Flattening filter free in intensity-modulated radiotherapy (IMRT) – Theoretical modeling with delivery efficiency analysis

Purpose: The flattening filter (FF) has traditionally been used to flatten beams or create uniform fields in conformal and intensity-modulated radiation therapy (IMRT) but reduces the dose rate. Many studies have confirmed improvement in delivery efficiency by removing the FF, also known as flattening filter free (FFF), especially for small field stereotactic body radiation therapy (SBRT); but it is unclear if large treatment fields still favor the FFF beam. We propose a novel, unified approach to quantify delivery efficiency of the FFF and flattened beams. Methods: We modeled the FF effect by inverse conical filters and systematically studied delivery efficiency (beam-on time, BOT) by varying the filter thickness, including the FF and FFF mode. We formulated the BOT of different beams for any arbitrary fluence map in linear programming to solve the optimal inverse conical filter that minimizes the BOT. One-dimensional optimal filters of minimum BOT were also derived in closed form for conical fluence to gain insight for arbitrary clinical fluence maps. We evaluated the BOT of the FFF beam and flattened beam for conformal treatment fields of various dimensions ranging from 5 cm × 5 cm to 25 cm × 25 cm. We also analyzed the BOT for 698 clinical IMRT prostate fluence maps of field size 10 cm × 10 cm, 17 head-and-neck fluence maps of field size 15 cm × 15 cm, and additional realistic test data from 90° rotation and up to 40 cm × 40 cm enlargement of these clinical fluence maps, which were all initially generated with flattened beams. Results: The FFF beam minimized the BOT for A field size less than 20 cm in single leaf pair cases and for conformal fields of dimension less than 20 cm × 20 cm. The FFF beam also minimized the BOT for all tested prostate and head-and-neck cases. The median BOT ratios of the FFF beam to the flattened beam were 0.56 and 0.61 for prostate and head-and-neck cases, respectively. The FFF beam minimized the BOT for field size up to 30 cm × 30 cm and had similar BOTs to those of the flattened beam for field size greater than 30 cm × 30 cm in those clinically realistic test data. Conclusion: The filter modeling and BOT calculation enable us to quantify delivery efficiency of the FFF beam and flattened beam in a unified approach. The FFF beam minimized the BOT both theoretically and in simulations for all clinically relevant field sizes and fluence maps in IMRT. The results for conformal fields imply that the FFF beam requires less BOT than the flattened beam for volumetric modulated arc therapy (VMAT) treatments. The delivery efficiency consideration favors the FFF beam in intensity-modulated treatments and may eventually lead to removal of the FF in all future linear accelerator head designs.