3D-printed brain with a gradient of colors representing cell density in glioblastoma. Only higher cell densities are visible on MRI; this brain also shows lower cell densities as given by a mathematical model. Using mathematics to predict brain tumor responses to therapy

A model of an actual brain with a glioblastoma printed from 3D magnetic resonance imaging (MRI) scans and mathematical model predictions shows predicted tumor cell density bands from blue (less dense) to dark red (most dense). Typically, only the red and dark red regions are visible on an MRI scan.


Mathematical neuro-oncology is an exciting interdisciplinary field incorporating applied mathematics, artificial intelligence, clinical oncology, cancer biology, radiology, pathology and informatics. This discipline represents a major paradigm shift in the generation of practical clinical tools to benefit people diagnosed with brain tumors.

Mayo Clinic's Mathematical Neuro-Oncology Lab, led by Kristin R. Swanson, Ph.D., is at the forefront of this field developing numerous models of glioma tumors. Dr. Swanson and her research team are finding ways to make these models specific for predicting and simulating individualized tumor behavior under different treatment scenarios. To support this research, the lab has also amassed a large repository of patient-centric data, including segmented and measured images, treatments, pathologies, and patient demographics. Dr. Swanson's research team's current projects focus on growing and harnessing this resource to predict patient-specific tumor growth, find patient-specific markers of tumor progression and identify predictors of response to therapy in individuals.


Gliomas are diffuse and invasive brain tumors with the nefarious ability to recur despite extensive surgical resection. Chemotherapies also are seldom successful due to hindrance by the intricate capillary structure of the blood-brain barrier. Using a simple mathematical model of glioma growth and diffusion, the Mathematical Neuro-Oncology Lab has simulated a prediction of the degree to which magnetic resonance imaging (MRI) underestimates the actual extent of diffuse invasion of the brain by glioma cells. This simple model now includes additional factors and is useful in a number of settings.

About Dr. Swanson

Kristin R. Swanson, Ph.D., is a professor and vice chair of research in neurosurgery, and the Vasek and Anna Maria Polak Professor of Cancer Research at Mayo Clinic's campus in Phoenix, Arizona. Dr. Swanson's research focuses on combining predictive mathematical models and artificial intelligence with clinical oncology to determine how different treatments affect glioma tumors and patient outcome.