A novel bicompartmental mathematical model of glioblastoma multiforme

Glioblastoma multiforme (GBM) is the most common primary CNS neoplasm, and continues to have a dismal prognosis. A widely-used approach to the mathematical modeling of GBM involves utilizing a reaction-diffusion model of cell density as a function of space and time, which accounts for both the infiltrative nature of the tumor using a diffusion term, and the proliferation of tumor cells using a proliferation term. The current paper extends the standard models by incorporating an advection term to account for the so-called 'cell streaming' which is often seen with GBM, where some of the tumor cells seem to stream widely along the white matter pathways. The current paper introduces a bicompartmental GBM model in the form of coupled partial differential equations with a component of dispersive cells. The parameters needed for this model are explored. It is shown that this model can account for the rapid distant dispersal of GBM cells in the CNS, as well as such phenomena as multifocal gliomas with tumor foci distant from the core tumor site. The model suggests a higher percentage of tumor cells below the threshold of MRI images in comparison to the standard model. By incorporating an advection component, the proposed model is able to account for phenomena such as multicentric gliomas and rapid distant dispersion of a small fraction of tumor cells throughout the CNS, features important to the prognosis of GBM, but not easily accounted for by current models.