Cellular survival and isoeffect formulae: a study in applied radiobiology.

The Ellis formula for the sterilization of tumors is compared with isoeffect curves for sterilizing doses as a function of the fractionation number N. Using cell parameters from human kidney cells irradiated in cell cultures we get a good agreement over a wide range of N values. The exponents obtained from the calculations are 0,26-0,30 and 0,36 for 200 keV X-rays, Co-60 rays and high energy electrons respectively. A reduction of tumor cells to 10(-8) seems sufficient for tumor sterilization. For normal tissue Ellis has proposed another formula (for X-rays) where a time factor T0,11 concerns homeostatic repair and proliferation of normal alls. The Ellis formula can be simplified when we assume that all treatment schemes be given with the same weekly dose-rate, i.e. have the same "hardness". Cell survivals according to this formula have been calculated and tolerance doses for other radiations giving the same effect computed. Only for electrons do the tolerance doses exceed the sterilizing doses. The Ellis formula does not represent isoeffects and can only be regarded as an approximation. Tolerance doses can be calculated giving the same cell survivals for all N-values, i.e. isoeffects, and a comparison with sterilizing doses shows a good agreement with clinical experience. However, the influence of the overall-dose rate still is an unsolved problem which can only be solved experimentally.