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A Computational Stress-Deformation Analysis of Arterial Wall Tissue

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  eScholarship provides open access, scholarly publishingservices to the University of California and delivers a dynamicresearch platform to scholars worldwide. Electronic Thesis and DissertationsUC Berkeley Peer ReviewedTitle:  A Computational Stress-Deformation Analysis of Arterial Wall Tissue Author: Krone, Ryan Taylor  Acceptance Date: 2010 Series: UC Berkeley Electronic Theses and Dissertations Degree: Ph.D., Mechanical EngineeringUC Berkeley Advisor(s): Zohdi, Tarek, Steigmann, David Committee: Strain, John Permalink: http://www.escholarship.org/uc/item/2b76c21s Abstract:Copyright Information:  All rights reser ved unless otherwise indicated. Contact the author or srcinal publisher for anynecessary permissions. eScholarship is not the copyright owner for deposited works. Learn moreat http://www.escholarship.org/help_copyright.html#reuse  A Computational Stress-Deformation Analysis of Arterial Wall Tissue  byRyan Taylor KroneA dissertation submitted in partial satisfaction of therequirements for the degree of Doctor of PhilosophyinMechanical Engineeringin theGRADUATE DIVISIONof theUNIVERSITY OF CALIFORNIA, BERKELEYCommittee in charge:Professor David Steigmann, Co-chairProfessor Tarek Zohdi, Co-chairProfessor John StrainFall 2010  A Computational Stress-Deformation Analysis of Arterial Wall Tissue Copyright 2010 byRyan Taylor Krone  1 Abstract A Computational Stress-Deformation Analysis of Arterial Wall Tissue byRyan Taylor KroneDoctor of Philosophy in Mechanical EngineeringUniversity of California, BerkeleyProfessor David Steigmann, Co-chairProfessor Tarek Zohdi, Co-chairUnderstanding the mechanical behavior of arterial walls under various physi-ological loading and boundary conditions is essential for achieving the following:(1) improved therapeutics that are based on mechanical procedures (e.g. arterialsegmenting and suturing), (2) study of mechanical factors that may trigger the on-setof arterialaneurysms (i.e. focalblood-filled dilatations of thevessel wallcaused by disease) and (3) investigations on tissue variations due to health, age, hyperten-sion and atherosclerosis, all of which hold immense clinical relevance. In general,the physiological conditions on an any arterial segment can include axial stretch,torsionaltwistandtransmural(internal,radial)pressurewhichoftenprovokelargewall-tissue deformations that require theories of continuum hyperelasticity. Fur-ther, the presence of collagen fibers throughout the two structural layers (media,adventitia) of the arterial wall require anisotropic strain energy functions for morehistological accurate models. Nonlinear computational methods are therefore es-sentialforthisclassofboundary-value-problems(BVPs)whichoftendonotcontainclosed-form solutions.We begin by modeling the arterial vessel wall as a thin sheet in the form of a circular cylinder in the reference configuration. We seek to employ a bio-typestrain energy function on this constitutive framework to investigate the onset of non-linear instabilities in a thin-walled, hyperelastic tube under (remote) axialstretch and internal pressure. Viscoelastic e ff  ects are also considered in this model.We then build to investigating the e ff  ects of various combinations of axial stretchand transmural pressure on the global deformation and through-thickness stressand strain fields of an arterial segment modeled as a two-layer, fiber-reinforcedcomposite and idealized as a thick-walled cylinder in the reference configuration.Wefurtherconsider(inbothmodels)thepresenceoflocaltissuelesions,orportionsof the arterial wall having either sti ff  er (i.e. thrombosis or scar tissue) or softer (i.e.diseased tissue) material characteristics, relative to the surrounding tissue. Weaccount for this by appropriately scaling the elastic constants of the strain energy
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