PURPOSE: The aim of this study was to determine fluence corrections necessary to convert absorbed dose to graphite, measured by graphite calorimetry, to absorbed dose to water. Fluence corrections were obtained from experiments and Monte Carlo simulations in low- and high-energy proton beams. METHODS: Fluence corrections were calculated to account for the difference in fluence between water and graphite at equivalent depths. Measurements were performed with narrow proton beams. Plane-parallel-plate ionization chambers with a large collecting area compared to the beam diameter were used to intercept the whole beam. High- and low-energy proton beams were provided by a scanning and double scattering delivery system, respectively. A mathematical formalism was established to relate fluence corrections derived from Monte Carlo simulations, using the fluka code [A. Ferrari et al., "fluka: A multi-particle transport code," in CERN 2005-10, INFN/TC 05/11, SLAC-R-773 (2005) and T. T. Böhlen et al., "The fluka Code: Developments and challenges for high energy and medical applications," Nucl. Data Sheets 120, 211-214 (2014)], to partial fluence corrections measured experimentally. RESULTS: A good agreement was found between the partial fluence corrections derived by Monte Carlo simulations and those determined experimentally. For a high-energy beam of 180 MeV, the fluence corrections from Monte Carlo simulations were found to increase from 0.99 to 1.04 with depth. In the case of a low-energy beam of 60 MeV, the magnitude of fluence corrections was approximately 0.99 at all depths when calculated in the sensitive area of the chamber used in the experiments. Fluence correction calculations were also performed for a larger area and found to increase from 0.99 at the surface to 1.01 at greater depths. CONCLUSIONS: Fluence corrections obtained experimentally are partial fluence corrections because they account for differences in the primary and part of the secondary particle fluence. A correction factor, F(d), has been established to relate fluence corrections defined theoretically to partial fluence corrections derived experimentally. The findings presented here are also relevant to water and tissue-equivalent-plastic materials given their carbon content.

Department of Medical Physics and Biomedical Engineering University College London London WC1E 6BT United Kingdom

Department of Medical Physics and Biomedical Engineering University College London London WC1E 6BT United Kingdom and Division of Acoustics and Ionising Radiation National Physical Laboratory Teddington TW11 0LW United Kingdom

Division of Acoustics and Ionising Radiation National Physical Laboratory Teddington TW11 0LW United Kingdom

Division of Acoustics and Ionising Radiation National Physical Laboratory Teddington TW11 0LW United Kingdom and Medical Physics Group EBG MedAustron GmbH A 2700 Wiener Neustadt Austria

National Eye Proton Therapy Centre Clatterbridge Cancer Centre Wirral CH63 4JY United Kingdom

Proton Therapy Center Budinova 1a Prague 8 CZ 180 00 Czech Republic

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