Purpose: Critical analysis of existing and obtaining more accurate data on the spatial dose distributions created in the water phantom by pencil beams (PB) of monoenergetic and bremsstrahlung photons with energies from 0.25 to 20.0 MeV, and approximation of these distributions for the purpose of calculating doses in radiation therapy. Material and Methods: Using the Monte Carlo method, the EGSnrc program and the MATLAB mathematical package, these distributions were calculated for monoenergetic photons in the energy range from 0.25 to 19.75 MeV in increments of 0.5 MeV, for bremsstrahlung photons with a maximum energy of 4.0, 6.0, 10.0, 15.0, 18.0 MeV and for the gamma-radiation spectrum of the therapeutic apparatus ROCUS. The calculation results are converted into the so-called dose kernel of photon pencil beam. The obtained dose kernel values are compared with previously published data and the observed discrepancies are discussed. Depths in water were studied from 1.0 to 40 cm in increments of 0,5 cm and along the radius from 0.02 to 46.0 cm with an uneven grid. For bremsstrahlung and photons with the spectrum of the Rocus apparatus, the possibility of approximating dose kernel values using approximation formulas convenient for calculating doses in radiation therapy has been investigated. Results: On the basis of the results obtained, a new version of the library of dose kernels of a pencil photon beam for water was created, which differs from previous versions by the use for calculating a better description and modeling of the physical processes of the interaction of photons and charged particles with matter, more adequate data on the interaction cross sections and significantly lower values of statistical uncertainties of the results. For bremsstrahlung and photons with the spectrum of the Rocus apparatus, a mathematical model of dose kernels of a pencil beam is proposed, which includes decomposition of the dose kernels into components of the primary and scattered doses, approximation formulas and empirical coefficients convenient for integration. The values of empirical coefficients are determined by fitting to the results of the calculation of dose kernels using a combination of the random search method and the nonlinear regression method. Conclusion: The results obtained in this work will improve the algorithms and increase the accuracy of dose calculation when planning remote therapy with photon beams.

Gold nanoparticles are promising radiosensitizers for proton radiotherapy. However, the physical mechanisms of gold nanoparticles radiosensitization remain unclear. In the present study, the Geant4 toolkit was used to estimate by the Monte-Carlo simulation the changes (1) in the contribution of primary and secondary particles to the absorbed dose, (2) in the dose-averaged linear energy transfer, and (3) in the relative biological effectiveness of a 150 MeV proton beam caused by the addition of 50 mg/mL of gold nanoparticles to the irradiated water phantom. In the presence of gold nanoparticles no significant changes in the absorbed dose and the Bragg peak position were found, at the same time a redistribution of the contribution of secondary particles to the absorbed dose was recorded. An increase in the contributions from protons (~16%), recoil nuclei (~58%), α-particles (~400%), deuterons (~900%), tritons (~3000%), and photons (~7000%) was observed ~10 mm beyond the Bragg peak. The contribution of the secondary electrons decreased by ~35%. This redistribution led to ~5-fold increase in the dose-averaged linear energy transfer at the distal edge of the Bragg curve; this, in turn, may cause the ~1.4−2.2-fold increase in the relative biological effectiveness within this region. Thus, it is critically important to take into account the presence of gold nanoparticles when dosimetric planning proton radiotherapy in order to avoid unwanted damage to the normal tissues around the tumor.

A new version of dose kernels library of photon pencil beams for water has been created to calculate a more perfect description and modelling of the physical processes of photons and charged particles' interaction with matter, with more adequate data on the interaction cross sections and significantly lower values of the statistical uncertainties of the results. The library includes data for monoenergetic photons in the energy range of 0.25-19.75 MeV, data for bremsstrahlung photons with a maximum energy of 4.0 MeV, 6.0 MeV, 10.0 MeV, 15.0 MeV, 18.0 MeV, and data for the spectrum of the ROKUS therapeutic apparatus. Dose kernels were calculated using the Monte-Carlo method by the EGSnrc code. Depths in water from 1.0 to 40 cm and along the radius from 0.02 to 46.0 cm were studied. A convenient mathematical approximation model of dose kernel of a pencil beam is proposed.

An analytical model of the dose kernel of a narrow photon beam (pencil beam) with a bremsstrahlung spectrum with maximal energy at 6 MeV was created, allowing determination of the primary and scattered components of the absorbed dose to be determined in a water phantom with error levels acceptable in practice. A simple method for the dosimetry of photon beams with small round cross sections with 6-MV bremsstrahlung spectra using this model is proposed, combining absolute measurement of the dose absorbed in the water at a reference point in the machine-specific reference geometry and calculation of the deep dose distribution using simple analytical equations for round beams with cross sections of any radius.

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.