THE LINEAR-QUADRATIC TRANSFORMATION OF DOSE-VOLUME HISTOGRAMS IN FRACTIONATED RADIOTHERAPY

Background and purpose: Dose-volume histograms (DVHs) are often used i n radiotherapy to provide representations of treatment dose distributi ons. DVHs are computed from physical dose and do nor include radiobiol ogical factors; therefore, the same DVH will be computed for a treatme nt plan whatever fractionation regimen is used. However, dose heteroge neity resulting from variation of daily treatment dose within the volu me will have biological effects due to spatial heterogeneity of fracti on size as well as total dose, The purpose of the paper is to present a radiobiological (LQ) transformation of the physical dose distributio n which incorporates fraction size effects and may be better suited to the prediction of biological effects. Methods: An analytic formula is derived for the linear-quadratic transformation of a normal distribut ion of dose to give the corresponding distribution of biologically equ ivalent dose given as 2 Gy fractions. This allows LQ-transformed DVHs to be computed from physical DVHs, The resultant LQ-DVH depends on the assumed value of the relevant alpha/beta ratio. It is a modified dose distribution (corrected for spatial heterogeneity of fraction size) b ut does not incorporate time factors or volume effects. Results: The a nalysis shows that the LQ-transformed distribution is always broader t han the distribution of physical dose, Radiobiological 'hot spots' and 'cold spots' are further from the mean than physical distributions wo uld indicate, The difference between conventional DVHs and LQ-transfor med DVHs is dependent on the fractionation regimen used. LQ-DVHs for a single dose distribution (treatment plan) can be computed for differe nt fractionation regimens with some simplifying assumptions (e.g. no t ime-factor-dependence of late effects). Regimens calculated to be radi obiologically equivalent at a single point nevertheless result in non- equivalent LQ-DVHs when spatial variation of daily treatment dose is i ncluded. The difference is especially important for tumour sites (such as breast and head and neck) for which considerable dose heterogeneit y may occur and for which different treatment regimens are in use. Con clusions: LQ-DVHs should be computed in parallel with conventional DVH s and used in the evaluation of treatment plans and fractionation regi mens and in the analysis of high-dose side-effects in patients. (C) 19 98 Elsevier Science Ireland Ltd.