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Abstract Introduction: Glioblastomas are the most malignant and most common gliomas in adults. Mathematical modeling is a powerful tool for analyzing problems of tumor formation and growth. It allows one to develop and test hypotheses which can lead to a better understanding of this malignancy. Objective: To construct a mathematical model to describe the effects of genetic mutations on the growth of glioblastoma tumor cells in the absence and presence of anticancer drug carmustine released locally from polymer implants. Materials and Methods: A modified logistic equation (in both algebraic and differential forms) is proposed to describe the effect of genetic mutations on the growth of glioblatoma. The model predictions are adapted to available experimental and clinical findings. A semi – empirical equation similar to the probability density function of gamma distribution is used to describe the diffusion of carmustine from a polymer – implant (wafer) into the brain. Parameters of this equation are estimated from available experimental data for monkey brain. This equation is combined with the differential form of the above – mentioned modified logistic equation to describe the wafer therapy of glioblastoma in human brain. The prediction of this combined model is compared with the pattern of recurrence of glioblastoma reported in literatures. Results: In all cases good agreements between models prediction and experimental and clinical findings are observed. Application of the model is discussed. Conclusion: The model describes the effect of genetic mutations on the growth of glioblastoma in the absence and presence of carmustine properly. A Combination of the present model with that of Swanson and co-workers can lead to a better understanding of glioblastoma invasiveness. It is possible to use the model prospectively, optimizing the design of new experiments.

Keywords: Carmustine, Glioblastoma, Models- Theoretical, Mutation, Neoplasms

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