XXIII Congresso da Sociedade Brasileira de Radioterapia

Dados do Trabalho


Evaluation of the range of clinical proton beams using Bethe equation for materials with different densities than water


Proton therapy is an alternative technique to conventional radiotherapy, with increasing use in clinical and research environments due to its characteristics and benefits. A current topic of research related to proton therapy is the impact of uncertainties associated with the reach of charged particles on tumor coverage.


This work aims to verify the relative error between Monte Carlo simulations and results obtained by numerically solving the complete Bethe equation for the range of a proton beam in materials with different densities than that of the water.


The simulations were performed by using TOPAS, a Monte Carlo software. The Bethe equation was numerically solved in order to determine the proton beam range. The phantom was a parallelepiped with an entry face of 5 x 5 cm2, and a depth of 1.3 times the expected proton beam range in the material. Regarding the phantom composition, in each simulation it is homogeneously composed of one of the following tissue-equivalent materials: adipose tissue, water, brain, lung and compact bone. The composition of such materials were obtained from the National Institute of Standards and Technology (NIST). Inside the phantom a mesh of 100 bins per cm is defined in the longitudinal direction, which is used to determine the dose measure in the medium, in Gy. The Monte Carlo simulation was performed assuming a Gaussian proton beam, with mean energy of 50, 100, 150, 200, 250 and 300 MeV, energy spread of 0.75% and beam spot size = 0.65 cm (σ). To validate the results, water was used as a reference and a beam of 150 MeV, the MC simulation presented a relative error of 0.98% with the NIST and 0.53% with the Bethe equation. From this, the relative error of the equation in ratio to the simulation for the other materials was calculated.


The adipose tissue showed the lowest error at 50 MeV, with 0.43% and the highest at 300 MeV, with an error of 2.33%. Water had the lowest error at 150 MeV with 0.53% and the highest at 200 MeV with 1.37%. The brain had the lowest error, 0.65%, at 100 MeV and the highest error, 1.84%, at 300 MeV. The lung had the smallest, 0.11% at 300 MeV and the largest, 0.8% at 100 MeV. The compact bone presented the smallest error at 300 Mev, 2.83% and the largest error at 50 MeV, with 7.23%.


The adipose tissue, a material with lower density, had a better behavior at low energies, similarly the bone, for having a higher density, had a better performance at high energies.