Fast calculation of nanodosimetric quantities in treatment planning of proton and ion therapy

Details of the pattern of ionization formed by particle tracks extends knowledge of dose effects on the nanometer scale. Ionization detail (ID), frequently characterized by ionization cluster size distributions (ICSD), is obtained through time-consuming Monte Carlo (MC) track-structure simulations. In this work, TOPAS-nBio was used to generate a highly precise database of biologically significant ID quantities, sampled with randomly oriented 2.3 nm diameter cylinders, 3.4 nm (10 base pairs) long, inside a chromatin-size cylinder, irradiated by 1-1000 MeV/u ions of Z = 1-8. A macroscopic method developed to utilize the database using condensed-history MC was used to calculate distributions of the ICSD first moment M-1(C2) and cumulative probability F-3(C2) in a 20 x 20 x 40 cm(3) water phantom irradiated with proton and carbon spread-out Bragg peak (SOBP) of 10.5 cm range, 2 cm width. Results were verified against detailed MC track-structure simulations using phase space scored at several depths. ID distributions were then obtained for intensity modulated proton and carbon radiotherapy plans in a digitized anthropomorphic phantom of a base of skull tumor to demonstrate clinical application of this approach. The database statistical uncertainties were 0.5% (3 standard deviations). Fluence-averaged ID as implemented proved unsuitable for macroscopic calculation. E-dep-averaged ID agreed with track-structure results within 0.8% for protons. For carbon, maximum absolute differences of 2.9% +/- 1.6% and 5.6% +/- 1.9% for M-1(C2) 1, 1.7% +/- 0.8% and 1.9% +/- 0.4% (1 standard deviation) for F-3(C2) , were found in the plateau and SOBP, respectively, up to 11.5% +/- 5.6% in the tail region. Macroscopic ID calculation was demonstrated for a realistic treatment plan. Computation times with or without ID calculation were comparable in all cases. Pre-calculated nanodosimetric data may be used for condensed-history MC for nanodosimetric ID-based treatment planning in ion radiotherapy in the future. The macroscopic approach developed has the calculation speed of condensed-history MC while approaching the accuracy of full track structure simulations.