Contact Mechanics and Failure Modes of Compliant Polymeric Bearing Materials

For Knee Cartilage Replacement

A Thesis

Submitted to the Faculty

Of

Drexel University

By

Mariya Shabbir Tohfafarosh

in partial fulfillment of the

requirements for the degree

Of

Doctor of Philosophy

September 2016

© Copyright 2017

Mariya Shabbir Tohfafarosh. All Rights Reserved.

ii

And, when you want something, all the universe conspires in helping you to achieve it.

- Paulo Coelho, The Alchemist

iii Acknowledgements

It takes a whole village to cultivate a Ph.D.

I want to thank my advisor and mentor, Dr. Steven Kurtz, who placed faith in my abilities and provided valuable insights into my journey of exploring the convoluted world of finite element modeling and material failure analysis.

I am grateful to my committee members, Dr. Sriram Balasubramariam, Dr. Michele

Marcolongo, Dr. Margaret Wheatley, Dr. Judd Day and Dr. Rahmim Seliktar, for asking critical questions, providing constructive criticism and giving direction to improve this work.

I also appreciate Dr. Doruk Baykal for being a great mentor, and for teaching me how to be a good researcher over friendly banters.

Thanks to Ryan Siskey for his wisdom and accommodating my testing needs, and Dr.

Jonathan Kiel for an insightful discussion about the fascinating world of polymer science.

Thank you, Dr. Kevin Mansmann, for financially supporting my work and for giving me first-hand experience of the intricacy of human-centric product design.

This work would not have been possible without the never-ending discussions, constant support, and encouragement from my friends and fellow Implant Research Center members – Daniel MacDonald, Josa Hanzlik, Sai Veruva, Sevi Kocagoz, James Peters,

Genymphas Higgs and Christina Arnholt – you guys and gals made this journey bearable and memorable!

Last but not the least, this expedition would not have been possible without the endless love and emotional support of my parents, my brother, my sister-in-law and my niece. iv Special thanks to my love, Mohammed, for helping me retain my sanity and reminding me to laugh during this interesting life-experiment of “pursuing a doctorate.” v

Table of Contents LIST OF TABLES ...... IX

LIST OF FIGURES ...... X

ABSTRACT ...... XIII

CHAPTER 1 : INTRODUCTION ...... 1

HUMAN KNEE AND ARTICULAR CARTILAGE ...... 1

OSTEOARTHRITIS ...... 2

CURRENT TREATMENTS ...... 3

Total Knee Arthroplasty ...... 3

Partial Knee Replacement ...... 4

CURRENT ARTHROPLASTY MATERIALS ...... 5

COMPLIANT ARTHROPLASTY MATERIAL CANDIDATES ...... 6

Polyurethane/Polycarbonate Urethane ...... 7

Hydrogels...... 10

CHALLENGES IN DEVELOPMENT OF SYNTHETIC CARTILAGE IMPLANT ...... 13

KNEE BIOMECHANICS ...... 14

RESEARCH OVERVIEW ...... 16

SPECIFIC AIMS...... 17

CHAPTER 2 : LITERATURE REVIEW – KNEE IMPLANT DESIGN PARAMETERS AND ARTHROPLASTY MATERIAL FAILURE THEORIES ...... 20

INTRODUCTION ...... 20

CURRENT IMPLANT DESIGNS ...... 22 vi COMPLIANT BEARING MATERIAL IMPLANT DESIGN ...... 24

COMPLIANT MATERIAL FAILURE CRITERIA AND MODES ...... 35

RESEARCH GAP AND GOAL OF THESIS ...... 40

CHAPTER 3 : EFFECT OF RADIATION STERILIZATION ON CHEMICAL, MECHANICAL AND TRIBOLOGICAL PROPERTIES OF A NOVEL HYDROGEL.42

ABSTRACT ...... 42

INTRODUCTION ...... 42

MATERIALS & METHOD ...... 45

Swell Ratio Evaluation ...... 45

Mechanical Testing...... 46

Finite Element Analysis ...... 46

Chemical Evaluation ...... 49

Wear Testing ...... 49

RESULTS ...... 51

Material Model Verification ...... 51

Chemical Evaluation ...... 53

Tribological Properties ...... 54

DISCUSSION ...... 57

CONCLUSION ...... 59

CHAPTER 4 : EFFECT OF CONFORMITY, THICKNESS AND MATERIAL PROPERTIES ON THE CONTACT MECHANICS OF COMPLIANT POLYMERIC MATERIALS FOR USE IN KNEE ARTHROPLASTY ...... 61

ABSTRACT ...... 61

INTRODUCTION ...... 62 vii MATERIALS & METHOD ...... 66

Mechanical Testing...... 66

Model Construction and Validation ...... 67

Parametric Modeling ...... 69

RESULTS ...... 70

Mechanical Testing...... 70

Model Validation ...... 71

Parametric Evaluation ...... 72

DISCUSSION ...... 84

CONCLUSION ...... 87

ACKNOWLEDGEMENT ...... 88

CHAPTER 5 : MECHANICAL FAILURE MODALITY OF COMPLIANT ARTHROPLASTY MATERIALS UNDER PHYSIOLOGICALLY RELEVANT LOADING CONDITIONS ...... 89

ABSTRACT ...... 89

INTRODUCTION ...... 90

MATERIALS & METHOD ...... 92

Uniaxial Tensile Test to Failure ...... 93

Unconfined Compression Test ...... 93

Plane Strain Compression Test ...... 94

RESULTS ...... 98

Uniaxial Tensile Test to Failure ...... 98

Unconfined Compression Test to Failure ...... 100

Plane Strain Compression Test ...... 103 viii DISCUSSION ...... 106

CONCLUSION ...... 113

CHAPTER 6 : CONCLUSION AND FUTURE WORK ...... 115

CONCLUSIONS ...... 115

FUTURE WORK ...... 118

LIST OF REFERENCES ...... 120

APPENDIX 1: FEBIO PARAMETER OPTIMIZATION ...... 141

APPENDIX 2: DETERMINATION OF HYDROGEL CRYSTALLINITY ...... 144

APPENDIX 3: MATLAB SCRIPT FOR EVALUATING YOUNG’S MODULUS FROM THE TENSILE DATA AT 0-10% STRAIN ...... 147

APPENDIX 4: MATLAB SCRIPT FOR EVALUATING DIFFERENT FAILURE CRITERIA ...... 150

VITA ...... 151

ix List of Tables

Table 3-1: Swelling and equilibrium mechanical properties (Mean ± SD) of unsterilized, electron beam and gamma sterilized hydrogel samples...... 53

Table 4-1: Summary of the average mechanical properties of different formulations of hydrogel and polycarbonate urethane under uniaxial tension...... 71

Table 4-2: Simulated stresses, strain and contact area results for a combination of implant design parameters under normal walking load (2400N)...... 76

Table 4-3: Simulated stresses, strain and contact area results for a combination of implant design parameters under stair climbing load (5200N)...... 77

Table 4-4: The correlations between an increase in implant conformity as well as thickness and the stresses, strain and contact area under different loading conditions...... 80

Table 5-1: Experimentally determined tensile and compression properties of hydrogel and polycarbonate urethane formulations, along with the articular cartilage mechanical properties from the literature...... 103

Table 5-2: Failure criteria of hydrogel and polycarbonate urethane formulations at two different strain rates calculated at their corresponding compressive yield point. ... 105

x List of Figures

Figure 1-1: Six - Degrees of Motion of a Normal Knee Joint...... 14

Figure 3-1: Curve fitting of unconfined compression reaction load (N) vs. time (s) behavior of hydrogel at 10% strain and during stress-relaxation. The experimental and model data curves overlapped almost exactly with R2 = 0.9993 ± 0.0004 for all formulations...... 48

Figure 3-2: Experimental and simulated (E = 0.146 MPa; v = 0.10; and k = 3.8 x 10-14 m4/N.s) strain curves for the confined creep of cartilage...... 52

Figure 3-3: ATR-FTIR spectra (900 – 1200cm-1 range) for control, electron beam (Ebeam) and gamma sterilized hydrogel samples for low, medium and high water content formulations...... 54

Figure 3-4: Optical microscope images (x30) of control (C), electron beam (E), and gamma (G) sterilized hydrogel samples at 0MC, 2MC in bovine serum and 2MC in distilled water...... 55

Figure 3-5: A bar plot with the y-axis representing the total volumetric loss (mm3) and wear rate (mm3/MC) for all wear tested unsterilized and sterilized hydrogel specimens after 2 million cycles in each lubricant...... 56

Figure 4-1: A three-dimensional, axisymmetric medial knee model was created in SolidWorks using the radii of curvature from the literature [178], followed by meshing in Abaqus. The material properties, as well as boundary, contact and loading conditions, were assigned in FEBio...... 68

Figure 4-2: Medial knee FEM validation using the medial contact area (mm2) and average medial contact stress (MPa) of the knee joint (without menisci) under different axial loads as reported by Fukubayashi et al. and Kurosawa et al. [182]. The error bar represents one standard deviation of the reported cadaveric study results. 72

Figure 4-3: Visual representation of maximum principal stress (MPa) and maximum contact area (mm2) (top) and Von Mises stress (MPa) (bottom) for HG48 hydrogel formulation at varying implant thickness and conformity under normal walking load...... 73 xi Figure 4-4: Effect of conformity on the Von Mises and maximum shear stress of a 3mm thick Bionate I implant under normal walking and stair climbing loads...... 75

Figure 4-5: Medial knee finite element model prediction of maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and maximum contact area for different formulations of hydrogel and polycarbonate urethane under normal walking and stair climbing loads. The error bars represent the range of each parameter for a given material at various implant conformity and thickness...... 79

Figure 4-6: The percent effect size of the implant design factors (main and 2-way interactions) on various contact mechanics outputs...... 82

Figure 4-7: Plots of implant conformity vs. thickness vs. different contact mechanic parameters under normal walking load to evaluate the optimal design space for compliant bearing materials...... 83

Figure 5-1: Stress-strain curve of the HG53 hydrogel formulation at material yield. The downward shift of the loading part of the curve, between two consecutive cycles, suggests that lower load is supported at the same strain level, which is attributed to plastic deformation in the material...... 95

Figure 5-2: Plane strain compression test fixture with a hydrogel sample used in this study...... 95

Figure 5-3: Finite element simulation of the plane strain compression test using FEBio. (Left to right) Undeformed state of specimen undergoes 50% compression to give the reaction force and displacement outputs, which was utilized for curve-fitting the experimental results...... 97

Figure 5-4: True stress-strain curve of different formulations of polycarbonate urethane Bionate (left) and hydrogel (right) subjected to a uniaxial tensile test at the crosshead speed of 30mm/min...... 99

Figure 5-5: Average Young’s modulus (MPa), Poisson’s ratio, ultimate stress (MPa) and elongation (mm/mm) for different formulations of hydrogel and polycarbonate urethane, tensile tested at various crosshead speeds. The gray region represents the mechanical properties range for articular cartilage [174, 193, 202, 203]...... 102 xii Figure 5-6: (a) Compression force vs. displacement response of different formulations of hydrogel and polycarbonate urethane at 50% compression. Experimental and model predicted force responses of (b) polycarbonate urethane Bionate II and (c) HG43 hydrogel formulation were overlaid to demonstrate repeatability and predictability...... 104

Figure 5-7: Comparison between predicted knee finite element model (FEM) response for normal walking and stair climbing loads from the previous chapter, and the predicted plane strain compression (PSC) response at a strain rate of 10% /s (represents walk) and 100%/s (represents climb)...... 110

Figure 7-1: DSC thermal plots of hydrogel formulations HG43, HG48 and HG53...... 145

xiii Abstract

Contact Mechanics and Failure Modes of Compliant Polymeric Bearing Materials For Knee Cartilage Replacement Mariya Shabbir Tohfafarosh Steven M. Kurtz, Ph. D.

Osteoarthritis (OA) is the most common cause of disability affecting millions of people worldwide. Total knee replacement is the current state-of-the-art treatment to alleviate pain and improve mobility among patients in the late stage of knee OA. The current gold standard materials for total knee arthroplasty are cobalt-chromium and ultra- high molecular weight polyethylene (UHMWPE). However, wear debris and implant loosening-related revision persists; consequently, total knee replacements are not universally recommended for all patient subgroups with OA. This work explores the potential of using compliant polymeric materials in knee cartilage replacement devices, which are closer in lubrication and mechanical properties of articular cartilage, to prevent excessive removal of underlying bone and prolong the need for a total knee replacement.

Two materials investigated in this thesis are polycarbonate urethane, Bionate 80A, and a novel hydrogel, Cyborgel, both of which have shown promising wear and lubrication properties under physiological loads. Polycarbonate urethane has been previously tested for the effects of gamma sterilization and has shown no significant changes in its mechanical strength or chemical bonds. Since an important aspect of medical device development is the sterilization process, this thesis first evaluated the effect of 30-35 kGy electron beam and gamma radiation on the polymer swell ratio, and the mechanical, chemical and tribological behavior of the novel hydrogel. Three different xiv formulations were mechanically tested, and biphasic material properties were identified

using finite element analysis. Fourier transform infrared spectroscopy was used to

investigate chemical changes, while the wear properties were tested for 2 million cycles in bovine serum. The results showed no significant difference (p > 0.05) in the swell ratio, mechanical and tribological properties of the electron beam and gamma sterilized hydrogel sample as compared to the control samples. However, chemical spectra of electron beam sterilized samples revealed minor changes, which were absent in unsterilized and gamma sterilized samples.

Upon successful sterilization evaluation, both polycarbonate urethane and the novel hydrogel were investigated for the contact mechanics of compliant-on-compliant artificial knee bearings using a finite element analysis approach. A simplified, axisymmetric, finite element model of a medial knee compartment was developed and validated, and a design of simulation experiments was carried out to evaluate the effect of implant conformity, implant thickness and material properties on the contact mechanics of compliant knee bearings under normal walking and stair climbing loads. All input parameters, namely, implant conformity, implant thickness and material properties, significantly (p<0.001) affected the maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and contact area. The knee implant contact mechanics demonstrated sensitivity to all the three design factors, and a correlation between resulting stresses and implant conformity as well as thickness was observed. However, the conformity had the highest effect-size on the contact mechanics. The maximum principal stress value halves and the contact area doubles when ≥ 95% implant conformity (i.e. the ratio of femoral to tibial surface’s radii xv of curvature) and ≥ 3mm thickness was used, hence, these parameters were recommended for the design of compliant knee bearings.

Finally, a battery of mechanical tests was carried out to evaluate the failure criteria of the proposed compliant polymers under physiological loads and strain rates.

Uniaxial tests, including tension and unconfined compression, and biaxial tests, such as plane strain compression, were carried out to characterize the mechanical behavior of different material formulations at physiologically relevant testing rates. The materials failed under tension between 250 – 750% true strain, while those under uniaxial and biaxial compression test sustained compression of 50 - 70% engineering strain (39 - 53% true strain) without any signs of cracking or fracture. The tension was determined to be the primary failure mode for the proposed materials, and the tensile test was used to define the failure criteria of the materials. The unconfined compression tests were used to define the yield stresses and strains under compression, which is the main mode of loading for the knee joint. The results of the plane strain compression were modeled using a finite element model and the maximum principal stress, von Mises stress, maximum shear stress, and maximum principal strain failure criteria were predicted at the corresponding yield strain of each material formulation. Upon comparing the knee model contact stress and strain prediction under normal walking and stair climbing loads with those of the empirical failure criteria at yield, the polycarbonate urethane showed better overall potential for use in compliant knee implants, while the hydrogels exhibited higher potential for delamination or fracture, especially if appropriate implant conformity and thickness are not employed. The outcome of this study and the previous parametric model xvi results helped to determine a niche design space within which designing a knee implant with compliant bearing materials may be feasible.

In summary, the potential of compliant bearing materials was thoroughly examined in this thesis, and the results provided a foundation for future testing and development of a compliant cartilage replacement implant. Such an implant would be a promising improvement and alternative to conventional total knee replacements.

1

Chapter 1 : Introduction

Human Knee and Articular Cartilage

The knee is the largest and one of the most complex synovial joints in the human

body. The basic structure and function of the knee joint includes: i) femur, tibia and

patella bones, which withstand compressive loads on the joint; ii) articulating femoral,

tibial and patellar cartilage, and crescent-shaped menisci, which help in joint load

distribution; and, iii) anterior cruciate, posterior cruciate, medial collateral and lateral

collateral ligaments, which act as passive elastic structures and can be loaded only under

tension [1, 2]. Articular cartilage performs as a load-bearing soft tissue in most of the synovial joints in the human body. The ability of cartilage to withstand high loads and repetitive physical stresses is due to its extracellular composition, which is made of 80% water, with the 20% solid matrix consisting of about 5% chondrocytes, 60% collagen,

30% proteoglycans and 5-10% proteins and ions [3-5]. Collagen fibers, which align

parallel in the superficial zone, random in the middle zone and perpendicular close to the

subchondral bone, are mainly responsible for supporting the matrix under tensile load [3,

6, 7]. Proteoglycans are responsible for supporting the tissue under compression by trapping water molecules in their matrix, thus, acting as a cushion [8]. In the presence of

synovial fluid, cartilage provides a lubricating surface and distributes the load uniformly

to prevent a high-stress concentration in the joint [9]. However, due to the avascular

nature of the cartilage, the chondrocytes embedded in the matrix do not get nutrients

efficiently. Consequently, the self-repair response is much slower compared with other

tissues in the body [10, 11]; sometimes resulting in excessive wear that can cause 2 osteoarthritis [7].

Osteoarthritis

Osteoarthritis (OA) is a degenerative joint disorder, which is one of the leading causes of pain and locomotor disability affecting over 100 million people worldwide [12,

13]. The pathological characteristics of OA are either loss of cartilage due to old age or

traumatic injury with associated underlying bony changes, such as subchondral bone

collapse or osteophyte formation. These changes initiate a focal lesion that progressively

extends across the articulating surface, partially or entirely degrading the joint [7, 14].

More than 20 million people in the US suffer from knee osteoarthritis. It is

estimated that by 2030, 20% of Americans (about 70 million people) greater than 65

years of age are at a risk of osteoarthritis. More than 650,000 total knee replacements

were carried out in the USA in 2008, more than 77,500 were performed in the UK in

2009, and 103,601 were executed in South Korea between 2002 and 2005 [15], and these

numbers are estimated to grow 673% by 2030 [16]. According to a report based on the

Center for Disease Control 1997-2003 data, the total healthcare and lost wages cost to the

US economy due to osteoarthritis, and rheumatic conditions (an autoimmune disease

affecting joints) in 2003 was $128 billion, which is about 1.2% of 2003 gross national

product [17]. About 6.6 million cases of knee injury were reported by the emergency department in the US between 1999 through 2008 [18], with the highest injury rate in

men reported between 15 and 24 years. Knee injuries are the most common cause of

cartilage damage among young athletes. Sports-related traumatic injuries usually occur

due to sudden impact loading during strenuous activities, while the less severe repetitive 3 injuries cause the joint to degrade over time, resulting in osteoarthritic symptoms at a

young age [19]. The overall burden of OA is increasing with an aging global population

and sports-related injuries as well as automobile accidents and the obesity epidemic [20].

Hence, effective treatment for osteoarthritis is a highly investigated topic in the scientific

and clinical communities.

Current Treatments

The current methods for treating osteoarthritis can be either non-invasive or

invasive. The non-invasive approach includes oral or topical analgesics, partial

offloading by bracing, anti-inflammatory drugs, steroids or hyaluronic acid injections and

physical therapy [14]. The invasive method includes restorative treatments, such as osteochondral plugs and partial or total joint replacement [14]. Although the conservative

treatments may temporarily relieve pain and improve joint functionality, the long-term

effectiveness of treatments such as massage, traction, and stretching is not very

promising. On the other hand, restorative treatment options such as microfracture,

autologous chondrocyte implantation (ACI), osteochondral autograft/allograft transfer

(OAT), and mosaicplasty are also available; however, these treatments do not necessarily

restore full activity or prevent further deterioration of the joint [21].

Total Knee Arthroplasty

End-stage osteoarthritis has been treated with either partial or total knee arthroplasty (TKA) since the 1970s. Partial knees will be discussed in the next section;

TKA is a surgical procedure in which the bearing surface of the femoral and/or the tibial bones are replaced at the knee with artificial implants composed of metal and/or polymer.

The known advantage of TKA is pain relief and overall functional improvement of the 4 joint. However, there are associated surgery-related risks and implant-related complications, including patient dissatisfaction, excessive bone loss, and material

incompatibility in the body.

An important clinical factor that has a major impact on the overall success of a

TKA is patient satisfaction, which reflects not only overall pain reduction but also an

improvement in their quality of life. Despite possessing an artificial knee, many patients

expect a level of functionality allowing them to participate in a wide range of recreational

activities such as dancing and golfing, and therefore, are disappointed with the inability

to achieve full range of motion after a joint replacement surgery [22]. Mahomed et al.

reported that 40% of TKA patients expected no limitations to their usual activities, and

76% expected no pain after surgery. However, despite improved implant designs and

surgical techniques, studies have indicated that only 82% to 89% of patients were

satisfied with their primary total knee arthroplasty [23]. Despite its success, this

procedure may not be ideal for younger, active patients, who will be at a risk of one or

more revision surgeries during their lifetime.

Partial Knee Replacement

One alternative to traditional total knee replacements is a unicompartmental or

partial knee replacement, especially recommended for younger patients with a limited

extent of end-stage osteoarthritis to achieve a quick recovery and maintain an active

lifestyle [24, 25]. Unicompartmental knee arthroplasty (UKA) was first introduced by

Marmor in 1973 and was used to resurface a single compartment of the knee [26]. UKA is

indicated for the younger, more active patients involved in sports, who have their OA

limited to a single condyle of the knee. UKA reduces the amount of bone resection, 5 reduces pain, quickens recovery postoperatively, and allows more treatment options in future, in case full replacement or other treatments are required [27]. Studies have shown

an implant survival rate of 84% to 98% at 10-12 years post-UKA [28]. A study reported that upon comparing UKA to TKA in patients possessing both the devices, 75% of the patients felt the UKA was “closer to a normal knee” than their contralateral TKA. UKA patients also reported a better range of motion and ambulatory function as well as better pain control after surgery as compared to TKA patients [29]. Overall, a single

compartment knee arthroplasty has shown promising results over TKA and is increasingly preferred by surgeons.

Current Arthroplasty Materials

Currently, the most commonly used joint arthroplasty materials include

components fabricated from metallic alloys, ceramics, and ultra-high molecular weight

polyethylene (UHMWPE) [30]. Total knee replacement implants have up to three

components containing metallic alloys, including the femoral component, the tibial

baseplate, and, in certain metal-backed designs, the patellar component. These metal components allow for the potential of corrosion or metal ion release in the body [31]. The

prevalence of metal sensitivity among the general population is approximately 10% to

15%, with an average sensitivity to nickel is 13.1%, and that to cobalt and chromium is about 3% [32]. The metal ions released from the metallic orthopedic implants may cause

local and systemic adverse effects, aseptic loosening and hypersensitivity reactions [33-

35]. Therefore, there is a motivation to seek alternatives to metal implant components.

In the 1960s, Sir John Charnley introduced UHMWPE for use in the bearing

couple opposing the metallic femoral head in total hip replacement surgery. To date, 6 UHMWPE is widely used as a joint replacement candidate with several advances made to

improve its material properties and implant design. However, UHMWPE may oxidize in

vivo, and its wear debris has historically contributed to implant loosening and osteolysis.

UHMWPE implants have shown a revision rate of 1% per year for the first ten years [30].

Therefore, to address these limitations, alternative compliant biomaterials have been

introduced in the field of joint arthroplasty.

Compliant Arthroplasty Material Candidates

Compliant biomaterials, such as hydrogels and polycarbonate urethanes, have been investigated as candidates for synthetic cartilage implants. The intended use of

compliant bearing materials is to replace the worn cartilage without excessive bone

resection, a common outcome in partial and total joint arthroplasty. However, the limiting

parameter for such application is the mechanical strength of the compliant bearing

materials, and their ability to withstand several times a patient’s body weight during daily

activities, including walking, running, squatting, and stair climbing. However, this

limitation may be offset by their compliance and superior lubrication mechanics

compared to higher modulus, semi-crystalline polymers such as UHMWPE and polyether

ether ketone (PEEK). UHMWPE and other semi-crystalline polymers, such as PEEK, exhibit mixed or boundary lubrication modes in the joint, which means the lubrication film between the two bearing surfaces gets too thin to separate the opposing surfaces

under load, resulting in direct contact and implant wear [36]. On the contrary, the fluid

film formation of artificial articular cartilage is dominated by elastohydrodynamic

lubrication (EHL) and micro-EHL mechanisms, in which the fluid film thickness

approaches the order of material asperity height, resulting in elastic deformation of the 7 surfaces [37]. When hydrogel with high water content is used as a synthetic articular

cartilage, a biphasic lubrication mechanism may be achieved, which may allow the

interstitial fluid pressurization to support a significant fraction of the contact load [3].

Therefore, the advantage of using compliant materials is that they could, at least in

theory, potentially mimic the theoretical lubrication mechanism of a natural synovial joint

with extremely low friction and minimal wear [38], provided of course, that the materials

are sufficiently durable for this application. This dissertation is focused on two such

potential compliant arthroplasty material candidates, namely polycarbonate urethane

(PCU) and hydrogels.

Polyurethane/Polycarbonate Urethane

Polyurethanes make up a family of polymers that have been widely used for biomedical applications. Due to its diverse range of mechanical and biological properties, such as biocompatibility, toughness, durability, flexibility, and biostability, many different polyurethane formulations are used in implantable medical devices, such as artificial heart systems, catheters, mammary implants, semi-occlusive dressings and drug delivery systems [39]. The first use of polyurethane foam in orthopedics for healing bone

was found in the 1960s [40]. Several generations of polyurethanes have since been

designed to improve the properties for long-term implantation. In the past decade,

polycarbonate urethane (PCU) was developed by removing the susceptible ester and ether

linkages in the soft segment of the polyurethane, specifically to prevent cracking and

degradation in vivo. DSM Biomedical (Berkeley, CA) commercially produces PCU

under the trade name of Bionate®. PCU is resistant to hydrolytic and oxidative

degradation, metal ion oxidation, environmental stress cracking, and mineralization [41]. 8 Additionally, PCU has exhibited encouraging mechanical properties with tensile modulus similar to cartilage [42], and compressive modulus of 20MPa, which is comparable to 5-

19MPa instantaneous compressive modulus range of the native tissue [43]. PCU Bionate

80A formulation has shown excellent resistance to 25kGy gamma radiation with no significant changes to its mechanical strength or chemical bonds [44]. Although the study found 9% reduction in the ultimate strength of Bionate 80A after five years of aging, the material demonstrated higher oxidative stability as compared to UHMWPE. Overall,

PCU has shown potential for use as an alternative compliant bearing material. Some state-of-art clinical and animal implants have been developed from polyurethane carbonate as discussed below.

TriboFit® Acetabular Buffer Hip System

The TriboFit® Acetabular Buffer (Active Implants Corporation, Netanya, Israel) is developed using polycarbonate urethane (Bionate 80A) to function as the natural hip on the acetabular side of the hip joint. In this hip system, the PCU acetabular buffer articulates with a CoCr alloy femoral head. The acetabular implant is only 3mm thick, which enables the use of larger head sizes, thereby, reducing dislocation risk. This implant received the European CE mark in 2006, and since then it has been commercialized in selected markets [45]. A comparison wear study was conducted between conventional UHMWPE, cross-linked UHMWPE (50kGy irradiated) and PCU acetabular buffers of similar geometry against cobalt alloy femoral components for 5 million cycles (MC), and the researchers found an average material loss of 19.1mm3/MC for PCU; 25mm3/MC for cross-linked UHMWPE; and ~100mm3/MC for conventional

UHMWPE [46]. Therefore, PCU has shown about 24% reduced wear as compared to the 9 cross-linked UHMWPE. Another study for 20MC found a low volumetric wear rate of

5.8 – 7.7 mm3/MC and a low particle generation rate of 2 - 3 x 106 particles/MC,

compared to UHMWPE wear rate of 25 x 1012 particles/MC [47, 48]. The authors

attributed the lower wear rate of the PCU acetabular buffer to the full fluid-film

lubrication mechanism [49, 50].

NUsurface Meniscus Implant

Another polycarbonate urethane implant developed by Active Implants (Netanya,

Israel) is the NUsurface meniscus implant. This meniscus replacement is designed as a

structural composite from polycarbonate urethane (Bionate 80A) reinforced

circumferentially with UHMWPE fibers. It is intended for use as an interposition joint implant and is developed to articulate against the existing cartilaginous surface of both the femur and the tibial condyle. Since this implant is designed to be free-floating and can

be slid between the femoral and tibial cartilage, it does not require bone anchoring.

Consequently, it keeps the bones and ligaments intact and provides more options for joint

surgery in future. NuSurface is in clinical use since it received the European CE mark in

2008 [51]. Similar to its hip counterpart, the meniscus implant has been investigated for

mechanical properties, stability, uniform pressure distribution, creep and wear properties

under physiological conditions. Under dynamic implant wear test of 5MC, under ISO

14243 gait loading conditions, the average wear rate reported for this meniscal implant

was 14.5mg/MC [52]. Additionally, the ability of polycarbonate urethane to resist creep is

expected to preserve the conformity of the articulating surfaces [53]. Thus, the NuSurface

implant has shown promising results in vitro, and it is currently under a multi-centered, 10 randomized, interventional, superiority clinical study in the US to verify its effectiveness

[54].

SynACART Joint Resurfacing

Polycarbonate urethane has also been developed in the form of a bilayer cylindrical plug to surgically treat osteochondral defects in the knee joint of veterinary patients, under the tradename of SynACART (Arthrex Medical, Columbia City, IN). A recent pre-clinical study investigated the use of cylindrical PCU plugs, with porous titanium substrate, to treat osteochondral defects in dogs [55]. The PCU – titanium composite demonstrated successful cellular ingrowth in the porous matrix and no damage on the PCU surface after three months of implantation in vivo. The study showed promising results for clinical application of focal cartilage defects in the femoral condyle [55].

In summary, polycarbonate urethane has been successfully used as a bearing material in the development of orthopedic implants ranging from an osteochondral plug to a meniscal cushion bearing for the knee joint. Based on its material properties and success in vitro and in vivo, it is considered a promising candidate for use in total joint arthroplasty.

Hydrogels

Another family of compliant alternative bearing material includes hydrogels, which were first discovered for biological use by Wichterle and Lim in 1960 [56].

Hydrogels are hydrophilic polymer networks that swell in water and can be tailored to attain desired mechanical properties for a range of biomedical applications, such as contact lenses, drug delivery devices as well as a scaffold for tissue engineering. Due to 11 their ability to store water and to mimic certain cartilage-like mechanical and lubricating properties [57], hydrogels are an attractive candidate for several applications in orthopedics from treating focal lesions to load-bearing applications [58-60]. Hydrogels

have been studied for cell scaffolding and joint resurfacing applications due to their

ability to be delivered arthroscopically, and potentially delay total joint replacement [61].

Some of the recently investigated hydrogels and their intended applications are as

follows: alginate-polyacrylamide is developed to attain extremely high stiffness [62];

poly(vinyl alcohol) hydrogel is used in the treatment of the hip joint disorders [58], and

poly(vinyl alcohol)-acrylamide hydrogels are investigated as a potential synthetic

articular cartilage [63]. Other hydrogels studied for similar bio-applications are poly(2-

acrylomido-2-methylpropanesulfonic) (PAMPS) and double network hydrogels [64],

poly-(2-Acrylamido-2-methylpropane sulfonic acid)/poly-(N,N'-dimethyl acrylamide)

(PAMPS/PDMAAm) double-network (DN) hydrogel [65], poly (acrylic acid) (PAA) and

poly (2-hydroxyethyl methacrylate) (p(HEMA). Hydrogels have shown not only suitable

mechanical strength for orthopedic bearing applications but also promising tribological

properties, due to their lubricious nature and inherently low coefficient of friction. For

example, P (2-hydroxyethyl methacrylate) (p(HEMA)) hydrogel exhibited a coefficient

of friction between 0.01 - 0.06 for different formulations [66]. Overall, hydrogels have shown potential to be considered an alternative compliant bearing material candidate.

A number of hydrogels are commercially available for treating osteochondral

defects. CARTIPATCH (Tissue Bank of France, Lyon, France) is an autologous

chondrocyte implantation product made of an agarose-alginate hydrogel matrix, indicated

for the treatment of isolated osteocartilaginous lesions [67]. Puramatrix™ (3DM Inc., 12 Cambridge, MA) is a self-assembling hydrogel made of 16 peptides for use as an injectable, flowable bone and cartilage regeneration scaffold [68, 69]. CaReS® (Arthro

Kinetics Biotechnology, Krems, Austria), is a patented collagen type I matrix which is implanted for the treatment of a full localized small cartilage defects of up to 8cm2 [70].

Several other hydrogels investigated for treating articular cartilage defects are reviewed by Spiller et al. [57].

SaluCartilage is the current state-of-the-art synthetic cartilage implant developed by SaluMedica LLC (Smyrna, GA), which received a CE mark in 2002 for commercialization in Europe. SaluCartilage is a made of poly (vinyl alcohol) (PVA) cryogel, which is manufactured by repeated freeze-thaw cycles to increases the polymer entanglement, thus improving the mechanical strength [71]. PVA hydrogel is intended and clinically evaluated for the treatment of focal cartilage defects in the knee joint [72].

SaluCartilage, SaluMedica LLC (now marketed as Cartiva, Cartiva Inc., Alpharetta, GA), was retrospectively evaluated for 5 to 8 years long implantation of PVA hydrogel plugs for the treatment of knee chondral focal defects [61]. The study concluded that patients responded well after the first 4-5 years of the implanted with PVA hydrogel plugs. At present, Cartiva is a press-fit implant intended to treat osteoarthritis of the metatarsophalangeal joint, which is a common site for trauma, repetitive microtrauma, severe bunion deformities and recurrent hallux deformity after surgery. Cartiva is already approved in Europe, Canada, and Brazil. Recently, a Food and Drug Administration

(FDA) review panel recommended its premarket approval based on the promising results of a 236 patient, prospective and randomized clinical trial [73]. If approved by the FDA, 13 this hydrogel synthetic cartilage device would be first of its kind allowed for use in the

US.

This thesis will focus on the investigation of a novel hydrogel, Cyborgel™

(Formae, Inc., Paoli, PA). Cyborgel is intended for use as a synthetic cartilage implant, replacing the entire articulating surface, which is a step forward from the treatment of smaller-sized osteochondral defect. The bulk material properties of Cyborgel have been characterized by Baykal et al. using three different biphasic analytical models [74].The

authors reported an aggregate modulus of 5.6 MPa and permeability of 0.029 x 10-14

m4/N s (as compared to cartilage range: aggregate modulus - 0.54 - 0.70 MPa;

permeability - 0.006 – 0.76 x 10-14 m4/N s [3, 75, 76]). The authors also investigated the coefficient of friction of Cyborgel against a ceramic disc using a pin-on-disc tribometer, under a series of test speeds and applied loads. The reported average coefficient of friction was 0.03 for Cyborgel [74] compared to 0.014 for articular cartilage [77].

Furthermore, a tribological evaluation using hydrogel-on-hydrogel configuration of this

material has been carried out for 5 million cycles, and the wear rates of -1.4 ± 8.3 and

6.6 ± 35.3 mm3/MC for submerged (in-water) and in-air gravimetric measurements, respectively, have been reported [78]. Hence, Cyborgel has shown potential for use as a cartilage replacement material, which warrants further investigation in this thesis as a potential candidate for orthopedic implants.

Challenges in Development of Synthetic Cartilage Implant

Compliant bearing materials have been investigated for a number of different

joints in the body, such as the hip, knee, shoulder, foot, and ankle. However, the success

of the knee cartilage replacement has been limited to osteochondral plugs with the 14 maximum osteochondral defect size of less than 15mm diameter. It is critical to expand

the use of compliant bearing materials for replacing the entire cartilage surface of the

knee joint, one compartment at a time. The main challenge to achieving this goal is the

complexity of the knee joint, which makes designing and fabricating a total or partial

cartilage implant complicated. Besides the geometrical complexity, there are also a

variety of loads, displacements, and torques acting at the joint, which subject the knee

articulating surfaces to a range of compression and shear stresses. To successfully design

a cartilage replacement implant, it is crucial to understand the biomechanics and the range of complex motions of a knee joint.

Knee Biomechanics

The knee joint can sustain load up to 5 - 6 times body weight over a wide range of

flexion angles up to 140° [79]. As shown in Figure 1-1, a healthy knee femur undergoes six degrees of movement relative to tibia during daily activities such as walking and

sitting on a chair as well as more intense activities such as running, stair climbing,

playing sports, and deep squatting.

Figure 1-1: Six - Degrees of Motion of a Normal Knee Joint. 15 The load acting on the joint varies depending on the activity, the phase of the

activity as well as the amount of knee flexion at a given point in the activity. Per ISO

14243-3, a normal knee joint undergoes up to 2500N load during the stance phase of a gait cycle. A knee can experience flexion angles from 0° during the stance phase of a normal gait up to 30° - 60° during the swing phase of a normal walk [80]. The load

distribution across the two compartments of the knee – medial and lateral - is non-

uniform, with the medial compartment sustaining approximately 60-70% of the load, while the remaining load is carried by the lateral compartment [81]. During a typical

walking cycle, the knee joint is subjected to about 3-4 times the body weight of an

individual, which increases up to 7 times the body weight for strenuous activities such as

stair climbing, running and squatting according to classical biomechanics models [30].

Generally, the tibiofemoral contact forces recorded in vivo are lower than the forces

predicted by the classical biomechanical models [82, 83]. Researchers have also made

attempts to record the in vivo forces experienced by a replaced knee joint using telemetry

[84]. Biomechanics of a totally replaced knee varies significantly as compared to a

healthy knee [85]. Literature has shown that the total knee replacement patients walk with

a less total range of knee motion than their healthy counterparts. Moreover, the joint

replacement patients walk with less knee flexion during the swing phase of gait and the

loading phase of stance as compared to the controls [86]. Therefore, it is crucial to take

into account the complex physiological loads as well as translational and rotational

motions occurring in the joint when designing and characterizing the performance of a

synthetic cartilage implant. 16 Research Overview

Osteoarthritis (OA) affects the lifestyle of millions of people, who experience

mild to severe cartilage degeneration resulting in a reduced range of motion and joint

pain. Knee implants have been used since the 1960s, and are continuously optimized with

the introduction of new materials to improve both patient satisfaction and clinical

performance. Although the Ti-alloy, CoCr alloy, and highly crosslinked UHMWPE

implants have been successfully used in total joint replacement, there are still some

unresolved concerns associated with their use in vivo. The goal of this dissertation is to

evaluate the potential use of compliant bearing materials (polycarbonate urethane and a

novel hydrogel, Cyborgel) in knee cartilage replacement. The success of such an artificial

cartilage knee implant will depend on fully characterizing its mechanical and failure

behavior as well as investigating the compliant-on-compliant bearing material contact mechanics for an optimal implant design. A successfully designed compliant bearing has the potential to improve the outcome for knee OA patients, giving them pain-free mobility.

This thesis will extensively review compliant bearing materials knee implant designs, and biomaterial failure modes, followed by evaluating the effect of sterilization on the material properties, investigating implant design parameters, and determining the failure behavior of these compliant materials. Chapter 2 will provide a detailed literature review on a variety of implant design parameters that affect the contact mechanics of polymer and compliant material-based knee bearings. Additionally, the failure theories applicable to metal, semi-crystalline and compliant polymers will be reviewed for material failure characterization. Chapter 3 will evaluate the effects of the electron beam 17 and gamma radiation on the swelling ratio, mechanical, chemical and tribological

behavior of the novel hydrogel. Inverse finite element modeling will be used for mechanical characterization of this hydrogel to verify that a biphasic neo-Hookean material model can accurately predict the mechanical behavior of this hydrogel with less than 5% uncertainty (Specific Aim 1 below). Chapter 4 will develop and validate an axisymmetric medial compartment knee finite element model to evaluate the performance of different formulations of two compliant materials under physiological knee loads. A full factorial design of experiments will be carried out to determine the influence of implant design parameters, such as implant thickness, implant conformity, and material properties, on the knee contact parameters such as maximum principal stress, Von Mises

Stress, the maximum shear stress, the maximum principal strain, maximum contact

pressure and maximum contact area (Specific Aim 2 below). Chapter 5 will examine the

mechanical performance of polycarbonate urethane and the novel hydrogel under uniaxial

tension, unconfined compression, and biaxial plane strain compression. Using the results

of these tests, the primary mode of material failure will be determined, and material yield

properties will be calculated. Additionally, the material failure properties determined in

this chapter will be used to interpret the simulation results from Chapter 4, and a

guideline for designing a compliant material implant will be provided (Specific Aim 3

below). Chapter 6 will summarize the overall findings from this body of research, along

with implications of this work and future directions.

Specific Aims

1. Evaluate the effect of the electron beam and gamma sterilization on the chemical,

mechanical and tribological properties of a novel hydrogel. 18 Hypothesis: The material properties of this hydrogel will be insensitive to the electron beam and gamma radiation. Secondly, a biphasic neo-Hookean material model can predict the equilibrium mechanical behavior of this hydrogel with less than 5% uncertainty.

Significance: Results of the study showed that the candidate hydrogel withstood two types of radiation sterilization applied at medical device sterilization dose. Both the radiations did not significantly alter the swell ratio, the mechanical, chemical and tribological behavior of the material, except the electron beam was found to cause minor changes in the chemical properties of the hydrogel. The biphasic neo-Hookean material model successfully predicted the stress relaxation behavior of the hydrogel with less than

1% uncertainty.

2. Develop and validate a parametric finite element model of the medial knee compartment to evaluate the contact mechanics of compliant knee bearing implant designs by varying implant conformity, implant thickness and material properties under physiological loads of normal walking and stair climbing.

Hypothesis: The validated medial knee finite element model can predict the contact parameters with less than 10% uncertainty. Further, to define a niche design space for feasible use of compliant polymeric materials in knee applications.

Significance: Parametric modeling will provide a correlation between the implant conformity/thickness and the contact stresses and strains of a compliant material implant.

This knowledge will improve the potential of designing a knee joint implant for load- bearing applications using compliant polymers. 19

3. Determine the failure theory that can accurately predict the failure behavior of

compliant arthroplasty materials under tension, compression and plane strain

compression test at physiologically relevant testing conditions.

Hypothesis: The aim was to evaluate the mechanical performance of both the compliant

polymers under tension and compression. However, the articular cartilage is mainly

subjected to compression and shear forces in vivo, therefore, it was hypothesized that

either the compression or shear would be the primary failure mode for these materials.

Significance: Determination of an accurate failure modality for compliant arthroplasty material will be an important step towards understanding the failure mechanisms occurring in lower strength load-bearing implants. The failure criteria determined in this aim will assist in interpreting the results from Specific Aim 2, which is essential to define a design envelope for compliant knee bearings.

20 Chapter 2 : Literature Review – Knee Implant Design Parameters and Arthroplasty Material Failure Theories

The primary goal of this chapter is to provide a literature review on the different

design parameters for the past and current knee arthroplasty designs and materials,

including ultra-high molecular weight polyethylene (UHMWPE), and compliant

materials such as hydrogels and polyurethanes. An overview of the various modes of arthroplasty material failure will also be provided ranging from the most classic theories to those applicable to hyperelastic materials.

Introduction

The earliest knee prosthesis for replacing damaged bone and articulating cartilage

was developed as a metal tibial plateau by McKeever in 1960 [87]. Since then, a large

number of changes have been made to improve the knee implant designs, such as

multiple tibial, femoral and patellar components; and using corrosion-resistant materials,

such as UHMWPE, ceramic and titanium alloys. These enhancements were made to

accommodate the cruciate ligaments, to increase the contact surface area and reduce

stress, to reduce wear or implant loosening, to promote cellular growth, and to provide

better functionality and mobility to the patients [88]. The overall implant performance and

knee biomechanics are affected by a number of implant design factors, such as implant

thickness, implant conformity, material property, implant fixation method, alignment,

patient-related factors, and surgical technique. Hence, a number of studies have been conducted, clinically, experimentally or through a finite element analysis, to determine the contributory factors for successful implant performance in the body [89-93]. For a

new implant design, repetitive experimental studies on a knee simulator are required, 21 which can precisely reproduce various translational and rotational motions occurring in the joint [94-96]. However, knee simulator studies can take several months and cost in hundreds of thousands, consequently, finite element (FE) analysis is a widely used method to study the mechanical behavior of the knee joint since 1972 [97]. A number of researchers have used FE analysis in orthopedics to investigate stress responses of single- and multiple-phase normal and osteoarthritic articular cartilage under different loading conditions, which are summarized in a list of review articles over the last three decades

[98-101].

For the literature review in this thesis, a generalized literature search for knee implant design using FEA was carried out, and over 3000 articles, conference proceedings, theses, and books were identified from Engineering Village and PubMed using the following keywords: ((((finite element OR computational OR FE) WN All fields) AND ((design) WN All fields)) AND ((knee OR cartilage) WN All fields)),

English only. A few pioneering works on designing knee implants using the current state- of-art materials were selected to discuss in this chapter. However, the search had to be narrowed down to focus on elastomeric materials such as polyurethane (PU), polycarbonate urethane (PCU) and hydrogels using the following keywords: ((((implant design) WN All fields) AND ((gel OR hydrogel OR soft material OR polycarbonate urethane OR polyurethane OR synthetic cartilage OR artificial cartilage) WN All fields))

AND ((knee) WN All fields)), English only in Engineering Village and PubMed on April

21st, 2016. After removing conference proceedings, press releases, book sections and duplicate entries, 56 relevant articles were identified. Of those publications, all major works that focused on evaluating implant design parameters such as congruency, material 22 strength, thickness, lubrication mechanism, wear, counter-bearing, and composite

material matrix are reviewed below. Publications comparing implant designs or wear

properties of UHMWPE with those of compliant materials are also discussed here to

assess the potential of designing knee implants using the proposed materials.

Current Implant Designs

The current gold standard of knee replacement systems includes a cobalt-chromium

(CoCr) femoral component articulating against a UHMWPE tibial insert. This combination has been investigated the most since the 1980s when Bartel et al. studied the

effect of implant conformity, thickness and material properties on the contact stresses in

UHMWPE total joint replacement implants [90, 91, 102]. The authors found that the

implant conformity and thickness affect the contact stresses associated with surface

damage, which generates polyethylene debris. The contact stresses are more sensitive to

articulating surface conformity in the medial-lateral direction than in the anterior-

posterior direction. A finite element analysis of the tibial contact stress as a function

of the polyethylene thickness showed that a tibial insert thickness of more than eight to

ten millimeters is desirable from the contact stress perspective [90]. For metal-backed

implants, Bartel et al. reported that a minimum plastic thickness of four to six mm should

be maintained for nearly conforming contact surfaces [91]. A similar study by El-Deen et

al. carried out a multiple regression analysis to test whether the contact area can be

influenced by the UHMWPE insert thickness. The authors found no evidence confirming

that a thickness over 10mm could significantly reduce the contact area; consequently,

10mm was considered optimal thickness for tibial inserts [103]. These results were only

applicable to the fixed total knee systems, which reported that increasing the insert 23 thickness from 6.8mm to 8mm decreased the contact pressure; however, for the mobile

bearing, the inferior contact surface of 8mm thick design had higher contact pressure than

those in the 6.8mm design [104]. A computational wear model for UHMWPE was also

developed to evaluate the effect of different level of surface conformity and material

properties on the survival of the total knee prostheses. Interestingly, the most conforming

surface had three times more predicted wear compared to the least conforming flat insert.

Additionally, the moderately cross-linked UHMWPE performed better than the

conventional UHMWPE [105]. Based on the literature reports, a UHMWPE insert with

higher conformity provided more surface area for wear, and higher wear rate depending

on the applied loads and material properties.

A tribological evaluation of hemiarthroplasty design against bovine knee cartilage

was carried out by McCann et al. [106]. The authors reported a strong correlation

between wear and contact stress as well as shear stress. By decreasing conformity of

hemiarthroplasty bearings, an increase in cartilage contact stress was observed, which

resulted in higher friction, higher shear stress and increased cartilage degeneration [106].

The contact stresses in unicompartmental knee implant, which is known to preserve bone

stock, was also evaluated for parameters such as bearing congruency, thickness and

alignment during a step-up activity by Simpson et al. Only the fully congruent bearing experienced the least von Mises and contact stresses, while the partially congruent and the non-congruent metal-backed designs experienced much higher contact stresses. The fully congruent bearing was the only design that could be as thin as 2.5mm without approaching the polyethylene failure limit [107]. It was apparent from these studies that

lower conformity in hemiarthroplasty or uni-condylar implant designs is at a higher risk 24 of higher wear damage. Based on several studies reviewed here, the thickness is one of the most significant contributors to the success of UHMWPE tibial components; followed by bearing conformity, especially for hemiarthroplasty or uni-compartmental implant design. The material properties did not seem to have much influence on the resulting contact stresses and area of the implant, except for moderate changes in the wear rate and reduced stress shielding on the surrounding bone [108].

Compliant Bearing Material Implant Design

In the past two decades, compliant bearing materials have been investigated as a

potential candidate for knee arthroplasty. One of the reasons for the success of

elastomeric materials, such as polyurethane (PU), polycarbonate urethane (PCU) and

hydrogels, is their high deformability, which allows conformance to the counter-surface,

thereby, increasing the contact area and reducing the overall contact pressure. As compared to traditional bearing materials, compliant materials are better at replicating the lubrication mechanism of the native cartilage [50]. Low surface roughness of

polyurethanes results in lower asperity contact as they get depressed to achieve full fluid- film lubrication [109]. A wear analysis of polyurethane (Pellethane 80A) was carried out

by Schwartz et al. on a dual axis wear simulator, which demonstrated lower wear rate for

polyurethane as compared to UHMWPE [110]. Similar to UHMWPE, polyurethane has

also been evaluated to understand the effect of design parameters on the implant

performance. A study designed and prototyped polyurethane knee prostheses as a flat

tibial component and observed that the polyurethane (material strength: 20MPa) had

sufficient durability to survive for 5 million cycles in a knee wear simulator [111]. Jones

et al. conducted a series of friction tests to investigate three different tibial 25 bearing conformities (low, medium, and high) and three thicknesses (2mm, 3mm, and

4mm) of polyurethane Corethane 80A. All the three conformities performed well with extremely low friction, and without any influence on the mode of lubrication. Although the effect of thickness on the shear stress at the polymer-substrate interface was

significant, however, that on lubrication was minimal [109]. Polyurethane (PU) has also

been investigated in a tribological study, which tested medial compartmental of bovine

knees on a knee simulator against healthy medial tibia as a negative control; stainless

steel hemiarthroplasty as a positive control; and three PU hemiarthroplasty tibial plates of

different strength (1.4 MPa, 6.5 MPa, and 22 MPa). The two PU bearings with the lower modulus demonstrated reduced levels of contact stress, shear stress, and similar

tribological performance to the negative control. The highest modulus PU formulation

(22 MPa) demonstrated higher levels of friction-related shear stress and wear on the opposing cartilage, although not as severe as the wear from the stainless steel group [112].

Therefore, this study concluded that in the case of tibial-only implantation, a lower

modulus PU implant would produce the lowest cartilage wear and degradation. In another

comparison study, unicompartmental knee spacers were made out of CoCr, UHMWPE,

and PU, and three different spacer design contours (conventional, flat and C-shaped)

were investigated using a static finite element model of a knee in full extension and at 90-

degree flexion. The results showed that the spacers made out of PU exerted lesser contact pressure onto the femoral cartilage, with the C-shaped spacer exhibited the lowest femoral cartilage contact pressure in full extension; and the contoured spacer had the lowest contact pressure among the other spacers at 90-degree knee flexion. This study

concluded that the knee spacers made out of softer material and higher conformity can 26 better withstand the joint forces under various motions [113]. The literature also suggested that the compliant arthroplasty implants are at the risk of introducing an abrupt material change from the compliant polymer to the rigid substrate layer, which could result in high shear stress at the polymer-substrate interface and potential debonding of the polymer. To address this concern, a multilayer composite of polyurethane was investigated by Stewart et al. to determine the optimal thickness and material strength for cushion knee implant designs. The co-authors determined that a 4 mm thick surface layer with an elastic modulus of 20 MPa, and a 4mm thick structural support layer with an elastic modulus of 1000 MPa would be optimal for knee replacements [114]. Although

compliant materials have much lower strength than the current gold standard arthroplasty

materials, conformity plays a crucial role in the implant survival to an extent that a

congruent compliant bearing material may function at half the optimal thickness of

UHMWPE.

Polycarbonate urethane (PCU), which is a sub-set of polyurethanes, is developed

by removing the susceptible ester and ether linkages in the soft segment of the

polyurethanes, specifically to prevent cracking and degradation for long-term use in orthopedic applications [115]. Scholes et al. investigated the tribological and lubrication

properties of 8mm thick PCU uni-condylar knee prostheses against cobalt-chromium- molybdenum (CoCrMo) femoral components [116]. An average PCU wear rate of less

than 1mm3/million cycles was found in the wear study, and the coefficient of friction was

observed between 0.004 - 0.1, depending on the lubricant. Almost full fluid-film

lubrication was achieved when the polycarbonate urethane samples were tested in

physiologically relevant lubricant, which makes PCU-CoCrMo a promising alternative 27 bearing combination. Besides knee prostheses, polycarbonate urethane has also been

investigated for the development of a meniscal implant, NUsurface (Active Implants Inc.,

Israel) [117].

Similar to polycarbonate urethane, a limited number of hydrogels have also been

investigated for use in knee arthroplasty. Polyvinyl alcohol (PVA) hydrogel is

specifically proposed and investigated as a promising biomaterial for use as an artificial

cartilage. Suciu et al. ran a durability study on PVA knee prostheses under simulated

anterior-posterior displacement during walking. The study investigated the effect of

thickness and water content on the wear factor of the hydrogel after 100,000 walk cycles

against the metal femoral component and reported that PVA hydrogel with 45 – 50%

water content produced the lowest wear factor. Additionally, since the PVA hydrogel is a

poroelastic-hydrated material, a thicker gel layer (from 2 to 3.6 mm) produced lower

wear factor due to longer duration of fluid pressurization, which in turn maintained lower

friction force on the solid matrix. Another interesting observation in this study was that

PVA hydrogel manufactured on a hydrophobic mold (PTFE) presented a 16 - 27% lower

wear factor compared to a hydrophilic mold (glass) because of the superficial layer of

polymer chains formed in the vicinity of the hydrophobic substrate. [118]. The same

group of authors also experimentally investigated the wear characteristics of the PVA

hydrogel tibial plateau. Micro-pockets were machined in the rigid femoral component so

that as the water exuded out of the hydrogel, it fills and pressurizes the pockets, thus,

developing poro-elasto-hydrodynamic lubrication. This study evaluated a variety of wear- influencing factors such as the number of walking cycles, femoral porosity, depth of the micro-pockets, water content and molecular weight of the PVA hydrogel. For a million 28 walking cycles, PVA hydrogel with a molecular weight of 12,300 and 77% water content

articulating against a smooth femoral component had a wear factor of 10-6-10-5 mm3/Nm;

when the same PVA hydrogel was tested against a 50 μm deep micro-pockets on 15% of

the femoral surface, the wear factor reduced to 10-7 - 10-6 mm3/Nm (80% reduction). The

highest wear reduction due to the micro-pockets presence was observed in

PVA hydrogel with 77% water content, which is comparable to the natural cartilage

[118]. Besides these studies for knee prostheses, hydrogel wear and biomechanical

performance have also been evaluated in vitro or in an animal study for meniscal

applications [119] [120].

Despite improvements in the implant design, bearing material failure is the key

bottleneck in the survival and performance of knee prostheses. The key stresses

experienced by the knee joint are tension and compression, which are also the main cause

of stress-related fracture and implant wear. Many of the above studies evaluated the

performance of the bearing material in terms of contact stress, contact area, maximum principal stress, maximum shear stress, von Mises stress, maximum principal strain, frictional properties and wear properties. Among current arthroplasty materials, the metal implants undergo fracture, fatigue, and corrosion in the physiological environment, and may also generate wear particles [35]. Polymers mainly fail due to yielding, wear, fatigue,

fracture, creep, and chemical damage. Most of the metal and polymers show either brittle

or ductile failure behavior under mechanical testing [121]. For ductile materials, the onset

of plastic deformation, also known as yield, is considered failure; while brittle fracture is

characterized by a rapid onset and propagation of the crack, without significant plastic

deformation [121, 122]. The vulnerability of arthroplasty bearing materials also comes 29 from the changes in their mechanical integrity due to prolonged cyclic loading. When an elastic material is subjected to a constant load, it undergoes creep, which is a result of a combined effect of viscoelastic deformation, chemical and physical bond rupture, shear yielding, crazing and void formation leading to failure [123]. Repetitive loading and

unloading can cause fatigue, which is resultant stress built up in a material that could act

as foci for the initiation of sub-surface cracking and failure [124]. Fatigue in a viscoelastic

polymer is complicated since the viscoelasticity causes damping of the load, which in

turn creates heat. This heat is difficult to dissipate due to low thermal conductivity of the polymer; consequently, the material overheats and fails, not through fatigue, but due to

creep or heat softening [125].

Various material failure theories have been proposed since 1638, the first one by

Galileo, who subjected stones columns to a simple tensile test to support his hypothesis

that their strength is proportional to their cross-sectional areas and is independent of their lengths. He concluded that a fracture would occur when the “absolute resistance to fracture (critical stress)” was attained [126]. There are a number of material failure

theories reported in the literature on isotropic materials such as maximum normal stress,

maximum strain theory, maximum shear stress theory (Tresca) and maximum distortion

energy theory to name a few [127]. According to these theories, material failure occurs

when the stress or strain or shear in the material increases beyond the yield stress or strain

or shear value. Most classic theories discussed here are well known [128], and are

outlined below for the reader:

Maximum normal/principal stress theory (1858) 30 W.J.M Rankine proposed a maximum normal stress-based failure theory, which

stated that the permanent deformation of ductile material would occur when the

magnitude of maximum principal stress reaches the yield point stress of the material

tested under uniaxial tension. Similarly, under uniaxial compression, the material is

considered to have yielded when the minimum principal stress reaches the yield point

stress. The failure criterion is defined as

σt ≥ fy or |σc| ≥ fy,

where σ is the stress in tension (t) or compression (c), and fy is the yield point stress.

For brittle material, the ultimate strength is considered the failure stress; hence, the

design criterion should be such that the maximum principal stress must not exceed the

working stress (S) for the material: σt ≤ S.

Saint Venant – Maximum Principal Strain Theory (1837) This theory states that a ductile material failure occurs when the maximum strain

reaches the yield point strain under uniaxial tension test; or when the minimum strain

reaches the yield point strain under uniaxial compression. The design criterion for the

maximum strain ( ) theory is given by: < ( + ), where ν = Poisson’s 𝜎𝜎1 𝑣𝑣 𝜀𝜀𝑦𝑦 𝜀𝜀𝑦𝑦 𝐸𝐸 − 𝐸𝐸 𝜎𝜎2 𝜎𝜎3 ratio, E = Young’s modulus and are the principal stresses.

σ𝑖𝑖 Few limitations of this theory are that it overestimates the elastic strength of ductile

materials, and inaccurately predicts the failure value under biaxial testing or in the

presence of hydrostatic pressure.

Maximum shear stress theory (Coulombs, Guest, Tresca) 31 Initially devised by Coulomb and later developed by Guest and Tresca, the

maximum shear stress theory says that failure by yielding in a ductile material will occur

when the maximum shear stress reaches a yield stress value during a simple uniaxial

tension or compression test. The maximum shear is equal to half the difference between

the maximum and minimum principal stresses. For the simple tensile test, the maximum

shear is half the tensile yield stress (F):

τmax = ½ (σmax – σmin) = ½F

The design criterion using this theory for an allowable stress (S) is given by (σmax – σmin)

≤ S, for σmin < 0. For ductile materials, yield happens along 45° slip planes, which are the

planes for maximum shear stress. However, this theory is not applicable to brittle

materials.

Maximum distortion energy or Von Mises yield (or strain) failure criterion This theory, proposed first by R. Von Mises in 1913, says yielding will occur in a

ductile material when the distortion energy density reaches the elastic limit in the simple

uniaxial tensile test. This theory is for addressing ductile, isotropic materials, and the

design criterion as per this theory is:

( – ) ( – ) ( – ) < , where are the principal stresses. 2 2 2 σ1 σ2 + σ2 σ3 + σ3 σ1 � 2 σyield σ𝑖𝑖 In the case of plane stress state (σ3 = 0): – + < . 2 2 1 1 2 2 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 The von Mises strain criterion is similar� σto theσ von𝜎𝜎 Misesσ stressσ failure criterion and defined as:

( – ) ( – ) ( – ) < , where are the principal strains. 2 2 2 ε1 ε2 + ε2 ε3 + ε3 ε1 yield 𝑖𝑖 � 2 ε ε 32 Maximum strain energy theory A second criterion for yielding in isotropic materials is based on strain energy

concept. The theory was proposed by M.T. Huber of Poland in 1904 and was further

developed by E von Mises and H. Hencky (1925). The yield condition for combined

stress is established by equating the distortion strain energy for yield in a simple tension

test to the distortion strain energy under combined stress. The design criterion based on

this theory is as follows:

+ + – 2v( + + ) < Yield Stress, where are the 2 2 2 �σ1 σ2 σ3 σ1σ2 σ2σ3 σ3σ1 σ𝑖𝑖 principal stresses.

Coulomb stress theory According to the Coulomb stress criterion, failure occurs on a plane when the

principal stresses exceed a specific value: σCoulumb ≥ (σ1 – σ3) + µ(σ1 + σ3), where σ1 is

the largest principal stress, σ3 is the smallest principal stress and µ is the coefficient of

friction.

Hydrostatic stress theory It states that isotropic stresses are exerted due to the presence of fluid surrounding a polymer. The material fails when the fluid pressure increases beyond a certain value.

Hydrostatic stress is an average of the three normal stress components (σi) of any stress

tensor. The failure criterion is:

( + + ) < � 3 𝜎𝜎𝑥𝑥 𝜎𝜎𝑦𝑦 𝜎𝜎𝑧𝑧 𝜎𝜎𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝑐𝑐 33 Although the classic failure theories satisfactorily predict the failure behavior of metals and rigid polymers, they are not accurate for the viscoelastic polymers, which undergo mechanical changes with time and temperature. A literature search for viscoelastic polymer failure theories was conducted in Engineering Village and PubMed databases with a set of keywords in the title, abstract or the body of the article on April 26th, 2016.

100 articles were found in Compendex, Inspec, Inspec Archive & CBNB database of

Engineering Village between 1884 and 2016 using an advanced search with the following keywords: (((((failure criterion OR constitutive model OR theory) WN ALL) AND ((gel

OR polyurethane) WN ALL)) NOT ((tissue OR cells OR protein OR rock OR cement OR filled OR electric OR metal OR ceramic OR glass OR asphalt OR dentin OR paste OR coating OR adhesive OR foam OR fiber-reinforced OR laminate OR braid OR composite) WN ALL)) AND ((large deformation) WN ALL)) AND (English WN LA).

Similarly, 5 articles were found on PubMed using these keywords: (((((failure criterion

OR constitutive model OR theory)) AND (gel OR polyurethane)) NOT (tissue OR cells

OR protein OR rock OR cement OR filled OR electric OR metal OR ceramic OR glass

OR asphalt OR dentin OR paste OR coating OR adhesive OR foam OR fiber-reinforced

OR laminate OR braid OR composite)) AND large deformation) AND English

[Language]. After removing conference proceedings, press release, book sections and duplicate entries, a total of 45 peer-reviewed journal articles were identified as relevant.

These publications are briefly discussed below specifically to understand the failure modes and mechanisms of viscoelastic polymers, such as polycarbonate urethane and hydrogels. 34 The viscoelastic polymers failure was first expressed by Reiner-Weissenberg energy-based failure criteria in 1939 [129]. This criterion stated that the instant of polymer failure depends on a conjunction between distortion free energy and dissipated energy, while the rupture time is obtained by assuming the maximum allowable stress

[130]. Since then, a number of constitutive models have been developed to understand the mechanical behavior of brittle, ductile, elastic, amorphous, semi-crystalline polymers and rubber-like materials. Prominent failure theories and constitutive models for isotropic- hyperelastic solids were proposed by Mooney (1940), Rivlin (1948), Valanis-Landel

(1967), and Ogden (1972). Arruda and Boyce (1993) proposed a model for deformation of the rubber-like material in different loading scenarios, which could be described with a limited number of parameters [131]. Arruda-Boyce model was based on the Langevin chain statistic, which modeled a rubber chain segment between chemical crosslinks as a number of rigid links (N) of equal length l. The parameter N is related to locking stretch

λL, the stretch at which the chains reach their fully extended state:

= .

𝜆𝜆𝐿𝐿 √𝑁𝑁 Basing on the works of Boyce, a chain stretch failure criteria [132, 133] was developed for semi-crystalline ultra-high molecular weight polyethylene, in which the failure determined by an estimation of the average molecular chain stretch and was given by:

= , where are the principal strains. 2𝜀𝜀 2𝜀𝜀 2𝜀𝜀 𝑒𝑒 1+ 𝑒𝑒 2+ 𝑒𝑒 3 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎 𝑖𝑖 𝜆𝜆 � 3 ε Bergstrom et al. carried out an in-depth evaluation of uniaxial and multiaxial failure of UHMWPE using eight different failure criteria such as maximum principal 35 stress, Mises stress, Tresca stress, hydrostatic stress, Coulomb stress, maximum principal

strain, Mises strain and chain stretch failure criteria. Among all the criteria, the chain

stretch failure criteria captured the failure behavior of UHMWPE materials most

accurately, while the von Mises strain predicted the failure behavior with least accuracy

[132]. Weissmann et al. proposed a new brittleness criterion for low-density polyethylene

films by determining their transition-temperature from ductile to brittle failure at different

strain rates. The authors found that at low strain rates the transition temperature was

independent of the strain rate; this temperature was defined as cold brittleness temperature, which was related to the energy dissipation of the material during dynamic mechanical tests [134].

Compliant Material Failure Criteria and Modes

Since both polycarbonate urethane and hydrogels are viscoelastic rubber-like

materials, the failure criteria defined for rubbers may be of interest here. In 1966, Grosch

et al. proposed that the energy density of rubbers to break (UB) is related to hysteresis at

2/3 break (HB) expressed by UB = KHB , where K is a material specific property. When the

energy density is plotted against hysteresis, the results that fell under the break value is the criterion of failure [135]. Harwood et al. further expanded this failure criterion to

make it strain- and temperature-sensitive for all amorphous rubbers [136]. Hamdi et al.

proposed a fracture criterion of rubber-like material based on an elongation concept. The

criterion predicted the fracture of a smooth specimen under plane stress conditions such as simple tension, equal biaxial tension and biaxial tension [137]. A universal viscoelastic

model described a definitive relationship between creep, constant strain-rate, and stress

relaxation analysis for viscoelastic polymeric compounds. This model was extended to 36 understand the similarities between failure criteria involving creep, constant strain rate

and stress relaxation [138].

Polyurethane is used in a number of implantable medical devices, such as artificial heart systems, catheters, mammary implants, semi-occlusive dressings and drug delivery systems [39]; hence, a wide variety of failure modes are reported in the literature

depending on the application. The key failure mechanism experienced by polyether

urethane implants in vivo is oxidative degradation, which is a result of cleavage in the

backbone of the polymer. These biodegradation properties of polyether urethane have

been evaluated for cardiovascular pacing leads, and two mechanisms have been reported:

metal-ion oxidation and environmental stress cracking [115, 139-142]. Wiggins et al.

reported a synergistic effect between chemical and physical degradation in explanted

polyether urethane lead insulation [140]. In another study by the same group, dynamic

loading of polyurethane film in a simulated physiological environment resulted in

accelerated oxidation and induced surface cracking [143]. Christenson et al. also found

that the in vivo and accelerated degradation studies supported oxidation as the dominant

mechanism of biodegradation for polyether urethane as well as polycarbonate urethane,

with the latter concluded as the most suitable polyurethane formulation for use in medical

devices [142]. The mechanical behavior and failure mechanism of polyurethane foam

have been reported in abundance in the literature [144-147]. Most of these works

subjected the polymer foam to a series of uniaxial and multiaxial compression, tension,

shear and hydrostatic test to determine the failure criteria. Pettarin et al. found that

polyurethane foam exhibited a typical isotropic brittle behavior under tension, but that

response turned ductile under compressive load. The authors defined the polyurethane 37 foam failure as a combination of brittle crushing of cellular material criterion and elastic buckling criterion [144]. Peroni et al. defined the failure criteria for the polyurethane foam in term of polymer yielding behavior [147]. Although these works provided insight into the performance of polyurethane under different loading conditions, the physical structure of the foam is quite different from the current configuration of interest for knee arthroplasty application. Only a few studies came close to evaluating polyether urethane and polycarbonate urethane failure mechanism for load-bearing applications. Miller et al. investigated PCU and similar compliant polymers under a series of microscopic and macroscopic tests to evaluate compressive cyclic ratcheting and fatigue in an aqueous solution [148]. PCU displayed a rapid creep response initially but quickly leveled out for the rest of the test. Under cyclic testing, the samples immediately recovered over 90% of maximum strain and later achieved full recovery. The overall performance of PCU was promising, with mechanical compressive modulus closest to the native meniscus tissue and ability to remain largely undamaged under the load, except for cyclic ratcheting. A polycarbonate (PCU) acetabular buffer implant has also been investigated for failure mechanisms and damage features against a native acetabular surface for 11 months [149].

With the help of some surface analysis and gravimetric techniques, the implant was found to have severe abrasion to the backside of the buffer as the primary damage mode.

Stippling damage on the articular surface indicated that adhesive wear was the failure mechanism, which aggravated movement of the buffer against the acetabulum and increased back-side abrasion.

Hydrogels have been mainly investigated under different mechanical loading conditions to determine which failure mode fits them the best, depending on the intended 38 application. Stammen et al. investigated the failure strain and stress of a novel polyvinyl

alcohol hydrogel, which was intended for a load bearing application in articular joints, under shear and unconfined compression tests [150]. Compressive failure was characterized between 45 and 60% strain. The strain-rate dependent viscoelastic properties of the hydrogel formulations were confirmed, statistically, under compression but not under shear. This behavior was attributed to the dominance of fluid flow and related frictional drag. Bertagnoli et al. performed a confined compression and fatigue testing on a hydrolyzed polyacrylonitrile hydrogel implant, which was intended to replace degenerated nucleus pulposus [151]. A series of compressive “bulge” tests, confined

compression “lift” tests and a10 million cycles fatigue test was conducted to determine the mode of failure; however, all material performed well under all those conditions.

Extrusion testing in a cadaveric model confirmed that the failure mode was fracture under compression. Similarly, Seitz et al. reported fracture and large strain failure behavior in self-assembled triblock copolymer gels [152]. Compressive experiments were performed

to develop a strain energy function that accurately captured the strain hardening behavior

of the copolymer gels. The gels exhibited a transition from rough, slow crack propagation

to smooth, fast crack propagation for a characteristic length.

Rheology is also proposed in the literature to measure the small and large

deformation in polymer gels and define the failure envelope of a range of materials.

Smith failure envelope technique, which was initially applied to the rupture of bulk

elastomers, can also be applied to gels [153]. The gel was tested for three or more

different strain rates and range of temperatures, and the failure stress vs. strain was

plotted to define the failure envelope. The failure mechanism of a polyvinyl alcohol 39 cryogel was investigated for use in a shoulder implant [154]. The criteria of whether the implant could survive and perform in the shoulder were made based on von Mises and

maximum principal strain criterion. Although a number of studies have investigated the

failure modes of hydrogels, not many failure criteria have been developed for

characterizing hydrogels to the author’s knowledge. One theory specifically devised for

hydrogels was presented by Tang et al [155]. The authors developed a bulge test

apparatus to measure the mechanical properties and observe the failure behavior of a nanocomposite poly (N-isopropyl acrylamide) hydrogel films. The authors proposed a

dehydration failure criterion of the hydrogel tested on different-size orifices apparatus, and when the strain exceeded a threshold value, the hydrogel underwent volume phase transition, thinning out extremely and bulged into a balloon abruptly and failed. The pressure-deflection relation of this criterion was given as follows:

= 4 + , where G is shear modulus, h is deflection of the apex, a is radius 𝐺𝐺𝐺𝐺 2 7 3 4 𝑎𝑎 3 𝑃𝑃of orifice� apparatus.𝑎𝑎 ℎ ℎ �

Besides the mechanical failure mechanisms, an important factor that may affect a

medical device survival and performance is the sterilization process, which can include

dry heat sterilization, gas sterilization, chemical sterilization or radiation [156].

Polycarbonate urethane (Bionate 80A) has already shown excellent resistance to 25kGy

gamma radiation with no significant changes to its mechanical strength or chemical

bonds [44]. Although the study found 9% reduction in the ultimate strength of PCU after five years of aging, Bionate has shown higher oxidative stability as compared to

UHMWPE [44]. However, sterilization is known to potentially change the mechanical 40 and chemical integrity of hydrogels by inducing cross-linking in the polymeric networks.

Kanjickal et al. studied the effects of sterilization on poly (ethylene glycol) hydrogels and

reported that ethylene oxide and gamma sterilization caused elevated cross-linking in the

polymer, thus reducing the swell ratio [157]. Furthermore, a statistically significant lower surface roughness was recorded in gamma-sterilized samples compared to the

unsterilized samples. Similarly, Lee et al. investigated the effect of gamma sterilization on an aqueous solution of alginate and found a decrease in viscosity and an exponential increase in alginate degradation at as low as 10kGy radiation dose [158]. Therefore,

failure evaluation of the novel hydrogel post-sterilization is critical to ensure the material

performance.

Wear is another critical mode of failure for polymers that are used in arthroplasty.

By replacing the UHMWPE with compliant materials, there is an expected improvement in the lubrication regime and reduction in the amount of wear debris. However, as

discussed in the first chapter, polycarbonate urethane and the novel hydrogel being

investigated in this thesis have already shown favorable tribological properties under

physiologically relevant loads.

Research Gap and Goal of Thesis

Compliant materials, such as polyurethane, polycarbonate urethane, and hydrogels,

have been used for biomedical applications for decades, but their use in orthopedic

devices is limited. Polyurethane has been studied for load-bearing applications; however,

it is prone to oxidative degradation in vivo. Hence, polycarbonate urethane was developed

specifically to prevent cracking and degradation in long-term orthopedic implants. While

PCU has been used in spinal, hip, and meniscal implant and osteochondral plugs, it is yet 41 to be employed as an artificial knee cartilage replacement. Similarly, only polyvinyl alcohol hydrogel has been developed into scaffolds, osteochondral plug and meniscal

implant, but no success has been achieved to use in a knee prosthesis. Both of these

promising materials have to be investigated for load-bearing application in partial or total

knee arthroplasty. To achieve this goal, this thesis will answer the following questions for

polycarbonate urethane and a novel hydrogel, Cyborgel:

1) Would the proposed materials be able to survive the sterilization process, especially

the hydrogel, which is known to lose chemical and structural integrity post-

sterilization?

2) If a knee replacement implant is to be made of compliant polymers, what would be

the design criteria to maximize implant survival by minimizing the contact stress

and wear rate, which are two common causes of device failure?

3) Which implant design parameters would have the most impact on the biomechanics

of compliant knee implants? How can they be optimized?

4) What is the most prominent mode of failure for these compliant materials under

physiological knee loads and strain rates?

42 Chapter 3 : Effect of Radiation Sterilization on Chemical, Mechanical and Tribological Properties of a Novel Hydrogel

Abstract

Hydrogels are known to possess cartilage-like mechanical and lubrication properties; however, hydrogel sterilization is challenging. Cyborgel™, a proprietary hydrogel, is intended for use as a cartilage replacement implant. This study evaluated the effect of 30-35 kGy electron beam and gamma radiation on the polymer swell ratio, and the mechanical, chemical and tribological behavior of this hydrogel. Three different formulations were mechanically tested, and material parameters were identified using finite element analysis. FTIR spectroscopy was used to investigate chemical changes.

Wear testing was carried out for 2 million cycles in bovine serum, followed by 2 million cycles in distilled water. No significant difference was found in the swell ratio, mechanical and tribological properties of control hydrogel samples or those exposed to electron beam or gamma radiation. However, chemical spectra of electron beam sterilized samples revealed minor changes, which were absent in unsterilized and gamma sterilized samples.

Introduction

Osteoarthritis is a joint disorder, which causes cartilage wear and degradation due

to old age or traumatic injury. Due to the avascular nature of articular cartilage and its

limited ability to self-repair, end-stage osteoarthritis is commonly treated by total joint

arthroplasty [7]. More than 600,000 total knee replacements were performed in 2009

[159], and that number is estimated to grow in the future [16]. Currently the most

commonly used joint arthroplasty materials include components fabricated from metallic 43 alloys, ceramics, and ultra-high molecular weight polyethylene (UHMWPE) [30].

However, in the physiological environment, metal ions and corrosion products from the

implanted devices may result in adverse local tissue reactions [34]. UHMWPE, on the

other hand, may oxidize in vivo, and its wear debris can lead to implant loosening and

osteolysis [30]. Although total joint arthroplasty is generally successful, the procedure is not ideal for younger, active patients, who will be at risk of one or more revision surgeries during their lifetime. Knee resurfacing is an alternative to traditional knee replacements and is recommended for younger patients to achieve quick recovery and

maintain an active lifestyle [24]. Joint resurfacing techniques include arthroscopic

procedures such as microfracture, soft tissue graft, osteochondral grafts, and cell

transplantation with or without scaffold [25]. Hydrogels, a bio-compliant material, have

been studied for cell scaffolding and biological joint resurfacing applications [160]

because of their ability to be delivered arthroscopically, and potentially prolong a total

joint replacement [61].

Hydrogels are hydrophilic polymer networks that swell in water and can be

tailored to attain cartilage-like mechanical and lubricating properties [57]. These

characteristics make them an attractive candidate for several biomedical and tissue

engineering applications, including load-bearing applications [58-60]. Cyborgel™, a

proprietary hydrogel, is intended for use in a cartilage replacement implant. It has been

reported to produce a low coefficient of friction of 0.03 on a pin-on-disk tester [74]

compared to 0.014 for articular cartilage [77]. Its bulk material properties have been previously characterized by Baykal et al. using three different analytical models [74], and

the authors reported an aggregate modulus of 5.6 MPa and permeability of 0.029 x 10-14 44 m4/N.s (cartilage range: aggregate modulus - 0.54 - 0.70 MPa; permeability - 0.006 –

0.76 x 10-14 m4/N.s [3, 75, 76]). Furthermore, Baykal et al. performed a tribological

evaluation using hydrogel-on-hydrogel configuration of this material for 5 million cycles

and reported wear rates of -1.4 ± 8.3 and 6.6 ± 35.3 mm3/ million cycles based on in- water and in-air measurements [78]. Hence, this hydrogel has shown potential for use as a

cartilage replacement material, which warrants further investigation for use in a medical

device.

An important aspect of medical device manufacturing is the sterilization process, which can include dry heat sterilization, gas sterilization, chemical sterilization or radiation [156]. However, sterilization is known to potentially change the mechanical and chemical properties of hydrogels by inducing cross-linking in the polymeric networks.

Kanjickal et al. studied the effects of sterilization on poly (ethylene glycol) hydrogels and reported that ethylene oxide and gamma sterilization caused elevated cross-linking in the polymer, thus reducing the swell ratio [157]. Furthermore, a statistically significant lower surface roughness was recorded in gamma-sterilized samples compared to the unsterilized samples. Similarly, Lee et al. investigated the effect of gamma sterilization on an aqueous solution of alginate and found a decrease in viscosity as well as an exponential increase in alginate degradation at as low as 10kGy radiation dose [158]. The objective of this study was to evaluate the effects of radiation sterilization on the swelling, mechanical, chemical and tribological behavior of Cyborgel™. We hypothesized that the electron beam and gamma irradiation would not affect the material properties of this hydrogel. 45 Additionally, Liu et al. [161] and several other researchers [162-164] have used indentation and finite element analysis (FEA) for mechanical characterization of soft tissues and hydrogels. Material properties characterization of this hydrogel using FEA will facilitate future simulations for implant design optimization. Hence, a supplementary aim of this study was to verify a biphasic neo-Hookean material model that can accurately predict the mechanical behavior of this hydrogel with less than 5% uncertainty.

Materials & Method

Three different formulations, with varying water content, of a proprietary hydrogel (CyborGel™, Formae Inc., Paoli, PA) were utilized in this study. Samples of each formulation were separated into three groups: the first group was subjected to 30-35 kGy gamma radiation (Steris Isomedix, Whippany, NJ); the second group was subjected to 30 kGy electron beam radiation (Steris Isomedix, Whippany, NJ); and the third group was not irradiated and served as a control. Thus, a total of nine groups were evaluated in this study (3 formulations × 3 sterilization conditions).

Swell Ratio Evaluation

The water content of the nonsterilized and sterilized samples was assessed by gravimetric measurements (g) before and after desiccation in an oven at 95°C for 24 hours. The water content was calculated using the following equation:

(%) = 1 100

𝐷𝐷𝐷𝐷𝐷𝐷 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ𝑡𝑡 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 � − � 𝑥𝑥 𝑊𝑊𝑊𝑊𝑊𝑊 𝑊𝑊𝑊𝑊𝑊𝑊𝑊𝑊ℎ𝑡𝑡 46 Mechanical Testing

Cylindrical samples (n = 3 per formulation and sterilization type; diameter = 4.64

± 0.07 mm and height = 9.59 ± 0.17 mm) were used for mechanical testing. All the

samples were subjected to unconfined compression on a mechanical load frame (4505

Instron, Norwood, MA). Specimens were compressed to attain 10% strain at 0.013mm/s strain rate and then allowed to undergo stress relaxation for 3100s. Initially, data was

collected at 10Hz for the 10% strain ramp, followed by data acquisition frequency of 1Hz

during stress relaxation. The reaction force, displacement and time were recorded and

used for curve-fitting purposes as discussed below.

Finite Element Analysis

From the measured dimensions of the cylindrical hydrogel samples, axisymmetric

cylindrical models were geometrically created and meshed in FEBio (Musculoskeletal

Research Laboratories, University of Utah, UT), a finite element analysis software

specifically developed for biomechanical applications [165]. Based on a study comparing

different material models for the novel hydrogel [166], the biphasic isotropic elastic material model was concluded to accurately predict the mechanical behavior of the hydrogel under confined and unconfined compression. Biphasic materials are used to model a porous medium consisting of a mixture of a porous, permeable solid matrix and

interstitial fluid. However, the biphasic isotropic elastic material model in FEBio is only

valid for small strains and small rotations; hence, the neo-Hookean material model was

chosen to simulate the unconfined compression stress response of the hydrogel [167]. The

neo-Hookean material is an extension of Hooke’s law for large deformation and is

suitable to use for rubber-like substances and biological tissues. In this material model, 47 the solid matrix is represented by neo-Hookean constitutive material while the liquid

phase is represented by an incompressible fluid. The neo-Hookean material response is

derived from the following hyperelastic strain energy function given as:

= ( 3) + ( ) 2 2 𝜇𝜇 𝜆𝜆 2 𝑊𝑊 𝐼𝐼1 − − 𝜇𝜇 𝑙𝑙𝑙𝑙𝑙𝑙 𝑙𝑙𝑙𝑙𝑙𝑙

Where, I1 is the first invariants of the right Cauchy-Green deformation tensor C, J is the

determinant of the deformation gradient tensor, and are Lamé constants.

𝜇𝜇 𝑎𝑎𝑎𝑎𝑎𝑎 𝜆𝜆 A constitutive relation for the hydraulic permeability of the interstitial fluid

flowing within the porous, deformable solid matrix is given by:

=

𝑤𝑤 −𝑘𝑘 ∇𝑝𝑝 Where, w is the volumetric flux of the fluid relative to the solid, is the interstitial fluid

pressure gradient, and k is the hydraulic permeability tensor. ∇𝑝𝑝

The neo-Hookean material model uses a standard displacement-based element

formulation, which would lead to element locking when modeling materials with nearly

incompressible material behavior. Hence, linear hexahedral elements were used to mesh the cylindrical models. Mesh sensitivity analysis was carried out to determine the optimal number (12,000) of hexahedral elements. The material model was verified by simulating

the confined creep response of articular cartilage under 15kPa compressive stress, and the

results were compared against the experimental data from a study by Boschetti et al.

[168]. 48 For each hydrogel specimen, the unconfined compression was simulated as

described by Mass et al. [165]. The samples were constrained at the bottom and subjected

to 10% strain on the top surface, followed by stress-relaxation. The fluid pressure was

constrained to zero at the outer radial surface. Using the parameter optimization

algorithm in FEBio (Appendix 1), mechanical properties (Young’s Modulus, E; Poisson’s

ratio, v; and permeability, k) of each hydrogel specimen for all formulations were

determined by curve-fitting the experimental load response (Figure 3-1).

Figure 3-1: Curve fitting of unconfined compression reaction load (N) vs. time (s) behavior of hydrogel at 10% strain and during stress-relaxation. The experimental and model data curves overlapped almost exactly with R2 = 0.9993 ± 0.0004 for all formulations.

R2 and normalized root mean square error (NRMSE) between the experimental

and FE model prediction were calculated. Using the following equation, normalized 49 RMSE was calculated as the ratio of the RMSE to the difference between the maximum

and minimum experimental load values.

( , , ) ∑𝑛𝑛 2 𝑖𝑖 𝑥𝑥𝑝𝑝 𝑖𝑖− 𝑥𝑥𝑒𝑒 𝑖𝑖 = � , where n is the total number of values; xp, i are the ( , 𝑛𝑛 , ) 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑥𝑥𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚− 𝑥𝑥𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚 predicted values; and xe, i are the experimental values. xe,max and xe,min are maximum and

minimum experimental values, respectively. One way ANOVA t - test (SPSS 22.0, IBM)

were used to evaluate differences in the swell ratio and mechanical properties between all

the hydrogel specimens of the control and irradiated groups.

Chemical Evaluation

Cylindrical samples, identical to the specimens used for mechanical testing, were

used for chemical characterization. Attenuated total reflectance - Fourier transform infrared spectroscopy (Nicolet Continuum Thermo Fisher Scientific Inc., Waltham, MA) was used for all the specimens (n = 3 per formulation and treatment type). Three randomly chosen sites on each specimen were scanned. Each spectrum was acquired with

64 co-added scans over the spectral region of 450 – 4000 cm-1. The spectra baselines

were normalized and corrected for atmospheric artifacts. Spectra of each formulation and

treatment type were averaged and overlaid for comparison.

Wear Testing

Control, gamma sterilized and electron beam sterilized hemispherical hydrogel

caps (of medium water content formulation) with 0.76 ± 0.10-inch outer diameter, and a

slightly convex articulating surface with 8.0 ± 0.20-inch radius of curvature were used for 50 this part of the study. Using a stainless steel backing pin, hydrogel samples were mounted

on a 6-station Pin-on-Disc tribometer (OrthoPOD, AMTI, Watertown, MA) and

articulated against ceramic discs (Biolox Delta, Ceramtec AG, Germany) with an initial average roughness (Ra) of 8 ± 3 nm. Based on the conclusion of a previous study that

evaluated wear properties of this hydrogel, the material wear is negligible and

undetectable [78]; hence, ceramic discs were intentionally used in an attempt to produce

wear for comparison between sterilized and control samples. Three hemispherical caps

per radiation type were tested, while two hemispherical caps per group were used as

controls to compensate for any lubricant-induced polymer swelling in the tested samples.

The samples were subjected to an elliptical wear pattern under a constant load of 50N,

which corresponded to a maximum contact stress of about 2.5MPa (determined using

pressure film and finite element analysis), with a 10% lift off at the end of each cycle.

Following a 48 hour pre-soak, samples were tested for 2 million cycles (MC) in alpha

calf serum (Wear Testing Fluid, HyClone, Logan, UT; 20g/L protein concentration) used

as a lubricant at 37 ± 0.1°C. At every 0.25MC, each sample was photo-documented using

an optical microscope, and three submerged gravimetric measurements were recorded in

distilled water at 17.8 ± 0.1°C using Archimedes’ basket setup (YDK01 Density kit,

Sartorius Inc., Germany) as previously described [78]. After 2 million cycles of testing in

bovine serum, samples were submerged in distilled water, which was replaced daily, and

left at room temperature to attain weight stabilization for at least 50 days, until the

weights of the samples from two consecutive days did not differ more than 0.1%. The

same samples were then subjected to additional 2MCs of wear testing in ultrapure

distilled water (Direct-Q UV System, Millipore SAS, France). The coefficient of friction 51 was measured on a linear trajectory for all tested samples before dismounting them for interval analysis. At the end of the wear testing, all the samples were desiccated at 95°C for 24 hours, and their dry weight was correlated with the corresponding submerged weight to evaluate the standard error associated with the submerged measurement technique.

The average submerged gravimetric weight was converted into a volumetric loss

(mm3) using individual hydrogel cap volume, which was determined with the help of computer tomography (microCT 80, Scanco Medical, Switzerland). Individual wear rates were calculated using linear regression of the volumetric loss (mm3) at each interval analysis. One way ANOVA t-test (SPSS 22.0, IBM) were used to evaluate differences in wear rates between control and irradiated groups.

Results Material Model Verification

The biphasic neo-Hooken model in FEBio was able to fit the experimental confined creep response of cartilage [168] with 4.5% uncertainty (Figure 3-2). 52

Figure 3-2: Experimental and simulated (E = 0.146 MPa; v = 0.10; and k = 3.8 x 10-14 m4/N.s) strain curves for the confined creep of cartilage.

Mechanical Properties

The water content and equilibrium mechanical properties of all hydrogel formulations are listed in Table 3-1. No significant difference in water content was found between the unsterilized vs. the electron beam or gamma irradiated samples within each formulation (p = 0.339 for low; p = 0.096 for medium; and p = 0.626 for high water content material). The simulated compressive reaction load correlated well with the experimental load response of each specimen (for all specimens: R2 = 0.9993 ± 0.0004).

The normalized RMSE value for each group was found to be within 1% uncertainty: 0.66

± 0.10% for control; 0.69 ± 0.19% for electron beam sterilized; and 0.82 ± 0.63% for gamma sterilized samples. No significant difference was found between the mechanical parameters of unsterilized and sterilized specimens (the range of p values for all formulations were: 0.423 ≤ p ≤ 0.546 for E; 0.141 ≤ p ≤ 0.913 for v; and 0.163 ≤ p ≤

0.977 for k). 53 Table 3-1: Swelling and equilibrium mechanical properties (Mean ± SD) of unsterilized, electron beam and gamma sterilized hydrogel samples.

Hydrogel Specimens (n = 3) Low WC Medium WC High WC Control 43.1 ± 0.9 48.1 ± 1.5 53.7 ± 0.5 Water Content Electron Beam Sterilized 42.6 ± 0.6 46.1 ± 0.2 54.0 ± 0.3 % Gamma Sterilized 42.8 ± 0.6 47.8 ± 0.8 53.8 ± 0.3

Control 32.7 ± 0.0 19.3 ± 0.4 12.7 ± 0.4 Young's Modulus (MPa) Electron Beam Sterilized 33.1 ± 0.4 19.8 ± 0.8 13.4 ± 0.4 Gamma Sterilized 33.2 ± 0.7 17.9 ± 2.8 12.8 ± 1.8 Control 0.06 ± 0.01 0.12 ± 0.01 0.15 ± 0.01 Poisson's Ratio Electron Beam Sterilized 0.07 ± 0.01 0.15 ± 0.03 0.15 ± 0.02 Gamma Sterilized 0.05 ± 0.01 0.10 ± 0.02 0.16 ± 0.03 Control 0.35 ± 0.02 0.40 ± 0.02 0.41 ± 0.02 Permeability (x 10-16 m4/N.s) Electron Beam Sterilized 0.34 ± 0.05 0.33 ± 0.03 0.40 ± 0.04 Gamma Sterilized 0.37 ± 0.02 0.55 ± 0.21 0.45 0.10

Chemical Evaluation

Among the nine groups studied, the chemical spectra did not show any dissimilarity between the absorbance peaks, with one exception. The electron beam sterilized specimens showed an additional peak in 900 – 1150 cm-1 range (Figure 3-3), which was

not present in either unsterilized or gamma sterilized specimens, indicating that the

electron beam sterilization is causing a slight chemical change in the hydrogel. In

addition, on all of the FTIR spectra, a distinct water peak was apparent in the range 3200

– 3800 cm-1; however, a slightly higher water peak was also observed for the electron

beam sterilized sample compared to control and gamma sterilized samples. 54

Figure 3-3: ATR-FTIR spectra (900 – 1200cm-1 range) for control, electron beam (Ebeam) and gamma sterilized hydrogel samples for low, medium and high water content formulations.

Tribological Properties

Wear testing in bovine serum produced burnishing at the contact surface, but hydrogel mold machine marks were still visible in the majority of the specimens after

2MC of testing. However, testing in distilled water for 2MC resulted in adhesive wear at the contact surface as shown in Figure 3-4. 55

Figure 3-4: Optical microscope images (x30) of control (C), electron beam (E), and gamma (G) sterilized hydrogel samples at 0MC, 2MC in bovine serum and 2MC in distilled water.

In bovine serum, load soak-compensated volumetric changes for both control and sterilized hydrogel caps resulted in polymer swelling-related weight gain. On the contrary, wear testing in distilled water resulted in measurable weight loss, as shown in the Figure 3-5. All samples completed 2MC in bovine serum; however, four out of nine specimens (2 control, 1 electron beam, 1 gamma) wore completely through at 400k cycles in distilled water, but the remaining samples completed the 2MC in distilled water.

No significant difference was found between the total volumetric loss (VL) and wear rate

(WR) of control vs. sterilized samples in bovine serum (p = 0.315 for VL; and 0.455 for

WR) and distilled water (p = 0.918 for VL; and 0.713 for WR). Average load soak- 56 compensated volumetric loss and wear rate plots in bovine serum and distilled water are

shown in Figure 3-5. The Pearson’s correlation coefficient between the dry and

submerged weights at the end of testing was 0.998 (p < 0.001, n = 15), which illustrates

that the submerged technique is a reliable method for hydrogel wear quantification.

Figure 3-5: A bar plot with the y-axis representing the total volumetric loss (mm3) and wear rate (mm3/MC) for all wear tested unsterilized and sterilized hydrogel specimens after 2 million cycles in each lubricant.

The coefficient of friction in bovine serum was 0.06 ± 0.01 at 0MC, which increased

to 0.08 ± 0.01 after 2MC (p = 0.005). The weight stabilization of the hydrogels took up to

60 days. The coefficient of friction in distilled water was 0.28 ± 0.20 at 0MC, but it

decreased to 0.10 ± 0.01 for samples that wore at 400k cycles and to 0.11 ± 0.05 for rest

of the samples at 2MC. The difference in coefficient of friction between the same 57 samples tested in bovine serum and distilled water is due to the fluid film formation between the hydrogel and the ceramic surface, which is affected by the lubricant fluid properties.

Discussion

The results of this study suggested that the swell ratio, mechanical strength and the tribological behavior of the proposed hydrogel were insensitive to radiation sterilization. The permeability of this hydrogel remained consistent between the unsterilized and sterilized groups of material. Researchers have previously observed a direct relationship between swell ratio and permeability of thermo-sensitive hydrogels i.e. as the swell ratio decreases, the mobility of the solute gets restricted due to the smaller pore size of the gel network [169]. Thus, the stability of the swell ratio after radiation sterilization implies little change in the permeability for the hydrogel we studied. This observation was supported by the permeability estimates based on mechanical testing results, with a biphasic neo-Hookean material model yielded comparable permeability values for sterilized and unsterilized specimens. A biphasic neo-Hookean material model was sufficient to predict the stress relaxation response of the proposed hydrogel and resulted in less than 1% error; however, simulating the creep response of the articular cartilage yielded ~5% error as discussed in the results section. This error can be attributed to the structural composition of the articular cartilage. The presence of collagen fibers, proteoglycans aggregates, ions, protein molecules and water makes the cartilage matrix a multiphasic fiber-reinforced composite material. Consequently, the mechanical behavior of the tissue is more complex than what can be depicted by a biphasic elastic model [3].

In the present study, the cartilage creep compression results concurred with Boschetti et 58 al. observation that using a constant cartilage permeability, which is known to change

with the strain rates, would not be able to precisely describe the transient response of the

native tissue [168].

The chemical spectra of the hydrogel for unsterilized and gamma sterilized samples did not show any dissimilarity between the peaks that could indicate bonds are

breaking or crosslinking in the polymeric networks. The electron beam sterilized

samples, however, showed an additional peak in the 900 – 1150 cm-1 range for all

formulations. This infrared band could be due to C-O bond stretching, which is known to

produce a strong band in the 1000 – 1300 cm-1 region, C-O-H out-of-plane bending fingerprinted at 930 cm-1 or a combination of both bonds. The creation of C-O-H bonds is

plausible given the excess water within the hydrogel system, but the broadness of the

peak indicates that the formation of C-O bonds is more likely. A third possibility is

aliphatic C-N stretching, which shows a band in 1020 – 1200 cm-1 range [170]. All of

these changes in polymer chemistry would be the consequence of electron beam

radiation, which is known to promote chain scission and crosslinking reactions in

polymers. Findings of our study differ from the results reported in the literature for other

hydrogels. Kanjickal et al. subjected poly (ethylene glycol) hydrogel to 25kGy gamma

irradiation and observed a significant reduction in polymer swelling (p<0.05) as well as a

decrease in surface roughness (p<0.05) [157]. Similarly, alginate showed a decline in hydrogel viscosity at 10kGy and exponential increase in degradation rate in 10-30kGy dose range [158]. Because device sterilization typically employs a dose ranging from 10

to 30kGy [156], the current study subjected the hydrogels to 30-35kGy gamma and

30kGy electron beam radiation. 59 The pin-on-disc wear study produced undetectable wear in control and sterilized

group when tested in bovine serum for 2MC, which is consistent with previously reported

results [78]. However, considerable weight loss was recorded when the samples were

articulated against the same counter-surface in distilled water, which is not a

physiological lubricant. Tao et al. reported similar results, while evaluating the

tribological properties of natural swine joint cartilage on a pin-on-disc tester, that the

coefficient of friction and wear rate decreases from dry friction to distilled water to serum

lubricant [171]. The use of distilled water in this study was mainly to be able to serve as a

positive control since wear was not clearly evident in bovine serum.

A limitation of this study is the sample size (n = 3 per treatment type per

formulation) available for this study. Using the power analysis, it was determined that to

detect a difference of 0.2MPa in mechanical strength or a distinct wear rate differences

between the groups, a significant number of samples (>50) would be required. However,

even if such difference is statistically detected, it may not be sufficient to affect the

overall mechanical performance of the hydrogel or its wear rates in bovine serum, which

is physiologically more relevant lubricant than distilled water.

Conclusion

In this study, a biphasic neo-Hookean material model accurately predicted the

loading behavior of Cyborgel™. Swell ratio and mechanical properties of the hydrogel

were not affected when exposed to the standard sterilization dosage (30-35 kGy) of gamma and electron beam radiation. No chemical crosslinking or bond breaking was detected in gamma-radiated samples, while an unexpected peak was observed in electron beam radiated samples. No detectable change in the tribological properties of this 60 hydrogel was found when tested in a physiologically appropriate lubricant such as bovine serum. In distilled water, however, differences in wear rate were detectable, which could be either due to the lubricant effect or additional wear testing of the samples. Hence, it can be concluded that neither sterilization method induced severe changes in mechanical, chemical and tribological properties of Cyborgel™; however, chemical spectra of electron beam presented minor discrepancies. Therefore, gamma sterilization is a preferable method for Cyborgel™ sterilization. 61 Chapter 4 : Effect of Conformity, Thickness and Material Properties on the Contact Mechanics of Compliant Polymeric Materials for Use in Knee Arthroplasty

Abstract

Current materials used in total knee arthroplasty lack the surface and mechanical properties of the native cartilage leading to excessive implant wear in vivo. In this study, polycarbonate urethane and a novel hydrogel were investigated as alternative compliant materials for use in knee arthroplasty. A simplified, axisymmetric, finite element (FE) model of the medial knee compartment was developed and validated, and a design of experiments was carried out to evaluate the effect of implant conformity, implant thickness and material properties on the contact mechanics of compliant knee implant under normal walking and stair climbing loads. All input parameters, namely, implant conformity, implant thickness and material properties, significantly (p<0.001) affected the resulting maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and maximum contact area.

However, the conformity had the highest effect-size on the contact mechanics. The maximum principal stress value halves and the contact area doubles when ≥ 95% implant conformity and ≥ 3mm thickness was used. The Von Mises and maximum shear stress also decreased over 95% conformity for all implant thicknesses. Based on these results, the optimal parameters would be ≥ 95% implant conformity with ≥ 3mm thickness, which is the average thickness of articular cartilage in the human joint. Overall, a highly congruent and deformable implant has the potential for use in knee cartilage replacement. 62 Introduction

Osteoarthritis (OA) is a degenerative joint disease and is one of the leading causes

of pain and locomotor disability worldwide. OA of the knee is commonly treated by total knee arthroplasty [7] with more than 650,000 total knee replacements conducted in the

USA in 2008; more than 77,500 performed in the UK in 2009, and 103,601 done in South

Korea between 2002 and 2005 [15]. These numbers are expected to grow 673% by the

year 2030 [16]. Currently, the most common knee arthroplasty components are fabricated

from metallic alloys, ceramics, and ultra-high molecular weight polyethylene

(UHMWPE) [30]. However, UHMWPE and metallic components are much stiffer

compared to cartilage and lack the shock absorption, lubrication and deformation properties of the native tissue. Consequently, use of such arthroplasty materials leads to bone stress shielding [172] and generates wear debris [173]. Investigation of compliant

materials with lower strength, cartilage-like mechanical properties (10-20MPa) [174], and

minimum wear rates is needed to address these issues.

Polycarbonate urethane and hydrogel are two such alternative bio-compliant

materials. Polycarbonate urethane (PCU) was developed specifically to prevent cracking

and degradation in long-term implants for orthopedic applications. PCU has exhibited a

tensile modulus similar to cartilage [42], and a compressive modulus of 20MPa, which is

comparable to 5-19MPa instantaneous compressive modulus of the cartilage [43]. A wear

study of PCU acetabular cups for 5 million cycles (MC) yielded 24% less wear with an

average material loss of 19.1mm3/MC for PCU as compared to 25mm3/MC for crosslinked UHMWPE cups (50kGy irradiated) [46]. Another study for 20MC found even lower volumetric wear rate of 5.8 – 7.7 mm3/MC and a low particle generation rate of 2-3 63 x 106 particles/MC for PCU compared to 25 x 1012 particles/MC for UHMWPE [47, 48].

In the knee joint, a PCU meniscal implant tested for 5MC under ISO gait loading

conditions resulted in an average wear rate of 14.5mg/MC [52].

Hydrogels, on the other hand, are hydrophilic polymer networks that swell in water and can be tailored to attain desired mechanical properties for a range of biomedical applications, such as contact lens, drug delivery devices as well as a scaffold

for tissue engineering. Due to their ability to store water, and cartilage-like mechanical

and lubrication properties [57], hydrogels are an attractive candidate for use in

orthopedics from treating focal lesions to load-bearing applications [58-60]. Cyborgel™, a proprietary hydrogel being investigated in this work, is intended for use in a cartilage replacement implant. Its bulk material properties have been previously reported as an aggregate modulus of 5.6 MPa and permeability of 0.029 x 10-14 m4/N.s (cartilage range:

aggregate modulus - 0.54 - 0.70 MPa; permeability - 0.006 – 0.76 x 10-14 m4/N.s [3, 75,

76]). It has been reported to produce a low coefficient of friction of 0.03 on a pin-on-disk

tester [74] compared to 0.014 for articular cartilage [77]. Furthermore, a wear study of

Cyborgel-against-Cyborgel configuration on a pin-on-disc tester for 5MC reported wear rates of -1.4 ± 8.3 and 6.6 ± 35.3 mm3/MC based on in-water and in-air measurements,

respectively [78]. Another study of Cyborgel-on-ceramic configuration for 2MC also reported similar results [175]. Hence, polycarbonate urethane and the novel hydrogel are

promising candidates for use as compliant arthroplasty materials and further investigation

of their performance under physiological loading conditions is warranted.

The knee is one of the most complex joints in the body with a variety of bones,

ligaments, and soft tissues. It experiences six degrees of freedom with a series of forces, 64 displacements, and torques acting upon it. Therefore, developing an effective knee

implant requires a thorough understanding of the joint mechanics. Contact mechanics of a

knee replacement device are affected by a variety of factors, such as implant geometry,

thickness, material properties and loading conditions [90, 91]. Polyethylene implants have

been investigated since the 1980s to determine the optimal design parameters for achieving minimal wear and preventing implant failure in the body [90, 91, 103, 107, 176].

Compliant materials, such as polyurethane (PU), polycarbonate urethane (PCU) and

hydrogels, have been recently investigated for optimal designing of a knee implant. Choh

et al. compared uni-compartmental knee spacer made of cobalt-chromium, UHMWPE,

and polyurethane, and evaluated the spacers design contours (conventional, flat and C-

shaped) using a static finite element model of a knee in full extension and at 90-degree

flexion [113]. The results concluded that the polyurethane spacers exerted the least contact pressure onto the femur cartilage, with the C-shaped spacer exhibited the lowest pressure in full extension, and the conventional spacer had the lowest contact pressure at

90-degree knee flexion. This study suggested that the knee spacers made out of softer

material and higher conformity can better withstand the joint forces in various motions.

Several other experimental and simulation studies have also been carried out to

understand the influence of different parameters on polyurethane knee implants [109, 112,

114]. The tribological and lubrication properties of 8mm thick PCU unicondylar knee

prostheses were also investigated against a cobalt-chromium-molybdenum (CoCrMo) femoral component [116]. The average PCU wear rate of less than 1mm3/MC was found

in the wear study, and the friction coefficient was observed between 0.004 - 0.1.

Additionally, polycarbonate urethane has also been used for a meniscus implant design 65 optimization using finite element modeling [117]. Suciu et al. tested the durability of polyvinyl alcohol (PVA) hydrogel knee prostheses under simulated anterior-posterior displacement during walking [118]. The study investigated the effect of thickness and

water content on the wear factor of the hydrogel after 100,000 gait cycles against the

metal femoral component. PVA hydrogel with 45 – 50% water content produced the

lowest wear factor, and since the PVA hydrogel is a poroelastic-hydrated material, a

thicker gel layer (from 2 to 3.6 mm) produced lower wear factor due to longer fluid

pressurization and lower friction force on the solid matrix.

To fully comprehend the wear and failure mechanisms of an implant design, it

needs to be tested on a mechanical simulator, which can precisely reproduce

physiological loads as well as translational and rotational motions of the joint. However,

repetitive knee simulator studies are exceptionally time and cost prohibitive; therefore,

alternative methods such as mathematical modeling or finite element analysis (FEA) are

employed to evaluate the implant’s performance. A well-known theoretical method is the

Hertz theory of elastic contact [177], although it is not a good approximation of the knee

contact mechanics for a few reasons. First, Hertz theory assumes contact occurring

between two elastic spheres and that the contact area between the two is small. This

assumption does not hold true for a normal knee, and would not be true for compliant

materials due to their high compressibility creating large contact area. Second, Hertz

theory assumes bodies of semi-infinite thickness, an unrealistic posit for hydrogels and

polyurethane carbonate with definite size and dimension. Finite element analysis, on the

other hand, has proven to be a more reliable and efficient tool for simulating in vivo joint

biomechanics [101]. Understanding the contact mechanics of any new arthroplasty 66 material under the physiological condition is essential to predict its performance in vivo,

and this can be effectively and efficiently achieved with the help of FEA.

Therefore, the objective of this study is to develop and validate a finite element

medial-compartment knee model, which can be used to evaluate the performance of compliant materials under physiological loads. Using the validated model, the contact

mechanics of the compliant-on-compliant knee implant were investigated by varying the

implant thickness, femoral-tibial conformity, and mechanical properties under

physiological loads for normal walking and stair climbing. This parametric modeling will

help in understanding the correlation between the implant conformity or thickness and the

contact parameters of a compliant material knee implant. This knowledge will be useful

in defining a niche design space for feasible use of compliant polymeric bearing materials

in knee applications.

Materials & Method

Three different formulations, with varying water content (HG43, HG48 and

HG53), of a proprietary hydrogel (CyborGel™, Formae Inc., Paoli, PA), and two

formulations of medical grade polycarbonate urethane (PCU Bionate 80A I and II, DSM

Medical, Berkeley, CA) with an average molecular weight around 150,000 – 200,000

g/mol were tested and modelled in this study.

Mechanical Testing

For uniaxial tension test, dog-bone samples for all formulations of both the

materials were dimensioned and tested as per the ASTM D638 - Standard Test Method

for Tensile Properties of Plastics. Tensile test to failure was performed on a universal 67 mechanical tester (Criterion, MTS Systems Corp., Eden Prairie, MN). As per ASTM-

D638 recommendations, all of the samples (n = 5 for each formulation) were pre- conditioned for 20 loading-unloading cycles to 1% strain and then were tested at three different crosshead speeds of 30, 75 and 150 mm/min as previously reported in the literature [132]. Axial and transverse strains were measured using a non-contacting video extensometer (Zwick-Roell Video Extensometer System, Kennesaw, GA). A total of 75 specimens were tested (5 samples per formulation x 5 materials x 3 crosshead speeds).

Young’s modulus and Poisson’s ratio were calculated over the elastic region of the stress-

strain curve, and the ultimate stress and elongation were recorded at failure.

Model Construction and Validation

This study modeled the medial compartment of the knee due to its larger anatomical size compared to the lateral compartment [178], and because it carries about

60% of the total joint load [179]. A simplified, axisymmetric, three-dimensional model of the articulating surfaces of the medial knee compartment (right femur, tibia and articulating cartilage) was constructed in SolidWorks (2015, Dassault Systems, Forest

Hill, MD). The radii of curvature of a natural knee joint were recreated based on the

findings of a previously reported study [178], in which the radius of curvature of the

femoral or tibial surface is defined as the circular profile tangential to the junction of two contacting cartilage surfaces of an extended knee. Following mesh sensitivity analysis, all the components were meshed with 8-node hexahedral elements of size 0.6mm in Abaqus

(V6.4.1, Dassault Systems Simulia Corp, Forest Hill, MD). Using FEBio

(Musculoskeletal Research Laboratories, University of Utah, UT) [165], the femur and

tibia were modeled as rigid bodies, while the articulating cartilage surfaces were assigned 68 neo-Hookean material properties with Young’s modulus (E) = 12MPa and Poisson’s ratio

(v) = 0.45 [180, 181] for model validation. A flowchart of the FE model development is

shown in Figure 4-1.

Figure 4-1: A three-dimensional, axisymmetric medial knee model was created in SolidWorks using the radii of curvature from the literature [178], followed by meshing in Abaqus. The material properties, as well as boundary, contact and loading conditions, were assigned in FEBio.

The lateral and radial displacements of the femoral and tibial cartilage were

restricted at the center but the components were free to expand towards the outer edges.

The femoral and the tibial cartilage were fixed to the femur and tibia, respectively, and 69 were in a frictionless sliding contact with each other. The material model and the mesh

density were validated using a cadaveric study [182], in which the entire knee joint was

subjected to axial loads of 200N, 500N, 1000N and 1500N in full extension, and the

resulting contact areas and average contact pressures were reported. Since the medial

knee compartment bears 60% of the total load and the model was axisymmetric, only a

quarter of these loads were applied in the current study.

Parametric Modeling

Once the model was validated (as discussed in the results section), a parametric

evaluation was carried out with the following variables: i) Material property - three

formulations of hydrogel (HG43, HG48 and HG53) and two formulations of

polycarbonate urethane (Bionate I and II); ii) Implant thickness - 2, 3 and 4 mm; and (iii)

Implant conformity - 90, 95 and 99% conformance between the radius of curvature of

femoral condyles (constant) and tibial plateau (varied). The average Young’s modulus

and Poisson’s ratio determined from the tensile test were used as the material property

input for both the hydrogel and polycarbonate urethane. Implant thickness is defined as

the thickness of compliant materials on either side of the contact junction. The range for

implant thickness was chosen based on the average femoral and tibial cartilage in the

human knee joint [183, 184]. Implant conformity is defined as a ratio of Rf to Rt where Rf

and Rt are the femoral and tibial radii of curvature, respectively. The range for implant

conformity was chosen to mimic the natural synovial joint conformance achieved in the presence of articular cartilage and the menisci. Additionally, previous literature has

suggested that the effect of increasing conformity ratio on the reduction of contact

stresses was more pronounced for conformity above 80% [185]. 70 Two loading conditions were axially applied to the model such as (i) a quarter of

the ISO recommended medial compartment normal gait load (60% of 2400N); and (ii) a

quarter of the medial compartment stair-climbing load (60% of 5200N). The simulation

results were recorded in terms of the maximum principal stress (MPa), Von Mises stress

(MPa), maximum shear stress (MPa), maximum principal strain, maximum contact

pressure (MPa) and maximum contact area (mm2). A total of 90 scenarios were simulated

(5 material formulations x 3 implant conformities x 3 implant thicknesses x 2 loading conditions) to determine the effect of implant design parameters on the contact mechanics of compliant polymeric implant for use in knee arthroplasty.

The correlation between implant conformity as well as implant thickness and the contact parameters were also evaluated using linear regression analysis and Pearson’s correlation (SPSS 24.0, IBM). Additionally, a full-factorial statistical analysis was conducted using ANOVA (Minitab 17, State College, PA) to determine which input parameters, namely implant conformity, implant thickness and material strength, significantly affects the outputs, namely maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and maximum contact area. In this design of experiment study, the effect size, which is the impact of design factors on the output variables, was evaluated by taking a ratio of each effect variance to the total variance.

Results Mechanical Testing

Both the hydrogel and polycarbonate urethane showed ductile mechanical

behavior under tension with the linear range between 15 – 20% strain for various 71 formulations. With an assumption of isotropic linear elasticity, Young’s modulus and

Poisson’s ratio of different hydrogel and polycarbonate urethane formulations were calculated over the 10% strain region, while the ultimate tensile strength and elongation were reported at failure. No significant differences (p>0.05) were found in Young’s modulus, Poisson’s ratio, ultimate strength, or elongation within each formulation of the hydrogel and polycarbonate urethane at different crosshead speeds. All the test results were averaged and listed in Table 4-1.

Table 4-1: Summary of the average mechanical properties of different formulations of hydrogel and polycarbonate urethane under uniaxial tension.

Uniaxial Tensile Properties

Formulation Young’s Modulus Poisson’s ratio Ultimate Stress Elongation E (MPa) ν (MPa) (mm/mm)

Bionate I 13.9 ± 1.5 0.47 ± 0.02 57.9 ± 5.9 7.5 ± 2.7 Bionate II 18.5 ± 1.1 0.46 ± 0.02 62.1 ± 4.0 6.9 ± 1.6 HG43 17.4 ± 2.6 0.48 ± 0.06 7.7 ± 0.7 2.4 ± 0.7 HG48 8.4 ± 1.2 0.47 ± 0.06 5.7 ± 0.5 3.0 ± 1.1 HG53 4.7 ± 0.5 0.46 ± 0.03 4.8 ± 0.5 3.7 ± 0.9

Model Validation

As shown in Figure 4-2, the FEM predicted medial contact area and average contact stress of the cartilage surfaces were within one standard deviation (error bars) of the reported values from the cadaveric study by Fukubayashi et al. and Kurosawa et al.

The error in the model prediction was 10.9 ± 11.5% for medial contact area and 3.3 ±

1.9% for average medial contact stress. 72 400 3.5 Fukubayashi 1980 Kurosawa 1980

) 2 350 FEM 3 FE Model

300 2.5

250 2 (MPa)

200 Average Stress Contact 1.5

-

150 1 Medial Contact Area (mm Medial 100 0.5 0 500 1000 0 500 1000 1500 Applied Load (N) Applied Load (N) Figure 4-2: Medial knee FEM validation using the medial contact area (mm2) and average medial contact stress (MPa) of the knee joint (without menisci) under different axial loads as reported by Fukubayashi et al. and Kurosawa et al. [182]. The error bar represents one standard deviation of the reported cadaveric study results.

Parametric Evaluation

A visual representation of the changes in the maximum principal stress, maximum contact area and von Mises stress with an increase in implant thickness and conformity for hydrogel HG48 formulation is illustrated in Figure 4-3. As thickness and conformity

increased, there is a substantial decrease in the maximum principal stress, and increase in the contact patch between the two articulating surfaces. Similarly, a decline of the Von

Mises stresses is apparent with an increase in the implant conformity. The stress concentrated at the femoral bone and femoral component junction at 90% conformity, which dissipated radially with an increase in conformance. However, the effect of an increase in the implant thickness on the Von Mises stresses is not as distinct. Similar stress patterns were observed among all the formulations of both the materials.

73

Figure 4-3: Visual representation of maximum principal stress (MPa) and maximum contact area (mm2) (top) and Von Mises stress (MPa) (bottom) for HG48 hydrogel formulation at varying implant thickness and conformity under normal walking load.

74 The effects of implant conformity on the Von Mises stress and maximum shear stress

were further evaluated at the polymer and substrate junction for both loading conditions as shown in Figure 4-4. For a 3mm thick Bionate I implant design, both the stress distributions shift from the central axis of the implant loading towards the outer edge as the conformity increases from 90 to 99%. The Von Mises stress is mainly concentrated at the junction of the contacting surfaces for both 90 and 95% conforming implants.

However, for the 99% implant conformity, the stress disseminates out and concentrates towards the outer edge of the polymer-substrate junction. The maximum shear stress demonstrated similar behavior but at a lower magnitude as compared to the Von Mises stress.

The model predictions of the compliant polymer-against-compliant polymer configuration for both hydrogel and polycarbonate urethane formulations were recorded in Table 4-2 and Table 4-3, for normal walking and stair climbing loads. For both the loading conditions, the maximum principal stress ranged from 1.7 – 10.5MPa for hydrogel and 1.9 – 9.7MPa for polycarbonate urethane; the Von Mises stress ranged between 0.5 – 2.8MPa for hydrogel and 0.5 - 2.6MPa for polycarbonate urethane; the maximum shear stress ranged between 0.3 – 1.7MPa for hydrogel and 0.3 – 1.5MPa for polycarbonate urethane; the maximum principal strain ranged between 0.04 –

0.34(mm/mm) for hydrogel, and 0.04 – 0.15(mm/mm) for polycarbonate urethane; the maximum contact pressure ranged between 1.6 – 10.9MPa for hydrogel, and 1.9 –

9.9MPa for polycarbonate urethane; and the maximum contact area ranged between 139

– 592mm2 for hydrogel, and 152 – 546mm2 for polycarbonate urethane. Therefore, the

resultant stresses and contact area range for three hydrogel formulations and two 75 polycarbonate urethane formulations are quite similar, except that the higher water content hydrogels are more deformable under a given load than the urethanes. All the contact stresses and strains are graphically represented in Figure 4-5 using box plots. The error bars of the box plots represent the range of each parameter for a given material at various implant conformity and thickness.

Figure 4-4: Effect of conformity on the Von Mises and maximum shear stress of a 3mm thick Bionate I implant under normal walking and stair climbing loads. 76 Table 4-2: Simulated stresses, strain and contact area results for a combination of implant design parameters under normal walking load (2400N).

Max Von Max Max Max Max Principal Mises Shear Principal Contact Contact (%)

(mm) Stress Stress Stress Strain Stress Area

Material 2 Thickness Thickness

Conformity (MPa) (MPa) (MPa) (mm/mm) (MPa) (mm ) 90 6.05 1.62 0.93 0.10 6.14 164 2 95 4.52 1.01 0.63 0.08 4.58 219

99 2.49 0.52 0.30 0.04 2.46 420 90 4.59 1.64 0.94 0.10 4.69 211 3 95 3.50 1.18 0.68 0.08 3.56 280 99 2.06 0.74 0.42 0.05 2.06 492 Bionate I 90 3.89 1.66 0.96 0.10 3.99 247 4 95 3.00 1.23 0.71 0.08 3.02 327 99 1.94 0.96 0.55 0.06 1.91 522 90 6.41 1.75 1.00 0.09 6.44 152 2 95 4.75 1.17 0.67 0.07 4.78 205

99 2.57 0.55 0.32 0.04 2.52 403 90 4.92 1.78 1.02 0.09 4.97 194 3 95 3.73 1.27 0.73 0.06 3.76 259 99 2.13 0.71 0.41 0.04 2.12 473 Bionate II 90 4.21 1.81 1.04 0.09 4.25 226 4 95 3.22 1.33 0.77 0.07 3.20 303 99 2.00 0.93 0.54 0.05 1.95 512 90 6.95 1.95 1.12 0.10 7.08 139 2 95 5.26 1.34 0.77 0.07 5.33 188 99 2.91 0.64 0.37 0.04 2.87 361 90 5.19 1.91 1.10 0.09 5.30 184 3 95 3.98 1.41 0.81 0.07 4.05 243 HG43 99 2.31 0.69 0.40 0.04 2.31 443 90 4.35 1.91 1.10 0.09 4.46 218 4 95 3.36 1.42 0.82 0.07 3.38 289 99 2.10 0.95 0.55 0.05 2.07 495 90 5.26 1.34 0.77 0.13 5.42 192 2 95 3.80 0.88 0.50 0.10 3.82 277 99 2.15 0.50 0.29 0.05 2.12 489 90 3.87 1.31 0.75 0.13 3.98 260 3 95 2.94 0.94 0.54 0.10 3.02 343 HG48 99 1.85 0.79 0.45 0.06 1.86 537 90 3.25 1.34 0.78 0.14 3.40 304 4 95 2.56 1.01 0.58 0.10 2.61 394 99 1.79 0.97 0.56 0.10 1.78 541

77 Table 4-2: contd.

Max Von Max Max Max Max Principal Mises Shear Principal Contact Contact (%)

(mm) Stress Stress Stress Strain Stress Area

Material 2 Thickness Thickness

Conformity (MPa) (MPa) (MPa) (mm/mm) (MPa) (mm ) 90 4.12 1.05 0.59 0.22 4.00 325 2 95 3.15 0.64 0.36 0.15 3.12 375 99 1.85 0.59 0.35 0.09 1.80 550 90 3.50 0.98 0.57 0.19 3.21 350 3 95 2.35 0.70 0.40 0.13 2.45 410 HG53 99 1.66 0.81 0.47 0.14 1.68 559 90 2.60 1.10 0.64 0.19 2.90 440 4 95 2.15 0.86 0.50 0.14 2.21 490 99 1.87 0.95 0.55 0.16 1.61 562

Table 4-3: Simulated stresses, strain and contact area results for a combination of implant design parameters under stair climbing load (5200N).

Max Von Max Max Max Max Principal Mises Shear Principal Contact Contact (%)

(mm) Stress Stress Stress Strain Stress Area

Material 2 Thickness

Conformity (MPa) (MPa) (MPa) (mm/mm) (MPa) (mm ) 90 9.50 2.30 1.31 0.15 9.75 206 2 95 7.40 1.64 0.95 0.12 7.63 299

99 4.00 1.03 0.59 0.06 3.96 511 90 7.10 2.36 1.38 0.14 7.30 274 3 95 5.42 1.70 0.98 0.11 5.58 367 99 3.50 1.55 0.90 0.09 3.53 543 Bionate I 90 6.03 2.48 1.45 0.14 6.35 316 4 95 4.75 1.85 1.07 0.11 4.86 418 99 3.53 1.90 1.10 0.11 3.41 546 90 9.70 2.42 1.39 0.13 9.98 196 2 95 7.21 1.64 0.94 0.10 7.33 271

99 4.08 1.00 0.58 0.05 4.03 497 90 7.55 2.53 1.46 0.12 7.68 256 3 95 5.72 1.81 1.04 0.09 5.84 342 99 3.57 1.53 0.88 0.07 3.57 537 Bionate II 90 6.40 2.63 1.52 0.12 6.80 292 4 95 5.02 1.97 1.13 0.09 5.08 389 99 3.48 1.86 1.07 0.09 3.43 543

78 Table 4-3: contd.

Max Von Max Max Max Max Principal Mises Shear Principal Contact Contact (%)

(mm) Stress Stress Stress Strain Stress Area

Material 2 Thickness Thickness

Conformity (MPa) (MPa) (MPa) (mm/mm) (MPa) (mm ) 90 10.50 2.76 1.60 0.13 10.90 181 2 95 8.02 1.90 1.10 0.09 8.23 246 99 4.57 0.93 0.53 0.05 4.52 455 90 7.93 2.76 1.59 0.13 8.26 243 3 95 6.15 2.01 1.16 0.10 6.33 318 HG43 99 3.82 1.50 0.86 0.07 3.84 521 90 6.60 2.80 1.65 0.13 7.10 279 4 95 5.25 2.12 1.22 0.10 5.37 372 99 3.61 1.92 1.11 0.09 3.60 536 90 8.75 2.10 1.20 0.20 8.90 248 2 95 6.25 1.37 0.78 0.15 6.50 355 99 3.60 1.15 0.65 0.11 3.58 549 90 6.20 2.00 1.15 0.19 6.40 316 3 95 4.75 1.38 0.80 0.14 4.75 421 HG48 99 3.28 1.60 0.93 0.14 3.40 577 90 5.60 2.15 1.25 0.20 5.75 360 4 95 3.80 1.35 0.80 0.22 4.34 472 99 3.63 1.89 1.09 0.17 3.31 581 90 7.50 1.70 0.93 0.34 7.40 381 2 95 5.40 1.12 0.65 0.26 5.70 453 99 3.35 1.26 0.74 0.21 3.25 580 90 6.30 2.05 1.15 0.32 5.74 406 3 95 4.20 1.20 0.66 0.23 4.25 488 HG53 99 3.10 1.60 0.92 0.24 3.20 589 90 4.80 1.80 1.00 0.28 4.90 496 4 95 3.80 1.33 0.83 0.23 3.83 568 99 3.75 1.88 1.08 0.28 3.10 592

79

Figure 4-5: Medial knee finite element model prediction of maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and maximum contact area for different formulations of hydrogel and polycarbonate urethane under normal walking and stair climbing loads. The error bars represent the range of each parameter for a given material at various implant conformity and thickness. 80 The linear regression and Pearson’s correlation results for the increase in implant

conformity and implant thickness on the contact parameters are listed in Table 4-4. The

results show that for both the loading conditions, the implant conformity is significantly

(p<0.001) linearly correlated to the contact parameters; however, the linear dependence of the contact parameters on the implant thickness is not consistently observed.

Table 4-4: The correlations between an increase in implant conformity as well as thickness and the stresses, strain and contact area under different loading conditions.

Normal Walking Stair Climbing Contact Parameters Increase in Increase in Increase in Increase in Implant Implant Implant Implant Conformity Thickness Conformity Thickness Maximum Decrease Decrease Decrease Decrease Principal (r = -0.762; (r = -0.408; (r = -0.787; (r = -0.423; Stress (MPa) p<0.001) p=0.005) p<0.001) p=0.004)

Decrease No correlation Decrease Increase Von Mises (r = -0.791; (r = 0.192; (r = -0.700; (r = 0.313; Stress (MPa) p<0.001) p=0.207) p<0.001) p=0.036) Maximum Decrease No correlation Decrease Increase Shear Stress (r = -0.789; (r = 0.195; (r = -0.688; (r = 0.329; (MPa) p<0.001) p=0.199) p<0.001) p=0.027) Maximum Decrease No correlation Decrease No correlation Principal (r = -0.538; (r = 0.077; (r = -0.343; (r = 0.080; Strain p<0.001) p=0.617) p=0.021) p=0.600) Maximum Decrease Decrease Decrease Decrease Contact (r = -0.772; (r = -0.392; (r = -0.795; (r = -0.409; Pressure p<0.001) p=0.008) p<0.001) p=0.005) (MPa) Maximum Increase Increase Increase No correlation Contact Area (r = 0.775; (r = 0.297; (r = 0.799; (r = 0.291; (mm2) p<0.001) p=0.047) p<0.001) p=0.053) 81 The increase in implant conformity had an inverse effect on the contact stresses

and strain, and a direct effect on the contact area for both the loading conditions. Upon

increasing the implant thickness, the maximum principal stress and maximum contact

pressure showed negative correlation and maximum contact area demonstrated positive

correlation under the normal walking condition; rest of the contact parameters did not

show any significant correlation with the changes in implant thickness. However, at a

higher load for stair climbing, the Von Mises and maximum shear stress also showed a

positive correlation to changes in implant thickness, while the maximum contact area was

not significantly affected. Maximum principal strain exhibited no significant correlation

with the increase in implant thickness for both the loads. Based on these results, it can be

deduced that increasing the implant conformity is advantageous in reducing the contact

stresses and increasing the contact area under both normal and vigorous activity.

Increasing the implant thickness only correlated well with a decrease in maximum

principal stress and maximum contact pressure for both loading condition; however, the overall correlation between the implant thickness and the contact mechanics parameters was not as consistent.

For further statistical evaluation, ANOVA was used to analyze the effect of each factor on the outcome variables. A full factorial design of experiments analysis was carried out to check for the sensitivity of the contact parameters to the changes in the implant design factors such as conformity, thickness, and material properties. The main effect of each implant design factor was statistically significant (p<0.001) for all the contact parameters under both normal walking load as well as stair climbing load. A majority of the two-way interactions between these design factors also showed 82 significance (p<0.05), except material and thickness interaction. However, the full three- way interaction between these factors did not have a statistically significant effect on the contact mechanics under both loading conditions. The effect size i.e. the percent impact of the main factors and factors-interactions on the output variables was also calculated and those percentages are plotted in Figure 4-6. Five out of the six output variables are majorly impacted by the implant conformity, followed by either implant thickness or material properties as the secondary influencer. The maximum principal strain was the only contact parameter that was affected largely by the material properties, followed by implant conformity.

Figure 4-6: The percent effect size of the implant design factors (main and 2-way interactions) on various contact mechanics outputs. 83 By combining the stresses, strain and contact area results for all the materials, interpolative contour plots were created to see the effects of conformity and thickness, simultaneously, on each contact mechanic parameter in Figure 4-7.

Contour Plot of Maximum Principal Stress vs Conformity, Thickness Contour Plot of Von Mises Stress vs Conformity, Thickness

99 99 Maximum Von Mises Principal Stress 98 Stress 98 < 0.60 < 2.0 0.60 – 0.75 97 2.0 – 2.5 97 0.75 – 0.90 2.5 – 3.0 0.90 – 1.05 96 3.0 – 3.5 96 1.05 – 1.20 y y 3.5 – 4.0 1.20 – 1.35 t t i i 95 4.0 – 4.5 95 1.35 – 1.50 m m r r 4.5 – 5.0 1.50 – 1.65 o o f f 5.0 – 5.5 1.65 – 1.80 n n 94 94 o 5.5 – 6.0 o 1.80 – 1.95

C 6.0 – 6.5 C > 1.95 93 > 6.5 93

92 92

91 91

90 90 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 Thickness Thickness

Contour Plot of Maximum Shear Stress vs Conformity, Thickness Contour Plot of Maximum Principal Strain vs Conformity, Thickness

99 99 Maximum Maximum Shear Stress Principal 98 < 0.35 98 Strain 0.35 – 0.43 < 0.04 97 0.43 – 0.51 97 0.04 – 0.06 0.51 – 0.59 0.06 – 0.08 96 0.59 – 0.67 96 0.08 – 0.10

y 0.67 – 0.75 y 0.10 – 0.12 t t i i 95 0.75 – 0.83 95 0.12 – 0.14 m m r r 0.83 – 0.91 0.14 – 0.16 o o f f 0.91 – 0.99 0.16 – 0.18 n n 94 94 o o 0.99 – 1.07 0.18 – 0.20 C C > 1.07 0.20 – 0.22 93 93 > 0.22

92 92

91 91

90 90 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 Thickness Thickness

Contour Plot of Maximum Contact Stress vs Conformity, Thickness Contour Plot of Maximum Contact Area vs Conformity, Thickness

99 99 Maximum Maximum Contact Contact 98 Stress 98 Area < 2.1 < 170 97 2.1 – 2.6 97 170 – 210 2.6 – 3.1 210 – 250 96 3.1 – 3.6 96 250 – 290 y y 3.6 – 4.1 290 – 330 t t i i 95 4.1 – 4.6 95 330 – 370 m m

r 4.6 – 5.1 r 370 – 410 o o

f 5.1 – 5.6 f 410 – 450 n 94 n 94 o 5.6 – 6.1 o 450 – 490 C 6.1 – 6.6 C 490 – 530 93 > 6.6 93 > 530

92 92

91 91

90 90 2.0 2.5 3.0 3.5 4.0 2.0 2.5 3.0 3.5 4.0 Thickness Thickness

Figure 4-7: Plots of implant conformity vs. thickness vs. different contact mechanic parameters under normal walking load to evaluate the optimal design space for compliant bearing materials.

84 Although 2mm implant thickness has shown lower stresses and high

deformability during gait as compared to the UHMWPE, it may be functioning beyond

the material yield limits and at a higher risk of failing under vigorous activities.

Therefore, greater than or equal to 3mm thickness is recommended, which is closer to the

average cartilage thickness in the natural knee joint [183, 184]. Additionally, for all the materials, the highest stresses corresponded to 90% conformity; therefore, this study does not recommend using those implant design parameters. The maximum principal stress value halves and the contact area doubles when ≥ 95% implant conformity and ≥ 3mm thickness is used. The Von Mises and maximum shear stress also decreased over 95% conformity for all implant thicknesses. Based on these results, the optimal parameters would be ≥ 95% implant conformity with ≥ 3mm thickness, which is the average thickness of articular cartilage in the human joint.

Discussion

The primary aim of this study was to evaluate the influence of implant design

factors on the overall contact mechanics of a potential compliant material knee implant.

The model was successfully developed and validated with about 10% error from the reported empirical test results, which can be attributed to patient factors, such as age, gender, weight, and race. The parametric model results confirmed that the contact mechanics of the medial knee joint were sensitive to all the implant design factors such as thickness, conformity, and material properties under physiological loads for normal walking and stair climbing. 85 The current study suggests that the use of compliant materials in a knee implant is plausible for a highly congruent implant design with lower cartilage-like thickness. The results of this study are similar to those using the ultra-high molecular weight polyethylene [90, 91, 185], which identified implant conformity and thickness to play a major role in the knee implant design performance and survival. Due to the mechanical and wear properties of the polyethylene, however, a minimum of 8mm implant thickness has been suggested in the previous literature [90, 91, 186] to prevent excessive implant wear. Unlike UHMWPE, hydrogels and polycarbonate urethane are lubricious materials with reports of reduced or minimal wear in vitro due to their superior lubrication properties. Using a compliant implant material offers the advantage of keeping the overall implant thickness to the minimal, thus preventing excessive patient bone resection. The reduced thickness of the compliant material implant is compensated by the high deformability of the material, and close to full femoral-tibial geometric conformity.

Due to high implant conformity, the resulting increase in the contact patch and lower maximum contact pressure are instrumental in improving the lubrication film thickness at the joint, which in turn minimizes the implant wear [50]. Furthermore, the mechanical failure of a ductile material is governed by the Von Mises stress and the maximum shear stress according to the distortion of energy and Tresca failure theory, respectively. The

Von Mises stress and maximum shear stress in this study ranged between 0.5 to 2.5MPa, which is quite low compared to the values (5-10MPa maximum shear stress) reported by

Bartel et al. for polyethylene [90]. Both the hydrogel and polycarbonate urethane have shown high deformability and lower wear rates as compared to the UHMWPE, which is 86 prone to oxidization in vivo and generation of wear debris leading to implant loosening and osteolysis.

Implant design parameters should be selected by considering vigorous activities, such as running, dancing and playing sports, which subject the joint to higher contact and shear stress. The preliminary conclusion that the optimal parameters would be ≥ 95% implant conformity with ≥ 3mm thickness warrants further investigation of the yield and failure stresses of these materials. It is important to ensure whether the stresses and strains for ≥ 95% implant conformity and ≥ 3mm thickness are less than the yield limit of the materials or would the materials undergo plastic deformation during extraneous activities. Additionally, polycarbonate urethane and most of the hydrogels (for load- bearing application) are prepared by injection molding of the polymer onto an anchoring substrate; therefore, the evaluation of stresses acting at the polymer-substrate junction is essential for the performance and survival of the implant in the body.

There are a few limitations of this study. First of all, this was a simplified, axisymmetric model of a medial knee compartment without the accompanying bone or soft tissues. This study investigated the contact mechanics of the implants, without evaluating the stresses on the underlying bone. The reasoning behind this study was to understand the compliant-on-compliant contact mechanics and determine if the proposed materials and the implant design would be able to withstand the applied physiological loads without surpassing the material failure limits. The compliant-on-compliant contact loads are so low that it would not cause stress concentration or stress shielding of the underlying bone. Secondly, only the medial compartment of the knee was modeled, which is chose because it carries about 60% of the total load and is more prone to injuries 87 than the lateral compartment [187]. Another limitation was that the femoral radius of curvature was taken from a fully extended knee. A normal knee femur is known to have multiple simultaneous radii of curvature under flexion and extension; consequently, in the past, total knee replacement femoral components were developed to accommodate multi- radius of curvature in the design. However, in recent comparison studies between the multiaxial and single radius of curvature (a single fixed axis of rotation with a posterior center of flexion) implant designs, the single radius implants have shown evidence of improved functionality, stability, range of motion and pain [188, 189]. Since the compliant materials are highly deformable, it is assumed that a single radius of curvature implant would be able to accommodate the sliding and rolling motion of the femoral component.

Finally, due to the axisymmetric nature of the model, only the axial load was applied to the model without the rotational motion of the knee. A full medial compartment model is required to investigate the effect of the flexion-extension on the contact mechanics of the implant.

Conclusion

This parametric study showed that a compliant-on-compliant implant has the potential for use in knee replacement. All the design factors, such as the femoral-tibial implant conformity, implant thickness, and material properties, significantly (p<0.001) affected the contact mechanics of the knee joint under a normal walking load as well as high load-bearing activity such as stair climbing. However, the conformity had the highest effect-size on the contact mechanics. Based on the predicted maximum principal stress, Von Mises stress, maximum shear stress, maximum principal strain, maximum contact pressure and maximum contact area results, the optimal parameters for a 88 compliant material knee implant would be ≥ 95% implant conformity with ≥ 3mm

thickness. However, to determine which material formulation has a potential to perform

under the physiological knee load, their failure properties will need to be investigated.

Overall, this paper was a preliminary attempt to evaluate the contact mechanics of a simplified finite element medial knee model under axial load, but incorporating the

flexion and friction at the contact surface would be a more realistic evaluation of stresses

acting on the articulating surfaces.

Acknowledgement

Hydrogel specimens and institutional funding were provided by Formae, Inc.

Polycarbonate urethane Bionate 80A I and II were provided by courtesy of DSM

Medical, Berkeley, CA. 89 Chapter 5 : Mechanical Failure Modality of Compliant Arthroplasty Materials under Physiologically Relevant Loading Conditions

Abstract

Determining the material failure criteria is crucial in understanding the

mechanism behind the failure of load-bearing orthopedic materials and improving their

lifespan. Compliant arthroplasty materials, three formulations of a novel hydrogel and two formulations of polycarbonate urethane, were investigated under a battery of mechanical tests such as uniaxial tension and unconfined compression, and biaxial plane strain compression test to determine their yield and failure properties under physiological loads and strain rates. All the material failed under uniaxial tension; however, none of them failed under uniaxial compression or biaxial compression. Therefore, the tension was considered the primary mode of failure for the proposed materials. Different material failure properties such as maximum principal stress, Von Mises stress, maximum shear stress and maximum principal strain were calculated at compressive yield strain. A comparison was carried out between the material yield properties calculated from the plane strain compression results, and the stresses and strain predicted from the medial knee model under normal walking and stair climbing loads (Chapter 4). Overall results demonstrated that the hydrogels were prone to undergo stresses beyond their yield limit,

which may lead to delamination or fracture of the implant. The polycarbonate urethane, however, demonstrated promising results with higher material yield properties than those encountered in the knee model. Therefore, polycarbonate urethane was the preferred candidate for use in compliant knee implants, provided high conformity and appropriate thickness were employed in designing the knee replacement implant. 90 Introduction

Material failure is a major bottleneck in the performance of a load bearing implant used for a total joint replacement. The knee is a major load-bearing joint in the body,

which undergoes millions of compressive load cycles in a lifetime, under several times the body weight [190, 191]. Although compression and shear are critical failure modalities

for the knee cartilage surfaces, cracking or fracture towards the edge of the contact patch under tension, is also a common method of material failure. The vulnerability of arthroplasty material also comes from the changes in its mechanical integrity due to prolong loading. When an elastic material is subjected to a constant load, it undergoes creep, while repetitive loading can cause fatigue in the material. The resultant stress builds up at the contact patch acts as foci for the initiation of sub-surface cracking, which may lead to material failure in the implant.

Cartilage microenvironment has been studied extensively using different modes of mechanical testing to understand its failure mechanism. Sasazaki et al. investigated failure mechanism of bovine cartilage under tension and found matrix reorganization followed by matrix rupture to failure, regardless of whether the applied strain was parallel or perpendicular to the collagen orientation [192]. Similar behavior was observed under

compression when cartilage failed structurally under sudden high loads, which resulted in

the loss of constituent matrix [193]. Kerin et al. evaluated the over time effect of cyclic loading on the mechanical strength of cartilage when the water loss generates stress concentration within the tissue [194]. When the native articular cartilage undergoes

extensive wear and failure in vivo, the recommended mode of treatment is a joint

replacement surgery. Despite enhanced mechanical strength and fracture-resistance of 91 current arthroplasty material, they are still prone to failure due to a number of factors.

The metal implants can undergo fracture or corrosive failure in the physiological environment due to the abundance of oxygen and acidic conditions, and generate corrosion ions and wear particles [35]. Polymers mainly fail due to yielding, wear, fatigue, fracture, creep or chemical damage. Bergstrom et al. carried out an in-depth evaluation of uni- and multi-axial failure of ultra-high molecular weight polyethylene

(UHMWPE) using different static failure criteria such as maximum principal stress,

Mises stress, Tresca stress, hydrostatic stress, Coulomb stress, maximum principal strain,

Mises strain and chain stretch failure criteria. Among all the criteria, the chain stretch failure criteria most accurately captured the failure behavior of UHMWPE materials, while the von Mises strain predicted the failure behavior with the least accuracy [132].

Compliant arthroplasty materials, such as polycarbonate urethane and a variety of

hydrogels, have also been investigated for use in orthopedics due to their cartilage-like

mechanical and lubrication properties. Hydrogels, for tissue engineering applications, have been analyzed for fracture toughness using a variety of test methods, such as tensile, tear, compression and single edge notch test [195]. Stammen et al. investigated the failure

strain and stress of a novel polyvinyl alcohol hydrogel under shear and unconfined

compression tests for load bearing application in the articular joints [150]. Bertagnoli et al. evaluated the performance characteristics of a nucleus pulposus replacement device by conducting a confined compression and fatigue testing on a hydrogel implant, which remained intact and resulted in promising failure force and lateral bending as well as flexion moment values [151]. Similarly, polycarbonate urethane has also been

mechanically investigated under tension and compression by several studies for use as a 92 film in tissue engineering or load-bearing application [196-198]. Bionate polycarbonate

urethane has been evaluated for its wear properties in-depth for the TriboFit acetabular

buffer [47, 48] and NuSurface meniscal implant [52]. However, no studies to the author’s

knowledge have reported the primary failure mode of these compliant materials under

different static fracture modes, and the amount of stresses and strains these two materials

are capable of withstanding under physiological loads and strain rates.

The goal of this study is to determine the primary failure criteria under different static testing modes such as tension, compression and biaxial plane strain compression at physiological strain rates. It was hypothesized that either compression or shear would be

the primary failure modes of the proposed compliant materials for the given application

in the knee joint. By combining the yield and failure properties from this study and the

parametric model results from Chapter 4, a niche design space will be defined, within

which designing knee implant with complaint bearing materials will be feasible.

Materials & Method

Three different formulations, with varying water content (HG43, HG48, and

HG53), of a proprietary hydrogel (CyborGel™, Formae Inc., Paoli, PA) were tested. Two

formulations of a medical grade polycarbonate urethane (PCU Bionate 80A I and II,

DSM Medical, Berkeley, CA), with an average molecular weight around 150,000 –

200,000 g/mol, were also characterized under the same testing conditions. Three different mechanical tests were carried out, as described below, to characterize the materials under

(i) uniaxial tension – for tensile yield and fracture properties; (ii) uniaxial compression – for compressive yield properties; and (iii) biaxial plane strain compression – for

maximum shear properties. 93 Uniaxial Tensile Test to Failure

Dog-bone samples (n = 5) of all formulations of hydrogel (cross-section width:

6.43 ± 0.18mm; thickness: 3.41 ± 0.26mm) and polycarbonate urethane (cross-section

width: 4.56 ± 0.02mm; thickness: 0.33 ± 0.03mm) were dimensioned and tested per

ASTM D638 standard. Tensile testing to failure was performed on a universal mechanical tester (Criterion, MTS Systems Corp., Eden Prairie, MN). Following preconditioning for 20 loading-unloading cycles to 1% strain, the samples were tested at

three different crosshead speeds of 30, 75 and 150 mm/min as previously reported in the

literature [132]. Axial and transverse strains were measured using a non-contacting video

extensometer (Zwick-Roell Video Extensometer System, Kennesaw, GA). A total of 75

specimens were tested (5 specimens per formulation x 5 materials x 3 strain rates). Since

the linear region of the stress-strain curve of different formulations ranged between 15 -

20% strain, Young’s modulus, and Poisson’s ratio were calculated at 10% strain for

uniformity using a Matlab script (Appendix 3). The ultimate tensile strength and

elongation were reported at failure for all the formulations. One-way ANOVA t-test

(SPSS 24.0, IBM) was used to evaluate the difference in the mechanical properties at

different crosshead speeds.

Unconfined Compression Test

Cylindrical samples (n = 5 for each formulation) of hydrogel (height: 4.83 ±

0.18mm; diameter: 4.78 ± 0.16mm) and polycarbonate urethane (height: 3.23 ± 0.03mm;

diameter: 4.30 ± 0.03mm) were used for unconfined compression testing. All samples

were placed in a distilled water bath at room temperature and were tested under

unconfined compression on a mechanical load frame (858 Mini Bionix II, MTS Systems 94 Corp., Eden Prairie, MN). Under displacement control mode, specimens were pre-

conditioned for 20 loading-unloading cycles to 1% strain, followed by an incremental 5%

strain loading-unloading cycles between 10 – 70% at the strain rate of 10 or 100%/s. The

10% strain rate represented the lower rate of deformation during normal gait, while 100%

strain rate loading represented high-impact activities such as running, playing tennis and

jumping [199, 200]. Samples were allowed to recover for a minute between two

consecutive cycles. The load and displacement data was recorded at 512 Hz, and the

stress-strain curve was plotted to determine the compressive stress at a given strain.

Samples were determined to be yielding (past their elastic recovery zone) when the

loading part of the stress vs. strain plot showed a distinct downward shift between two

subsequent cycles as described previously [193] and illustrated in Figure 5-1. A total of

50 specimens were tested (5 samples per formulation x 5 materials x 2 strain rates). A

paired t-test (SPSS 24.0, IBM) was used to check for the viscoelastic material behavior,

which may lead to different mechanical properties at various crosshead speeds.

Plane Strain Compression Test

Rectangular specimens (n = 5 for each formulation, thickness: 3.5 ± 0.3 mm,

length: 16 mm, width: 4.0 ± 0.2 mm) of hydrogel and polycarbonate urethane were

compressed by a 16 mm long x 8mm wide stainless steel platen at room temperature.

Using a metal channel fixture [201], the sample was loaded from the top while constrained to strain in one direction and allowed to freely flow in the other direction as shown in Figure 5-2. The channel fixture was lubricated to keep the surfaces frictionless.

95

Material yielding – downward stress shift as compared to the previous cycle

Figure 5-1: Stress-strain curve of the HG53 hydrogel formulation at material yield. The downward shift of the loading part of the curve, between two consecutive cycles, suggests that lower load is supported at the same strain level, which is attributed to plastic deformation in the material.

Figure 5-2: Plane strain compression test fixture with a hydrogel sample used in this study.

Per the plane strain compression assumptions, the strain in the constrained

direction and the stress in the material flow direction becomes zero. Samples were 96 subjected to a constant crosshead strain speed of either 10 or 100%/s on a mechanical

load frame (858 Mini Bionix II, MTS Systems Corp., Eden Prairie, MN). A strain rate of

10%/s represented normal walking; while a strain rate of 100%/s represented high- intensity activities such as running, stair climbing or playing sports [199, 200].

Specimens were compressed up to 50% strain or failure, whichever occurred first. Upon completion of the test, all the samples were visually investigated for cracks or fracture. A total of 50 specimens were tested (5 samples per formulation x 5 materials x 2 strain rates). The experimental data was recorded as a reaction force and displacement of the top fixture. Due to the biaxial nature of this test, the resultant stress and strain vectors could not be determined without using a sophisticated testing apparatus for recording force and displacements in two different directions. Consequently, finite element (FE) analysis was employed as discussed below.

Finite Element Modeling

In order to simulate the resultant stresses and strains of a plane strain compression test, a simplified finite element models were created using the measured dimensions of all tested samples and were meshed in a finite element analysis software, FEBio

(Musculoskeletal Research Laboratories, University of Utah, UT) [165], as shown in

Figure 5-3. Mesh sensitivity analysis was carried out to determine the optimal number

(16,000) of hexahedral elements. In order to mimic the boundary and loading conditions of the plane strain compression test, the top and bottom platens were modeled as rigid

bodies while the hydrogel or polycarbonate urethane specimen was modeled using a neo-

Hookean material, which has been previously validated in Chapter 4. Similar to the bench test, the displacement of the material was restricted to only two directions and the 97 load was applied from the top down. A total of 50 simulations (5 materials x 5 specimen x 2 strain rate) were carried out.

Figure 5-3: Finite element simulation of the plane strain compression test using FEBio. (Left to right) Undeformed state of specimen undergoes 50% compression to give the reaction force and displacement outputs, which was utilized for curve-fitting the experimental results.

The predicted compression reaction force was recorded and used for curve fitting the experimental load vs. time data. R2 and normalized root mean square error (n-RMSE) were calculated between the experimental and FE predicted results to check for accuracy.

Normalized RMSE was calculated as the ratio of the RMSE to the difference between the maximum and minimum experimental load values. For ductile materials, permanent deformation sets in once the material passes the yield stress/strain point. Therefore, although the plane strain compression test was carried out up to 50% deformation, the FE model principal stresses and strains tensor (as a function of applied deformation) were recorded at the yield point strain, which was determined in the previous section from the unconfined compression results. The following equations were used to evaluate each failure criteria. 98 Maximum principal stress - the maximum principal stress, ( ), was

𝑖𝑖 recorded. 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 σ

( – ) ( – ) ( – ) Von Mises stress - < , where are the 2 2 2 σ1 σ2 + σ2 σ3 + σ3 σ1 yield 𝑖𝑖 � 2 σ σ principal stresses. Since the stress in the material flow direction becomes zero, the von

Mises stress equation simplifies to – + . 2 2 �σ1 σ1𝜎𝜎2 σ2

Maximum shear (Tresca) stress - τmax = ½ (σmax – σmin). For ductile materials, yield

happens along 45° slip planes, which are the planes for maximum shear stress.

Maximum principal (compressive) strain – the minimum principal strain, ( ),

𝑖𝑖 was recorded. 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ε

A Matlab script (Appendix 4) was developed to calculate the different failure criteria

using the equations above.

Results Uniaxial Tensile Test to Failure

The uniaxial tensile stress-strain curves for various formulations of the novel hydrogel and polycarbonate urethane samples are shown in Figure 5-4. Both the hydrogel and polycarbonate urethane exhibited ductile material behavior with the linear strain region ranging between 15 – 20% for various formulations. 99

Figure 5-4: True stress-strain curve of different formulations of polycarbonate urethane Bionate (left) and hydrogel (right) subjected to a uniaxial tensile test at the crosshead speed of 30mm/min.

For uniformity, Young’s modulus and Poisson’s ratio were calculated from the slope of 0 - 10% strain, while the ultimate tensile strength and elongation were reported at failure for all the formulations. For the hydrogel, the mechanical strength decreased with increase in the water content (p < 0.05); while for polycarbonate urethane, there was no significant difference between the two 80A grade materials. The ultimate strength of hydrogel was in the range of 4 - 8MPa depending on the formulations; polycarbonate urethane, on the other hand, had an ultimate strength of 57 – 62MPa, which is about ten times more than the hydrogel. In terms of break elongation, hydrogel stretched for 300-

400%, while the polycarbonate urethane stretched about 600-700% i.e. they both undergo large deformation before failure. Statistically, no significant differences (p>0.05) was found in Young’s modulus, Poisson’s ratio, ultimate strength, and elongation within each formulation of the hydrogel and polycarbonate urethane tested at different crosshead speeds. Hence, under tension, the viscoelastic, time-dependent behavior of these 100 materials was not statistically apparent among samples tested at 30, 75 and 150mm/min.

All the test results were averaged and plotted in the Figure 5-5, along with the range of articular cartilage mechanical properties as reported in the literature (highlighted in gray)

[174, 193, 202, 203].

Unconfined Compression Test to Failure

A typical stress-strain curve of unconfined compression can be seen in Figure 5-1,

with three consecutive cycles showing before and after material yield. For the hydrogel

formulations, the yield strain increased with increase in the water content, while the yield

compressive stress decreased. Polycarbonate urethane formulation Bionate I

demonstrated higher yield strain and stress as compared to Bionate II. Between the two

materials, the mechanical strength of Bionate 80A I and II were comparable to the lowest

water content hydrogel formulation (HG43). Statistically significant difference (p < 0.05) in the yield strain and stress was found in the HG43, HG48 and Bionate I specimens,

which were tested at 10% and 100% per second strain rates. No significant difference (p

> 0.05) was found for HG53 and Bionate II, which may be due to the non-homogeneity in the samples. Overall, the viscoelastic behavior in two hydrogel formulations and one polycarbonate urethane formulation was confirmed. The tensile and compressive mechanical properties of both the materials are summarized in Table 5-1, along with the articular cartilage mechanical properties from the literature. Although not listed in Table

5-1, the elastic limit (tensile yield) of the materials was within the range of 15-20% strain as compared to 25 – 35% compressive yield strain.

101

Figure 5-5: Continued on next page. 102

Figure 5-5: Average Young’s modulus (MPa), Poisson’s ratio, ultimate stress (MPa) and elongation (mm/mm) for different formulations of hydrogel and polycarbonate urethane, tensile tested at various crosshead speeds. The gray region represents the mechanical properties range for articular cartilage [174, 193, 202, 203]. 103 Table 5-1: Experimentally determined tensile and compression properties of hydrogel and polycarbonate urethane formulations, along with the articular cartilage mechanical properties from the literature.

Tension Properties (n = 15) Young’s Ultimate Formulation Poisson’s ratio Elongation (%) Modulus (MPa) Strength (MPa) Bionate I 13.9 ± 1.5 0.47 ± 0.02 57.9 ± 5.9 7.5 ± 2.7 Bionate II 18.5 ± 1.1 0.46 ± 0.02 62.1 ± 4.0 6.9 ± 1.6 HG43 17.4 ± 2.6 0.48 ± 0.06 7.7 ± 0.7 2.4 ± 0.7 HG48 8.4 ± 1.2 0.47 ± 0.06 5.7 ± 0.5 3.0 ± 1.1 HG53 4.7 ± 0.5 0.46 ± 0.03 4.8 ± 0.5 3.7 ± 0.9 Cartilage 10 – 20 0.5 ± 0.03 4.7 ± 2.1 1.1 ± 0.3 [174, 193, 202, 203] Compression Properties (n = 5) 10% Strain rate 100% Strain rate Yield Strain Yield Stress Yield Strain Yield Stress Formulation (mm/mm) (MPa) (mm/mm) (MPa) Bionate I 0.26 ± 0.02 8.1 ± 0.8 0.31 ± 0.02 10.9 ± 1.4 Bionate II 0.31 ± 0.02 8.7 ± 1.2 0.34 ± 0.02 10.1 ±0.9 HG43 0.20 ± 0.00 4.7 ± 0.4 0.26 ± 0.02 6.8 ± 0.7 HG48 0.26 ± 0.02 3.2 ± 0.2 0.30 ± 0.00 4.3 ± 0.4 HG53 0.30 ± 0.00 2.8 ± 0.1 0.32 ± 0.03 3.1 ± 0.6 Cartilage 0.3 ± 0.07 failure strain and 35.7 ± 11.0 MPa failure stress [174, 193, 202, 203]

Plane Strain Compression Test

After undergoing 50% compression, all the specimens remained intact; no damage such as cracks or fracture was observed among all the formulations of hydrogel and polycarbonate urethane. The mechanical behavior of all hydrogel and polycarbonate urethane formulations tested under plane strain condition is illustrated in Figure 5-6(a). 104 The experimental force-displacement responses were repeatable and predictable as demonstrated in Figure 5-6(b) and (c).

(a)

(b) (c)

Figure 5-6: (a) Compression force vs. displacement response of different formulations of hydrogel and polycarbonate urethane at 50% compression. Experimental and model predicted force responses of (b) polycarbonate urethane Bionate II and (c) HG43 hydrogel formulation were overlaid to demonstrate repeatability and predictability.

105 The average load capacity at 50% strain for Bionate I was 1502 ± 121N (16.5 ±

0.6 MPa); Bionate II was 1260 ± 140N (15.5 ± 1.0 MPa); HG43 is 1321 ± 140 N (14.4 ±

0.7 MPa); HG48 was 906 ± 100N (10.8 ± 0.5 MPa); and HG53 was 771 ± 63 (8.4 ± 0.3

MPa). No significant difference was found between the reaction load recorded at 10 and

100% strain rate. The neo-Hookean material model accurately predicted (R2 = 0.9977 ±

0.0013) the experimental force response of the proposed materials. The average normalized root-mean-square error for all the formulations of both the materials was 1.72

± 1.04%.

The simulated principal stress and strain tensors were recorded at the material yield strain of each formulation, and the failure criteria were calculated in Matlab. The failure properties of all the material formulations are summarized in Table 5-2.

Table 5-2: Failure criteria of hydrogel and polycarbonate urethane formulations at two different strain rates calculated at their corresponding compressive yield point.

Failure Criteria Bionate I Bionate II HG43 HG48 HG53

Failure predicted at strain rate of 10%/s (Represents Normal Walking)

Maximum Principal Stress 6.70 ± 0.24 7.95 ± 0.39 4.43 ± 0.26 4.65 ± 0.27 4.05 ± 0.12 (MPa) Von Mises Stress (MPa) 5.80 ± 0.21 6.89 ± 0.34 3.84 ± 0.22 4.03 ± 0.23 3.52 ± 0.10 Max. Shear (Tresca) Stress 1.74 ± 0.12 2.09 ± 0.09 1.09 ± 0.16 1.20 ± 0.18 0.86 ± 0.06 (MPa) Maximum Principal Strain 0.229 ± 0.000 0.265 ± 0.001 0.182 ± 0.001 0.228 ± 0.00 0.257 ±0.000

Failure predicted at strain rate of 100%/s (Represents Stair Climbing)

Maximum Principal Stress 8.34 ± 0.30 8.97 ± 0.44 6.04 ± 0.34 5.55 ± 0.31 4.41 ± 0.13 (MPa) Von Mises Stress (MPa) 7.23 ± 0.26 7.77 ± 0.38 5.24 ± 0.28 4.82 ± 0.27 3.84 ± 0.11 Max. Shear (Tresca) Stress 2.08 ± 0.15 2.30 ± 0.10 1.40 ± 0.22 1.38 ± 0.21 0.91 ± 0.06 (MPa) Maximum Principal Strain 0.264 ± 0.000 0.285 ± 0.001 0.228 ± 0.001 0.257 ± 0.00 0.271 ±0.000 106 Discussion

This study was intended to evaluate the primary failure modality of compliant

arthroplasty material under a variety of mechanical tests such as uniaxial tension,

unconfined compression, and biaxial plane strain compression test. All the materials

failed under uniaxial tension; however, none of them failed under uniaxial compression

or biaxial compression up to 70% strain. It is physically infeasible to subject the material

under compression at the same strain level (250 – 750%) as seen in tensile testing.

Secondly, even 70% strain of materials is beyond the physiological range of compression

seen at the knee joint in vivo. Therefore, the proposed hypothesis that both the materials will fail primarily under compression or shear was not confirmed; instead, the results suggested that the failure mode for both hydrogel and polycarbonate urethane was

tension. The results of the tensile test provided the material mechanical properties, and

ultimate stress, and elongation at break. The unconfined compression results provided the yield stresses and strains of the materials, which are critical to understand since compression is the primary mode of loading in the knee. The biaxial compression test provided a more realistic understanding of the material behavior under more than a simple uniaxial tension or compression test, and also provided data for calculation of the maximum allowable shear stress and Von Mises stress.

The mechanical test results of this study were similar to other reported studies on polycarbonate urethane and various hydrogels. Khan et al. tested polycarbonate urethane films under tension for tissue engineering application [196]. The reported break

elongation of 740% and tensile strength of 12MPa were similar to those for Bionate I and

II in the current work. The authors reported lower average fracture strength of 13MPa 107 compared to our average of 60MPa ultimate strength; however, this discrepancy may be

due to the difference in the thickness of the samples and the strain rate of 10mm.min-1.

Another study investigating the mechanical properties of modified polycarbonate

urethane, with a similar thickness to our samples, reported about 30MPa tensile break

strength and a relative break elongation of 312 – 352% [198]. The present study results

are comparable to those reported in DSM Medical’s product specification sheet using a different ASTM standard [204]. Geary et al. made an attempt to characterize Bionate 80A

and 75A polycarbonate urethanes for orthopedic application under tension and

compression [197]. Although a clear distinction in the strength of 80A compared to the

other formulation was apparent from the stress-strain curve, the researchers were unable

to determine its ultimate strength and break elongation due to a limitation in the testing apparatus. Therefore, the current study provided critical information about 80A formulation, which is predominantly used in the manufacturing of commercially available orthopedic implants. Several researchers [150, 151, 195, 204, 205] have evaluated

the mechanical capabilities of various hydrogels. Stammen et al. characterized polyvinyl

alcohol under shear and unconfined compression test [150] and reported results similar to

those found in the present work. The compression modulus was tested over the range of

10 - 60% strain and hydrogel failure was reported at 45 and 60% strain for two different

formulations. Similar to the current study results, the compressive data was found

statistically dependent on the strain magnitude and rate; however, under shear test, it was

not statistically independent of the strain rate [150]. Smith et al. characterized the

toughness of photopolymerized (meth) acrylate hydrogel networks by performing a

uniaxial tensile test on a range of different water content samples, under a range of 108 temperature [204]. The authors concluded that the primary factors influencing the toughness of hydrogels were the test temperature relative to the glass transition

temperature, the water content, and the network structure of the polymer. Similar results

were found in the current study in which the mechanical properties, such as Young’s modulus, Poisson’s ratio, ultimate strength, and elongation were influenced by the water

content of hydrogel. Under plane strain compression test, both the hydrogel and

polycarbonate urethane samples did not fracture at 50% strain (40% true strain). This

observation is similar to Tritz et al. study, which tested sprayed and molded alginate

hydrogel under plane strain compression for a range of strain rates and reported strain

rate dependence of alginate sample and rupture at 80% strain [205]. Overall, the

mechanical failure properties of both the materials were either comparable or better than

that of the natural articular cartilage. The ultimate strength of hydrogel was in the range

of 4 - 8MPa depending on the formulations, which is comparable to that of cartilage

around 5MPa [203]. Polycarbonate urethane, on the other hand, had an ultimate strength

of 57 – 62MPa, which is about ten times more than that of the cartilage under tension. In

terms of elongation, cartilage has reported stretching over 100% [203], while hydrogel

stretched for 300-400%, and polycarbonate stretched about 600-700%. Both the

material’s break elongation is 2 to 8 times that of the articular cartilage i.e. they are

largely deformable before failure.

In order to evaluate the feasibility of using compliant materials in vivo, the contact

parameters of a compliant knee implant under physiological loads were compared against

the material properties at yield. The simulated maximum principal stress, Von Mises

stress, maximum shear stress and maximum principal strain from Chapter 4 were plotted 109 against those values derived from the empirical plane strain compression test in the current study. The plots for various formulations of polycarbonate urethane (Bionate) and hydrogel are shown in Figure 5-7.

Figure 5-7: Continued on next page. 110

Figure 5-7: Comparison between predicted knee finite element model (FEM) response for normal walking and stair climbing loads from the previous chapter, and the predicted plane strain compression (PSC) response at a strain rate of 10% /s (represents walk) and 100%/s (represents climb).

111 The finite element model prediction for the maximum principal stress ranges

between 2 and 11MPa for different hydrogel and polycarbonate urethane formulations,

while the empirical maximum principal stress experienced by the materials at yield is 4 to

10 MPa. Based on the plots above, the predicted maximum principal stress in the knee model with hydrogel would surpass the hydrogel’s yield stress under both normal gait load and stair climbing loads. The polycarbonate urethane formulations predicted stress at normal walking would stay below their yield properties; however, under higher loading conditions, the polycarbonate urethanes may also surpass their yield properties.

Furthermore, the mechanical failure of a ductile material is governed by the Von Mises stress and the maximum shear stress according to the distortion of energy and Tresca failure theory, respectively. Both hydrogel and polycarbonate urethane have shown lower

Von Mises stress predicted in the knee model for walking and stair climbing as compared to their yield properties determined from the plane strain compression test. The safety factor between the predicted and experimental Von Mises stress is at least double for the hydrogel and at least quadruple for the polycarbonate urethane. However, the hydrogels did not show equally promising results for maximum shear stress. While the polycarbonate urethanes have at least twice the safety factor between the experimental and predicted maximum shear stress for walking and stair climbing, the maximum shear stress of the hydrogels predicted under knee load has similar values as the experimentally determined yield values under walking and stair climbing loads. Therefore, if the tested hydrogels are used in a knee implant, they will be functioning in a range that is beyond the maximum allowable shear stress for normal as well as vigorous activities. As

mentioned in Chapter 4, one of the limitations of the medial knee model was that it was 112 only axially loaded, therefore, when knee flexion and other complex motions are

simultaneously applied there is a potential for an increased shear stress at the joint.

Hence, hydrogels may potentially delaminate or fracture under the shear stress, and

therefore, they are not recommended. The maximum principal strain also allowed for a good safety factor between the predicted and experimental values for different material formulations, except for hydrogel formulations HG53, which has a higher deformability under stair climbing load and deforms beyond the material yield.

Overall, to prevent the material yielding under physiological loads, implant conformity and thickness must be selected such that the resultant stresses and strain do not exceed the yield limit of the materials under vigorous activities. Among all the hydrogel formulations, the lowest water content hydrogel (HG43) performed the best under the applied loads; however, they all demonstrated a higher potential for yield- related failure under maximum principal stress and maximum shear stress compared to the polycarbonate urethane formulations. If a material surpasses its yield point then it would undergo plastic deformation, which could cause irreversible damage to the implant. However, this does not necessarily imply that the material will fail at that point, instead these hyperelastic materials may undergo strain hardening and potentially function well beyond their yield limit. UHMWPE has shown similar yield behavior to the

proposed hydrogel; however, it functions well at contact stresses beyond its yield limit

without fracture of the material [206]. In order to test this hypothesis for hydrogels, bench

testing needs to be performed for millions of cycles to evaluate their performance beyond

the yield limits. Based on the current study results, the polycarbonate urethane is a better

candidate for use in compliant knee implants, provided high implant conformity, and 113 appropriate thickness is employed (per Chapter 4) in the designing of the knee cartilage replacement implant.

Additionally, this study only evaluated the failure properties of compliant

materials under static load. However, a knee joint undergoes millions of dynamic loading

cycles under high loads, flexion and displacement. Hence, a future work investigating the

fatigue behavior of these compliant materials is required, which may possibly be the

ultimate mode of failure of polycarbonate urethane and the novel hydrogel.

Conclusion

Determining material failure mode is crucial in understanding the mechanism behind the

failure of load-bearing orthopedic materials and improving the lifespan of these implants.

At present, the tension was concluded as the primary mode of failure; however, both the proposed materials withstood high strain under compression, which is the relevant mode

of loading in the knee joint. However, upon comparing the predicted knee contact

parameters under walking and stair climbing loads with empirically determined material

yield properties, the hydrogel formulations barely have any safety factor, especially in

terms of maximum principal stress and maximum shear stress, and can potentially undergo irreversible damage and fracture. On the contrary, polycarbonate urethane

showed promising results with higher material yield properties than those encountered in

the knee model. Using a compliant material with appropriate implant conformity and

thickness will assist in achieving better material safety factor and improve the chances of

implant survival in vivo. Although this study provided insight into the compliant material

failure properties and feasibility for use in knee resurfacing implant, dynamic testing is 114 required to determine the material integrity and performance under physiological loading conditions for millions of cycles.

115 Chapter 6 : Conclusion and Future Work Conclusions

This research explored the potential of using compliant polymeric materials in partial knee replacement. Since a majority of the gold standard arthroplasty materials lack the lubrication and mechanical characteristics of natural cartilage tissue, they give rise to implant loosening, osteolysis, and revision surgery over a patient’s lifetime. Compliant polymeric implants have been developed for a number of joints, such as hip, spine, knee

and metatarsophalangeal joint, to treat the full or partial joint surface and in the form of cylindrical plugs for treating osteochondral defects. This work investigated two promising compliant materials, medical grade polycarbonate urethane, Bionate, and a

novel hydrogel, Cyborgel, to determine their suitability for knee cartilage replacement.

In this dissertation the following questions were addressed:

1) Would the proposed materials be able to survive the sterilization process,

especially the hydrogel, which is known to lose chemical and structural integrity

post-sterilization?

2) If a knee replacement implant is to be made of compliant polymers, what would

be the design criteria to maximize implant survival by minimizing the contact

stress and wear rate, which are two common causes of device failure?

3) Which implant design parameters would have the most impact on the

biomechanics of compliant knee implants? How can they be optimized?

4) What is the most prominent mode of failure for these compliant materials under

physiological knee loads and strain rates? 116 The first question was addressed in-depth in Chapter 3, which evaluated three

different formulations of the novel hydrogel after subjecting them to gamma and electron

beam radiation. The sterilized and control hydrogels underwent mechanical, chemical and

tribological testing to analyze possible effects on the mechanical and structural integrity

as well as wear behavior of the hydrogels. This work also characterized the equilibrium

mechanical properties of the hydrogel using a biphasic neo-Hookean material model,

which was validated against articular cartilage confined creep response. Although

sterilized hydrogel did not show any changes in the mechanical properties or the wear

rate, which was once again confirmed to be negligible, chemical analysis showed a minor

discrepancy in electron beam irradiated samples as compared to control and gamma

sterilized specimens. Thus, hydrogel sterilization with gamma irradiation was determined

to be the preferred method for hydrogel-based medical device sterilization.

The second and third questions regarding the design of compliant arthroplasty

implant were addressed in Chapter 4. A design of experiment using parametric finite

element modeling of the medial knee compartment was carried out with varying implant

conformance, implant thickness, and material properties. This study was first of its kind to evaluate compliant-on-compliant material contact mechanics under physiological ISO gait and stair climbing loads. All input parameters, namely, implant conformity, implant

thickness and material properties, significantly (p<0.05) affected the resulting maximum

principal stress, Von Mises stress, maximum shear stress, maximum principal strain,

maximum contact pressure and maximum contact area. However, the conformity had the

highest effect-size on the contact mechanics. The maximum principal stress value halves

and the contact area doubles when ≥ 95% implant conformity and ≥ 3mm thickness were 117 used, which were determined to be the optimal parameters for the survival of complaint

material implant in the body under normal and vigorous daily activities.

Finally, the last question about the failure of the material was investigated in

Chapter 5. The study evaluated the performance of the two materials under uniaxial

tension, unconfined compression and biaxial compression tests carried out at

physiological loads and strain rates. The tension was determined to be the primary mode

of failure for the proposed materials, while they survived under uniaxial and biaxial

compression test in the range of 50 - 70% engineering strain (39 - 53% true strain) without any signs of cracking or fracture. Maximum principal stress, von Mises stress, maximum shear stress and maximum principal strain were calculated at the compressive

yield strain and compared against the stresses and strain experienced by the knee medial compartment under normal walking and stair climbing loads. Overall results demonstrated that the hydrogels, at the knee loads, were prone to undergo higher stress

and strain beyond their yield limit, and may lead to delamination or fracture of the

implant under both normal walking and more vigorous activities. Polycarbonate urethane

showed promising results with higher material yield properties than those predicted by

the knee model, hence, it was the preferred material for potential compliant knee implant.

Thus, the present research recommended a niche design space for compliant knee implant

with ≥ 95% implant conformity, ≥ 3mm thickness and material properties similar to

polycarbonate urethane, provided the material performs equally well under dynamic

testing in physiologically relevant conditions.

The overall contributions of this thesis were: (i) comprehensive evaluation of a

novel hydrogel for the effect of various irradiation types and determining the most 118 suitable sterilization method; (ii) developing a validated, simplified finite element model

of the medial knee compartment, along with a validated material model, for evaluating

the contact mechanics of compliant material-on-compliant material implant configuration

under physiological loads; (iii) identifying parameters affecting the design of compliant

knee replacement implant and identifying the optimal design niche for implant survival

and performance; and (iv) evaluating hydrogel and polycarbonate urethane under a

battery of mechanical test to determine the yield properties under compression, which are

crucial information to understand material failure.

Future Work

While the above studies have shown that compliant knee implant is promising for

use in knee cartilage replacement, some additional testing and analyses are required.

Dynamic mechanical testing such as cyclic creep or fatigue testing for several millions of

cycles is needed to determine if the hydrogel and polycarbonate urethane would be able

to sustain physiologically relevant dynamic loading conditions. Both of the materials

have been tribologically tested for at least 5 million cycles in different shapes and

geometry; however, as demonstrated by the present work, the surface geometry plays a

critical role in the stress distribution and overall performance of a given material. Hence,

a thorough wear study using a knee configuration implants is required to accurately

assess their performance and identify the stress regions in the design.

Additionally, this was a preliminary attempt to evaluate contact mechanics of an

axisymmetric finite element medial knee model under physiological load; however,

incorporating the flexion and friction at the contact surface would be a more realistic

evaluation of stresses and strain acting on the surface. In future, development of a full 119 knee model with the full axial loads, flexion, and anterior-posterior displacement would provide a more realistic prediction of the contact mechanics at the articulating surfaces.

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Appendix 1: FEBio Parameter Optimization

The following range of parameters was used for optimization:

Cyborgel E (MPa) v k (10-16 m4/Ns)

Low WC

Medium WC 5 – 40 0.01 – 0.49 0.1 – 100

High WC

Each finite element model (for instance, C1-1_Optimization.feb) developed in FEBio with

the boundary conditions and 10% strain as described in Chapter 3 – Methods and

Materials. The developed model was ran through parameter optimization algorithm as

below:

C1-1_Optimization.feb

0.001

0.001

Rigid.Fz

142

35, 5, 40

0.05, 0.01, 0.49

0.00005, 0.00001, 0.001

0, 0

.

. (time, load experimental data)

.

3800, -14.00

Once the experimental data was fitted, the accuracy of the predicted load response and

the experimental response were checked by calculating the normalized root-mean-square

error (NRMSE) using the following Matlab script:

( , , ) ∑𝑛𝑛 2 𝑖𝑖 𝑥𝑥𝑝𝑝 𝑖𝑖− 𝑥𝑥𝑒𝑒 𝑖𝑖 = � , where n is the total number of values; xp,i are the ( , 𝑛𝑛 , ) 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝑥𝑥𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚− 𝑥𝑥𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚 predicted values; and xe,i are the experimental values.

143 ------Matlab Code ------%% Read Text File % Select File clc clear all close all [filename, pathname, filterindex] = uigetfile('*.txt', 'Pick a TXT code file'); [a,b,c,] = textread (fullfile (pathname,filename), '%f %f %f ','headerlines', 5,'delimiter',',');

A = [a,b,c,] %% Process the Data % Experimental Data t = smooth (A(:,1), 1); x = smooth (A(:,2), 1); xmax = max(x); xmin = min(x);

% Model Predicted Data y = smooth (A(:,3), 1); coeff = [ones(size(x)), x] \ y; yfit = coeff(1) + (coeff(2) * x);

Rsq = 1 - (sum((y - yfit).^2)/sum((y - mean(y)).^2)) NRMSE = 100 * (sqrt (sum ((y – x)^2)))/(xmax – xmin); plot(t, x) hold on plot(t, y)

title(sprintf('title of plot slope: %d, R2: %d, NRMSE: %d', coeff(2), Rsq, NRMSE))

144 Appendix 2: Determination of Hydrogel Crystallinity

Formulation tested: Three hydrogel formulations - HG43, HG48 and HG53

Equipment: Differential Scanning Calorimeter Q100 (TA Instruments, New Castle, DE)

Method: In this pilot study, all the hydrogel formulation samples were analyzed over a temperature range of -80°C to 200°C. In a nitrogen environment, a heating and cooling rate of 5°C/min was used after attaining initial equilibrium at 20°C.

Results: The thermal energy plots for all three hydrogels are presented in Figure 7-1.

HG43

Figure 7-1: Continued on next page. 145

HG48

HG53

Figure 7-1: DSC thermal plots of hydrogel formulations HG43, HG48 and HG53.

146 A broad water-related peak was observed around 0° and 100°C, consequently, there is a possibility of the water peak overshadowing any polymer related thermal peak, which is critical for the molecular evaluation of the material. Additionally, to determine the crystallinity of the material, enthalpy of 100% crystalline material is required. To obtain a fully crystalline hydrogel, the samples would need to be in the dry solid form; however, hydrogels are prone to change in chemical structure when exposed to heated desiccation.

Hence, at present, the enthalpy and resulting crystallinity of the hydrogel formulations could not be determined. Additional testing of either the powdered form of the polymer or a different technique must be used to ascertain the crystallinity of the hydrogels.

147 Appendix 3: Matlab script for evaluating Young’s modulus from the tensile data at 0-10% strain

------Matlab Code ------%% Read Text File % Select File clc clear all close all [filename, pathname, filterindex] = uigetfile('*.txt', 'Pick a TXT code file'); [a,b,c,d,e] = textread (fullfile (pathname,filename), '%f %f %f %f %f','headerlines', 7,'delimiter',',');

%% Process the Data % Enter the length and width len = 3.43; wid = 6.55;

% Apply the formulas

AxStrain = (d - d(1))/d(1); LatStrain = (e - e(1))/e(1); Stress = b/(len*wid);

%% To determine Young’s Modulus

A =[a b c d e AxStrain LatStrain Stress];

UltimateStrength = max(A(:,8)) index = (A(:,6) <= 0| A(:,6) >= 0.10); A(index,:) = [];

148 x = smooth(A(:,6), 1); y = smooth(A(:,8), 1);

figure, hold on plot(x, y); xlabel ('Strain (mm/mm)'); ylabel ('Stress (MPa)');

coeff = [ones(size(x)), x] \ y; yfit = coeff(1) + (coeff(2) * x);

Rsq = 1 - (sum((y - yfit).^2)/sum((y - mean(y)).^2)) plot(x, yfit, 'r')

title(sprintf('title of plot slope: %d, R2: %d',coeff(2),Rsq))

%% To determine Poisson’s ratio

A =[a b c d e AxStrain LatStrain Stress];

BreakElongation = max(A(:,6)) index = (A(:,6) <= 0| A(:,6) >= 0.10); A(index,:) = [];

x = smooth(A(:,6), 1); y = smooth(A(:,7), 1);

figure, hold on plot(x, y); xlabel ('Axial Strain (mm/mm)'); ylabel ('Lateral Strain (mm/mm)');

coeff = [ones(size(x)), x] \ y; yfit = coeff(1) + (coeff(2) * x); 149

Rsq = 1 - (sum((y - yfit).^2)/sum((y - mean(y)).^2)) plot(x, yfit, 'r') title(sprintf('title of plot slope: %d, R2: %d',coeff(2),Rsq))

150 Appendix 4: Matlab script for evaluating different failure criteria

------Matlab Code ------clc clear all close all

%% Process the Data % Enter the Principal Stresses and Strains PStress2 = [-9.558 -8.789 -8.324 -9.668 -9.854];

PStress3 = [-16.49 -16.19 -15.15 -17.1 -16.23];

PStrain1 = [0.5213 0.4493 0.4585 0.4899 0.4758];

PStrain3 = [-0.3778 -0.3781 -0.3758 -0.3768 -0.3763];

%% Calculate different failure criteria for i = 1:4

VonMisesStress (i,:) = sqrt((PStress2(i))^2 - (PStress2(i)*PStress3(i)) + (PStress3(i))^2);

MaxShear (i,:) = (PStress2(i) - PStress3(i))/2; end

151 Vita

MARIYA TOHFAFAROSH

Ph.D., Biomedical Engineering, Drexel University, 2017 GPA 3.92

M.S., Biomedical Engineering, Drexel University, 2013 GPA 3.87

B.S., Biomedical Engineering, New Jersey Institute of Technology, 2010 GPA 3.96 Minor: Business

PUBLICATIONS AND PRESENTATIONS:

Peer Reviewed Publications Tohfafarosh, M., Sevit, A., Patel, J., Kiel, J.W., Greenspon, A., Prutkin, J. M., Kurtz, S. M. (2016). Characterization of the Outer Insulation in Long Term Implanted Leads. J Long Term Eff Med Implants, 26 (3), 225-232. Tohfafarosh, M., Baykal, D., Kiel, J. W., Mansmann, K., & Kurtz, S. M. (2016). Effects of gamma and e-beam sterilization on the chemical, mechanical and tribological properties of a novel hydrogel. J Mech Behav Biomed Mater., 53, 250-256. Bakhtina, A., Tohfafarosh, M., Lichtler, A., & Arinzeh, T. L. (2014). Characterization and differentiation potential of rabbit mesenchymal stem cells for translational regenerative medicine. In Vitro Cell Dev Biol Anim, 50(3), 251-260. Kurtz, S. M., MacDonald, D. W., Kocagoz, S., Tohfafarosh, M., & Baykal, D. (2014). Can pin-on-disk testing be used to assess the wear performance of retrieved UHMWPE components for total joint arthroplasty? Biomed Res Int, 2014, 581812. Arnholt, C. M., MacDonald, D. W., Tohfafarosh, M., Gilbert, J. L., Rimnac, C. M., Kurtz, S. M., et al. (2014). Mechanically assisted taper corrosion in modular TKA. J Arthroplasty, 29 (9 Suppl), 205-208.

Selected Conference Presentations Tohfafarosh M, Baykal D, Mansmann K, Kurtz SM. Computational material modeling and evaluation of sterilization effects on a novel hydrogel. Podium presentation, 2nd International Conference on BioTribology. Toronto, Canada. May 11-14, 2014.

Tohfafarosh M, Sevit A, Patel J, Greenspon A, Prutkin J, Kurtz SM. “Cardiac lead retrieval analysis: insulation degradation hinders long-term performance.” Poster presentation, Society For Biomaterials. Boston, MA. April 10-13, 2013.