This thesis presents and analyzes a mathematical model for necrotizing enterocolitis (NEC), a devastating disease that attacks the gastrointestinal tract of pre-term infants. Mathematical models for NEC have been developed in the past. These modes are extremely valuable and provide important insights into the disease. However, all of the models developed previously are one dimensional, ordinary differential equation models and, therefore, simulate only the transient effects of NEC but do not fully model its spatial effects. The mathematical model presented here is a three dimensional model in the form of a system of nonlinear partial differential equations. A three dimensional model is needed to accurately simulate diffusion and advection of the major factors in NEC, to account for the different effects of NEC in the different regions in the body, and to fully integrate all the effects of such mechanisms as epithelial cell degradation and migration.
This thesis presents medical research regarding NEC, constructs inflammatory cascades related to the disease, and develops the system of partial differential equation system. Also, full mathematical analysis of the system of equations. The mathematical analysis of the system of partial differential equations and the associated a mixed finite element analysis are, perhaps, the most important parts of the thesis. The results of this analysis have significance for the NEC system and have significance independent of the NEC system. Furthermore, finite element analysis (using the mixed method) is done on this coupled system and convergence is proven, a new and very important result. No mixed method finite element analysis has previously been published for this system. Similar analysis is done on the rest of the partial differential equations in the system. At the end of the thesis, computer simulations are done using the mathematical model. These simulations demonstrate that the NEC mathematical model presented here produces realistic results consistent with the actual progression of the disease. (Abstract shortened by UMI.)
|Advisor:||Yotov, Ivan, Trenchea, Catalin|
|Commitee:||Rubin, Jonathan, Swigon, David, Trenchea, Catalin, Vodovotz, Yoram, Yotov, Ivan|
|School:||University of Pittsburgh|
|School Location:||United States -- Pennsylvania|
|Source:||DAI-B 76/02(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Convergence, Coupled system, Disease progression, Mixed finite elements, Necrotizing enterocolitis, Nonlinear partial differential equations|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be