The mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differencesThe mathematical path to develop a heterogeneous, anisotropic and 3-dimensional glioma model using finite differences Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2015-10-252009enSeveral mathematical models have been developed to express glioma growth behavior. The most successful models have used the diffusion-reaction equation, with the most recent ones taking into account spatial 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 all related heterogeneity and anisotropy issues. This paper presents a complete mathematical framework on how to derive the solution of the equation using different numerical schemes of finite differences. Moreover, the derived mathematics can be customized to incorporate various cell proliferation schemes. Lastly, a comparative study of the numerical scheme helps us select the best of them and then apply it to real clinical data.http://creativecommons.org/licenses/by/4.0/1-49th International Conference on Information Technology and Applications in Biomedicine Marias Kostas Zervakis Michail Ζερβακης Μιχαηλ Sakkalis, Vangelis Roniotis Alexandros Ρονιωτης Αλεξανδρος Karatzanis Ioannis Institute of Electrical and Electronics Engineers Basic medical sciences Basic sciences, Medical Biomedical sciences Health sciences Preclinical sciences Sciences, Medical medical sciences basic medical sciences basic sciences medical biomedical sciences health sciences preclinical sciences sciences medical Anisotropic magnetoresistance Mathematical model Finite difference methods Neoplasms Linear systems Differential equations Brain modeling Tensile stress Partial differential equations Information technology