Small elongated MLC fields: Novel equivalent square field formula and output factors

This study evaluates different approaches for estimating the equivalent square field size (ESF) to derive the Output Correction Factors (OCF) according to the IAEA TRS-483 protocol, for small fields, focusing on rectangular fields generated by MLCs. A novel formula is proposed for estimating the ESF to be used alongside the TRS-483 formalism for Field Output Factor (FOF) determination.

FOF for fields from 0.5 to 4 cm side shaped with MLC (jaws fixed to 4.4 × 4.4 cm²) were measured using two Varian TrueBeam (with Millennium and HD-MLC), at isocenter, 10 cm depth, with 6 and 10 MV beam energies, both with and without flattening filter, with microDiamond, DiodeE, and PinPoint3D detectors. Measured ratios were corrected using the OCF from the TRS-483 Tables to determine the FOF. The field size for each setting was determined as the FWHM of the scanning profiles acquired with the microDiamond detector. The ESF was determined using three methods: the Equivalent Area method (according to TRS-483), the Sterling Formula, and a new method according to the following formula: $EqSqFS=\left[2·min{\left(X,Y\right)}^a·max{\left(X,Y\right)}^{\left(2-a\right)}\right]/\left(X+Y\right)$ , with $a$ here empirically set to 1.12.

Corrected FOF for square fields showed good agreement among the detectors with the Equivalent Area as ESF, validating the TRS-483 procedure. For even slightly elongated fields data demonstrated the inadequacy of the equivalent area method. The Sterling formula improved the results but still exhibits substantial differences for the smallest fields. The proposed EqSqFS effectively addresses these shortcomings, showing a description very close to the physical one provided by Ringholtz with the pencil beam method, which utilizes a kernel model to characterize both primary and scatter components of the dose.

A new approach for ESF estimation is introduced, which is valid for elongated small fields, to be used in combination with TRS-483 OCF.