Water or realistic compositions in proton radiotherapy? An analytical study

Pre-clinical tests and simulation studies for radiotherapy are generally carried out using water or simplified materials. Investigating the effects of defining compositionally realistic media in proton transport studies was the objective of this work. Accurate modeling of the Bragg curve is a fundamental requirement for such a study.

An equation previously validated by experiments provides an appropriate analytical method for proton dose calculation in depth of the target. Owing to the dependency on protons ranges and the probability of undergoing non-elastic nuclear interactions (NNI), this formula comprises three parameters with values specified for initial proton energy and for the target material. As a result, knowledge of the depth-dose distribution using this analytical model is limited to the materials for which the data has been provided in nuclear data tables. In this study, we used our general formulas for calculating the protons ranges and the probability of undergoing NNI in desired compounds and mixtures with an arbitrary number of constituent elements. Furthermore, the protons dose distribution in the depth of these targets was leading off with determining the parameters appeared in the employed model using our mathematically easy to handle relations. For a number of tissues which may be of interest in proton radiotherapy studies but are missing in reference data tables, the mentioned parameters were calculated. Moreover, the resultant values for the protons ranges and the probability of undergoing NNIs were compared with those in water.

The results showed that the differences between the position of Bragg peaks in water and realistic media considered in this study were energy dependent, and ranged between a few millimeters. For proton beams of arbitrary chosen initial energies, the maximum dose delivered to the realistic media varied between about -0.02-4.42% in comparison with that to water.

The effects observed (both in penetration and in the magnitude of the Bragg peaks) may be overshadowed by the different dose prescriptions depending on the quality of the treatment planning system, and dosimetry protocols used at the various therapy centers.