Description
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.
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.
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Details
Title
- A two strain spatiotemporal mathematical model of cancer with free boundary condition
Contributors
- Alvarez, Roberto L (Author)
- Milner, Fabio A (Thesis 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)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2014
Subjects
Resource Type
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Note
- thesisPartial requirement for: Ph.D., Arizona State University, 2014
- bibliographyIncludes bibliographical references (p. 39-42)
- Field of study: Applied mathematics
Citation and reuse
Statement of Responsibility
by Roberto L. Alvarez