Theoretical approaches and Monte Carlo simulations in a clinical proton beam

Proton therapy is an interesting alternative to conventional radiotherapy, especially for treating localized tumors near important and/or sensitive parts of the human body. Protons, due to their electric charge and mass, interact with the propagating media in such a way that a well localized maximum - known as the Bragg peak - is observed if a depth dose deposition curve is plotted. Since the Bragg peak location depends on the initial proton energy beam, by adjusting this parameter it can be placed over the tumor to be treated. In addition, because the dose deposition goes to zero right after this peak, the health tissue after the tumor is spared if proton therapy is adopted. However, despite the aforementioned advantages, many issues prevent a wider adoption of proton therapy over radiotherapy. In addition to the very high implementation cost, unsolved technical issues, such as, the uncertainty in the proton beam range within the medium, or the correct dose prediction at the Bragg peak, must be addressed. This research aims to investigate the validity of theoretical approximations for the solution of Bethe equation. Such approaches are compared to results from Monte Carlo simulations, executed with the MCNPX code, and reference values ​​from the literature as well for the proton beam range and the energy deposition in the medium. A parameter is proposed and adopted to quantify the global difference between the theoretical approximations evaluated in this work with respect to the Monte Carlo simulation results.