[Interactive determination of the parameters of mathematical models for planning radiotherapy of malignant tumors. I. Mathematical models for calculating dose tolerance, adequate doses and the likelihood of development of radiation complications in normal organs and tissues]

Abstract

Mathematical models for calculating tolerance doses, adequate doses and the likelihood of radiation complications in the body's normal tissues are considered. To determine the parameters of these models that describe the outcomes of radiation exposure of complicated biological systems, a method of local adjustment of the parameters of the models has been developed, which will be described in parts 2 and 3 of the proposed paper. In part 1 (the present paper), particular emphasis is laid on the inclusion of an important parameter, such as a volume, into Ellis and LQ models. A mathematical model is presented for calculating the likelihood of a radiation complication in the tissue, which is the basis for deriving a formula to calculate an adequate uniform tissue radiation dose that is equivalent to the nonuniform tissue distribution of a dose in terms of the likelihood of radiation complications.