Modelling tumour growth dynamics as a means of determining fractionation protocols in radiotherapy

The use of fractionation for improving treatment outcomes in the practice of radiotherapy for tumour control is well established. Successful fractionation protocols employ dosages of sufficient size, applied at adequately frequent intervals, to bring about the required destruction of the tumour tissue without incurring unacceptable radiation damage to the surrounding non-tumour tissue. A simple mathematical model of the growth dynamics for tumour and non-tumour tissue is developed and their time evolution in response to a single-dose radiation event determined. This is used to investigate the relationship between survival fraction for tumour and non-tumour cell populations, the dosage size and the interval between doses for a range of alternative fractionation protocols. It is demonstrated that the most effective protocols employ dosage fractions at time intervals determined by the growth kinetics of both tissues. Furthermore, it is shown how effective alternative fractionation protocols may be determined.