Calculating percent depth dose with the electron pencil-beam redefinition algorithm

In this work, we investigated the accuracy of the electron pencil-beam redefinition algorithm (PBRA) in calculating central-axis percent depth dose in water for rectangular fields. The PBRA energy correction factor, C(E), was determined so that PBRA-calculated percent depth dose best matched that measured in water. The hypothesis tested in this study was that a method can be implemented into the PBRA that will enable the algorithm to calculate central-axis percent depth dose in water at 100-cm source-to-surface distance with an accuracy of 2% or 1-mm distance-to-agreement for rectangular-field sizes ³ 2x2 cm2. Preliminary investigations showed that C(E), determined using a single percent depth dose for a large field (i.e., having side-scatter equilibrium), was insufficient for the PBRA to accurately calculate percent depth dose for all square fields ³ 2x2 cm2. Therefore, two alternative methods for determining C(E) were investigated. In Method 1, C(E), modeled as a polynomial in energy, was determined by fitting the PBRA calculations to measured percent depth dose for each individual rectangular field. In Method 2, C(E) for square fields, described by a polynomial in both energy and side of square, W, i.e., C=C(E,W), was determined by fitting the PBRA calculations to measured percent depth dose for a small number of square fields. C(E) for other square fields was determined using the function C(E,W), and C(E) for rectangular field sizes was determined using the geometric mean of C(E) for the two square fields of the dimension of the rectangle (square root method). PBRA calculations using both methods were evaluated by comparing with measured square and rectangular-field percent depth doses at 100-cm SSD for the Siemens Primus radiotherapy accelerator equipped with a 25x25-cm2 applicator at 10 and 15 MeV. To improve the fit of C(E) to the electron component of percent depth dose, it was necessary to modify the PBRA?s photon depth-dose model to include dose buildup. Results showed that the PBRA was able to predict percent depth dose within criteria for all square and rectangular fields using both methods. Results showed that a 2nd or 3rd order polynomial in energy (Methods 1 and 2) and field size (Method 2) was typically required. Although time of dose calculation for Method 1 is approximately twice that of Method 2, it is recommended that Method 1 be used for clinical implementation of the PBRA due to its being more accurate (most measured depth doses predicted within approximately 1%) and simpler to implement.