Estimating the extent of glioblastoma invasion

Abstract Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in form advection–diffusion–reaction equations. The patient-wise parametrization these models, and their validation experimental data has found be difficult, as time sequence measurements are mostly missing. Also clinical interest lies actual (invisible) extent for particular MRI/DTI scan not predictive estimate. Therefore we propose stationalized approach estimate glioblastoma (GBM) at given scan. underlying dynamics can derived from an instationary GBM model, falling into wide class advection-diffusion-reaction stationalization introduced analytic solution Fisher-KPP equation, simplest considered class. We investigate applicability 1D 2D, presence inhomogeneous diffusion coefficients on real 3D DTI-dataset.