Simultaneous dose and dose rate optimization via dose modifying factor modeling for FLASH effective dose

Abstract Background Although the FLASH radiotherapy (FLASH) can improve the sparing of organs‐at‐risk (OAR) via the FLASH effect, it is generally a tradeoff between the physical dose coverage and the biological FLASH coverage, for which the concept of FLASH effective dose (FED) is needed to quantify the net improvement of FLASH, compared to the conventional radiotherapy (CONV). Purpose This work will develop the first‐of‐its‐kind treatment planning method called simultaneous dose and dose rate optimization via dose modifying factor modeling (SDDRO‐DMF) for proton FLASH that directly optimizes FED. Methods SDDRO‐DMF models and optimizes FED using FLASH dose modifying factor (DMF) models, which can be classified into two categories: (1) the phenomenological model of the FLASH effect, such as the FLASH effectiveness model (FEM); (2) the mechanistic model of the FLASH radiobiology, such as the radiolytic oxygen depletion (ROD) model. The general framework of SDDRO‐DMF will be developed, with specific DMF models using FEM and ROD, as a demonstration of general applicability of SDDRO‐DMF for proton FLASH via transmission beams (TB) or Bragg peaks (BP) with single‐field or multi‐field irradiation. The FLASH dose rate is modeled as pencil beam scanning dose rate. The solution algorithm for solving the inverse optimization problem of SDDRO‐DMF is based on iterative convex relaxation method. Results SDDRO‐DMF is validated in comparison with IMPT and a state‐of‐the‐art method called SDDRO, with demonstrated efficacy and improvement for reducing the high dose and the high‐dose volume for OAR in terms of FED. For example, in a SBRT lung case of the dose‐limiting factor that the max dose of brachial plexus should be no more than 26 Gy, only SDDRO‐DMF met this max dose constraint; moreover, SDDRO‐DMF completely eliminated the high‐dose (V70%) volume to zero for CTV10mm (a high‐dose region as a 10 mm ring expansion of CTV). Conclusion We have proposed a new proton FLASH optimization method called SDDRO‐DMF that directly optimizes FED using phenomenological or mechanistic models of DMF, and have demonstrated the efficacy of SDDO‐DMF in reducing the high‐dose volume or/and the high‐dose value for OAR, compared to IMPT and a state‐of‐the‐art method SDDRO.