Estimation of the lateral variation of photon beam energy spectra using the percentage depth dose reconstruction method

In photon-collapsed cone convolution (pCCC) algorithm of the Monaco treatment planning system (TPS), the central-axis energy spectrum is assumed constant throughout the entire irradiation area. To consider lateral variations, an off-axis softening factor is applied to attenuation coefficients during the total energy released per unit mass calculation. We evaluated this method through comparison studies of percentage depth doses (PDDs) and off-axis ratios (OARs) calculated by Monaco and measured for a 6 MV photon beam at various off-axis angles and depths. Significant differences were observed, with relative differences exceeding ± 1%. Therefore, this method may not accurately represent lateral variations of energy spectra. We propose directly implementing energy spectra on both central-axis and off-axis to improve dose calculation accuracy for large field. To this end, we introduce reconstruction of PDDs from monoenergetic depth doses (MDDs) along off-axis angles, thereby estimating energy spectra as functions of radial distance. This method derives energy spectra quickly without significantly increasing the beam modeling time. MDDs were computed through Monte Carlo simulations (DOSRZnrc). The variances between reconstructed and measured PDDs were minimized using the generalized-reduced-gradient method to optimize energy spectra. Reconstructed PDDs along off-axis angles of 0°, 1.15°, 2.29°, 3.43°, 4.57°, 5.71°, 6.84°, 7.97°, 9.09°, 10.2° to estimate energy spectra at radial distances of 0-18 cm in 2 cm increments and OARs calculated using estimated energy spectra at 5, 10, and 20 cm depths, well agreed with measurement (relative differences within ± 0.5%). In conclusion, our proposed method accurately estimates lateral energy spectrum variation, thereby improving dose calculation accuracy of pCCC algorithm.