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

• Published in: Moscow University physics bulletin Vol. 71; no. 4; pp. 431 - 439
• Main Authors: Klimanov, V. A., Moiseev, A. N., Kolyvanova, M. A., Romodanov, V. L., Chernyaev, A. P.
• Format: Journal Article
• Language: English
• Published: New York Allerton Press 2016; Springer Nature B.V
• Subjects: Approximation; Biophysics and Medical Physics; Computer simulation; Exponential functions; Kernels; Mathematical analysis; Mathematical and Computational Physics; Monte Carlo simulation; Pencil beams; Photon beams; Physics; Physics and Astronomy; Point spread functions; Quality assurance; Radial distribution; Radiation dosage; Radiation therapy; Theoretical; Three dimensional models; differential pencil beam; ROKUS treatment machine; 3D treatment planning; photons; collapsed cone convolution; external radiation therapy; pencil beam; pencil beam algorithm
• ISSN: 0027-1349; 1934-8460
• DOI: 10.3103/S0027134916040111

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.