Finite Element Analysis of a Novel Design for a Non

Finite Element Analysis of a Novel Design for a Non-Migrating Biliary

Stent using Abaqus

By

Jared D. Mitchell

A Thesis Submitted to the Graduate Faculty of

VIRGINIA TECH – WAKE FOREST UNIVERSITY

SCHOOL OF BIOMEDICAL ENGINEERING & SCIENCES

In Partial Fulfillment of the Requirements

for the Degree of

MASTER OF SCIENCE

Biomedical Engineering

May 2016

Winston-Salem, North Carolina

Approved by:

Philip J. Brown, PhD, Advisor, Chair

Examining Committee:

Joel D. Stitzel, PhD

Clifford Howard Jr., MD

ii

ACKNOWLEDGEMENTS

I would first off like to thank my advisor, Dr. Philip Brown. His help and

guidance has provided me with a far greater ability to visualizing problems as well as

approach those design problems in an efficient and comprehensive manner. His

knowledge and ability to coherently convey that knowledge, make learning from him that

much easier.

The environment that exists in the VT - WFU Center for Injury Biomechanics

cannot be matched. The relationships between the students, faculty, and staff make

working simple.

Wake Forest Innovations has allowed me the opportunity to work on such great

projects such as this. I would like to thank Kenneth Russell, from WFI who has been

nothing but supportive in my collaborations between the biomedical engineering

department and Wake Forest Innovations.

I would also like to acknowledge my peers and friends that I have within the

program all of whom I have been able to go to for help or lean on for guidance. I would

also like to thank specifically Greg Gillispie for not only being a great friend but also

listening and helping me talk though problems.

I cannot thank the engineering department at Washington & Lee University

enough. Specifically Dr. Joel Kuehner and Dr. Jonathan Erickson each were integral in

developing my engineering knowledge as well as fostering my passion for engineering.

My family has been nothing but supportive throughout my academic career.

Without them and their support none of this would be possible.

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TABLE OF CONTENTS

List of Tables .......................................................................................................................... v

List of Figures ........................................................................................................................ vi

List of Abbreviations ............................................................................................................. xi

Abstract .................................................................................................................................1

CHAPTER I: INTRODUCTION & BACKGROUND .............................. 2

Biliary System Anatomy .........................................................................................................2

Causes for Biliary Stenting ......................................................................................................3

Early History of Biliary Drainage (Prior to 1978) ......................................................................3

Modern Biliary Stents: Plastic vs. Metallic ...............................................................................5

Chapter Summaries .............................................................................................................. 12 Chapter II: Finite Element Analysis of a Non-Migrating Biliary Stent Deployment ................... 12

Chapter III: Finites Element Analysis of Migration Reducing Hook Variations for a Novel Biliary

Stent .......................................................................................................................................... 12

Chapter IV: Parametric Study of a Deployment Hinge using Finite Element Analysis .............. 12

Chapter V: Summary of Research .............................................................................................. 12

References ........................................................................................................................... 13

CHAPTER II: FINITE ELEMENT ANALYSIS OF A NON-

MIGRATING BILIARY STENT DEPLOYMENT .................................16

1. Abstract ....................................................................................................................... 17

2. Introduction ................................................................................................................ 18

3. Methods ...................................................................................................................... 19

4. Results ......................................................................................................................... 24

5. Discussion .................................................................................................................... 32

6. Conclusion ................................................................................................................... 33

7. Acknowledgement ....................................................................................................... 34

8. References ................................................................................................................... 35

iv

CHAPTER III: FINITE ELEMENT ANALYSIS OF MIGRATION

REDUCING HOOK VARIATIONS FOR A NOVEL BILIARY STENT

.......................................................................................................................37

1. Abstract ....................................................................................................................... 38

2. Introduction ................................................................................................................ 39

3. Methods ...................................................................................................................... 40

4. Results ......................................................................................................................... 48

5. Discussion .................................................................................................................... 58

6. Conclusion ................................................................................................................... 59


8. References ................................................................................................................... 61

CHAPTER IV: PARAMETRIC STUDY OF A DEPLOYMENT

HINGE USING FINITE ELEMENT ANALYSIS ...................................63

1. Abstract ....................................................................................................................... 64

2. Introduction ................................................................................................................ 65

3. Methods ...................................................................................................................... 66

4. Results ......................................................................................................................... 73

5. Discussion .................................................................................................................... 80

6. Conclusion ................................................................................................................... 82


8. References ................................................................................................................... 84

CHAPTER V: SUMMARY OF RESEARCH ..........................................86

SCHOLASTIC VITA ..................................................................................87

v

LIST OF TABLES

Table 1: Stent-related complications in selected randomized controlled trials and single-

arm prospective studies.1 .................................................................................................. 10

Table 2: Reflects the Abaqus plastic deformation input table .......................................... 23

Table 3: Resultant Inflation Stiffnesses for the Stent Portion, Hook Portion, and Total

Stent factoring in prior or post hook out of plane bending. .............................................. 31

Table 4: Length of stents with respect to hook variation .................................................. 43


Table 6: Hook Variation Deployment Hook and Mid-Stent Diameters ........................... 50

Table 7: Dimension of Slot Length and Side Joint Thickness when Slot Width is in “A”

State (0.06mm) .................................................................................................................. 68

Table 8: Dimension of Slot Length and Side Joint Thickness when Slot Width is in “B”

State (0.10mm) .................................................................................................................. 68


Table 10: Pertinent values corresponding to each hinge type (All dimensional units are in

mm) ................................................................................................................................... 77

vi

LIST OF FIGURES

Figure 1: Anatomy of the Biliary System [3] ..................................................................... 2

Figure 2: A, Percutaneous pigtail stent placement; B, corresponding radiographic image

[4] ........................................................................................................................................ 5

Figure 3: Figure of plastic stents with anti-migration designs [2] ...................................... 7

Figure 4: Balloon Expansion of a metallic stent [1] ........................................................... 8

Figure 5: Self-Expandable Metal Stent naturally expanding to deployed position upon

retracting of sheath [1] ........................................................................................................ 9

Figure 6: Four-bar Linkage Hook Design ......................................................................... 20

Figure 7: Full Stent Model: A) Top view of the full stent with length dimensions. B)

Isometric of full stent. C) Side view of full stent with external diameter dimension. ...... 20

Figure 8: 1/24th of the full stent ....................................................................................... 21

Figure 9: Partitioning and Meshing of Non-Migration Stent. A) Stent depicting partition

locations. B) stent depicting overall hexahedral mesh...................................................... 22

Figure 10: Stent Material Model for Stainless Steel Grade 316: Mises Stress vs. Plastic

Strain ................................................................................................................................. 23

Figure 11: Stent Mesh showing specific node locations monitored for radial expansion

displacement comparison. ................................................................................................. 24

vii

Figure 12: Full Stent Model Deployed: ............................................................................ 25

Figure 13: Stent Body Displacement vs. Time: This shows the stent body's displacements

in the X, Y, & Z directions, as well as, the displacement magnitude with respect to time.

........................................................................................................................................... 26

Figure 14: Hook Tip Displacement vs. Time: This shows the hook tip's displacements in

the X, Y, & Z directions, as well as, the displacement magnitude with respect to time. . 26

Figure 15: .Radius vs. Time for Mid-Stent and Hook Tip: With an initial internal radius

of roughly 1.4 mm, this figure shows the radius of the significant locations with respect

to time. .............................................................................................................................. 27

Figure 16: Foreshortening vs. Time: This reports the overall change in stent length with

respect to time. .................................................................................................................. 28

Figure 17: Stent Mises Stress with detail view of areas with stress/strain concentrations

(units of MPa) ................................................................................................................... 29

Figure 18: Stent Peak Equivalent Plastic Strain with detail view of areas with stress/strain

concentrations ................................................................................................................... 29

Figure 19: Mises Stress vs. Strain profiles for the interior arch of the stent body strut as

well as the internal arch of the hook hinge ....................................................................... 30

Figure 20: Force vs. Radial Displacement. This figure shows the force-displacement

profile for the inflation of the stent ................................................................................... 31

Figure 21: Four-bar Linkage Hook Design ....................................................................... 41

viii

Figure 22: A, Generic Hooked Stent; B, Flexible Tip Hooked Stent; C, Double Four-Bar

Hooked Stent ..................................................................................................................... 41

Figure 23: Generic Stent displaying measurement locations of hook portion, stent body,

and initial external diameter .............................................................................................. 42

Figure 24: Partitioning and Meshing of Stent Variations. A, Generic Stent Partitioning; B,

Associated generic stent hexahedral mesh; C, Flexible Hook Tip Stent Partitioning; D,

Associated flexible hook tip stent hexahedral mesh; E, Double Four-Bar Stent

Partitioning; F, Associated double four-bar stent hexahedral mesh ................................. 44

Figure 25: Stent Material Model for Stainless Steel Grade 316: Stress vs. Plastic Strain 46

Figure 26: Test comparison showing hook compression test step versus the axial tip test

step performed. ................................................................................................................. 47

Figure 27: Generic Stent Model Deployed: ...................................................................... 48

Figure 28: Flexible Hook Tip Stent Model Deployed: ..................................................... 49

Figure 29: Double Four-Bar Stent Model Deployed: ....................................................... 49

Figure 30: Displacement Magnitude vs. Time for all hook variations ............................. 50

Figure 31: Hook Variation Overlay .................................................................................. 50

Figure 32: Displacement vs. Time at middle of the stent and at the hook for all hook

variations during deployment. .......................................................................................... 51

ix

Figure 33: Displacement vs. Time at hook tip for all hook variations during the

compression and axial testing step of the simulation. ....................................................... 52

Figure 34: Generic Stent Deployed vs. Deformed: A) Fully Deployed Generic Stent; B)

Generic Stent under compressive load; C) Generic Stent hook after axial hook testing .. 53

Figure 35: Flexible Hook Tip Stent Deployed vs. Deformed: A) Fully Deployed Flexible

Hook Tip Stent; B) Flexible Hook Tip Stent under compressive load; C) Flexible Hook

Tip after axial hook testing ............................................................................................... 54

Figure 36: Double Four-Bar Stent Deployed vs. Deformed: A) Fully Deployed Double

Four-Bar Stent; B) Double Four-Bar Stent under compressive load; C) Double Four-Bar

hook after axial hook testing ............................................................................................. 55

Figure 37: Force vs. Displacement during different steps for the Generic Stent .............. 56

Figure 38: Force vs. Displacement during different steps for the Flexible Hook Tip Stent

........................................................................................................................................... 57

Figure 39: Force vs. Displacement during different steps for the Double Four-Bar Stent 57

Figure 40: Base hinge model with study parameters identified. ....................................... 66

Figure 41: Dimensions of all Hinge Conditions (NOTE: All dimensions are in mm and all

figures are not to scale) ..................................................................................................... 67

Figure 42: Stent Material Model for Stainless Steel Grade 316: Stress vs. Plastic Strain 69

Figure 43: A, Partitioning of the AAA Hinge; B, Mesh associated with the AAA Hinge 70

x

Figure 44: Figure depicting fixed end boundary condition and forces applied to nodes at

opposite end ...................................................................................................................... 71

Figure 45: Additional Test Setups for AAA Hinge. A: Strictly Moment Test Setup ; B:

Lateral Bending Test Setup ............................................................................................... 72

Figure 46: BBB Hinge. ..................................................................................................... 73

Figure 47: Moment vs. Angle for hinges with slot width in the ‘A’ state. ...................... 74

Figure 48: Moment vs. Angle for hinges with slot width in the ‘B’ state. ....................... 75

Figure 49: Linear Stiffness Model for initial and secondary deformation ........................ 76

Figure 50: Normalized Failure Angle and Mises Stress for each hinge type ................... 77

Figure 51: Initial and Secondary Stiffness for each hinge type ........................................ 78

Figure 52: A, deformation cause by force at nodes. B, deformation cause by rigid

cylinder boundary conditioning ........................................................................................ 78

Figure 53: Simulation performed on AAA Hinge to analyze lateral bending .................. 79

Figure 54: Mises Stress vs. Angle for Different Loading Mechanisms for the AAA Hinge

........................................................................................................................................... 79

Figure 55: Deformation at 55 degrees: A: Hinge with nodal force applied; B: Hinge with

rigid cylinder moment application; C: Generic Stent with balloon expansion. ................ 80

xi

LIST OF ABBREVIATIONS

CAD Computer Aided Design

CBD

Common Bile Duct

Co-Cr

Cobalt-Chromium

ERCP

Endoscopic retrograde cholangiopancreatography

FEA

Finite Element Analysis

MEMS

Microelectromechanical systems

MOJ

Malignant obstructive jaundice

PE

Polyethylene

PTBD

Percutaneous Transhepatic Biliary Drainage

PTFE

Polytetrafluoroethylene

PU

Polyurethane

RUC Repeating Unit Cell

SEMS

Self-Expandable Metal Stent

SS

Stainless Steel

WFI

Wake Forest Innovations

1

ABSTRACT

Biliary stenting is most frequently caused by an interruption in the ability to drain

bile into the duodenum. This obstructive jaundice is commonly a result of a stricture from

a tumor located at the pancreas’s head, peri-ampulary area, bile duct, or gall bladder.

Jaundice can also occur from anastomotic strictures which result from post-surgery

biliary complications. In order to restore patency, stenting of the biliary tree is performed

by means of endoscopic retrograde cholangiopancreatography (ERCP). There are two

main types of stents each having their respective advantages and disadvantages.

Unfortunately, nearly 30% of all biliary stents fail and require removal, exchange, or

intervention. One common mode of failure is migration, which occurs 17% of the time

with fully covered metallic stents.

The first part of this research presents deployment characteristics and behaviors of

a novel stent designed by Wake Forest Innovations (WFI). The overall design requires

evaluation during deployment to analyze its ability to return patency and identify

potential shortcomings. The second area of this thesis reports simulation results

performed on different variations of the anti-migration hooks developed for the novel

stent. These are the main component of the stent designed specifically to reduce

migration. Lastly, a parametric study of hinge dimensions was analyzed. The hinge is an

integral part of the anti-migration hook which allows the hook to not only deploy

properly, but also relieve stress that would otherwise occur at certain locations within the

stent.

2

Chapter I: Introduction & Background

BILIARY SYSTEM ANATOMY

The biliary system is comprised of the liver, gallbladder, and bile ducts. Its main

function is the production, storage, and secretion of bile [5, 6]. The most superior portion

of the biliary system is the liver. Bile production starts in the liver and enters the common

hepatic duct via the merging left and right hepatic ducts. The cystic duct, which drains

the gallbladder, meets with the hepatic duct which then forms the common bile duct

(CBD). After this junction, the common bile duct travels posteriorly behind the first part

of the small intestine, known as the duodenum, for a short distance where it is then

enveloped by the pancreas. The pancreatic duct joins the common bile duct in the

duodenal wall to form the Ampulla of Vater terminating in the duodenum after passing

through the Sphincter of Oddi [7].

Figure 1: Anatomy of the Biliary System [3]

3

CAUSES FOR BILIARY STENTING

Strictures occurring in the biliary system are often treated with biliary stenting [8-

12]. Most often bile duct strictures results from an unresectable tumor at the pancreas

head, peri-ampullary area, bile duct, or gall bladder [9, 13]. A surrounding tumor causes

increase pressure on the common bile duct resulting in a narrowing or obstruction of the

biliary tract. Strictures, although less frequently, may also occur from swelling as a result

of a liver transplant or cholecystectomy (gallbladder removal) [8]. Strictures resulting

from anastomosis are localized and short due to scaring [14].This narrowing or

obstruction of the biliary duct system is known as obstructive jaundice. Obstruction in the

biliary tract can lead to impaired immune defense leaving patients exposed to infection,

discomfort, and severe abdominal itching [9]. Stenting is performed as a palliative

treatment for patients to relieve this discomfort and pain [12, 13, 15]. There are both

malignant and benign cases associated with obstructive jaundice caused by unresectable

tumors [8-11]. Because of the increased severity of the malignant cases and the desire to

relieve the associated pain, biliary stenting is often seen in higher frequency with patients

diagnosed with malignant obstructive jaundice (MOJ) [9].

EARLY HISTORY OF BILIARY DRAINAGE (PRIOR TO 1978)

Prior to stenting within the biliary tract, clinicians would treat obstructive

jaundice by draining or bypassing the blocked duct [9]. Cholecystojejunostomy,

choledochojeunostomy, or hepaticojejunostomy are the three main bypass surgeries

associated with the biliary system for treatment of obstructive jaundice. These different

4

treatments are performed laproscopically depending on the location of the stricture. A

cholecystojejunostomy establishes a connection between the gallbladder and jejunum

(portion of the small intestine directly following the duodenum). A

choledochojeunostomy establishes a connection between the common bile duct and

jejunum. A hepaticojejunostomy establishes a connection between the liver and jejunum.

These surgical techniques can in some instances act as a curative treatment for benign

obstructive jaundice. They, however, still are associated with high morbidity and/or

mortality [16, 17].

With the inventions of the Chiba needle [18] and the duodenoscopes [19],

drainage of biliary obstruction became the treatment of choice in the 1970’s. Not only

was it reported to have a much higher success rate at 95% [20, 21], but it also was a less

invasive procedure. Percutaneous transhepatic biliary drainage (PTBD) was a way to

drain the biliary system both internally and externally (see Figure 2 below). This

procedure requires percutaneous entry of a catheter into the liver. The catheter then

travels through the hepatic duct and biliary ducts until reaching the duodenum. This

catheter allows not only for external flushing, but also allows for internal drainage into

the duodenum. Internal drainage is advantageous because it prevents significant bile loss

and electrolyte imbalance [9]. This procedure, however, requires much more maintenance

and intervention from clinicians. A similar method, endoscopic retrograde

cholangiopancreatography (ERCP), allows for drainage of the biliary system. ERCP does

so minimally invasively. It is performed by inserting an endoscope through the mouth

and through the gastrointestinal tract until the duodenal papilla can be located.

Nasobiliary tubes are then inserted into the common bile duct which allows bile drainage

5

to occur. While this is a minimally invasive technique to drain the bile duct, nasobiliary

tubes, like percutaneous catheters, are very pliable and can easily dislodge [9].

MODERN BILIARY STENTS: PLASTIC VS. METALLIC

In efforts to reduce the frequency of medical practitioner intervention, biliary

stents were developed and first used in 1978 by Burcharth and Pereiras [22, 23]. Biliary

stents allowed for internal drainage of bile from the liver and gallbladder into the

duodenum without the external loss. This mitigated the effect that external drainage has

on electrolyte imbalance and possible immune deficiencies. The first plastic stents were

made of varying materials. Polytetrafluoroethylene (PTFE or Teflon), polyethylene (PE),

and polyurethane (PU) were the most common polymers used [9]. All of these materials

possess different physical characteristics; mainly rigidity and melting point were

Figure 2: A, Percutaneous pigtail stent placement; B, corresponding radiographic image [4]

6

considered for material selection. Rigidity was a selection criterion because of its

correlation to overall stent patency. Melting point was used because many plastic stents

were melted and bent into a shape that would resemble an individual patient’s biliary

duct.

While plastic stents solved the need for doctors to routinely drain the biliary

system, it brought about other problems that required intervention. The two main reasons

for plastic stent dysfunction are migration and clogging which account for 15% and 80%

respectively of dysfunctional plastic stents [8]. In order to solve initial stent migration

three novel developments were made in the Tannenbaum Stent, the Cotton-Leung Stent,

and the Pigtail Stent. All of these stents had anti-migration characteristics associated with

the ends of the stent. The Tannenbaum Stent (Figure 3A below) prevented proximal

migration and mitigated distal migration. It prevented proximal migration due to the

flared ends that resembles Christmas tree branches (Tannenbaum is German for

Christmas tree, hence the name Tannenbaum stent). Similarly the Cotton-Leung Stent

(Figure 3B below) helped with migration due to its flared portion at each end. The

Tannenbaum and Cotton-Leung stents, however, do not perform as well in preventing

distal migration. Distal migration may occur because the anchoring flaps on the proximal

end are compressed by the surrounding biliary tissue and as a result are not as resistive to

migration. Distal migration, however, is not an uncommon occurrence. With distal

migration plastic stents are often spontaneously eliminated. The major advantage of the

Cotton-Leung stent versus the Tannenbaum stent is that the Cotton-Leung stent has a port

in the side of the tapered tip. This port allows for drainage even if the stent migrates

distally blocking the distal tip of the stent due to the duodenal wall. Pigtail stents (Figure

7

3C below), while they perform well with respect to migrating, are prone to bacteria

biofilm buildup which can result in stent clogging. Plastic stents in general are much

more prone to bacteria biofilm build up and have an overall short life patency.

Metallic stents provide a much more long term palliative treatment than plastic

stents and are therefore used to treat patients with a longer life expectancy [8]. Metallic

stents fall into two categories: balloon inflatable stents and self-expandable metal stent

(SEMS). The main difference between the two is their means of deployment. For balloon

inflatable stents, upon retracting of the sheath exposing the stent, a balloon is inflated

underneath the stent placing a pressure on the internal face of the stent causing it to

A B

C Figure 3: Figure of plastic stents with anti-migration

designs [2]

A) Tannenbaum Stent

B) Cotton-Leung Stent (Cook Medical, Winston-

Salem, NC)

C) Pigtail Stent

8

expand. This balloon is inflated until the final diameter is achieved (accounting for the

recoil).

While balloon inflatable stents are typically stainless steel (SS), self-expandable

metallic stents are most often Nitinol. Nitinol is a combination of nickel and titanium that

is used due to its shape memory characteristics [24]. Nitinol or SEM stents are deployed

differently in that when the sheath is retracted exposing the stent, the stent will actually

open to its final deployed diameter naturally. The final configuration of the stent is set

prior to deployment. To do this, the stent is first placed in its deployed position outside of

the body. It is then heat treated in order to relieve stresses and make the current

configuration its natural and desired contour. After this, the stent is crimped such that it

Figure 4: Balloon Expansion of a metallic stent [1]

9

can be loaded onto the catheter for insertion. This way, when deployed, the stent will

return to its desired, natural, and heat set position within the biliary duct.

Under balloon inflatable and self-expandable stents are uncovered, partially

covered and covered stents; each of which possesses different advantages and

disadvantages as well as reasons for implementation. Uncovered stents allow for tissue

ingrowth and overgrowth. This can be troublesome and lead to stent dysfunction

requiring retrieval. As seen in Table 1, often times with uncovered stents tissue ingrowth

(growth around the stent) and overgrowth (growth at the ends of the stent) are the cause

for stent dysfunction. 18% of uncovered stents fail in regard to tissue ingrowth and 7% as

Figure 5: Self-Expandable Metal Stent naturally expanding to deployed

position upon retracting of sheath [1]

10

a result of tissue overgrowth. This accounts for roughly 95% of the failed uncovered

stents. The remaining 5% come from clogging, 4%, and ‘other complications’ accounting

for the final 1% [8]. Covered stents solve the tissue in- and overgrowth problem. Covered

stents were developed with this intention such that they would not disturb the biliary

lining. With the covering, however, came migration as the common mode of dysfunction.

Partially covered stents were the middle ground between covered and uncovered but

seemingly only distributed the dysfunction cause between migration, clogging, tissue

ingrowth, and tissue overgrowth.

In order to fully understand the advantages and disadvantages of both material

types of biliary stents, the applications of each type of stent should be thoroughly

evaluated prior to drawing a conclusion. This is because different stents are associated

with different applications. For example you may not see as many stent migration cases

with plastic stents because plastic stents are often used in malignant cases in which the

life expectancy is not nearly as long a benign case [8]. Because of this short life

expectancy associated with benign cases (less than four months) [12], stent dysfunction

Table 1: Stent-related complications in selected randomized controlled trials and single-arm prospective studies.1

11

due to migration may be under reported. In this scenario a sufficient amount time may not

have elapsed to see if the stent would have failed due to migration.

Stent migration is a prevalent issue that, if solved, could reduce overall stent

dysfunction drastically. A fully covered stent that did not migrate could result in lowering

dysfunction from roughly 20% to only 5%. This would significantly reduce the frequency

a doctor would have to intervene in order to restore biliary patency. This reduced

interventions frequency and continued biliary patency, would bring with it a much higher

quality of life. It would also limit or eliminate other possible complications that could

arise from placement procedures or stent migration.

12

CHAPTER SUMMARIES

Chapter II: Finite Element Analysis of a Non-Migrating Biliary Stent Deployment

Finite element simulations were performed on the non-migrating stent in order to

evaluate pertinent parameters as well as overall efficacy of the design.

Chapter III: Finites Element Analysis of Migration Reducing Hook Variations for a

Novel Biliary Stent

Analysis of three different hook variations was tested to see how altered hooks would

respond to deployment along with compressive biliary forces that would be exerted by

the common bile duct.

Chapter IV: Parametric Study of a Deployment Hinge using Finite Element

Analysis

To evaluate the stress and strain relief associated with varying certain variables, a

parametric study was performed in order to evaluate the optimal hinge dimensions.

Chapter V: Summary of Research

This chapter provides an overview of the research completed in conjunction with this

thesis.

13

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89(5 Pt 1): p. 589-3.

24. Song, H.-Y., J.H. Kim, and C.J. Yoon, Self-Expandable Stents in the

Gastrointestinal Tract, in Self-Expandabl Stents in the Gastrointestinal Tract, R.

Kozarek, T. Baron, and H.-Y. Song, Editors. 2013, Springer: New York. p. 35-49.

16

Chapter II: Finite Element Analysis of a Non-Migrating Biliary

Stent Deployment

Jared Mitchell1, Clifford Howard Jr.

2, Philip J. Brown

1

1Virginia Tech – Wake Forest University Center for Injury Biomechanics,

Winston-Salem, NC

2 Wake Forest Baptist Health Medical Center, Winston-Salem, NC

17

1. ABSTRACT

Finite element simulations were performed on a novel design for a non-migrating

biliary stent in order to understand deployment characteristics as well as mechanical

properties associated with the stent. Simulations were performed using Abaqus/Standard

and the stent model was imported from SolidWorks using the SolidWorks Associative

Interface. Due to radial and planar symmetry, one-twenty-fourth of the complete stent

was modelled. The use of this recurring section allows for symmetry constraints and

boundary conditions to be implemented such that the simulations will act as if a complete

stent were present. An elasto-plastic stainless steel material model was developed which

corresponded to the stent. A rigid cylinder expansion was incorporated to act as a balloon

would in a balloon-inflatable stent deployment. As the cylinder expanded the general

contact algorithm set up in Abaqus caused an interaction between the cylinder (balloon)

and the stent. From this interaction arose contact force applied to the stent resulting in

stent expansion and full deployment into its desired position. Simulations were set up to

have three steps: inflation, deflation, and settling. This would account for how a balloon

inflatable stent is practically inserted. Having these three steps would also allow for

monitoring of radial displacement, foreshortening, and recoil. In addition to analyzing

these three parameters, stent stiffness and stress concentration areas were are also

reported.

18

2. INTRODUCTION

Obstructive jaundice can leave a patient with impaired immune defenses and

predisposed to bacterial infection [1]. Strictures resulting in obstructive jaundices are

most often caused by tumors located at the pancreas head [1-6]. Anastomotic strictures

may also occur from swelling as a result of a liver transplant or cholecystectomy

(gallbladder removal) [2]. Strictures resulting from anastomosis are localized and short

due to scaring at the Sphincter of Oddi (where the CBD meets the duodenum) [7].

Narrowing of the bile duct can cause deficiencies in the secretion of bile into the

duodenum (the first part of the small intestine following the stomach). In instances with

biliary duct complications, stenting has become a common practice [6].

Stents were designed and developed to keep vessels within the body open [8].

Biliary stent implementation is often times placed by taking the delivery system through

the mouth, past the stomach and finding the major ampulla (Ampulla of Vater). This

process is known as Endoscopic retrograde cholangiopancreatography (ERCP) [3]. There

are two methods for delivery each associated with a certain metallic stent type. For

balloon expandable stents, the delivery system also contains a catheter, the stent, and the

balloon. For self-expandable metal stents (SEMS) the balloon is not needed (however,

can be used for dilation). Upon catheter insertion and proper placement location found,

the sheath of the catheter is retracted and the balloon is inflated underneath the stent

causing a pressure on the internal face of the stent. This pressure expands the stent. After

the predetermined radius for the stent is reached, the balloon is then deflated and, along

with the catheter, is removed leaving only the stent [3, 9].

19

This chapter will report on finite element (FE) simulations resembling this

deployment process. Simulations were performed on the non-migrating stent to better

evaluate the unique deployment geometry and understand mechanically how the stent

performs. This will be analyzed by monitoring the stiffness of the stent during inflation

and deflation of the balloon such that all steps of the deployment have been included.

3. METHODS

Stent, Balloon, & Compression Sheet Modeling:

Development of the non-migration stent was performed using Dassault Systemes’

SolidWorks 2015. SolidWorks is a commonly used 3D modelling software package that

allows the user to develop models for prototyping or simulation. This use of computer

software is known as computer-aided design (CAD) [10]. The hook design is novel to

Wake Forest Innovation and is located at either end of the stent body. The concept behind

the hook deployment stems from a simple four-bar linkage configuration. In this design,

as the stent diameter increases, the mid-hook support will be drawn opposite of the

foreshortening direction and, given the hook structure, cause out-of-plane bending. The

complete stent has an overall length of 19.18 mm. There are twelve total hooks (six on

the proximal side and six on the distal side). The two hook sections on either side occupy

9.18 mm (4.59 mm each) and the stent body section occupies the remaining 10.00 mm of

the 19.17 mm. The stent was designed with an initial diameter of 3.00 mm to fit in a

roughly 10 French catheter.

20

A

C B

Figure 7: Full Stent Model: A) Top view of the full stent with length dimensions. B) Isometric of full stent.

C) Side view of full stent with external diameter dimension.

Figure 6: Four-bar Linkage Hook Design

21

Using the common knowledge of repeating unit cells (RUCs), this allowed us to

model only one twenty-fourth of the stent and balloon. A one twenty-fourth section was

reached due to the inherent symmetry that exists within the stent. First, the distal end

mirrors the proximal end. There is also radial symmetry in that each hook is identical to

one another. Lastly, the hook itself is symmetric about the mid-plane resulting in a 1/24th

section. This symmetry had the added benefit in that it greatly reduced computational

requirements and simulation time.

All of the CAD, however, was not done using SolidWorks. The balloon was

modelled using Abaqus’ modeling package. While the stent was modeled as a solid body,

the balloon was modeled as a surface.

Simulation Assembly Set-Up: Constraints, Meshing, and Boundary Conditions:

The simulation software used was Simulia’s Abaqus/CAE version 6.14. In order

to import the stent model from SolidWorks into Abaqus, a SolidWorks/Abaqus “plug-in”

was used. This allowed for minor design optimization to be made in SolidWorks, while

still preserving the added features developed in Abaqus (i.e. partitioning, meshing,

constraints, boundary conditions, and material assignments).

Figure 8: 1/24th of the full stent

22

The stent is meshed using hexahedral elements. The one twenty-fourth section of

the stent is comprised of 6864 elements and 10965 nodes of Abaqus’ C3D8R type. This

type is an 8-node linear brick with a reduced integration and hourglass control. In order to

generate an appropriate mesh the stent had to be partitioned. This was done in order to

eliminate the possibility of distorted element. Edges of the stent were also seeded such

that at no point is there a cross section with less than 3 by 3 elements. This will allow for

appropriate monitoring of stresses in all modes of bending.

Sdlkfjsd’f

The stent material model was resembled after stainless steel 316 [11]. An elasto-

plastic material model was used with the following parameters: Density = 8000 kg/m3 ;

Young’s Modulus = 193 GPa ; Poisson’s Ratio = 0.27 ; Yield Strength = 193 MPa ; See

Table 2 and Figure 10 for parameters associated with plastic deformation.

Figure 9: Partitioning and Meshing of Non-Migration Stent. A) Stent depicting partition locations. B) stent

depicting overall hexahedral mesh

A

B

23

Table 2: Reflects the Abaqus plastic deformation input table

Yield Stress (MPa) Plastic Strain

193 0

193 0.003

316 0.0037

400 0.03

550 0.14

700 0.5

701 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1100

200

300

400

500

600

700

800

Str

ess (

MP

a)

Plastic Strain

SS 316: Stress vs. Plastic Strain

Figure 10: Stent Material Model for Stainless Steel Grade 316: Mises Stress vs. Plastic Strain

24

The balloon was attributed a material model that was ten times as rigid as the

stainless steel 316 material model. This was used as a “dummy material” simply to run

the simulation. Because of the boundary condition that was attributed to the balloon

model and the fact that the balloon was not being analyzed a material was only necessary

to have the simulation run properly.

In order to simulate balloon inflation, a rigid cylinder expansion was attributed to

the nodes of the balloon surface [12]. This BC is applied to a 1.0 mm/s velocity radially

outward from the balloon’s central axis for 2.5 s. Following inflation, a deflation occurs

drawing the balloon back in. This occurs over 3 s with a -0.75 mm/s velocity boundary

control. After deflation, a settling step occurs for 2.5 s (0 mm/s velocity control on the

balloon). Displacements, stresses, and strains were monitored for each element in the

model throughout the entire simulation. Contact forces occurring between the internal

face of the stent and the balloon surface were reported.

4. RESULTS

The stent deploys as expected. Upon balloon inflation, the resultant stent diameter

increases. As the stent diameter increases, the hooks tips displace farther than the stent

body portion.

Figure 11: Stent Mesh showing specific node locations monitored for radial expansion displacement comparison.

25

In order to comprehend stent deployment, displacements were reported for all

elements of the full stent with the main focus on the stent body versus hook tip

displacements/coordinates (See Figure 12 above for corresponding locations). The

maximum displacement of 2.506 mm for the stent body occurs at the end of balloon

inflations. Simultaneously, the hook tip reaches its maximum displacement of 4.669 mm.

With an initial stent diameter of 3 mm, these displacements correspond to diameters of

roughly 8 mm and 12 mm respectively.

Figure 12: Full Stent Model Deployed:

A, Top view of the full stent after deployment.

B, Side view of full stent after deployment.

C, Isometric of full stent after deployment.

A B

C

26

0 1 2 3 4 5 6 7 8-0.5

0

0.5

1

1.5

2

2.5

3

Dis

pla

cm

ent

(mm

)

Time (s)

Stent Body Displacement vs. Time

X-Direction

Y-Direction

Z-Direction

Magnitude

Figure 13: Stent Body Displacement vs. Time: This shows the stent body's displacements in the X, Y, & Z

directions, as well as, the displacement magnitude with respect to time.

0 1 2 3 4 5 6 7 8-1

0

1

2

3

4

5

Dis

pla

cm

ent

(mm

)

Time (s)

Hook Tip Displacement vs. Time

X-Direction

Y-Direction

Z-Direction

Magnitude

Figure 14: Hook Tip Displacement vs. Time: This shows the hook tip's displacements in the X, Y,

& Z directions, as well as, the displacement magnitude with respect to time.

27

When a stent is deployed, often times its total length will decrease. This decrease

in length is known as foreshortening. Contrary to foreshortening, recoil is measured by

the how far the stent increases in length as a result of unloading occurring on the internal

stent face. While foreshortening corresponds to an increase and diameter, recoil is

analogous to a decrease in stent diameter. In this case, the stent foreshortens by roughly

10% of its initial length. After foreshortening, the stent then restores a portion of the

decrease in length and recoils by nearly 0.16 mm. These values correspond to an initial

length of 19.17 mm to an inflated, or minimum, length of 17.24 mm ultimately recoiling

to a fully deployed length of 17.41 mm.

Figure 15: .Radius vs. Time for Mid-Stent and Hook Tip: With an initial internal radius of roughly 1.4 mm,

this figure shows the radius of the significant locations with respect to time.

0 1 2 3 4 5 6 7 80

1

2

3

4

5

6

7

8

Radiu

s (

mm

)

Time (s)

Radius vs. Time

Mid-Stent

Hook Tip

28

In addition to displacements, stress concentrations were monitored. Stress and

strain management is important in stents mainly because the structures that comprise the

stent are often times only microns thick. It is important to make sure that the stent will

not fail upon deployment [13]. Hence why there exist extensive simulations prior to

prototyping and testing. In order to determine how our stent would perform, we probed

areas of high stress and strain. There areas of highest values occurred on the interior arch

of the stent body strut as well as the internal arch of the hook hinge.

Figure 16: Foreshortening vs. Time: This reports the overall change in stent length with

respect to time.

0 1 2 3 4 5 6 7 80

0.5

1

1.5

2

2.5

Change in S

tent

Length

(m

m)

Time (s)

Change in Stent Length vs. Time

29

Figure 17: Stent Mises Stress with detail view of areas with stress/strain concentrations (units of MPa)

Figure 18: Stent Peak Equivalent Plastic Strain with detail view of areas with stress/strain concentrations

30

In order to evaluate the stiffness of the stent during deployment, contact forces

were monitored during the overall loading of the stent (inflation). Stiffness looks at the

force required to displace the stent radially (see Figure 20 below). As you can see from

Figure 20, the stent has a drastic change in force at roughly 0.27s. At this point the hook

begins to bend out of plane. Because of this, two stiffnesses have been attributed to each

feature: a pre- and post-hook out of plane bending stiffness (see Table 3).

Figure 19: Mises Stress vs. Strain profiles for the interior arch of the stent body strut as well as the internal

arch of the hook hinge

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

100

200

300

400

500

600

700

Strain

Str

ess (

MP

a)

Stress vs. Strain

Hook Hinge

Stent Strut

SS 316 Tensile Strength

31

Table 3: Resultant Inflation Stiffnesses for the Stent Portion, Hook Portion, and Total Stent factoring in prior or

post hook out of plane bending.

Pre-Bending Stiffness

(N/mm)

Post-Bending Stiffness

(N/mm)

Stent Portion 23.43 2.18

Hook Portion 17.49 1.85

Total Stent 40.49 4.03

Figure 20: Force vs. Radial Displacement. This figure shows the force-displacement profile for the inflation

of the stent

0 0.5 1 1.5 2 2.5 30

2

4

6

8

10

12

14

16

18

Displacement (mm)

Forc

e (

N)

Force vs. Radial Displacement

Stent Portion Inflation

Hook Portion Inflation

Inflation Total

32

5. DISCUSSION

In terms of methodology, a rigid cylinder expansion of the balloon model is a

sufficient means for the balloon inflation. Research has also gone into the modeling

behind the different techniques for balloon inflation [12]. Even though rigid cylinder

expansion “can be used interchangeably” (Gervaso et. al) with an internal balloon

pressure inflation [12], a pressure simulation may be a possible next step for this stent.

Given the novel design of the stent notion that the hook requires less pressure to deploy

(Figure 20), applying a pressure the internal face of the balloon model may yield a

different deployment shape as well as different loading parameters of the stent structures.

A pressure simulation may be able to account for these variations.

This stent is of smaller length and larger diameter as it relates to other biliary

stents. It is stated in literature that smaller length and larger diameter stents are more

prone to migration [6, 9, 14]. The rationale behind our dimensions was done

intentionally. Solving migration with respect to anastomotic stricture is the more difficult

that other biliary strictures because of the short landing zone [7]. Not only would this

stent solve migration with anastomic strictures, but features could be scaled and/or

augmented such that this stents could meet the needs of other applications.

One important figure to note is Figure 20. This figure helps show the relative

stiffnesses of the stent body versus the hook portion. There is one discontinuity within the

inflation traces. The discontinuity which occurs at roughly 0.27 s is due to the start of the

hook bending out of plane. Initially the hook portion acts just like the stent, only

expanding as a cylinder. Looking at Figure 14, for the first quarter of a second the radii

follow the same path. After that, however, the hook tip radius increases at a much faster

33

rate. This local maximum occurring at roughly a quarter of a second in Figure 20 is due

to the resistance of the four-bar linkage to brake from its 2D motion and include bending

out of plane. The reason a drop in overall force can also be seen in the stent body portion

is due to the joined relationship that exists. As the stent portion inflates it will foreshorten

and draw the hook portion closer to the mid-plane. Because the radial increase and out of

plane bending are coupled, this decrease in resistance to bend out of plane is seen in the

reduced force required to continue to inflate the overall stent.

The stress concentration that occur in the stent, primarily in the hinge portion,

approach or have already passed the tensile strength of the stent. The tensile strength for

annealed stainless steel 316 is 586 MPa [15, 16]. With this material the stent would fail

and not be able to pass testing for implementation. There are two ways to solve this. One

solution is to improve and alter features such that the stresses are less prominent in the

specified stress-strain concentration areas. The second way to eradicate this problem

would be to switch the material used. In this case, a cobalt chromium alloy may be a

viable solution. Co-Cr alloys are relatively stiffer and comes with a much higher tensile

strength ranging from 951 – 1220 MPa [15-17]. This material may not only prevent the

stent from failing, but also help in added stiffness which would increase the overall

rigidity of the stent.

6. CONCLUSION

The hooks of the stent deploy as desired. The ultimate goal was to achieve a hook

design that would displace the proximal and distal ends of the stent greater than the

middle. This also wanted to be done in such a fashion that it would reduce the ability for

34

the stent to migration. With this deployment mechanism, this would prevent migration

within the common bile duct and reduce the need for intervention of medical

practitioners. This stent could not only be used in the common bile duct but also be

modified and used to solve migration issues occurring elsewhere in the body. This stent is

an innovative design that is vastly different from current biliary stents.

7. ACKNOWLEDGEMENT

Funding for this project was provided by Wake Forest Innovations. Additional help

and support was provided by the Virginia Tech – Wake Forest University Center for

Injury Biomechanics.

35

8. REFERENCES






Endoscopy, 2012. 44(3): p. 277-98.



4. van Boeckel, P.G., F.P. Vleggaar, and P.D. Siersema, Plastic or metal stents for

benign extrahepatic biliary strictures: a systematic review. BMC Gastroenterol,

2009. 9: p. 96.





7. Williams, E.D. and P.V. Draganov, Endoscopic management of biliary strictures

after liver transplantation. World J Gastroenterol, 2009. 15(30): p. 3725-33.

8. Hontz, R.A., M.D. Tripp, and L.P. Kline, Stents keep occluded vessels open. RN,

1991. 54(3): p. 50-4.

9. Chaurasia, O.P., et al., Endoscopic techniques for retrieval of proximally migrated

biliary stents: the Amsterdam experience. Gastrointest Endosc, 1999. 50(6): p.

780-5.

36

10. Bonsignore, C., Open Stent Design, ed. C. Commons. 2011, Fremont, CA: Nitinol

Devices & Components Inc. .

11. Hibbeler, R.C., Mechanics of Materials. 1994, Macmillan: New York.

12. Gervaso, F., et al., On the effects of different strategies in modelling balloon-

expandable stenting by means of finite element method. J Biomech, 2008. 41(6):

p. 1206-12.

13. S. Chua, B.M., M. Hashmi, Finite Element Simulation of Stent and Balloon

Interaction. Journal of Materials Processing Technology, 2003. 143: p. 591-597.

14. Johanson, J.F., M.J. Schmalz, and J.E. Geenen, Incidence and risk factors for

biliary and pancreatic stent migration. Gastrointest Endosc, 1992. 38(3): p. 341-

6.

15. Brunski, J., ed. Biomaterials Science an Introduction to Materials in Medicine.

ed. B. Ratner, et al. 2004, Elsevier Academic Press: San Diego.

16. Park, J. and Y. Kinm, eds. Metallic Biomaterials. Biomaterials Principles and

Applications, ed. C. Press. 2003: Boca Raton.

17. Davis, J., Metallic Materials, in Handbook of Medical Devices. 2003, ASM

International: Materials Park. p. 21-50.

37

Chapter III: Finite Element Analysis of Migration Reducing

Hook Variations for a Novel Biliary Stent


2, Philip J. Brown

1


Winston-Salem, NC


38

1. ABSTRACT

During modeling, various hook designs were developed to prevent stent

migration. These variations’ primary objective is to control the amount of traction

experienced on the stent by the surrounding tissue. SolidWorks was used to generate the

different models and finite element analysis simulations were performed using

Abaqus/Standard. An elasto-plastic stainless steel material model was developed which

corresponded to the stent and a rigid cylinder expansion was performed to act as a

balloon inflation deployment. As the cylinder expands, the general contact algorithm set

up in Abaqus causes an interaction between the cylinder (balloon) and the stent. From

this interaction, contact force applied to the stent result in stent expansion progressing to

full deployment into its desired configuration. Simulations were set up to have four steps:

inflation, deflation, settling, with the last being an additional step testing the hook in

different bending modes. These simulations account for how each hook variation affects

the deployment process as well as how well they perform given external loading. This

will allow for the monitoring of geometric and mechanical characteristics of each hook

variation as well as stiffness and associated stress concentration areas.

39

2. INTRODUCTION

Obstructive jaundice can leave a patient with impaired immune defenses and

predisposed to bacterial infection [1]. Strictures resulting in obstructive jaundices are

most often caused by tumors located at the pancreas head [1-6]. Anastomotic strictures

may also occur from swelling as a result of a liver transplant or cholecystectomy

(gallbladder removal) [2]. Strictures resulting from anastomosis are localized and short

due to scaring at the Sphincter of Oddi (where the CBD meets the duodenum) [7].

Narrowing of the bile duct can cause deficiencies in the secretion of bile into the

duodenum (the first part of the small intestine following the stomach). In instances with

biliary duct complications, stenting has become a common practice [6].

Stents were designed and developed to keep vessels within the body open [8].

Biliary stent implementation is often times placed by taking the delivery system through

the mouth, past the stomach and finding the major ampulla (Ampulla of Vater). This

process is known as Endoscopic retrograde cholangiopancreatography (ERCP) [3]. There

are two methods for delivery each associated with a certain metallic stent type. For

balloon expandable stents, the delivery system also contains a catheter, the stent, and the

balloon. For self-expandable metal stents (SEMS) the balloon is not needed (however,

can be used for dilation). Upon catheter insertion and proper placement location found,

the sheath of the catheter is retracted and the balloon is inflated underneath the stent

causing a pressure on the internal face of the stent. This pressure expands the stent. After

the predetermined radius for the stent is reached, the balloon is then deflated and, along

with the catheter, is removed leaving only the stent [3, 9].

40

Stent occlusion and dysfunction occurs approximately 50% of the time [9]. One

common mode of stent dysfunction is migration [2]. In order to reduce dysfunction due to

migration, interaction with the surrounding tissue is necessary. This chapter will show

possible solutions to increase traction between the stent and biliary and limit migration.

3. METHODS

Stent, Balloon, Compression Sheet, and Axial Testing Solid Modeling:

Development of the non-migration stent was performed using Dassault Systemes’

SolidWorks 2015. SolidWorks is a commonly used 3D modelling software package that

allows the user to develop models for prototyping or simulation. This use of computer

software is known as computer-aided design (CAD) [10]. The hook design is novel to

Wake Forest Innovation and is located at either end of the stent body. The concept behind

the hook deployment stems from a simple four-bar linkage configuration. In this design,

as the stent diameter increases, the mid-hook support will be drawn opposite of the

foreshortening direction and, given the hook structure, cause out-of-plane bending.

Multiple hook variations were developed such that interaction with the bile duct

could be optimized. We have modeled three different hooks each with the same stent

body: a generic hook, a flexible hook tip, and a double four-bar hook.

41

Each stent has their design advantage to help interact with the surrounding tissue.

The generic stent theoretically should maintain rigidity more than the other two. The

flexible tip hooked stent, has hook tips that when they come in contact with the biliary

duct or duodenal lining with deform and create a larger contact surface. The larger the

contact surface the greater the resistance to migrate. Last is the double four-bar stent.

A

C

B

Figure 22: A, Generic Hooked Stent; B, Flexible Tip Hooked Stent; C, Double Four-Bar Hooked Stent

Figure 21: Four-bar Linkage Hook Design

42

This has two four-bar hooks (similar to the generic hooks) arranged in series. This stent,

upon deployment, will deploy both hooks and create blunted loading of the ductal

system. Both the generic and flexible tipped stent have an overall length of 19.18 mm,

while the double four-bar stent has a length of 21.18 mm. The hook portion for the

generic and flexible tip stents is 4.59 mm in length. The double four-bar stent has roughly

a millimeter longer hook region at 5.50 mm. All of the stents have a stent body length of

roughly 10.00mm (double four-bar: 10.18 mm). The initial external diameter (for catheter

sizing) is 3.00 mm for the shorter two stents and 2.60 mm for the longer double four-bar

stent. This decreased radius allows for greater deformation needed to reach the desired

deployment radius of the hook tip.

A

C B

Figure 23: Generic Stent displaying measurement locations of hook portion, stent body, and initial external

diameter

43

Table 4: Length of stents with respect to hook variation

Stent Total Length

(mm)

Stent Body

Length (mm)

Hook Portion

Length (mm)

Initial Diameter

(mm)

Generic 19.18 10.00 4.59 3.00

Flexible Tip 19.18 10.00 4.59 3.00

Double 4-bar 21.18 10.18 5.50 2.60

Using the common knowledge of repeating unit cells (RUCs), this allowed us to

model only one twenty-fourth of the stent and balloon. A one twenty-fourth section was

reached due to the inherent symmetry that exists within the stent. First, the distal end

mirrors the proximal end. There is also radial symmetry in that each hook is identical to

one another. Lastly, the hook itself is symmetric about the mid-plane resulting in a 1/24th

section. This symmetry had the added benefit in that it greatly reduced computational

requirements and simulation time.

All of the CAD was not done using SolidWorks. The balloon, compression sheet,

and the axial tip testing solid were modelled using Abaqus’ modeling package. While the

stent and testing solid were modeled as a solid bodies, the balloon and compression sheet

were modeled as surfaces.

Simulation Assembly Set-Up: Constraints, Meshing, and Boundary Conditions:

The simulation software used was Simulia’s Abaqus/CAE version 6.14. In

order to import the stent model from SolidWorks into Abaqus, a SolidWorks/Abaqus

“plug-in” was used. This allowed for minor design optimization to be made in

44

SolidWorks, while still preserving the added features developed in Abaqus (i.e.

partitioning, meshing, constraints, boundary conditions, and material assignments).

All of the stents were meshed using Abaqus’ hexahedral C3D8R type elements.

This element type is an 8-node linear brick with a reduced integration and hourglass

control. For proper meshing, each stent required partitioning. This was done in order to

eliminate the possibility of “distorted elements.” Edges of the stents were also seeded

such that no cross section of a stent contained less than 3 by 3 elements.

Figure 24: Partitioning and Meshing of Stent Variations. A, Generic Stent Partitioning; B, Associated generic

stent hexahedral mesh; C, Flexible Hook Tip Stent Partitioning; D, Associated flexible hook tip stent hexahedral

mesh; E, Double Four-Bar Stent Partitioning; F, Associated double four-bar stent hexahedral mesh

A

B

F

E

D

C

45

The stent material model was resembled after stainless steel 316 [13]. An elasto-plastic

material model was used with the following parameters: Density = 8000 kg/m3 ; Young’s

Modulus = 193 GPa ; Poisson’s Ratio = 0.27 ; Yield Strength = 193 MPa ; See Table 5

and Figure 25 for parameters associated with plastic deformation.



193 0

193 0.003

316 0.0037

400 0.03

550 0.14

700 0.5

701 1

46

The balloon, compressive surface, and axial tip test solid were attributed material

models that were at least ten times as rigid as the stainless steel 316 material model. This

was used as a “dummy material” simply to run the simulation. Because of the boundary

condition that was attributed to the balloon model and the fact that the balloon was not

being analyzed a material was only necessary to have the simulation run properly.

The entire simulation took place over four steps: inflation, deflation, settling, and

testing step. In order to simulate balloon inflation, a rigid cylinder expansion was

attributed to the nodes of the balloon surface [12]. This BC is applied to a 1.0 mm/s

velocity radially outward from the balloon’s central axis for 2.5 s. Following inflation, a

deflation occurs drawing the balloon back in. This occurs over 3 s with a -0.75 mm/s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1100

200

300

400

500

600

700

800

Str

ess (

MP

a)

Plastic Strain


Figure 25: Stent Material Model for Stainless Steel Grade 316: Stress vs. Plastic Strain

47

velocity boundary control. After deflation, a settling step occurs for 2.5 s (0 mm/s

velocity control on the balloon). Then the testing step occurs. This is done one of two

ways. Either a rigid sheet is compressed over the hook portion of the stent or an axial tip

test drives a portion of a ring alongside the stent engaging and interacting with the tip of

the stent hook (see Figure 26 below).

Element displacements, stresses, and strains were monitored for each element

throughout the model. Contact forces were reported for regions that interacted with the

balloon and/or the testing surface or solid. Monitoring of these parameters would allow

us to understand overall hook performance during deployment as well as environmental

loading conditions.

Figure 26: Test comparison showing hook compression test step versus the axial tip test step

performed.

48

4. RESULTS

Each hook deploys differently from one another. However, all result in an overall stent

diameter increase during inflation. As the stent diameter increases, the hooks tips displace

into their desired positions. The main goal of these different hook designs was to see the

differences in deployment. In order to compare the different stents, displacements at the

middle of the stents as well as the end of hook tip were recorded.

Figure 27: Generic Stent Model Deployed:

A, Top view after deployment.

B, Side view after deployment.

C, Isometric after deployment.

A B

C

49

A B

C Figure 29: Double Four-Bar Stent Model Deployed:




A B

C Figure 28: Flexible Hook Tip Stent Model Deployed:




50

Table 6: Hook Variation Deployment Hook and Mid-Stent Diameters

Hook Variation Mid-Stent Diameter (mm) Hook Tip Diameter (mm)

Generic 7.628 11.697

Flexible Hook Tip 7.628 11.452

Double Four-Bar 7.630 10.662

Figure 31: Hook Variation Overlay

0 1 2 3 4 5 6 7 8 90

1

2

3

4

5

6

Time (s)

Dis

pla

cem

ent

(mm

)

Displacement vs. Time

Generic Hook

Generic Mid-Stent

Flexible Tipped Hook

Flexible Tipped Mid-Stent

Double Four-bar Hook

Double Four-bar Mid-Stent

Figure 30: Displacement Magnitude vs. Time for all hook variations

51

Generic

Flexible Hook Tip

Double Four-Bar

Mid-Stent Hook Tip

Figure 32: Displacement vs. Time at middle of the stent and at the hook for all hook variations during deployment.

0 2 4 6 8

0

1

2

3

Dis

pla

cm

ent

(mm

)

Time (s)

X-Direction Y-Direction Z-Direction Magnitude

0 2 4 6 8

0

2

4

6

0 2 4 6 8

0

1

2

3

0 2 4 6 8

0

2

4

6

0 2 4 6 8

0

1

2

3

0 2 4 6 8

0

2

4

6

52

8 9 10 11 12 133

3.5

4

4.5

5

5.5

Time (s)

Dis

pla

cem

ent

(mm

)

Stent Testing Step: Displacement vs. Time

8 9 10 11 12 133

3.5

4

4.5

5

5.5

8 8.5 9 9.5 10 10.5 11 11.5 12 12.53

3.5

4

4.5

5

5.5

Compression Axial Testing

Generic

Flexible Hook Tip

Double Four-Bar

Figure 33: Displacement vs. Time at hook tip for all hook variations during the compression and axial testing

step of the simulation.

53

A

B

C

Figure 34: Generic Stent Deployed vs. Deformed: A) Fully Deployed Generic Stent; B) Generic Stent under

compressive load; C) Generic Stent hook after axial hook testing

54

Figure 35: Flexible Hook Tip Stent Deployed vs. Deformed: A) Fully Deployed Flexible Hook Tip Stent; B)

Flexible Hook Tip Stent under compressive load; C) Flexible Hook Tip after axial hook testing

C

A

B

55

A

B

C

Figure 36: Double Four-Bar Stent Deployed vs. Deformed: A) Fully Deployed Double Four-Bar Stent; B) Double

Double Four-Bar Stent under compressive load; C) Double Four-Bar hook after axial hook testing

56

Stiffness of the different hook variations was also monitored during the two different

testing steps in the simulations. The resultant forces are reported for the contact surface

that interacts with the testing part (either the compression sheet or the axial tip testing

solid). The values reported are for one hook (1 of 12 contained in the entire stent).

Note: Figures 36, 37, & 38 are Force vs. Displacement profiles for one hook. In each

stent, there are a total of 12 hooks.

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Displacment (mm)

Forc

e (

N)

Generic Stent: Force vs. Displacement During Different Steps

Inflation

Compression

Axial Testing

Figure 37: Force vs. Displacement during different steps for the Generic Stent

57

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Displacment (mm)

Forc

e (

N)

Flexible Hook Tip Stent: Force vs. Displacement During Different Steps

Inflation

Compression

Axial Testing

Figure 38: Force vs. Displacement during different steps for the Flexible Hook Tip Stent

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

Displacment (mm)

Forc

e (

N)

Double Four-Bar Stent: Force vs. Displacement During Different Steps

Inflation

Compression

Axial Testing

Figure 39: Force vs. Displacement during different steps for the Double Four-Bar Stent

58

5. DISCUSSION

All of the hook variations have different deployment profiles. While they all have

roughly the same deployed stent body diameter, the hooks of each are very different. The

generic stent has the largest deployment diameter associated with the hook tip at

11.697mm. The flexible tipped and double four-bar stents have smaller radii, 11.452mm

and 10.662mm respectively.

The main basis for comparison is how each of these hooks would respond to the

biliary tissue. One of the possible disadvantages with the generic stent is that there may

not be enough traction distally to prevent a proximal migration. With the generic stent

hook configuration and assuming only the hook tip interacts with the biliary duct system,

there is relatively less contact between the hooks and the biliary lining than the flexible

and double four-bar hook configurations.

While the generic stent may not provide enough traction, the flexible hook tip and

double four-bar stent are designed to deform in such a manner that with cause increased

interaction. In Figure 35 we can see that upon compression the tip of the flexible hook tip

stent bends to contour what would be the biliary lining. As opposed to the generic stent,

the flexible hook tip stent would provide added traction that would ultimately increase

interaction with the lining and reduce the risk of migration. The flexible hook tip stent

would also reduce the risk of perforation due to the blunter loading of the tissue.

Likewise with the flexible hook tip stent, the double four-bar stent would also

increase interaction with the biliary lining, although does so by a very different means.

Upon deployment, it will take a shape that will interact with the lining greater than the

generic stent. From Figure 36 it is visible to see that the stent, when compressed, will

59

have the mid-hook brace run parallel with the biliary duct. This will be coaxial to the

stent body as well as the bile duct. This will ultimately increase the amount of traction

and in turn reduce migration. Relative to the generic stent, the double four-bar hooked

stent would also reduce the risk of perforation due to the blunter loading of the tissue.

Each stent has a location that exceeds the tensile strength. The tensile strength for

annealed stainless steel 316 is 586 MPa [15, 16]. With this material, each of the stents

would fail at different locations. There are multiple remedies for this situation. One

solution is to improve and alter features such that the stresses are less prominent in the

specified stress concentrated areas. The second way to improve this problem would be to

switch the material used. In this case, a cobalt chromium alloy may be a viable solution.

Co-Cr alloys are relatively stiffer and comes with a much higher tensile strength ranging

from 951 – 1220 MPa [15-17]. This material may not only prevent the stent from failing

but also help by adding to the overall stent stiffness.

It is worth noting that these simulations have not incorporated a biliary-duodenal

model. These higher deformation structures may have to be altered as the design process

continues to prevent biliary, duodenal, and/or papillary injury.

6. CONCLUSION

The hooks variations deploy in very different manners. The main objective was to

design hook variations that would interact with the biliary duct in different ways.

Increasing the traction between the stent and ductal system would reduce stent migration.

With these distinct designs, increased stent – biliary interaction would occur and reduce

60

stent migration. This would be a major help and reduction in the frequency at which

medical practitioners would have to perform biliary stent exchanges.

7. ACKNOWLEDGEMENT




61

8. REFERENCES






Endoscopy, 2012. 44(3): p. 277-98.



4. van Boeckel, P.G., F.P. Vleggaar, and P.D. Siersema, Plastic or metal stents for

benign extrahepatic biliary strictures: a systematic review. BMC Gastroenterol,

2009. 9: p. 96.






1991. 54(3): p. 50-4.

8. Chaurasia, O.P., et al., Endoscopic techniques for retrieval of proximally migrated

biliary stents: the Amsterdam experience. Gastrointest Endosc, 1999. 50(6): p.

780-5.

9. Ahrendt, S.A. and H.A. Pitt, A history of the bilioenteric anastomosis. Arch Surg,

1990. 125(11): p. 1493-500.

62

10. Donelli, G., et al., Plastic biliary stent occlusion: factors involved and possible

preventive approaches. Clin Med Res, 2007. 5(1): p. 53-60.

11. Gouma, D.J., Stent versus surgery. HPB (Oxford), 2007. 9(6): p. 408-13.

12. Bonsignore, C., Open Stent Design, ed. C. Commons. 2011, Fremont, CA: Nitinol

Devices & Components Inc. .

13. Hibbeler, R.C., Mechanics of Materials. 1994, Macmillan: New York.

14. Gervaso, F., et al., On the effects of different strategies in modelling balloon-

expandable stenting by means of finite element method. J Biomech, 2008. 41(6):

p. 1206-12.

15. Brunski, J., ed. Biomaterials Science an Introduction to Materials in Medicine.

ed. B. Ratner, et al. 2004, Elsevier Academic Press: San Diego.





63

Chapter IV: Parametric Study of a Deployment Hinge using

Finite Element Analysis


2, Philip J. Brown

1


Winston-Salem, NC


64

1. ABSTRACT

Parametric studies can often be performed to optimize a design. After performing

initial simulations on full models of novel biliary stents, it was noticed that often times

the stent would fail during deployment due to material failure (surpassing the tensile

strength). This mainly occurs at the side junction of a hinge contained within the stent.

The hinge is necessary in the stent design because of its anti-migration hooks that

displace and deploy further than the main body of the stent. These hinges make it

possible for this precise deformation to occur. To evaluate hinge performance, the width

and length of the hinge’s oval slot, as well as, the side junction thickness were varied. All

hinge configurations were modeled, assigned an elasto-plastic stainless steel 316 material

model, and prescribed the same loading condition using Abaqus. Stresses, strains,

displacements, and overall stiffness were monitored throughout the simulation and

reported.

65

2. INTRODUCTION

A cantilever beam is a beam rigidly fixed at one end with the other unconstrained.

Because of is unique properties and esthetic appeal, cantilevers structures can often be

seen in many buildings. They also, however, can be seen in parts on a much finer scale

(i.e. Microelectromechanical systems [MEMS]). This simplistic configuration provides a

template that is easily understood and is ideal for material analysis. A simple cantilever

allows for monitoring of bending and stiffness, among other variables, to be recorded and

analyzed. All of which can be studied with the use of simulations [1, 2].

Hinges are often placed in beams to reduce the amount of stress seen in a location.

This occurs because of the hinges inability to transmit moments or, in other words, it

eliminates the internal moment seen at the hinge’s location [1, 2]. This can be beneficial

if a beam requires a large deformation, but you do not want to surpass the tensile strength

of the material. Having a hinge in place can, by reducing the internal moment, ultimately

reduce the stresses experienced in a specific part.

A stent is either a metallic or plastic tube that is used to restore patency to a

passageway within the body [3-7]. There are many different types with the most common

being vascular and gastrointestinal stents. In order to implant metallic stents within the

body, it must be deployed by either a balloon expansion or it itself have self-expanding

properties. In both of these scenarios loading of the stent must occur.

A portion of the Wake Forest Innovations non-migrating biliary stent has been

modelled as a cantilever beam which contains a hinge. This portion has been modelled to

better understand the stresses, strains, displacements/angle in the hinge in order to

optimize its design and understand the overall hinge performance.

66

3. METHODS

Hinge Dimensioning and Parameter Variation:

A solid model of the hinge portion from the stent was modeled using Simulia’s

Abaqus/CAE version 6.14. The hinges modeled measure between 0.14 mm to 0.22 mm

with additional length both distally and proximally to allow for appropriate boundary

conditioning. In order to evaluate performance of the hinge, three parameters were

varied. The parameters varied were slot width, slot length, and side joint thickness (seen

highlighted in Figure 39). With two variations for each parameter, there exist a total of

eight possible cases (see Figure 40 for all hinges simulated). In each case the stiffness as

well as the stress contained in the hinge were monitored and reported for comparison.

Figure 40: Base hinge model with study parameters identified.

BLUE: slot width ; RED: slot length ; ORANGE: side joint thickness

67

0.1

0 0.2

25

0.0

3

0.0

6 0.1

9

0.0

5

0.0

6 0.1

9

0.0

3

AA

A

0.0

6 0.2

2

0.0

6 0.2

2

0.0

5

0.1

0 0.2

75

0.0

5

0.1

0

0.2

25

0.0

5

0.1

0 0.2

75

AA

B

AB

A

BB

B

BA

B

BB

A

BA

A

AB

B

0.0

3

0.0

3

Fig

ure

41

: D

imen

sio

ns

of

all

Hin

ge

Co

nd

itio

ns

(NO

TE

: A

ll d

imen

sion

s are

in

mm

an

d a

ll f

igu

res

are

not

to s

cale

)

68

For simplicity and labelling purposes, each hinge was given a three letter identity.

Each letter (“A” or “B”) corresponds to a value associated with a particular dimension.

The first letter denotes the slot width, the second, the slot length and the third and last, the

side joint thickness. For slot width, A indicated a 0.06 mm width while B designates a

0.10 mm dimension. Likewise with side joint thickness, the A dimension measures 0.03

mm and B indicates 0.05 mm. Due to symmetry and constraints of the hinge, the slot

length for the A and B state depend on the slot width. When the slot width is in the A

state, slot length is either 0.19 mm (A) or 0.225 mm (B). If the slot width is in the B state

then the slot length is 0.23 mm (A) or 0.275 mm (B). (The B state dimension for the slot

length is roughly 1.2 times that of the A state.) This identifying was performed such that

data and processing could be easily read and understood (See Table 6 & 7 and Figure 40

for clarification. As an example an “ABA Hinge” would have the following dimensions:

[A] Slot Width = 0.06 mm ; [B] Slot Length = 0.225 mm ; [A] Side Joint Thickness =

0.03 mm).

Table 7: Dimension of Slot Length and Side Joint Thickness when Slot Width is in “A” State (0.06mm)

Slot Width = 0.06 mm “A State” Dimension (mm) “B State” Dimension (mm)

Slot Length 0.19 0.225

Side Thickness 0.03 0.05

Table 8: Dimension of Slot Length and Side Joint Thickness when Slot Width is in “B” State (0.10mm)

Slot Width = 0.10 mm “A State” Dimension (mm) “B State” Dimension (mm)

Slot Length 0.23 0.275

Side Thickness 0.03 0.05

69

The hinge material resembles that of stainless steel 316 [8, 9]. An elasto-plastic material

model was used with the following parameters: Density = 8000 kg/m3 ; Young’s

Modulus = 193 GPa ; Poisson’s Ratio = 0.27 ; Yield Strength = 193 MPa ; See Table 8

and Figure 41 for parameters associated with plastic deformation.



193 0

193 0.003

316 0.0037

400 0.03

550 0.14

700 0.5

701 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1100

200

300

400

500

600

700

800

Str

ess (

MP

a)

Plastic Strain


Figure 42: Stent Material Model for Stainless Steel Grade 316: Stress vs. Plastic Strain

70

Simulation Set-Up: Constraints, Meshing, and Boundary Conditions/Loads:

The simulations performed used Abaqus/CAE version 6.14 and were implicit

(Abaqus/Standard) simulations. All of the hinges were meshed using Abaqus’ hexahedral

C3D8R type elements. This element type is an 8-node linear brick with reduced

integration and hourglass control. Partitioning was done such that the each hinges’

associated mesh was symmetric and did not contain any distorted elements.

In order to mimic a cantilever, a fixed boundary condition is applied to the end of

the hinge portion. This will not allow the nodes associated with this face to move (or

rotate) in any direction. Opposite the fixed end, a force is applied in the y-direction to

each node that is on the mid-transverse plane. This is the driving force behind the rotation

of the hinge about the Z-axis. This force was a 0.01 N force applied to each of the 19

nodes for 2 seconds. See Figure 43 for boundary conditions.

A

B

Figure 43: A, Partitioning of the AAA Hinge; B, Mesh associated with the AAA Hinge

71

The loading at the end maintains a force in the Y direction even as the hinge

rotates; this results in some tension to occur in the hinge. While this is what occurs during

actual deployment, an additional test was performed on the AAA hinge to compare a pure

moment about the origin to a force applied to the 19 described nodes. In this pure

moment scenario, a rigid cylinder was given a velocity in the Y direction (See Figure 44A

for setup). This would result in the contact force creating a moment about the origin

rotating the hinge about the Z axis with added tension. This was done by applying a 0.1

mm/s Y - velocity to the all of the nodes of the cylinder for 5 seconds.

Similar to this test, the AAA Hinge was also tested in lateral bending (bending not

in the designed hinge direction). This was done by a similar rigid cylinder movement

(See Figure 44B for setups), but was only simulated for 3 seconds as opposed to 5.

Figure 44: Figure depicting fixed end boundary condition and forces applied to nodes at opposite end

72

For all simulations, hinge stresses, strains, and deformation angle was reported.

From these monitored outputs, the angle at which the stent would failure was also

determined. After analyzing the full stent’s deployment, it was noted that the deployed

angle at the hinge was roughly 55 degrees. Because of this, the stress at 55 degrees was

reported for all hinge designs.

B

A

Figure 45: Additional Test Setups for AAA Hinge. A: Strictly Moment Test Setup ; B: Lateral

Bending Test Setup

73

A

B

C

Figure 46: BBB Hinge.

A: Isometric of BBB Hinge prior to deformation

B: Isometric of deformed BBB Hinge

C: Side View of deformed BBB Hinge

The AAA Hinge has the same dimensions as the hinge used in the full stent.

Comparisons were made between the the two methods of bending, force applied to the

end nodes (with some tension in the hinge) and the rigid cylinder moment creating only a

moment about the origin, to the actual generic stent deployment.

4. RESULTS

All of the hinges performed with primary bending occuring at the hinge (as

opposed to the fixed end).

74

0 20 40 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Mom

ent

(N*m

m)

Angle (degrees)

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 20 40 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Hinge Failure Angle

‘A State’ Slot Width (0.06 mm)

Side Joint Thickness

0.03 mm [A] 0.05 mm [B]

Slo

t L

ength

0.1

9 m

m [

A]

0.2

25 m

m [

B]

Figure 47: Moment vs. Angle for hinges with slot width in the ‘A’ state.

75

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Mom

ent

(N*m

m)

Angle (degrees)

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 20 40 60 800

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 20 40 600

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Hinge Failure Angle

‘B State’ Slot Width (0.10 mm)

Side Joint Thickness

0.03 mm [A] 0.05 mm [B]

Slo

t L

ength

0.2

3 m

m [

A]

0.2

75 m

m [

B]

Figure 48: Moment vs. Angle for hinges with slot width in the ‘B’ state.

76

Figure 49 and Table 10 show the initial stiffness associated with the hinge is

much greater than the stiffness associated with late deformation. In order to quantify the

stiffness of the hinge throughout the bending, linear models have been fit to the Moment

vs. Angle plots. The hinge has been approximated to have two different stiffnesses

corresponding to how the hinge is deforming: an initial stiffness and a post initial loading

stiffness. It, however, is worth noting that the initial stiffness is not the elastic stiffness as

the hinge yields in most instances after a deformation of roughly one degree. The

stiffnesses (slopes) of each portion were recorded for comparison.

0 10 20 30 40 50 600

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Mom

ent

(N*m

m)

Angle (degrees)

AAA Hinge: Moment vs. Angle

Hinge Failure Angle

Figure 49: Linear Stiffness Model for initial and secondary deformation

77

Table 10: Pertinent values corresponding to each hinge type (All dimensional units are in mm)

Slot Width 0.06 0.10

Slot Length 0.19 0.225 0.23 0.275

Side Thickness 0.03 0.05 0.03 0.05 0.03 0.05 0.03 0.05

Failure Angle

(Degrees) 41.9 43.0 60.1 55.7 63.7 52.6 78.6 64.5

Mises Stress at

55 degrees

(MPa)

613.0 607.1 580.7 587.7 572.5 592.5 557.9 565.4

Initial Stiffness

(N*mm/rad) 0.286 0.404 0.204 0.430 0.189 0.359 0.131 0.300

Deformed

Stiffness

(N*mm/rad)

0.012 0.025 0.009 0.015 0.008 0.012 0.005 0.014

The failure angel and stress values were normalized to 550 and 586 MPa respectively.

This is because the actual stent deploys to roughly 550 and the tensile strength of the SS

316 material replicated is 586 MPa [9, 10]. This will allow for comparison to the actual

deployment.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

AAA ABA AAB ABB BAA BBA BAB BBB

No

rmal

ize

d V

alu

e

Hinge Type

Failure Angle

Mises Stress at55 degrees

Figure 50: Normalized Failure Angle and Mises Stress for each hinge type

78

An additional test was performed on the AAA hinge (which possesses the same

dimensions as the hinge used in the generic stent). This was used to validate that the

loading each hinge experienced is justifiable and would correlate appropriately to how

the actual hinge would act during deployment.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

AAA ABA AAB ABB BAA BBA BAB BBB

Stif

fne

ss (

N*m

m /

rad

)

Hinge Type

Initial Stiffness

DeformedStiffness

Figure 51: Initial and Secondary Stiffness for each hinge type

A B

Figure 52: A, deformation cause by force at nodes. B, deformation cause by rigid

cylinder boundary conditioning

79

A

B

Figure 53: Simulation performed on AAA Hinge to analyze lateral bending

0 10 20 30 40 50 600

100

200

300

400

500

600

700

Str

ess (

MP

a)

Angle (degrees)

Generic Stent Hinge Angle vs. Time

AAA Hinge w/ Nodal Force

AAA w/ Cylinder Boundary Conditioning

Generic Stent Hinge

AAA Hinge in Lateral Bending

Figure 54: Mises Stress vs. Angle for Different Loading Mechanisms for the AAA Hinge

80

5. DISCUSSION

All of the hinges have different deflections associated with their bending. All,

however, have bending occurring at the hinge. A true cantilever beam under similar

loading conditions would result in bending occurring throughout the beam. In each

simulation, a vast majority of the bending occurs at the hinge location.

While each hinge allows for bending in the appropriate plane, the manner in

which their deformation occurs depends mainly on their parameter dimension. Variations

in the parameters ultimately cause resulting changes in the overall stiffness of the hinge.

Take the side joint thickness for example. In every case, an increased thickness (the B

A B

C

Figure 55: Deformation at 55 degrees: A: Hinge with nodal force applied; B: Hinge with rigid

cylinder moment application; C: Generic Stent with balloon expansion.

81

state versus the A state) is associated with increased rigidity. This allows us to conclude

that side thickness plays an important role in the stiffness attributed to the overall hinge.

Each hinge was attributed two linear approximated stiffnesses (Table 10 & Figure 49).

The initial stiffness, however, is not associated with the elastic deformation of the hinge

but extended into plastic deformation. Each hinge tends to eclipse their yield stress after

roughly one degree of rotation.

In addition to stiffnesses, stresses and failure angle were monitored. One of the

values recorded was the stress that occurs at 55o of rotation. 55

o was used because, after

evaluating the full stent, the hinge contained in the hook portion deforms to rough 55o

when fully deployed. This value reported indicated whether or not the hinge would fail

upon deployment under the full stents loading conditions. Likewise with failure angle,

this provides a benchmark for determining the maximum amount of rotation that can

occur prior to reaching the tensile strength. Figure 50 is a plot that can be used for

determining failure of the hinge. In this figure the failure angle and stress at 55o

are

normalized to 55o and 586 MPa respectively. This is because, as previously stated, the

deployed angle is 55o

and the tensile strength of annealed stainless steel 316 (the material

model used) is 586 MPa [9, 10]. When evaluating a hinge types (Figure 50), normalized

failure angle value above 1 (and/or a stress at 55o below 1) indicated that the hinge would

not fail if deployed in the full stent.

This study was designed to evaluate hinge dimensions and there effect of

performance. Just because one hinge fails does not mean that those dimensions will not

be used. Because these hinges are implemented within non-migrating stents stiffness is a

major factor. Increased stiffness has been shown to reduce migration [11]. In order to

82

maintain its position in the biliary duct, a hinge may require a certain stiffness. With

certain hinges while the material may not fail, the stent as a whole may fail and migrate

from its desired position. An additional alteration can be made in order to maintain

stiffness and possibly expunge material failure: change the material to a cobalt chromium

alloy. Co-Cr, although less common than stainless steel, is a relatively stiffer material and

also brings with it a higher tensile strength ranging from 951 – 1220 MPa [8]. This may

not only prevent material failure but also could help provide added stiffness which may

have an added benefit in helping with stent migration.

6. CONCLUSION

All of the hinges performed differently and some, given the prescribed loading

conditions, fail. Just because they fail, however, does not mean that the parameters

associated with the hinge are unusable. It is quite the contrary. Each hinge has its

advantages and disadvantages as does each stent. In general, a stent has different

dimensions associate with not only the application but also the person. This study

provides us with a broad spectrum of hinge designs such that we can select the

appropriate hinge or the appropriate dimensions to start from for the specific application

being targeted.

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7. ACKNOWLEDGEMENT




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8. REFERENCES

1. Beer, F., et al., eds. Mechanics of Materials. Sixth ed. 2012, McGraw-Hill.

2. Hibbeler, R.C., ed. Structural Analysis. Eighth ed. 2012, Pearson Presntice Hall:

Upper Saddle River.



Endoscopy, 2012. 44(3): p. 277-98.


Stents in the Gastrointestinal Tract, R. Kozarek, T. Baron, and H.-Y. Song, Editors.

2013, Springer: New York. p. 15-31.


1991. 54(3): p. 50-4.

6. Mueller, P.R., et al., Biliary stent endoprosthesis: analysis of complications in 113

patients. Radiology, 1985. 156(3): p. 637-9.

7. Burcharth, F., A new endoprosthesis for nonoperative intubation of the biliary

tract in malignant obstructive jaundice. Surg Gynecol Obstet, 1978. 146(1): p. 76-

8.





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10. Brunski, J., ed. Biomaterials Science an Introduction to Materials in Medicine. ed.

B. Ratner, et al. 2004, Elsevier Academic Press: San Diego.

11. Isayama, H., et al., Measurement of radial and axial forces of biliary self-

expandable metallic stents. Gastrointest Endosc, 2009. 70(1): p. 37-44.

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Chapter V: Summary of Research

The thesis presents research performed to alter the current concept of biliary

stents and reduce dysfunction due to migration. Through the implementation of additional

hook structures added to the overall stent, the following objectives were analyzed and

completed:

1. Finite element analysis of the stents deployment to monitor hook

displacement.

2. Compare different hook variations to see how versions might deploy

differently as well as interact with the surrounding tissue differently.

3. Compare different hook hinge designs in order to prevent failure as well as

understand dimensions to optimize hook stiffness.

This research will help limit dysfunction due to migration that occurs not only in

biliary stents but also in other areas as well. Because this design concept can cross over to

other stent applications this idea can help reduce migration in other locations within the

body. The stents designed and developed in this thesis (at the time of writing) do not have

intellectual property protection. Because of this, publication of this research will be held

until appropriate patents have been accepted and completed. In the future research from

Chapters II and III may be submitted for publication in the Journal of Medical Devices.

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Scholastic Vita

Jared D. Mitchell Graduate Student & Research Engineer Virginia Tech – Wake Forest University Center for Injury Biomechanics 575 N. Patterson Ave, Suite 120 Winston-Salem, NC 27101

Mobile: (516) 780-2606

Work: (336) 713-1263 [email protected]

EDUCATION Virginia Tech – Wake Forest University, Winston-Salem, NC May 2016 School of Biomedical Engineering & Sciences Master of Science, Biomedical Engineering Advisor: Dr. Philip J. Brown Washington and Lee University, Lexington, VA May 2014 Bachelor of Science in Physics-Engineering Advisor: Dr. Joel Kuehner EXPERIENCE VT – WFU Center for Injury Biomechanics 2014-Present Graduate Student & Researcher Analyze head impact exposure in the sport of lacrosse and how it relates to Traumatic

Brain Injury Monitor head accelerations using i1 Biometrics Vector mouthguards which are

equipped with an accelerometer and a gyroscope Wake Forest Innovations 2014-Present Medical Device Research Engineer Work alongside doctors, nurses, and physicians to develop innovative medical devices Design biomedical devices for production using SolidWorks 2015 Perform necessary Finite Element Analysis simulations using Abaqus CAE 6.14 Washington and Lee University Physics & Engineering Department 2012-2014 R.E. Lee Scholar: Research Assistant to Professor Joel Kuehner Improving Heat Transfer for a Heated Horizontal Cylinder Performed PIV (Particle Image Velocimetry) measurements of water flow around a

heated horizontal cylinder using LaVision’s DaVis Investigated flow in the boundary layer as it relates to heat transfer SKILLS

Abaqus Adobe Photoshop AutoCAD Autodesk Inventor Kinovea Labview Matlab Microsoft Office SolidWorks

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PROFESSIONAL CERTIFICATIONS & WORKSHOPS Abaqus/CAE: Import Geometry and Meshing (April 2015) Abaqus/CAE: Introduction to Abaqus/CAE (June 2015) LS-DYNA: Introduction to LS-DYNA (September 2015)

PUBLICATIONS

1. Kuehner J, Hamed A, Mitchell J, “Experimental Investigation of the Free Convection Velocity Boundary Layer and Plume Formation Region for a Heated Horizontal Cylinder”, 10/22/2014, International Journal of Heat and Mass Transfer (journal article)

2. Mitchell J, Brown P, Olympio M. “Design Behind Improving Efficiency in Endotracheal Tube Changes”, Tampa, FL, Biomedical Engineering Society Annual Meeting, October 2015 (poster)

3. Brown P, Gillispie G, Mitchell J, West J, Stitzel J, Hsu W. “Biomechanical Analysis of Coaxial and Cortical Trajectory Pedicle Screws in Lumbar Spine Fusion Constructs”, Tampa, FL, Biomedical Engineering Society Annual Meeting, October 2015 (poster)

4. Brown P, Gillispie G, Mitchell J, West J, Stitzel J, Hsu W. “Hybrid Fusion Technique of Standard Pedicle and Cortical Bone Screws in Lumbar Spine Fusion” Orlando, FL, Orthopedic Research Society Annual Meeting, March 2016 (poster)

Documents

Finite Element Analysis of a Novel Design for a Non