A practical method for the calculation of multileaf collimator shaped fields output factors

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.

Output ratio in air for MLC shaped irregular fields

For accurate monitor unit calculation, it is important to calculate the output ratio in air, Sc, for an irregular field shaped by MLC. We have developed an algorithm to calculate Sc based on an empirical model [Med. Phys. 28, 925-937 (2001)] by projecting each leaf position to the isocenter plane. Thus it does not require the exact knowledge of the head geometry. Comparisons were made for three different types of MLC: those with MLC replacing the inner collimator jaws; those with MLC replacing the outer collimator jaws; and those with MLC as a tertiary attachment. When the MLC leaf positions are substantially different from the secondary collimators (or the rectangular field encompassing the irregular field), one observes an up to 5% difference in the value of head-scatter correction factor, HCF, defined as the ratio of output ratio in air between the MLC shaped irregular field and that of the rectangular field encompassing the irregular field. No collimator exchange effect was observed for rectangular fields shaped by MLC (e.g., 5x30 and 30x5 cm2 diagonal) when the secondary collimators are fixed, unlike that for the rectangular fields shaped by the inner and outer collimator jaws, where it can be 1-2%. For the same MLC shaped irregular field, the value of Sc increases from the Elekta, to the Siemens, to the Varian accelerators, with an up to 4% difference. The calculation agrees with measurement to within 1.2% for points both on and off the central-axis. The fitting parameters used in the algorithm are derived from measurements for square field sizes on the central-axis.

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.

A three-source model for the calculation of head scatter factors

Accurate determination of the head scatter factor Sc is an important issue, especially for intensity modulated radiation therapy, where the segmented fields are often very irregular and much less than the collimator jaw settings. In this work, we report an Sc calculation algorithm for symmetric, asymmetric, and irregular open fields shaped by the tertiary collimator (a multileaf collimator or blocks) at different source-to-chamber distance. The algorithm was based on a three-source model, in which the photon radiation to the point of calculation was treated as if it originated from three effective sources: one source for the primary photons from the target and two extra-focal photon sources for the scattered photons from the primary collimator and the flattening filter, respectively. The field mapping method proposed by Kim et al. [Phys. Med. Biol. 43, 1593-1604 (1998)] was extended to two extra-focal source planes and the scatter contributions were integrated over the projected areas (determined by the detector's eye view) in the three source planes considering the source intensity distributions. The algorithm was implemented using Microsoft Visual C/C++ in the MS Windows environment. The only input data required were head scatter factors for symmetric square fields, which are normally acquired during machine commissioning. A large number of different fields were used to evaluate the algorithm and the results were compared with measurements. We found that most of the calculated Sc's agreed with the measured values to within 0.4%. The algorithm can also be easily applied to deal with irregular fields shaped by a multileaf collimator that replaces the upper or lower collimator jaws.