Nuclear-interaction correction of integrated depth dose in carbon-ion radiotherapy treatment planning

In treatment planning of charged-particle therapy, tissue heterogeneity is conventionally modeled as water with various densities, i.e. stopping effective densities ρ(S), and the integrated depth dose measured in water (IDD) is applied accordingly for the patient dose calculation. Since the chemical composition of body tissues is different from that of water, this approximation causes dose calculation errors, especially due to difference in nuclear interactions. Here, we propose and validate an IDD correction method for these errors in patient dose calculations. For accurate handling of nuclear interactions, ρ(S) of the patient is converted to nuclear effective density ρ(N), defined as the ratio of the probability of nuclear interactions in the tissue to that in water using a recently formulated semi-empirical relationship between the two. The attenuation correction factor Φ(w)(p), defined as the ratio of the attenuation of primary carbon ions in a patient to that in water, is calculated from a linear integration of ρ(N) along the beam path. In our treatment planning system, a carbon-ion beam is modeled to be composed of three components according to their transverse beam sizes: primary carbon ions, heavier fragments, and lighter fragments. We corrected the dose contribution from primary carbon ions to IDD as proportional to Φ(w)(p), and corrected that from lighter fragments as inversely proportional to Φ(w)(p). We tested the correction method for some non-water materials, e.g. milk, lard, ethanol and water solution of potassium phosphate (K2HPO4), with un-scanned and scanned carbon-ion beams. In un-scanned beams, the difference in IDD between a beam penetrating a 150 mm-thick layer of lard and a beam penetrating water of the corresponding thickness amounted to -4%, while it was +6% for a 150 mm-thick layer of 40% K2HPO4. The observed differences were accurately predicted by the correction method. The corrected IDDs agreed with the measurements within ±1% for all materials and combinations of them. In scanned beams, the dose estimation error in target dose amounted to 4% for a 150 mm-thick layer of 40% K2HPO4. The error is significantly reduced with the correction method. The planned dose distributions with the method agreed with the measurements within ±1.5% of target dose for all materials not only in the target region but also in the plateau and fragment-tail regions. We tested the correction method of IDD in some non-water materials to verify that this method would offer the accuracy and simplicity required in carbon-ion radiotherapy treatment planning.