Mathematical derivation of optimal treatment schedules for the radiotherapy of human tumours. Fractionated irradiation of exponentially growing tumours

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Abstract
A mathematical model is developed to allow derivation of optimal treatment schedules for the radiotherapy of exponentially- growing tumours. Preliminary calculations based on available data suggest that optimal schedules would (in general) be more protracted than conventional schedules and might achieve a significantly better tumour cell kill without causing excessive damage to normal connective tissue. The model is too simple, and the data inadequate, for the conclusions reached to be used as a guide to clinical practice at present. However, the analysis can be extended to more realistic models which may be of clinical benefit when the appropriate data can be obtained.