Dose to water versus dose to medium in proton beam therapy

Dose in radiation therapy is traditionally reported as the water-equivalent dose, or dose to water. Monte Carlo dose calculations report dose to medium and thus a methodology is needed to convert dose to medium into dose to water (or vice versa) for comparison of Monte Carlo results with results from planning systems. This paper describes the development of a formalism to convert dose to medium into dose to water for proton fields when simulating the dose with Monte Carlo techniques. The conversion is based on relative stopping power but also considers energy transferred via nuclear interactions. The influence of different interaction mechanisms of proton beams (electromagnetic versus nuclear) is demonstrated. Further, an approximate method for converting doses retroactively is presented. Based on the outlined formalism, five proton therapy patients with a total of 33 fields were analyzed. Dose distributions, dose volume histograms and absolute doses to assess the clinical significance of differences between dose to medium and dose to water are presented. We found that the difference between the two dose reporting definitions can be up to 10% for high CT numbers if analyzing the mean dose to the target. The difference is clinically insignificant for soft tissues. For the structures analyzed, the mean dose to water could be converted to dose to medium by applying a correction factor increasing linearly with increasing average CT number in the volume. We determined that an approximate conversion method, done retroactively with an energy-independent stopping power ratio and without considering nuclear interaction events separately (as compared to on-the-fly conversion during simulation), is sufficiently accurate to compute mean doses. It is insufficient, however, when analyzing the beam range. For proton beams stopping in bony anatomy, the predicted beam range can differ by 2-3 mm when comparing dose to tissue and dose to water.