Effect of beam blocking on linac head scatter factors

Two-argument total scatter factor for small fields simultaneously collimated by MLC and jaws: application to stereotactic radiosurgery and radiotherapy

Direct use of the total scatter factor (S _tot) for independent monitor unit (MU) calculations can be a good alternative approach to the traditional separate treatment of head/collimator scatter (S _c) and phantom scatter (S _p), especially for stereotactic small fields under the simultaneous collimation of secondary jaws and tertiary multileaf collimators (MLC). We have carried out the measurement of S _tot in water for field sizes down to 0.5  ×  0.5 cm² on a Varian TrueBeam STx medical linear accelerator (linac) equipped with high definition MLCs. Both the jaw field size (c) and MLC field size (s) significantly impact the linac output factors, especially when c [Formula: see text] s and s is small (e.g. s  <  5 cm). The combined influence of MLC and jaws gives rise to a two-argument dependence of the total scatter factor, S _tot(c,s), which is difficult to functionally decouple. The (c,s) dependence can be conceived as a set of s-dependent functions ('branches') defined on domain [s _min, s _max  =  c] for a given jaw size of c. We have also developed a heuristic model of S _tot to assist the clinical implementation of the measured S _tot data for small field dosimetry. The model has two components: (i) empirical fit formula for the s-dependent branches and (ii) interpolation scheme between the branches. The interpolation scheme preserves the characteristic shape of the measured branches and effectively transforms the measured trapezoidal domain in (c,s) plane to a rectangular domain to facilitate easier two-dimensional interpolation to determine S _tot for arbitrary (c,s) combinations. Both the empirical fit and interpolation showed good agreement with experimental validation data.

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.

A widely tested model for head scatter influence on photon beam output

PURPOSE

To construct and test a semi-analytical model describing the effects on Monitor Unit (MU) verification caused by scattering in the treatment head. The implementation of the model should be accomplished using a small set of experimental data. Furthermore, the model should include a geometry dependent estimation of the resulting uncertainty.

MATERIAL AND METHODS

The input required by the created model consists of basic treatment head geometry and 10 measured output factors in air (OFair) for square fields. It considers primary energy fluence, scattered radiation from an extra-focal source and from secondary collimators, as well as backscatter to the monitor chamber. Measurements and calculations were performed in open symmetric and asymmetric fields at points located both on and off the collimator axis, as well as at arbitrary treatment distances. The model has been verified for 19 photon beams in the range from 4 up to 50 MV, provided by nine different treatment units from six manufacturers.

RESULTS

The presented model provided results with errors smaller than 1% (2 S.D.) in typical clinical situations for all beams tested. In more exceptional situations, i.e. combinations of unconventional treatment head designs, very elongated fields, and dosimetry points far away from the isocenter, the total uncertainty increased to approximately 2%. The spread in the results was further analysed in order to create a method for predicting the uncertainties under different treatment conditions.

CONCLUSIONS

A general head scatter model that is easy to implement has been developed and can be used as the basis for computerised MU verification. The model handles all commercially available treatment units adequately and also includes an estimation of the resulting uncertainty.

Irregular field calculation on the central beam axis of photon beams using sector-integration

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.

Dependence of the tray transmission factor on collimator setting and source-surface distance

When blocks are placed on a tray in megavoltage x-ray beams, generally a single correction factor for the attenuation by the tray is applied for each photon beam quality. In this approach, the tray transmission factor is assumed to be independent of field size and source-surface distance (SSD). Analysis of a set of measurements performed in beams of 13 different linear accelerators demonstrates that there is, however, a slight variation of the tray transmission factor with field size and SSD. The tray factor changes about 1.5% for collimator settings varying between 4x4 cm and 40 x 40 cm for a 1 cm thick PMMA tray and approximately 3% for a 2 cm thick PMMA tray. The variation with field size is smaller if the source-surface distance is increased. The dependence on the collimator setting is not different, within the experimental uncertainty of about 0.5% (1 s.d.), for the nominal accelerating potentials and accelerator types applied in this study. It is shown that the variation of the tray transmission factor with field size and source-surface distance can easily be taken into account in the dose calculation by considering the volume of the irradiated tray material and the position of the tray in the beam. A relation is presented which can be used to calculate the numerical value of the tray transmission factor directly. These calculated values can be checked with only a few measurements using a cylindrical beam coaxial miniphantom.