On empirical methods to determine scatter factors for irregular MLC shaped beams

Multileaf collimators (MLCs) are in clinical use for more than a decade and are a well accepted tool in radiotherapy. For almost each MLC design different empirical or semianalytical methods have been presented for calculating output ratios in air for irregularly shaped beams. However, until now no clear recommendations have been given on how to handle irregular fields shaped by multileaf collimators for independent monitor unit (MU) verification. The present article compares different empirical methods, which have been proposed for independent MU verification, to determine (1) output ratios in air (Sc) and (2) phantom scatter factors (Sp) for irregular MLC shaped fields. Ten dedicated field shapes were applied to five different types of MLCs (Elekta, Siemens, Varian, Scanditronix, General Electric). All calculations based on empirical relations were compared with measurements and with calculations performed by a treatment planning system with a fluence based algorithm. For most irregular MLC shaped beams output ratios in air could be adequately modeled with an accuracy of about 1%-1.5% applying a method based on the open field aperture defined by the leaf and jaw setting combined with the equivalent square formula suggested by Vadash and Bjärngard [P. Vadash and B. E. Bjärngard, Med. Phys. 20, 733-734 (1993)]. The accuracy of this approach strongly depends on the inherent head scatter characteristics of the accelerator in use and on the irregular field under consideration. Deviations of up to 3% were obtained for fields where leaves obscure central parts of the flattening filter. Simple equivalent square methods for Sp calculations in irregular fields did not provide acceptable results (deviations mostly >3%). Sp values derived from Clarkson integration, based on published tables of phantom scatter correction factors, showed the same accuracy level as calculations performed using a pencil beam algorithm of a treatment planning system (in a homogeneous media). The separation of head scatter and phantom scatter contributions is strongly recommended for irregular MLC shaped beams as both contributions have different factors of influence. With rather simple methods Sc and Sp can be determined for independent MU calculation with an accuracy better than 1.5% for most clinical situations encountered in conformal radiotherapy.