A framework for defining FLASH dose rate for pencil beam scanning

Purpose To develop a method of (a) calculating the dose rate of voxels within a proton field delivered using pencil beam scanning (PBS), and (b) reporting a representative dose rate for the PBS treatment field that enables correspondence between multiple treatment modalities. This method takes into account the unique spatiotemporal delivery patterns of PBS FLASH radiotherapy. Methods The dose rate at each voxel of a PBS radiation field is approximately the quotient of the voxel's dose and effective irradiation time. Each voxel's effective irradiation time starts when the cumulative dose rises above a chosen threshold value, and stops when its cumulative dose reaches its total dose minus the same threshold value. The above calculation yields a distribution of dose rates for the voxels within a PBS treatment field. To report a representative dose rate for the PBS field, we propose a user-selectable parameter of pth percentile of the dose rate distribution, such that (100 - p) % of the field is above the corresponding dose rate. To demonstrate the method described above, we design FLASH transmission fields using 250 MeV protons and calculate the PBS dose rate distributions in both two-dimensional (2D) and three-dimensional (3D) models. To further evaluate the formalism, we provide an example of a clinical PBS treatment field. Results With the 2D PBS transmission field, it is demonstrated that the time to accumulate the total dose at a voxel is limited to a fraction of the delivery time of the entire field. In addition, the spatial distributions of dose and dose rate are quite different within the field. For the 10 x 10 cm(2) PBS field irradiating a 3D water phantom, the prescribed dose of 10 Gy at 10 cm depth is delivered in 1.0 s. The dose rate decreases in the irradiated volume with increasing depth (until the Bragg peak) due to increase of beam spot size by Coulomb scattering. For example, 95% of the irradiated volume between 0 and 10 cm depth receive >40 Gy/s, whereas between 0-20 cm and 0-30 cm depth, 95% of the irradiated volume received >36 Gy/s and >24 Gy/s, respectively. For the clinical PBS treatment field, the scanning pattern conforms to the PTV. PBS dose rate data are presented for the PTV and adjacent normal organs. Conclusion We have developed a method of calculating the dose rate distribution of a PBS proton field and have recommended nomenclature for reporting PBS treatment dose rate. We believe that standardizing the method for calculating and reporting PBS treatment dose rates, in a manner that corresponds with other treatment modalities, will advance the research and potential application of PBS FLASH radiotherapy.