Mathematical modelling for spatial optimization of irradiation during proton radiotherapy with nanosensitizers

A spatially distributed mathematical model is presented that simulates the growth of a non-invasive tumour undergoing treatment by fractionated proton therapy with the use of non-radioactive tumour-specific nanosensitizers. Nanosensitizers are injected intravenously before each irradiation to increase the locally deposited dose via a chain of reactions with therapeutic protons. Modelling simulations show that the use of nanosensitizers allows increasing treatment efficacy. However, their effect is restricted by the necessity of decreasing the energy deposited in tumour in order to comply to the normal damage restrictions. Normalization of tumour microvasculature that accompanies the treatment, also compromises nanosensitizers effect as it impairs their inflow in tumour. It is shown that spatial optimization of irradiation, with conservation of total dose deposited in tumour, can increase tumour cell damage for each single irradiation. However, eventually it may not lead to the overall increase of treatment efficacy, in terms of minimization of the number of remaining viable tumour cells, due to the influence of tumour cell repopulation between irradiations. It is suggested that an efficient way towards minimization of tumour cell repopulation may be the faster suppression of angiogenesis by eradication of metabolically deprived tumour cells. This method can be efficient even despite the fact that it would also cause the decrease of supply of nanosensitizers into the tumour.