A practical method to calculate head scatter factors in wedged rectangular and irregular MLC shaped beams for external and internal wedges

Factor based methods for absorbed dose or monitor unit calculations are often based on separate data sets for open and wedged beams. The determination of basic beam parameters can be rather time consuming, unless equivalent square methods are applied. When considering irregular wedged beams shaped with a multileaf collimator, parametrization methods for dosimetric quantities, e.g. output ratios or wedge factors as a function of field size and shape, become even more important. A practical method is presented to derive wedged output ratios in air (S(c,w)) for any rectangular field and for any irregular MLC shaped beam. This method was based on open field output ratios in air (S(c)) for a field with the same collimator setting, and a relation f(w) between S(c,w) and S(c). The relation f(w) can be determined from measured output ratios in air for a few open and wedged fields including the maximum wedged field size. The function f(w) and its parametrization were dependent on wedge angle and treatment head design, i.e. they were different for internal and external wedges. The proposed method was tested for rectangular wedged fields on three accelerators with internal wedges (GE, Elekta, BBC) and two accelerators with external wedges (Varian). For symmetric regular beams the average deviation between calculated and measured S(c,w) / S(c) ratios was 0.3% for external wedges and about 0.6% for internal wedges. Maximum deviations of 1.8% were obtained for elongated rectangular fields on the GE and ELEKTA linacs with an internal wedge. The same accuracy was achieved for irregular MLC shaped wedged beams on the accelerators with MLC and internal wedges (GE and Elekta), with an average deviation < 1% for the fields tested. The proposed method to determine output ratios in air for wedged beams from output ratios of open beams, combined with equivalent square approaches, can be easily integrated in empirical or semi-empirical methods for monitor unit calculations.