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• W2893329061 abstract "The role of mathematics in cancer research has steadily increased over time. Multidisciplinarycollaboration in cancer research is essential and mathematical applications cansignificantly contribute to many areas of cancer research. For example, mathematicalmodels can provide deeper insight and establish a framework for understanding propertiesof cancer cells. Modeling the effects of radiation on cancer cells is one of the mostinteresting areas in mathematical biology and a variety of models by using the Targettheory and DNA fragmentations have been applied to describe how radiation influencetumor cells. In this study, two new mathematical frameworks are proposed to model thepopulation dynamics of heterogeneous tumor cells after the treatment with external beamradiation. The first model is derived based on the Target Theory and Hit Theory. Accordingto these theories, the tumor population is divided into m different sub-populationsbased on the different effects of ionizing radiations on human cells. This model consistsof a system of differential equations with random variable coefficients representingthe dynamics transition rates between sub-populations. The model is also describingthe heterogeneity of the cell damage and the repair mechanism between two consecutivedose fractions. In the second model, we study the population dynamics of breast cancercells treated with radiotherapy by using a system of stochastic differential equations. Accordingto the cell cycle, each cell belongs to one of three subpopulations G, S, or M,representing gap, synthesis, and mitosis subpopulations. Cells in the M subpopulationare highly radio-sensitive, whereas cells in the S subpopulation are highly radio-resistant.Therefore, in the process of radiotherapy, cell death rates of different subpopulations are not equal. In addition, since flow cytometry is unable to detect apoptotic cells accurately,the small changes in cell death rate in each subpopulation during treatment are considered.Therefore, a new definition for the lifespan of the tumor based on population size isintroduced. Tumor Lifespan is defined as the minimum number of dose fractions neededto remove the whole tumor. The stability of the first model is studied by considering threecases. For the first and second cases, we assumed that each cell has two and three targets(m = 2 and m = 3). Applying Routh-Hurwitz criterion, it is proven that the system isstable when the probability that one target becomes deactivated after the application ofa dose fraction (q) is greater than or equal to 0.5. Finally, the system stability for thethird case is investigated analytically when each cell assumed has m targets. By usingGershgorin theorem, it is shown that the system is stable where q > 0:5. In the secondmodel, the existence and uniqueness of the solution are proven and an explicit solutionfor the SDE model is presented. Moreover, the system stability is investigated via a necessaryand sufficient condition on model parameters. The transition rates are estimatedin a steady state condition. Subsequently, the model is solved numerically using Euler-Murayama and Milstein methods and the other parameters of the model are estimatedusing parametric and nonparametric simulated likelihood estimation parameter methods.Finally, we did a number of experiments on MCF-7 breast cancer cell line. The cell cycleanalysis assay has been used to analyze experimental data. Then the obtained data is appliedand able to calibrate and verify our models." @default.
• W2893329061 created "2018-10-05" @default.
• W2893329061 creator A5020933108 @default.
• W2893329061 date "2018-05-01" @default.
• W2893329061 modified "2023-09-27" @default.
• W2893329061 title "Mathematical modeling of the tumor cells population dynamics in breast cancer / Amin Oroji" @default.
• W2893329061 hasPublicationYear "2018" @default.
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