Effect of Irradiation Time on Biological Effectiveness and Tumor Control Probability in Proton Therapy

The biological effectiveness of proton beams may decrease with irradiation time because of sublethal damage repair (SLDR). The purpose of this study is to systematically evaluate this effect in hypofractionated proton therapy for various target sizes, depths, and prescribed doses per fraction.

Plans with a single spread-out Bragg peak beam were created using a constant relative biological effectiveness (RBE) of 1.1 to cover targets of 6 different sizes located at 3 different depths in water. Biological doses of 2, 3, 5, 10, and 20 Gy (RBE) were prescribed to the targets. First, to investigate the depth variation of the biological effectiveness, the biological dose in instantaneous irradiation was recalculated based on the microdosimetric kinetic model. SLDR was then taken into account in the microdosimetric kinetic model during treatments to obtain the irradiation time-dependent biological effectiveness for irradiation time T of 5 to 60 minutes and beam interruption time τ of 0 to 60 minutes. The tumor control probabilities were calculated for single-fraction proton therapy fields of different Ts and τs, and the curative doses were evaluated at a tumor control probability of 90%.

The biological effectiveness decreased with longer T and τ and higher prescribed dose. The maximum decrease in the biological effectiveness was 21% with a 20 Gy (RBE) prescribed dose. In single-fraction proton therapy, the curative dose increased linearly by approximately 33% to 35% with the increase of T from 0 to 60 minutes.

The biological effectiveness varies largely with T and τ because of SLDR during treatments. This effect was pronounced for high prescribed doses per fraction. Thus, the effect of SLDR needs to be considered in hypofractionated and single-fraction proton therapies in relation to size and depth of the target.