A generalised method for calculating repopulation-corrected tumour EQD2 values in a wide range of clinical situations, including interrupted treatments

Abstract

Any radiotherapy schedule can be characterised by its 2 Gy per fraction equivalent dose (EQD2). EQD2s are easily calculated for late-responding normal tissues but for tumours significant errors may arise if no allowance is made for any repopulation which occurs in the reference and/or the derived EQD2 schedule. This article presents a systematic approach to calculating tumour EQD2 values utilising the concept of biologically effective dose (BED) with inclusion of repopulation effects. A factor (f) is introduced which allows the inter-dependence between EQD2 and its delivery time (and, hence, the amount of repopulation involved) to be embedded within the formulation without any additional assumptions. There exists a transitional BED below which simple methods of calculating tumour EQD2 remain valid. In cases where simpler approaches are inadequate, the correct EQD2 may be determined from the reference schedule BED (BEDref) by the relationship: EQD2 = A × BEDref - B, where A and B are constants which involve the same radiobiological parameters as are conventionally used in deriving tumour BED values. Some Worked Examples illustrate application of the method to fractionated radiotherapy and indicate that there can be substantial differences with results obtained from using over-simplified approaches. Since reference BEDs are calculable for other types of radiotherapy (brachytherapy, permanent implants, high-LET applications, etc) the methodology allows estimation of tumour EQD2 values in a wide range of clinical circumstances, including cases which involve interrupted treatments.