[Estimation of the phantom scatter factor (Sp) of rectangular fields].

This study proposes a method to accurately estimate the phantom scatter factor (Sp) of arbitrary rectangular fields. We measured output doses in water and air; these measured values were based on square fields and a limited number of symmetric rectangular fields using 4 MV and 10 MV X-rays of a Varian Clinac-iX. We calculated Sp from these measured values. Then, using these Sp values, we estimated equations of Sp on square fields consisting of the primary dose, Day's scatter, and forward scatter. This equation may be used to estimate the Sp value on a square field, but it cannot estimate the Sp value on a rectangular field. We investigated the calculation method for an equivalent square of a rectangular field. As a result, this study's calculation method for an equivalent square, the area ratio correction method, was more accurate than the conventional Bjärngard's method. Therefore, when using the approximate equation of Sp on a square field and the equivalent square calculated by the area ratio correction method, a Sp value of an arbitrary rectangular field may be accurately estimated.

[Estimation of collimator scatter factor, S(c), of rectangular fields by a saturation model].

We estimated collimator scatter factor, S(c), of symmetric rectangular fields of any size by applying a two-component scatter model to measured in-air output data in width and length directions of measured rectangles. The in-air output was measured for symmetric rectangles with combined width and length sizes of 7 x 7 and 6 x 6 using 10 MV and 4 MV X-rays of Varian's Clinac 2100 C/D, respectively. The model consists of scatter components from the primary collimator and flattening filter and from the collimator jaws: the former shows a saturation curve and the latter increases linearly with enlarging field size. This model was fitted to the measured dataset firstly in the width and secondly in the length directions of rectangles; then, by compiling interpolated matrix data, the S(c) table of symmetric rectangles was constructed. In addition, using this S(c) table, values of S(c) were calculated for a few asymmetric rectangles by Day's method, and were in good agreement with measured values. Therefore, we think that our method is practical and precise for constructing the S(c) table of symmetric rectangles from measured data, and that using this table, the S(c) of any asymmetric rectangles may be calculated.

[Estimation of collimator scatter factor, S(c), of small field sizes using long-SCD method and two saturation models].

To estimate the collimator scatter factor, S(c) of small field sizes in which a mini-phantom cannot be fully included at the nominal treatment distance (NTD=100 cm), we measured the in-air output of 4 MV and 10 MV X-rays of a Varian's Clinac 2100 C/D using a mini-phantom at NTD and at a long source-to-chamber distance (SCD=200 cm) with field-size defined at the isocenter down to 4.6 x 4.6 cm(2) and 2.3 x 2.3 cm(2), respectively. We then compared the fitted curve to the NTD dataset by a cumulative exponential distribution model with that by a cumulative Gaussian distribution (error function) model containing a zero-field extrapolated term derived from the long SCD dataset. The results showed that the zero-field extensions of two fitted curves coincided for a 4 MV X-ray, but a large discrepancy was seen between them for a 10 MV X-ray. Therefore, the S(c) of small field sizes not measurable using a mini-phantom at the NTD can be well estimated by applying the cumulative exponential model to the NTD dataset in the case of a 4 MV X-ray beam filtrated with a cone-shaped flattener. However, to estimate the S(c) of such small field sizes in the case of a 10 MV X-ray beam filtrated with a bell-shaped flattener, we consider it preferable to also measure in-air output at a long SCD and to apply the cumulative Gaussian model as described here.

[Approximation of collimator scatter factor Sc by a saturation model].

To more easily estimate accurate values of collimator scatter facor, S(c), we suggest a two-component saturation model that accounts for scatter from the primary collimator and flattening filter and from the collimator jaws. This model, which assumes an exponential distribution of scatter intensity, was tested by in-air measurements using a mini-phantom for 4 MV and 10 MV X-rays of a Clinac 2100 C/D linear accelerator. The results showed a good fit of this model to our measured data (R(2)>0.9993). When the measured value was divided into the primary collimator/flattening filter component and the collimator jaw component, as expected, the former component showed a rapid and full saturation curve with increased field size, while the latter showed an almost linearly increasing curve. Therefore, we think that this saturation model is useful for the estimation of S(c) and is applicable to monitor unit calculation for an asymmetric field.