of

simulation has deformed the distal ends beyond the maximum inflated diameter of a balloon.

So realistically a balloon-expandable stent should never be able to expand beyond the

maximum inflated diameter of the balloon as it is the balloon that is the element that is

transferring the pressure load to the stent.

Figure 34 – Deformed end-phase of free expansion of stent in Abaqus by applying a uniform pressure load to the

inner surface of the stent. Note the over-expansion of the distal ends of the stent beyond the maximum inflated

body section of the stent (~3.5mm).


47

As can be seen, the uniform pressure on the inner surface of the stent does not relate to

a uniform dilatation throughout the length of the stent. Being the weakest area of the structure

the distal ends of the stent dilate greater than the body section of the stent. The outcome is that

the distal ends of the stent will continue to expand beyond the maximum diameter of an

inflatable balloon and induce highly concentrated stresses on the artery that do not normally

occur. The amount of dog-boning that this simulation causes induces areas of high stress on

the arterial wall and the potential of perforating the arterial wall. This result verifies the

requirement of using connector elements and restraining them when using this method of

expansion. Connector wire elements can be attached to the nodes on the distal edges of the

stent at one end and attached to ground (the centre axis running longitudinally through the

stent model) and adding a constraint that the displacement of the nodes from the ground must

not exceed 1.75mm such that the maximum deformation of the distal ends of the stent will

have a 3.5mm diameter. This restraint is necessary to mimic the realistic expansion of a

balloon-expandable stent where the induced pressure will only be present while the stent is

still in contact with the expanding balloon within.

These restraints on the connector elements at the distal ends of the stent are depicted in

Figure 35 and will be included in the model for all further simulations by the method of

uniform pressure load on the inner surface of the stent.

Figure 35 - The original PS 154 stent with the inclusion of wire connector elements. The connector elements

must be restrained from expanding larger than the maximum inflated size of the balloon.


48

5. Results and Discussion

Figure 36 - Initial setup of model including the artery (green), stent (red) and balloon (white) in Abaqus.

Simulations of the expansion of the original PS 154 stent as well as several modified

models were conducted by the method of expansion from an internally positioned balloon

model. The initial setup for all simulations can be seen above in Figure 36. Several modified

stent models were analysed for consideration in optimising the original design parameters of

the PS 154 stent.

5.1. Original Palmaz Schatz PS 154

The expansion of the original PS 154 slotted-tube stent was successfully simulated

with the inclusion of an inflating balloon. The results to be reviewed for each simulation

include the stress distribution in the artery and stent, the luminal gain achieved, vessel

straightening, elastic recoil, stent foreshortening, dog-boning and the ratio of kinetic energy to

internal energy. The expansion stages of the simulation can be seen below in Figure 37

depicting the initial setup phase and the final expanded phase.


49

Figure 37 - Side transparent view of the expansion stages. The tip image depicts the initial setup of the model,

and the bottom image depicts the final expanded phase.

5.1.1. Stress Distribution

The potential injury to the arterial wall due to the apposition of the stent after

deployment can be described by the stress distribution [11]. As has been discussed, the degree

of injury to the arterial wall is a major factor in the future potential of restenosis. The ideal

stent should provide the necessary support and structure for the vessel whilst minimising the

stress induced on the arterial wall by the stent.

Figure 38 below depicts the stress distribution on the arterial wall when the distal ends

of the stent make first impact with the arterial wall. As is expected there is localised areas of

high stress where the corners of the stent come in contact with the artery when the level of

dog-boning is at its highest value. The resistance from the arterial wall on the distal ends tend

to decrease the level of dog-boning from this point as the central body of the stent begins to

expand faster relative to the distal ends.

Figure 38 – Contour plot of the stress distribution in the arterial wall at first impact of the distal ends of the stent

with the arterial wall.


50

Figure 39 - Contour plot of the residual stress distribution in the arterial wall after the balloon has been deflated

and removed from the artery.

The residual stress distribution can be seen in Figure 39. The residual dog-boning of the stent

causes localised stress concentrations appositional to the distal ends of the stent. The position

of the maximum residual principle stress in the arterial wall is depicted and has a magnitude

of 0.175MPa.

5.1.2. Luminal Gain

Figure 40 - Superposition of the initial and final geometry of the stent from the side and front views.

Figure 40 above depicts the superposition of the pre and post-deployment phases of

the PS 154 stent. As can be seen, the final geometry of the stent exhibits a near uniform

dilation throughout its length with only a slight dog-boning visible in the distal ends of the

stent.

The major reason for the deployment of stents is to restore blood flow by increasing

the luminal area in stenosed segments of arteries. The degree of luminal gain can be studied

by comparing the pre-deployment and post-deployment luminal area. The amount of luminal

gain is a measure of the stent’s ability to re-enlarge a stenosis.


51

The luminal gain is directly related to the radial expansion of the arterial wall. A node

in the centre of the inside surface of the artery appositional to the deployed stent was

examined to determine the luminal gain achieved.

Figure 41 - Graph of the radial displacement of the arterial wall and the corresponding luminal gain in area of the

vessel compared to the expansion pressure loading.

As can be seen above in Figure 41, the artery does not begin to expand radially until

the stent came in contact with it, which occurred at roughly 0.14MPa applied pressure. The

centre of the artery achieves a maximum radial expansion of 53mm corresponding to a 103%

luminal gain for the artery. The elastic recoil can be viewed also as the increase in luminal

area of the artery decreases by 4% to a final value of 99% once the pressure loading had been

removed.

5.1.3. Vessel Straightening

The degree of vessel straightening is a measure of the flexibility of a stent and can also

be a cause of injury to the arterial wall that can increase the chance of restenosis. Comparison

of the tortuosity of the vessel before and after stent deployment measures the amount of vessel

straightening that has occurred. Needless to say, vessel straightening is not of concern when

analysing results from simulations on the straight hollow cylinder artery created in Abaqus.

5.1.4. Elastic Recoil

The PS 154 stent exhibited elastic recoil of -1.089% measured from the centre of the

stent and a positive 0.011% at the distal end. The stent actually experienced very slight

longitudinal recoil of 0.0010%.


52

5.1.5. Stent Foreshortening

Figure 42 - Graph of the percentage foreshortening of the stent vs the pressure loading.

The PS 154 stent reached a maximum foreshortening of -5.71% during the unloading of the

pressure within the balloon and had a final value of -5.50%.

5.1.6. Dog-boning

Figure 43 - Graph of the radial displacement of nodes at the centre and at the distal end of the stent as well as the

corresponding % dog-boning.


53

The original PS 154 stent reached a maximum dog-boning of 24.4% quite early on in

the simulation. The distal ends of the stent expanded much quicker than the central body of

the stent until the distal ends of the stent came in to contact with the arterial wall. The contact

between the distal ends of the stent and the artery occur at roughly 0.15MPa when the radial

expansion of the distal ends slows and the expansion of the central body increases relative to

the distal ends. Once the body of the stent becomes fully expanded the percentage of dog-

boning starts to plateau around 5-6%. Once the pressure is released from the balloon the dog-

boning increases again slightly to its final value of 7.03%.

5.1.7. Ratio of Kinetic and Internal Energy

Figure 44 - Ratio of Kinetic Energy to Internal Energy throughout the simulation of the expansion of the original

PS 154 stent

The graph of the ratio of the kinetic energy to internal energy of the simulation has

two distinct peaks of note. The first spike occurs around the 5-second mark when the

expanding stent first came in to contact with the arterial wall consequently causing the arterial

wall to commence deforming with the balloon and stent. The second peak begins at the 9

second mark, increasing linearly until 10 seconds and then decreasing linearly again until the

end of the simulation. This peak is caused by the final surge in pressure increase in the

balloon in the final second of the first step where the pressure is increased from 0.224MPa to

0.7MPa in one second. Refer back to Figure 25 to see the pressure ramping profile to see this

behaviour.

The simulation of the expansion of the original PS 154 stent can pass for a quasi-static

process as the ratio maintains a very low value throughout the simulation. Abaqus guidelines


54

suggest the ratio be kept below 5% for the simulation, however this simulation did not even

breach 1.0%. This result is credit to the combination of a suitable degree of mass scaling

utilised and an appropriate pressure ramping profile.

5.2. Modified Geometry – PS 154

The original PS 154 stent parameters were modified to search for stent characteristics

to optimise the parameters of the original design. The length, diameter and thickness of the

original parameters were kept constant throughout all modifications. This thesis chose to

explore the effect altering three separate mechanical parameters of the stent design with the

aim of reducing stress distribution in the artery, dog-boning and foreshortening of the stent

and elastic recoil of the artery and stent after the balloon has been deflated and removed.

The first of these modifications involved increasing and decreasing the number of

circumferential slot sites. The original PS 154 parameters included 12 evenly spaced slot sites

around the circumference of the stent. This thesis performed the same expansion simulations

on stents based on the PS 154 geometry but with both eight and sixteen circumferential slot

sites.

The second of these modifications was to alter the original design of the stent by

filleting (curving) the ends of the stent as well as the interior of the slots. The original PS 154

stent design is made of straight edges and perpendicular corners. This thesis investigates the

possibility that the sharp distal corners of the stent pinching the artery during expansion can

be avoided by a smoother contact from the curved edges and thus reducing the stress induced

on the arterial wall.

The third modification involves increasing and decreasing the distal strut width of the

stent in an effort to alter the stiffness of the distal ends of the stent with a particular focus on

decreasing the rate of dog-boning that the stent exhibits throughout its expansion.

5.2.1. Eight Circumferential Slots

The original design was altered to decrease the

number of circumferential slot sites from 12 to 8. The

ratio of the size of the slots to the struts was maintained,

so effectively the slots and longitudinal struts are wider

than the original design.

Figure 45 - Isometric view of the Solidworks

model of the PS 154 stent modified to only have

8 circumferential slot sites.


55

Figure 46 - Side transparent view of the expansion process. The top image depicts the point of first impact

between the stent and the artery, and the bottom image depicts the final stage of the simulation.

The expansion progression process can be seen above in Figure 46. The large degree

of dog-boning should be noted in the top image when the stent first comes in contact with the

artery. As the struts of the stent have been made thicker in this model the central body of the

stent requires a greater pressure load before they begin to deform. In the bottom image it can

be seen that the expansion of the stent has caused significant local deformation of the artery at

the cross-links of the stent and in particular at the distal ends.

The effect of this large deformation is depicted in the following stress distribution

contour plots, Figures 47 and 49. The initial impact of the distal ends of the stent with the

arterial wall causes localised high stress areas where the artery has become pinched by the

corners of the stent.


56

Figure 47 – Contour plot of the stress distribution of the artery when distal ends of stent make first contact

Below in Figure 48 it can be seen that the geometry of the stent when first contact with

the artery is made. It should be noted that the main body of the stent has undergone next to no

deformation by the time the distal ends of the stent make contact with the artery. This large

degree of dog-boning at the point of impact can cause injury to the arterial wall and

potentially increase the risk of restenosis.

Figure 48 - Superposition of original pre-deployment phase of stent (dark green) and the geometry of the stent

when fist making contact with the arterial wall (light blue).

Figure 49 depicts the residual stress distribution in the arterial wall once the balloon

has been deflated. The von Mises maximum stress zones are at the sites of the distal corners

where they remain pinching the arterial wall. As the number of distal corners is reduced

compared to the original design it means that these localised high stress areas are of an even

higher magnitude as there are fewer of the spots resulting in a residual maximum principle

stress 35% greater that the original stent design. Minor von Mises stress distribution can be

seen along arterial wall appositional to the longitudinal struts of the stent.


57

Figure 49 - Residual stress distribution of the arterial wall once the balloon has been deflated.

Figure 50 - Symbol plot depicting the magnitude and direction of residual principle stresses in the arterial wall at

the end of the simulation.

Figure 50 is a symbol plot depicting the magnitude and direction of the residual

principle stresses. The highest magnitude is at the previously mentioned localised areas

corresponding to the corners of the distal ends. Interestingly, the areas between these distal

corner contact points exhibit high stress also in the tangential direction as the artery is being

stretched due to the large deformation of the artery at these points.


58

Figure 51 - Graph of the Luminal Gain achieved vs. the applied pressure loading.

The stent first comes in to contact with the centre of the artery at a pressure loading of

roughly 0.15MPa at which point it initially recoils due to the deformation of the artery at the

distal ends occurring before the central body. The luminal gain reaches a maximum of 93%

and recoils by only 2% once the pressure is unloaded from the balloon. The artery exhibits

extremely low levels of elastic recoil as the added thickness of the struts transfer greater radial

strength than the original design.

Figure 52 - Graph of the percentage foreshortening of the stent vs. the pressure loading.


59

This model reaches a maximum foreshortening of -14.542% and a final foreshortening

of -14.066%. This high level of foreshortening is due to the larger slot size that causes the

expanded phase to reassemble a diamond pattern with a non-uniform dilation of the stent

throughout its length. Such a high level of foreshortening is unacceptable for a coronary artery

as the shearing of the foreshortening stent with the artery would cause much vascular injury.



As has been discussed earlier, the stent exhibits a very high degree of dog-boning

during the initial expansion as the overall radial strength of the stent is greater than the

original model. This relationship is quite apparent in Figure 53. The stent reaches a maximum

dog-boning of 44.62%. This means that the central body of the stent will have a higher

resistance to expansion, however the distal ends are still quite weak as they are open half-

cells. The level of dog-boning drops quickly once the distal ends of the stent come in to

contact with the arterial wall. The final dog-boning value is 15.59% after exhibiting very low

elastic recoil during deflation of the balloon.


60

Figure 54 - Graph of the ratio of kinetic energy to internal energy throughout the expansion simulation.

There appears to be two distinct spikes in the ratio of kinetic energy to internal energy

throughout the simulation. The first large spike occurs around the 8.5 second stage when the

central body of the stent begins to deform quickly as the distal ends of the stent are already

fully expanded, the result of this is a very rapid increase in the luminal area of the artery. The

second smaller spike is associated with the pressure ramping profile where the largest portion

of pressure increase occurs between seconds 9 and 10 of step 1.

The ratio maintained a level well below the 5% threshold recommended by Abaqus

developers to achieve a quasi-static process.

5.2.2. Sixteen Circumferential Slots

Figure 55 - Isometric view of the Solidworks model of the PS 154 stent modified to include 16 circumferential

slot sites.


61

The original design was then modified to increase the number of circumferential slot

sites from 12 to 16. As before with the stent with 8 circumferential sites, the ratio of the size

of the slots to the struts was maintained, so effectively the slots and longitudinal struts are

narrower than the original design.

Figure 56 - Side transparent view of the expansion process. The top image depicts the initial setup of the stent,

balloon and artery, the second image depicts point of first impact between the stent and the artery, and the

bottom image depicts the final stage of the simulation.

Figure 56 above depicts the expansion progression sequence from the initial setup, to

the first contact with the artery and the final stage of the simulation. From the sequence above

it can be seen that this stent exhibits a very uniform dilation throughout the length of the stent.

There is a very slight degree of dog-boning when the stent makes first contact with the artery

but near negligible compared to previous simulations. The final stage of the simulation

depicts a fully expanded and uniform dilation of the stent with what appears to be slight

negative dog-boning. Overall the expansion sequence appears to be very uniform with all


62

struts of the stent providing equal support to the artery which should in turn decrease the

maximum stress induced in the arterial wall.

Figure 57 - Contour plot of the stress distribution of the artery when distal ends of stent make first contact.

Figure 57 above depicts the stress distribution in the arterial wall when the stent makes

first contact with the artery. As can be seen the distal ends of the stent are the location of the

highest stress, however the stress is also quite evenly distributed appositional to the

longitudinal struts especially in the central zone. This is a behaviour unseen in previous

simulations as the level of dog-boning is usually at its peak when the distal ends of the stent

make first impact with the artery.

Figure 58 - Superposition of the initial and final geometry of the stent from the side view.


63


The residual stress distribution in the arterial wall can be seen above in Figure 59. As

can be seen the central zone of the artery appositional to the longitudinal struts of the stent are

now the area of the maximum stress. A noteworthy observation of the residual stress

distribution is that the distal corners of the stent are not causing highly concentrated stress like

previous simulations. This is due to the fact that the stent exhibits a slight negative dog-

boning at the end of the simulation, so the distal ends of the stent are not poking in to the

arterial wall. The maximum residual stress is 63% less than the maximum observed for the

original PS 154 stent. This drastic reduction in residual stress is due to the stent support being

spread over a greater area focused around

the central body of the stent as opposed

to highly concentrated points at the distal

ends of the stent for previous models.

The consequence of reduced residual

stress distribution is that the arterial wall

is less likely to be injured and result in

neointimal hyperplasia and restenosis of

the artery. Figure 56 is a symbol plot

depicting the magnitude and direction of

residual stresses in the arterial wall at the

end of the simulation and it further exemplifies the uniform stress distribution appositional to

all longitudinal struts of the stent.

Figure 60 - Symbol plot depicting the magnitude and direction of

residual principle stresses in the arterial wall at the end of the

simulation.


64


As can be seen above in Figure 61, the stent first came in to contact with the artery at a

low pressure loading of 0.07MPa at which point the radial expansion of the arterial wall was

very rapid, quickly jumping to a luminal gain of 105%. This rapid expansion suggests that the

pressure loading was too great for this stent or the pressure increased too quickly. This would

be the case as this stent has narrower struts and hence would have a lower radial strength

compared to previous stents, hence requiring less pressure in the balloon to fully expand it.

Figure 62 - Graph of the ratio of kinetic energy to internal energy throughout the expansion simulation.


65

Further evidence of the rapid expansion can be seen in the graph of kinetic energy to

internal energy for the simulation in Figure 62. The graph has large spike around the 2.5

second mark in excess of 25% and then commences oscillating with a decreasing amplitude

for the remainder of the simulation. The huge spike would be associated with the rapid

expansion of both the stent and its high velocity impact with the arterial wall. The ratio

exceeds the suggested 5% threshold substantially and thus suggests that the process might not

be considered quasi-static.



The graph of the degree of dog-boning throughout the simulation of the 16-configuration stent

can be seen above in Figure 63. The graph displays an interesting phenomenon that occurs for

this stent, the stent reaches a maximum dog-boning of 14.7% when the distal ends of the stent

first come in to contact with the artery, however the dog-boning is quickly reversed reaching a

minimum of -8.0%. This again can be explained by the rapid expansion of the stent due to the

radial strength of the stent being weaker. The stent has a final dog-boning of 0.03%, which

indicates that the dilation of the stent is almost completely uniform throughout its length,

which is ideal for spreading the stress distribution over the entire outer surface area of the

stent. The shock-wave effect displayed between 0.05MPa and 0.10MPa is an indication that

the radial strength is significantly weaker than the original model and that a lower maximum

pressure loading should be used to expand the stent as a slower rate to avoid such a shock-

wave effect.


66

5.2.3. Curved End PS 154

The original design was slightly modified by

removing material at the distal ends of the stent to

incorporate curved ends. As the original stent design

had caused quite localised stress at the distal corners

of the stent due to the slight dog-boning, this thesis

suggested that curving the sharp distal corners of the

stent could potentially decrease the injury sustained

by the arterial wall during deployment. The interior

slots had inner fillets added also. All of the original

parameters of the stent were kept intact otherwise.

Figure 65 - Side transparent view of the expansion process. The top image depicts the initial setup of the stent,

balloon and artery, the second image depicts point of first impact between the stent and the artery, and the

bottom image depicts the final stage of the simulation.

The sequence of expansion for the curved stent throughout the simulation can be seen

above in Figure 65. From the second image in can be seen that the stent first made contact

Figure 64 - Isometric view of the Solidworks model of the

PS 154 stent modified to include curved ends and curved

inner slot ends.


67

with the arterial wall with its curved distal ends. The stress distribution on the arterial wall at

first impact is shown below in Figure 66. As is expected, the corners of the distal ends are the

sites of the maximum stress in the artery. The stress however is greater than the original stent

as the curved ends of the stent represent a lower area for the application of force to the artery

thus the stress experienced is greater. Although the curved ends may prevent injury to the

artery by removing the sharp corners of the original design, it does however induce a greater

stress on the arterial wall.

Figure 66 - Contour plot of the stress distribution of the artery when distal ends of stent make first contact.


The plot of the residual stress distribution for the curved stent still displays the

maximum stress areas adjacent to the distal ends of the stent due to the slight final dog-

boning. The maximum stress is 34% greater than recorded in the original PS 154 stent

simulation. The stress distribution through the central body of the stent however depicts a

relatively uniform distribution adjacent to the longitudinal struts. The symbol plot in Figure


68

68 depicts the direction and magnitude of the residual stresses in the arterial wall give further

evidence to this as the longitudinal struts support the artery quite uniformly.

Figure 68 - Symbol plot depicting the magnitude and direction of residual principle stresses in the arterial wall at

the end of the simulation.


The luminal gain of the simulation achieved a maximum of 65% before elastically

recoiling slightly to a final value of 60%.


69

Figure 70 - Graph of the percentage foreshortening of the stent vs. the pressure loading.

The graph of foreshortening for the modified stent expansion can be seen in Figure 70.

The graph is similar to that of the original PS 154 stent with a maximum value of -5.368%

and a final value of -5.014% showing less than 0.5% difference to the original design. This is

to be expected as slot length and width of the curved model are identical to the original

design.




70

Figure 71 depicts the amount of dog-boning exhibited throughout the simulation. The

stent reached a maximum of 26.30% when the distal ends first came in to contact with the

arterial wall then followed by a rapid expansion of the central body of the stent. The final

dog-boning of the stent was 3.80%, which is only half of the final value for the original PS

154 stent.

5.2.4. Altering the width of PS 154 distal strut

The width of the distal strut of the original PS 154 stent is 0.30mm. Altering this parameter

alters the relative stiffness of the distal ends of the stent. It is understood that dog-boning

occurs as the distal ends of slotted-tube stents are weaker than the central body of the stent as

they are only a half-cell slot that does not have the same restraints from expansion that the

fully closed slots of the central body exhibit. Decreasing the rate of dog-boning throughout

the simulation could be achieved by increasing the stiffness of the distal ends of the stent

compared to the central body of the stent to promote an even dilation of the stent throughout

its expansion. Three modified stents were created in Solidworks that had distal strut widths of

0.25mm, 0.35mm and 0.40mm, which can be seen in Figure 69 alongside the original stent.

Figure 72 - Screenshots of the three modified stents in terms of width of the distal strut. From left to right, the

distal strut width is 0.25mm, 0.30mm (original stent parameter), 0.35mm and 0.40mm.

The three modified stents were expanded within the hollow cylindrical artery model in

Abaqus with the same setup as the expansion of the original PS 154 stent. A summary of the

results for the expansion simulation of the three modified stents can be seen below compared

to the original PS 154 results.

Distal strut width (mm) 0.25 0.30 (original) 0.35 0.40

Max Dog-Boning% 26.48 23.48 22.01 20.69

Final Dog-Boning% 7.77 7.75 6.98 7.13

Max Foreshortening% -4.80 -5.66 -5.00 -5.20

Final Foreshortening% -4.39 -5.24 -4.61 -4.82

Max Stress in Artery (MPa) 0.208 0.199 0.192 0.201

Residual Max Stress in Artery (MPa) 0.180 0.175 0.160 0.185


71

There is a trend for the maximum dog-boning throughout the expansion whereby the

value decreases as the distal strut width is increased. Generally, the maximum dog-boning of

the stent is experienced when the distal ends of the stent first make contact with the arterial

wall, at this point the artery exerts an elastic resistance force on the distal ends which causes

the central body of the stent to catch up by expanding at a faster rate until it too makes contact

with the arterial wall. This trend is as expected as the increased width increases the stiffness

of the distal ends relative to the central body of the stent. The increased relative stiffness of

the distal ends results in a greater resistance to expansion from the balloon.

The final rate of dog-boning is of greater concern as it will be the source of on-going

trauma to the artery. The stent with 0.35mm distal strut width was found to minimise the

residual dog-boning of the PS 154 stent.

Observation of the stress distribution throughout the artery for the four simulations

revealed almost identical stress distribution contour plots, with the areas of max stress

concentrated as the distal ends of the stent due to residual dog-boning. The 0.35mm distal

strut width stent was observed to reduce the residual maximum stress induced in the arterial

wall by 8.6% compared to the original stent parameters. The reduction in residual stress can

be attributed to the decreased rate of final dog-boning and hence the concentration of the

stress distribution on the arterial wall appositional to the distal ends of the stent.

5.3. Optimised Stent Design

This thesis set out to identify potential modifications to the original PS 154 stent to optimise

the design hence reducing the incidence of restenosis and thrombosis. Three sets of simulation

tests were run to identify whether altering the number of circumferential slot sites, adding

curved features and whether altering the distal strut width would result in favourable clinical

outcomes. A summary of results for the distal strut width stents was provided above and the

remaining stents are listed below.

Original

Parameters

8 Circumferential

Slots

16 Circumferential

Slots Curved model

Max DB % 23.483 44.619 14.220 26.303

Final DB % 7.753 15.588 0.456 3.804

Max FS % -5.660 -14.542 -2.631 -5.368

Final FS % -5.229 -14.066 -2.363 -5.014

ER cent % -1.089 -0.712 -1.706 -0.909

ER dist % -0.011 -0.756 -1.064 -2.303

LR % 0.0010 -0.0022 -0.0007 -0.0013


72

When considering the number of circumferential slot sites it was found that the results

for the stent with 16 slot sites displayed the lowest rates of dog-boning and foreshortening but

the greatest levels of elastic recoil. What must be noted for this testing is that increasing the

number of circumferential slot sites decreased the width of the longitudinal struts, and vice

versa for the 8-configuration stent. The longitudinal strut width has a large influence on the

radial strength of a stent. The low levels of dog-boning and foreshortening of the 16-

configuration stent could be attributed to the decreased radial strength of the stent. It was

concluded that further testing of the radial strength of these stents is required before a

definitive choice can be made on this design parameter. The 16-configuration stent would

need to display improved dog-boning and foreshortening outcomes without a significant

decrease in radial strength. Slotted tube stents have one of the highest degrees of radial

strength of all stents so a decrease in radial strength is only an issue if the decrease means the

stent is unable to provide on-going support for the artery.

Slight reduction of dog-boning and foreshortening is observed when the distal ends

and inner edges of the slots are filleted. The curved model however had an unprecedented

34% increase in the residual maximum stress induced in the arterial wall compared to the

original design appositional to the distal ends of the stent. This can be attributed to the

reduction in area that the stress is transferred through to the artery due to material at the

corners of the distal ends being removed. Although the curved model may reduce injury

caused to the artery due to pinching, a 34% increase in residual maximum stress significantly

increases the chance of restenosis. An optimised stent design should not include curved distal

ends.

Analysis of the simulations of the stents with altered distal strut widths found that

increasing the width from 0.30mm to 0.35mm resulted in a 9.9% reduction in the residual rate

of dog-boning and an 8.6% reduction in the residual maximum stress induced on the arterial

wall. Increasing the distal strut width further to 0.40mm saw a decreased final dog-boning rate

but a slightly greater residual maximum stress on the arterial wall. It is believed that

increasing the distal strut width from 0.30mm to 0.35mm will improve the clinical outcomes

of the PS 154 stent and reduce the incidence of restenosis and thrombosis.


73

6. Conclusion and Recommendations

This thesis sought to optimise the design of the Palmaz Schatz PS 154 stent, but more

importantly to identify general trends from altering mechanical design parameters of a slotted

tube stent to improve its long-term clinical performance. Clinically relevant results were

observed for the expansion of the PS 154 stent in a realistic coronary artery model, however

due to the complexity of the model and difficulty of setup all design optimisation simulations

were undertaken within a hollow cylindrical tube artery model. The hollow cylindrical tube

artery model enabled easy setup of the balloon-stent-artery assembly and for the expansion

simulations to be repeated with accurate results.

Three geometrical aspects of the original PS 154 stent were altered to determine the

advantages and disadvantages of the modifications. The three geometrical modifications

explored in this thesis was altering the number of circumferential slots sites, adding curved

distal corners and altering the distal strut width of the original stent. The results were then

analysed to determine whether alterations made a negative or positive effect on reducing

residual stress distribution in the artery, elastic recoil, stent foreshortening and dog-boning to

predict their impact on the incidence of restenosis and thrombosis. The optimised stent design

incorporates an increased distal slot width and the potential for additional circumferential slot

sites.

As has been explored, different stent designs have different mechanical characteristics

that change their suitability for a range of anatomical sites and arterial lesions. It is necessary

for the interventional cardiologists to understand the differences in mechanical characteristics

of all commercially available stents so that they are able to choose the best candidate for all

anatomical sites and arterial lesions, which unfortunately is not always the case. This indicates

that there is currently a knowledge divide between interventional cardiologists and biomedical

engineers. It is suggested that building upon the methodology created for this thesis that this

knowledge divide can be conquered. Optimised stent designs can be determined by finite

element analysis of the expansion of stents within a simplistic hollow cylindrical artery

model. Patient-specific 3D artery models can be generated within the hospital and have

optimised stents implanted to determine the best stent candidate for the patient’s specific

arterial lesion composition and its anatomical region. With advancements in computing power

it is not unrealistic that simulations that currently take up to 24 hours could be completed in a

fraction of that time in the future. This could enable user-friendly software packages to be

created for interventional cardiologists to be able to determine the ideal stent candidate for

each patient’s specific requirements onsite within cardiac catheterisation departments.


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Future work should look to model the plaque build-up within the artery model. The

inclusion of the atherosclerotic plaques was ignored in the simulations for this thesis due to

the complexity of the model and its associated contact issues during the simulation. In further

studies one could consider modelling different atherosclerotic plaque compositions to

simulate the expansion of a stent within an artery to give clinically relevant results. It would

be interesting to consider a calcified atherosclerotic plaque that has fracture characteristics

and is an incompressible material and to include it in to a model. It would be assumed that the

inclusion of atherosclerotic plaques in to simulations would alter the design optimisation

outcomes of the stents. A generalised set of optimised stent parameters for each plaque

composition scenario can be determined to further improve the clinical outcomes of arterial

stents.

As stents are used on diseased segments of arteries the reality is that the surface of the

arterial wall is severely stenosed and irregular in its shape. Future work should also aim

determine a similar generalised set of optimised stent parameters for a wide range of

anatomical regions. More realistic and clinically relevant results could be achieved by

modelling anatomical regions such as curved segments, bifurcational and ostial sites. The

irregular geometry of the surface of the arterial wall is particularly important to determine

whether a particular stent design has significant tissue prolapsing back in to the lumen of the

artery.

Future studies could look to model the associated drug release for drug-eluting stents.

Computational fluid dynamics (CFD) software could be used to analyse the release of drugs

in to the blood stream and arterial wall as well as monitoring fatigue of the stent associated

with long-term deployment in the artery and cyclic blood pressure presence. Utilising CFD

could assist in accurately predicting the incidence of restenosis and thrombosis.


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8. Appendix 8.1. Consistent unit requirement in Abaqus

Documents

Thesis Final (3 files merged)