A Validated Mathematical Model of Tumour-Immune Interactions for Glioblastoma

This paper provides a new mathematical approach for modelling the influence of the cells of the immune system, more precisely of microglial cells, on the progression of malignant primary brain tumours. A hybrid approach is used to model the cellular tumour progression, the development of the local nutrient concentration and of the density of the extracellular matrix (ECM). Microglia present in the surrounding of brain tumours are activated and attracted by signals emitted by tumour cells, which are described by a partial differential equation. The secretion of matrix degrading enzymes from microglia/macrophages can be modelled with the help of an additional term for the degradation of the ECM. This supports a more invasive migration of tumour cells. Parameter estimation and model validation use data from published studies and from our own in-vitro experiments. To our knowledge, we present for the first time a model of microglial cells in the context of tumour growth. The simulations reproduce quantitatively the in-vitro experimental data on glioma cells invasion and proliferation. Moreover, the experimental in-silico results match with the cell behaviour reported in the literature. The proposed model, thus, is a promising approach for modelling brain tumour growth at the cellular level taking the innate immune system into account.