A universal parameterized gradient-based method for photon beam field size determination

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To propose a universal, parameterized gradient-based method (PGM) for radiation field size determination.


The PGM locates the beam profile's edge by parameterizing its penumbra region with a modified sigmoid function where the inflection point can be determined in a closed form. The parametrization was validated with filter-flattened (FF), flattening-filter-free (FFF) and wedged profiles measured on two Elekta linac models (Synergy and Versa HD). Gamma analysis with the delta dose function set to zero was used to quantitatively assess the parameterization accuracy. Field sizes of FF beams were calculated with the PGM and the full width at half maximum (FWHM) methods for comparison. To assess the consistency of the PGM and the FWHM method with geometric scaling across different depths, the calculated field size at a reference depth was scaled to other depths and compared with the field sizes calculated from the measured profiles. The method was also validated against a maximum-slope method (MSM) with wedge and FFF profiles. We also evaluated the robustness of the three methods with respect to measurement noise, varying scanning step sizes, detector characteristics, and beam energy/modality.


Small distance-to-agreement (0.02 ± 0.02 mm) between the measured and parameterized penumbra region was observed for all profiles. The differences between the field sizes calculated with the FWHM method and the PGM were consistent (0.9 ± 0.3 mm), with the FWHM method yielding larger values. With geometrical scaling, the PGM and the FWHM method produced maximum differences of 0.26 and 1.16 mm, respectively. For wedge and FFF beams, the mean differences relative to FF fields were 0.15 ± 0.09 mm and 0.57 ± 0.91 mm for the PGM and the MSM, respectively. The PGM was also found to produce more consistent results than the FWHM method and the MSM when measurement noise, scanning step size, detector characteristics, and beam energy/modality changed.


The proposed PGM is universally applicable to all beam modalities (FF, wedge and FFF) for accurate field size determination. Compared to the FWHM and the MSM, it is more robust to variations in measurement condition and detection system.

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