Constitutive Modeling for Biodegradable Polymers
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CONSTITUTIVE MODELING FOR BIODEGRADABLE POLYMERS FOR APPLICATION IN ENDOVASCULAR STENTS A Dissertation by JOÃO FILIPE DA SILVA SOARES Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY May 2008 Major Subject: Mechanical Engineering CONSTITUTIVE MODELING FOR BIODEGRADABLE POLYMERS FOR APPLICATION IN ENDOVASCULAR STENTS A Dissertation by JOÃO FILIPE DA SILVA SOARES Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Approved by: Co-Chairs of Committee, Kumbakonam R. Rajagopal James E. Moore, Jr. Committee Members, Jay D. Humphrey Joseph E. Pasciak Head of Department, Dennis O’Neal May 2008 Major Subject: Mechanical Engineering iii ABSTRACT Constitutive Modeling of Biodegradable Polymers for Application in Endovascular Stents. (May 2008) João Filipe da Silva Soares, Licenciatura, Universidade Técnica de Lisboa Co-Chairs of Advisory Committee: Dr. K. R. Rajagopal Dr. James E. Moore, Jr. Percutaneous transluminal balloon angioplasty followed by drug-eluting stent implantation has been of great benefit in coronary applications, whereas in peripheral applications, success rates remain low. Analysis of healing patterns in successful deployments shows that six months after implantation the artery has reorganized itself to accommodate the increase in caliber and there is no purpose for the stent to remain, potentially provoking inflammation and foreign body reaction. Thus, a fully biodegradable polymeric stent that fulfills the mission and steps away is of great benefit. Biodegradable polymers have a widespread usage in the biomedical field, such as sutures, scaffolds and implants. Degradation refers to bond scission process that breaks polymeric chains down to oligomers and monomers. Extensive degradation leads to erosion, which is the process of mass loss from the polymer bulk. The prevailing mechanism of biodegradation of aliphatic polyesters (the main class of biodegradable polymers used in biomedical applications) is random scission by passive hydrolysis and results in molecular weight reduction and softening. In order to understand the applicability and efficacy of biodegradable polymers, a two pronged approach involving experiments and theory is necessary. A constitutive model involving degradation and its impact on mechanical properties was developed through an extension of a material which response depends on the history of the motion and on a scalar parameter reflecting the local extent of degradation and depreciates the mechanical properties. A rate equation describing the chain scission process confers characteristics of stress relaxation, creep and hysteresis to the material, arising due to the iv entropy-producing nature of degradation and markedly different from their viscoelastic counterparts. Several initial and boundary value problems such as inflation and extension of cylinders were solved and the impacts of the constitutive model analyzed. In vitro degradation of poly(L-lactic acid) fibers under tensile load was performed and degradation and reduction in mechanical properties was dependent on the mechanical environment. Mechanical testing of degraded fibers allowed the proper choice of constitutive model and its evolution. Analysis of real stent geometries was made possible with the constitutive model integration into finite element setting and stent deformation patterns in response to pressurization changed dramatically as degradation proceeded. v DEDICATION To my dearest Filipa Arinto vi ACKNOWLEDGMENTS I am truly indebted to Dr. Rajagopal, the Abbé Faria of my Chateau d’If, for granting me this unique opportunity of learning from him. He is the utmost contributor to my development, not only on the academic level but also from a personal standpoint. During my five years being his apprentice, mechanics, mathematics, their history and intricate connections were presented to me in novel ways, either at his insightful lectures or during meetings in his office. Most important of all is his ability to present himself as a followable role model and his uncharacteristic stance of “always question authority”. I am sure that I will not find such anywhere else. Dr. Moore and his pragmatic knowledge helped me to look at my research from the practical standpoint, functioning almost as the perfect balance between theory and practice. I thank him for all the important opportunities for the development of an academic career with all the posters, presentations, and grant writing. I am also grateful for all the resources needed for my research, and most of all, his teachings on his savvy of the academic world. My courtesy should also be extended to his family for making times away from mine so much more bearable. I must thank Dr. Jay Humphrey and Dr. Joe Pasciak for serving on my committee. I also thank Dr. Luís Faria and Dr. Adélia Sequeira for all the support needed to seize this opportunity. My thanks should also be extended to Dr. Luoyi Tao, Dr. Arun Srinivasa, Dr. John Criscione, Dr. Theofanis Strouboulis and Dr. Raytcho Lazarov for the useful discussions. The experimental part of my work would never be possible without Dr. Melissa Grunlan, Yaping You and Dirk Rosenstock. Thanks must also be extended to Dr. Jay Walton for substituting for my defense. I am grateful to my parents, sister and friends for offering their kind words of encouragement and support. I thank Dr. Moore’s lab mates Mike Moreno, Clark Meyer, Julian Bedoya, Luke Timmins, Shiva Yazdani, Ellie Rahbar as well as other journal club members; and Dr. Rajagopal’s fellow graduate students, Krishna Kannan, Sharat Prasad, Anand Mohan, Wakar Malik, Parag Ravindran, Sai Krishna and all others not listed but vii not forgotten. Finally, I thank Timothy Forrest and his family for serving as such outstanding hosts of the United States of America. The financial support provided by FCT – Fundação para a Ciência e Tecnologia (SFRH/BD/17060/2004) is also gratefully acknowledged. viii TABLE OF CONTENTS Page ABSTRACT..................................................................................................................... iii DEDICATION ...................................................................................................................v ACKNOWLEDGMENTS.................................................................................................vi TABLE OF CONTENTS............................................................................................... viii LIST OF FIGURES..........................................................................................................xii LIST OF TABLES ..........................................................................................................xix CHAPTER I INTRODUCTION...........................................................................................1 A. Cardiovascular stents.............................................................................1 1. Responses to stenting...................................................................2 2. Drug eluting stents .......................................................................4 B. Biodegradable stents..............................................................................7 1. Polymeric stents...........................................................................7 2. Concept of biodegradable stents ..................................................8 3. Design of biodegradable stents ..................................................10 C. Polymer degradation............................................................................11 1. Terminology...............................................................................12 2. Mechanisms of polymer degradation.........................................14 3. Degradation of aliphatic polyesters ...........................................16 4. Influence of the mechanical environment on degradation.........17 D. Erosion and elimination.......................................................................19 E. Models of degradation and erosion .....................................................21 1. Models for polymer degradation................................................21 2. Models for polymer erosion.......................................................23 3. Models for mechanical properties reduction..............................24 II PRELIMINARIES........................................................................................26 A. Kinematics...........................................................................................26 1. Bodies, motions and configurations...........................................26 2. Measures of deformation ...........................................................28 3. Relative motions and histories...................................................30 4. Kinematical linearization...........................................................32 B. Balance laws........................................................................................33 1. Balance of mass .........................................................................34 ix CHAPTER Page 2. Forces and moments ..................................................................35 3. Euler’s laws of mechanics .........................................................35 C. Cauchy’s stress theory.........................................................................36