Variation of the relative biological effectiveness with fractionation in proton therapy: Analysis of prostate cancer response

BackgroundIn treatment planning for proton therapy a constant Relative Biological Effectiveness (RBE) of 1.1 is used, disregarding variations with linear energy transfer, clinical endpoint, or fractionation.PurposeTo present a methodology to analyze the variation of RBE with fractionation from clinical data of tumor control probability (TCP) and to apply it to study the response of prostate cancer to proton therapy.Methods and materialsWe analyzed the dependence of the RBE on the dose per fraction by using the LQ model and the Poisson TCP formalism. Clinical tumor control probabilities for prostate cancer (low and intermediate risk) treated with photon and proton therapy for conventional fractionation (2 Gy(RBE)x37 fractions), moderate hypofractionation (3 Gy(RBE)x20 fractions) and hypofractionation (7.25 Gy(RBE)x5 fractions) were obtained from the literature and analyzed aiming at obtaining the RBE and its dependence on the dose per fraction.ResultsThe theoretical analysis of the dependence of the RBE on the dose per fraction showed three distinct regions with RBE monotonically decreasing, increasing or staying constant with the dose per fraction, depending on the change of (alpha, beta) values between photon and proton irradiation (the equilibrium point being at (alpha p/beta p) = (alpha X/beta X)(alpha X/alpha p)). An analysis of the clinical data showed RBE values that decline with increasing dose per fraction: for low risk RBE approximate to 1.124, 1.119, and 1.102 for 1.82 Gy, 2.73 Gy and 6.59 Gy per fraction (physical proton doses), respectively; for intermediate risk RBE approximate to 1.119 and 1.102 for 1.82 Gy and 6.59 Gy per fraction (physical proton doses), respectively. These values are nonetheless very close to the nominal 1.1 value.ConclusionsIn this study, we have presented a methodology to analyze the RBE for different fractionations, and we used it to study clinical data for prostate cancer and evaluate the RBE versus dose per fraction. The analysis shows a monotonically decreasing RBE with increasing dose per fraction, which is expected from the LQ formalism and the changes in (alpha, beta) values between photon and proton irradiation. However, the calculations in this study have to be considered with care as they may be biased by limitations in the modeling assumptions and/or by the clinical data set used for the analysis.