Mathematical modeling of glioma on MRI

The advent of Magnetic Resonance Imaging (MRI) has enabled quantification of glioma growth with millimetric accuracy. Thus, it is now possible to monitor the growth curve of tumor diameter for each patient. Mathematical modeling contributes to the analysis of these curves and to determining individual parameters characterizing tumor dynamics. We will focus on the most studied model, based on a proliferation-diffusion equation. We will review how this approach, when applied to low-grade gliomas, has enabled defining a new way to quantify their natural history, leading to the inclusion of tumor kinetics among prognostic factors. Finally, quantitative imaging coupled with mathematical modeling is opening new avenues in our understanding of treatment effects, allowing to optimize therapeutic strategies for gliomas in the near future.