Impact of potentially variable RBE in liver proton therapy

Abstract

Currently, the relative biological effectiveness (RBE) is assumed to be constant with a value of 1.1 in proton therapy. Although trends of RBE variations are well known, absolute values in patients are associated with considerable uncertainties. This study aims to evaluate the impact of a variable proton RBE in proton therapy liver trials using different fractionation schemes. Sixteen liver cancer cases were evaluated assuming two clinical schedules of 40 Gy/5 fractions and 58.05 Gy/15 fractions. The linear energy transfer (LET) and physical dose distribution in patients were simulated using Monte Carlo. The variable RBE distribution was calculated using a phenomenological model, considering the influence of the LET, fraction size and α/β value. Further, models to predict normal tissue complication probability (NTCP) and tumor control probability (TCP) were used to investigate potential RBE effects on outcome predictions. Applying the variable RBE model to the 5 and 15 fractions schedules results in an increase in mean fraction-size equivalent dose (FED) to the normal liver of 5.0% and 9.6% respectively. For patients with a mean FED to the normal liver larger than 29.8 Gy, this results in a non-negligible increase in the predicted NTCP of the normal liver averaging 11.6%, ranging from 2.7% to 25.6%. On the other hand, decrease in TCP was less than 5% for both fractionation regimens for all patients when assuming a variable RBE instead of constant. Consequently, the difference in TCP between the two fractionation schedules did not change significantly assuming a variable RBE while the impact on the NTCP difference was highly case specific. In addition, both the NTCP and TCP decrease with increasing α/β value for both fractionation schemes, with the decreases being more pronounced when using a variable RBE compared to using RBE = 1.1. Assuming a constant RBE of 1.1 most likely overestimates the therapeutic ratio in proton therapy for liver cancer, predominantly due to underestimation of the RBE-weighted dose to the normal liver. The impact of applying a variable RBE (as compared to RBE = 1.1) on the NTCP difference of the two fractionation regimens is case dependent. A variable RBE results in a slight increase in TCP difference. Variations in patient radiosensitivity increase when using a variable RBE.

Figure 1.

NTCP for the sixteen cases as a function of mean FED (normalized to 1.5 Gy/fraction) using RBE=1.1 and variable RBE for the two fractionation schemes.

Figure 2.

NTCP difference between using RBE=1.1 and variable RBE for the sixteen cases for the two fractionation schemes.

Figure 3.

Normal liver V₃₀ for RBE=1.1 and variable RBE for the two fractionation schemes.

Figure 4.

TCP for the sixteen cases as a function of mean FED (normalized to 2 Gy/fraction) using RBE=1.1 and variable RBE for the two fractionation schemes.

Figure 5.

TCP difference between using RBE=1.1 and variable RBE for the sixteen cases for the two fractionation schemes.

Figure 6.

Distributions of the RBE weighted dose with RBE=1.1 (a) and dose-averaged LET (only the volumes receiving more than 5% of the prescribed dose were considered) (b) in case 2. The inner contour indicates the GTV and outer contour indicates the whole liver.

Figure 7.

DVHs of the RBE weighted doses in the normal liver (blue lines) and target region (red lines) with RBE=1.1 and variable RBE using different α/β values: (a) 5 fractions schedule; (b) 15 fractions schedule.