Optimal radiotherapy of tumour cells following exponential-quadratic survival curves and exponential repopulation kinetics

An analytical derivation is presented which permits deduction of theoretically optimal schedules where an exponential-quadratic function provides a better fit to the available survival curve data than the more conventional multi-target function. A comparison is made of the surviving fraction following optimal and conventional schedules for hypothetical tumours with doubling times ranging from 1 to 150 days, assuming survival curve parameters close to those of a typical line of mammalian cells. The results suggest advantages for optimal scheduling for very slow and very fast growing tumours. A non-uniform treatment schedule may be indicated for tumours where the growth rate accelerates as the tumour size is reduced. It is emphasized that the numerical results are used as illustrations of the method, and are not recommendations for departures from conventional practice in radiotherapy. (U.K.)