Abstract
Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we propose a mathematical model describing the spatio-temporal transition of LGGs into HGGs. Our modelling approach is based on two cellular populations with transitions between them being driven by the tumour microenvironment transformation occurring when the tumour cell density grows beyond a critical level. We show that the proposed model describes real patient data well. We discuss the relationship between patient prognosis and model parameters. We approximate tumour radius and velocity before malignant transformation as well as estimate the onset of this process.