Secondary bremsstrahlung and the energy-conservation aspects of kerma in photon-irradiated media

Abstract

Kerma, collision kerma and absorbed dose in media irradiated by megavoltage photons are analysed with respect to energy conservation. The user-code DOSRZnrc was employed to compute absorbed dose D, kerma K and a special form of kerma, Kncpt, obtained by setting the charged-particle transport energy cut-off very high, thereby preventing the generation of ‘secondary bremsstrahlung’ along the charged-particle paths. The user-code FLURZnrc was employed to compute photon fluence, differential in energy, from which collision kerma, Kcol and K were derived. The ratios K/D, Kncpt/D and Kcol/D have thereby been determined over a very large volumes of water, aluminium and copper irradiated by broad, parallel beams of 0.1 to 25 MeV monoenergetic photons, and 6, 10 and 15 MV ‘clinical’ radiotherapy qualities. Concerning depth-dependence, the ‘area under the kerma, K, curve’ exceeded that under the dose curve, demonstrating that kerma does not conserve energy when computed over a large volume. This is due to the ‘double counting’ of the energy of the secondary bremsstrahlung photons, this energy being (implicitly) included in the kerma ‘liberated’ in the irradiated medium, at the same time as this secondary bremsstrahlung is included in the photon fluence which gives rise to kerma elsewhere in the medium. For 25 MeV photons this ‘violation’ amounts to 8.6%, 14.2% and 25.5% in large volumes of water, aluminium and copper respectively but only 0.6% for a ‘clinical’ 6 MV beam in water. By contrast, Kcol/D and Kncpt/D, also computed over very large phantoms of the same three media, for the same beam qualities, are equal to unity within (very low) statistical uncertainties, demonstrating that collision kerma and the special type of kerma, Kncpt, do conserve energy over a large volume. A comparison of photon fluence spectra for the 25 MeV beam at a depth of ≈51 g cm−2 for both very high and very low charged-particle transport cut-offs reveals the considerable contribution to the total photon fluence by secondary bremsstrahlung in the latter case. Finally, a correction to the ‘kerma integral’ has been formulated to account for the energy transferred to charged particles by photons with initial energies below the Monte-Carlo photon transport cut-off PCUT; for 25 MeV photons this ‘photon track end’ correction is negligible for all PCUT below 10 keV.