Creating uniform cluster dose spread-out Bragg peaks for proton and carbon beams

Preliminary data have shown a close association of the generalized ionization cluster size dose (in short, cluster dose) with cell survival, independent of particle type, and energy, when cluster dose is derived from an ionization detail parameter preferred for its association with cell survival. Such results suggest cluster dose has the potential to replace RBE-weighted dose in proton and ion beam radiotherapy treatment plan optimization, should a uniform cluster dose lead to comparable biological effects. However, further preclinical investigations are warranted to confirm this premise.

To present an analytical approach to create uniform cluster dose spread-out Bragg peaks (SOBP) for evaluation of the potential of cluster dose to result in uniform biological effect.

We modified the coefficients of the Bortfeld and Schlegel weight formula, an analytical method typically used for the creation of radiation dose SOBP in particle therapy, to produce uniform cluster dose SOBP of different widths (1-5 cm) at relevant clinical proton and carbon beam energies. Optimum parameters were found by minimization of the ratio between the maximum and minimum cluster dose in the SOBP region using the Nelder-Mead method.

The coefficients of the Bortfeld and Schlegel weight formula leading to uniform cluster dose SOBPs were determined for each combination of beam energy and SOBP width studied. The uniformity of the resulting cluster dose SOBPs, calculated as the relative difference between the maximum and minimum cluster dose within the SOBP, was within 0.3%-3.5% for the evaluated proton beams and 1.3%-3.4% for the evaluated carbon beams.

The modifications to the analytical approach to create radiation dose SOBPs resulted in uniform cluster dose proton and carbon SOBPs over a wide range of beam energies and SOBP widths. Such SOBPs should prove valuable in preclinical investigations for the selection of nanodosimetric quantities to be used in proton and ion therapy treatment planning.