Mathematical modeling of brain tumor cell growth for passive, active and oxygen transport mechanism with microgravity condition / Norfarizan Mohd Said

The unpredictable conduct of the brain tumor cells present difficulties in creating precise models. The limitation of medical imaging in forecasting the nature of the tumor growth and the costly techniques for diagnostic and treatment posed an obstacle to the effort in understanding and fighting this life-threatening disease. As the tumor itself can only be detected and treated through the biological process, a good mathematical model should represent the important biological aspects with useful solution that contribute to further understanding of the problem. Addressing the current challenges in developing a realistic model by bridging the theoretical with the clinical applications, this research aims to govern mathematical models for brain tumor cell growth by emphasizing the cell migration and proliferation as the key characteristics. The models of passive and active cell mechanisms are representing the tumor cell migration while the model of oxygen transport mechanism configures the cell proliferation. New parameters for oxygen and gravity effects are included as the model novelty. The conditions of microgravity and oxygen deprivation are presented using the microscopic model of the tumor cellular dynamics. The models developed are in the form of parabolic equations which is discretized using the Finite Difference Method (FDM) with weighted average approximation. Numerical iterative methods, namely Jacobi (JAC), Red-Black Gauss-Seidel (RBGS), Red-Black Successive Over Relaxation (RBSOR) and Alternating Group Explicit (AGE) method are used to solve the discretized models…