Calculation of relative biological effectiveness for proton beams using biological weighting functions

Purpose: The microdosimetric weighting function approach is used widely for beam comparison studies. The suitability of this model to predict the relative biological effectiveness (RBE) of therapeutic proton beams was studied. The RBEα (i.e., linear approximation) dependence on the type of biological end point, initial proton energy, energy spread of the input proton beam, and depth of beam penetration was investigated. Methods and Materials: Proton transport calculations for a proton energy range from 70 to 250 MeV were performed to obtain proton energy spectra at a given depth. The corresponding microdosimetric distributions of lineal energy were calculated. To these distributions the biological response function approach was applied to calculate RBEα the biological effectiveness based on a linear dose-response relationship. The early intestinal tolerance assessed by crypt regeneration in mice and the inactivation of V79 cells were taken as biological end points. Results: The RBEα values approach about 1 in the plateau region and gradually increase with the proton penetration depth. In the center of the Bragg peak, at the maximum dose delivery, the values of RBEα range from 1.1 (250-MeV beam, early intestinal tolerance in mice) to 1.9 (70-MeV beam, Chinese hamster V79 cells in G1/S phase). Distal to the Bragg peak, where only a small fraction of dose is delivered, the RBEα was found to be even higher. For modulated proton beams we found an increasing RBEα with depth in the spread-out Bragg peak (SOBP). Values up to 1.37 at the distal end of the SOBP plateau (155-MeV beam, SOBP between 5.3 and 13.2 cm) were obtained. Conclusion: More experimental work on the determination of microdosimetric weighting functions is needed. The results of the presented calculations indicate that for therapy planning it may be necessary to account for a depth dependence on proton RBE, especially for lower energy