Use of Gaussian-type functions for flux-based dose calculations in carbon ion therapy

In radiation therapy, it is very important to ensure that the radiation dose is correctly delivered to the patient. This is achieved by obtaining quantitative dose measurements for beam calibration in the treatment planning system. Dose calculations should be performed with the required accuracy to a degree of uncertainty of less than 1%. The measurement of the absorbed dose in and around body tissues irradiated with carbon ions requires careful use of materials selected from established phantom and radiation detectors. The main advantage of such materials is that when information on the energy and nature of charged particles at the desired point is incomplete or inaccurate, they can allow determination of the absorbed dose. In general, radiation interactions in a tissue representation caused by carbon ions can be characterized by calculating the linear stopping power. Carbon ions have a limited penetration depth within human tissues that depends on the energy and stopping power of these ions as they penetrate into the body. The purpose of the present study was to calculate the stopping power, range and dose to intestinal and prostate tissues of carbon ions. The stopping power values of these tissues were specified by the effective charge approach method. The 5ZaPa-NR-CV, pcemd-4 and pcSseg-4 sets of Gaussian-type functions were employed for the calculation of electronic charge density. Range calculations were made by means of the Gaussian quadrature method, making use of the continuous slowing down approximation. Flux-based dose calculations were also carried out in accordance with the Bragg-Gray theorem using the Geant4 and FLUKA simulation toolkits. The results were compared with each other and with the SRIM and CasP datasets. Then, depth-dose distributions and range values were verified by positron emission activity using the GATE toolkit. Among the different types of Gaussian functions used here, the best semi-analytical result was found for the 5ZaPa-NR-CV set. The results obtained in the present study can be used for dose verification and dose reconstruction in charged particle radiotherapy and for radiation research on the interaction of radiation with matter. The results calculated here will be useful for quantifying uncertainties associated with stopping power, range, and reconstruction of dose in charged particle therapy.