The impact of fractionation in SBRT: Analysis with the linear quadratic model and the universal survival curve model

Abstract

Background. Since the impact of fractionation in SBRT has not been systematically investigated, this modelling study was performed to see how the therapeutic window is affected for a range of fractions at target doses commonly administered in SBRT. Material and methods. Isoeffective tumour-doses (constant cell survival) were calculated with the linear quadratic (LQ) and the universal survival curve (USC) models for 2–20 fractions. The isoeffective tumour-regimes (with α/β = 10 Gy) were used to calculate the sparing of normal tissues (with α/β = 3 Gy) for an increasing number of fractions. Sparing was calculated as an increase in cell survival and decrease in normal tissue complication probability (NTCP) as compared to a common scheme with 3 fractions of 22 Gy to the centre of the target [(15 Gy to the periphery of the planning target volume (PTV)]. Results. At a high dose per fraction, above about 15 Gy, the USC model predicted much lower fractionation sensitivity than the LQ model. This holds true for both tumour and normal tissues. The USC model also predicted greater sparing of normal tissues outside the PTV as compared to the LQ model. Especially at dose levels of the order of 30–50% to that in the centre of the target. The decrease in NTCP predicted by the USC model was of the order of 30% for 10 fractions as compared to the NTCP for 3 fractions. With the LQ model the corresponding decrease was of the order of 10%. Conclusion. The USC model generally predicts a larger therapeutic window than the LQ model for an increasing number of fractions than today's practice in SBRT.