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.