Mathematical models of the biological effect of ionizing particles; their importance in radiobiology and radiotherapy

The relations between the lethal effects of fractionated irradiation on the individual cells and proliferation processes through which the damaged cells are replaced are most important for radiotherapeutical practice. The relation Ssub(N)=exp(-N.αsub(d).dsup(γ).f(t)) where N is the number of fractionated doses, d is the size of fractionated doses, f(t) describes the effect of repair parameters, and αsub(d), γ describes the lethal effect of each fractionated dose, was derived for the proportion of cells surviving at the end of fractionated irradiation. The fact that the form of the relation is the same as that used for the description of survival curves and, in addition, parameters αsub(d), γ are used in both cases may significantly contribute to the ease of applying radiobiological findings in radiotherapeutic practice. Mathematical models are described of the biological effects of ionizing radiation on the cell and the basic effects are discussed which the models should take into consideration, such as survival curves, different dose rates, different oxygen concentrations, and the relative biological efficiency of the various types of ionizing radiation. (Z.M.)