Modeling the growth and invasion of gliomas, from simple to complex: The goldie locks paradigm

As with all mathematical modeling, the scope of the question to be explored determines the scope of the most appropriate model. The case is no different for the modeling of primary brain tumors (gliomas), ranging from too simple, not accounting for the major feature of gliomas (extensive invasion), to too complicated, with too many variables and no easy way to translate from culture media in vitro to brain tissue in vivo. We settle on a "just right" approach which utilizes currently available magnetic resonance imaging (MRI) to estimate two defining characteristics, net rates of proliferation (ρ) and diffusion (D). Most importantly, these parameters are predictive of clinical behavior, and can be tailored to individual patients in vivo and in real time. These two rates combine to generate a linear radial growth pattern of the MRI visible portion of each glioma. Further, we introduce a novel method for the calculation of glioma invasion through grey and white matter.