Radiobiological significance of beamline dependent proton energy distributions in a spread-out Bragg peak

Similar target doses can be achieved with different mixed radiation fields, i.e., particle energy distributions, produced by a practical proton beam and a range modulator. The dose delivered in particle therapy can be described as the integral of fluence times the total mass stopping power over the particle energy distributions. We employed Monte Carlo simulations to explore the influence on the relative biological effectiveness (RBE) of the energy and the energy spread of the proton beam incident on a range modulator system. Using different beams, the conditions of beam delivery were adjusted so that similar spread out Bragg peak (SOBP) doses were delivered to a simulated water phantom. We calculated the RBE for inactivation of three different cell lines using the track structure model. The RBE depends on the details of the dose deposition and the biological characteristics of the irradiated tissue. Our calculations show that, for differing beam conditions, the corresponding differences in the total mass stopping power distributions are reflected in differences in the RBE. However, these differences are remarkable only at the very distal edge of the SOBP, for low doses, and/or for large differences in beam setup.