Biologically effective dose using reciprocal repair for varying fraction doses and fraction intervals

Abstract

Hyperfractionated regimes are being used more frequently; this has created a clinical need for more sophisticated biologically effective dose (BED) calculations. A formula is given for calculating BED assuming reciprocal repair in the case of changing dose per fraction and changing interfraction interval. Example applications are given for hyperfractionated schedules. It is shown that the formula is useful for calculating isoeffective schedules for a treatment with unplanned gaps and for comparing regimes in trial design. This work should be of value for comparing risk across accelerated schedules when an organ of the central nervous system is at risk. Uncertainties in choice of parameter and model are discussed: the bi-exponential model of repair is invoked for this purpose.

Radiation repair models for clinical application

“…More practical (but mathematically more complex) second-order equations for non-equally spaced fractions have also been derived. 21 second-order rePair equations for Protracted does delivery Equations (11) and (12) consider the case of acute dose delivery. When the delivery is itself more protracted the corresponding BED equation for a single dose of duration T is: 17,20…”

Brain necrosis after fractionated radiation therapy: Is the halftime for repair longer than we thought?

“…Interfraction repair corrections are considered using three alternative repair models: First, the reciprocal-repair model as developed by Buckle and Lewis, 28 second, a monoexponential repair model, and third, a biexponential repair model is considered. In these models, the biologically effective dose (BED) is determined by the fractional dose d i , total dose D, α/β, the starting time for the ith fraction S i , and a time parameter or parameters.…”

“…(1). This substitution can be carried through the derivation as it appears in Appendix A in Buckle and Lewis 28 and one arrives at Eq. (1).…”

Radiobiological Modelling in Radiation Oncology

“…There are several mathematical models which predict the probability of cell kill and therefore tumour control (Chadwick and Leenhouts 1973;Kellerer and Rossi 1978;Thames 1985;Curtis 1986;Brenner et al 1998;Joiner 2004;Guerrero and Li 2004;Buckle and Lewis 2008;Park et al 2008;Webb and Nahum 1993;Kallman et al 1992;Ebert and Hoban 1996;Zaider and Minerbo 2000;Dasu et al 2003;Nahum et al 2003;Tome and Fowler 2003;Carlone et al 2004;Levin-Plotnik et al 2004;Zaider and Hanin 2008).…”