Simultaneous dose and dose rate optimization (SDDRO) of the FLASH effect for pencil‐beam‐scanning proton therapy

Abstract

Purpose Compared to CONV‐RT (with conventional dose rate), FLASH‐RT (with ultra‐high dose rate) can provide biological dose sparing for organs‐at‐risk (OARs) via the so‐called FLASH effect, in addition to physical dose sparing. However, the FLASH effect only occurs, when both dose and dose rate meet certain minimum thresholds. This work will develop a simultaneous dose and dose rate optimization (SDDRO) method accounting for both FLASH dose and dose rate constraints during treatment planning for pencil‐beam‐scanning proton therapy. Methods SDDRO optimizes the FLASH effect (specific to FLASH‐RT) as well as the dose distribution (similar to CONV‐RT). The nonlinear dose rate constraint is linearized, and the reformulated optimization problem is efficiently solved via iterative convex relaxation powered by alternating direction method of multipliers. To resolve and quantify the generic tradeoff of FLASH‐RT between FLASH and dose optimization, we propose the use of FLASH effective dose based on dose modifying factor (DMF) owing to the FLASH effect. Results FLASH‐RT via transmission beams (TB) (IMPT‐TB or SDDRO) and CONV‐RT via Bragg peaks (BP) (IMPT‐BP) were evaluated for clinical prostate, lung, head‐and‐neck (HN), and brain cases. Despite the use of TB, which is generally suboptimal to BP for normal tissue sparing, FLASH‐RT via SDDRO considerably reduced FLASH effective dose for high‐dose OAR adjacent to the target. For example, in the lung SBRT case, the max esophageal dose constraint 27 Gy was only met by SDDRO (24.8 Gy), compared to IMPT‐BP (35.3 Gy) or IMPT‐TB (36.6 Gy); in the brain SRS case, the brain constraint V12Gy≤15cc was also only met by SDDRO (13.7cc), compared to IMPT‐BP (43.9cc) or IMPT‐TB (18.4cc). In addition, SDDRO substantially improved the FLASH coverage from IMPT‐TB, e.g., an increase from 37.2% to 67.1% for lung, from 39.1% to 58.3% for prostate, from 65.4% to 82.1% for HN, from 50.8% to 73.3% for the brain. Conclusions Both FLASH dose and dose rate constraints are incorporated into SDDRO for FLASH‐RT that jointly optimizes the FLASH effect and physical dose distribution. FLASH effective dose via FLASH DMF is introduced to reconcile the tradeoff between physical dose sparing and FLASH sparing, and quantify the net effective gain from CONV‐RT to FLASH‐RT.

A quantitative FLASH effectiveness model to reveal potentials and pitfalls of high dose rate proton therapy

“…As such, it would not be straightforward to directly optimize the FLASH dose reduction using our framework. However, our presented FLASH effectiveness model is independent of the used optimizer, and thus it would be possible to include this model into the cost function of any other optimizer, resulting in a similar framework as the simultaneous dose and dose rate optimizer recently presented by Gao et al 26 In summary, our model is the first quantitative representation of previous findings, that is, that transmission plans and fewer treatment fields are likely to induce higher FLASH effects than conventional planning scenarios. 12 The sensitivity analysis additionally revealed that, in order to achieve a clinical benefit of the transmission plan compared to the clinical reference plan, hypofractionated treatments with increased fraction doses will be required.…”

“…As such, it would not be straightforward to directly optimize the FLASH dose reduction using our framework. However, our presented FLASH effectiveness model is independent of the used optimizer, and thus it would be possible to include this model into the cost function of any other optimizer, resulting in a similar framework as the simultaneous dose and dose rate optimizer recently presented by Gao et al 26 …”

FLASH radiotherapy treatment planning and models for electron beams

“…They include simple parameter thresholds, such as dose, dose rate and dose rate volume histogram thresholds and aim typically to quantify voxels or a dose fraction per voxel that fulfil these criteria, assuming a binary FLASH effect [115,[118][119][120][121]. Furthermore, more complex metrics, such as dose-averaged dose rate and '95% of the dose in a voxel delivered within a certain time', have been proposed for UHDR treatments with a more complex delivery time structure, such as scanned beams delivered via multiple portals [75,115,119,[122][123][124]. While latter metrics have been developed in the context of UHDR PT, they could be equally applied to UHDR electron beam RT.…”

“…D CONV , is the dose delivered in UHDR mode, resp. in CONV mode, for an isoeffect for the tumor) [75,120,123,126]. This has been used by some treatment planning studies either using generic DMF factors [97,120,123,127] or utilising a modelling based on the radiolytic oxygen depletion hypothesis [75].…”

“…• A direct prediction of TCP/NTCP for a given UHDR plan is also an option for the quantification of the FLASH effect for treatment planning, but has, to our knowledge, not yet been applied in UHDR treatment planning studies. FLASH predictors may also be built into cost functions for the optimization of UHDR treatment plans [75,123].…”