Theoretical “iso-survival” formulae for fractionated radiation therapy

Abstract

A formula describing the cellular response in irradiated tissues and tumors was found to require at least 3 exponential components (for irreversible single-hit damage, multi-target inactivation with early repair, and a cellular repopulation factor) in order to conform with observed dose-time relationships. On this basis a computer program was designed to determine and compare the proportion of cells surviving various standard fractionation procedures producing identical skin reactions and similar tumor responses. Parameters were adjusted sequentially to minimise variance, thus deriving "best-fitting" estimates of all the relevant factors. Results showed that the mean cellular lethal dose D0 was about 100 rads in both skin and tumor (no anoxic component could be resolved). The proportion of radiation damage due to the irreversible component was apparently greater in the tumor (nearly 1/2) than in normal skin (about 1/3). Similarly, extrapolation numbers were high (26 to 30) in the normal skin cells but smaller in the tumor. Mean cellular regeneration times were between 3 and 5 days for irradiation skin, but apparently slower, certainly over 10 days, in the tumor. The computed surviving fraction was about 10-8 in the cured tumor, capatible with an estimated viable tumor-cell population of the order of 10[degree] cm-3. Cellular survival was about 10-5 in the larger skin fields but approached 10-7 in smaller fields, a difference sufficient to explain the dependence of tolerance dosage on field-size, although the possibility of a correlated change in D0 could not be excluded. Applying appropriate parameters to this model, optimal values could be assigned for over-all treatment time, number of fractions, and dose-per-fraction, thus defining a technique promising the maximum likelihood of uncomplicated cure.