Proliferation-invasion (reaction-diffusion) models of glioma

Kristin Swanson, James Murray and colleagues modelled glioblastoma as a reaction-diffusion process: cells proliferate at rate rho and diffuse at rate D, faster along white matter. Fitting the two parameters to serial MRI gives a patient-specific 'velocity' of growth and an estimate of tumour cell density beyond the visible edge, which has been used to individualise radiotherapy margins, to define 'days gained' as a response measure, and to predict survival. The model is the most clinically tested biophysical tumour model but requires two pretreatment scans and simplifies the biology of invasion.