In this paper a new mathematical model for the population of tumor growth treated by radiation is... more In this paper a new mathematical model for the population of tumor growth treated by radiation is proposed. The cells dynamics population in each state and the dynamics of whole tumor population are studied. Furthermore, a new definition of tumor lifespan is presented. Finally, the effects of two main parameters, treatment parameter (q), and repair mechanism parameter (r) on tumor lifespan are probed, and it is showed that the change in treatment parameter (q) highly affects the tumor lifespan.
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new ... more Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According to the Target Theory, the tumor population is divided into m different subpopulations based on the diverse effects of ionizing radiation on human cells. A hybrid model con- sists of a system of differential equations with random variable coefficients representing the transition rates between subpopulations is proposed. This model is utilized to sim- ulate the dynamics of cell subpopulations within a tumor. The model also describes the cell damage heterogeneity and the repair mechanism between two consecutive dose fractions. As such, a new definition of tumor lifespan based on population size is intro- duced. Finally, the stability of the system is studied by using the Gershgorin theorem. It is proven that the probability of target inactivity post ...
In this paper, a new mathematical model is proposed for studying the population dynamics of breas... more In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to 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 subpopulation are 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. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 b...
In this paper a new mathematical model for the population of tumor growth treated by radiation is... more In this paper a new mathematical model for the population of tumor growth treated by radiation is proposed. The cells dynamics population in each state and the dynamics of whole tumor population are studied. Furthermore, a new definition of tumor lifespan is presented. Finally, the effects of two main parameters, treatment parameter (q), and repair mechanism parameter (r) on tumor lifespan are probed, and it is showed that the change in treatment parameter (q) highly affects the tumor lifespan.
Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new ... more Radiation Therapy (XRT) is one of the most common cancer treatment methods. In this paper, a new mathematical model is proposed for the population dynamics of heterogeneous tumor cells following external beam radiation treatment. According to the Target Theory, the tumor population is divided into m different subpopulations based on the diverse effects of ionizing radiation on human cells. A hybrid model con- sists of a system of differential equations with random variable coefficients representing the transition rates between subpopulations is proposed. This model is utilized to sim- ulate the dynamics of cell subpopulations within a tumor. The model also describes the cell damage heterogeneity and the repair mechanism between two consecutive dose fractions. As such, a new definition of tumor lifespan based on population size is intro- duced. Finally, the stability of the system is studied by using the Gershgorin theorem. It is proven that the probability of target inactivity post ...
In this paper, a new mathematical model is proposed for studying the population dynamics of breas... more In this paper, a new mathematical model is proposed for studying the population dynamics of breast cancer cells treated by radiotherapy by using a system of stochastic differential equations. The novelty of the model is essentially in capturing the concept of the cell cycle in the modeling to be able to evaluate the tumor lifespan. According to 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 subpopulation are 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. Subsequently, the proposed model is calibrated using experimental data from previous experiments involving the MCF-7 b...
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