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

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. 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. 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. 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 . 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.

Ronga MG ，Deut U ，Bonfrate A ，De Marzi L ... -  《-》

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

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. 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). 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. 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. 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.

Deut U ，Ronga MG ，Bonfrate A ，De Marzi L ... -  《-》

Implementation and validation of a very-high-energy electron model in the matRad treatment planning system.

While electron beams of up to 20 MeV are commonly used in radiotherapy, the use of very-high-energy electrons (VHEEs) in the range of 100-200 MeV is now becoming a realistic option thanks to the recent advancements in accelerator technology. Indeed, VHEE offers several clinically attractive features and can be delivered using various conformation methods (including scanning, collimation, and focussing) at ultra-high dose rates. To date, there is a lack of research tools for fast simulation of treatment plans using VHEE beams. This work aims to implement and validate a simple and fast dose calculation algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for VHEE radiation therapy, with energies up to 200 MeV. A treatment planning system (TPS) toolkit with VHEE modality would indeed allow for further preclinical investigations, including treatment plan optimization and evaluation, and thus contribute to the gradual introduction of VHEE radiotherapy in clinical practice. A VHEE pencil beam scanning double Gaussian model was introduced into the open-source TPS matRad environment along with new functions and options dedicated to VHEE dose calculations. Various geometries and field configurations were then calculated in matRad (up to 200 MeV and 15 × 15 cm2, with complex bone or lung heterogeneities) and the results were compared to Monte Carlo simulations in the TOPAS/Geant4 toolkit. Two types of beam model (divergent or focused) were also tested. Examples of clinical treatment plans were computed, and the results were compared between the two codes. VHEE modality was fully implemented in matRad with GUI capabilities while preserving all original TPS features. New relevant options such as the importation of specific spot-lists or adjustment of the lateral dose calculation cutoff to optimize the calculation speed were validated. Single spot and square field dose distributions were validated in water alone as well as in clinically relevant inhomogeneities. Dose maps from the VHEE model in matRad were in good agreement with TOPAS (2D gamma index [2%/1 mm] with passing rates superior to 90%, <6% mean dose differences), except for large interface heterogeneities. This work describes the implementation of a simple but efficient VHEE simulation model in matRad. A few configurations were studied in order to validate the model against accurate Monte Carlo simulations, demonstrating its usefulness for carrying out preliminary studies involving VHEE radiotherapy.

Sitarz M ，Ronga MG ，Gesualdi F ，Bonfrate A ，Wahl N ，De Marzi L ... -  《-》

Treatment planning for radiotherapy with very high-energy electron beams and comparison of VHEE and VMAT plans.

Bazalova-Carter M ，Qu B ，Palma B ，Hårdemark B ，Hynning E ，Jensen C ，Maxim PG ，Loo BW Jr ... -  《-》

Characteristics of very high-energy electron beams for the irradiation of deep-seated targets.

Driven by advances in accelerator technology and the potential of exploiting the FLASH effect for the treatment of deep-seated targets (>5 cm), there is an active interest in the construction of devices to deliver very high-energy electron (VHEE) beams for radiation therapy. The application of novel VHEE devices, however, requires an assessment of the tradeoffs between the different beam parameter choices including beam energies, beam divergences, and maximal field sizes. This study systematically examines the dosimetric beam properties of VHEE beams, determining their clinical usefulness while marking their limits of applications for different beam configurations. We performed Monte Carlo simulations of the dose distributions of electron beams for different energies (25-250 MeV), source-to-surface distances (SSD) (50 cm, 100 cm, parallel), and field sizes (2 cm2  × 2 cm2 to 15 cm2  × 15 cm2 ) in water using a research version of the RayStation treatment planning system (RaySearch Labs 9A IONPG). The beam was simulated using a monoenergetic point source and perfect collimation. Central axis percentage depth dose (PDD) and transverse dose profiles at multiple depths were evaluated and compared to those of MV photon beams. Profile characteristics including therapeutic range (TR) at 90%, proximal fall-off (PFO) at 90%, lateral penumbra (LP) at 90%-10%, and field width (FW) at 90% were obtained. Very high-energy electrons beams with SSD 100 cm and parallel beams (infinite SSD) exhibit a linear to near-linear increase of TR as a function of energy in the simulated energy range and reach values well beyond the typical depths of lesions encountered in clinics (<20 cm). Their TR show a marked field size dependence only for field sizes <10 cm2  × 10 cm2 . For VHEE beams with SSD 50 cm, TR are largely reduced (4-8 cm). For beam energies >150 MeV with large SSD (>100 cm), for many configurations, there is no substantial difference in PDD when adding an opposed beam. This may potentially reduce the number of VHEE beams needed for treatment by a factor of two compared to a treatment using lower energies and lower SSD. In order to cover deep-seated targets homogeneously, VHEE devices with a parallel beam must provide a maximum field size up to several centimeters larger than the tumor size. For the investigated diverging beams, there is not such a significant field width reduction with depth for larger fields as it is compensated by divergence. Penumbrae of VHEE beams are smaller than those of clinical MV photon beams for lower depths (<5 cm) but increase quickly for larger depths. There is only a relatively small dependence of penumbra on the SSD of the beam. The findings presented in this study assess the performance of VHEE beams and offer a first estimate of treatment indications and tradeoffs for a given design of a VHEE device. SSD >100 cm results in clinically more favorable PDD. Beam energies of 100 MeV and above are needed to cover common tumors (5-15 cm in-depth) conformally. Higher energies provide an additional benefit specifically for small and deep-seated lesions due to their reduced lateral penumbrae.

Böhlen TT ，Germond JF ，Traneus E ，Bourhis J ，Vozenin MC ，Bailat C ，Bochud F ，Moeckli R ... -  《-》