An analytical method to calculate equivalent fields to irregular symmetric and asymmetric photon fields.

Equivalent field is frequently used for central axis depth-dose calculations of rectangular- and irregular-shaped photon beams. As most of the proposed models to calculate the equivalent square field are dosimetry based, a simple physical-based method to calculate the equivalent square field size was used as the basis of this study. The table of the sides of the equivalent square or rectangular fields was constructed and then compared with the well-known tables by BJR and Venselaar, et al. with the average relative error percentage of 2.5 ± 2.5% and 1.5 ± 1.5%, respectively. To evaluate the accuracy of this method, the percentage depth doses (PDDs) were measured for some special irregular symmetric and asymmetric treatment fields and their equivalent squares for Siemens Primus Plus linear accelerator for both energies, 6 and 18MV. The mean relative differences of PDDs measurement for these fields and their equivalent square was approximately 1% or less. As a result, this method can be employed to calculate equivalent field not only for rectangular fields but also for any irregular symmetric or asymmetric field.

Analytical approach for determining beam profiles in water phantom of symmetric and asymmetric fields of wedged, blocked, and open photon beams.

Nowadays, in most radiotherapy departments, the commercial treatment planning systems (TPS) used to calculate dose distributions needs to be verified; therefore, quick, easy-to-use, and low-cost dose distribution algorithms are desirable to test and verify the performance of the TPS. In this paper, we put forth an analytical method to calculate the phantom scatter contribution and depth dose on the central axis based on the equivalent square concept. Then, this method was generalized to calculate the profiles at any depth and for several field shapes - regular or irregular fields - under symmetry and asymmetry photon beam conditions. Varian 2100 C/D and Siemens Primus Plus linacs with 6 and 18 MV photon beam were used for irradiations. Percentage depth doses (PDDs) were measured for a large number of square fields for both energies and for 45° wedge, which were employed to obtain the profiles in any depth. To assess the accuracy of the calculated profiles, several profile measurements were carried out for some treatment fields. The calculated and measured profiles were compared by gamma-index calculation. All γ-index calculations were based on a 3% dose criterion and a 3 mm dose-to-agreement (DTA) acceptance criterion. The γ values were less than 1 at most points. However, the maximum γ observed was about 1.10 in the penumbra region in most fields and in the central area for the asymmetric fields. This analytical approach provides a generally quick and fairly accurate algorithm to calculate dose distribution for some treatment fields in conventional radiotherapy.