Title page for ETD etd-05142010-104541


Type of Document Master's Thesis
Author Cooper, Michele
URN etd-05142010-104541
Title Mathematical Modeling of Vascular Tumor Growth and Development
Degree Master of Science
Department Engineering Science and Mechanics
Advisory Committee
Advisor Name Title
Puri, Ishwar K. Committee Chair
De Vita, Raffaella Committee Member
Finkielstein, Carla V. Committee Member
Tanaka, Martin L. Committee Member
Keywords
  • mathematical model
  • angiogenesis
  • vascular tumor
  • tumorigenesis
Date of Defense 2010-05-12
Availability restricted
Abstract
Mathematical modeling of cancer is of significant interest due to its potential to aid in our understanding of the disease, including investigation into which factors are most important in the progression of cancer. With this knowledge and model different paths of treatment can be examined; (e.g. simulation of different treatment techniques followed by the more costly venture of testing on animal models). Significant work has been done in the field of cancer modeling with models ranging from the more broad systems, avascular tumor models, to smaller systems, models of angiogenic pathways. A preliminary model of a vascularized tumor has been developed; the model is based on fundamental principles of mechanics and will serve as the framework for a more detailed model in the future. The current model is a system of nonlinear partial differential equations (PDEs) separated into two basic sub-models, avascular and angiogenesis. The avascular sub-model is primarily based of Fickian diffusion of nutrients into the tumor. While the angiogenesis sub-model is based on the diffusion and chemotaxis of active sprout tips into the tumor. These two portions of the models allow the effects of microvessels on nutrient concentration within the tumor, as well as the effect of the tumor in driving angiogenesis, to be examined. The results of the model have been compared to experimental measurements of tumor growth over time in animal models, and have been found to be in good agreement with a correlation coefficient of (r2=0.98).
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