Ionization detail parameters and cluster dose: a mathematical model for selection of nanodosimetric quantities for use in treatment planning in charged particle radiotherapy

Objective. To propose a mathematical model for applying ionization detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP). Approach. Our model provides for selection of preferred ID parameters (I _p ) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopic I _p and macroscopic RTP. Selection of I _p is demonstrated using published cell survival measurements for protons through argon, comparing results for nineteen I _p : N _k , k = 2, 3, …, 10, the number of ionizations in clusters of k or more per particle, and F _k , k = 1, 2, …, 10, the number of clusters of k or more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation. Main results. The preferred I _p were N ₄ and F ₅ for aerobic cells, N ₅ and F ₇ for hypoxic cells. Significant differences were found in cell survival for beams having the same LET or the preferred N _k . Conversely, there was no significant difference for F ₅ for aerobic cells and F ₇ for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for these I _p had the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert that I _p exist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation. Significance. Our model provides a practical means to select preferred I _p from radiobiological data, and to convert I _p to the macroscopic cluster dose for particle RTP.