CT calibration for two-dimensional scaling of proton pencil beams

For proton dose calculations in heterogeneous media, it was shown in a previous work that the conventional pencil beam approach based on pathlength scaling does not properly account for scattering effects in nonwater media (Szymanowski and Oelfke 2002 Phys. Med. Biol. 47 3313-30). A two-dimensional scaling method was therefore introduced, which is able to predict with high accuracy the propagation of proton pencil beams both along the depth and the lateral directions in inhomogeneous media. In order to integrate this improved pencil beam algorithm in a CT based treatment planning system, two CT calibration curves are needed. The first one relates the Hounsfield numbers to the relative stopping powers, as for the conventional pencil beam approach. The second curve is to relate the Hounsfield numbers to the material-specific lateral scaling factors. The purpose of this work is to provide the CT calibration curves needed for the integration of the pencil beam algorithm featuring the two-dimensional scaling method. Similarly to as suggested by Schneider et al (1996 Phys. Med. Biol. 41 111-24) for the calibration curve in terms of stopping powers, we follow a stoichiometric procedure to get the calibration curve in terms of material-specific lateral scaling factors. The calibration curves for a CT scanner of the type Siemens Somatom Plus 4 are obtained from the analytical calculation of the CT Hounsfield numbers, relative stopping powers and material-specific lateral scaling factors for human biological tissues.