Modelling glioblastoma resistance to temozolomide. A mathematical model to simulate cellular adaptation in vitro.

Drug resistance is one of the biggest challenges in the fight against cancer. In particular, in the case of glioblastoma, the most lethal brain tumour, resistance to temozolomide (the standard of care drug for chemotherapy in this tumour) is one of the main reasons behind treatment failure and hence responsible for the poor prognosis of patients diagnosed with this disease. In this work, we combine the power of three-dimensional in vitro experiments of treated glioblastoma spheroids with mathematical models of tumour evolution and adaptation. We use a novel approach based on internal variables for modelling the acquisition of resistance to temozolomide that was observed in experiments for a group of treated spheroids. These internal variables describe the cell's phenotypic state, which depends on the history of drug exposure and affects cell behaviour. We use model selection to determine the most parsimonious model and calibrate it to reproduce the experimental data, obtaining a high level of agreement between the in vitro and in silico outcomes. A sensitivity analysis is carried out to investigate the impact of each model parameter in the predictions. More importantly, we show how the model is useful for answering biological questions, such as what is the intrinsic adaptation mechanism, or for separating the sensitive and resistant populations. We conclude that the proposed in silico framework, in combination with experiments, can be useful to improve our understanding of the mechanisms behind drug resistance in glioblastoma and to eventually set some guidelines for the design of new treatment schemes.