A method to predict rectangular field output factors (OFs) of photon open beams for the Saturne 41 linear accelerator has been developed. The procedure is similar to the sector-integration method but the radiotherapy quantities corresponding to circular fields (circular functions) are calculated from one-dimensional OFs. In this case the one-dimensional OFs are defined as rectangular field OFs, where one side remains constant and equal to the maximum field size. The circular quantities are numerically obtained by inversion of the sector-integration equation which relates both the one-dimensional OFs and the circular function. Two one-dimensional OFs were used to take into account the asymmetry between the x and y collimator systems (collimator exchange effect). The resulting pair of circular functions corresponds to the x and y collimator systems, respectively. They contain all the information relative to head, air, and medium (phantom) scatter and, consequently, there is no need to account for the geometry of the head or fitting parameters. Using the sector-integration method, the OFs for any rectangular field can be calculated by integrating the obtained circular functions. To improve results, a procedure is given to account for corner collimators overlapping. Results agree with data to within approximately 0.4% at 6-15 MV photon beams. The proposed method is thus clinically acceptable for routine calculation. Furthermore, the circular function calculation algorithm could be extended to other radiotherapy quantities.
A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.
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