abstract: In a 2004 paper, John Nagy raised the possibility of the existence of a hypertumor \emph{i.e.}, a focus of aggressively reproducing parenchyma cells that invade part or all of a tumor. His model used a system of nonlinear ordinary differential equations to find a suitable set of conditions for which these hypertumors exist. Here that model is expanded by transforming it into a system of nonlinear partial differential equations with diffusion, advection, and a free boundary condition to represent a radially symmetric tumor growth. Two strains of parenchymal cells are incorporated; one forming almost the entirety of the tumor while the much more aggressive strain
appears in a smaller region inside of the tumor. Simulations show that if the aggressive strain focuses its efforts on proliferating and does not contribute to angiogenesis signaling when in a hypoxic state, a hypertumor will form. More importantly, this resultant aggressive tumor is paradoxically prone to extinction and hypothesize is the cause of necrosis in many vascularized tumors. / Dissertation/Thesis / Doctoral Dissertation Applied Mathematics 2014
| Identifer | oai:union.ndltd.org:asu.edu/item:25882 |
| Date | January 2014 |
| Contributors | Alvarez, Roberto (Author), Milner, Fabio A (Advisor), Nagy, John D (Committee member), Kuang, Yang (Committee member), Thieme, Horst (Committee member), Mahalov, Alex (Committee member), Smith, Hal (Committee member), Arizona State University (Publisher) |
| Source Sets | Arizona State University |
| Language | English |
| Detected Language | English |
| Type | Doctoral Dissertation |
| Format | 50 pages |
| Rights | http://rightsstatements.org/vocab/InC/1.0/, All Rights Reserved |
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