A multinomial model of tumor growth treated by radiotherapy

A main challenge in radiotherapy is to personalize the treatment by adapting the dose fractionation scheme to the patient. One way is to model the treatment effect on the tumor growth. In this study, we propose a new multinomial model based on a discrete-time Markov chain, able to take into account both of cell repair and cell damage heterogeneity. The proposed model relies on the ‘Hit’ theory in Radiobiology and assumes that a cancer cell contains m targets which must be all deactivated to produce cell death. The malignant cell population is then split up into m categories to incorporate the variation of cancer cell radio-sensitivity according to their states. This work gives also a new formulation of the tumor control probability (TCP) suited to the perspective of dynamic fractionation schedules in radiotherapy.