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COMPUTATION AND ANALYSIS OF TUMOR GROWTH
Title
COMPUTATION AND ANALYSIS OF TUMOR GROWTH
Creator
Turian, Emma
Date
2016, 2016-05
Description
The ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment....
Show moreThe ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment. Parameters that control tumor morphology may also contribute to its invasive ability. In this thesis, we investigate tumor growth using a two-phase Stokes model. We first examine the morphological changes using the surface energy of the tumor-host interface and investigate its nonlinear dynamics using a boundary integral method. In an effort to understand the interface stiffness, we then model the tumor-host interface as an elastic membrane governed by the Helfrich bending energy. Using an energy variation approach, we derive a modified Young-Laplace condition for the stress jump across the interface, and perform a linear stability analysis to evaluate the effects of viscosity, bending rigidity, and apoptosis on tumor morphology. Results show that increased bending rigidity versus mitosis rate contributes to a more stable growth. On the other hand, increased tumor viscosity or apoptosis may lead to an invasive fingering morphology. Comparison with experimental data on glioblastoma spheroids shows good agreement especially for tumors with high adhesion and low proliferation. Next, we evaluate tumor regression during cancer therapy by a combined modality involving chemotherapy and radiotherapy. The goal is to address the complexities of a vascular tumor (e.g. apoptosis and vascularization) during treatment. We introduce an apoptotic time delay and study its impact on tumor regression using numerical and asymptotic techniques. In particular, we implement the linear-quadratic model and identify two extreme sets of parameter data, namely the slow, and fast tumor response to therapy. Numerical simulations for the slow response set show good agreements with data representing non-small cell lung carcinoma. Using the evolution equation for tumor radius with time delay, we find that tumors with shorter time interval to the onset of apoptosis shrink faster.
Ph.D. in Applied Mathematics, May 2016
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MODELS AND SIMULATIONS OF SPROUTING ANGIOGENESIS
Title
MODELS AND SIMULATIONS OF SPROUTING ANGIOGENESIS
Creator
Langman, Catherine
Date
2016, 2016-05
Description
All living mammalian cells need to consume oxygen and nutrients for cellular processes and need a way to remove waste from those cellular...
Show moreAll living mammalian cells need to consume oxygen and nutrients for cellular processes and need a way to remove waste from those cellular processes. Capillary networks provide places for such exchanges to occur. The process of creating new capillaries from existing blood vessels is called angiogenesis. Understanding angiogenesis is critical to the advancement of knowledge in the life sciences, as well as in medical applications where blood vessels play an important role. Angiogenesis is a complex process composed of many subprocesses which are not yet fully understood and take place over varying temporal and spatial scales. Mathematically modeling and simulating angiogenesis, and evaluating the capillary networks that result from angiogenesis, can help further understanding of angiogenesis and improve therapeutic treatments. This thesis examines mathematical models and simulations of sprouting angiogenesis and proposes two generic models of sprouting angiogenesis based on descriptions found in educational and scientific literature. Future research opportunities for scientific study and educational study using these models as a starting place are discussed.
M.S. in Applied Mathematics, May 2016
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