Is there a need for a revised table of equivalent square fields for the determination of phantom scatter correction factors?

Abstract

The use of the British Journal of Radiology (BJR) (supplement 17) tables of equivalent square fields for dose calculations is widespread. A revised version of the supplement was published recently, with a more elaborate discussion, but without changes in data given in these tables (Br. J. Radiol. suppl 25). The tables were generated for use in dose calculations, with relative beam data such as PDD, BSF, PSF, all with d(max) as the reference depth. However, the current philosophy in dose calculational methods is based on quantities defined at a reference depth, d(ref) = 10 cm, on a separation of phantom and head scatter, and on the use of the relative depth-dose or tissue-phantom ratios normalized at d(ref). By using these quantities as a starting point, problems at shallow depths related to the influence of contaminating electrons in the beam can be eliminated. Recently, a comprehensive set of phantom scatter factor data with d(ref) = 10 cm has been published for a set of square field sizes and a wide range of photon beam energies, showing that phantom scatter is a smoothly varying function of field size and quality index. It is not a priori evident that the conventional concept of equivalent squares for rectangular fields is also fully applicable for phantom scatter factors and phantom scatter related quantities at a depth of 10 cm. It was questioned whether or not new tables of equivalent square fields are needed for this purpose. In this paper, new tables have been constructed for four photon beam energies in the range of Co-60 to 25 MV (quality index from 0.572 to 0.783). The small differences between the outcome of these new tables allowed the construction of one averaged table of equivalent square fields. Phantom scatter factors were calculated for rectangular fields based on the use of the BJR table and on the use of the newly constructed tables and the differences were quantified. For Co-60 no improvements could be shown when using the new averaged table, but for beam energies of 6 to 10 MV small improvements of the order of 0.5 to 1.0% were found. For a higher beam energy of 25 MV the improvement is smaller. Deviations resulting from the BJR table are within the limits of accuracy as stated by the authors. Therefore, for clinical use, the continued use of the BJR table of equivalent squares for phantom scatter factors and phantom scatter related quantities of rectangular fields is justified, irrespective of photon beam energy.

An investigation of a model of percentage depth dose for irregularly shaped fields

“…each of these right triangles, the scatter-to-primary ratio can be obtained by integrating Equation (3). Let us assume that the two short sides of a right triangle are X and Y, and thus the apex angle is ‫ס‬ arctan(Y/X).…”

“…When calculating PDD or any of the other ratios related to the volume scatter for rectangular fields, an approximate equivalent square is used in the computation. Much research has gone into finding better models for determining the equivalent square [3,4]. For an irregularly shaped field, scattering effects are obtained by performing integration over the given field.…”

A generalized calibration procedure for in vivo transit dosimetry using siemens electronic portal imaging devices

“…Therefore, the water-equivalent or radiological thickness, w, and the depth, w iso , can be easily determined as the product of t and d iso by the relative mean physical densities, obtained from the linear relation existing between electronic density and physical density [27]. The equivalent square field is generally supplied automatically by some TPSs, otherwise it can be obtained by applying an equivalent square method [36].…”

A simple calculation method for determination of equivalent square field

“…[3–5] Many attempts have been made to calculate depth dose independent of equivalent field, and some algorithms (e.g. ALFARD) have been developed[4] in which equivalent field is one of its Kernel's major factors[6–8] and is used to calculate absorbed dose at an off-axis point. [9].…”