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 new method to measure the effect of the backscatter into the beam monitor chambers in linear accelerators is introduced from first principles. The technique, applicable to high-energy photon beams, is similar to the well-known telescopic method although here the heavy blocks are replaced by a very small, centred block on the shadow tray, thus the name 'ecliptic method'. This effect, caused mainly by backscattering from the secondary collimators, is known to be an output factor constituent and must be accounted for when detailed calculations involving the machine's head are required. Since its magnitude is generally small, experimental errors might obscure the behaviour of the phenomenon. Consequently, the procedure introduced goes along with an uncertainty assessment. Our theory was confirmed via measurements in cobalt-60 beams, where the studied effect does not contribute to the output factor. Measurements were also performed on our Saturne 41 linear accelerator and the results were qualitatively similar to those described elsewhere. The collimation systems were studied separately by varying one jaw setting while keeping the other at its maximum value. In the light of these results, we deduced an algorithm that can correlate the former data with the effect of backscattering to the beam monitor chambers for any rectangular field within 0.5%, which is of the order of the experimental uncertainty (0.6%). As we show, the experimental procedure is safe, simple, not invasive for the linac and requires only basic dosimetry equipment.
The formalism based on phantom and collimator scatter factors for high energy photon beams is deduced using a phase space description. The phantom scatter factors (Sp) depend on the field size and shape at the level of the phantom and are generally considered independent of the collimation details used to form the desired field provided the effect of contaminant electrons can be neglected. As demonstrated in this work, this behaviour leads to the applicability of the Clarkson method in irregular fields. However, for a given field formed with a tertiary collimator it is not a priori clear that the variations of extrafocal radiation due to secondary collimator setting do not affect the phantom scatter correction factors. In fact, the extrafocal radiation has a lower mean energy than that of unscattered photons, and this radiation can reach points well outside the radiation field increasing the irradiated phantom volume. Besides, transmission through the blocks contributes to phantom scatter. Therefore, for a given block-defined field, the associated phantom scatter dose, per unit of fluence in air on the central axis, should in principle increase when enlarging the secondary collimator field. To confirm this, isocentric Sp data for 6 MV photons were measured at 10 cm depth in water, reducing with cerrobend blocks several fields formed with the secondary collimators. In particular, when a 30 x 30 cm2 collimator field is reduced with blocks to a 7 x 7 cm2 field, the dose per unit of fluence in air is 1.4% higher than that of the square collimator field equating the given block field. Our calculations indicate that in this case the block transmission accounts for only 0.2% of this increment, showing that the remaining effect is due to extrafocal radiation. As a concluding remark, this work contributes to a better understanding of the classical Clarkson method for irregular fields giving, additionally, a formal interpretation of the commonly used 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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