Inter-comparison of relative stopping power estimation models for proton therapy

Theoretical stopping power values were inter-compared for the Bichsel, Janni, ICRU and Schneider relative stopping power (RSP) estimation models, for a variety of tissues and tissue substitute materials taken from the literature. The RSPs of eleven plastic tissue substitutes were measured using Bragg peak shift measurements in water in order to establish a gold standard of RSP values specific to our centre's proton beam characteristics. The theoretical tissue substitute RSP values were computed based on literature compositions to assess the four different computation approaches. The Bichsel/Janni/ICRU approaches led to mean errors in the RSP of  -0.1/+0.7/-0.8%, respectively. Errors when using the Schneider approach, with I-values from the Bichsel, Janni and ICRU sources, followed the same pattern but were generally larger. Following this, the mean elemental ionisation energies were optimized until the differences between theoretical RSP values matched measurements. Failing to use optimized I-values when applying the Schneider technique to 72 human tissues could introduce errors in the RSP of up to  -1.7/+1.1/-0.4% when using Bichsel/Janni/ICRU I-values, respectively. As such, it may be necessary to introduce an additional step in the current stoichiometric calibration procedure in which tissue insert RSPs are measured in a proton beam. Elemental I-values can then optimized to match these measurements, reducing the uncertainty when calculating human tissue RSPs.