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We construct a minimal macroscopic model of glioblastoma growth including necrosis to explain the recently observed correlation between MRI-observed features and tumor growth speed. A theoretical study of the modified model was carried out. In particular, we obtained an expression for the minimal wave speed of the traveling wave solutions. We also solved numerically the model using a set of realistic parameter values and used these numerical solutions to compare the model dynamics against patient’s imaging and clinical data. The mathematical model provides theoretical support to the observation that tumors with broad contrast enhancing areas as observed in T1-weighted pretreatment postcontrast magnetic resonance images have worse survival than those with thinner areas.

Tumor width on T1-weighted MRI images of glioblastoma as a prognostic biomarker: a mathematical model