The dose kernels of pencil and differential pencil photon beams with the spectrum of treatment machines with a $^{60}$Co source in water and their analytical approximation

This article presents the results of calculations by the Monte Carlo method in the EGSnrc toolkit of the spatial distributions of absorbed energy or dose kernels in water for a pencil beam or differential pencil beam (point spread function) with the spectrum of ROKUS-M treatment machines. The photon spectrum of the ROKUS-M machines was also calculated by the Monte Carlo method. The calculated dose-kernel results were approximated separately for the radial distribution of the primary and the scattered component of dose kernels by sums of exponential functions divided by the squared radius for a differential pencil beam and by the radius for a pencil beam. This approximation makes direct implementation possible for wellknown model-based techniques for finding 3D dose distributions in external radiation therapy. A simple analytical procedure to verify approximation formulas is proposed. It is also applicable in independent checks of dose distributions along the treat beam axis, which is an important guideline of the Radiation Therapy Quality Assurance Program.