Patient‐specific simulation of brain tumour growth and regression

Abstract

The medical relevance of brain tumours is characterised by its locally invasive and destructive growth. With a high mortality rate combined with a short remaining life expectancy, brain tumours are identified as highly malignant. A continuum‐mechanical model for the description of the governing processes of growth and regression is derived in the framework of the Theory of Porous Media (TPM). The model is based on medical multi‐modal magnetic resonance imaging (MRI) scans, which represent the gold standard in diagnosis. The multi‐phase model is described mathematically via strongly coupled partial differential equations. This set of governing equations is transformed into their weak formulation and is solved with the software package FEniCS. A proof‐of‐concept simulation based on one patient geometry and tumour pathology shows the relevant processes of tumour growth and the results are discussed.