Recent developments in time-dose modelling

Two recent innovations in time-dose models are reviewed: the linear-quadratic (L-Q) and the variable-exponent Time-Dose Factor (TDF) models. The basic L-Q equations for fractionated and continuous (brachytherapy) regimes are presented as well as those for incomplete repair and short half life radionuclides. None of these equations has provision for a repopulation factor, so a "wasted ERD" parameter is introduced, which is a linear function of overall treatment time, with incorporation of a lag time if desired. For low dose rate therapy, an effective treatment time is defined, at which the ERD reaches its maximum value when the rate of increase due to irradiation equals the rate of decrease due to repopulation. The variable-exponent TDF model has a volume-effect parameter and scaling factors which make TDFs of 100 correspond to tolerance for all volumes of tissue treated, for both fractionated and continuous therapy. These, as well as the exponents, are all tissue-specific. Volume-effect and scaling factors are also appropriate for the L-Q equations. With these it is possible to apply the TDF and L-Q models to problems which involve inhomogeneous dose distributions. Several examples of the use of these models are presented.