Dose calculations of photon beams using a finite‐size pencil beam model

Abstract

This work investigates the finite‐size pencil beam (FSPB) model for calculating dose deposition from photon beams generated by a clinical linear accelerator. The FSPB model, first published by Bourland and Chaney, uses the superposition of preconvolved “finite‐size pencil beams” of small cross‐sectional area to determine the dose deposition in a uniform water phantom. In the dose computation, FSPBs for a range of energy bins are pieced together like mosaic tiles to collectively form the cross section of the full beam. Depending on the full beam resolution, the superposition calculation can be much faster than full convolution. The results stress the importance of a knowledge of the photon spectrum of the beam for accurate dose calculations. However, published methods of indirect spectral measurements using transmission measurements through beam attenuators require mathematical fits with a large number of parameters and constraints. A simple strategy is presented for fitting transmission data that models important physical characteristics of photon beams produced in linear accelerators. The fitting equation has these advantages over previous methods: (1) the equation describes the shape of a bremsstrahlung spectrum based on physical expectations; (2) only three fit parameters are required with a single constraint. Results are presented for 4 and 6 MV photon beams. Comparisons of calculated and measured TMRs and output factors of open fields show excellent agreement. Results include discussions of FSPB generation, the method of spectral measurement, the effect of beam softening across the field cross section, and the method for modeling this effect using different FSPB weighting factors as a function of energy and location.