Abstract
A previous paper (Wheldon and Kirk, 1976) presented the mathematical derivation of optimal treatment schedules in radiotherapy, assuming a single-hit multi-target radiation survival curve (see Elkind and Whitmore, 1967) and exponential repopulation kinetics for tumour cells, and utilizing the Cumulative Radiation Effect (CRE) representation of radiation damage to normal connective tissue (Kirk et al., 1971). Recently, attention has been focused on cell survival curves which, contrary to the multi-target model, have non-zero initial slopes (Alper, 1975). Some evidence favours an exponential-quadratic survival curve with non-zero initial slope and continuously steepening slope as radiation dose increases (Neary, 1965; Sinclair, 1969; Kellerer and Rossi, 1971; Chadwick and Leenhouts, 1973; Douglas and Fowler, 1975).
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