Geant4 models for simulation of multiple scattering

High-Density Glass Scintillators for Proton Radiography-Relative Luminosity, Proton Response, and Spatial Resolution

Proton radiography is a promising development in proton therapy, and researchers are currently exploring optimal detector materials to construct proton radiography detector arrays. High-density glass scintillators may improve integrating-mode proton radiography detectors by increasing spatial resolution and decreasing detector thickness. We evaluated several new scintillators, activated with europium or terbium, with proton response measurements and Monte Carlo simulations, characterizing relative luminosity, ionization quenching, and proton radiograph spatial resolution. We applied a correction based on Birks's analytical model for ionization quenching. The data demonstrate increased relative luminosity with increased activation element concentration, and higher relative luminosity for samples activated with europium. An increased glass density enables more compact detector geometries and higher spatial resolution. These findings suggest that a tungsten and gadolinium oxide-based glass activated with 4% europium is an ideal scintillator for testing in a full-size proton radiography detector.

Simulation of particle release for Diffusing Alpha-Emitters Radiation Therapy

We used Monte Carlo simulations to study release of ²²⁴Ra daughter nuclei from the seed used for Diffusing Alpha-Emitters Radiation Therapy (DART). Calculated desorption probabilities for ²¹⁶Po (15%) and ²¹²Pb (12%) showed that they make a significant contribution to total release from the seed. We also showed that the dose to tissue from decays inside the 10 mm long seed exceeds 2.9 Gy for initial ²²⁴Ra activity of 3 μCi (111 kBq).

Research on the proximity functions of microdosimetry of low energy electrons in liquid water based on different Monte Carlo codes

PURPOSE

The proximity function is an important index in microdosimetry for describing the spatial distribution of energy, which is closely related to the biological effects of organs or tissues in the target area. In this work, the impact of parameters, such as physic models, cut-off energy, and initial energy, on the proximity function are quantitated and compared.

METHODS

According to the track structure (TS) and condensed history (CH) low-energy electromagnetic models, this paper chooses a variety of Monte Carlo (Monte Carlo, MC) codes (Geant4-DNA, PHITS, and Penelope) to simulate the track structure of low-energy electrons in liquid water and evaluates the influence of the electron initial energy, cut-off energy, energy spectrum, and physical model factors on the differential proximity function.

RESULTS

The results show that the initial energy of electrons in the low-energy part (especially less than 1 keV) has a greater impact on the differential proximity function, and the choice of cut-off energy has a greater impact on the differential proximity function corresponding to small radius sites (generally less than 10 nm). The difference in the electronic energy spectrum has little effect on the result, and the proximity functions of different physics models show better consistency under large radius sites.

CONCLUSIONS

This work comprehensively compares the differential proximity functions under different codes by setting a variety of simulation conditions and has basic guiding significance for helping users simulate and analyze the deposition characteristics of microscale electrons according to the selection of an appropriate methodology and cut-off energy.

Improved Limit on Tensor Currents in the Weak Interaction from ^{8}Li β Decay

The electroweak interaction in the standard model is described by a pure vector-axial-vector structure, though any Lorentz-invariant component could contribute. In this Letter, we present the most precise measurement of tensor currents in the low-energy regime by examining the β-ν[over ¯] correlation of trapped ^{8}Li ions with the Beta-decay Paul Trap. We find a_{βν}=-0.3325±0.0013_{stat}±0.0019_{syst} at 1σ for the case of coupling to right-handed neutrinos (C_{T}=-C_{T}^{'}), which is consistent with the standard model prediction.

The detective quantum efficiency of cadmium telluride photon-counting x-ray detectors in breast imaging applications

PURPOSE

In breast imaging applications, cadmium telluride (CdTe) photon counting x-ray detectors (PCDs) may reduce radiation dose and enable single-shot multi-energy x-ray imaging. The purpose of this work is to determine the upper limits of the detective quantum efficiency (DQE) of CdTe PCDs for x-ray mammography and to compare them with the published DQEs of energy-integrating detectors (EIDs) and other PCDs.

METHODS

We calibrated and validated a Monte Carlo (MC) model of the DQE of CdTe PCDs using an XCounter CdTe PCD. Our model accounted for charge sharing, electronic noise, and charge summation logic. We used a 28 kVp Mo/Mo spectrum hardened by 3.9 cm of Lucite to optimize the detector thickness and energy threshold for pixel sizes of 50, 85, and 100 μ m with and without inter-pixel charge summation logic. The figure of merit used for optimization was the integral of the DQE, which is equivalent to the detectability index for a delta function task function, which represents a high-frequency task.

RESULTS

For an electronic noise level equal to that of the XCounter, the optimal DQE(0) without charge summing was 0.74. Charge summing for charge-sharing correction reduced DQE(0) by 14% due to an increase in electronic noise. Reducing the electronic noise to ∼0.5 keV per pixel in combination with charge summing resulted in DQE(0) ≈ 0.78 for 85  μ m pixels, which is approximately equal to that of a-Se and slot-scanning silicon-strip PCDs. At higher spatial frequencies, and for matched pixel sizes, the DQE was inferior to that of a-Se EIDs and superior to that of slot-scanning silicon-strip PCDs in the scan direction but inferior in the slit direction.

CONCLUSIONS

(1) CdTe PCDs have the potential to provide a zero-frequency DQE equal to that of a-Se EIDs and slot-scanning silicon-strip PCDs, but this will require electronic noise levels ∼0.5 keV per pixel. (2) At mid-to-high spatial frequencies the DQE of CdTe PCDs may be (a) inferior to that of a-Se EIDs and slot-scanning silicon-strip PCDs in the slit direction, and (b) superior to slot-scanning silicon-strip PCDs in the scan direction.

Monte Carlo-derived ionization chamber correction factors in therapeutic carbon ion beams

The accuracy of electromagnetic transport in the GEANT4 Monte Carlo (MC) code was investigated for carbon ion beams and ionization chamber (IC)-specific beam quality correction factors were calculated. This work implemented a Fano cavity test for carbon ion beams in the 100-450 MeV/u energy range to assess the accuracy of the default electromagnetic physics parameters. TheUrbanand theWentzel-VImultiple Coulomb scattering models were evaluated and the impact ofmaxStep,dRover,andfinal rangeparameters on the accuracy of the transport algorithm was investigated. The optimal production thresholds for an accurate calculation offQvalues, which is the product of the water-to-air stopping power ratio and the IC-specific perturbation correction factor, were also studied. ThefQcorrection factors were calculated for a cylindrical and a parallel-plate IC using carbon ions in the 150-450 MeV/u energy range. Modifying the default electromagnetic physics parameters resulted in a maximum deviation from theory of 0.3%. Therefore, the default EM parameters were used for the remainder of this work. ThefQfactors were found to converge for both ICs with decreasing production threshold distance below 5μm. ThefQvalues obtained in this work agreed with the TRS-398 stopping power ratios and other previously reported results within uncertainty. This study highlights an accurate MC-based technique to calculate the combined stopping power ratio and the perturbation correction factor for any IC in carbon ion beams.

Monte Carlo methods for device simulations in radiation therapy

Monte Carlo (MC) simulations play an important role in radiotherapy, especially as a method to evaluate physical properties that are either impossible or difficult to measure. For example, MC simulations (MCSs) are used to aid in the design of radiotherapy devices or to understand their properties. The aim of this article is to review the MC method for device simulations in radiation therapy. After a brief history of the MC method and popular codes in medical physics, we review applications of the MC method to model treatment heads for neutral and charged particle radiation therapy as well as specific in-room devices for imaging and therapy purposes. We conclude by discussing the impact that MCSs had in this field and the role of MC in future device design.

Light absorption enhancement and radiation hardening for triple junction solar cell through bioinspired nanostructures

Multi-junction solar cells constitute the main source of power for space applications. However, exposure of solar cells to the space radiation environment significantly degrades their performance across the mission lifetime. Here, we seek to improve the radiation hardness of the triple junction solar cell, GaInP/Ga(In)As/Ge, by decreasing the thickness of the more sensitive middle junction. Thin junctions facilitate the collection of minority carriers and show slower degradation due to defects. However, thinning the junction decreases the absorption, and consequently, the expected photocurrent. To compensate for this loss, we examined two bioinspired surface patterns that exhibit anti-reflective and light-trapping properties: (a) the moth-eye structure which enables vision in poorly illuminated environments and (b) the patterns of the hard cell of a unicellular photosynthetic micro-alga, the diatoms. We parametrize and optimize the biomimetic structures, aiming to maximize the absorbed light by the solar cell while achieving significant reduction in the middle junction thickness. The density of the radiation-induced defects is independent of the junction thickness, as we demonstrate using Monte Carlo simulations, allowing the direct comparison of different combinations of middle junction thicknesses and light trapping structures. We incorporate the radiation effects into the solar cell model as a decrease in minority carrier lifetime and an increase in surface recombination velocity, and we quantify the gain in efficiency for different combinations of junction thickness and the light-trapping structure at equal radiation damage. Solar cells with thin junctions compensated by the light-trapping structures offer a promising approach to improve solar cell radiation hardness and robustness, with up to 2% higher end-of-life efficiency than the commonly used configuration at high radiation exposure.

Image quality evaluation of projection- and depth dose-based approaches to integrating proton radiography using a monolithic scintillator detector

The purpose of this study is to compare the image quality of an integrating proton radiography (PR) system, composed of a monolithic scintillator and two digital cameras, using integral lateral-dose and integral depth-dose image reconstruction techniques. Monte Carlo simulations were used to obtain the energy deposition in a 3D monolithic scintillator detector (30 × 30 × 30 cm³poly vinyl toluene organic scintillator) to create radiographs of various phantoms-a slanted aluminum cube for spatial resolution analysis and a Las Vegas phantom for contrast analysis. The light emission of the scintillator was corrected using Birks scintillation model. We compared two integrating PR methods and the expected results from an idealized proton tracking radiography system. Four different image reconstruction methods were utilized in this study: integral scintillation light projected from the beams-eye view, depth-dose based reconstruction methods both with and without optimization, and single particle tracking PR was used for reference data. Results showed that heterogeneity artifact due to medium-interface mismatch was identified from the Las Vegas phantom simulated in air. Spatial resolution was found to be highest for single-event reconstruction. Contrast levels, ranked from best to worst, were found to correspond to particle tracking, optimized depth-dose, depth-dose, and projection-based image reconstructions. The image quality of a monolithic scintillator integrating PR system was sufficient to warrant further exploration. These results show promise for potential clinical use as radiographic techniques for visualizing internal patient anatomy during proton radiotherapy.

Evaluation of the GEANT4 transport algorithm and radioactive decay data for alpha particle dosimetry

A Fano cavity test was implemented in GEANT4 Monte Carlo code to evaluate the alpha particle transport algorithm. GEANT4 alpha emission data for ²¹²Pb, ²²³Ra, ²²⁷Th, and ²²⁵Ac was compared with the MIRD and RADAR decay databases. Optimal electromagnetic transport parameters (dRover of 0.1 and final range of 1 μm) were recommended since the calculated results with the default parameters differed up to 4.7% from the theoretical results. Good agreement was found between the three decay databases besides a few discrepancies.

Monte Carlo calculation of perturbation correction factors for air-filled ionization chambers in clinical proton beams using TOPAS/GEANT

INTRODUCTION

Current dosimetry protocols for clinical protons using air-filled ionization chambers assume that the perturbation correction factor is equal to unity for all ionization chambers and proton energies. Since previous Monte Carlo based studies suggest that perturbation correction factors might be significantly different from unity this study aims to determine perturbation correction factors for six plane-parallel and four cylindrical ionization chambers in proton beams at clinical energies.

MATERIALS AND METHODS

The dose deposited in the air cavity of the ionization chambers was calculated with the help of the Monte Carlo code TOPAS/Geant4 while specific constructive details of the chambers were removed step by step. By comparing these dose values the individual perturbation correction factors p_cel, p_stem, p_sleeve, p_wall, p_cav⋅p_dis as well as the total perturbation correction factor p_Q were derived for typical clinical proton energies between 80 and 250MeV.

RESULTS

The total perturbation correction factor p_Q was smaller than unity for almost every ionization chamber and proton energy and in some cases significantly different from unity (deviation larger than 1%). The maximum deviation from unity was 2.0% for cylindrical and 1.5% for plane-parallel ionization chambers. Especially the factor p_wall was found to differ significantly from unity. It was shown that this is due to the fact that secondary particles, especially alpha particles and fragments, are scattered from the chamber wall into the air cavity resulting in an overresponse of the chamber.

CONCLUSION

Perturbation correction factors for ionization chambers in proton beams were calculated using Monte Carlo simulations. In contrast to the assumption of current dosimetry protocols the total perturbation correction factor p_Q can be significantly different from unity. Hence, beam quality correction factors [Formula: see text] that are calculated with the help of perturbation correction factors that are assumed to be unity come with a corresponding additional uncertainty.

Report on G4-Med, a Geant4 benchmarking system for medical physics applications developed by the Geant4 Medical Simulation Benchmarking Group

BACKGROUND

Geant4 is a Monte Carlo code extensively used in medical physics for a wide range of applications, such as dosimetry, micro- and nanodosimetry, imaging, radiation protection, and nuclear medicine. Geant4 is continuously evolving, so it is crucial to have a system that benchmarks this Monte Carlo code for medical physics against reference data and to perform regression testing.

AIMS

To respond to these needs, we developed G4-Med, a benchmarking and regression testing system of Geant4 for medical physics.

MATERIALS AND METHODS

G4-Med currently includes 18 tests. They range from the benchmarking of fundamental physics quantities to the testing of Monte Carlo simulation setups typical of medical physics applications. Both electromagnetic and hadronic physics processes and models within the prebuilt Geant4 physics lists are tested. The tests included in G4-Med are executed on the CERN computing infrastructure via the use of the geant-val web application, developed at CERN for Geant4 testing. The physical observables can be compared to reference data for benchmarking and to results of previous Geant4 versions for regression testing purposes.

RESULTS

This paper describes the tests included in G4-Med and shows the results derived from the benchmarking of Geant4 10.5 against reference data.

DISCUSSION

Our results indicate that the Geant4 electromagnetic physics constructor G4EmStandardPhysics_option4 gives a good agreement with the reference data for all the tests. The QGSP_BIC_HP physics list provided an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. New tests should be included in the next stage of the project to extend the benchmarking to other physical quantities and application scenarios of interest for medical physics.

CONCLUSION

The results presented and discussed in this paper will aid users in tailoring physics lists to their particular application.

Radio-enhancement effects by radiolabeled nanoparticles

In cancer radiation therapy, dose enhancement by nanoparticles has to date been investigated only for external beam radiotherapy (EBRT). Here, we report on an in silico study of nanoparticle-enhanced radiation damage in the context of internal radionuclide therapy. We demonstrate the proof-of-principle that clinically relevant radiotherapeutic isotopes (i.e. 213Bi, 223Ra, 90Y, 177Lu, 67Cu, 64Cu and 89Zr) labeled to clinically relevant superparamagnetic iron oxide nanoparticles results in enhanced radiation damage effects localized to sub-micron scales. We find that radiation dose can be enhanced by up to 20%, vastly outperforming nanoparticle dose enhancement in conventional EBRT. Our results demonstrate that in addition to the favorable spectral characteristics of the isotopes and their proximity to the nanoparticles, clustering of the nanoparticles results in a nonlinear collective effect that amplifies nanoscale radiation damage effects by electron-mediated inter-nanoparticle interactions. In this way, optimal radio-enhancement is achieved when the inter-nanoparticle distance is less than the mean range of the secondary electrons. For the radioisotopes studied here, this corresponds to inter-nanoparticle distances <50 nm, with the strongest effects within 20 nm. The results of this study suggest that radiolabeled nanoparticles offer a novel and potentially highly effective platform for developing next-generation theranostic strategies for cancer medicine.

Comparison of penh, fluka, and Geant4/topas for absorbed dose calculations in air cavities representing ionization chambers in high-energy photon and proton beams

Purpose

The purpose of this work is to analyze whether the Monte Carlo codes penh, fluka, and geant4/topas are suitable to calculate absorbed doses and fQ/fQ0 ratios in therapeutic high‐energy photon and proton beams.

Methods

We used penh, fluka, geant4/topas, and egsnrc to calculate the absorbed dose to water in a reference water cavity and the absorbed dose to air in two air cavities representative of a plane‐parallel and a cylindrical ionization chamber in a 1.25 MeV photon beam and a 150 MeV proton beam — egsnrc was only used for the photon beam calculations. The physics and transport settings in each code were adjusted to simulate the particle transport as detailed as reasonably possible. From these absorbed doses, fQ0 factors, fQ factors, and fQ/fQ0 ratios (which are the basis of Monte Carlo calculated beam quality correction factors kQ,Q0) were calculated and compared between the codes. Additionally, we calculated the spectra of primary particles and secondary electrons in the reference water cavity, as well as the integrated depth–dose curve of 150 MeV protons in water.

Results

The absorbed doses agreed within 1.4% or better between the individual codes for both the photon and proton simulations. The fQ0 and fQ factors agreed within 0.5% or better for the individual codes for both beam qualities. The resulting fQ/fQ0 ratios for 150 MeV protons agreed within 0.7% or better. For the 1.25 MeV photon beam, the spectra of photons and secondary electrons agreed almost perfectly. For the 150 MeV proton simulation, we observed differences in the spectra of secondary protons whereas the spectra of primary protons and low‐energy delta electrons also agreed almost perfectly. The first 2 mm of the entrance channel of the 150 MeV proton Bragg curve agreed almost perfectly while for greater depths, the differences in the integrated dose were up to 1.5%.

Conclusion

penh, fluka, and geant4/topas are capable of calculating beam quality correction factors in proton beams. The differences in the fQ0 and fQ factors between the codes are 0.5% at maximum. The differences in the fQ/fQ0 ratios are 0.7% at maximum.

On the accuracy and efficiency of condensed history transport in magnetic fields in GEANT4

The purpose of this work was to investigate the accuracy and efficiency of electron transport in GEANT4 with and without a magnetic field present. Fano cavity simulations were performed in GEANT4 version 10.02 and 10.04.p01 using two multiple scattering (MSC) algorithms for two slab and one pseudo-ion chamber geometries. An iterative approach was used to optimize the transport parameters to obtain agreement with theory. Similar to previous works, the step lengths had to be severely restricted to obtain agreement with theory when using the Urban MSC model in GEANT4 v10.02. Using the Goudsmit-Saunderson MSC model with the UseSafetyPlus MSC step limitation in GEANT4 v10.04.p01 limited the maximum discrepancy from theory to 0.5%. Minor adjustments to the transport parameters were needed to obtain agreement within 0.16% of theory for all simulation configurations without a magnetic field present. The maximum deviation from theory was within 2% for all simulation configurations in the presence of a magnetic field except for two setups that exhibited discrepancies of up to 10.8%. This anomalous behavior was mitigated by forcing single scattering within the detector gas volume. Further adjustments to the transport parameters resulted in agreement with theory at the 0.21% level. Agreement with theory in the absence of a magnetic field can be obtained without significantly restricting the step size if the Goudsmit-Saunderson MSC model is used with the UseSafetyPlus MSC step limitation in GEANT4 v10.04.p01. The large discrepancies from theory observed for two simulation setups with a magnetic field present were attributed to an issue with energy loss sampling over a step when strict magnetic field transport parameters are used. This problem can be corrected by forcing single scattering within the detector gas volume; however, more work is needed to identify the cause of this anomalous behavior. This work has shown that GEANT4 can perform accurate electron transport with and without a magnetic field present without applying significant step-size reductions.

Two-dimensional noise reconstruction in proton computed tomography using distance-driven filtered back-projection of simulated projections

We present a formalism for two-dimensional (2D) noise reconstruction in proton computed tomography (pCT). This is necessary for the application of fluence modulated pCT (FMpCT) since it permits image noise prescription and the corresponding proton fuence optimization. We aimed at extending previously published formalisms to account for the impact of multiple Coulomb scattering (MCS) on projection noise, and the use of filtered back projection (FBP) reconstruction along curved paths with distance driven binning (DDB). 2D noise reconstruction for a beam of protons with parallel initial momentum vectors, and for projections binned both at the rear tracker and with DDB, was established. Monte Carlo (MC) simulations of pCT scans of a water cylinder were employed to generate pCT projections and to calculate their noise for use in 2D noise reconstruction. These were compared to results from an analytical model accounting for MCS for rear tracker binning as well as against the previously published central pixel model which ignores MCS. Image noise reconstructed with the formalism for rear tracker binning and DDB were compared to MC results using annular regions of interest (ROIs). Agreement better than 8% was obtained between the noise of projections calculated with MC simulation and our model. Noise from annular ROIs agreed with our noise reconstructions for rear tracker binning and DDB. The central pixel model ignoring MCS underestimated projection and thus image noise by up to 40% towards the object's edge. The use of DDB decreased the image noise towards the object's edge when compared to rear tracker binning and yielded more uniform noise throughout the image. MCS should not be neglected when predicting image noise for pixels away from the center of an object in a pCT scan due to the increasing influence of the gradient of the object's hull closer to the edges.

Geant4-DNA example applications for track structure simulations in liquid water: A report from the Geant4-DNA Project

This Special Report presents a description of Geant4-DNA user applications dedicated to the simulation of track structures (TS) in liquid water and associated physical quantities (e.g., range, stopping power, mean free path…). These example applications are included in the Geant4 Monte Carlo toolkit and are available in open access. Each application is described and comparisons to recent international recommendations are shown (e.g., ICRU, MIRD), when available. The influence of physics models available in Geant4-DNA for the simulation of electron interactions in liquid water is discussed. Thanks to these applications, the authors show that the most recent sets of physics models available in Geant4-DNA (the so-called "option4" and "option 6" sets) enable more accurate simulation of stopping powers, dose point kernels, and W-values in liquid water, than the default set of models ("option 2") initially provided in Geant4-DNA. They also serve as reference applications for Geant4-DNA users interested in TS simulations.

CPU time optimization and precise adjustment of the Geant4 physics parameters for a VARIAN 2100 C/D gamma radiotherapy linear accelerator simulation using GAMOS

We have verified the GAMOS/Geant4 simulation model of a 6 MV VARIAN Clinac 2100 C/D linear accelerator by the procedure of adjusting the initial beam parameters to fit the percentage depth dose and cross-profile dose experimental data at different depths in a water phantom. Thanks to the use of a wide range of field sizes, from 2  ×  2 cm² to 40  ×  40 cm², a small phantom voxel size and high statistics, fine precision in the determination of the beam parameters has been achieved. This precision has allowed us to make a thorough study of the different physics models and parameters that Geant4 offers. The three Geant4 electromagnetic physics sets of models, i.e. Standard, Livermore and Penelope, have been compared to the experiment, testing the four different models of angular bremsstrahlung distributions as well as the three available multiple-scattering models, and optimizing the most relevant Geant4 electromagnetic physics parameters. Before the fitting, a comprehensive CPU time optimization has been done, using several of the Geant4 efficiency improvement techniques plus a few more developed in GAMOS.

Benchmarking GATE/Geant4 for 16O ion beam therapy

Oxygen ([Formula: see text]) ions are a potential alternative to carbon ions in ion beam therapy. Their enhanced linear energy transfer indicates a higher relative biological effectiveness and a reduced oxygen enhancement ratio. Due to the limited availability of [Formula: see text] ion beams, Monte Carlo (MC) transport codes are important research tools for investigating their potential. The purpose of this study was to validate GATE/Geant4 for [Formula: see text] ion beam therapy using experimental data from literature. Five hadron physics lists and two electromagnetic options were benchmarked against measured depth dose distributions (DDDs) and charge-changing cross sections. The simulated beam ranges deviated by less than 0.5% for all physics configurations and only a few points exceeded the gamma index criterion (2%/1 mm). However, the simulated partial charge-changing cross sections deviated considerably for some hadron physics configurations. Best agreement with the experimental values was obtained with the quantum molecular dynamics model (QMD), and we therefore suggest using this model in Geant4 to accurately describe the fragmentation of [Formula: see text] ion beams into lighter fragments ([Formula: see text]).

Evaluation of the range shifter model for proton pencil-beam scanning for the Eclipse v.11 treatment planning system

Existing proton therapy pencil‐beam scanning (PBS) systems have limitations on the minimum range to which a patient can be treated. This limitation arises from practical considerations, such as beam current intensity, layer spacing, and delivery time. The range shifter (RS) — a slab of stopping material inserted between the nozzle and the patient — is used to reduce the residual range of the incident beam so that the treatment ranges can be extended to shallow depths. Accurate modeling of the RS allows one to calculate the beam spot size entering the patient, given the proton energy, for arbitrary positions and thicknesses of the RS in the beam path. The Eclipse version 11 (v11) treatment planning system (TPS) models RS‐induced beam widening by incorporating the scattering properties of the RS material into the V‐parameter. Monte Carlo simulations with Geant4 code and analytical calculations using the Fermi‐Eyges (FE) theory with Highland approximation of multiple Coulomb scattering (MCS) were employed to calculate proton beam widening due to scattering in the RS. We demonstrated that both methods achieved consistent results and could be used as a benchmark for evaluating the Eclipse V‐parameter model. In most cases, the V‐parameter model correctly predicted the beam spot size after traversing the RS. However, Eclipse did not enforce the constraint for a nonnegative covariance matrix when fitting the spot sizes to derive the phase space parameters, which resulted in incorrect calculations under specific conditions. In addition, Eclipse v11 incorrectly imposed limits on the individual values of the phase space parameters, which could lead to incorrect spot size values in the air calculated for beams with spot sigmas <3.8 mm. Notably, the TPS supplier (Varian) and hardware vendor (Ion Beam Applications) inconsistently refer to the RS position, which may result in improper spot size calculations.

PACS number(s): 87.53.Jw, 87.53.Kn, 87.55.kd, 87.56.‐v