Very high-energy electron dose calculation using the Fermi-Eyges theory of multiple scattering and a simplified pencil beam model.

BACKGROUND: Very high-energy electrons (VHEE) radiotherapy, in the energy range of 100-200 MeV is currently considered a promising technique for the future of radiation therapy and could benefit from the promises of ultra-high dose rate FLASH therapy. However, to our knowledge, no analytical calculation models have been tested for this type of application and the approximations proposed for multiple scattering with electron beams have not been extensively evaluated at these high energies. PURPOSE: In this work, we discuss the derivation of a simple and fast algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for fast dose calculation for VHEE beams (up to 200 MeV). Similar to the Gaussian pencil beam models used for electron or proton beams, this pencil beam kernel is separated into a central and an off-axis term. Monte Carlo simulations are performed to compare the analytical calculations with simulations and to determine the parametrizations used in the model at the highest electron energies. METHODS: The normalized electron planar fluence distribution is described in water according to the Fermi-Eyges theory of multiple Coulomb scattering and a double Gaussian distribution model. The main quantities used in the model and their calculation (mass angular scattering power, mean energy, range straggling) are discussed and tested for electron energies up to 200 MeV. The TOPAS/Geant4 Monte Carlo (MC) toolkit is used to compare analytical calculations with MC simulations for a theoretical pencil beam irradiation and to find the best parameters describing the range straggling. The model is then tested on a realistic simulation of a pencil beam scanning beamline with treatment field dimensions up to 15 × 15 cm2  and for deep-seated targets. RESULTS: Radial dose distributions of a pencil beam in water were calculated with the model and compared with the results of a complete Monte Carlo simulation. A good agreement (within 2%/2 mm gamma passing rate superior to 90%, and a mean deviation between calculated and simulated pencil beam radial spread smaller than 0.6 mm) was observed between analytical dose distributions and simulations for energies up to 200 MeV and field sizes up to 15 × 15 cm2 . CONCLUSIONS: A parameterization of an electron source and an analytical pencil beam model were proposed in this work, thereby allowing a suitable reproduction of the lateral fluence of a VHEE beam and good agreement between calculations and simulated data. Further improvement of the method would require the consideration of a model describing the large-angle scattering of the electrons. The results of this work could support future research into VHEE radiotherapy and might be of interest for use together with VHEE broad beams produced by scanned narrow pencil beams.

Secondary radiation dose modeling in passive scattering and pencil beam scanning very high energy electron (VHEE) radiation therapy.

BACKGROUND: Electrons with kinetic energy up to a few hundred MeV, also called very high energy electrons (VHEE), are currently considered a promising technique for the future of radiation therapy (RT) and in particular ultra-high dose rate (UHDR) therapy. However, the feasibility of a clinical application is still being debated and VHEE therapy remains an active area of research for which the optimal conformal technique is also yet to be determined. PURPOSE: In this work, we will apply two existing formalisms based on analytical Gaussian multiple-Coulomb scattering theory and Monte Carlo (MC) simulations to study and compare the electron and bremsstrahlung photon dose distributions arising from two beam delivery systems (passive scattering with or without a collimator or active scanning). METHODS: We therefore tested the application of analytical and MC models to VHEE beams and assessed their performance and parameterization in the energy range of 6-200 MeV. The optimized electron beam fluence, the bremsstrahlung, an estimation of central-axis and off-axis x-ray dose at the practical range and neutron contributions to the total dose, along with an extended parameterization for the photon dose model were developed, together with a comparison between double scattering (DS) and pencil beam scanning (PBS) techniques. MC simulations were performed with the TOPAS/Geant4 toolkit to verify the dose distributions predicted by the analytical calculations. RESULTS: The results for the clinical energy range (between 6 and 20 MeV) as well as for higher energies (VHEE range between 20 and 200 MeV) and for two treatment field sizes (5 × 5 and 10 × 10 cm2 ) are reported, showing a reasonable agreement with MC simulations with mean differences below 2.1%. The relative contributions of photons generated in the medium or by the scattering system along the central-axis (up to 50% of the total dose) are also illustrated, along with their relative variations with electron energy. CONCLUSIONS: The fast analytical models parametrized in this study allow an estimation of the amount of photons produced behind the practical range by a DS system with an accuracy lower than 3%, providing important information for the eventual design of a VHEE system. The results of this work could support future research on VHEE radiotherapy.