Abstract
Abstract The growth of brain glioma concentration is spatio-temporally modeled by using reaction-diffusion. The model assumes heterogeneity in one dimensional space based on grey and white matter arrangement. In this study, model is combined with three different types of growth function. The exponential function produces a linear model, while the logistic and Gompertzian function produce a nonlinear model. The models are solved numerically by finite difference method Crank-Nicolson scheme. Tumor attributes including maximum concentration, number of cell, mean radial distance, and growth speed are also obtained to observe the growth pattern of brain glioma. Python-based desktop application is developed to simulate the numerical solutions and display the results quantitatively and visually. Analysis of the simulation results show differences in growth pattern based on the parameters used. Based on simulation and analysis, the maximum concentration of Gompertzian growth reaches a turning point that is much faster (about 2.8 times) than the other two.
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