Analytical representation of enhanced dynamic wedge factors for symmetric and asymmetric photon fields

Abstract

The Enhanced Dynamic Wedge (EDW) presents many advantages over the physical wedge. However, in order to calculate monitor units (MUs) necessary to deliver a certain dose at a certain point, EDW factors (EDWFs) need to be determined. In this work, based on analysis of the golden segmented treatment table (GSTT) and the MU fraction model, an empirical analytic formula has been developed to calculate EDW factors for symmetric and asymmetric fields. This formalism is an extension of the MU fraction model. However in comparison with previous studies [J. P. Gibbons, Med. Phys. 25, 1411-1418 (1998) and M. Miften et al., Med. Dosim. 25, 81-86 (2000)], this formula is simpler, and easier to use. It is applicable to EDW fields of different sizes, wedge angles and different photon energies. For 6 and 18 MV beams from a Varian 21EX accelerator with 7 EDW angles (Varian Oncology Systems, Palo Alto, CA), more than 250 measured EDWFs for symmetric and asymmetric fields with different off-axis distances and field sizes were compared with model calculations. Results show that 80% and 98% of calculated EDWFs match corresponding measured values to within 0.5% and 1.0%, respectively, the maximum deviation being 1.3%.

Analytical representation for Varian EDW factors at off‐center points

“…It should also be mentioned that Gibbons 10 earlier developed a more complicated analytical model for EDW factors. Although according to earlier studies, 10,11 compared to FMA their models appear to reduce the discrepancies between the measured and calculated wedge factors at the center of field, our study 12 found that FMA actually performs no worse than the models by Gibbons and Yu. While satisfactory agreement between calculated and measured center-of-field EDW factors has been reported, the above-mentioned analytical models generally fail to accurately predict wedge factors at off-center points ͑see Sec. III͒.…”

“…͑8͒. Letters "B" and "C" in the same figures describe the agreement between the measured wedge factors and factors calculated with the help of the FMA and the model by Yu,11 respectively. Comparison between measured and calculated WFs at off-center points for different symmetric and asymmetric fields, wedge angles, and photon energies are shown in Tables II and III. More specifically, the latter tables contain maximum and average absolute diff͑%͒ obtained by using Eq.…”

“…2,[4][5][6][7][8][9][10][11] Enhanced dynamic wedge factors at the center of a radiation field can be described analytically. [9][10][11] One model, referred to below as the fractional MU approximation ͑FMA͒, is based on the assumption that an EDW factor equals the fraction of the total MU delivered while the point of calculation is within the unblocked field. 9,10 The reported agreement between the measured and calculated wedge factors is within 2%-4% for most symmetric and asymmetric fields.…”

Monitor unit calculations for external photon and electron beams: Report of the AAPM Therapy Physics Committee Task Group No. 71

“…Finally, Yu 98 and Kuperman 99 modified the MU fraction model by shifting the calculation point in the Y-direction (i.e., along the direction of jaw motion), although the magnitude and field size dependence of this shift is controversial. 100 The methods above also apply for calculations to points along the principal axis in the wedge-gradient direction.…”

Enhanced dynamic wedge and independent monitor unit verification

“…By its dynamic nature it inherently presents more difficulty in accurate output predictions than the static PW. This is clearly evident in the amount of published material that has appeared in the literature over recent years 10,[14][15][16][19][20][21][22][23][24] . The EDW factor, unlike the PW factor, varies significantly with field size and must be accurately predicted for the field size employed if an accurate determination of MU is to be achieved.…”