A complete mathematical study of a 3D model of heterogeneous and anisotropic glioma evolutionA complete mathematical study of a 3D model of heterogeneous and anisotropic glioma evolution Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2015-10-232009enGlioma is the most aggressive type of brain cancer. Several mathematical models have been developed towards identifying the mechanism of tumor growth. The most successful models have used variations of the diffusion-reaction equation, with the recent ones taking into account brain tissue heterogeneity and anisotropy. However, to the best of our knowledge, there hasn't been any work studying in detail the mathematical solution and implementation of the 3D diffusion model, addressing related heterogeneity and anisotropy issues. To this end, this paper introduces a complete mathematical framework on how to derive the solution of the equation using different numerical approximation of finite differences. It indicates how different proliferation rate schemes can be incorporated in this solution and presents a comparative study of different numerical approaches.http://creativecommons.org/licenses/by/4.0/2807 - 2810 Annual International Conference of the IEEE Engineering in Medicine and Biology Society EMBC Zervakis Michalis Ζερβακης Μιχαλης Roniotis Alexandros Ρονιωτης Αλεξανδρος Sakkalis, Vangelis Institute of Electrical and Electronics Engineers Medical