# Patient-Specific Mathematical Neuro-Oncology: Using a Simple Proliferation and Invasion Tumor Model to Inform Clinical Practice

Glioblastoma multiforme (GBM) is the most common malignant primary brain tumor associated with a poor median survival of 15–18 months, yet there is wide heterogeneity across and within patients. This heterogeneity has been the source of significant clinical challenges facing patients with GBM and has hampered the drive toward more precision or personalized medicine approaches to treating these challenging tumors. Over the last two decades, the field of Mathematical Neuro-oncology has grown out of desire to use (often patient-specific) mathematical modeling to better treat GBMs. Here, we will focus on a series of clinically relevant results using patient-specific mathematical modeling. The core model at the center of these results incorporates two hallmark features of GBM, proliferation $$(\rho )$$ and invasion (D), as key parameters. Based on routinely obtained magnetic resonance images, each patient’s tumor can be characterized using these two parameters. The Proliferation-Invasion (PI) model uses $$\rho$$ and D to create patient-specific growth predictions. The PI model, its predictions, and parameters have been used in a number of ways to derive biological insight. Beyond predicting growth, the PI model has been utilized to identify patients who benefit from different surgery strategies, to prognosticate response to radiation therapy, to develop a treatment response metric, and to connect clinical imaging features and genetic information. Demonstration of the PI model’s clinical relevance supports the growing role for it and other mathematical models in routine clinical practice.