Mathematical modeling of tumor growth has been an active area of research for the past several decades. Early theoretical approaches to understanding cancer utilized diffusion models to predict mass tumor growth. Over the years, more biological data has become available and computational power has drastically increased, allowing a greater number of topics to be explored and a larger number of theoretical techniques to be exploited in mathematical models of tumor progression.;Many key questions can still benefit from more theoretical investigations. Limited work has been done on incorporating intra- and inter-cellular feedback and tumor and environmental heterogeneity into cancer models. The general goal of my research is to develop models that account for the feedback that occurs between a growing tumor and the evolving host. This allows the entire tumor system to be quantitatively studied, which is important since the individual components involved in tumor growth interact in nonlinear and stochastic ways to determine system behavior. My thesis work builds to the long-term goal of developing a "virtual patient," which takes as input patient-specific data, and outputs patient prognosis and treatment information. While we have yet to develop a "virtual patient," we have been able to answer many questions about tumor progression and treatment through our modeling efforts, including: (1) Under what conditions can a tumor overcome its limited blood supply and grow to a macroscopic size? (2) How do the geometry and topology of the environment in which a tumor grows impact the shape, size and spread of a tumor? What are the consequences for patient prognosis? (3) What is the likelihood that advantageous or deleterious genetic mutations arise within a tumor and how do these mutations impact growth dynamics? (4) Why do certain treatments aimed at targeting the tumor's blood supply ultimately fail to eradicate the cancer? What strategies have the potential to effectively treat the cancer?;This thesis will discuss the individual models that were designed to answer the above questions, as well as preliminary work on incorporating microscopic tissue structure in tumor growth models. The work presented in this thesis culminates with a project in which the individual models are merged into a comprehensive cancer simulation tool. From the comprehensive model, we can demonstrate the biological conditions that are necessary to incorporate in a clinically-relevant cancer simulation tool.
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