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ON SOLUTIONS FOR THE MOVING BOUNDARY PROBLEM DESCRIBING AN ERODING VASCULAR GRAFT

Jiao, Kai (2017) ON SOLUTIONS FOR THE MOVING BOUNDARY PROBLEM DESCRIBING AN ERODING VASCULAR GRAFT. Master's Thesis, University of Pittsburgh. (Unpublished)

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Abstract

Synthetic accellular biodresorbable vascular grafts, which can degrade and vanish with time, are an important type of tissue engineered vascular grafts (TEVGs) with great clinical potential for blood vessel replacement surgeries. In order to study the in vitro degradation process of the graft in stationary solvent, a mathematical model is established using mixture theory. Balance laws and jump conditions across singular surfaces are used to determine the moving boundary conditions at surfaces of the vascular graft. The resulting system of equations is a moving boundary problem in the form of second order partial differential equations for the inner and outer domains. Regular perturbation theory is applied for both problems and first order solutions for the two moving boundaries are obtained. To test the accuracy of the approximate solutions, numerical solutions to the full problem are obtained and compared with the perturbation solutions. In vivo, degradation of the scaffold includes blood flow inside the inner domain. At the end of this thesis, we provide a formulation of this more general case.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Jiao, Kaikaj71@pitt.edukaj71
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRobertson, Anne M.rbertson@pitt.edu
Committee MemberGaldi, Giovanni P.galdi@pitt.edu
Committee MemberCho, Sung Kwonskcho@pitt.edu
Committee MemberBabaee, Hessamh.babaee@pitt.edu
Date: 25 September 2017
Date Type: Publication
Defense Date: 20 July 2017
Approval Date: 25 September 2017
Submission Date: 24 July 2017
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 86
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: MS - Master of Science
Thesis Type: Master's Thesis
Refereed: Yes
Uncontrolled Keywords: TEVGs Biodresorbable Vascular Grafts Mixture Theory Degradation Moving Boundary Problem Perturbation Theory
Date Deposited: 25 Sep 2017 20:55
Last Modified: 25 Sep 2017 20:55
URI: http://d-scholarship.pitt.edu/id/eprint/32842

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