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

Report on G4-Med, a Geant4 benchmarking system for medical physics applications developed by the Geant4 Medical Simulation Benchmarking Group P. Arce CIEMAT, Madrid, Spain D. Bolst Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia M.-C. Bordage CRCT (INSERM and Paul Sabatier University), Toulouse, France J. M. C. Brown Department of Radiation Science and Technology, Delft University of Technology, Delft, The Netherlands P. Cirrone INFN LNS, Catania, Italy M. A. Cort´ es-Giraldo Universidad de Sevilla, Sevilla, Spain D. Cutajar Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia G. Cuttone INFN LNS, Catania, Italy L. Desorgher Institute of Radiation Physics (IRA), Lausanne University Hospital, Lausanne, Switzerland P. Dondero SWHARD srl, Genova, Italy A. Dotti SLAC National Accelerator Laboratory, Stanford, CA, USA B. Faddegon University of California, San Francisco, CA, USA C. Fedon Radboud University Medical Center, Nijmegen, The Netherlands S. Guatelli a) Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia S. Incerti Universit´e de Bordeaux, CNRS/IN2P3, UMR5797, Centre d’ ´ Etudes Nucl´eaires de Bordeaux Gradignan, Gradignan, France V. Ivanchenko Tomsk State University, Tomsk, Russian Federation CERN, Geneva, Switzerland D. Konstantinov NRC “Kurchatov Institute”- IHEP, Protvino, Russian Federation I. Kyriakou Medical Physics Laboratory, University of Ioannina, Ioannina, Greece G. Latyshev NRC “Kurchatov Institute”- IHEP, Protvino, Russian Federation A. Le Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia C. Mancini-Terracciano Physics Dep., University of Rome “Sapienza”and INFN, Sec. of Rome, Rome, Italy M. Maire LAPP, IN2P3, Annecy, France 19 Med. Phys. 48 (1), January 2021 0094-2405/2021/48(1)/19/38 © 2020 American Association of Physicists in Medicine 19 A. Mantero SWHARD srl, Genova, Italy M. Novak CERN, Geneva, Switzerland C. Omachi Nagoya Proton Therapy Center, Nagoya, Japan L. Pandola INFN LNS, Catania, Italy A. Perales Medical Physics Department of Cl´ınica Universidad de Navarra, Pamplona, Spain Y. Perrot IRSN, Fontenay-aux-Roses, France G. Petringa INFN LNS, Catania, Italy J. M. Quesada Universidad de Sevilla, Sevilla, Spain J. Ramos-M´ endez University of California, San Francisco, CA, USA F. Romano INFN Catania Section, Catania, Italy Medical Physics Department, National Physical Laboratory, Teddington, UK A. B. Rosenfeld Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia L. G. Sarmiento Lund University, Lund, Sweden D. Sakata Centre For Medical Radiation Physics, University of Wollongong, Wollongong, Australia T. Sasaki KEK, Tsukuba, Japan I. Sechopoulos Radboud University Medical Center, Nijmegen, The Netherlands Dutch Expert Center for Screening (LRCB), Nijmegen, The Netherlands E. C. Simpson Department of Nuclear Physics, Research School of Physics, Australian National University, Canberra, Australia T. Toshito Nagoya Proton Therapy Center, Nagoya, Japan D. H. Wright SLAC National Accelerator Laboratory, Stanford, CA, USA (Received 10 July 2019; revised 26 April 2020; accepted for publication 30 April 2020; published 12 December 2020) 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 Medical Physics, 48 (1), January 2021 20 ARCE et al.: G4-Med 20 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 G4EmStan- dardPhysics_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. © 2020 American Association of Physicists in Medicine [https:// doi.org/10.1002/mp.14226] Key words: benchmarking, Geant4, medical physics, Monte Carlo 1. INTRODUCTION Geant4 1–3 is a Monte Carlo (MC) toolkit describing particle transport and interactions in matter. Originally developed for high energy physics, it was later extended to the low energy domain (down to the eV scale) for medical physics and space science applications. Today Geant4 is widely used in medical physics in critical applications such as verification of radiotherapy treatment planning systems, and the design of equipment for radiotherapy and nuclear medicine. It is also used in medical imaging for dosimetry, to improve detectors and reconstruction algorithms, and for radiation protection assessments. 4,5 In the medical physics domain, Geant4 can be used in stand-alone applications or via software tools like GAMOS, 6 GATE, 7 PTSim, 8,9 and TOPAS. 10 Given the extensive use of Geant4 in medical physics, a systematic benchmarking of the accuracy of the Geant4 physics models in this domain is paramount. This is crucial in a field where MC simulations are often regarded as a gold standard. In this work, we describe G4-Med, a group of currently 18 tests, executed on the CERN computing infrastructure to benchmark and to perform regression tests of new development tags and public releases of Geant4. The tests are contributed by the members of the Geant4 Medical Simulation Benchmarking Group 11 to benchmark Geant4 for medical physics applications. They range from the benchmarking of fundamental physics quantities to more complex simulations typical of medical physics applications. We show the results of the tests obtained for Geant4 version 10.5 and report on their benchmarking against reference data. For the sake of brevity, we show only a subset of the results. The full results can be downloaded using the geant-val web interface. 12 G4-Med has been set up with the aim to assess the appropriateness of any Geant4 release in the medical domain and to monitor the impact of software development, including physics refinements, on physical quantities and applications of interest for medical physics. The results of the benchmarking are also intended to provide recommendations on the most appropriate physics configuration provided by Geant4 with the prebuilt physics constructors and physics lists 3 to adopt in specific user applications. The project documentation can be found at the G4-Med web page. 11 Section 2describes the general method adopted in this study. This is then followed by sections that describe tests devoted to benchmarking electromagnetic physics (10 tests, Section 3), hadronic physics (3 tests, Section 4), and testing both these physics sets together (5 tests, Section 5). For clarity, Table 1lists the tests of G4-Med, their name in the geantval interface 12 and corresponding subsections. The subsections briefly describe the tests and their results. This table also reports the source of the tests. We conclude our report with a summary of our findings in Section 6. This report has gone through the peer review and approval processes of the Geant4 Editorial Board, which reviews all scientific papers emerging from the Geant4 Collaboration (Geant4 Collaboration website 13 ). 2. METHODOLOGY All tests included in G4-Med have been integrated into the geant-val environment 14 developed at CERN to perform Geant4 benchmarking and regression testing. The geant-val system provides a convenient web-based validation tool for Geant4 developers. It allows for storage of the Geant4 tests results in analysis objects, such as histograms and scatter plots, together with meta information, such as: Geant4 version, name of the test, energy and momentum of the incident particle, name of the target/detector, and physics list used in the simulation. The main web interface 12 allows for visual and statistical comparison among results produced using different versions of Geant4, or a comparison with reference experimental results. In addition, users can download plots or data in various formats. The tests are executed automatically for all the global development tags and public releases of Medical Physics, 48 (1), January 2021 21 ARCE et al.: G4-Med 21 Geant4 at the CERN computing facility. All results derived from the benchmarking and regression testing, including plots and statistical analysis, are generated automatically and are accessible through the web interface. 12 In general, the tests use the same set of electromagnetic (EM) and hadronic physics constructors, with exceptions for tests aimed at validating the Geant4 EM multiple and single scattering models and specific hadronic cross sections and models. Simulation parameters, such as the secondary particles production threshold (cut) or the maximum step size, were appropriately set for each simulation scenario and are included in the description of each test. In all the tests, the % difference between the results of the Geant4 simulations and reference data was calculated, then compared to the 1 σuncertainty affecting the reference data (called rref in the following sections). If the difference was smaller than rref the agreement was considered satisfactory. 3. ELECTROMAGNETIC PHYSICS BENCHMARKING TESTS This section describes the 10 tests in G4-Med where only the Geant4 EM physics component is activated and all the other processes are disabled. The tested Geant4 EM physics constructors are briefly described here as released within Geant4 10.5. In all the EM constructors under investigation, the set of EM processes are the same. Photon interactions include the photoelectric effect, Compton and Rayleigh scattering, and pair/triplet production (gamma conversion). Electron and positron interactions are ionization, bremsstrahlung, and elastic scattering. Positrons can also annihilate at rest and in flight. Protons and heavier ions have ionization, elastic scattering and nuclear stopping. G4EmStandardPhysics,G4EmLivermorePhysics,G4Em PenelopePhysics,G4EmStandardPhysics_option3 and G4Em StandardPhysics_option4 EM constructors, called here Opt0, Livermore,Penelope,Opt3, and Opt4, respectively, were considered in this work and correspond to different combinations of models deriving from either Geant4 Standard,Livermore or Penelope packages. The EM physics constructors and models, reported briefly in Table 2, are described in detail in the Geant4 Physics Reference Manual. The Standard sublibrary describes electromagnetic interactions in the range between 1 keV and 10 PeV, and is focusedonhighenergyphysicsapplicationssuchasthe simulation of LHC experiments. 3,28 The Livermore models provide a more accurate description of EM physics processes in the low energy domain. They are based on the Livermore Evaluated Data libraries and are documented in Ivanchenko et al, 29 Allison et al, 30 and Chauvie et al. 31 Penelope features the specific low-energy models for electrons, positrons, and photons, originally developed for the PENELOPE Monte Carlo code 32 andthenimplementedin Geant4. They can describe particle interactions down to 100 eV. The Opt4 constructor contains a combination of models for each EM physics process deemed to offer the best performance in term of precision at the cost of CPU efficiency. 33 The benchmark results of the current paper will also be used to discuss the expected better physical accuracy of Opt4 against the other EM constructors under investigation. Opt4 uses the G4GoudsmitSoundersonMscModel to describe multiple TABLE I. Tests of G4-Med with their name in the geant-val interface and the subsections of this report with their description and results. Test Name in geantval interface 12 Source Subsection Photon attenuation PhotonAttenuation Amako et al. 15 3.A Electron electronic stopping power ElectDEDX *3.B Electron backscattering ElectBackScat Dondero et al. 17 3.C Electron forward scatter from foils at 13 and 20 MeV ElecForwScat Faddegon et al. 18 3.D Bremsstrahlung from thick targets Bremsstrahlung Faddegon et al. 19 3.E Fano cavity Fano cavity ** 3.F Low-energy electron dose point kernels LowEElectDPK ** 3.G Microdosimetry microyz **Kyriakou et al. 20 3.H Brachytherapy Brachy-Ir *** 3.I Monoenergetic xray internal breast dosimetry Mammo Fedon et al. 21,22 3.J Nucleus–nucleus hadronic inelastic scattering cross sections NucNucInelXS NA 4.A 62 MeV/μ12C fragmentation LowEC12Frag Mancini et al 23 4.B Charge-changing cross section for 300 MeV/μ carbon ions C12FragCC Toshito et al 24 4.C 67.5 MeV proton Bragg curves in water LowEProton BraggBeak Faddegon et al 25 5.A Light ion Bragg peak curves LightIonBraggPeak NA 5.B Neutron yield of protons with energy 113 and 256 MeV and 290 MeV/u carbon ions ProtonC12 NeutronYield NA 5.C Fragmentation of a 400 MeV/μ12C ion beam in water FragTest Bolst et al 26 5.D Test on cell survival modeling for proton therapy Hadrontherapy ***, Petringa et al 27 5.E * : tests already executed by Geant4 developers for regression testing purposes; ** : tests released as Geant4 extended examples; *** : tests released as Geant4 advanced examples. Medical Physics, 48 (1), January 2021 22 ARCE et al.: G4-Med 22 TABLE II. Geant4 physics models to describe EM physics processes in Geant4 EM constructors under investigation. Geant4 Opt0 Opt3 Opt4 Livermore Penelope Rayleigh scattering and photoelectric effect Livermore PENELOPE Compton scattering Standard G4KleinNishina Model G4LowEPComptonModel for E<20 MeVBrown et al 36 Livermore for E <1GeV PENELOPE for E<1GeV  Gamma conversion Standard Standard PENELOPE for E <20 MeV Standard for E >20 MeV G4BetheHeitler5DModel for E<1 GeV, Standard for E >1GeV Bernard et al 2013 37 PENELOPE for E<1 GeV, Standard for E>1GeV eand eþionisation Standard Standard Livermore for efor E <100 keV, PENELOPE for eþ for E <100 keV, Standard for E >100 keV Livermore for E <100 keV Standard for E >100 keV PENELOPE eand eþbremsstrahlung Standard G4SeltzerBergerModel for E <1 GeV, G4eBremsstrahlungRelModel for E >1 GeV PENELOPE eþannihilation Standard PENELOPE eand eþmultiple scattering Urban model for E <100 MeV (Ivanchenko et al 39 ), Wentzel model for E >100 MeV Urban model Goudsmit–Saunderson model (Incerti et al 2018a 38 ) for E <100 MeV Wentzel model for E >100 MeV Coulomb scattering on off On Bremsstrahlung angular distribution ModifiedTsai 2BS PENELOPE :G4KleinNishinaModel for higher energies. Geant4 10.5 is considered. For details on the models the reader should refer to the Geant4 Physics Reference Manual. 28 Medical Physics, 48 (1), January 2021 23 ARCE et al.: G4-Med 23 scattering for ebelow 100 MeV and the ICRU73 stopping power data for ions heavier than helium (ICRU report No.73 34 ). In all the EM constructors, the multiple scattering of protons, muons, and other hadrons is modeled with the Wentzel model and the single scattering. In the case of ions, the Urban model is used for all energies. Opt3,Livermore, and Penelope constructors are considered as relatively accurate but less CPU demanding for medical applications. We therefore expect the Opt4 constructor to perform best overall in our benchmarking system, but we nevertheless study Opt3 and Livermore constructors, given their appeal in terms of computational efficiency. For electron scattering and Fano cavity tests, additional EM physics constructors are used, the G4EmStan- dardPhysicsSS,G4EmStandardPhysicsGS,G4EmStan- dardPhysicsWVI, called here SS,GS, and WVI, respectively. They have the same physics parameters of Opt0, apart from different modeling of either the Coulomb scattering or the multiple scattering. In SS, the single scattering model is used for the Coulomb scattering. GS and WVI adopt the Goudsmit–Saunderson (GS) and the Wentzel models, respectively, for multiple scattering. These physics constructors are mainly for Geant4 internal tests allowing study of various EM models alone, and are not meant for production physics configurations. For completeness, Table 3shows the values of EM parameters relevant for medical physics applications, listed for each of the EM constructors under investigation. The minimum energy is the minimum kinetic energy used to build the EM physics tables. The lowest electron energy parameter defines tracking cut for electrons and positrons. If after a step in a material, the particle energy is below this cut, this energy is added to the energy deposition and this particle is stopped. This parameter may be changed by the user and can be set to zero. The number of bins per decade is the number of bins per decade to be used when building the physics tables. The angular generator parameter activates the angular generator interface of the ionization process. The Mott corrections activate the Mott corrections in the electron multiple scattering. dRoverRange and finalRange are parameters of the method SetStepFunction used in the modeling of the multiple scattering. The lateral displacement due to multiple scattering is enabled by default for electrons and positrons, while it is set up differently in the EM constructors for muons and hadrons (see the Lateral displacement parameter in Table 3). The Skin and Range factor parameters are used to limit the step in multiple scattering of electrons and positrons. The Theta parameter is the angular limit between single and multiple scattering. The last two rows of Table 3report if the atomic de-excita- tion, including fluorescence x ray and Auger electrons emission, is active in the EM constructors. All model parameters are unchanged with respect to their defaults, that is, no fine tuning or optimization is performed within the constructor. 3.A. Photon attenuation test 3.A.1. Simulation setup The Photon Attenuation test, described and published in Amako et al, 15 has the name of PhotonAttenuation in the geant-val web interface. 12 This Geant4 application calculates the attenuation coefficients of photons with energy between 1 keV and 1 GeV striking a water target with normal incidence. The number of incident photons Nemerging without interacting in the target is counted and then the attenuation coefficient is calculated as l q¼1 qdln N N0  , where is the target density, dthe target thickness and N0the number of incident photons. The test calculates the photon attenuation coefficient in water of individual photon processes: Rayleigh scattering, photoelectric effect, Compton scattering and gamma conversion, as well as the total one. The photon attenuation coefficients are calculated in water, modeled as Geant4 NIST material G4_WATER (documented in the Geant4 Application Developer Manual 39 ). We compare the results of the Geant4 simulations to reference data of the United States National Institute of Standards and Technologies (NIST), included in the NIST XCOM database available online.. 16,40 The NIST XCOM database 16 was chosen as it is often used as a reference in medical radiation TABLE III. Geant4 EM parameters of the EM constructors under investigation. Geant4 EM parameter Opt0 Opt3 Opt4 livermore penelope SS GS WVI Minimum energy (eV) 100. 10. 10. 100. 100. 10. Lowest electron energy (keV) 1. 0.1 0.1 0.01 1. 0.01 Number of bins per decade 720 20 7 720 Angular generator False True True False False True Mott corrections False True True False False True dRoverRange for eand eþ 0.2 0.2 0.2 0.2 0.2 0.2 finalRange for e and eþ(mm) 1. 0.1 0.1 1. 1. 0.1 dRoverRange for muons and hadrons 0.1 0.05 0.05 0.1 0.1 0.05 Lateral displacement for muons and hadrons False True True False False True Skin 11 3 110 Range factor 0.04 0.04 0.08 0.04 0.06 0.04 Theta (rad) ππ π 0. π0.15 Luorescence Off On On On Off On Auger electrons and PIXE modeling Off Off Off On Off Off Geant4 10.5 is considered. Medical Physics, 48 (1), January 2021 24 ARCE et al.: G4-Med 24 physics. It provides photon attenuation coefficients between 1 keV and 100 GeV for all the elements of the periodic table, calculated with a theoretical approach based on Hubbell et al. 41 The quoted uncertainty for the reference data is about 1% for high energies and away from the atomic edges, while it can be substantially larger, up to 10–20%, for energies close to the atomic absorption edges. 42 From here, it was decided to adopt an uncertainty (rref ) of up to 10% and 1% for energies below and above 100 keV, respectively. The number of histories (photon events) in the simulations is adjusted depending on the energy at which the attenuation coefficients are calculated in order to obtain simulation statistical uncertainties below 1%. 3.A.2. Results and discussion Figure 1shows the results concerning the total attenuation coefficient of photons in water, while Fig. 2shows the attenuation coefficients for each individual photon process. The agreement between the Geant4 EM constructors and the reference data is summarized in Table 4. For the total attenuation coefficient, all the Geant4 EM constructors agree with the reference data within the uncertainty of the NIST XCOM in the entire energy range under study (up to 1 GeV). The 2% local difference at 20 keV (see Fig. 2) is due to differences in the photoelectric and Compton cross sections with respect to the NIST XCOM data. This is the point where we have the transition from photoelectric effect to Compton scattering as dominant process. The results show a maximum difference of approximately 10% in the case of Rayleigh scattering for energies below few keV (see Table 4for more details). Then such differences decrease to <1% for higher energies. This is due to different modeling of this process in the Livermore Evaluated Data libraries and NIST, highlighted in Amako et al 15 and Cirrone et al. 42 Among the EM constructors considered, Opt0 is the one showing the biggest differences with respect to the reference data. In the case of photoelectric effect attenuation coefficient, all the EM constructors agree with the reference data within 1 rref (1 σuncertainty of the reference data), with the exception at around 1–2 MeV, where the photoelectric attenuation coefficient changes significantly in slope and at high energies (above 500 MeV) where the photoelectric effect is not important anymore. There is a local difference of about 2% at 20 keV between the Geant4 EM constructors and the reference data, which contributes to the difference at this energy in the case of the total attenuation coefficient. In the case of Compton scattering, an agreement within 1 rref was observed for the entire energy range under investigation for Opt4, with maximum differences of <1.5%. Opt0, Opt3, and Penelope show differences above 5% at low energies (still within 1 rref, see details in Table 4). Livermore and Penelope show local differences of a few percent at around 500 MeV–1 GeV; however, here the Compton cross section is one order of magnitude lower than the gamma conversion cross section. The gamma conversion attenuation coefficient vanishes below the pair production threshold of 1.022 MeV, as expected. In this case, we observed differences equal or above 5% close to the threshold energy for all the EM constructors. Opt0,Opt3, and Livermore have differences up to 3% in the energy range between 3 and 10 MeV and up to 1% for higher energies. In general, Opt3,Opt4,Livermore, and Penelope have a good agreement with the reference data. The results are material dependent, but in water, all models are consistent with each other and with NIST XCOM within a few percent. A slightly overall better agreement with the reference data was found when considering Opt4. Nevertheless, it is important to note that the Geant4 EM physics constructors were compared here to theoretical data with modeling limitations. Therefore, this test should be extended in the future to include comparisons to available experimental measurements and other data libraries. The results of this test are in agreement with those reported in Cirrone et al 42 and Amako et al. 15 The readers should consult these publications for results of this test when considering other target materials. 3.B. Electron electronic stopping power test In this test, the electron electronic stopping power is calculated in a set of target materials and compared to the ESTAR 3− 10 2− 10 1− 10 110 2 10 3 10 /g) 2 (cmρ/μ 1− 10 1 10 2 10 3 10 NIST XCOM Livermore Penelope Opt0 Opt3 Opt4 Total Energy (MeV) 3− 10 2− 10 1− 10 110 2 10 3 10 Ratio (Sim/NIST) 0.9 0.95 1 1.05 1.1 FIG. 1. Top plot: Total attenuation coefficient in water with respect to the photon energy. Bottom plot: Ratio of the results obtained with Geant4 and the NIST XCOM reference data. The black dashed lines in the bottom plot represent the uncertainties of the NIST XCOM data (rref ). The statistical uncertainty affecting the Geant4 simulation results is below 1%. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 25 ARCE et al.: G4-Med 25 3− 10 2− 10 1− 10 110 2 10 /g) 2 (cmρ/ R μ 9− 10 8− 10 7− 10 6− 10 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 NIST XCOM Livermore Penelope Opt0 Opt3 Opt4 Rayleigh Energy (MeV) 3− 10 2− 10 1− 10 110 2 10 Ratio (Sim/NIST) 0.9 0.95 1 1.05 1.1 3− 10 2− 10 1− 10 110 2 10 3 10 /g) 2 (cmρ/ c μ 5− 10 4− 10 3− 10 2− 10 1− 10 1 NIST XCOM Livermore Penelope Opt0 Opt3 Opt4 Compton Energy (MeV) 3− 10 2− 10 1− 10 110 2 10 3 10 Ratio (Sim/NIST) 0.9 0.95 1 1.05 1.1 3− 10 2− 10 1− 10 110 2 10 3 10 /g) 2 (cmρ/ p μ 10− 10 9− 10 8− 10 7− 10 6− 10 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 4 10 5 10 6 10 NIST XCOM Livermore Penelope Opt0 Opt3 Opt4 Photoelectric Energy (MeV) 3− 10 2− 10 1− 10 110 2 10 3 10 Ratio (Sim/NIST) 0.9 0.95 1 1.05 1.1 10 2 10 3 10 /g) 2 (cmρ/ conv γ μ 5− 10 4− 10 3− 10 2− 10 1− 10 NIST XCOM Livermore Penelope Opt0 Opt3 Opt4 Gamma Conversion Energy (MeV) 10 2 10 3 10 Ratio (Sim/NIST) 0.9 0.95 1 1.05 1.1 FIG. 2. Comparison of the attenuation coefficients for each individual photon process: Rayleigh scattering (top left), photoelectric effect (top right), Compton scattering (bottom left), gamma conversion (bottom right). The plots show the attenuation coefficients as calculated using Geant4 against the NIST XCOM data; the ratio of Geant4 results and the reference data is shown as well. The black dashed lines in the lower plot represent the uncertainties of the NIST XCOM data (rref ). The statistical uncertainty affecting the Geant4 simulation results is below 1%. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 26 ARCE et al.: G4-Med 26 collision stopping power data, that is available online in the NIST Reference Database. 43 Electronic and collision stopping powers are the same physical quantity; however, the ICRU Report No. 85 44 recommends the use of the specific term electronic. From this observation, the term electronic was adopted here. This technical test was developed for the regression testing of Geant4 for both low energy and high energy physics applications to demonstrate the level of agreement between available models of electron stopping powers. Here details of the simulation, results, and discussion are provided for electrons with an incident energy between 10 keV and 10 GeV. In the geant-val web interface, 12 the test has the name ElectDEDX. 3.B.1. Simulation setup Monoenergetic electrons originate in the center of a target. The simulation tests only the ionization processes of the Opt0,Penelope,Livermore,Opt3, and Opt4 EM constructors, in the case of no energy loss fluctuations and no generation of secondary particles. Assuming small energy losses, the stopping power is calculated as the energy deposited in the first step of the track, divided by the true step length, which takes into account multiple scattering correction. The electronic stopping power is calculated for targets made of Al, Ar, Cu, Au, and Pb, in order to represent a range of atomic numbers. Water is considered as a target as well because it is of interest for medical physics. The target materials are modeled from the Geant4 NIST material database, described in the Geant4 Application Developer Manual. 39 The ESTAR electronic stopping power values are calculated based on Bethe theory, with a density-effect correction evaluated according to Sternheimer, as described in the documentation of the NIST Standard Reference Database. 43 The uncertainties of the ESTAR electronic stopping powers for electrons are estimated to be 1–2% above 100 keV, 2–3% in low atomic number materials, and 5–10% in high atomic number materials between 10 and 100 keV. At energies below 10 keV the stopping powers from ESTAR are expected to be too large due to the omission of shell corrections and are recognized not to be accurate. 45 Therefore, we do not report data below 10 keV. 3.B.2. Results and discussion Figure 3shows the electronic stopping power and ratio of the simulation results with respect to the ESTAR data libraries, in the case of water, Al and Au. These two elements have been chosen as they represent low and high atomic numbers, respectively. The simulation results do not have any statistical uncertainty because there is no multiple scattering, no energy loss fluctuations and no secondary particles generation. The agreement between the simulation results and ESTAR data is within the uncertainty of the reference data for all target materials. Between 100 keV and 1 GeV, the difference between Geant4 simulation results and ESTAR data is <1%, below 100 keV the difference is within 3% for all models except for Penelope in Au, which is within a 5% agreement (still within the uncertainty of the reference data rref ). Above 1 GeV, the difference increases due to different bremsstrahlung models in Geant4 and ESTAR computations. The results also indicate some interpolation problems in Livermore stopping powers below 100 keV, which is however within the model uncertainty. 3.C. Electron backscattering test Electron backscattering is an important process in several physics applications including medical physics. It occurs when electrons, incident on a target, are scattered in the backward direction. The capability of properly reproducing this complex interaction in Geant4 has considerably improved in TABLE IV. Difference between Geant4 simulation results and NIST XCOM. Test Difference with respect to the reference data Opt0 Opt3 Opt4 Livermore Penelope Total ≤1rref Ray \1rref , in particular: <10% for E <10 keV, ≤5% for 10 keV <E<100 keV, <1% for E >100 keV <1rref, in particular: <10% for E ≤3 keV, ≤5% for 3 keV <E<10 keV, <1% for E >10 keV Photo <1rref, with exceptions at 1–2 MeV and E ≥500 MeV Comp 1rref , in particular: >5% for E<10 keV, ≤5% for 10 keV <E<20 keV, ≤1% for E > 20 keV \1rref 1rref 1rref , in particular: >5% for E<6 keV,≤5% for 6 keV <E<60 keV ≤1% for E >60 keV Conv ≤5% for 2 MeV, ≤3% for 3 MeV <E <10 MeV,≤1% for E >10 MeV ≤1% for E ≥2 MeV (<1rref )≤5% for 2 MeV, ≤3% for 3 MeV <E<10 Me V≤1% for E >10 MeV ≤1% for E ≥2 MeV (≤1rref ) rref is the 1 σuncertainty of the reference data. Ray: Rayleigh scattering; Photo: photoelectric effect; Comp: Compton scattering; Conv: pair and triplet production. Medical Physics, 48 (1), January 2021 27 ARCE et al.: G4-Med 27 low energy fluence where contributions of experimental artifacts to the uncertainty may be underestimated. 3.F. Fano Cavity test to verify the multiple scattering and boundary crossing algorithm This test is released as an extended example of Geant4 with the name FanoCavity. It is based on Poon et al. 64 and Kawrakow. 65 It was designed to check the accuracy of the condensed history (CH) electron transport, especially the stability of the related stepping algorithms with respect to increasing values of the maximum allowed energy loss along an individual electron step. In case of Geant4, the corresponding continuous step limit parameter is the dRoverRange which is the maximum allowed step length in units of fraction of the (charged) particle range. This test is available under the name FanoCavity in the geant-val web interface. 12 3.F.1. Simulation setup The different factors involved in the electron transport, that is, the step limitation, effects of energy loss, modeling of multiple Coulomb scattering, are tested using the Fano cavity principle described in Fano. 66 The model of ionization chamber used is the one described in Poon et al. 64 : a cylinder made of 5 mm water (G4_WATER) walls and a 2 mm cavity filled with steam (G4_WATER with a density of 1.0 mg/cm 3 ). A beam of 1.25 MeV gamma rays parallel to the cylinder axis traverses it. With this setup, under idealized conditions, the ratio of the dose deposited divided by the beam energy fluence must be equal to the mass energy transfer coefficient of the wall material. The needed equilibrium condition for charged particles is realized using the beam regeneration after each Compton interaction: the scattered photon is reset to its initial state, energy, and direction after the Compton process. Consequently, interactions are uniformly distributed within the wall material. It is important to mention, that unlike the other tests used in this benchmark, the Fano cavity test requires its special physics modeling conditions. Therefore, the test fully relies on custom, local to the test EM physics constructors with special models for ionization and Compton scattering. Ionization is simulated using a model similar to the standard G4Mol- lerBhabha (see the Geant4 Physics Reference Manual for details) with the density dependent correction term of the corresponding stopping power removed. Moreover, in order to have the same stopping power both in the wall and cavity, the bremsstrahlung process is not modeled. The special model for Compton scattering guarantees the conservation of the charged particle fluence by utilising the above mentioned beam regeneration. To speed up the simulation, it is possible to increase the Compton cross section and the secondary particles that have no chance of reaching the cavity (when the range is smaller than 0.8 times the distance to the cavity) are killed. To prevent the generation of δ-rays, the global production cut is set to 10 km, in order to be in the continuous slowing down approximation (CSDA). On top of these options, the finalRange (see Table 3) of the energy loss is set to 10 μm, which corresponds to a kinetic energy of 20 keV in water. As it was already mentioned, this test was designed to check the accuracy of the CH electron transport. Therefore, five different local physics lists were used in the benchmark all with exactly the same special description of the physics interactions except the Coulomb scattering. The Coulomb scattering was modeled exactly as in the Opt0,GS,Opt3, Opt4, and WVI constructors in case of Opt0*,GS*,Opt3*, Opt4*, and WVI*, respectively. The *is used in the notations in order to clearly indicate that the physics constructors used in this test are not identical to the corresponding Geant4 EM physics constructors except the modeling of the electron Coulomb scattering and the corresponding stepping algorithm. 3.F.2. Results and discussion Figure 8shows the dependency of the ratio of the simulated dose and the theoretical one as a function of the dRover- Range parameter value for different physics constructors discussed in the previous section. Opt0 and GS constructors utilize the Urban 38 and the GS 37 models, respectively, to simulate multiple Coulomb scattering of electrons (below 100 MeV) with their special settings recommended for high energy physics (HEP) simulation applications. The corresponding settings include looser stepping algorithms since HEP applications, in general, are more tolerant of mistakes in the electron stepping especially when it comes with a significantly increased computing performance. As it is expected, both local physics constructors Opt0and GSshow a strong dependence on the dRoverRange.Opt0*and GS*show a dRoverRan g e value 2− 10 1− 10 1 Dose ratio (Sim/Theory) 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 Opt0 Opt3 Opt4 GS WVI FIG. 8. Dependency of the ratio of the simulated dose and the theoretical one as a function of the dRoverRange for different EM physics constructors. The statistical error bars affecting the simulation results are smaller than the symbols. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 34 ARCE et al.: G4-Med 34 deviation from the theoretical data values between approximately 1% and 7%, depending on the value of the dRover- Range. The same two multiple scattering models are used to describe the Coulomb scattering in Opt3(Urban) and Opt4 (Goudsmit–Saunderson) but with their more accurate settings, including the stepping algorithm, that are recommended for precision in critical applications. Accordingly, both multiple scattering models show significantly better stability under these settings. Opt3*shows an agreement between 1% and 2%, depending on the value of the dRover- Range. For the default value of the dRoverRange (0.2) (see dRoverRange for electrons and positrons in Table 3), the agreement is approximately 0.3%. Opt4provides a remarkably small (<0.2%) deviation from the theoretical dose value practically independently from the dRoverRange parameter value. In addition to Opt4, that contains the GS multiple scattering model with its most accurate configuration, 37 the WVIconstructor, that utilizes the so called mixed-simulation description of Coulomb scattering, also provides a high level of accuracy and stability (<0.2%). These results are in a perfect agreement with the findings described in a recent study, 67 in which a maximum deviation from the theoretical dose values of 0.16% was reported when the GS model with its Opt4 settings were used. Therefore, this test shows that Geant4 can transport electrons accurately without the need of applying significant step-size reduction, and irrespective of dRover- Range when using the Opt4 constructor, in the geometrical setup considered. 67 The Fano test subject of this section could be repeated by including photon transport and secondary particle production for completeness. It is recommended to repeat the test in the user’s geometry of interest. 3.G. Low-energy electron dose point kernels The simulation of radial energy deposition profiles from isotropic sources of electrons has proven to be a useful method of evaluating the performance of MC codes used in medical physics, in particular for the usage of radionuclides in targeted cancer therapy. 68,69 Although experimental data on electron Dose Point Kernels (DPK) in liquid water —the main component of biological medium —currently do not exist, preventing a full validation, we propose a benchmark comparing Geant4 performance to the EGSnrc Monte Carlo code. This application code can be found in Geant4 as the TestEm12 extended electromagnetic example. The test has the name LowEElectDPK in the geant-val web interface. 12 3.G.1. Simulation setup In this setup, electrons are emitted isotropically into a 4π solid angle from a point source placed in a spherical liquid water (defined as G4_WATER) volume. In this work, results are presented for 10, 15, 100, and 1000 keV incident monoenergetic electrons. At each simulation step, the energy deposition is randomly distributed along the step; the radial distribution of energy deposition from the emission point is then recorded in a histogram with a weight equal to the energy deposition value collected in the step. Radius values are scaled to the CSDA range (r0) of the electron at the selected incident energy (E0). The DPK distribution is then normalized to the number of incident electrons, to the selected histogram bin width, and to the incident kinetic energy value. Results are presented for 10 5 incident electrons. The simulation results have a statistical uncertainty lower than 3%. Opt0,Opt3,Opt4,Livermore, and Penelope have been adopted to describe the EM physics interactions. In addition, a maximum step size equal to the bin width of the histogram is applied to control the spatial accuracy of the energy deposition. 3.G.2. Results and discussion Figure 9presents the scaled DPK distributions obtained for each incident electron energy using the Geant4 electromagnetic physics constructors. The curve obtained with Opt0 is not shown as this constructor produces the same results of Opt3. These profiles are compared to EGSnrc predictions (Mainegra-Hing et al, 70 computed as described in the PhD thesis of Perrot 71 ). In this comparison with EGSnrc, energy loss fluctuations have not been considered in the simulations. All Geant4 EM physics constructors produce similar profiles as a function of scaled radius and incident energy. Opt3 shows lower maxima at 10, 15, and 100 keV, and larger profiles below about ðr=r0Þ¼0:4 than the EGSnrc simulation data. In the case of Opt4,Livermore, and Penelope constructors, one can observe a better agreement (within approximately 3%, corresponding to the statistical uncertaity of the Geant4 simulation results) with EGSnrc simulation data at all incident energies, thanks to the GS multiple scattering model, 37 which has been recently introduced in those three physics constructors (in Geant4 version 10.5, as the best alternative to the G4UrbanMscModel). This agreement is obtained under the condition that energy loss fluctuations are ignored in Geant4. Indeed, EGSnrc simulation data do not take into account these fluctuations. Such agreement is not observed when energy loss fluctuations are taken into account in the Geant4 simulations (data not shown). This underlines that, under this condition, the GS model used in the three above constructors is able to perform as EGSnrc and can provide more accurate simulation data. It remains, however, impossible to fully validate such simulations in the absence of experimental data in liquid water in this energy range. At higher incident electron energies, effects of energy loss fluctuations are not important and Geant4 Opt4 with GS model and EGSnrc results agree well, so it is possible to conclude that both simulation tools (on the one hand Geant4 Opt4 constructor with GS model, and EGSnrc on the other hand) can be regarded as a gold standard for such simulations. We show in this study the full benefit of the newly implemented GS model for the simulation of electron multiple scattering in liquid water, when compared to EGSnrc Monte Carlo code. Medical Physics, 48 (1), January 2021 35 ARCE et al.: G4-Med 35 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2EGSnrc Livermore Penelope Opt3 Opt4 1000 keV 0 r/r 0 0.2 0.4 0.6 0.8 1 1.2 0.9 0.95 1 1.05 1.1 0 0.2 0.4 0.6 0.8 1 1.2 ) 0 )/d(r/r 0 d(E/E 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2EGSnrc Livermore Penelope Opt3 Opt4 100 keV 0 r/r 0 0.2 0.4 0.6 0.8 1 1.2 Model/EGSnrc 0.9 0.95 1 1.05 1.1 0 0.2 0.4 0.6 0.8 1 1.2 ) 0 )/d(r/r 0 d(E/E 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2EGSnrc Livermore Penelope Opt3 Opt4 10 keV 0 r/r 0 0.2 0.4 0.6 0.8 1 1.2 Model/EGSnrc 0.9 0.95 1 1.05 1.1 0 0.2 0.4 0.6 0.8 1 1.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2EGSnrc Livermore Penelope Opt3 Opt4 15 keV 0 r/r 0 0.2 0.4 0.6 0.8 1 1.2 0.9 0.95 1 1.05 1.1 FIG. 9. Scaled DPK distributions for incident electrons of 10, 15, 100, and 1000 keV in liquid water, simulated using the five Geant4 EM physics constructors. Ratios of Geant4 and EGSnrc results are reported as well. Dashed lines indicate an agreement of 3%, which corresponds to the statistical uncertainty affecting the Geant4 Monte Carlo simulation results. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 36 ARCE et al.: G4-Med 36 3.H. Microdosimetry test 3.H.1. Introduction Microdosimetric spectra of lineal energy (or specific energy) are historically being used for describing radiation quality (see ICRU Reports 40 72 and 36 73 ), and many theoretical estimates of the relative biological effectiveness (RBE) of therapeutic beams are based on such calculations. 74,75 The use of the MC method for the calculation of stochastic energy deposition in an irradiated volume is facilitated by the use of condensed-history models in order to reduce simulation time, especially when we are dealing with radiotherapeutic energies. A dedicated example available in the Geant4 extended examples, called microyz, offers a way to calculate microdosimetric spectra in liquid water target spheres. Systematic studies of the microdosimetric performance of the low-energy condensed-history models available in Geant4 (i.e., Livermore and Penelope) and the track structure models available in Geant4-DNA 76,77-79 have been recently carried out for submicron volumes for the energy range 50 eV— 10 keV. 20,80,81 Here we investigate the microdosimetric performance of the Opt4 constructor at energies of radiotherapeutic interest (10 keV–1 MeV) in terms of calculating the frequency-mean lineal energy in liquid water spheres with a diameter of 1 μm (ICRU sphere). This test has been included in the G4-Med benchmarking system for regression testing purposes only. The test has the name microyz in the geant-val web interface. 12 3.H.2. Simulation setup The extended example microyz was used to calculate the probability density function of lineal energy by scoring the energy deposited by monoenergetic electrons within target spheres of liquid water (1 μm diameter) randomly overlapping their track. The procedure of scoring the energy deposition is provided in detail in Kyriakou et al. 20 For all simulations, the global production cut was set equal to the tracking cut. The effect of the step-size limit and tracking cut is also investigated. To obtain a statistical uncertainty below 1–2%, the number of electron tracks simulated was 10 6 for electron energies up to 100 keV and 10 5 above 100 keV. 3.H.3. Results and discussion Figure 10 presents the frequency–mean lineal energy as a function of incident energy for 10, 50, 100, 500, and 1000 keV electrons using two different values for the tracking cut, 100 eV and the commonly used value in condensed-history simulations of 1 keV. Results are presented for three different step-size limits (called SL in the Figure), the default step-size limit which for this test is equal to 1 mm, a step-size limit equal to the sphere diameter (1 μm), and a small step-size limit equal to 1/10 the sphere diameter (100 nm). We observe that for both values of the tracking cut (1 keV and 100 eV), the default step-size limit (equal to 1 mm in the present energy range) results in a significant overestimation that increases with electron energy (at 1 MeV incident electron energy it reaches a factor of 6 for the 100 eV cut, and a factor of 26 for the 1 keV cut). A step-size limit equal to the sphere diameter (1 μm) also results in sizeable overestimation (20–30% for 100 eV cut and 30–50% for 1 keV cut) compared to the small step-size limit. The influence of the tracking cut is reduced when smaller step-size limits are chosen. For example, with the small step-size limit examined (100 nm), decreasing the tracking cut from 1 keV to 100 eV affects the frequency–mean lineal energy by <7%. The test microyz assumes by design discrete simulation, that is, each individual interaction leading to any modification of the particle trajectory (energy, direction) is modeled explicitly as point-like interaction and is recorded during the simulation. This assumption is broken when employing the CH simulation technique which leads to the observed sensitivity to the CH step size. The extent of this artificial step size dependence is determined by the relation of the step size distribution to the size of the target sphere. Reducing this step size dependence requires that several steps are done by electrons inside the scoring sphere which may be achieved by defining a step-size limit less than the scoring sphere dimensions. For the commonly used tracking cuts studied in the present work (100 eV to 1 keV), a safe value for the step-size limit is equal to the 1/10 of sphere diameter. 3.I. Brachytherapy test The Brachytherapy Geant4 advanced example is used to calculate the dose rate distribution of a high dose rate Ener g y (keV) 10 2 10 3 10 m)µ (keV/ F y 1− 10 1 10 SL-Default, cut-100 eV SL-1000 nm, cut-100 eV SL-100 nm, cut-100 eV SL-Default, cut-1 keV SL-1000 nm, cut-1 keV SL-100 nm, cut-1 keV FIG. 10. Frequency–mean lineal energy as a function of the incident electron energy, using two different values for the tracking cut 100 eV and 1 keV. SL is the step-size limit. SL was set equal to 1 mm (default value for this test), 1μm and 100 nm. Error bars are not included since they are smaller than the symbols. The plot demonstrates that SL should be substantially less than the size of scoring volume. [Color figure can be viewed at wileyonlinelibrary.c om] Medical Physics, 48 (1), January 2021 37 ARCE et al.: G4-Med 37 brachytherapy 192 Ivr source in water. We compared the results of the simulation to the reference data published in Granero et al, 82 which were obtained with Geant4 version 7.1. Therefore, the test has a regression testing focus and is available in the geant-val interface 12 with the name Brachy-Ir. 3.I.1. Simulation setup The 192 Ir Flexisource, described in Granero et al, 82 has been modeled in the center of a water box (modeled as G4_WATER) with 30 cm size. The photon radiation field, detailed in Granero et al, 82 is emitted from the iridium radioactive core. Opt0,Opt3,Opt4,Livermore, and Penelope have been tested. A global production cut was fixed equal to 0.05 mm. A Geant4 scoring mesh was defined to calculate the energy deposition in the plane containing the source. The plane is subdivided in voxels with size equal to 0.25 mm along x, y and z.10 8 histories were simulated to obtain a statistical uncertainty of 1.5% in the results. The same statistical uncertainty affects the reference data. 82 3.I.2. Results and discussion Figure 11 shows the radial dose rate distribution about an 192 Ir brachytherapy source, as a measure of the energy deposition per unit of mass, along the transverse axis of the source, 90°from the source axis. As it can be observed in Fig. 11, the simulation results obtained with any Geant4 EM constructor agree with the reference within the uncertainty of the simulation data rref (1.5%), for almost all points, up to a distance of 8 cm from the radioactive core. At 10 cm, depth the agreement between Geant4 results and the reference data is within 3% (corresponding to 2 rref ) for all the EM constructors. No recommendation to use any of the EM constructors can be done at this stage with this test, because the reference data are derived from Geant4 as well (Geant4 7.1). 3.J. Monoenergetic x-ray internal breast dosimetry test An accurate and controlled evaluation of the radiation dose delivered during x-ray-based breast imaging is part of quality control procedures 83 and necessary for risk estimation (Dance et al 84 ). This simulation aims to compare the radiation dose predicted by means of Geant4 and experimental measurements performed at the SYRMEP beamline of the ELETTRA synchrotron light source (Trieste, Italy). Dose measurements were performed using thermoluminescent dosimeters, TLD-100H (ThermoFisher Scientific, Waltham, MA, USA), in absolute terms and down to the local deposition level, in a mammographic acquisition setup installed at the SYRMEP beamline. 85 The test has the name Mammo in the geant-val interface. 12 Details about the test and the experimental procedure can be found in Fedon et al. 21,22 3.J.1. Simulation setup The geometry implemented in the simulation is shown in Fig. 12 . A homogeneous semi-cylindrical breast phantom (with the dimensions of 18 cm ×10 cm) consisting of four 1-cm thick slabs was positioned within the plates of the compression system. The phantom (CIRS Inc.,Norfolk, VA, USA) reproduces the x-ray attenuation property of a breast with a 50% adipose and 50% fibroglandular tissue composition. Monoenergetic, parallel 20 keV photons are emitted from a rectangular, planar x-ray source (20 cm ×12 cm) toward the breast phantom. This source geometry models the monoenergetic nature of the SYRMEP beamline of the ELETTRA synchrotron when the double-crystal Si monochromator is set to 20 keV. The scored physical quantity in the simulation was the dose deposited in thirty sensitive volumes (i.e., each TLD) positioned on the xy phantom plane at four different phantom depths (i.e., the scoring planes shown in Fig. 12 ). The TLDs were modeled in terms of physical dimensions (i.e., 3.2 mm ×3.2 mm ×0.38 mm) and relative chemical composition ( 99.5% LiF, 0.2% Mg, 0.004% Cu, and 0.296% P) according to the manufacturer. For each simulation, 2 109photons were simulated to obtain a statistical uncertainty lower than 1% in all the scored quantities, estimated using the method of Sempau et al. 86 The experimental TLD procedure and the uncertainty analysis is 0246810 Dose rate distribution 2− 10 1− 10 1 10 Ref Livermore Penelope Opt0 Opt3 Opt4 Distance from source (cm) 0246810 Sim/Ref 0.96 0.98 1 1.02 1.04 FIG. 11. Radial dose rate distribution with respect to r, distance from the center of the 192 Ir brachytherapy source. The radial dose distribution is normalized at r=1 cm. Black squares in the top figure represent the reference data (from Granero et al82), the statistical uncertainties of the data are within the symbols. The bottom plot shows the ratio of the Geant4 simulation results and the reference data. The dashed lines indicate the statistical uncertainty affecting both the simulation results obtained with Geant4 10.5 and the reference data published in Granero et al,82 obtained with Geant4 7.1. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 38 ARCE et al.: G4-Med 38 described in detail in Fedon et al. 21 To normalize the photon fluence in the simulation to that used in the experiments, a scale factor was used, defined as the ratio between the experimentally kinetic energy released per unit mass in air (kerma) and the simulated air kerma, analytically evaluated in the MCsimulation. The constructors Opt0,Opt3,Opt4,Livermore, and Penelope were tested. A global production cut of 0.7 mm was adopted. 3.J.2. Results and discussion Dose comparison results for the depth of 3 cm are presented on the right side of Fig. 12. Data for the other depths can be found on the geant-val web interface. 12 In general, all physics constructors produce results that agree with each other within the combined experimental uncertainty. The mean combined uncertainty for the depth of 3 cm is 5.7% (uncertainty range from 5% to 7.7%). 21 It should be pointed out that a systematic bias appears to be present, since the MC data results consistently overestimated the experimental data. This overestimation is, however, within the combined experimental uncertainty. Among the Livermore,Penelope,Opt3, and Opt4 constructors, no clear trend is observed that can suggest the use of one over the others, since the results are within an accuracy of 5% with only few exceptions for Opt3 (ratio plot in Fig. 12). However, we noticed that the performance of Opt0 worsens with increasing depth, confirming previously observed trend. 87 A maximum relative difference of 7.7% is observed at 3 cm depth when using this constructor (position 7 in Fig. 12), whereas with the other EM constructors there is a better agreement with a largest difference of 6%. An accuracy of 5% might be considered large for a MC benchmark. However, in the case of breast dosimetry, this is a remarkable results considering the difficulties and inherent uncertainty in these types of measurements, where the recommended uncertainty range 12.5%. 21 Thus, these results, within the experimental uncertainty, can be considered a valid benchmark for this specific application. 4. HADRONIC PHYSICS BENCHMARKING TESTS Hadronic interactions are paramount in hadron therapy. In proton therapy, incident protons generate a secondary neutron field which scatters in the patient producing recoil protons, which will then deposit energy in the patient outside the target tumor and potientally in organs at risk. 88 In addition, it recently became evident that the few fragments generated in proton–tissue interactions cannot be neglected 89 because they can affect the average linear energy transfer (LET) values, thus changing the biological outcome. Such fragments are mainly produced at the entrance in the patient where the energy of the protons is higher . 89 In carbon ion therapy, a beam with an initial energy of 400 MeV/u, will have approximately 70% of the initial carbon ion beam undergo fragmentation before reaching the tumor target. Such fragments contribute to the dose in-field and are responsible for the dose delivered out-of-field, that is, laterally to the beam and beyond the Bragg peak. 90 The total contribution to the dose is approximately 30% for a carbon ion spread out Bragg peak with a maximum energy of 290 MeV/u. It is therefore crucial to benchmark the hadronic physics component of Geant4, which is often used as MC FIG. 12. Left and center: Dosimeter placement and irradiation geometry modeled in the test. Drawings are not to scale. Right: Dose comparison between experimental data (black symbols) and the five Geant4 EM physics constructors for the depth of 3 cm. All the other depths are available in the geant-val interface. The black error bars represent the combined standard experimental uncertainty (with a coverage factor, k =1), while the color ones are referred to the simulations data. The bottom plot shows the ratio between Geant4 and experimental data. The black dashed lines represent the 5% accuracy, a typical threshold accuracy considered in breast dosimetry. [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 39 ARCE et al.: G4-Med 39 code for hadron therapy. An accurate description of the same physical interactions is important for radiation protection studies as well. This section describes tests in G4-Med where only hadronic physics processes and models are tested and the electromagnetic physics is not considered in the simulation (Section 5is dedicated instead to tests which activate both the electromagnetic and the hadronic physics). The tests described in both sections (here and Section 5) were performed in the energy range of interest for hadron therapy. The test of section 4.A benchmarks the total hadronic inelastic cross section, which is described with the Glauber–- Gribov model in Geant4 (see the Geant4 Physics Reference Manual) against experimental measurements. The tests subject of Sections 4.B. and 4.C benchmark different hadronic ion inelastic scattering constructors, G4Ion BinaryCascade,G4IonQMDPhysics and G4IonINCLXXPhy- sics, to describe the final state of carbon ion hadronic inelastic interactions. Table 7summarizes the main features of the three constructors modeling ion fragmentation under study. It is important to note that the constructors adopt the same total inelastic cross section based on the Glauber–Gribov model, while providing different descriptions of the final state of the interactions (yield, energy, and angular distributions of the secondary particles). The three constructors handle the interactions of deuteron, triton, alpha particle, 3 He, and heavier nuclei. G4IonBinaryCascade (BIC) activates the LightIon BinaryCascade, which describes the interaction between the projectile and each participating single nucleon of the target nucleus described as a Gaussian wave packet . 91 G4IonQMD Physics activates the Quantum Molecular Dynamics (QMD) model. In this case, all nucleons of the target and projectile have their own wave function. 92 G4IonINCLXXPhysics uses the approach of the Li` ege intranuclear-cascade model called here INCL. 93,94 The target nucleons are treated as a free Fermi gas in a static potential well, whereas the projectile is modeled without Fermi motion. As result of this asymmetric treatment, the projectiles which can be modeled with INCL are limited to mass numbers less than A =19; otherwise, when the target mass is below A =19, target and projectile are interchanged internally and when both mass numbers are above A =19, the fragmentation interaction is modeled with BIC. In the high energy range, all the ion hadronic inelastic scattering constructors adopt the Fritiof parton string model (FTF). 95 In the energy overlap region (see Table 7), an interpolation between the two models is done. 4.A. Test of nucleus–nucleus hadronic inelastic scattering cross sections This test calculates the total cross section of hadron–nucleus and nucleus–nucleus collisions. The cross sections are then compared to reference experimental measurements publicly available in the Experimental Nuclear Reaction Data (EXFOR) database. 96 EXFOR provides libraries containing an extensive compilation of experimental nuclear reaction data. The total inelastic scattering hadronic cross sections are calculated for incident protons and carbon nuclei. The test was named NucNucInelXS in the geant-val web interface. 12 4.A.1. Simulation setup The benchmark test retrieves the total hadron–nucleus and nucleus–nucleus inelastic cross sections, which are stored in a data table via the use of the class G4HadronicProcessStore in the initialization phase of the simulation. The data table is then compared to the reference data. Only the Geant4 prebuilt physics list QGSP_BIC was benchmarked in this test as the total inelastic hadronic cross section in all the hadronic physics constructors, used in any prebuilt Geant4 physics list, are TABLE VI. References for the experimental datasets used in the electron backscattering test with the energy range and the target material. Dataset name Reference Material Energy range Sandia Lab. (1980) 46,47 Al, Au, Si 0.032 MeV–1.033 MeV Reimer, Tollkamp (1980) 48 Au, Si 1 keV - 30 keV Hunger, Kuchler (1979) 49 Au, Si 4–40 keV Cosslett, Thomas (1965) 50 Si 5–45 keV Bongeler (1993) 52 Si 1–10 keV Bishop (1963) 53 Au, Si 5–30 keV Heinrich (1966) 54 Au, Si 30 keV Neubert (1980) 55 Al, Si 15-60 keV Drescher (1970) 56 Au, Si 10–100 keV Wittry (1966) 57 Au, Si 5, 30 keV Bronstein (1969) 58 Au, Si 0.1–4keV El Gomati (1997) 59 Si 0.6–6keV The first column reports the dataset names used in Figs. 4 and 5. TABLE VII. Physics models activated in the ion hadronic inelastic scattering constructors under investigation. Constructor Physics models G4IonBinaryCascade G4BinaryLightIonReaction*for E<4 GeV/uFTF for E>2 GeV/u G4IonQMDPhysics G4BinaryLightIonReaction*for E<110 MeV/uQMD for 100 MeV/u<E<10 GeV/uFTF for E>1 GeV/u G4IonINCLXXPhysics INCL for E<3 GeV/uFTF for E>2.9 GeV/u * : the G4BinaryLightIonReaction activates the Geant4 Precompound Model (G4PreCompoundModel, Geant4 Physics Reference Manual). Medical Physics, 48 (1), January 2021 40 ARCE et al.: G4-Med 40 based on the Glauber representation with the Gribov screening correction on inelastic screening (GG model). 97 - 99 The total inelastic scattering cross sections of p þ12 6C; pþ16 8O;pþ27 13Al;pþ40 20Ca;12 6Cþ12 6C;and 12 6Cþ27 13Al are compared with the experimental data available in EXFOR. Such reactions were selected because of relevance for hadron therapy and because EXFOR provided an adequate number of reference experimental data. 3 10 Cross Section (mb) C 6 12 Proton + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) 0.6 0.8 1 1.2 1.4 Ratio (Exp/Sim) O 8 16 Proton + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) 3 10 Cross Section (mb) Al 13 27 Proton + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) 0.6 0.8 1 1.2 1.4 Ratio (Exp/Sim) Ca 20 40 Proton + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) 3 10 Cross Section (mb) C 6 12 Carbon + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) 0.6 0.8 1 1.2 1.4 Ratio (Exp/Sim) Al 13 27 Carbon + performed with QGSP_BIC 2 10 3 10 Energy (MeV/u) FIG. 13. Total hadronic inelastic scattering cross sections as a function of the kinetic energy of the projectile, calculated by means of the QGSP_BIC physics list. To note, differently from the other figures depicting the results of the tests of G4-Med, in the bottom plot ratios of reference data and Geant4 simulation results (and not the other way round) have been plotted for clarity reasons. Red curve: Geant4 cross section; data points: EXFOR reference experimental data.96 [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 41 ARCE et al.: G4-Med 41 4.A.2. Results and discussion Figure 13 shows the total inelastic cross sections calculated by means of the QGSP_BIC, as a function of the kinetic energy of the projectile, compared to the experimental data of the EXFOR database. Overall, for both incident protons and carbon ions, an agreement within 10% was observed for most of the incident projectile energies. Significant differences (20%–40%) were found for proton energies below 20 MeV in the case of a carbon target. These differences are caused by the large variations in the experimental inelastic cross sections for p+ 12 C, likely due to resonances that enhance the cross section, particularly near 10.5 MeV proton energy (e.g., Dyer et al, 100 Davids et al, 101 ). These variations will tend to arise for low energy proton induced reactions, particularly for light targets where the density of states is low. In the case of 12 C+ 27 Al, the data were consistently overestimated of about 10%. This reaction should be further investigated. 4.B. 62 MeV/u 12 C fragmentation test This test concerns the nuclear interaction models available in Geant4 for low-energy carbon ions. The name of the test is LowEC12Frag in the geant-val web interface. 12 The models were benchmarked against double-differential cross sections of the secondary fragments produced in the 12 C fragmentation at 62 MeV/u on a thin carbon target. This dataset has been acquired from De Napoli et al. 102 4.B.1. Simulation setup As described before, the two models available in Geant4 at low energy are the Binary Light Ions Cascade (BIC) 91 and the Liege Intranuclear Cascade (INCL). 93,94 There is a third model available in Geant4 to simulate the first part of a nuclear interaction, namely, the Quantum Molecular Dynamics (QMD). 92 However, QMD has, in its default physics constructor class (G4IonQMDPhysics), a lower energy threshold at 100 MeV/u. Below this threshold it uses BIC. Therefore, 3− 10 2− 10 1− 10 1 10 2 10 3 10 He at 62 MeV/u 4 →C nat C + 12 °= 2.2θ 3− 10 2− 10 1− 10 1 10 2 10 3 10 °= 7.6θ 0 20 40 60 80 100 3− 10 2− 10 1− 10 1 10 2 10 3 10 Exp. Data BIC INCL °= 18θ °= 4.9θ °= 14.4θ 0 20406080100 °= 21.8θ E [MeV/u] [mb/sr/(MeV/u)]Ω∂E/∂/σ 2 ∂ He at 62 MeV/u 4 →C nat C + 12 FIG. 14. Double-differential cross sections measured at different angles of α-particle production in the 12 C interaction with a thin C target at 62 MeV/u as a function of the α-particle kinetic energy. Experimental data from De Napoli et al 102 (in black) are compared with the two models available in Geant4 for ion interactions at this energy, namely INCL (in blue) and BIC (in red). [Color figure can be viewed at wileyonlinelibrary.com] Medical Physics, 48 (1), January 2021 42 ARCE et al.: G4-Med 42 in this test, we decided not to benchmark the QMD model. This selfsame benchmark with QMD included, performed with Geant4 10.4, can be found in Mancini et al. 23 In order to reduce the computation time, all interactions but the hadronic inelastic ones have been switched off. All secondaries are discarded after being produced and the target is much longer than the hadronic inelastic interaction length. In this way, all primaries undergo an inelastic interaction, which is also the only process simulated. Secondaries are saved immediately after being produced and the event interrupted. Data are selected to match the geometrical acceptance and the energy resolution of the experiment. The obtained spectra are scaled by the total inelastic cross section. 4.B.2. Results and discussion Figure 14 shows the comparison of the double-differen- tial cross sections of α-particles production at different emission angles. BIC shows a doubly peaked structure. The one at higher energy is due to the fragment produced in the statistical de-excitation of the projectile remnant, while the lower energy one comes from the de-excitation of the target. BIC underestimates the formation of fragments in the mid-rapidity region, here at roughly 30 MeV/u of kinetic energy of the emitted fragment, by up to one order of magnitude at small angles. Its minimum is approximately two decades smaller than the two neighbors regions at all angles, while the projectile-like and targetlike fragments formation is overestimated for all angles. A possible explanation could be that BIC approach is based on a time-invariant optical potential and this leads to an underestimation of the formation of a neck fragmentation events 103,104 in the overlapping region, roughly at mid-ra- pidity in semicentral reactions. On the contrary, INCL shows a single distribution peaked at lower energy, with respect to the experimental peak. The INCL predictions overestimate by around a factor ten the production of αparticles below 62 MeV/u but are compatible with the experimental data for particles produced with higher kinetic energy. This could be due to its complete-fusion model. Here we show only the plot with the comparison of the αparticle production. All other plots, with the different fragments, can be found at the geant-val web interface. 12 In conclusion, the results show that both of the tested models, BIC and INCL, exhibit limitations in reproducing doubly differential cross sections of fragments produced in the interaction of 12 C with a thin carbon target. Efforts are underway to interface new models to Geant4 dedicated to nuclear interactions below 100 MeV/u. 105,106 4.C. 300 MeV/u 12 C ion charge-changing cross section test The goal of this test is to validate the partial and total charge-changing cross sections of 12 C ions with energy 300 MeV/u as simulated by Geant4 against experimental data published in the literature by Toshito et al, 24 obtained with an emulsion plate in the NIRS P152 experiment. The test is named C12FragCC in the geant-val web interface. 12 The partial charge-changing cross section to B, Be, and Li fragments is about (428 21) mb, while the total is (1183 52) mb (including the production of B, Be, H, He, Li, N, O, α, deuteron, proton, neutron, and triton), accounting for approximately 36% with respect to the other ion species in the experiment. Therefore, a correct modeling of the carbon charge-changing process is needed for an accurate calculation of the dose in carbon ion therapy, especially out-of- field where organs at risk may be located, the LET and the radiobiological effectiveness (RBE). 4.C.1. Simulation setup In this simulation, all electromagnetic processes and decay physics are switched off and only hadron and ion transport processes are used to retrieve the carbon ion charge-changing cross section. The target geometry is a cubic water phantom with a 10 m length. The water is defined as G4_WATER in the Geant4 simulation. Carbon ions are irradiated from the surface of the phantom. Only projectile-like fragments were considered in this work. Target-like fragments are also important to the dose; however, it isdifficulttomeasuretheircrosssectioninanexperiment.When an interaction occurs in the simulation, the distance from the initial point to the interaction point is summed up as the track length only for projectile-like fragments which can be identified as they travel to the forward region (momentum along the initiated direction >600 MeV/c/u). The partial cross sections of B, Be, and Li isotopes were calculated by means of the simulation. This choice was dictated by the availability of experimental data in Toshito et al. 24 4.C.2. Results and discussion The results of the test are shown in Fig. 15 and summarized in Table 8. The partial cross sections calculated by means of the G4IonQMDPhysics of B, Be, and Li isotopes are 144.1, 77.90, and 97.66 mb, respectively. An agreement within the uncertainty of the reference data was observed for the total 12 C charge-changing cross section and for the Li isotope partial cross section. Differences of approximately 18% and 34% were found for the production of Be and B isotopes, respectively. The isotope production cross sections have a similar trend when substituting QMD with either BIC or INCL. The total fragmentation cross section is almost the same for all the ion physics constructors. 5. ELECTROMAGNETIC AND HADRONIC PHYSICS BENCHMARKING TESTS The tests included in this section activate both electromagnetic and hadronic physics processes, using prebuilt Geant4 physics lists. QGSP_BIC_HP,QGSP_BERT_HP, and Medical Physics, 48 (1), January 2021 43 ARCE et al.: G4-Med 43 was simulated for the correct reconstruction of the modulated beam (clinical Spread Out Bragg Peak or SOBP). A total of 3:6108histories were simulated in each simulation. Dose as a function of depth is calculated in a voxelized water phantom positioned at the end of the beam line. The water tank was divided into 400 ×400 ×0.01 mm 3 segments to reproduce the real experimental conditions. The water material is modeled with G4_WATER . Dose, fluence, and dose-aver- aged LET of the primary proton beam and generated secondaries were calculated in the simulations; αand βvalues were determined using equations (3) and (4), along with the LUTs. The QGSP_BIC_HP physics list was used. The dose-aver- aged LET at the cells was 4.5 keV/μm. The global production cut was set to 0.01 mm. 5.E.2. Results and discussion Figure 21 shows the SF curves as derived from the experimental measurements and the Geant4 simulation. The agreement between experimental data and Geant4 simulations data was evaluated applying the v2test in the case of two independent distributions. We obtained a v2value of 4.23 and 3.64 for the DU145 and MDA cell lines, respectively. The v2test confirmed the good agreement between the two distributions even if, as expected, at doses >3 Gy the differences become more evident (well above the 20%). 27 6. SUMMARY AND CONCLUSIONS G4-Med is a group of currently 18 tests, regularly executed on the CERN computing infrastructure via the geant-val platform, to benchmark Geant4 against reference data for medical physics applications. G4-Med can also be used for regression testing purposes of Geant4. The results of the tests are provided to the Geant4 user community on-line via the geant-val web interface. 12 This work was focused on the description of the tests of G4-Med and on the results of the benchmarking of Geant4 10.5 against reference data. Table XI is intended to provide a summary of the main results of the electromagnetic physics tests, subject of Section III. We encourage the readers to refer to the specific tests of interest, for a more detailed analysis of the results in specific scenarios of application of Geant4. The agreement is defined based on the discussion of the results of each individual test in Section III.SS and GS are not included in the Table as they have been used in a very limited set of tests. In the case of the test concerning photon attenuation coefficients in water (PhotonAttenuation), slightly better agreement with respect to reference data was found for Opt4. The test includes one material only at this stage and we will expand it to other materials in the near future. We will also consider to extend the comparison of Geant4 to other reference data. The electronic stopping power test (ElectDEDX) showed an agreement with ESTAR within the reference data uncertainty (1 rref ). This test is useful for regression testing purposes as it monitors a physical quantity important for the calculation of energy deposition in a target. The electron backscattering test shows an agreement with respect to the available experimental data that clearly depends on the electron energy range and the Geant4 EM physics constructor. In particular below 5 keV the results should be taken with caution for any constructor, including the suggested -1 Ω) 0 (N/N 2 4 6 8 10 12 14 16 18 Thickness = 288 mm, Z = 1 Angle (deg) 2−0246810 Ratio (Sim/Exp) 0.5 1 1.5 2 2.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Thickness = 347 mm, Z = 4 Angle (deg) 1−01234 0.5 1 1.5 2 2.5 -1 ) Ω)(MeV 0 (N/N 0 0.005 0.01 0.015 0.02 0.025 0.03 Thickness = 159 mm, Z = 2, Angle = 3deg Fragment Energy (MeV) 500 1000 1500 2000 Ratio (Sim/Exp) 0.5 1 1.5 2 2.5 Exp BIC QMD INCL FIG. 20. Example angular and energy fragment distributions comparing experimental measurements against alternative models available in Geant4 for a 400 MeV/u mono-energetic 12 C ion incident upon water. Left and Middle: Angular distribution of H (left) and Be (middle) produced with a water thickness of 288 mm and 347 mm, respectively. Right: An example energy distribution of He fragments recorded at an angle of 3°from the center of the 12 C ion beam when incident upon 159 mm of water. The dashed lines on the bottom ratio plots indicate the experimental uncertainty rref. [Color figure can be viewed at wileyonline library.com] Medical Physics, 48 (1), January 2021 50 ARCE et al.: G4-Med 50 ones. The best EM physics constructors to model the electron backscattering were found to be Opt4,SS,Livermore and Penelope. For electron forward scatter, the angular distribution of electron fluence at 1.18 m calculated with Opt4 was significantly underestimated (>1 standard deviation) in comparison to experimental data for foils of higher Zthan Be by 2–5%, with calculated results comparable to or better than the comparison with the other physics constructors. For bremsstrahlung from thick Be, Al, and Pb targets at radiotherapy energies, bremsstrahlung yields (≤1–2 standard deviations) were in better agreement with experimental data when using Opt3 and Opt4. For these constructors, the differences were significant (>1 standard deviation) at larger angles for the higher Ztargets (≥60°). The Fano cavity test (FanoCavity) was designed specifically to check the accuracy of the condensed history electron transport and this test demonstrates that the GS multiple scattering model (included in Opt4,Livermore, and Penelope) provides a high level of accuracy and stability. Similar results were obtained for the WVI*constructor. The Dose Point Kernel test (LowEElecDPK) demonstrates that the Opt4 constructor provides the best agreement with the selected standard (EGSnrc). This test is currently used as a regression testing benchmark for Geant4 allowing to verify the stability of DPK profiles along with Geant4 updates, especially when electron multiple scattering models undergo changes or updates. It remains impossible to validate Geant4 in terms of DPK in the absence of experimental data in water in the low electron energy range. The results of the microdosimetry test (microyz) demonstrate that, when using Geant4 condensed history approach in EM simulations of electron transport in microdosimetric applications, it is important to limit the step size. It is shown that 1/10 of the sensitive volume diameter is adequate. The Brachytherapy test (Brachy-Ir) has a regression testing purpose. Geant4 is compared against previous simulation results in calculating the radial dose rate distribution of a 192 Ir source. This test is of interest to monitor the evolution of Geant4 and will be extended in the near future to other brachytherapy sources. We intend also to compare the results of the simulation to dosimetric experimental measurements available in the literature. The test on monoenergetic x-ray internal breast dosimetry (Mammo) showed an agreement between Geant4 and experimental data within the experimental uncertainty. It was observed that Opt0 provided the worst performance among the EM constructors under study. In summary, the EM tests showed that Opt0 in general is the constructor with the least agreement with respect to the 0 0.5 1 1.5 2 2.5 3 3.5 4 Survival Fraction 1− 10 1 Experimental data LEM III-weighted method MDA-MB231 Dose [Gy] 0 0.5 1 1.5 2 2.5 3 3.5 4 MC/data ratio 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 0 0.5 1 1.5 2 2.5 3 3.5 4 Survival Fraction 1− 10 1 Experimental data LEM III-weighted method DU145 Dose [Gy] 0 0.5 1 1.5 2 2.5 3 3.5 4 MC/data ratio 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 FIG. 21. Experimental cell surviving fraction (SF) measured irradiating DU145 cells and MDA-MB231 (dotted points) and the corresponding curves calculated with the LEM III-weighted method (triangles). Ratios of Geant4 simulations to experimental data are also plotted. [Color figure can be viewed at wileyonlinelib rary.com] Medical Physics, 48 (1), January 2021 51 ARCE et al.: G4-Med 51 reference data. For the other physics constructors, the results of the tests should support users to select the appropriate EM physics constructor for their medical physics application. It was observed that Opt4 had good agreement with the reference data for all the tests. This result was expected as this constructor was developed to provide the most accurate Geant4 physics models, irrespective of CPU performance. Table XII summarizes the results obtained for the hadronic tests subject of Section 4. The test of nucleus–nucleus hadronic inelastic scattering cross sections (NucNucInelXS) considered a limited number of projectiles of interest for hadron therapy (protons and 12 C ions), incident on a limited number of targets. The choice of targets was performed based on the availability of experimental measurements in the EXFOR data library. 96 In general, an agreement within approximately 10% was found between Geant4 and the experimental data for the cases under study. The next step of this test is to find more reference experimental measurements to be able to benchmark the Geant4 inelastic scattering cross sections for more targets of interest for medical physics applications. The 62 MeV/u 12 C fragmentation test (LowEC12Frag) showed that both the Geant4 Ion Binary Cascade and the INCL models have limitations in reproducing doubly differential cross sections of fragments produced in the interaction of 12 C with a thin carbon target. The results of this test show a possible domain of improvement of Geant4 of interest for carbon ion therapy. The test on the 300 MeV/u 12 C ion charge-changing cross section (C12FragCC) demonstrated that all hadronic ion fragmentation models, G4IonQMDPhysics (QMD), G4IonBinaryCascade(BIC), and G4IonINCLXXPhysics (INCL), reproduce the total and Li partial charge-changing cross sections. However, they all underestimate the reference experimental data for Be and B fragments. Table 13 summarizes the results obtained for the hadronic tests subject of Section 5, where the EM constructor is varied while keeping the hadronic physics component modeled with QGSP_BIC_HP. The test modeling a 67.5 MeV proton Bragg Peak in water (LowEProtonBraggPeak) showed that Geant4 can reproduce the Bragg peak spread within the uncertainty of the experimental measurements and the range within 0.5 mm accuracy. This result was confirmed for higher proton energies (125–200 MeV/u) by the light ion Bragg curve test (Light- IonBraggPeak). In this case, an agreement within 0.1% TABLE XI. Summary of the results of the electromagnetic physics tests of Section 3. Test Reference Difference with reference data Photon attenuation NIST XCOM (Berger et al 41 ) ≤1rref for the total μ/ρ, more details in Table IV ElectDEDX ESTAR (Berger et al 127 ) <1rref ElectBackScat Exp data in Table V <3rref (<5%) for Ee[0:2 MeV < 15% for 5 keV <Ee\0.2 MeV and < 40% for E <5 keV for Opt0 and Opt3, <30% for E <5 keV for Opt4, Penelope and Livermore ElecForwScat Ross et al 61 Exp data Characteristic angle ≤3% for Be, Al, Cu, Ta, and Au foils, 3%-5% for Ti and C foils, for all EM constructors Bremsstrahlung Faddegon et al 63 Exp data <2rref for Opt0,Penelope, and Livermore <1rref for emission angles <60for Opt3 and Opt4 <2rref for emission angles >60for Opt3 and Opt4 Fano cavity NA <2% for Opt0, 0.03% for Opt3, 0.02% for Opt4 for dRoverRange equal to 0.2 (default value, see Table III) LowEElecDPK EGSnrc <10% for Opt3 (same for Opt0)<3% for Opt4,Livermore and Penelope Brachy-Ir Granero et al 83 , Geant4 7.1 <1rref Mammo Fedon et al 21,22 Exp data <7.7% for Opt0 and <6% (rref =5.7%) for the other EM constructors The second column reports the type of reference data, either from Monte Carlo simulations, theoretical or experimental (Exp) data. rref is the uncertainty of the reference data. TABLE XII. Summary of the results of the hadronic physics tests of Section 4. Test Reference Difference with reference data NucNucInelXS Zerkin et al 97 <10% overall C12FragCC Toshito et al 24 <1rref for total and Li cross sections 18% for Be isotopes, 34% for B isotopes for QMD 26% for Be isotopes, 36% for B isotopes for BIC 38% for Be isotopes, 48% for B isotopes for INCL The second column reports the reference data, which are all experimental and published in the literature. rref is the uncertainty of the reference data. TABLE XIII. Summary of the results of the hadronic physics tests of Section 5. Test Reference Physical quantity Difference with reference data LowEProton BraggPeak Faddegon et al 25 67.5 MeV proton Bragg Peak Spread Range <1rref (within 0.5 mm) <2rref (within 0.5 mm) for all EM constructors LightIon BraggPeak Schardt et al 14 125–200 MeV/μ protons, Rd82 100–400 MeV/μ 12CC, Rd82 <0.1% (<0.2 mm) <1.1% (<0.8 mm) for all cases apart from Opt0 The EM constructor is tested (Opt0,Opt3,Opt4,Livermore and Penelope) while keeping the same hadronic physics component (QGSP_BIC_HP). All the reference data are experimental measurements. rref is the uncertainty of the reference data. Medical Physics, 48 (1), January 2021 52 ARCE et al.: G4-Med 52 (<0.2 mm) was observed for Rd82. In the case of incident 100–400 MeV/u 12 C ions, an agreement within 1.1% was found for all EM constructors apart from Opt0 (Table XIII). Table XIV summarizes the results obtained for the hadronic tests subject of Section 5, where the EM constructor is kept constant while changing the hadronic physics component. The neutron yield produced by 113 and 256 MeV protons showed a marginally closer agreement when using QGSP_BIC_HP rather than QGSP_BERT_HP. The 400 MeV/u carbon ion fragmentation test (FragTest) showed that BIC and QMD produce similar yields of light fragments (Z =1–5), with similar kinetic energy and angular distribution. Worst agreement in terms of fragments yield was observed for INCL, however this model produces the best description in terms of angular distributions of the fragments. The results of this test are consistent with the outcome of the charge-changing cross section test which demonstrated a better agreement between BIC and QMD to the reference data than INCL. The test on the cell survival curves (Hadrontherapy), of interest for protontherapy, is intended to validate Geant4 against in-vitro radiobiological measurements. In particular, surviving fraction curves calculated with Hadrontherapy were compared with experimental data for different cell lines. A good agreement was found for low doses (up to 3 Gy), while significant discrepancies were evident at higher delivered doses. Provided the current stage of research in in silico radiobiological modeling (e.g., Abolfath et al 127 ), the overall agreement was deemed satisfactory. For hadron therapy, it is recommended not to use the EM constructor Opt0. The hadronic tests showed that QGSP_BIC_HP physics list (which models EM interactions with Opt4 in Geant4 10.5) provides an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. However, it should be noted that only few physical quantities (position and spread of the Bragg Peak, neutron yields, fragment yields) have been subject of testing. New tests should be included in the next stage of the project to validate Geant4 in terms of dosimetry against experimental measurements. Concerning the carbon ion fragmentation tests, the results show a slightly better performance when using QMD and BIC ion fragmentation models. The charge-changing cross section and fragmentation tests show that ion fragmentation modeling is a domain of possible improvement of Geant4. In conclusion, we encourage Geant4 users to use benchmarked Geant4 physics constructors and lists. The results presented and discussed in this paper will aid users tailoring physics lists to their particular application. The next phase of the project will proceed in two main directions. The first one is the benchmarking of the computing performance of the prebuilt Geant4 physics constructors and lists. We will use the regression testing to investigate the evolution of the Geant4 physics component for medical applications in terms of both accuracy and computing performance. The second main direction will be to extend the current tests and include new ones to cover domains which are currently not tested, for example, x-ray radiotherapy and nuclear medicine. ACKNOWLEDGMENTS The authors thank Krzysztof Genser and Daren Sawkey for their feedback aimed to improve the quality of the paper. D. Bolst acknowledges the support of the Australian Government Research Training Program Scholarship. M. A. Cort´ es-Giraldo, A. Perales, and J. M. Quesada acknowledge the financial support from the Spanish Ministry of Economy and Competitiveness under grant FPA2016-77689-C2-1-R. B. Faddegon and J. Ramos-M´ endez acknowledge partial financial support from the NIH grant U24CA215123. D. Bolst, S. Guatelli, D. Sakata, S. Incerti, and I. Kyriakou acknowledge financial support from the Australian Research Council, ARC DP170100967. S. Incerti acknowledges the financial support of CNRS through the IN2P3/MOVI Master Project and through the France-Greece PICS 8235 funding scheme. I. Kyriakou acknowledges additional financial support from the European Space Agency (Contract No. 4000126645/19/NL/BW). E. C. Simpson acknowledges financial support from the Australian Research Council under grant DP170102423. I. Sechopoulos and C. Fedon acknowledge financial support from the Susan G Komen Foundation for the Cure grant IIR13262248. S. Guatelli and D. Bolst acknowlege the use of computing resources of the Australian National Computing Infrastructure (NCI), through the NCMAS 2020 grant scheme. a) Author to whom correspondence should be addressed. Electronic mail: [email protected]. TABLE XIV. Summary of the results of the hadronic physics tests of Section 5. Test Reference Physical quantity Difference with respect to reference data ProtonC12 NeutronYield Meier et al 117 Meier et al 118 Neutron yield of 113 MeV and 256 MeV p <2rref for QGSP_ BIC_HP,<4rref for QGSP_BERT_HP ProtonC12 NeutronYield Satoh et al 119 Neutron yield 290 MeV/μ12C <11% against PHITS <50% against exp data for both for QGSP_BIC_HP and QGSP_BERT_HP FragTest Haettner et al 120 400 MeV/μ12C fragmentation yield QGSP_BIC_HP for hadrons BIC and QMD:<25% , INCL:<40% Hadrontherapy Petringa et al 27 Cell survival test 62 MeV proton beam QGSP_BIC_HP <20% for DU145 > 20% for MDA-MB-231 The EM constructor is kept constant (Opt4) while changing the hadronic physics component. All reference data are experimental. rref is the uncertainty of the reference data. Medical Physics, 48 (1), January 2021 53 ARCE et al.: G4-Med 53 REFERENCES 1. Agostinelli S, Allison J, Amako K, et al. Geant4 -a simulation toolkit. Nucl Instrum Methods Phys Res Sect A. 2003;506:250–303. 2. 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