Reconstruction of the 3-dimensional spread-out Bragg peak with the MINUIT fit package

The MINUIT fit package is used to obtain an optimized 3D spread-out Bragg peak (SOBP) in ion therapy. Once a 3D tumor shape is prepared in the Cartesian coordinate system, where the z-axis is set to the beam direction, the fit package automatically calculates the best combinations of the component beams to get the SOBP along the beam direction. A pencil beam scanning system in the transverse plane and a beam energy modulation system to control the Bragg peak position were assumed to be provided. Thus, for a given transverse beam position, we get a set of weighting values for the component beams to create a relevant SOBP according to the 3D tumor shape. The target function in the fit was designed to calculate the weight of each Bragg peak to maximize the flatness of the SOBP while minimizing the dose in the normal tissue area, thus maximizing the dose in the tumor. We made a GEANT4 simulation test bench to verify the 3D conformal irradiation of dose. The transverse beam scanning system and the energy modulators are also simulated, and the ion irradiation is performed according to the MINUIT fit results. The resulting radiation dose shape shows a good match with the original input tumor shape. Thus we were able to conclude that our method with the MINUIT fit package to obtain the 3D SOBP could be readily used in real-ion beam therapy.