Fluence correction factors for graphite calorimetry in a low-energy clinical proton beam: I. Analytical and Monte Carlo simulations.

The conversion of absorbed dose-to-graphite in a graphite phantom to absorbed dose-to-water in a water phantom is performed by water to graphite stopping power ratios. If, however, the charged particle fluence is not equal at equivalent depths in graphite and water, a fluence correction factor, kfl, is required as well. This is particularly relevant to the derivation of absorbed dose-to-water, the quantity of interest in radiotherapy, from a measurement of absorbed dose-to-graphite obtained with a graphite calorimeter. In this work, fluence correction factors for the conversion from dose-to-graphite in a graphite phantom to dose-to-water in a water phantom for 60 MeV mono-energetic protons were calculated using an analytical model and five different Monte Carlo codes (Geant4, FLUKA, MCNPX, SHIELD-HIT and McPTRAN.MEDIA). In general the fluence correction factors are found to be close to unity and the analytical and Monte Carlo codes give consistent values when considering the differences in secondary particle transport. When considering only protons the fluence correction factors are unity at the surface and increase with depth by 0.5% to 1.5% depending on the code. When the fluence of all charged particles is considered, the fluence correction factor is about 0.5% lower than unity at shallow depths predominantly due to the contributions from alpha particles and increases to values above unity near the Bragg peak. Fluence correction factors directly derived from the fluence distributions differential in energy at equivalent depths in water and graphite can be described by kfl = 0.9964 + 0.0024·zw-eq with a relative standard uncertainty of 0.2%. Fluence correction factors derived from a ratio of calculated doses at equivalent depths in water and graphite can be described by kfl = 0.9947 + 0.0024·zw-eq with a relative standard uncertainty of 0.3%. These results are of direct relevance to graphite calorimetry in low-energy protons but given that the fluence correction factor is almost solely influenced by non-elastic nuclear interactions the results are also relevant for plastic phantoms that consist of carbon, oxygen and hydrogen atoms as well as for soft tissues.

Water equivalence of some plastic-water phantom materials for clinical proton beam dosimetry.

Plastic-water phantom materials are not exactly water equivalent since they have a different elemental composition and different interaction cross sections for protons than water. Several studies of the water equivalence of plastic-water phantom materials have been reported for photon and electron beams, but none for clinical proton beams. In proton beams, the difference between non-elastic nuclear interactions in plastic-water phantom materials compared to those in water should be considered. In this work, the water equivalence of Plastic Water® (PW)1, Plastic Water® Diagnostic Therapy (PWDT)1 and solid water (WT1)2 phantoms was studied for clinical proton energies of 60 MeV and 200 MeV. This was done by evaluating the fluence correction factor at equivalent depths; first with respect to water and then with respect to graphite by experiment and Monte Carlo (MC) simulations using FLUKA. MC simulations showed that the fluence correction with respect to water was less than 0.5% up to the entire penetration depth of the protons at 60 MeV and less than 1% at 200 MeV up to 20 cm depth for PWDT, PW and WT1. With respect to graphite the fluence correction was about 0.5% for 60 MeV and about 4% for 200 MeV. The experimental results for modulated and un-modulated 60 MeV proton beams showed good agreement with the MC simulated fluence correction factors with respect to graphite deviating less than 1% from unity for the three plastic-water phantoms.

SU-E-T-146: Reference Dosimetry for Protons and Light-Ion Beams Based on Graphite Calorimetry.

PURPOSE: The IAEA TRS-398 code of practice can be applied for the measurement of absorbed dose to water under reference conditions with an ionization chamber. For protons, the combined relative standard uncertainty on those measurements is less than 2% while for light-ion beams, it is considerably larger, i.e. 3.2%, mainly due to the higher uncertainty contributions for the water to air stopping power ration and the W air-value on the beam quality correction factors kQ,Q0 . To decrease this uncertainty, a quantification of kQ,Q0 is proposed using a primary standard level graphite calorimeter. This work includes numerical and experimental determinations of dose conversion factors to derive dose to water from graphite calorimetry. It also reports on the first experimental data obtained with the graphite calorimeter in proton, alpha and carbon ion beams. METHODS: Firstly, the dose conversion has been calculated with by Geant4 Monte-Carlo simulations through the determination of the water to graphite stopping power ratio and the fluence correction factor. The latter factor was also derived by comparison of measured ionization curves in graphite and water. Secondly, kQ,Q0 was obtained by comparison of the dose response of ionization chambers with that of the calorimeter. RESULTS: Stopping power ratios are found to vary by no more than 0.35% up to the Bragg peak, while fluence correction factors are shown to increase slightly above unity close to the Bragg peak. The comparison of the calorimeter with ionization chambers is currently under analysis. For the modulated proton beam, preliminary results on W air confirm the value recommended in TRS-398. Data in both the non-modulated proton and light-ion beams indicate higher values but further investigation of heat loss corrections is needed. CONCLUSIONS: The application of graphite calorimetry to proton, alpha and carbon ion beams has been demonstrated successfully. Other experimental campaigns will be held in 2012. This work is supported by the BioWin program of the Wallon Government.