Malignant gliomas are brain tumors that differ from most other tumors by their aggressive diffuse invasion of the surrounding normal tissue which contributes to the dismal 6 to 12 months prognosis. The remarkable continuing development of medical imaging has increased the ability to detect gliomas, but has not been able to sufficiently define the extent of invasion of the tumor cells peripheral to the bulk tumor mass. For this reason, only the "tip of the iceberg" of the full lesion is visible by standard imaging tools (MRI, CT, PET). We use mathematical modeling to predict the true extent of the tumor given the limited information provided by standard clinical imaging. Our mathematical model can be applied to an individual patient to calculate the two factors (proliferation and infiltrative potential) precisely enough to display the past, present and future distributions of tumor cell concentrations down to the individual cell, well beyond the "edge "of the tumor defined by current imaging.

Clinicians routinely question the efficacy of treatment and, to date, have very few quantitative tools for assessing treatment response in real time. Further, as new experimental therapies (radio and chemo) are introduced, an early and robust measure of effect is necessary in individual patients. These problems are compounded for those therapies that target molecular changes that only a subset of tumors will have and others not have, since tissue sampling may not be available in all. It is clear to us that truly revolutionary research to improve the humbling prognosis of gliomas cannot proceed without knowledge of the in vivo interactions of the two most salient features of their progression - dispersal and net proliferation - provided through mathematical modeling.