Basic principles of mathematical growth modeling applied to high-grade gliomas: A brief clinical review for...

The battle against cancer has intensified in the last decade. New experimental techniques and theoretical models have been been proposed to understand the behavior, growth, and evolution of different types of brain tumors. Unfortunately, for glioblastoma multiforme (GBM), except for methylation of the O6-methylguanine-DNA methyltransferase (MGMT) promoter that has some benefit in the local control of tumors using alkylating agents such as temozolomide, to date personalized treatments do not exist. In this article, we present a comprehensive review of different aspects intertwined in the mathematical growth modeling applied to high-grade gliomas. We briefly cover the following fundamental aspects related to the conventional imaging in GBM: defining the tumor regions in GBM, segmentation of the tumor regions using magnetic resonance imaging (MRI) of the brain, response assessment using the neuro-oncology response criteria versus the Macdonald criteria, availability of software for the segmentation of MRI of the brain, mathematical modeling applied to tumor growth, principles of mathematical modeling, factors involved in tumor growth models, mathematical modeling based on imaging data, most common equations used in high-grade glioma growth modeling, integration of mathematical growth models in computer simulators, tumor growth modeling as a part of brain's complex system, and challenges in mathematical growth modeling. We conclude by saying that it is the combination of biomedical imaging and mathematical modeling that allows the assembling of clinically relevant models of tumor growth and treatment response; the most appropriate model will depend on the premise and findings of each experiment.