Theoretical “iso-survival” formulae for fractionated radiation therapy

Abstract

A formula describing the cellular response in irradiated tissues and tumours was found to require at least three 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 tumour 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 tumour (no anoxic component could be resolved). The proportion of radiation damage due to the irreversible component was apparently greater in the tumour (nearly half) than in normal skin (about one-third). Similarly, extrapolation numbers were high (26 to 30) in the normal skin cells but smaller in the tumour. Mean cellular regeneration times were between three and five days for irradiated skin, but apparently slower, certainly over ten days, in the tumour. The computed surviving fraction was about 10−8 in the cured tumour, compatible with an estimated viable tumour-cell population of the order of 108 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.