Computer Science Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/2756
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Item Modeling the Transfer of Drug Resistance in Solid Tumors(2018) Becker, Matthew Harrington; Levy, Doron; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be trans- ferred between cells, which is the focus of this dissertaion. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Dura ́n et al. studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small cell lung cancer) cell lines [1]. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this dissertation we develop three new mathematical model for the transfer of drug resistance between cancer cells. Our first model is based on incorporating a resistance phenotype into a model of cancer growth [2]. The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of [1]. The mathematical model further suggests that resistant cancer cells have a slower division rate than the sensitive cells. Our second model is a reaction-diffusion model with sensitive, resistant, and temporarily resistant cancer cells occupying a 2-dimensional space. We use this model as another extension of [1]. We show that this model, with competition and diffusion in space, provides an even better fit to the experimental data [1]. We incorporate a cytotoxic drug and study the effects of varying treatment protocols on the size and makeup of the tumor. We show that constant infusion leads to a small but highly resistant tumor, while small doses do not do enough to control the overall growth of the tumor. Our final model extends [3], an integro-differential equation with resistance modeled as a continuous variable and a Boltzmann type integral describing the transfer of P-gp expression. We again extend the model into a 2-dimensional spatial domain and incorporate competition inhibited growth. The resulting model, written as a single partial differential equation, shows that over time the resistance transfer leads to a uniform distribution of resistance levels, which is consisten with the results of [3]. We include a cytotoxic agent and determine that, as with our second model, it alone cannot successfully eradicate the tumor. We briefly present a second extension wherein we include two distinct transfer rules. We show that there is no qualitative difference between the single transfer rule and the two-transfer rule model.Item Mathematical Models of Immune Regulation and Cancer Vaccines(2012) Wilson, Shelby Nicole; Levy, Doron; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)An array of powerful mathematical tools can be used to identify the key underlying components and interactions that determine the mechanics of biological systems such as the immune system and its interaction with cancer. In this dissertation, we develop mathematical models to study the dynamics of immune regulation in the context of the primary immune response and tumor growth. Regulatory T cells play a key role in the contraction of the immune response, a phase that follows the peak response to bring cell levels back to normal. To understand how the immune response is regulated, it is imperative to study the dynamics of regulatory cells, and in particular, the conditions under which they are functionally stable. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and possibly turn into immune promoting cells. We develop dynamical models to investigate the effects of an unstable regulatory T cell population on the immune response. These models display the usual characteristics of an immune response with the added capabilities of being able to correct for initial imbalances in T cell populations. We also observe an increased robustness of the immune response with respect to key parameters. Similar conclusions are demonstrated with regards to the effects of regulatory T cell switching on immunodominance. TGF-beta is an immunoregulatory protein that contributes to inadequate anti-tumor immune responses in cancer patients. Recent experimental data suggests that TGF-beta inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model to gain insight into the cooperative interaction between anti-TGF-beta and vaccine treatments. Using numerical simulations and stability analysis we study the following scenarios: a control case of no treatment, anti-TGF-beta treatment, vaccine treatment, and combined anti-TGF-beta vaccine treatments. Consistent with experimental data, we show that monotherapy alone cannot successfully eradicate a tumor. Tumor eradication requires the combination of these therapeutic approaches. We also demonstrate that our model captures the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy.