Physical parameter optimization scheme for radiobiological studies of charged particle therapy.

We have developed an easy-to-implement method to optimize the spatial distribution of a desired physical quantity for charged particle therapy. The basic methodology requires finding the optimal solutions for the weights of the constituent particle beams that together form the desired spatial distribution of the specified physical quantity, e.g., dose or dose-averaged linear energy transfer (LETd), within the target region. We selected proton, 4He ion, and 12C ion beams to demonstrate the feasibility and flexibility of our method. The pristine dose Bragg curves in water for all ion beams and the LETd for proton beams were generated from Geant4 Monte Carlo simulations. The optimization algorithms were implemented using the Python programming language. High-accuracy optimization results of the spatial distribution of the desired physical quantity were then obtained for different cases. The relative difference between the real value and the expected value of a given quantity was approximately within ±1.0% in the whole target region. The optimization examples include a flat dose spread-out Bragg peak (SOBP) for the three selected ions, an upslope dose SOBP for protons, and a downslope dose SOBP for protons. The relative difference was approximately within ±2.0% for the case with a flat LETd (target value = 4 keV/µm) distribution for protons. These one-dimensional optimization algorithms can be extended to two or three dimensions if the corresponding physical data are available. In addition, this physical quantity optimization strategy can be conveniently extended to encompass biological dose optimization if appropriate biophysical models are invoked.