Browsing by Subject "Mathematical biology"

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    Modeling cancer evolution and inferring its parameters
    (2022-06) Gunnarsson, Einar
    Cancer is a group of diseases characterized by uncontrolled cell proliferation. The initiation of cancer usually involves a series of mutations in genes responsible for regulating the cell cycle. As the cancer-initiating cell expands into a tumor, the tumor cells continue to accumulate mutations, which induces substantial genetic heterogeneity within the tumor. In recent years, it has been increasingly recognized that epigenetic mechanisms, which are chemical changes to DNA or the chromatin structure which houses DNA, play an equally important role in tumor evolution. Due to their reversible and rapid nature, epigenetic mechanisms can enable cancer cells to switch dynamically between two or more phenotypic states, which commonly show differential responses to drug treatments. This dissertation consists of four projects which each involves using a mathematical model to study the evolutionary dynamics of cancer. The projects range from addressing the process of cancer initiation to the evolution of drug resistance, and they take both genetic and non-genetic perspectives. In Chapter 2, we study the dynamics of cancer initiation in multilayered tissue under a two-step mutational model of cancer. In Chapter 3, we study the accumulation of neutral mutations during tumor progression, which are mutations that do not affect the division rate of tumor cells. In Chapter 4, we study the role of phenotypic switching in the evolution of stable drug resistance. Finally, in Chapter 5, we develop a statistical framework for inferring the rates of cell division, cell death and phenotypic switching in cancer.
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    Stochastic Models of Epithelial Cancer Initiation and Glioblastoma Recurrence
    (2018-06) Storey, Kathleen
    Cancer development involves the inherently stochastic accumulation of genetic mutations, conferring growth advantages to the cells affected by these mutations. Thus, stochastic modeling provides useful insight when studying the evolutionary processes of cancer initiation and tumor progression. This thesis consists of three projects within the field of stochastic modeling of cancer evolution. First we explore the temporal dynamics of spatial heterogeneity during the process of carcinogenesis from healthy tissue. We utilize a spatial stochastic model of mutation accumulation and clonal expansion to describe this process. Under a two-step carcinogenesis model, we analyze two new measures of spatial population heterogeneity. In particular, we study the typical length-scale of genetic heterogeneity during carcinogenesis and estimate the size of the clone surrounding a sampled premalignant cell. Next we study the propagation speed of a premalignant clone during carcinogenesis. We approximate a premalignant clone in epithelial tissue containing w layers of proliferating cells (referred to as a ``basal zone'') with a biased voter model on a set of w stacked integer lattices. Using the dual process of the biased voter model, we determine the asymptotic propagation speed of the premalignant clone in this setting and compare it to the previously determined speed in epithelial tissue with a single layer of proliferating cells. We then use this speed to investigate clinical implications for primary tumors detected in various types of epithelial tissue. Finally we develop a multi-type branching process model of the tumor progression and treatment response in glioblastoma multiforme (GBM). GBM recurrence is often attributed to acquired resistance to the standard chemotherapeutic agent temozolomide (TMZ). Promoter methylation of the DNA repair gene MGMT is frequently linked to TMZ sensitivity. We develop and parameterize a model using clinical and experimental data, to investigate the interplay between TMZ and MGMT methylation during GBM treatment. Our model suggests that TMZ may have an inhibitory effect on maintenance methylation of MGMT after cell division. Incorporating this effect, we study the optimal TMZ dosing regimen for GBM patients with high and low levels of MGMT methylation at diagnosis.