Mathematical modelling of intermittent radiotherapy protocols for recurrent high-grade glioma

Cancer is one of the world’s deadliest diseases. Number of researchers have put time and efforts in finding an effective treatment, improving efficiency of cur- rent low cost treatment and finding the ways to help the patients develop their immune system that enable them to fight it. Although cancer is a leading cause of death, a little is known about the mech- anism of its growth and destruction. Mathematical models explaining these mechanisms are crucial to predict the behaviour of cancer cells proliferation. In this thesis, the main focus is on what’s referred to as high-grade glioma, a brain cancer whose prognosis is often depressing. Despite there has been a con- tinuous progress, standard treatments often lead to a poor outcome, suggesting that innovative approaches should be considered. A possibility in this sense is represented by deviations from traditional radiother- apy protocols. Here, different fractionation schedules are explored by means of a genetic algorithm. Starting from a certain mathematical model, fitted using a dataset of magnetic resonance images showing longitudinal tumour volumes dur- ing a hypofractionated stereotactic radiotherapy, the aim is to predict specific features for each patient and use them to provide a personalized radiotherapy protocol capable of improving the final therapy outcome, for example by further extending the patient survival time. Not only, the problem of a raising therapy resistance due to the remarkable cancer heterogeneity is a constant challenge in the clinical path. Multicompart- mental models are thus proposed to quantify the growth of a cancer resistant population, in order to exploit the genetic algorithm in designing effective coun- termeasures. A final analysis concerning the model reliability has been done, providing a concrete measure about how much accurate parameters’ prediction over time is, which is crucial since personalized medicine requires promptness in the treat- ment choices as the disease advances. Results of in silico experiments are promising: in the limit of an extremely simplified picture of a complex system as that of tumour dynamics, virtual im- provements have been achieved. This suggest that further efforts in the direction of an ever more personalized medicine may be worth it, hopefully leading to a less dismal scenario.