Fig. 1

A schematic representation of the long-term radiation and radiosensitizer model. \({V}_{1}\) consists of proliferating tumor cells.\({V}_{2}\), \({V}_{3}\), and \({V}_{4}\) are transit compartments consisting of damaged tumor cells. The growth rate of the proliferating cells is denoted by \({k}_{g}\) and the rate of natural cell death of all cells by \({k}_{k}\). As a result of the radiation treatment cells become radiation damaged and this affects them in two ways. Firstly, the growth rate is inhibited and secondly, a fraction of proliferating cells is irreversibly damaged at each radiation session. These damaged cells are moved to \({U}_{1}\) and can go through mitosis once, but their daughter cells (\({U}_{2}\)) cannot. Therefore, these radiation damage cells eventually also die. Both radiation effects are stimulated by the radiosensitizers. \({D}_{R}\) denotes the radiation dose and \(R{s}_{i}\) denotes the exposure of radiosensitizer i at the instant of radiation application