Radiotherapy treatments using Tsallis entropy statistical approach

Abstract

Several radiobiological models mimic the biologic effect of one single radiation dose on a living tissue. However, the actual fractionated radiotherapy requires accounting for a new magnitude, i.e., time. Here, we explore the biological consequences posed by the mathematical prolongation of a previous single radiation model to fractionated treatment. The survival fraction is obtained, together with the equivalent physical dose, in terms of a time dependent factor (similar to a repair coefficient) describing the tissue trend to recovering its radioresistance. The model describes how dose fractions add up to obtain the equivalent dose and how the repair coefficient poses a limit to reach an equivalent dose equal to the critical one that would completely annihilate the tumor. On the other hand, the surrounding healthy tissue is a limiting factor to treatment planning. This tissue has its own repair coefficient and thus should limit the equivalent dose of a treatment. Depending on the repair coefficient and the critical dose of each tissue, unexpected results (failure to fully remove the tumor) can be obtained. To illustrate these results and predictions, some realistic example calculations will be performed using parameter values within actual clinical ranges. In conclusion, the model warns about treatment limitations and proposes ways to overcome them. © Published under licence by IOP Publishing Ltd.