Scatter factor corrections for elongated fields

Design of mini phantom and measurement of cobalt-60 beam data parameters

Low cost mini phantoms were fabricated indigenously with different water equivalent material such as polymethyl methacrylate and Bee's wax of different shapes (with dome top surface and flat top surface). The beam parameters of the Co-60 machine, such as head scatter correction factor (S_h), phantom scatter correction factor (S_P), total scatter correction factor (S_C,P), collimator exchange effect were measured. Output ratio measurements were taken for both mini phantom and water phantom for different square and rectangular field sizes. Normalized output ratios were compared with ESTRO published values and (Storchi and Van Gasteren) S and G data. The percentage of variation between the measured and the literature values is about 0.7%. Collimator exchange effect were measured for water and mini phantom for different field size, were compared with ESTRO value. This was found to be 0.5% and 1.0% respectively. Phantom scatter correction factors were calculated for square and rectangular filed sizes; this was compared with ESTRO values, found to be 0.7% for square and 1.0% for rectangular filed size. It was also noted that there were no appreciable variation observed in ion chamber readings of different materials of mini phantoms for dome and flat surfaces. Mini phantom measurements were done for all types of phantoms and the measured values were compared with the existing data and they were in good agreement with the published values.

[Output-factors for squared, rectangular, and elongated photon fields of medical linear accelerators]

For reduction of data scattering in output-factor calculation, a new correction for Stirling's formula is introduced that takes into account the position of the upper and lower collimator jaw settings of linear accelerators. This correction factor requires two simple geometrical data of the treatment head, to describe the collimator exchange effect for open- as well as wedged fields. This model also implies a reduction of output measurements to only three field sizes, the minimum, the maximum, and a reference field size, without significant loss of accuracy in output factors.

An investigation of accelerator head scatter and output factor in air

Our purpose in this study was to investigate whether the Monte Carlo simulation can accurately predict output factors in air. Secondary goals were to study the head scatter components and investigate the collimator exchange effect. The Monte Carlo code, BEAMnrc, was used in the study. Photon beams of 6 and 18 MV were from a Varian Clinac 2100EX accelerator and the measurements were performed using an ionization chamber in a mini-phantom. The Monte Carlo calculated in air output factors was within 1% of measured values. The simulation provided information of the origin and the magnitude of the collimator exchange effect. It was shown that the collimator backscatter to the beam monitor chamber played a significant role in the beam output factors. However the magnitude of the scattered dose contributions from the collimator at the isocenter is negligible. The maximum scattered dose contribution from the collimators was about 0.15% and 0.4% of the total dose at the isocenter for a 6 and 18 MV beam, respectively. The scattered dose contributions from the flattening filter at the isocenter were about 0.9-3% and 0.2-6% of the total dose for field sizes of 4x4 cm2-40x40 cm2 for the 6 and 18 MV beam, respectively. The study suggests that measurements of head scatter factors be done at large depth well beyond the depth of electron contamination. The insight information may have some implications for developing generalized empirical models to calculate the head scatter.

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.

Calculation of head scatter factors at isocenter or at center of field for any arbitrary jaw setting

The purpose of this work is to calculate the head scatter factors for any arbitrary jaw setting by using two different semi-empirical methods. The head scatter factor at the center of field (COF) for any arbitrary jaw setting can be defined as H(COF)(X1,X2,Y1,Y2,r)=DairCOF(XI1,X2,Y1,Y2,r)/ [Dair(5,5,5,5,0)*OAR(r)], where X1, X2, Y1, and Y2 are the jaw positions; r is the distance between COF and isocenter (IC); OAR(r) is the Off-Axis-Ratio; DairCOF(X1,X2,Y1,Y2,r) is the dose in air measured at COF; Dair(5,5,5,5,0) is the dose in air measured at IC for the 10 x 10 cm2 field. In certain clinical situations, doses are prescribed at IC instead of COF for asymmetric fields. In these cases, head scatter factors should be determined at IC. It is found that the head scatter factors at IC for asymmetric fields [H(IC)(X1,X2,Y1,Y2)] are lower than H(COF)(X1,X2,Y1,Y2,r) for the same jaw setting by up to 4%. The values of H(IC)(X1,X2,Y1,Y2) and H(COF)(X1,X2,Y1,Y2,r) for a variety of jaw settings were measured using a miniphantom of 3-cm diameter for a 6- and a 18-MV photon beams. An equivalent square formula, derived presently at the source plane for any jaw setting, was used to calculate H(COF)(X1,X2,Y1,Y2,r). The calculation and the measurement agree within +/-1% (+/-0.5% for most clinical situations). To calculate H(IC)(X1,X2,Y1,Y2), we have generalized the Day's "quarter-field" method, i.e., H(IC)(X1,X2,Y1,Y2) = [H(X1,X1,Y1,Y1) + H(X1,X1,Y2,Y2) + H(X2,X2,Y1,Y1) + H(X2,X2,Y2,Y2)]/4. We found that the calculation and the measurement agree within +/-0.8% for the beams studied.

A generalized solution for the calculation of in-air output factors in irregular fields

Three major contributors of scatter radiation to the in-air output of a medical linear accelerator are the flattening filter, wedge, and tertiary collimator. These were considered separately in the development of an algorithm to be used to set up an in-air output factor calculation formalism for open and wedge fields of irregular shape. A detector's eye view (DEV) field defined at the source plane was used to account for the effects of collimator exchange and the partial blockage of the flattening filter by the tertiary collimator in the determination of head scatter. An irregular field determined at the source plane by a DEV was segmented and mapped back into the detector plane by a field-mapping method. Field mapping was performed by using a geometric conversion factor and equivalent field relationships for head scatter. The scatter contribution of each segmented equivalent field at the detector plane was summed by Clarkson integration. The same methodology was applied for determining both tertiary collimator and wedge scatter contribution. However, the field size that determined the amount of scatter contribution was not the same for each component. For tertiary collimator scatter and external wedge scatter, a field projected to the detector plane was used directly. Comparisons of calculated and measured values for in-air output factors showed good agreement for both open and external wedge fields. This algorithm can also be used for multileaf collimator (MLC) fields irrespective of the position of the MLC (i.e., whether the MLC replaces one secondary collimator or is used as a tertiary collimator). The measurement and parameterization of tertiary collimator scatter is necessary to account for its contribution to the in-air output. Because a source-plane field is mapped into the detector plane, no additional dosimetric data acquisition is necessary for the calculation of head scatter.

The equivalent square concept for the head scatter factor based on scatter from flattening filter

The equivalent field relationship between square and circular fields for the head scatter factor was evaluated at the source plane. The method was based on integrating the head scatter parameter for projected shaped fields in the source plane and finding a field that produced the same ratio of head scatter to primary dose on the central axis. A value of sigma/R approximately equal to 0.9 was obtained, where sigma was one-half of the side length of the equivalent square and R was the radius of the circular field. The assumptions were that the equivalent field relationship for head scatter depends primarily on the characteristics of scatter from the flattening filter, and that the differential scatter-to-primary ratio of scatter from the flattening filter decreases linearly with the radius, within the physical radius of the flattening filter. Lam and co-workers showed empirically that the area-to-perimeter ratio formula, when applied to an equivalent square formula at the flattening filter plane, gave an accurate prediction of the head scatter factor. We have analytically investigated the validity of the area-to-perimeter ratio formula. Our results support the fact that the area-to-perimeter ratio formula can also be used as the equivalent field formula for head scatter at the source plane. The equivalent field relationships for wedge and tertiary collimator scatter were also evaluated.

Calculating output factors for photon beam radiotherapy using a convolution/superposition method based on a dual source photon beam model

A realistic photon beam model based on Monte Carlo simulation of clinical linear accelerators was implemented in a convolution/superposition dose calculation algorithm. A primary and an extra-focal sources were used in this beam model to represent the direct photons from the target and the scattered photons from other head structures, respectively. The effect of the finite size of the extra-focal source was modeled by a convolution of the source fluence distribution with the collimator aperture function. Relative photon output in air (Sc) and in phantom (Scp) were computed using the convolution method with this new photon beam model. Our results showed that in a 10 MV photon beam, the Sc, Sp (phantom scatter factor), and Scp factors increased by 11%, 10%, and 22%, respectively, as the field size changed from 3 x 3 cm2 to 40 x 40 cm2. The variation of the Sc factor was contributed mostly by an increase of the extra-focal radiation with field size. The radiation backscattered into the monitor chamber inside the accelerator head affected the Sc by about 2% in the same field range. The output factors in elongated fields, asymmetric fields, and blocked fields were also investigated in this study. Our results showed that if the effect of the backscattered radiation was taken into account, output factors in these treatment fields can be predicted accurately by our convolution algorithm using the dual source photon beam model.

Clinical implementation of a two-component x-ray source model for calculation of head-scatter factors

A calculation method is described, which presumes that linac output has two components. One component is direct x rays from the target and the remaining component is an extra-focal, distributed source of radiation that is scattered from the flattening filter, primary collimator, and the jaws of the moveable collimator. This calculation method gives values for output factors that differ from measured values by no more than 0.5% for field widths from 4 to 40 cm, rectangular fields with long to short axis ratios as great as 10, symmetric and asymmetric fields, and source-to-axis distances from 65 to 360 cm. While this calculation method has great accuracy and flexibility, a minimal amount of input data is required: (1) measured output factors at a source-to-axis distance of 100 cm for square fields; (2) positions of the collimator with respect to the x-ray source target; and (3) output factors measured at various source-to-axis distances for a 10 cm x 10 cm field.

Equivalent square as a predictor of depth of dose maximum for megavoltage therapy beams

The depths of dose maxima, dmax, and surface doses of 6 MV, 10 MV, and 18 MV photon beams were measured for various square fields and rectangular fields with elongation ratios from 1 to 27. Rectangular fields with elongation ratios below 2 have essentially the same depths of dose maxima and surface doses as their corresponding equivalent square fields. For rectangular fields with elongation ratios above 2, the surface doses increase, and depths of dose maxima decrease with increasing elongation ratio in comparison to their respective values for their corresponding equivalent square fields. The shift of dmax toward the surface is more pronounced when the upper jaws rather than the lower jaws define the long axis of the field. This collimator exchange effect does not influence the surface dose. Even for the largest elongation ratios, the changes in dmax and surface dose from their equivalent square field values were minor and clinically insignificant, suggesting that the equivalent square approach provides a reliable method for predicting the values of dmax and surface dose for rectangular fields from square fields data.