Fluence correction factors and stopping power ratios for clinical ion beams

In radiation therapy, the principal dosimetric quantity of interest is the absorbed dose to water. Therefore, a dose conversion to dose to water is required for dose deposited by ion beams in other media. This is in particular necessary for dose measurements in plastic phantoms for increased positioning accuracy, graphite calorimetry being developed as a primary standard for dose to water dosimetry, but also for the comparison of dose distributions from Monte Carlo simulations with those of pencil beam algorithms.

In the conversion of absorbed dose to phantom material to absorbed dose to water the water-to-material stopping power ratios (STPR) and the fluence correction factors (FCF) for the full charged particle spectra are needed. We determined STPR as well as FCF for water to graphite, bone (compact), and PMMA as a function of water equivalent depth, z(w), with the Monte Carlo code SHIELD-HIT10A. Simulations considering all secondary ions were performed for primary protons as well as carbon, nitrogen and oxygen ions with a total range of 3 cm, 14.5 cm and 27 cm as well as for two spread-out Bragg-peaks (SOBP). STPR as a function of depth are also compared to a recently proposed analytical formula.

The STPR are of the order of 1.022, 1.070, and 1.112 for PMMA, bone, and graphite, respectively. STPR vary only little with depth except close to the total range of the ion and they can be accurately approximated with an analytical formula. The amplitude of the FCF depends on the non-elastic nuclear interactions and it is unity if these interactions are turned off in the simulation. Fluence corrections are of the order of a percent becoming more pronounced for larger depths resulting in dose difference of the order of 5% around 25 cm. The same order of magnitude is observed for SOBP.

We conclude that for ions with small total range (z(w-eq) ≤3 cm) dosimetry without applying FCF could in principle be performed in phantoms of materials other than water without a significant loss of accuracy. However, in clinical high-energy ion beams with penetration depths z(w-eq) ≥3 cm, where accurate positioning in water is not an issue, absorbed dose measurements should be directly performed in water or accurate values of FCF need to be established.