# Results of a Geant4 benchmarking study for bio-medical applications, performed with the G4-Med system

Pedro Arce, Jay Archer, Lorenzo Arsini, Alexander Bagulya, David Bolst, Jeremy Brown, Barbara Caccia, Andrew Chacon, Giuseppe Antonio Pablo Cirrone, Miguel Antonio Cortés-Giraldo, et al.

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## To cite this version:

Pedro Arce, Jay Archer, Lorenzo Arsini, Alexander Bagulya, David Bolst, et al. Results of a Geant4 benchmarking study for bio-medical applications, performed with the G4-Med system. Medical Physics: The international journal of medical physics research and practice, 2025, 52 (5), pp.2707-2761. 10.1002/mp.17678 . hal-05060859

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https://hal.science/hal-05060859v1

Submitted on 16 Jan 2026

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Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Results of a Geant4 benchmarking study for bio-medical applications, performed with the G4-Med system

Pedro Arce¹

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Jay W. Archer²

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Lorenzo Arsini³,⁴

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Alexander Bagulya⁵

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David Bolst²

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Jeremy M. C. Brown⁶

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Barbara Caccia⁷

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Andrew Chacon⁸

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Giuseppe Antonio Pablo Cirrone⁹,¹⁰

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Miguel Antonio Cortés-Giraldo¹¹

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Dean Cutajar²

Giacomo Cuttone⁹

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Paolo Dondero¹²

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Andrea Dotti¹³

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Bruce Faddegon¹⁴

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Serena Fattori⁹

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Christian Fedon¹⁵

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Susanna Guatelli²

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Akihiro Haga¹⁶

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Sebastien Incerti¹⁷

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Vladimir Ivanchenko¹⁸

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Dmitri Konstantinov¹⁹

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Ioanna Kyriakou²⁰

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Albert Le²

Zhuxin Li¹⁷

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Michel Maire²¹

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Alessandra Malaroda²,²²

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Carlo Mancini-Terracciano³,⁴

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Alfonso Mantero¹²

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Claire Michelet¹⁷

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Giuliana Milluzzo²³

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Francesca Nicolanti³,⁴

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Mihaly Novak²⁴

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Chihiro Omachi²⁵

Luciano Pandola⁹

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Jake Harold Pensavalle²⁶

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Álvaro Perales²⁷

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Yann Perrot²⁸

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Giada Petringa⁹

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Silvia Pozzi⁷

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José Manuel Quesada¹¹

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José Ramos-Méndez¹⁴

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Francesco Romano²³

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Anatoly B. Rosenfeld²

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Mitra Safavi-Naeini⁸

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Dousatsu Sakata²⁹

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Luis G. Sarmiento³⁰

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Takashi Sasaki³¹

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Yoshihide Sato¹⁶

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Alberto Sciuto⁹

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Ioannis Sechopoulos³²,³³

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Edward C. Simpson³⁴

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Ronny Stanzani¹²

Alessandra Tomal³⁵

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Toshiyuki Toshito²⁵

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Hoang Ngoc Tran¹⁷

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Christopher White²

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Dennis H. Wright¹³

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Correspondence

Susanna Guatelli, Centre for Medical
Radiation Physics, University of Wollongong,
Wollongong, New South Wales, Australia.

Email: susanna@uow.edu.au

Funding information

Australian Research Council, Grant/Award
Number: DP230103091; National Health and
Medical Research Council, Grant/Award
Number: ID2028435; MCINI/AEI, Grant/Award
Number: PID2021-1238790B-C21; China
Scholarship Council, Grant/Award Number:
201906680103; National Plan for NRRP

Abstract

**Background:** Geant4, a Monte Carlo Simulation Toolkit extensively used in bio-medical physics, is in continuous evolution to include newest research findings to improve its accuracy and to respond to the evolving needs of a very diverse user community. In 2014, the G4-Med benchmarking system was born from the effort of the Geant4 Medical Simulation Benchmarking Group, to benchmark and monitor the evolution of Geant4 for medical physics applications. The G4-Med system was first described in our Medical Physics Special Report published in 2021. Results of the tests were reported for Geant4 10.5.

**Purpose:** In this work, we describe the evolution of the G4-Med benchmarking system.

**Methods:** The G4-Med benchmarking suite currently includes 23 tests, which benchmark Geant4 from the calculation of basic physical quantities to the

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

© 2025 The Author(s). Medical Physics published by Wiley Periodicals LLC on behalf of American Association of Physicists in Medicine.

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Complementary Investments project,
Grant/Award Number: PNC0000003 (project
acronym: ANTHEM)

simulation of more clinically relevant set-ups. New tests concern the bench-
marking of Geant4-DNA physics and chemistry components for regression
testing purposes, dosimetry for brachytherapy with a ¹²⁵I source, dosimetry for
external x-ray and electron FLASH radiotherapy, experimental microdosimetry
for proton therapy, and in vivo PET for carbon and oxygen beams. Regression
testing has been performed between Geant4 10.5 and 11.1. Finally, a sim-
ple Geant4 simulation has been developed and used to compare Geant4 EM
physics constructors and physics lists in terms of execution times.

**Results:** In summary, our EM tests show that the parameters of the multi-
ple scattering in the Geant4 EM constructor *G4EmStandardPhysics_option3*
in Geant4 11.1, while improving the modeling of the electron backscatter-
ing in high atomic number targets, are not adequate for dosimetry for clinical
x-ray and electron beams. Therefore, these parameters have been reverted
back to those of Geant4 10.5 in Geant4 11.2.1. The x-ray radiotherapy test
shows significant differences in the modeling of the bremsstrahlung pro-
cess, especially between *G4EmPenelopePhysics* and the other constructors
under study (*G4EmLivermorePhysics*, *G4EmStandardPhysics_option3*, and
*G4EmStandardPhysics_option4*). These differences will be studied in an in-
depth investigation within our Group. Improvement in Geant4 11.1 has been
observed for the modeling of the proton and carbon ion Bragg peak with ener-
gies of clinical interest, thanks to the adoption of ICRU90 to calculate the low
energy proton stopping powers in water and of the Linhard-Sorensen ion model,
available in Geant4 since version 11.0. Nuclear fragmentation tests of inter-
est for carbon ion therapy show differences between Geant4 10.5 and 11.1 in
terms of fragment yields. In particular, a higher production of boron fragments is
observed with Geant4 11.1, leading to a better agreement with reference data
for this fragment.

**Conclusions:** Based on the overall results of our tests, we recommend to use *G4EmStandardPhysics_option4* as EM constructor and *QGSP_BIC_HP* with *G4EmStandardPhysics_option4*, for hadrontherapy applications. The Geant4-DNA physics lists report differences in modeling electron interactions in water, however, the tests have a pure regression testing purpose so no recommendation can be formulated.

KEYWORDS

benchmarking, bio-medical physics, Geant4

1 | INTRODUCTION

Geant4¹⁻³ is an open source Monte Carlo Simulation
Toolkit modeling particle interactions and transport in
matter. Geant4 has undergone continuous development
and enhancement since it was initially made avail-
able to the public in 1998. These improvements have
expanded the software's functionality to include newest
research findings to improve its accuracy and allowed it
to respond to the evolving needs of a very diverse user
community, which includes researchers in fields such
as high-energy physics, space, nuclear, and bio-medical
sciences. The software is developed by an interna-
tional scientific Collaboration, based at CERN, Geneva,
Switzerland, counting more than 100 contributors world-
wide. The Monte Carlo code is released with a new
public version every year in December. Prior to this, a
beta version is usually released in June, and subsequent
patches may be issued to fix errors.

As shown in Figure 1, since its first release, Geant4
has become increasingly popular in the bio-medical
physics community. Given its extensive use in the sci-
entific community and its wide set of physics models
offered to describe both electromagnetic and hadronic
physics interactions, in 2014 G4-Med, the first Geant4
benchmarking system for bio-medical physics applica-
tions was established. It was born as an effort of the
Geant4 Medical Simulation Group⁴ to benchmark dif-
ferent physics models of Geant4 in a set of exemplary
bio-medical application scenarios of interest.

This international effort was documented for the first
time in Arce et al.¹³ The tests, ranging from fundamental
physical quantities to more realistic applications, were
developed and executed with Geant4 10.5 on the CERN
computing infrastructure, via the *geant-val* system.¹⁴, ¹⁵

In this special report, we document the evolution of
the G4-Med benchmarking system in terms of new
tests that have been included and tests that have been
<figure><img src="image_58.png" /><figcaption>**FIGURE 1** Number of scientific publications in bio-medical physics found in the PubMed Central®⁵ archive, searching the general purpose Monte Carlo codes Geant4,¹⁻³ and FLUKA,⁶⁻⁸ and MCNP⁹ and EGSnrc¹⁰,¹¹ in keywords, titles and citations of papers recorded in the PubMed archive. The figure contains data (up to 2018) published in Mancini-Terracciano et al.,¹² Copyright Elsevier (2019).</figcaption></figure>

revised. We then report the results of the regression tests performed with Geant4 versions 10.5 and 11.1 (released in December 2022), which was the most recent release of Geant4 when the study described in this special report was started. Finally, we document for the first time the benchmarking of the execution times of the G4-Med tests when using different Geant4 physics lists and constructors. The latter is a critical information in those Geant4-based studies where the computing performance is an important factor.

## 2 | METHODOLOGY

The G4-Med benchmarking system, documented for the first time in Arce et al.,¹³ currently includes 23 tests, listed in Table 1 and covers different bio-medical application scenarios of interest. The tests are designed to benchmark Geant4 from the calculation of fundamental physical quantities to the simulation of more clinically relevant set-ups modeling a medical use of ionizing radiation. The tests in Table 1 are categorized according to the specific physics models and interactions being tested. These categories include electromagnetic physics tests (Section 3), tests for hadronic nuclear cross sections (Section 4), tests for both electromagnetic and hadronic physics (Section 5) and Geant4-DNA tests (Section 6).

New tests have been included to benchmark Geant4 for dosimetric calculations in water phantoms, for brachytherapy with an ¹²⁵I source (*Brachytherapy* test), external MV x-ray radiotherapy (*MV x-ray radiotherapy* test), and electron FLASH radiotherapy (*electron FLASH radiotherapy* test).

A new hadronic physics test benchmarks Geant4 for in vivo positron emission tomography (PET) for carbon ion therapy (*in vivo PET for carbon ion therapy* test), while the 62 MeV proton beam test, originally developed

for the calculation of cell survival curves irradiated with a 62 MeV spread out Bragg peak proton beam, has been extended to benchmark the track-averaged LET against experimental measurements.²⁴

The *Microdosimetry* test and the *Low energy electron Dose Point Kernels* test, described in Arce et al.,¹³ have been adapted to benchmark Geant4-DNA physics lists, while the *Chemistry* test has been introduced to benchmark different Geant4 models to describe the chemical stage of particle interactions in water.

The G4-Med benchmarking system runs all its tests in the *geant-val* environment.¹⁴,¹⁵ The *Chemistry* test is executed on the computing facility of the Laboratoire de Physique des Deux Infinis Bordeaux (LP2IB), while the other tests are executed on the CERN computing infrastructure. Tests can be executed whenever it is necessary to verify the functionality of Geant4 and support the development of Geant4 for bio-medical physics applications.

The new tests of the G4-Med benchmarking suite (in bold in Table 1) have been executed only with Geant4 11.1 as they were integrated in the system after the release of Geant4 11.0. Provided the differences in terms of kernel of Geant4 between version 10.5 and 11.1, it would be very impractical to maintain the tests for older versions of Geant4, while the maintenance is done systematically for newer versions of the Toolkit. Regression testing between Geant4 10.5 and 11.1 has been done for all the tests that were already integrated in the G4-Med system when Geant4 10.5 was the most recent version of the Monte Carlo code. All comparisons against reference data are performed with a 95% confidence level.

When the tests are released as extended or advanced examples of Geant4, apart from the case of the *Electron FLASH radiotherapy* test, the user can repeat the test locally with either the same or different simulation parameters. The exception of the *Electron FLASH radiotherapy* test is due to the fact that the beamline details, used in the test, cannot be released publicly with Geant4 because of nondisclosure agreements with third parties. Therefore, the results obtained with the advanced example may be different from those documented here.

The tests are summarized in the website dedicated to the G4-Med project,⁴ while the simulation results documented in this special report can be downloaded from the *geant-val* web interface.¹⁵

### 2.1 | Regression testing method

Regression testing between Geant4 versions 10.5 and 11.1 is performed to benchmark how the evolution of Geant4 and its physics capability affects the results of the G4-Med tests. The tests are executed via *geant-val* with the two different Geant4 versions, using the same simulation configuration and user-defined physics parameters (for example, *cut* and *maximum step*). The
<table><caption>TABLE 1 Tests of G4-Med with their name in the geant-val interface and the subsections of this report with their description and results.</caption><thead><tr><th>Test</th><th>Name in geant-val interface<sup>15</sup></th><th>Source</th><th>Section</th></tr></thead><tbody><tr><td colspan="4"><strong>Electromagnetic physics tests</strong></td></tr><tr><td>Brachytherapy<sup>125I</sup> and <sup>192</sup>Ir sources</td><td>Brachy</td><td>b</td><td>3 and 3.2</td></tr><tr><td>MV x-ray radiotherapy</td><td>medical_linac</td><td>b</td><td>3.3</td></tr><tr><td>Electron FLASH radiotherapy</td><td>eFLASHRadiotherapy</td><td>b</td><td>3.4</td></tr><tr><td>Electron backscattering</td><td>ElectBackScat</td><td>Dondero et al.<sup>16</sup></td><td>3.5.1</td></tr><tr><td>13-MeV electron forward scatter from foils</td><td>ElecForwScat</td><td>Faddegon et al.<sup>17</sup></td><td>3.5.2</td></tr><tr><td>Bremsstrahlung from thick targets</td><td>Bremsstrahlung</td><td>Faddegon et al.<sup>18</sup></td><td>3.5.3</td></tr><tr><td>Fano cavity</td><td>FanoCavity</td><td>a</td><td>3.5.4</td></tr><tr><td>Photon attenuation</td><td>PhotonAttenuation</td><td>Amako et al.<sup>19</sup></td><td>3</td></tr><tr><td>Electron electronic stopping power</td><td>ElectDEDX</td><td></td><td>3</td></tr><tr><td>Monoenergetic x-ray internal breast dosimetry</td><td>Mammo</td><td>Fedon et al.<sup>20,21</sup></td><td>3</td></tr><tr><td colspan="4"><strong>Hadronic nuclear cross section tests</strong></td></tr><tr><td>Nucleus–Nucleus hadronic inelastic scattering cross sections</td><td>NucNuclInelXS</td><td></td><td>4.1.1</td></tr><tr><td>62 MeV/u <sup>12</sup>C fragmentation</td><td>LowEC12Frag</td><td>Mancini-Terracciano et al.<sup>22</sup></td><td>4.1.2</td></tr><tr><td>Charge-changing cross section for 300-MeV/u carbon ions</td><td>C12FragCC</td><td>Toshito et al.<sup>23</sup></td><td>4.1.3</td></tr><tr><td colspan="4"><strong>Electromagnetic and hadronic physics tests</strong></td></tr><tr><td>62-MeV proton beam test: cell survival modeling and track-averaged LET</td><td>Hadrontherapy</td><td>b, Petringa et al.<sup>24,25</sup></td><td>5.2</td></tr><tr><td>In vivo PET for carbon ion therapy</td><td>heavy_ion_therapy</td><td>Chacon et al.<sup>26,27</sup></td><td>5.3</td></tr><tr><td>67.5-MeV proton Bragg curves in water</td><td>LowEProtonBraggBeak</td><td>Faddegon et al.<sup>28</sup></td><td>5.4.1</td></tr><tr><td>Light ion Bragg peak curves</td><td>LightIonBraggPeak</td><td></td><td>5.4.2</td></tr><tr><td>Neutron yield of protons with energy 113 and 256 MeV and 290-MeV/u carbon ions</td><td>ProtonC12NeutronYield</td><td></td><td>5.4.3</td></tr><tr><td>Fragmentation of a 400-MeV/u <sup>12</sup>C ion beam in water</td><td>FragTest</td><td>Bolst et al.<sup>29</sup></td><td>5.4.4</td></tr><tr><td colspan="4"><strong>Geant4-DNA tests</strong></td></tr><tr><td>Low energy electron</td><td>LowEElectDPK</td><td>a</td><td>6.3</td></tr><tr><td colspan="4"><strong>Dose Point Kernels</strong></td></tr><tr><td>Microdosimetry</td><td>microyz</td><td>a, Kyriakou et al.<sup>30</sup></td><td>6.4</td></tr><tr><td>Chemistry</td><td>chem6</td><td>a</td><td>6.5</td></tr></tbody></table>

Note: New tests (introduced in the G4-Med benchmarking suite since 2021) are in bold. All the other tests have been documented in detail in Arce et al.<sup>31</sup> The Geant4-DNA and Fano cavity tests have a purely regression testing purpose.

parameters' space is the same when comparing Geant4 10.5 and 11.1.

The results of the Geant4 regression testing are compared to the reference data, in the tests where such data exist. If the reference data are not available (see Low energy electron Dose Point Kernels and microdosimetry tests), the Geant4 models are compared to quantify the impact of their modeling differences on physical quantities of interest.

The ratios *r* of the simulation results *S*, obtained with either Geant4 10.5 or 11.1, and the reference data *R*, that is, *r*<sub>10.5</sub> = *S*<sub>10.5</sub>/*R* and *r*<sub>11.1</sub> = *S*<sub>11.1</sub>/*R*, are computed for each point of the dataset. If there is a small misalignment along the *x*-axis in the points at which the

simulated and reference data points are evaluated, the closest simulated data point is taken in the computation of the ratio.

The agreement between simulation results and reference data is calculated with a confidence level of 95%. If the calculated ratios, *r*<sub>10.5</sub> and *r*<sub>11.1</sub>, agree with 1 within their 2σ value, defined as σ = *r*<sub>Geant4_version</sub> × √((σ<sub>i,ref</sub>/R<sub>i</sub>)<sup>2</sup> + (σ<sub>i,sim</sub>/S<sub>i</sub>)<sup>2</sup>), where S<sub>i</sub>, R<sub>i</sub>, σ<sub>i,sim</sub>, and σ<sub>i,ref</sub> are the individual data points of the simulation results and reference data and associated uncertainties, respectively, then it is concluded that both Geant4 10.5 and 11.1 agree with the reference data. If instead, it is found that a release of Geant4 does not agree with 1 within 2σ, the

<footnote><sup>a</sup>Tests released as Geant4 extended examples.</footnote>

<footnote><sup>b</sup>Tests released as Geant4 advanced examples.</footnote>
difference is deemed significant. In this case, the 10.5 and 11.1 releases of Geant4 are compared in terms of the mean relative error (MRE), the normalized mean absolute error (NMAE), and the maximum difference (MD) with the reference data to quantify which release of Geant4 produces results closer to the reference data. The uncertainties affecting these metrics correspond to 1σ as we intend to have a more restrictive comparison in terms of regression testing between the two versions of Geant4.

The MRE is calculated as follows:

$$MRE_{\text{Geant4_version}} = \frac{1}{n} \left[ \sum_{i=1}^{n} \frac{|S_i - R_i|}{R_i} \right] \quad (1)$$

where $S_i$ and $R_i$ are the individual data points of the simulation results and reference data, respectively, while $n$ is the number of the data points of the distribution under testing.

The NMAE as defined in Equation (2) is also considered to describe the absolute deviation of simulations to the reference data.

$$NMAE_{\text{Geant4_version}} = \frac{\frac{1}{n} \sum_i |S_i - R_i|}{\frac{1}{n} \sum_i R_i} = \frac{\sum_i |S_i - R_i|}{\sum_i R_i} \quad (2)$$

Analogously to the calculation of the MRE, $S_i$ and $R_i$ are the individual data points of the simulation results and reference data, respectively, and $n$ is the number of the data points of the distribution under testing.

To complete the analysis, the MD between the simulation and the reference data, shown in Equation (3), is calculated for each Geant4 release under study to demonstrate the most extreme differences from the experimental data.

$$MD_{\text{Geant4_version}} = \max |S_i - R_i|, \quad (3)$$

where $S_i$ and $R_i$ are the individual data points of the simulation results and reference data, respectively.

Regression testing results are reported and commented on in this article only when there are significant differences (more than 2σ with the reference data) for any of the two releases of Geant4. Nevertheless, the complete data analysis performed in this work can be accessed through the G4-Med analysis website.32

## 2.2 | Computing performance

An important consideration when choosing a Geant4 physics list or constructor for a specific simulation scenario is first the accuracy of results, and then the

execution time. If a physics list is more accurate than another, compared to reference/experimental data, but significantly more computationally intensive, then the user may need to decide whether the added accuracy is required or if the added computing resources are justifiable.

The aim of this part of the project, documented in Section 7, is to benchmark the execution times of the Geant4 physics constructors and lists under testing in the G4-Med suite using a simple Geant4 simulation application.

## 3 | ELECTROMAGNETIC PHYSICS BENCHMARKING TESTS

The electromagnetic (EM) physics tests listed in Table 1 have been executed with Geant4 11.1 via the geant-val system. Following the methodology described in Arce et al.,13 the EM physics constructors under study are G4EmLivermorePhysics, G4EmPenelopePhysics, G4EmStandardPhysics_option3, and G4EmStandardPhysics_option4, called here Livermore, Penelope, Opt3, and Opt4, respectively. The EM physics constructor G4EmStandardPhysicsSS, called here SS, is considered in the electron backscattering test (see Section 3.5.1) as it uses the single scattering model to describe the Coulomb scattering. The EM constructor G4EmStandardPhysics has been excluded from the benchmarking study as our previous work13 demonstrated that it is not appropriate for bio-medical applications.

The EM physics constructors under study have been documented in Arce et al.13 and their evolution between Geant4 10.5 and 11.1 is reported in Section 3.1. Sections 3.2–3.4 describe the new tests, brachytherapy with an 125I source, MV x-ray radiotherapy, and Electron FLASH radiotherapy, respectively. Section 3.5 reports significant findings resulting from the regression testing of all the other tests, described in Arce et al.,13 between Geant4 10.5 and 11.1.

### 3.1 | Evolution of the Geant4 electromagnetic physics constructors under study

Livermore, Penelope, Opt3, and Opt4 EM constructors correspond to different combinations of models deriving from either Geant4 Standard, Livermore or Penelope packages (Geant4 Physics Reference Manual13,33). For a detailed description of the EM constructors, the reader can refer to Arce et al.,13 while here only significant revisions between Geant4 10.5 and 11.1 are commented.

Table 2 lists the Geant4 11.1 configuration of processes and corresponding models in each EM
<table><caption>TABLE 2 Geant4 physics models to describe EM physics processes up to 1 GeV, in the Geant4 EM constructors under investigation.</caption><thead><tr><th>Geant4</th><th>WVI</th><th>Opt3</th><th>SS</th><th>Opt4</th><th>Livermore</th><th>Penelope</th></tr></thead><tbody><tr><td>Rayleigh scattering and photoelectric effect</td><td>Livermore (EPICS2017) Li et al.<sup>36</sup></td><td></td><td></td><td></td><td></td><td>PENELOPE</td></tr><tr><td>Compton scattering</td><td>G4KleinNishina Model</td><td></td><td></td><td>G4LowEPComptonModel for E &lt; 20 MeV Brown et al.<sup>39</sup><br>G4KleinNishina for E &gt; 20 MeV</td><td>Livermore (EPICS2017) Li et al.<sup>36</sup></td><td>PENELOPE</td></tr><tr><td>Gamma conversion</td><td>G4BetheHeitler5DModel Bernard<sup>37, 38</sup></td><td></td><td></td><td></td><td>G4Livermore5DModel Li et al.<sup>36</sup></td><td>PENELOPE</td></tr><tr><td>e<sup>-</sup> and e<sup>+</sup> ionization</td><td>Standard</td><td></td><td></td><td>PENELOPE for E &lt; 100 keV, Standard for E &gt; 100 keV</td><td>Livermore for E &lt; 100 keV Standard for E &gt; 100 keV</td><td>PENELOPE</td></tr><tr><td>e<sup>-</sup> and e<sup>+</sup> bremsstrahlung</td><td>Geant4 Standard Model</td><td>G4SeltzerBergerModel for E &lt; 1 GeV, G4eBremsstrahlungReIModel for E &gt; 1 GeV</td><td></td><td></td><td></td><td>PENELOPE</td></tr><tr><td>e<sup>+</sup> annihilation</td><td>G4eplusTo2GammaOKVI Model<sup>33</sup></td><td>Standard</td><td></td><td></td><td></td><td>PENELOPE</td></tr><tr><td>e<sup>-</sup> and e<sup>+</sup> multiple scattering</td><td>Urban model for E &lt; 1 MeV, Wentzel model for E &gt; 1 MeV</td><td>Urban model</td><td>Not available</td><td>Goudsmit-Saunderson model<sup>40, 41</sup> for E &lt; 100 MeV Wentzel model for E &gt; 100 MeV</td><td></td><td></td></tr><tr><td>Coulomb scattering</td><td>on</td><td>off</td><td>on</td><td></td><td></td><td></td></tr><tr><td>Bremsstrahlung angular distribution</td><td>Modified Tsai</td><td>2BS</td><td>Modified Tsai</td><td>2BS</td><td></td><td>PENELOPE</td></tr></tbody></table>

Note: Geant4 11.1 is considered. For details on the models, the reader should refer to the Geant4 Physics Reference Manual.<sup>33</sup> Changes with respect to Geant4 10.5 are shown in bold.
constructor studied in this work. Since Geant4 11.1, the *Livermore* physics processes use by default the newly introduced EPICS2017 (Electron–Photon Interaction Cross Sections)³⁴⁻³⁶ data libraries to describe Rayleigh scattering, photoelectric effect, Compton scattering, and gamma conversion processes. The EPICS2017 models of Rayleigh scattering and photoelectric effect are also used in the *Opt3* and *Opt4* constructors. The *G4BetheHeitler5DModel*³⁷, ³⁸ is used for the sampling of the final state of gamma conversion to electron–positron pair in *Opt3*, *Opt4*, and *Livermore* EM configurations. In Geant4 11.1, in *Opt4*, the Penelope model substitutes the Livermore model to describe the ionization process of electrons with energy below 100 keV.

All the EM constructors use the same EM physics models for protons. The only change between Geant4 10.5 and 11.1 is the adoption of ICRU90 stopping power data for water, air, and graphite. For the other materials, NIST PSTAR data are used if available. If not, stopping powers are computed using ICRU49 evaluated data. A novel feature in Geant4 11.1 is that all the EM constructors, tested in this report, include a new ionization model for ions heavier than Helium, the *G4LindhardSorensenIonModel*.³³ In this model, the ICRU90 and ICRU73 data for stopping power are used below 2 MeV/u. The mean excitation energy of water *I* is equal to 78 eV, as recommended by the ICRU Report 90⁴² in both Geant4 10.5 and 11.1.

Table 3 reports multiple scattering parameters and other options. Differences between Geant4 10.5 and 11.1 are highlighted in bold. A significant change between Geant4 10.5 and 11.1 is that in *Opt3*, the *RangeFactor* has been changed from 0.04 to 0.03 and that the use of step limitation algorithm for multiple scattering⁴³ *UseDistanceToBoundary* has been substituted with *UseSafetyPlus*, with the intent of providing faster simulation, more robust tracking in magnetic field and more accurate simulation results for electron and positron backscattering. In the SS EM constructors, the use of the step limitation algorithm for multiple scattering *UseDistanceToBoundary* has been substituted with *UseSafetyPlus*.

## 3.2 | Brachytherapy test—¹²⁵I source

Since the publication of Arce et al.,¹³ the *Brachytherapy* test, which is released with Geant4 as an advanced example, has been extended to calculate the radial dose rate distribution of an *Oncura*™ brachytherapy ¹²⁵I Model 6711 source in water. The test has been included in the *geant-val* interface as an option of the *Brachytherapy* test. The results of the simulation are compared with reference data published in Dolan et al.,⁴⁴ which are experimental measurements performed with TLD detectors.

<table><caption>TABLE 3 Geant4 EM parameters (described in Arce et al.¹³ and in the Geant4 Physics Reference Manual³³) of the EM constructors under investigation.</caption><thead><tr><th rowspan="2">Geant4 EM parameter</th><th colspan="3">Opt4<br>Livermore</th></tr><tr><th>Opt3</th><th>Penelope</th><th>SS</th></tr></thead><tbody><tr><td>Minimum energy (eV)</td><td>10</td><td>100.</td><td>100</td></tr><tr><td>Lowest electron energy (keV)</td><td>0.1</td><td>0.1</td><td>0.01</td></tr><tr><td>Number of bins per decade</td><td>20</td><td>20</td><td>7</td></tr><tr><td>Mott corrections</td><td>on</td><td>on</td><td>on</td></tr><tr><td>dRoverRange for e<sup>-</sup> and e<sup>+</sup></td><td>0.2</td><td>0.2</td><td>0.2</td></tr><tr><td>finalRange for e<sup>-</sup> and e<sup>+</sup> (mm)</td><td>0.1</td><td>0.01</td><td>1</td></tr><tr><td>dRoverRange for muons and hadrons</td><td>0.2</td><td>0.1</td><td>0.2</td></tr><tr><td>finalRange (mm) for muons and hadrons</td><td>0.05</td><td>0.05</td><td>0.1</td></tr><tr><td>Skin for e<sup>-</sup> and e<sup>+</sup></td><td>1</td><td>3</td><td>1</td></tr><tr><td>Range factor for e<sup>-</sup> and e<sup>+</sup></td><td>0.03</td><td>0.08</td><td>0.04</td></tr><tr><td>Range factor for muons and hadrons</td><td>0.2</td><td>0.2</td><td>0.2</td></tr><tr><td>Msc StepLimitType</td><td colspan="3">fUseSafetyPlus<sup>a</sup></td></tr><tr><td>Fluorescence and Auger e<sup>-</sup></td><td colspan="3">On</td></tr><tr><td>PIXE modeling</td><td>Off</td><td>Off</td><td>On</td></tr></tbody></table>

Note: Geant4 11.1 is considered. Changes with respect to Geant4 10.5 are shown in bold.

ªThe use of *fUseSafetyPlus* is a new feature for the EM constructor *Opt3* and *SS*.

### 3.2.1 | Simulation set-up

The *Oncura*™ Model 6711, described in Dolan et al.,⁴⁴ has been implemented in the Geant4 simulation. The ¹²⁵I source emission is obtained by modeling the radioactive decay of iodine with the Geant4 *General Particle Source*. The iodine radioactive core is a cylinder with 0.247 mm radius and the length of the cylinder is 2.794 mm. These lengths take into account that the radioactive coating is implanted 3 µm deep onto the surface of the silver core. The ¹²⁵I source is modeled in the center of a water box (modeled as G4_WATER) with 30 cm size. The energy deposition is scored with a Geant4 scoring mesh with voxels 0.25 mm wide and the threshold of production of secondary particles is set equal to 0.05 mm. The radial dose rate distribution is calculated as the energy deposition per unit of mass, along the transverse axis of the source, 90° from the source axis.

10¹⁰ histories are executed to obtain a statistical uncertainty lower than 1% for distances up to 10 cm from the brachytherapy source. The statistical uncertainty was determined by executing 10 simulations with different random seeds and consisting each of 10⁹ histories and evaluating the standard error affecting the average dose values.

The reference data are experimental measurements performed with thermoluminescent dosimeters, which are documented in Dolan et al.⁴⁴
<figure><img src="image_59.png" /><figcaption>**FIGURE 4** Results of the MV x-ray radiotherapy test obtained with Geant4.11.1. Top left: longitudinal dose distribution in the water phantom. The curves are normalized to the dose value at a depth of 10 cm. Top right: transverse dose distribution at 10-cm depth in the water phantom. The curves are normalized at the center; the uncertainties of the simulation results are within symbols. Bottom: ratios of simulated and experimental data for the longitudinal (left) and transverse (right) profile. The shadowed area represents an agreement within 5% with the reference data. Experimental data from Caccia et al.⁴⁶</figcaption></figure>

available in Geant4 to understand more in detail the observed differences.

## 3.4 | Electron FLASH radiotherapy test

Among the most innovative radiotherapic techniques recently developed, FLASH radiotherapy, consisting of using ultra-high dose rate (UHDR) particle beams (40 Gy/s), is attracting an increasing interest in the medical physics community.

Preclinical studies have shown that the use of UHDR beams may substantially improve normal tissue sparing (so-called FLASH effect) while maintaining the same tumor control probability (TCP) compared to conventional dose-rate radiotherapy.⁵³,⁵⁴ A clinical translation of FLASH radiotherapy certainly requires the establishment of new protocols and guidelines for the beam delivery, and absolute and reference dosimetry.⁵⁵

For this reason, an extensive effort is currently dedicated to accurately model with Monte Carlo simulations the accelerator machines and the generated radiation field (from 1 cm up to 12 cm diameter), to be able to predict the beam quality and parameters at the irradiation point. In this context, within the framework of a consolidated collaboration between the CPFR (Centro Pisano Flash Radiotherapy) in Pisa and the INFN Catania Division, Italy, a Triode Electron Gun Equipped ElectronFlash Linac, manufactured by Sordina Iort Technologies S.p.A., was simulated in Geant4. The Linac,

installed at the CPFR,⁵⁶,⁵⁷ is able to accelerate 7 and 9 MeV pulsed electron beams at UHDR regime, and the device has been recently simulated in Geant4.

The test, presented here, is based on the eFLASHanas Geant4 advanced example. There are some differences between the two in terms of beamline modeling as the real Linac geometry is protected by a nondisclosure agreement with third parties. The simulation calculates and benchmarks the lateral dose distribution obtained at the reference position, namely 13 mm water depth, and the depth-dose distribution in water obtained at the exit of the applicator, with experimental data acquired during the commissioning phase of the EF linac in Pisa and reported in DiMartino et al.⁵⁷

### 3.4.1 | Simulation set-up

The simulation set-up is shown in Figure 8, it accurately models the geometrical configuration experimentally used in the preclinical research performed at the CPFR.

The primary radiation field is modeled as a 2.5 × 2.5 mm² electron source with an energy spectrum peaked at 9 MeV, which realistically reproduces the energy spectrum of electrons accelerated by the EF LINAC. The realistic energy spectrum was provided for the G4-Med test by the manufacturer (SIT Sordina) to assure a direct comparison of the simulations with the experimental data. For copyright reasons, a slightly modified version
<figure><img src="image_60.png" /><figcaption>**FIGURE 5** Results of the $\gamma$ index test for all the tested EM constructors (*Opt3*, *Opt4*, *Livermore*, and *Penelope*). Top row: longitudinal profiles. Bottom row: transverse profiles. Dotted line signifies a $\gamma$ index of 1.</figcaption></figure>

<figure><img src="image_61.png" /><figcaption>**FIGURE 6** Absolute dose profiles in the water phantom, obtained with $2 \times 10^{11}$ histories and the four EM constructors. Left: longitudinal profile. Right: transverse profile at 10 cm of depth. Results obtained with Geant4.11.1.</figcaption></figure>

of the LINAC geometry and source energy spectrum is included in the released Geant4 eFLASHRadiotherapy advanced example.

A water phantom is added downstream the accelerator at a distance of 73 cm. A plexiglass 73 cm long cylindrical hollow applicator with 10 cm internal diameter is added to shape the field size and obtain a uniform dose distribution with a flat lateral profile.⁵⁷

The depth-dose distribution along the water phantom is calculated using a scoring mesh with size $60 \times 2 \times 2 \text{ mm}^3$. The mesh is divided in 60 voxels along the x-axis (the voxel size is then $1 \times 2 \times 2 \text{ mm}^3$). The vertical transversal profile is retrieved at 13 mm depth in the water phantom, which corresponds to the maximum expected dose in the depth-dose distribution.⁵⁷ To calculate the transversal dose profile, a second scoring
<figure><img src="image_62.png" /><figcaption>FIGURE 7 Transverse dose profiles simulated with the full EM constructors Opt4, Penelope, and the same constructors using a different bremsstrahlung model: Opt4 with G4PenelopeBremsstrahlungModel, and Penelope with G4LivermoreBremsstrahlungModel. Results obtained with 10¹¹ histories.</figcaption></figure>

mesh has been added with size 1 × 120 × 1 mm³. This has been divided in 60 voxels along the y-axis (the voxel size is then 1 × 2 × 1 mm³). The EM constructors Opt3, Opt4, Livermore, and Penelope are tested. A global production cut of 0.1 mm is used. 10⁸ histories are set to obtain a statistical uncertainty lower than 1%. The statistical uncertainty was calculated by executing 10 separate simulations with the same number of events and different random seed.

### 3.4.2 | Results and discussion

Figure 9 shows the longitudinal and the transverse dose distributions in the water phantom obtained with the electron FLASH radiotherapy test. The results concerning the longitudinal dose distribution show an agreement between the simulation results obtained with Opt4, Livermore, and Penelope within 2σ, from the surface of the phantom down to approximately 3.5 cm depth. After that the agreement deteriorates; to note, at these distances, the dose is close to zero. Opt3 shows significant differences, up to 20%, from the surface of the water phantom to 1 cm depth. Then, the agreement is similar to the other EM physics constructors when compared to the experimental data.

In terms of lateral dose distributions, it can be noted that Opt4, Livermore, and Penelope provide a similar agreement with respect to the reference data, in-field. Out-of-field, there are larger differences, up to 50%, which are attributed to the high-dose gradient of this region where the uncertainty in the position can be relevant. Opt3 underestimates the dose in-field when compared to the other EM physics constructors. However, in order to evaluate more accurately the difference

between the simulated results and the experimental data, especially in the regions of the dose profile with a high gradient, the γ index test was performed for both the transversal and longitudinal dose profiles for all the Geant4 EM constructors under study, using a criterion of 4%/2 mm. A dose discrepancy (DD) of 4% and a distance-to-agreement (DTA) of 2% were chosen to take into account of the high dose uncertainty and high spatial resolution of the radiochromic films, respectively. As shown in Figure 10, all the EM constructors satisfy the condition of γ < 1 apart from Opt3.

The large differences found in the depth-dose and transverse dose profiles when using Opt3 are due to parameters of the multiple scattering model. The RangeFactor in Geant4 11.1 is 0.03 and the step limitation option is UseSafetyPlus (see Section 3.1). Based on the results of this test, a Geant4 patch, 11.2.1, has been released where both parameters have been reverted to the Geant4 10.5 variant. Figure 11 shows the new dose distributions obtained with reverting the multiple scattering parameters of Opt3 in Geant4 11.2.1. It is possible to observe that there is a better agreement between Geant4 11.2.1 and the reference data when compared to Geant4 11.1. Still, there are some discrepancies in the longitudinal dose distribution, which are under investigation.

## 3.5 | Regression testing results

The regression testing performed with the electron electronic stopping power test, photon attenuation test, monoenergetic x-ray internal breast dosimetry test and Brachytherapy test with an ¹⁹²Ir source have reported no differences between Geant4 10.5 and 11.1, and, therefore, are not documented in this report. The reader can refer to the geant-val website¹⁵ and to Archer³² to access the data analysis.

### 3.5.1 | Electron backscattering test

This test, documented in Dondero et al.¹⁶ and Arce et al.,¹³ calculates the fraction of electrons backscattered by a circular metallic target in vacuum and the electron backscattering coefficient, η, is defined as follows:

$$ \eta = \frac{e_{\text{back}}}{e_{\text{tot}}} \qquad (4) $$

where e$_{back}$ is the number of backscattered electrons and e$_{tot}$ is the total number of incident electrons. The backscattering coefficient has been calculated with the Geant4 EM constructors Opt3, Opt4, SS, Livermore, and Penelope. The statistical error affecting the backscattering coefficients is calculated by propagating the
<figure><img src="image_63.png" /><figcaption>**FIGURE 8** Schematic view of the simulation set-up of the *electron FLASH radiotherapy* test. The different components are indicated in the figure: the position of the electron source, the plastic shaping applicator, and the water phantom where the dose distributions are computed.</figcaption></figure>

<figure><img src="image_64.png" /><figcaption>**FIGURE 9** Results of the *electron FLASH radiotherapy* test. Top: longitudinal dose distribution in the water phantom. When not visible, the error bars are within the symbols. Bottom: transverse dose distribution at 13.5 mm depth in the water phantom. The curves are shown in absolute dose normalized to the number of primary particles (left) and normalized to the maximum dose calculated with *Opt4* (at 17 mm depth in the water phantom for the longitudinal distribution) (right). The plots in the last column show the ratio of the Geant4 simulations and reference data reported in DiMartino et al.⁵⁷ The shadowed area represents an agreement within 5%. Results obtained with Geant4 11.1.</figcaption></figure>

uncertainties of the two terms in the fraction, each of which corresponds to the statistical errors of their respective counts.

The simulation application reproduces the irradiation configurations of the Sandia Lab experimental data,⁵⁸,⁵⁹ used as reference in this work.

In this section, we report the results of the regression testing between Geant4 10.5 and 11.1, considering Be, C, Al, Ti, Mo, Ta, and U targets. The energy of the incident electrons varies from approximately 0.1 keV to 1 MeV. The angle of incidence of the electron beam varies from 0° to 75°. The simulation results are compared to
<figure><img src="image_65.png" /><figcaption>**FIGURE 10** γ index test results for the transversal (top) and longitudinal (bottom) dose profiles obtained with *Livermore*, *Penelope*, *Opt3*, and *Opt4*.</figcaption></figure>

<figure><img src="image_66.png" /><figcaption>**FIGURE 11** Results of the *electron FLASH radiotherapy* test, obtained with Geant4 11.2.1 and *Opt3* EM constructor. The RangeFactor is 0.04 and the step limitation option is *UseDistanceToBoundary* (only two parameters that have been changed between Geant4 11.1 and 11.2.1 in *Opt3*). The shadowed area represents an agreement within 5%. When not visible, the error bars are within the symbols. Reference data from DiMartino et al.⁵⁷</figcaption></figure>
Sandia Lab experimental data.⁵⁸,⁵⁹ In addition, we report for the first time the benchmarking of the results of this test against a new experimental data set, obtained within the EXACRAD Project of the European Space Agency<fnref n="1" />.

Figure 12 shows exemplary results of the regression testing when the Geant4-calculated backscattering coefficient is compared against the Sandia Lab experimental data.⁵⁸,⁵⁹

In the case of an aluminum target, when the electron beam is incident normally on the target (0° incidence), all the Geant4 EM constructors provide a similar level of agreement with respect to the reference data (within $2\sigma$), with the exception of Opt3 that tends to underestimate the backscattering electron coefficient, for both Geant4 10.5 and 11.1. In the case of 45° degrees incidence, all EM constructors have an overall agreement within $2\sigma$ for energies above 100 keV. For lower energies, Opt3 provides a better description of the backscattering coefficient when compared to the other EM constructors. When considering a 75° degree incidence, all the simulation results agree with the reference data within $2\sigma$.

When considering the tantalum target, Geant4 11.1 shows an overall better agreement for Opt3 and SS EM constructors, when compared to Geant4 10.5; for this release, all the Geant4 EM constructors show an agreement within $2\sigma$ with the reference data.

In the case of an uranium target with a normal incidence direction, all simulation results have an agreement within $2\sigma$ with the experimental results apart from the case of the SS constructor with Geant4 10.5, when the energy of the incident electrons is below 60 keV. Geant4 11.1 shows a better agreement than Geant4 10.5 with respect to the reference data in the case of the SS constructor (within $2\sigma$). When the electron beam is incident with an angle of 45°, the results obtained with Opt3, Opt4, Livermore, and Penelope agree with the reference data within $2\sigma$ apart from the case of the lowest electron kinetic energy (32. keV), where the difference is above 8%. In the case of the SS constructor, the results agree with the reference data within $2\sigma$ when the electron energy is above 60 keV for both Geant4 10.5 and 11.1. For lower energies, the difference is in the range of approximately 6%–18% and 4%–12% for Geant4 10.5 and 11.1, respectively, indicating a clear improvement for Geant4 11.1. In the case of 75° incidence, the agreement with the reference data is within $2\sigma$ for all the EM physics constructors apart from the case of the EM constructor SS, for Geant4 10.5.

Figure 13 reports the MRE for all the targets under study. It can be noted that for targets with lower atomic number (Be, C and Al), Opt3 and SS in Geant4 11.1 tend to provide similar or less overall agreement to the reference data when compared to Geant4 10.5. Instead, for higher atomic numbers (Mo, Ta, and U), Geant4 11.1 shows an overall improvement for Opt3 and SS constructors. The observed differences in terms of backscattering coefficients are due to modifications of the multiple scattering. Provided that the phenomenon of backscattering is more prominent for targets with higher atomic number, the results of this test show an overall improvement of Opt3 and SS in terms of backscattering modeling.

Figure 14 shows the results concerning the test calculating the backscattering coefficient for 30, 60, and 90 keV electrons, incident normally on the target, compared against the experimental measurements of the project Exacrad of the European Space Agency.

In the case of an Au target, the SS EM constructor provides a different description of the number of backscattered electrons depending on the version of Geant4 (Geant4 10.5 and 11.1 tend to overestimate and underestimate the backscattered electron coefficient, respectively), nevertheless the overall agreement with the reference data is within 5%. The results obtained with Opt4, Penelope, and Livermore show an agreement within 6% for both releases of Geant4. Opt3 shows a better agreement with the reference data in the case of Geant4 11.1 (within 6% against 8% for the case of Geant4 10.5). No release of Geant4 agrees within $2\sigma$ with the reference data.

In the case of the Bi target, again the SS constructor shows different descriptions of the electron backscattering coefficient depending on the release of Geant4 (Geant4 11.1 underestimating and Geant4 10.5 overestimating $\eta$ similarly to the Au target). Nevertheless, both releases show similar agreements with the reference data (within 3% for Geant4 10.5 and 4% for Geant4 11.1). Similarly to the case of the Au target, Opt3 shows a better agreement with the reference data in the case of Geant4 11.1 (within 6% against 9% for the case of Geant4 10.5). No release of Geant4 agrees within $2\sigma$ with the reference data apart at energy equal to 90 keV for Opt4, Penelope, and Livermore.

In the case of the silicon target, all EM constructors show an agreement within 10% with the reference data, apart from Opt3 that shows worse results for both Geant4 10.5 and 11.1 (agreement within approximately 25%).

In summary, this test shows an improvement in electron backscattering coefficient calculation for Geant4 11.1 in the case of Opt3, for gold and bismuth targets (high-Z targets). This improvement is ascribed to the revision of the multiple scattering parameters for this EM constructor (see Table 3). SS constructor provides

<footnote n="1">¹ Results were obtained under ESA Contract 4000121062/17/NL/LF "Experimental Evaluation of ATHENA Charged Particle Background from Secondary Radiation and Scattering in Optics (EXACRAD)." Relevant contribution has been given by Bernard Dirassen, ONERA, and Thierry Paulmier, ONERA, for experimental measurements of electron emission yield and spectra; Paolo Dondero, SWHARD SRL, Fan Lei, RadMod Research Ltd., Alfonso Mantero, SWHARD SRL, for simulations and data analysis; Simone Lotti, INAF IAPS-Roma, Silvano Molendi, INAF IASF-Milano, for coordination and project management.</footnote>
<figure><img src="image_67.png" /><figcaption>**FIGURE 12** Exemplary electron backscattering coefficients calculated for Al, Ta, and U targets, for different angles of incidence, compared against the Sandia Lab experimental data.⁵⁸,⁵⁹ The shadowed area represents a 5% agreement. When not visible, the error bars are within the symbols.</figcaption></figure>
<figure><img src="image_68.png" /><figcaption>FIGURE 13 Mean relative error (MRE) calculated for Be, C, Al, Ti, Mo, Ta, and U targets, compared against the Sandia Lab experimental data.⁵⁸,⁵⁹ The MRE is calculated over the incident angles and electron energies under study. Here the uncertainties are provided as $1\sigma$ (see Section 2.1).</figcaption></figure>

different calculations of electron backscattering coefficients for the high-Z targets but the overall agreement is similar. *Livermore*, *Opt4*, and *Penelope* exhibit a similar overall agreement with the reference data, attributed to their adoption of the same multiple scattering model and parameters (see Tables 2 and 3). For these constructors, there is no significant difference between Geant4 10.5 and 11.1.

### 3.5.2 | 13 MeV electron forward scatter from foils

This test, documented in detail in Arce et al.,¹³ is an experimental benchmark of the scatter of electrons with energy equal to 13 MeV, for a comprehensive set of scattering materials (Be, C, Al, Ti, Cu, Ta, Au), for thicknesses that result in a characteristic angle (or root mean square scattering angle) of 2°–8°.¹⁷,⁶⁰,⁶¹ The test is of particular interest for the benchmarking of Geant4 for electron therapy when using medical linear accelerators with thin targets intended to minimize electron energy loss and the generation of x-rays.

The 13 MeV electron beam has an experimental energy spread that is sufficiently small to consider it mono-energetic. The beam has a spot size of 0.1 cm FWHM and is normally incident on the exit window, a scattering foil of different thicknesses and compositions, a monitor chamber, and mylar slabs on either side of a region filled with helium. The scoring plane is perpendicular to the beam axis and is located 1.182 m from the exit window. The fluence of electrons is scored in radial spatial bins of 1 mm width.

Figure 15 shows the results of the test. The statistical uncertainty of the simulation results was calculated with the batch method, that is, splitting the simulations in sev-

eral jobs with different random seeds and retrieving the mean and standard error. This is negligible when compared to the uncertainty affecting the experimental data. Therefore, the uncertainty in the results is the published experimental uncertainty.

The agreement between Geant4 simulations and experimental data is generally within $2\sigma$ for all the EM constructors under study, when considering the Be and C targets, for both Geant4 10.5 and 11.1. All EM constructors provide an agreement within $2\sigma$ up to 80 and 100 mm for the Ti and Au targets, respectively, for both releases of Geant4. For larger distances, the agreement deteriorates down to 16% for all EM constructors apart from *Opt3* in the case of Geant4 11.1, especially for the Ti targets, where differences up to 28% are observed. The bottom plot of Figure 15 shows the ratio of the simulation and experimental data for *Opt3* and Geant4 11.2.1 and it is possible to observe that the agreement with experimental data improves again for this version of Geant4, due to the changes in the multiple scattering parameters of the Geant4 EM constructor *Opt3*. These results are consistent with the findings of the *electron FLASH radiotherapy* test (see Section 3.4).

### 3.5.3 | Bremsstrahlung from thick targets

This test focuses on the capability of Geant4 to model bremsstrahlung radiation produced by thick targets of Al and Pb. Here, a brief description of the test is provided. The reader can refer to Arce et al.¹³ for more details.

A mono-energetic electron beam with a diameter of 0.35 cm and energy 15.18 MeV is normally incident with constant fluence on a titanium exit window, followed by a silicon transmission current monitor, and, finally, a pure target encased in a steel target chamber.
<figure><img src="image_69.png" /><figcaption>**FIGURE 14** Top: electron backscattering coefficients and ratios to reference data calculated for 30, 60, and 90 keV electrons, incident on Au, Bi, and Si targets. The reference data are experimental measurements of the project Exacrad of the European Space Agency. The shadowed area shows an agreement within 5%. Bottom: mean relative error (MRE), calculated for each EM physics constructor under study. Here the uncertainties are provided as $1\sigma$ (see Section 2.1).</figcaption></figure>

The photon fluence is scored on the surface of several concentric spherical rings in a sphere of 1 m radius centered at the intersection of the beam axis with the upstream face of the target. A global production cut of 0.01 mm is adopted. The simulation results are compared to experiment (data documented in Faddegon et al.⁶², ⁶³).

The results of this test were first reported in Arce et al.¹³ for Geant4 10.5. Nevertheless, in that release, Geant4 did not propagate the statistical weight correctly and the results shown used a local version of Geant4 10.5 where this problem was fixed. The problem was

then fixed in the kernel of Geant4 in later releases of the Monte Carlo Toolkit and, here, we report the new results obtained with the test for Geant4 11.1.

The top plot of Figure 16 shows the bremsstrahlung spectra obtained with Geant4 11.1. The middle plot shows the ratios of the simulation results to the reference experimental measurements in log scale, while the bottom plot shows the ratio in linear scale for photon energies above 0.4 MeV.

The statistical uncertainty of the simulation results was calculated with the batch method. Similarly to the electron forward scattering test 3.5.2, this is negligible
<figure><img src="image_70.png" /><figcaption>**FIGURE 15** Top: fluence of forward-scattered electrons obtained with a 13-MeV electron beam incident on the following foils: 0.926 g/cm² Be, 0.546 g/cm² C, 0.14 g/cm² Al, 0.0910 g/cm² Ti, 0.0864-g/cm² Cu, 0.443 g/cm² Ta, and 0.0312 g/cm² Au. When not visible, the error bars are within the symbols. Middle: ratio of the fluences of the forward-scattered electrons, plotted against the lateral position, for the different foils, for Geant4 10.5 and 11.1. Bottom: ratio of the fluences of the forward-scattered electrons, for Opt3 with Geant4 versions 11.1 and 11.2.1. The shadowed area represents an agreement of 5%.</figcaption></figure>
<figure><img src="image_71.png" /><figcaption>**FIGURE 16** Top: Bremsstrahlung spectra obtained with a 15.18 MeV electron beam incident on targets of Al and Pb. Middle: ratio of the simulation results to the experimental reference data in log scale. Bottom: ratio of the simulation results to the experimental reference data on a linear scale. Note: Only every *fifth* data point is shown on the ratio plots for clarity and points outside the axis limits are not visible in the linear scaled ratio plot but are shown in the log scaled plot. The shadowed area represents an agreement within 5%.</figcaption></figure>
when compared to the uncertainty affecting the experimental data, therefore the uncertainty affecting the results is the experimental uncertainty.

In the case of both Al and Pb targets, Geant4 seems to underestimate the photon fluence at energies below approximately 0.3 MeV, when compared to the reference data. This discrepancy, observed for the combination of low energy and low fluence, was attributed in the benchmark paper Faddegon et al.⁶² to collimator effects and charged particle contamination that were not included in the uncertainty estimates.

For both targets, apart the low energy and low fluence combination case, the agreement between Geant4 simulation results and reference data is in general within 2σ for all the Geant4 EM constructors.

### 3.5.4 | Fano cavity test

The Fano cavity test is designed to check the accuracy of the condensed history (CH) electron transport when simulating the response of detectors with gaseous cavities. In particular, 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.⁶⁴ This test is recommended by the AAPM Research Committee Task Group 268.⁶⁵

A beam of 1.25 MeV gamma rays is incident normally and uniformly on the flat ends of an ionization chamber, which consists of 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/cm³).⁶⁶ The direction of the photon beam is along the cylinder axis and there is particle equilibrium in the ionization chamber.

As explained in Arce et al.,¹³ this test requires specific physics modeling conditions, and the physics constructors used in this test (indicated with a * for clarity) differ from the corresponding Geant4 EM physics constructors except the modeling of the electron Coulomb scattering and the corresponding stepping algorithm. Ionization is simulated with the *G4MollerBhabha* model (see the Geant4 Physics Reference Manual¹⁵ for details). In order to have the same stopping power in the wall and cavity, the density correction term in the electronic stopping power formula is not applied. The Fano Cavity test conditions imply no energy transfer via bremsstrahlung radiation. Therefore this process is not registered.

After each Compton interaction, the scattered photon is reset to its initial state, energy, and direction. Consequently, interaction sites are uniformly distributed within the wall material, obtaining particle equilibrium. With this set-up, the ratio of the dose deposited divided by the beam energy fluence should be equal to the mass-energy transfer coefficient of the wall material. The EM physics constructors under study are *Opt3*\* and *Opt4*\*.

<figure><img src="image_72.png" /><figcaption>**FIGURE 17** Ratio of simulated dose and the theoretical value plotted against the *dRoverRange* parameter. The shadowed area represents a 1% agreement with the unity.</figcaption></figure>

Livermore and Penelope are not considered as they have the same multiple scattering model of *Opt4*.

Figure 17 shows the dose ratio calculated with the simulation and the theoretical value, varying the *dRover-Range*, which is a parameter of the Geant4 multiple scattering. While the results obtained with *Opt4*\* do not change from Geant4 10.5 and 11.1, those with *Opt3*\* vary, but, still, the agreement with unity is within 1%.

## 4 | NUCLEAR FRAGMENTATION CROSS SECTIONS BENCHMARKING TESTS

Three independent tests are included in the G4-Med benchmarking suite to evaluate the total hadronic inelastic cross section, which is described with the Glauber–Gribov model in Geant4,³³ and three different nuclear fragmentation models available in Geant4, the Binary Light Ion Cascade (BIC), the Quantum Molecular Dynamics (QMD), and the Liege Cascade (INCL) models,¹³ describing the final state of the fragmentation process.

The BIC models nuclear fragmentation in the energy range between 0 and 6 GeV/u, by describing the interaction between the projectile and the participating nucleons of the target nucleus.¹³ The residual nucleus is in pre-equilibrium state and is de-excited to the equilibrium state using the precompound model Geant4.³³ The final de-excitation is performed by the Geant4 de-excitation module. It invokes the Fermi Break-Up, neutron and light ion evaporation, fission for heavy fragment emission, GEM model for light fragment emission, and photon evaporation to model the nuclear gamma cascade Geant4.³³ A significant change between Geant4 10.5 and 11.1 is in the modeling of the
de-excitation channels in the Fermi Break-Up model. Many more reaction channels are considered in Geant4 11.1 (from 991 to 5421 reactions).⁶⁷

The QMD models ion nuclear fragmentation between 100 MeV/u and 10 GeV/u. Below 100 MeV/u, the BIC is used. The QMD describes the interaction between the projectile and all the nucleons of the target nucleus.¹³

The INCL models fragmentation and all the subsequent processes, including nuclear de-excitation, in the energy range between 0 and 3 GeV/u. The target nucleons are treated as a free Fermi gas in a static potential well, whereas the projectile is modeled without Fermi motion.¹³

Above the limit of applicability of the BIC, QMD, and INCL, the Fritiof parton string model Geant4³³ is adopted, nevertheless, it is not tested in this work as the energy range is too high for bio-medical applications.

## 4.1 | Regression testing results

### 4.1.1 | Test of nucleus–nucleus hadronic inelastic scattering cross sections

This test, described in detail in Arce et al.,¹³ calculates the total cross section of hadron–nucleus and nucleus–nucleus collisions, which is then compared to reference experimental measurements of the Experimental Nuclear Reaction Data (EXFOR) database.⁶⁸ The total inelastic scattering hadronic cross sections are calculated for incident protons and carbon nuclei, for the following reactions: p+¹²C, p+¹⁶O, p+²⁷Al, p+⁴⁰Ca, ¹²C+p+¹²C, and ¹²C+p+²⁷Al. In Geant4, the total inelastic scattering hadronic cross section is based on the Glauber representation with the Gribov screening correction on inelastic screening⁶⁹⁻⁷² and it is used in all the Geant4 hadronic physics constructors.

Figure 18 shows the results of the regression testing between Geant4 10.5 and 11.1. The total inelastic cross sections is plotted as a function of the kinetic energy of the projectile and is compared to the experimental data of the EXFOR database. The cross sections do not have any statistical uncertainty because they are model-based calculation. Both releases of Geant4 provide the same level of agreement with the reference data, for both incident protons and carbon ions. In the case of incident protons, there is an overall agreement within 2σ, apart from some isolated points. In the case of incident carbon ions, the agreement is within 2σ when the target is ¹²C, while in the case of the reaction ¹²C + ²⁷Al, Geant4 consistently overestimates the cross section of about 5%–10%, when compared to the reference data for both releases of Geant4.

Figure 19 shows the total inelastic cross section in the energy range between 1 and 100 MeV/u. It is possible to observe that for incident protons, the cross section is lower up to 10 MeV in the case of Geant4 11.1, while

there is no difference for incident carbon nuclei. The difference between Geant4 10.5 and 11.1 proton cross sections is due to the change of Coulomb barrier parameterization in the cross section computation. In 10.5, an empirical parameterization¹ was used. In version 11.1, hadronic cross sections are obtained from tabulation of ParticleHP evaluated data based on the best known experimental data and at higher energies on the Glauber–Gribov theory.³ The approach of Geant4 11.1 is, therefore, deemed more accurate.

### 4.1.2 | 62 MeV/u ¹²C fragmentation test

This test, described in detail in Arce et al.,¹³ calculates the double-differential cross sections of light fragment production of 62 MeV/u ¹²C ions incident on a thin natural carbon target. The secondary fragments under investigation are ¹H, ²H, ³H, ⁴He, ⁶Li, ⁷Li, ⁷Be, ⁹Be, ¹⁰B, and ¹¹B. The calculated cross sections are compared to experimental measurements reported in De Napoli et al.⁷³ Simulations are executed modeling the nuclear fragmentation with the Binary Light Ions Cascade (BIC)⁷⁴ and the Liege Intranuclear Cascade (INCL).⁷⁵,⁷⁶ The QMD⁷⁷ is not subject of the test, as, below 100 MeV/u, its Geant4 physics constructor (G4IonQMDPhysics) switches to the BIC.¹³

The regression testing shows that the cross section of production of ¹H isotopes does not change between Geant4 10.5 and 11.1, while there are some differences for ⁴He, ⁶Li, ⁷Li, ⁷Be, ⁹Be, ¹⁰B, and ¹¹B, for both INCL and BIC fragmentation models. Nevertheless, the overall agreement against experimental data does not change between Geant4 10.5 and 11.1. Figures 20 and 21 show as exemplary case the double differential cross section of production of ¹⁰B and its ratio against the reference data, respectively. In this case, the differential double cross section is slightly higher in Geant4 11.1 than in Geant4 10.5, but the overall agreement with the reference data remains the same. Specifically, BIC continues to show a doubly peaked structure due to the de-excitation of the projectile and target remnants, while underestimating the mid-rapidity region. INCL, on the other hand, continues to overestimate production in that region, showing a single distribution. Possible explanations for these behaviors could include the fact that the BIC approach is based on a time-invariant optical potential, which leads to an underestimation of neck fragmentation events, whereas INCL uses a complete-fusion approach.¹³

### 4.1.3 | 300 MeV/u ¹²C ion charge-changing cross section test

This test, described in detail in Arce et al.,¹³ benchmarks the partial and total charge-changing cross sections of
<figure><img src="image_73.png" /><figcaption>**FIGURE 18** Total inelastic cross sections for the nuclear reactions under study. The Geant4 cross sections, obtained with QGSP_BIC_EMY and represented with red and blue lines for Geant4 10.5 and 11.1, respectively, do not have any statistical uncertainty because they are model-based calculation. The shadowed area represents an agreement within 10%.</figcaption></figure>
<figure><img src="image_74.png" /><figcaption>**FIGURE 19** Total inelastic cross section, obtained with QGSP_BIC_EMY and represented with red and blue lines for Geant4 10.5 and 11.1, zoomed in the energy range between 1 and 100 MeV/u, together with the ratios (represented with gray continuous lines) of the cross sections calculated with Geant4 11.1 and 10.5.</figcaption></figure>

$^{12}$C ions with energy 300 MeV/u as simulated by Geant4 against experimental data published in Toshito et al.,²³ obtained with an emulsion plate in the NIRS P152 experiment.

In this simulation, 300 MeV/u carbon ions are inci-
dent on a water (G4_WATER) phantom with a 10 m
side. All electromagnetic processes and decay physics
are switched off and only hadron and ion transport
<figure><img src="image_75.png" /><figcaption>FIGURE 20 $^{10}$B production double-differential cross sections, obtained with 62 MeV/u $^{12}$C ions incident on a thin natural carbon target, calculated with Geant4 10.5 and 11.1. The simulation uncertainty is calculated, assuming a Poisson distribution, proportional to the square root of the number of events in each bin. Reference experimental measurements from De Napoli et al.⁷³</figcaption></figure>

<figure><img src="image_76.png" /><figcaption>FIGURE 21 Ratio of the simulation and reference data for $^{10}$B production double-differential cross sections, obtained with 62 MeV/u $^{12}$C ions incident on a thin natural carbon target. The shadowed area represents a 10% agreement. Reference experimental measurements from De Napoli et al.⁷³</figcaption></figure>
<figure><img src="image_77.png" /><figcaption>**FIGURE 22** Top: comparison of Geant4 simulation results obtained with Geant4 10.5 and 11.1 against experimental data²³ for ¹²C total and partial charge-changing cross sections. The energy of the incident ¹²C ion beam is 300 MeV/u. The error bars of the simulation results are within the symbols. Bottom: ratio of simulated and reference data for Geant4 10.5 and 11.1. The shadowed area represents an agreement within 10%.</figcaption></figure>

processes are modeled. Projectile-like fragments are then identified as they travel in the forward direction (momentum along the initiated direction > 600 MeV/c/u) and retrieved. Partial charge-changing cross sections are then calculated for B, Be, and Li isotopes. The statistical uncertainty affecting the simulation results is calculated as follows. The $\frac{\sqrt{N}}{N}$ is used to estimate the relative error $\sigma_{SIM}$ of the number *N* of the generated fragments, assuming a Poisson statistics. Then, the uncertainty of the calculated cross section CS is obtained by multiplying CS with $\sigma_{SIM}$.

Figure 22 shows the results of the regression testing between Geant4 version 10.5 and 11.1. The bottom plot shows the ratio of the simulation and reference data. The agreement within $2\sigma$ is confirmed for the total cross section and Li partial cross section when using Geant4 version 11.1. In the case of the Be partial cross section, Geant4 11.1 provides poorer agreement than 10.5 with

respect to the experimental measurements. Depending on the specific fragmentation model, a degradation of the level of agreement of approximately 10%–15% has been found. However, in Geant4 11.1, the calculation of the Boron partial cross section improves significantly, especially for the BIC model. In the case of QMD and INCL, the difference to the reference data decreases to below 20%, while the BIC model provides an agreement with the reference data within $2\sigma$. The increase of B yield is coherent with the increase of the double-differential cross sections observed for Geant4 11.1 in the test with 62 MeV/u ¹²C ions incident on the thin natural carbon target (Section 4.1.2).

Overall, in this test, when compared to INCL and QMD, BIC, and BIC HP provide a better agreement against reference data.

## 5 | ELECTROMAGNETIC AND HADRONIC PHYSICS BENCHMARKING TESTS

This section reports the results of the G4-Med tests where both electromagnetic and hadronic physics processes are objects of the testing. Section 5.1 briefly describes the physics lists of Geant4 benchmarked in this work and summarizes the evolution of the Geant4 hadronic physics from Geant4 10.5 to 11.1, of interest for bio-medical physics applications. Section 5.2 shows new developments of the *Hadrontherapy* test in terms of experimental microdosimetry. Section 5.3 describes a new test introduced in the G4-Med benchmarking system for in vivo PET for heavy ions. Finally, Section 5.4 reports significance results of the regression testing of existing tests, documented in Arce et al.¹³ performed with Geant4 10.5 and 11.1.

### 5.1 | Evolution of the Geant4 hadronic physics from Geant4 10.5 to 11.1, of interest for bio-medical applications

The Geant4 physics lists, modeling both electromagnetic and hadronic physics interactions, subject of the benchmarking of Geant4 for hadrontherapy, are *QGSP_BIC HP*, *QGSP_BIC AllHP*, *QGSP_BERT HP*, *QGSP_INCLXX HP*, and *Shielding*, and they are briefly described in Table 5.

From Geant4 version 10.5 to 11.1, there have been limited changes in the hadronic physics models relevant for bio-medical applications, in the hadronic inelastic cross sections and physics lists used in this benchmark. Consistency improvements, clean-up, and optimization of the code have been performed, but without reported relevant impact in the situations of interest in this study, other than the data they use.

New versions of the hadronic data sets are used in Geant4 11.1. First of all, the new G4NDL.4.7, for
<table><caption>TABLE 5 Geant4 physics models of the hadronic physics list used in this report.</caption><thead><tr><th>Geant4 physics list</th><th>QGSP_BIC_HP</th><th>QGSP_BIC_AIIHP</th><th>QGSP_BERT_HP</th><th>QGSP_INCLXX_HP</th><th>Shielding</th></tr></thead><tbody><tr><td>EM physics</td><td>Opt4<br>G4EmExtraPhysics<br>Modeling synchrotron radiation and gamma/e-/e+ nuclear processes</td><td></td><td>G4EmStandardPhysics</td><td></td><td></td></tr><tr><td>Radioactive decay</td><td>G4RadioactiveDecayPhysics<br>Modeling of rare decays of hadrons (pion, kaons, etc.) is not relevant for the G4-Med tests</td><td></td><td></td><td></td><td></td></tr><tr><td>Hadron elastic scattering</td><td>G4HadronElasticPhysicsHP</td><td></td><td></td><td></td><td></td></tr><tr><td rowspan="2">Other hadronic physics processes</td><td>G4HadronPhysics<br>QGSP_BIC_HPa</td><td>G4HadronPhysics<br>QGSP_BIC_AIIHPb</td><td>G4HadronPhysics<br>QGSP_BERT_HPa</td><td>G4Hadron<br>Physics INCLXX</td><td>G4HadronPhysics<br>Shielding<br>BERT_HPa &lt; 3 GeV,<br>FTPF_HPa &gt; 3 GeV</td></tr><tr><td>G4IonElasticPhysics</td><td></td><td></td><td></td><td>G4IonElasticPhysics</td></tr><tr><td>Ion elastic physics</td><td>G4IonPhysics<br>(G4BinaryLightIonReaction)</td><td>G4IonPhysicsPHP<br>(G4ParticleHPInelastic &lt; 200 MeV,<br>G4BinaryLightIonReaction above)</td><td>G4IonPhysics<br>(G4BinaryLightIonReaction)</td><td>G4IonINCLXXPhysics</td><td>G4IonQMDPhysics</td></tr></tbody></table>

<footnote>a. HP: use of evaluated databases only for neutrons.</footnote>

<footnote>b. _AIIHP: use of evaluated databases for n, p, d, i, $^3$He, and α particles.</footnote>
data-driven models for neutron transport, is used in the “_HP” physics lists. With respect to G4NDL.4.5 (present in Geant4 10.5), the new dataset incorporates new neutron cross sections and final states obtained from the JEFF-3.3 data library, and includes new materials for the simulation of thermal neutrons. The dataset G4TENDL.1.4, used by the “_AllHP” physics lists, was released with Geant4 version 11.0 and uses ENDF/B-VIII.0 and TENDL-2019 libraries (vs. G4TENDL.1.3.2 present in Geant4 version 10.5, which used ENDF/B-VII.1 and TENDL-2014 libraries).

With respect to G4PARTICLEXS.1.1 present in Geant4 10.5, the G4PARTICLEXS.4.0 dataset present in Geant4 11.1 was derived using cross section data from G4NDL.4.7 for neutrons with energies below 20 MeV, from G4TENDL.1.4 for protons below 150 MeV and light ions at selected energy ranges, and from new data for gamma-nuclear cross sections below 130 MeV. This dataset is used in all non-HP precompiled Physics Lists.³³ For gamma-nuclear cross section, the same cross section class G4PhotoNuclearCrossSection is used above 130 MeV.

G4ENSDFSTATE.2.3, used in Geant4 11.1 and released with Geant4 10.7, incorporates minor changes in nuclear levels and isomer lifetimes versus G4ENSDFSTATE.2.2 present in version 10.5. After dedicated efforts, G4ENSDFSTATE.2.3 is coherent with G4-PhotonEvaporation.5.7 and G4RadioactiveDecay.5.6 datasets.

G4PhotonEvaporation.5.7, released with Geant4 version 10.7, updates data on nuclear levels and transition probabilities versus G4PhotonEvaporation.5.3 in Geant4 10.5. These data are used in the Geant4 nuclear de-excitation module used in the physics list containing “BIC,” “INCLXX,” or “QMD” in its name, as well as in “_AllHP” physics lists.

G4RadioactiveDecay.5.6, released with Geant4 version 10.7, incorporates various updates, additions, and fixes with respect to G4RadioactiveDecay.5.3, present in Geant4 10.5. The radioactive decay module is used by default in the physics list Shielding and those including “_HP” or “_AllHP” in their name.

## 5.2 | Hadrontherapy test

The Hadrontherapy test is released in Geant4 as an advanced example (called Hadrontherapy) since 2003. The test has been included in the G4-Med benchmarking system since its first release in 2019. It was originally focused on comparing clonogenic cells’ Survival Fraction (SF) curves with experimental radiobiological data (see Arce et al.¹³). The regression testing between Geant4 10.5 and 11.1 of the calculation of the SF curve did not report any change between the two releases of Geant4, therefore the results will not be shown here.

An additional functionality has been recently included in the test, focused on the calculation of track-averaged LET ($\bar{L}_T$) curves and their comparison against experimental microdosimetric data, obtained at the CATANA facility, Laboratori Nazionali del Sud, Istituto Nazionale di Fisica Nucleare in Catania⁷⁸,⁷⁹ (INFN-LNS, Italy).

### 5.2.1 | Simulation set-up

The CATANA protontherapy clinical beamline, installed at LNS-INFN, is modeled in detail in terms of materials and geometry. A voxelized water phantom is set at the end of the beamline, to replicate a standard water tank, conventionally adopted in a clinical environment, for depth dose curve reconstruction. For this test, the tank is segmented into slices with size 400 × 400 × 0.01 mm³.

The proton beam is simulated with a Gaussian energy distribution, centered at a nominal energy of 62.40 MeV and a standard deviation of 0.25 MeV. The beam spot is modeled as circular, following a bivariate Gaussian distribution with a standard deviation of 5 mm. A Gaussian angular distribution is assumed for the beam, with a standard deviation of 0.028°. Proton beam energy modulation is achieved using a plastic modulator wheel, generating a modulation width of 11 mm in water and a maximum proton range of 30 mm in water. Each simulation execution comprises a total of 3.6 × 10⁶ histories. The production cut for secondary electrons, defining the threshold below which secondary particles are not individually generated and tracked, is set equal to 0.1 mm.

The track-averaged LET, $\bar{L}_T$, is computed using QGSP_BIC_HP, QGSP_BERT HP, and QGSP_BIC_AllHP,³³ and compared against $y_F$ values defined in the ICRU Report 36,⁸⁰ derived from experimental microdosimetric spectra acquired at 13 different depths in water. These spectra were obtained using the MicroPlus probe detector⁸¹ developed at the Centre for Medical and Radiation Physics, University of Wollongong, Australia.⁸¹

The term averaged LET refers to the mean value of the electronic stopping power when considering all particles traversing a specific volume within a radiation field. The track-averaged LET ($\bar{L}_T$) is calculated as described by Petringa et al.,²⁴ with an approach analogous to the method C suggested by Cortés-Giraldo and Carabe⁸² to avoid biased results:

$$ \bar{L}_T = \frac{\sum_{j=1}^{n} \left[ \sum_{i=1}^{N} L_i l_i \right]_j}{\sum_{j=1}^{n} \left[ \sum_{i=1}^{N} l_i \right]_j}, \quad (5) $$

where $l$ represents the track length of a particle in the given volume. $l_i$ is the total electronic stopping power evaluated at each particle step $i$, calculated using
<figure><img src="image_78.png" /><figcaption>FIGURE 23 $\bar{L}_T$ curves obtained with Geant4 11.1, when using QGSP_BIC HP (red), QGSP_BERT HP (orange), and QGSP_BIC_AIIHP (blue), against $y_F$ values obtained experimentally (Petringa et al.²⁴). $L_T$ uncertainties have been calculated as the standard deviation of 10 simulations executed with different seeds, and they are of the order of 1%. The shadowed area represents an agreement within 10%.</figcaption></figure>

the method ComputeElectronicDEDX() of the Geant4 G4EmCalculator class. The G4EmCalculator calculates restricted and total stopping power and CSDA range via access to precomputed tables or by recomputation of corresponding values. The index *i* iterates over the total number of steps *N* taken by a specific particle within the considered volume, while the index *j* iterates over all primary and secondary particles traveling within that volume.

## 5.2.2 | Results

Figure 23 shows the comparison of the track-averaged LET curve ($\bar{L}_T$), obtained with QGSP_BIC HP, QGSP_BERT HP, and QGSP_BIC_AIIHP. The $L_T$ uncertainties have been calculated as the standard deviation of 10 simulations executed with different seeds, and they are of the order of 1%. The simulation results are compared to the reference $y_F$ values. It is possible to observe that the Geant4 simulations agree within 15% with the reference data. There is no significant difference in the results due to the choice of Geant4 physics lists, among those under study.

## 5.3 | In vivo PET test for carbon and oxygen ion therapy

This test has been introduced in the G4-Med benchmarking system relatively recently and is documented in Chacon et al.²⁶ and Chacon et al.²⁷ It quantitatively assesses the capability of Geant4 in predicting positron-emitting fragment production using three

<table><caption>TABLE 6 Beam parameters for each ion species and energy.</caption><thead><tr><th>Incident ion</th><th>Energy (MeV/u)</th><th>σ<sub>x</sub> (mm)</th><th>σ<sub>y</sub> (mm)</th><th>Beam flux (pps)</th></tr></thead><tbody><tr><td><sup>12</sup>C</td><td>148.5</td><td>2.77</td><td>2.67</td><td>1.8 × 10<sup>9</sup> ± 3.8 × 10<sup>7</sup></td></tr><tr><td><sup>12</sup>C</td><td>290.5</td><td>3.08</td><td>4.70</td><td>1.8 × 10<sup>9</sup> ± 6.4 × 10<sup>7</sup></td></tr><tr><td><sup>12</sup>C</td><td>350</td><td>2.50</td><td>2.98</td><td>1.8 × 10<sup>9</sup> ± 4.6 × 10<sup>7</sup></td></tr><tr><td><sup>16</sup>O</td><td>148</td><td>2.79</td><td>2.89</td><td>1.1 × 10<sup>9</sup> ± 2.8 × 10<sup>7</sup></td></tr><tr><td><sup>16</sup>O</td><td>290</td><td>2.60</td><td>4.90</td><td>1.1 × 10<sup>9</sup> ± 7.0 × 10<sup>7</sup></td></tr></tbody></table>

Note: All beams had an energy spread of 0.2% of the nominal energy. The uncertainty of the beam energy is estimated to be ± 0.5 MeV/amu while the uncertainty affecting $\sigma_x$ (mm) and $\sigma_y$ (mm) is 0.05 mm. Ninety-five percent confidence intervals are listed for beam flux.

hadronic inelastic fragmentation models: BIC, QMD, and INCL.

Experimental data of the absolute yields of positron-emitting fragments ($^{10}$C, $^{11}$C, and $^{15}$O), generated during the irradiation of gelatin, PMMA, and polyethylene block phantoms with $^{12}$C and $^{16}$O ion beams, serve as reference data. These beams, with energies equal to 148.5, 290.5, and 350 MeV/u for $^{12}$C and 148 and 290 MeV/u for $^{16}$O, were measured using the OpenPET scanner at HIMAC, Japan, as detailed in Chacon et al.²⁶ and Akamatsu et al.⁸³

The focus is on the comprehensive comparison of simulated positron yields against experimental measurements across three key regions: entrance, build-up and Bragg peak, and tail regions.

The experimental set-up, described in Chacon et al.,²⁶ involves irradiating phantoms made of PMMA, polyethylene, or gelatin, using monoenergetic carbon and oxygen ion beams as listed in Table 6. The PMMA chemical composition is $C_5H_8O_2$, with a density of (1.189 ± 0.001) g/cm³ while the polyethylene composition is $C_2H_4$ with a density of (0.939 ± 0.001) g/cm³. The density of gelatin is (1.001 ± 0.002) g/cm³ and it is distilled water (made with Milli-Q). No detectable/trace elements other than H and O are assumed to be present.

Positron annihilation profiles were acquired using a DOI-PET scanner prototype from QST,⁸³ with subsequent decomposition into contributions from $^{11}$C, $^{10}$C, and $^{15}$O by fitting the time activity curve, voxel by voxel, at the end of the irradiation period. The profile is taken using the full width at tenth maximum (FWTM) of the beam, parallel to the path of the beam in the phantom.

### 5.3.1 | Simulation set-up

The in vivo PET test models the experimental setup as accurately as possible. The selection of physics models followed the configurations specified in the Geant4 advanced hadrontherapy example. The physics lists is QGSP_BIC HP with Opt3 as EM physics constructor. Opt3 was chosen in this specific test because it is computationally faster than Opt4, without affecting
the accuracy of the calculation of the physical quantity under study, the positron yield, which depends on the modeling of the nuclear fragmentation and radioactive decay, when considering that *Opt3* and *Opt4* use the same heavy ion ionization model.

The nuclear fragmentation is modeled with BIC, QMD, and INCL. The heavy ion beams are modeled as two-dimensional Gaussian pencil beams, with same sigmas ($\sigma$) as observed experimentally and detailed in Table 6. An air gap of 1.75 m separates the beam's origin from the phantom's surface to replicate the experimental conditions as accurately as possible. Phantoms, constructed in dimensions of 100 x 100 x 300 mm³, are composed of either polyethylene, polymethyl methacrylate (PMMA), or gelatin housed in an open-top PMMA container. The gelatin phantom features a 4 mm wall thickness and is filled with water. All material properties are defined based on the NIST definitions.

Each simulation configuration is executed with 2 × 10⁷ histories. The identification of positron-emitting fragments is done tracing the origins of annihilating positrons. The spatial and temporal coordinates, alongside the parent ID of each positron annihilation, is recorded with a spatial resolution of 1.5 mm³ across the entire phantom, reflecting the capabilities of the OpenPET system for image reconstruction. A Gaussian filter, characterized by a 2.6 mm FWHM, is applied to emulate the point spread function of the PET imaging system. Line profiles, extracted at the FWTM of each beam, traverses the phantom along the beam path. These profiles are normalized to the number of incident particles simulated. Data are grouped into 20 batches for statistical analysis, with the calculation of mean and standard deviation for each. This approach yields a statistical confidence level of 10% in the mean/standard deviation across the majority of the beam's trajectory.

The results are analyzed in three regions, entrance, Bragg peak, and tail. The entrance and the Bragg peak regions are separated by the proximal edge in the z dimension (along the path of the beam), defined as the first point at which the dose deposited along the central axis exceeds the entrance plateau dose by more than 5% of the difference between peak dose and the entrance plateau dose. The Bragg peak and the tail regions are separated by the distal edge in z, defined as the last point at which the deposited dose is greater than 5% of the absolute peak dose value. The simulations are performed with Geant4 11.1.

### 5.3.2 | Results and discussion

Figures 24–26 show the positron emission yield for the incident ¹²C and ¹⁶O ion beams in the gelatine, PMMA, and polyethylene phantoms, respectively, calculated with

Geant4 11.1. The plots have inserts showing the ratio of the Geant4 simulated and experimental data.

There can be observable differences between Geant4 simulations and reference data depending on the irradiation configuration and specific regions of the signal (e.g., entrance, Bragg peak, or distal regions). Table 7 summarizes the results for the tests performed with Geant4 11.1 in terms of MRE and NMAE to identify the fragmentation model that aligns best with the experimental data used in this study. The results are presented specifically for Geant4 11.1 because this test is newly introduced in the G4-Med benchmarking system and has not been evaluated with earlier Geant4 versions. A more detailed discussion of localized discrepancies and comparisons across different versions of Geant4 can be found in Chacon et al.²⁷

The results, including the MRE and NMAE analysis, show that the INCL has the least agreement against the experimental measurements. The BIC provides an overall better agreement for the entrance and Bragg peak region, while the QMD outperforms the BIC in the distal region (tail).

## 5.4 | Regression testing results

### 5.4.1 | 67.5 MeV proton Bragg peak in water

This test, documented in detail in Arce et al.¹³ and in Faddegon et al.,²⁸ calculates the Bragg peak in water of protons of mean energy 67.5 MeV and a gaussian energy spread of 0.4 MeV. The beam is incident on a water phantom, after traversing a tantalum (Ta) foil of either 101.6 or 381 µm thickness.

The physics list includes one of the EM constructors, *Livermore*, *Penelope*, *Opt3*, or *Opt4*, coupled with hadronic physics, which is modeled by means of *QGSP_BIC_HP*.¹³, ⁸⁴

The simulation results are compared to experimental measurements documented in Faddegon et al.,²⁸ in terms of range $R_{80}$ (corresponding to the 80% Bragg peak distal fall-off), and spread $\sigma$ (indicated here as $\sigma^*$ for clarity) of a Gaussian describing the width of the Bragg peak as defined in Bortfeld.⁸⁵ The $R_{80}$ and spread $\sigma^*$ are obtained from the fit of an analytical function reported in Bortfeld.⁸⁵ For the measured data, uncertainties include both experimental uncertainties and fitting errors. For the Monte Carlo simulation, uncertainties include statistical (evaluated by executing multiple times the simulation with different random seeds) and fitting errors and are reported at 1 standard deviation.

Figure 27 shows the $R_{80}$ and the spread $\sigma$. It can be observed that, while there is no difference between the two releases of Geant4 in terms of $R_{80}$ (agreement within $2\sigma$ with the reference data), there is a slight improvement in Geant4 11.1 in terms of gaussian
<figure><img src="image_79.png" /><figcaption>**FIGURE 24** Top row: positron yield per incident $^{12}$C ion, with energy 148.5 MeV/u (left), 290.5 MeV/u (middle), and 350 MeV/u (right). Bottom row: $^{16}$O ion, with energy 148 MeV/u (left) and 290 MeV/u (right). The positron yield is plotted with respect to the depth in the gelatin phantom. The yellow areas indicate the Bragg peak regions. The bottom plots in each row show the ratio between simulated and experimental data. The shadowed area represents an agreement within 10%, while the uncertainties ($2\sigma$) affecting the simulation results are shown as a shade around the curve. Experimental measurements from Chacon et al.$^{26}$</figcaption></figure>

spread $\sigma^*$. In the case of the 101.6 µm thick Ta target, the difference of Gaussian spread between simulations and reference data is below 0.10 and 0.14 mm for Geant4 11.1 and 10.5, respectively. In the case of the 381.0 µm thick Ta target, the difference of Gaussian spread between simulations and experiments is below 0.15 and 0.2 mm for Geant4 11.1 and 10.5, respectively. Opt3 and Opt4 EM constructors provide the best agreement against reference data in the case of Geant4 11.1. The improvement observed in Geant4 11.1 maybe be due to the ICRU90 adoption to calculate the low energy proton stopping powers in water.

### 5.4.2 | Light ion Bragg peak curves

This test, documented in detail in Arce et al.,¹³ is aimed to compare $R_{82}$ (range of heavy ions at 82% dose fall-off) in water, between Geant4 and experimental measurements performed at GSI,⁸⁶ for proton and $^{12}$C beams with energies of interest for hadron therapy (beam ranges are below 30 cm in water). The EM physics constructors under investigation are Opt3, Opt4, *Livermore*, and *Penelope*, while the hadronic physics component is defined, for all the simulations, with *QGSP_BIC HP*, similarly to what done in Arce et al.¹³

Figure 28 reports the differences of $R_{82}$ between Geant4 calculations and experimental measurements, for incident protons and $^{12}$C ions. In the Bragg curves, the statistical uncertainty of the dose was calculated following the history-by-history method described by Walters et al.⁵² The number of histories was such that the uncertainty of the dose scored at maximum and distal part (>50% dose) was below 1.5%. It was then verified that the uncertainty propagated to the depth $R_{82}$ was approximately below the scoring cell thickness (50 µm) at 1 sigma level. Thus, the uncertainty ($1\sigma$) affecting $R_{82}$ was defined to be ±50 µm. This happens thanks to the sharp dose gradients observed at the distal fall-off. For example, for 200-MeV protons, the dose fall-off from 85 to 80% happened in about 300 µm, being the worst-case scenario for protons. As for carbon ions, at 400-MeV dose fall-off from 90 to 70% was observed in about 400 µm. As a result, the experimental uncertainty is 200 µm and the statistical uncertainty of the simulation results is 50 µm.

Taking into account the uncertainties affecting the results, it is possible to observe a general improvement in the calculation of the position of the Bragg peak of approximately 0.2 mm for incident protons in Geant4 11.1.

In the case of incident carbon ions, while Geant4 10.5 tends to underestimate the position of $R_{82}$, Geant4 11.1
<figure><img src="image_80.png" /><figcaption>**FIGURE 25** Top row: positron yield per incident $^{12}$C ion, with energy 148.5 MeV/u (left), 290.5 MeV/u (middle), and 350 MeV/u (right). Bottom row: $^{16}$O ion, with energy 148 MeV/u (left) and 290 MeV/u (right). The positron yield is plotted with respect to the depth in the PMMA phantom. The yellow areas indicate the Bragg peak regions. The bottom plots in each row show the ratio between simulated and experimental data. The shadowed area represents an agreement within 10%, while the uncertainties ($2\sigma$) affecting the simulation results are shown as a shade around the curve. Experimental measurements from Chacon et al.$^{26}$</figcaption></figure>

overestimates it. Geant4 11.1 predicts more accurately the position of the Bragg peak up to 250-MeV/u incident energy ($R_{82}^{sim} - R_{82}^{exp}$ is within 0.3 and -0.6 mm for Geant4 11.1 and 10.5, respectively). For higher energies, the absolute difference between simulated and experimental $R_{82}$ is very similar for the two releases of Geant4. In the case of 400 MeV/u, the highest incident energy under study, the difference between simulated and experimental $R_{82}$ is approximately 0.85 and 1 mm for Geant4 10.5 and 11.1, respectively. There is no difference in the results due to the adoption of *Livermore*, *Opt3*, *Opt4*, and *Penelope* EM constructors, because the model of heavy ion ionization process is the same in all these EM constructors.

### 5.4.3 | Neutron yield with protons and $^{12}$C ions in thick targets

This test, described in detail in Arce et al.,$^{13}$ calculates the neutron yield in thick targets, produced by incident protons with energy 113 and 256 MeV and 290 MeV/u $^{12}$C ions. The simulation results are compared to experimental measurements documented in Meier et al.$^{87,88}$ for protons and from Satoh et al.$^{89}$ for carbon ions interacting in water. Table 8 reports the radius, thickness,

and material of each target bombarded with either protons or $^{12}$C ions. The physics lists under study are *QGSP_BIC HP* and *Shielding*.

The neutron yield per incident primary particle per steradian per energy (equally spaced logarithmic energy intervals) is scored at specific angular bins; for proton beams, 7.5°, 30°, 60°, and 150° for 113 MeV and 30°, 60°, 120°, and 150° for 256 MeV; 15°-90° at 15° angular steps for carbon ions. Its statistical uncertainty has been calculated by repeating the same simulation with different random seeds and calculating the mean and standard error. The statistical uncertainty of the simulation results is a lot smaller than the experimental uncertainty, which ranges from 7 to 20% and it is dominated by the detector efficiency and cross section data used for the derivation of neutron yields Meier et al.$^{90}$

Figure 29 shows the integral neutron yields with respect to the angle of emission of neutrons, calculated in the set of configurations listed in Table 8. Difference between Geant4 10.5 and 11.1 releases is observed only for protons incident on a Fe target, when using *QGSP_BIC HP*. No difference is reported when using the *Shielding* physics list.

When considering the differential neutron yield cross sections, there are differences between the two releases
<figure><img src="image_81.png" /><figcaption>**FIGURE 26** Top row: positron yield per incident ¹²C ion, with energy 148.5 MeV/u (left), 290.5 MeV/u (middle), and 350 MeV/u (right). Bottom row: ¹⁶O ion, with energy 148 MeV/u (left) and 290 MeV/u (right). The positron yield is plotted with respect to the depth in the polyethylene phantom. The yellow areas indicate the Bragg peak regions. The bottom plots in each row show the ratio between simulated and experimental data. The shadowed area represents an agreement within 10%, while the uncertainties (2σ) affecting the simulation results are shown as a shade around the curve. Experimental measurements from Chacon et al.²⁶</figcaption></figure>

<table><caption>**TABLE 7** Results obtained with Geant4 11.1, summarized using MRE and NMAE metrics (see Section 2).</caption><thead><tr><th>Target material</th><th>Particle</th><th>Energy (MeV/u)</th><th>Entrance</th><th>Build-up and Bragg peak</th><th>Tail region</th></tr></thead><tbody><tr><td rowspan="6">Gelatin</td><td>¹²C</td><td>148</td><td>QMD</td><td>QMD/BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>290</td><td>QMD</td><td>QMD</td><td>QMD</td></tr><tr><td>¹²C</td><td>350</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>148</td><td>QMD</td><td>QMD/BIC</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>290</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>148</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td rowspan="6">PMMA</td><td>¹²C</td><td>290</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>350</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>148</td><td>BIC</td><td>QMD</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>290</td><td>BIC</td><td>QMD/BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>148</td><td>BIC</td><td>QMD/BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>290</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td rowspan="6">Polyethylene</td><td>¹²C</td><td>350</td><td>QMD/BIC</td><td>QMD/BIC</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>148</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹⁶O</td><td>290</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>148</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>290</td><td>BIC</td><td>BIC</td><td>QMD</td></tr><tr><td>¹²C</td><td>350</td><td>QMD/BIC</td><td>QMD/BIC</td><td>QMD</td></tr></tbody></table>

of Geant4 only in the case of protons incident on a Fe target, shown in Figure 30. Differences up to 20% between the two releases of Geant4 are observed in the calculation of the neutron yield below 10 MeV neutron energy, when using QGSP_BIC_HP.

This is the only test in the G4-Med suite that benchmarks Geant4 in terms of neutron production and the results of the regression testing show that more tests are needed to monitor neutron production (in addition to neutron physics).
<figure><img src="image_82.png" /><figcaption>FIGURE 27 Comparison of R<sub>80</sub> and Gaussian spread σ* between Geant4 10.5/11.1 predictions and reference data, for a 67.5 MeV proton beam incident on a water phantom. Reference data from Faddegon et al.<sup>28</sup></figcaption></figure>

<figure><img src="image_83.png" /><figcaption>FIGURE 28 Difference of R<sub>82</sub> between Geant4 simulations and reference data.<sup>86</sup> The differences are plotted against the energy of the incident particles (protons and <sup>12</sup>C). The error bars are calculated at a 95% confidence level.</figcaption></figure>

<table><caption>TABLE 8 Target dimensions, material, and density for each proton energy and carbon ion beam configuration.</caption><thead><tr><th>Material</th><th>Radius (cm)</th><th colspan="2">Protons</th><th>Thickness (cm)</th><th colspan="2">Density (g/cm³)</th></tr></thead><tbody><tr><td></td><td>113 MeV</td><td>256 MeV</td><td>113 MeV</td><td>256 MeV</td><td></td><td></td></tr><tr><td>Aluminum</td><td>3.65</td><td>8.0</td><td>4.00</td><td>20.0</td><td>2.699</td><td></td></tr><tr><td>Carbon</td><td>3.65</td><td>8.0</td><td>5.83</td><td>30.0</td><td>1.867</td><td></td></tr><tr><td>Iron</td><td>3.65</td><td>8.0</td><td>1.57</td><td>8.0</td><td>7.867</td><td></td></tr><tr><td></td><td></td><td colspan="2">Carbon ions (290 MeV/u)</td><td></td><td></td><td></td></tr><tr><td>G4_WATER</td><td>—</td><td>—</td><td>—</td><td>18.0</td><td>1.0</td><td></td></tr></tbody></table>

Note: Table from Arce et al.<sup>13</sup>

### 5.4.4 Fragmentation of a 400 MeV/u <sup>12</sup>C ion beam in water

This test, published in Bolst et al.<sup>29</sup> and described in detail in Arce et al.,<sup>13</sup> benchmarks Geant4's modeling of the fragmentation process against experimental measurements of a <sup>12</sup>C ion beam incident upon a water target performed at GSI.<sup>91</sup>

A 400 MeV/u <sup>12</sup>C ion pencil beam, with an energy Gaussian spread of 0.15% and a FWHM of 5 mm, is incident on a water phantom with different thicknesses (59, 159, 258, 279, 288, 312, and 347 mm). For each

water thickness, secondary fragments and their energy spectra are recorded at different angles at a distance of about 3 m after the water thickness. The physical quantities compared by the benchmark are the yield, angular, and kinetic energy distributions of light fragments, from hydrogen to boron. With the six water thicknesses and five fragment elements, a total of 35 angular distributions and 151 energy distributions are compared between experiment and simulation.

The QGSP_BIC HP physics list is used to model particle interactions. The Geant4 EM constructor Opt4 is adopted to model the electromagnetic interactions. The
<figure><img src="image_84.png" /><figcaption>FIGURE 29 Integral neutron yields with respect to the angle of emission of neutrons, calculated with Geant4 and compared against reference data from Meier et al.⁸⁷,⁸⁸ for protons and from Satoh et al.⁸⁹ for incident carbon ions. The error bars are within the symbols.</figcaption></figure>

tests are performed changing the model of hadronic inelastic scattering of heavy ions: BIC, QMD, and INCL.

Figure 31 shows the fragment yield calculated with respect to the depth in water when using Geant4 10.5 and 11.1, while Figure 32 plots the ratio of simulation results and reference data and Figure 33 reports the MRE. The simulation error bars represent the statistical uncertainty when generating a total of $10^7$ primary $^{12}$C ions for each water thickness. The error bar sizes were calculated by dividing the results into 10 groups and calculating the associated standard deviation.

When considering BIC, Geant4 11.1 provides results that, overall, agree better with the reference data for H, He, and B fragment yields, when compared to Geant4 10.5 (see Figure 33). In particular, the MD with the reference data goes from about 20 to 10% for H, from about 30 to 20% for He, from about 40 to 20% for B, when moving from Geant4 10.5 to 11.1. In the case of INCL, Geant4 11.1 shows a better overall agreement against reference data in the case of He (MD of about 25%–20% for Geant4 10.5 and 11.1, respectively) and B fragments (MD of about 60 and 40% for Geant4 10.5 and 11.1, respectively). In the case of the QMD model, Geant4 10.5 agrees better with the experimental results in the case of the He fragment at shallower depths (MD of about 5 and 10% within 16-cm depth in water, for Geant4 10.5 and 11.1, respectively). An overall better agreement with Geant4 11.1 has been obtained for QMD for the B fragment yield (MD of about 40 and

15% for Geant4 10.5 and 11.1, respectively, down to a depth of 30 cm), similarly to the other Geant4 fragmentation models. There is no change between Geant4 10.5 and 11.1 for the Li and Be yields, for any of the Geant4 fragmentation models.

Figure 34 shows the MRE of the angular and kinetic energy distributions, calculated for the light fragments, at different depths in the water medium, for both Geant4 10.5 and 11.1. It is possible to observe that, for both BIC and INCL, there is a slightly less overall agreement in terms of angular distribution of the fragments with Geant4 11.1. Instead, similar agreement against the reference data is obtained for the two releases of Geant4 in terms of kinetic energy distributions.

## 6 | GEANT4-DNA BENCHMARKING TESTS

The Geant4-DNA package is extensively used in radio-biological studies; therefore, we felt the need to include new tests in the G4-Med benchmarking suite, to monitor the evolution of Geant4-DNA physics, physicochemical and chemical stage simulation capabilities. So far, we have included three tests to benchmark Geant4-DNA physics (Low energy electron Dose Point Kernels and microdosimetry tests) and the physicochemical/chemical stages of particle interactions in the Chemistry test.
<figure><img src="image_85.png" /><figcaption>**FIGURE 30** Neutron yields produced by protons in a Fe thick target. Top plot: 113 MeV protons incident on a 1.57 cm thick Fe target. Bottom plot: 256 MeV protons incident on a 8.0 cm thick Fe target. In each plot, top row: neutron yield; second row: ratio of Geant4 results and reference data; third row: ratio of the results obtained with Geant4 11.1 and 10.5. The shadowed area represents an agreement within 10%. When not visible, the error bars are within the symbols. Reference data: Meier et al.⁸⁷,⁸⁸</figcaption></figure>
<figure><img src="image_86.png" /><figcaption>**FIGURE 31** Fragment yield calculated with respect to depth. Experimental data from Haettner et al.⁹¹ The error bars of the simulation results are within the symbols.</figcaption></figure>

<figure><img src="image_87.png" /><figcaption>**FIGURE 32** Ratio of Geant4 simulation results and reference data in terms of fragment yields. Experimental data from Haettner et al.⁹¹ The shadowed area represents an agreement within 10%.</figcaption></figure>

## 6.1 | Geant4-DNA physics constructors

The Geant4-DNA extension of Geant4 has been providing a range of processes and physical models since 2007. It focuses on simulating particle interactions with liquid water, which is the primary component of the biological environment. This is particularly relevant for studying the impact of ionizing radiation on biological targets at the DNA level.⁹²⁻⁹⁷ These processes and models apply to electrons, protons, neutral hydrogen

atoms, helium nuclei, and their charge states, as well as to a number of incident ions.

The processes to which electrons are subjected in the energy range associated to bio-medical physics applications include ionization, electronic excitation, vibrational excitation, elastic scattering, and dissociative electron attachment. For protons, neutral hydrogen atoms, helium nuclei, and their charge states, ionization, electron excitation, and elastic scattering are available. For ions heavier than helium, only ionization is currently
<figure><img src="image_88.png" /><figcaption>**FIGURE 33** Mean relative error (MRE) calculated for H (left), He (middle), and B (right), for the calculation of the fragments yields. The MREs of fragment yields are calculated by averaging the ratio of experiment and simulation for all six water thicknesses for the particular fragment species. Here, the reported uncertainties correspond to $1\sigma$ are provided as $1\sigma$ (see Section 2.1).</figcaption></figure>

<figure><img src="image_89.png" /><figcaption>**FIGURE 34** Mean relative error (MRE) calculated for the angular (top) and kinetic energy (bottom) distributions of fragments, for both Geant4 10.5 (red) and 11.1 (blue). The MRE is calculated for individual distributions (35 angular and 151 energy distributions). Here, provided as $1\sigma$ (see Section 2.1).</figcaption></figure>
taken into account. These processes are described by alternative models, following different approaches (theoretical, semi-empirical) and covering different energy domains. They are either analytically coded or can use cross section interpolation.

For ease of use, the processes and models are grouped into alternative Geant4-DNA physics constructors. The existence of different physics constructors in Geant4-DNA reflects the continuous efforts to be able to perform track structure simulations for electrons in condensed media with improved accuracy and reduced computational effort. Unfortunately, the absence of experimental data in the liquid-water phase does not allow them to be validated, but only benchmarked against other in silico calculations. Three alternative constructors are tested in this work: Geant4-DNA *Option2*, *Option4*, and *Option6*. Each one of these three constructors contains different physics process models for electron transport but a unique model for proton, helium, and ion processes. The emphasis given on electrons stems from the fact that they exist as secondaries from the ionization of atoms of the medium under study and are responsible for the spatial energy deposition of radiation in matter.

Both Geant4-DNA *Option2* and *Option4* physics constructors (called here *Geant4-DNA-Opt2* and *Geant4-DNA-Opt4*) are based on the dielectric theory of inelastic scattering, where condensed phase effects are included through the use of a material-dependent function for the computation of the corresponding cross sections (ionization, electronic excitation) for electrons. *Geant4-DNA-Opt4* is an improved version of *Geant4-DNA-Opt2* which, among other improvements, uses a refined partitioning algorithm, leading to higher ion-pair energies, smaller penetration distances, and less diffused dose-point kernels, and performs simulations in a more accurate manner at the lower energy range.⁹⁸ However, in its publicly available version, it has a limited energy range of applicability compared to *Geant4-DNA-Opt2*. An extended relativistic version of *Geant4-DNA-Opt4* has recently been developed and will be available in a future version of Geant4-DNA in order to replace *Geant4-DNA-Opt2*.⁹⁹ The Geant4-DNA *Option6* physics constructor, called here *Geant4-DNA-Opt6*, is a re-engineering of the original CPA100 code for electrons.¹⁰⁰ It adopts the Binary Encounter Bethe formalism¹⁰¹,¹⁰² for the analytical computation of ionization cross sections and the dielectric response function formalism for the computation of electronic excitation. The three Geant4-DNA physics constructors under study cover a different energy range of applicability for electrons (7.4 eV to 1 MeV for *Geant4-DNA-Opt2*, 10 eV to 10 keV for *Geant4-DNA-Opt4* and 11 eV to 255 keV for *Geant4-DNA-Opt6*) and, for convenience, since Geant4 version 11.1, the default high energy limits of *Geant4-DNA-Opt4* and *Geant4-DNA-Opt6* for electrons have been extended up to 1 MeV

using the inelastic cross sections of the *Geant4-DNA-Opt2* constructor. Different approaches are provided for the implementation of elastic scattering, which is of critical importance in the spatial deposition of energy because of the deflections suffered by the electrons, in the three constructors. All models, including the relevant processes for protons, neutral hydrogen atoms, helium nuclei and their charge states, and ions, are further described in the 2018 Geant4-DNA review.⁹⁵ Further, the upper energy limit for proton transport was increased from 100 to 300 MeV by incorporating excitation and ionization models based on the relativistic plane wave born approximation (RPWBA).¹⁰³ Geant4 photon processes (photoelectric effect, Compton scattering, gamma conversion, Rayleigh scattering) and models (Livermore, Klein-Nishina, 5D and Livermore, respectively, documented in Section 3.1) are also available in these constructors.

## 6.2 | Geant4-DNA chemistry constructors

Water molecules that have been ionized and excited through interactions with primary and secondary particles participate in a decomposition process through dissociation channels. These energetically charged water fragments undergo a sequence of breakdown processes, rapidly generating primary water radiolysis products such as $H_3O^+$, $^1OH$, $H^+$, $OH^-$, and $H_2$.¹⁰⁴ Subexcited electrons gradually undergo a thermalization process to reach thermal equilibrium at about 0.025 eV to form solvated electrons.

In Geant4-DNA, it is assumed that primary water radiolysis species and solvated electrons form within 1 ps, after which they are expected to diffuse through Brownian dynamics and eventually react. The diffusion and reaction of species through these initial heterogeneous distributions (spurs) along the tracks are described by either the step-by-step (SBS) approach¹⁰⁴,¹⁰⁵ or the independent reaction time (IRT) approach with two model variants: IRT¹⁰⁶⁻¹⁰⁸ and IRT-sync.¹⁰⁹ While SBS transports species in discrete steps (or time steps $\Delta t$) through Brownian motion until a chemical encounter defines a reaction, the IRT model tends to directly calculate a reaction probability. The IRT approach assumes that reactions are independent and that the diffusion of reactants from their initial positions to the reaction site is not influenced by other chemical species or volume boundaries. In this context, on the basis of reaction probabilities, the reaction times can be sampled for every potential pair of reactants. These times are then sorted in ascending order, creating a list of potential reactions. Reactions are processed sequentially, starting with those with the shortest reaction time. Products formed from reactions in progress may undergo further reactions
<table><caption>**TABLE 9** Dissociation schemes and branching ratios available in the four chemistry constructors (*chem_default*, *chem_option1*, *chem_option2*, and *chem_option3*).</caption><thead><tr><th rowspan="2">Process</th><th rowspan="2"></th><th rowspan="2">Channel</th><th colspan="2">Branching ratios</th></tr><tr><th>chem_option3<br>Shin et al.<sup>113</sup></th><th>chem_default<br>chem_option1<br>chem_option2<br>Karamitros<br>et al.<sup>104</sup></th></tr></thead><tbody><tr><td rowspan="2">Ionization</td><td>H<sub>2</sub>O<sup>+</sup></td><td>H<sub>3</sub>O<sup>+</sup> + *OH</td><td>100</td><td>100</td></tr><tr><td rowspan="2">A<sup>1</sup>B<sub>1</sub></td><td>H<sup>+</sup> + *OH</td><td>65</td><td>65</td></tr><tr><td rowspan="6">Excitation</td><td rowspan="6">B<sup>1</sup>A<sub>1</sub></td><td>H<sub>2</sub>O + ΔE</td><td>35</td><td>35</td></tr><tr><td>H<sub>3</sub>O<sup>+</sup> + *OH + e<sup>-</sup><sub>aq</sub></td><td>50</td><td>55</td></tr><tr><td>H<sup>+</sup> + *OH</td><td>25.35</td><td>—</td></tr><tr><td>H<sub>2</sub> + 2 *OH</td><td>3.25</td><td>15</td></tr><tr><td>2H<sup>+</sup> + O(<sup>3</sup>P)<sup>a</sup></td><td>3.9</td><td>—</td></tr><tr><td>H<sub>2</sub>O + ΔE</td><td>17.5</td><td>30</td></tr><tr><td rowspan="6">Electron capture</td><td rowspan="2">Rydberg A + B, C +<br>D Diffuse bands,</td><td>H<sub>3</sub>O<sup>+</sup> + *OH + e<sup>-</sup><sub>aq</sub></td><td>50</td><td>50</td></tr><tr><td>H<sub>2</sub>O + ΔE</td><td>50</td><td>50</td></tr><tr><td>DEA</td><td>OH<sup>-</sup> + *OH + H<sub>2</sub></td><td>100</td><td>100</td></tr><tr><td rowspan="4">Recombination</td><td>H<sup>+</sup> + *OH</td><td>35.75</td><td>55</td></tr><tr><td>H<sub>2</sub> + 2 *OH</td><td>13.65</td><td>15</td></tr><tr><td>2H<sup>+</sup> + O(<sup>3</sup>P)<sup>a</sup></td><td>15.6</td><td>—</td></tr><tr><td>H<sub>2</sub>O + ΔE</td><td>35</td><td>30</td></tr></tbody></table>

with other reactants, thereby being added to the reaction list.

Since IRT models optimize the diffusion actions, this approach has a much better computational performance than the SBS model, especially when dealing with a large number of species. The synchronous IRT (IRT-sync documented in Tran et al.¹⁰⁹) model proposes an implementation of the IRT model to allow access to spatial-temporal information at certain times. This implementation uses as the time step the randomly sampled time given by the IRT model until the next expected reaction. In other words, instead of optimizing the time step to the next reaction like the SBS model does, the IRT-sync model calculates the reaction time directly using the IRT model. This procedure is repeated until the end of the simulation. This means that after each time step, it is necessary to synchronize the time and position of all diffusing species. This is a drawback of the IRT-sync approach. However, due to synchronization at each time step, IRT-sync provides users with spatio-temporal information for all chemical species, which can then be coupled with information on geometric boundaries or the biological target.

The chemistry constructors in Geant4-DNA specify the dissociation scheme (see Table 9), the chemical reactions and the models involved in water radiolysis. In Geant4 11.1, Geant4-DNA provides G4EmDNA-Chemistry (*chem_default*), G4EmDNAChemistry_option1 (*chem_option1*), G4EmDNAChemistry_option2

(chem_option2), and G4EmDNAChemistry_option3 (chem_option3) that deploy different sets of reactions concerning water radiolysis and DNA reactions, accompanied by reaction constant data. While *chem_default*, *chem_option1*, and *chem_option2* constructors use a dissociation scheme following the PARTRAC code,¹¹⁰ the chemistry constructor *chem_option3* applies the B1A1 dissociation channel proposed by the TRACs code.¹¹¹, ¹¹² *chem_default*, *chem_option1*, and *chem_option2* use the SBS model by default, while in the chemistry constructor *chem_option3*, a user interface allows users to choose either SBS, IRT, or IRT-sync.

## 6.3 | Low-energy electron Dose Point Kernels test

This test is described in detail in Arce et al.¹³ and is of interest for the application of the Geant4-DNA extension in dosimetry calculations in radiopharmaceutical therapy.¹¹⁴, ¹¹⁵

Mono-energetic electrons, with energy 10, 15, and 100 keV, are emitted isotropically into a $4\pi$ solid angle from a point source placed in a spherical liquid water (defined as G4_WATER) volume. Radial energy deposition profiles are calculated. 10⁵ histories are executed to obtain statistical uncertainties of about 0.3% in the simulation results. The uncertainty has been

<footnote><sup>a</sup>Oxygen atom in triplet state P. Geant4 version 11.1 is considered.</footnote>
<figure><img src="image_90.png" /><figcaption>**FIGURE 35** Top plots: Dose Point Kernel in water, obtained for 10, 15, and 100 keV electrons. Bottom plots: ratio of the results obtained with either Geant4-DNA physics list *Geant4-DNA-Opt4* or *Geant4-DNA-Opt6* and *Geant4-DNA-Opt2*. Results obtained with the *LowEElectDPK* test and Geant4 11.1. The error bars of the simulation results are within the symbols. To note, for 100-keV electrons, *Geant4-DNA-Opt4* provides the same results as *Geant4-DNA-Opt2*.</figcaption></figure>

evaluated calculating average and standard error from a batch of identical simulations with different random seeds.

The test, originally included in the G4-Med suite to benchmark Geant4 electromagnetic physics constructors using a CH approach,¹³ has been adapted to benchmark Geant4-DNA physics lists, as track structure codes are recognized to be more accurate to calculate energy deposition distributions in volumes with sub-cellular dimensions.¹¹⁶ Geant4-DNA physics constructors *Geant4-DNA-Opt2*, *Geant4-DNA-Opt4*, and *Geant4-DNA-Opt6* are tested.

Figure 35 shows the results of the test. We observe that *Geant4-DNA-Opt2* and *Geant4-DNA-Opt4* provide similar results, while *Geant4-DNA-Opt6* estimates the peak of the energy deposition distribution slightly closer to the source of the incident electrons.

**6.4 | The Microdosimetry test**

The *Microdosimetry* test is released as the Geant4 extended example *microyz*. The test was already existing in the G4-Med benchmarking system¹³ but it has been revised and adapted to test *Geant4-DNA-Opt2*, *Geant4-DNA-Opt4* and *Geant4-DNA-Opt6*. It calculates microdosimetric spectra of lineal and specific energy and their corresponding frequency-weighted and dose-weighted quantities for the case of monoenergetic electrons traversing liquid water spheres, randomly

placed along the track structure of the incident electron in a semi-infinite water medium.³⁰

**6.4.1 | Simulation set-up**

Monoenergetic electrons are incident on liquid water with energies equal to 100 eV, 1 keV, 10 keV, 100 keV, and 1 MeV, covering both the imaging and therapeutic range, that is, secondaries from hadron therapy or primaries from radionuclide therapy.¹¹⁷ The sensitive volume sphere has a diameter of 10 nm, which is a mean distance of interest for studies like double-strand break induction.¹¹⁸ Additionally, spheres with a 1 µm diameter are considered as they are of interest for tissue-equivalent proportional counter measurements for radiation protection.¹²⁰

The test is used for regression testing purposes only, to study how changes in the physics models of Geant4 impact the calculation of microdosimetric quantities. In this study, we present results for the dose-mean lineal energy, which is the dose-weighted probability function of the lineal energy that takes into account the higher dose deposition of the greater valued lineal energies.¹²¹ In the *microyz* example, the lineal energy is calculated as the ratio of the energy imparted to matter in a given volume (sensitive volume) by a single energy deposition event and the mean chord length of that volume, as
defined in Braby et al.¹¹⁶ The dose–mean lineal energy is calculated by summing over all the lineal energies $y_i$ calculated in each track $i$, times the contribution of each $y_i$ to the dose within the sensitive volume under study.

$$<y_D> = \sum_{i=1}^{N} d_i y_i \qquad (6)$$

with $d_i = f_i y_i / <y_F>$, $<y_F>$ being the frequency-weighted lineal energy calculated by $<y_F> = \sum_{i=1}^{N} f_i y_i$, $f_i$ the probability weighting factor and $N$ the total number of tracks (histories) simulated including primary and secondary particles. The lineal energies $y_i$ for each track $i$ are calculated in the Geant4 code by randomly placing a sphere of a user-defined size along a certain distance from an energy deposit within the track. Details on the algorithm followed in the *microyz* example can be found in Kyriakou et al.³⁰, ¹¹⁷ The energy cutoff is kept equal to 10 eV for the three physics constructors investigated and the sub-excitation processes are deactivated.

The statistics for each energy varies according to the incident energy in order to avoid very large simulation times. In consideration of the fact that the microdosimetric simulations using the track structure models of Geant4-DNA are computationally demanding, they were executed for each energy more than once with different random seeds in order to ensure a statistical uncertainty below 0.1% up to 10 keV, below 0.5% for 100 keV, and below 1% for 1 MeV.

In the *geant-val* testing suite, the three Geant4-DNA physics constructors mentioned above are compared up to 10 keV because this is the upper limit of applicability of the specific electron elastic and inelastic models used in Geant4-DNA-Opt4.⁹⁸

## 6.4.2 | Results

Figure 36 shows the dose–mean lineal energy, $y_D$, as a function of the incident electron kinetic energy. Results are reported for Geant4 11.1. For a water sphere of 10-nm diameter, differences between the three physics constructors are more pronounced compared to the larger diameters. Geant4-DNA-Opt6 produced $y_D$ values higher than those calculated with Geant4-DNA-Opt2, with a MD of about 28%. These differences are caused by the much different inelastic cross sections of this constructor. Overall, differences between Geant4-DNA-Opt2 and Geant4-DNA-Opt4 are smaller as a result of the similar inelastic models with the differences attributed to the particular ionization and excitation contributions in each model. Additionally, Geant4-DNA-Opt6 contains energy loss for elastic scattering that leads to a decrease of the frequency mean lineal energy values⁹⁸ and especially in the case of smaller diameters

(not shown in this study) but does not affect the $y_D$. In the case of 100 nm and 1-µm diameter water sphere, the different Geant4-DNA physics constructors produce smaller differences; up to 6% for Geant4-DNA-Opt6 and up to 4% for Geant4-DNA-Opt4, when compared to Geant4-DNA-Opt2. It must be taken into consideration that above 10 keV for Geant4-DNA-Opt4 and 255 keV for Geant4-DNA-Opt6, the Geant4-DNA-Opt2 physics constructor is used and we expect that the comparison would be more rigorous if each model was used up to 1 MeV, which will be shown in a future work. In any case, the low (especially the sub-kilo electron volt) energy behavior affects the energy deposition distribution at sub-micron volumes.

## 6.5 | The chemistry test

The Chemistry test is based on the Geant4 extended example *chem6*, which illustrates how to compute radiochemical yields (G-values) versus time or linear energy transfer (LET). The time-dependent radiolytic yield is often defined as the number of molecules, at a given time, for 100 eV of deposited energy. To reduce simulation execution times, in Geant4-DNA, the G-values are calculated for a short energy range of the ionizing particle that is referred to as the “track segment G-value”. Two parameters are used for energy threshold selection, the minimum energy deposition *eLossMin* and the maximum energy deposition *eLossMax*. While the simulation is aborted if the total energy deposition of a simulated event (that is, the primary particle and all associated secondaries) is larger than *eLossMax*, the incident particle is killed if its energy loss exceeds *eLossMin*.¹¹³ The G-value of each event is calculated and cumulated to calculate $N$, the total number of events, and $\bar{G}$, the average value of the G-value. Then, the uncertainty affecting

the G-value is calculated as $\sqrt{\frac{\sum_i G_i^2}{N} - \bar{G}^2}$, where $i$ is an event and $G_i$ indicates the G-value calculated in the event $i$. 10³ histories are executed in this test.

The *chem6* Geant4 example uses the chemistry constructor *chem_option3*. This constructor offers users an interface to facilitate the addition or removal of chemical reactions or evaluate the influence of chemical reaction-diffusion models, such as the *SBS*, the independent time reaction (IRT), and the synchronized independent time reaction (IRT-sync) models, on water radiolysis simulations.

### 6.5.1 | Simulation set-up

In this test, we perform a simulation to compute time-dependent G-values for the chemical models *SBS*, *IRT*, and *IRT-sync*, for 1-MeV incident electrons with
<figure><img src="image_91.png" /><figcaption>**FIGURE 36** Top plots: Dose-mean lineal energy $y_D$ with respect to the kinetic energy of the incident electrons, for a water sphere of 10 nm (left), 100 nm (middle), and 1 µm diameter (right). Bottom plots: ratio of the results obtained with either Geant4-DNA-Opt4 or Geant4-DNA-Opt6 with the default Geant4-DNA-Opt2. Results obtained with the microdosimetry test and Geant4 11.1. When not visible, the error bars are within the symbols.</figcaption></figure>

<table><caption>**TABLE 10** Reactions and associated reaction rate coefficients ($k$) used by IRT and IRT-sync are either partially or totally diffusion-controlled.</caption><thead><tr><th>Reaction</th><th>k × 10<sup>10</sup><br>M<sup>-1</sup>s<sup>-1</sup></th><th>Partially<br>diffusion-controlled</th><th>Totally<br>diffusion-controlled</th></tr></thead><tbody><tr><td>H<sup>+</sup> + e<sup>-</sup><sub>aq</sub> + H<sub>2</sub>O → OH<sup>-</sup> + H<sub>2</sub></td><td>2.5</td><td></td><td>X</td></tr><tr><td>H<sup>+</sup> + *OH → H<sub>2</sub>O</td><td>1.55</td><td>X</td><td></td></tr><tr><td>H<sup>+</sup> + H<sup>+</sup> → H<sub>2</sub></td><td>0.503</td><td></td><td>X</td></tr><tr><td>H<sub>2</sub>O<sub>2</sub> + e<sup>-</sup><sub>aq</sub> → OH<sup>-</sup> + *OH</td><td>1.1</td><td>X</td><td></td></tr><tr><td>H<sub>3</sub>O<sup>+</sup> + e<sup>-</sup><sub>aq</sub> → H<sup>+</sup> + H<sub>2</sub>O</td><td>2.11</td><td>X</td><td></td></tr><tr><td>H<sub>3</sub>O<sup>+</sup> + OH<sup>-</sup> → 2H<sub>2</sub>O</td><td>11.3</td><td></td><td>X</td></tr><tr><td>*OH + e<sup>-</sup><sub>aq</sub> → OH<sup>-</sup></td><td>2.95</td><td>X</td><td></td></tr><tr><td>*OH + *OH → H<sub>2</sub>O<sub>2</sub></td><td>0.55</td><td>X</td><td></td></tr><tr><td>e<sup>-</sup><sub>aq</sub> + e<sup>-</sup><sub>aq</sub> + 2H<sub>2</sub>O → 2OH<sup>-</sup> + H<sub>2</sub></td><td>0.636</td><td></td><td>X</td></tr></tbody></table>

eLossMin and eLossMax equal to 10 and 10.1 keV, respectively. Table 10 shows the reaction list and reaction constants used in the test.

## 6.5.2 | Results and discussion

Figure 37 shows the G-values of $e_{aq}^-$, $H_2O_2$, and *OH species, calculated using the SBS, IRT-sync, and IRT models, against available experimental

measurements.122–124 The G-values are calculated with Geant4 11.1. Figure 38 shows the ratio of the G-values calculated with either IRT or IRT-sync and SBS.

In the case of $H_2O_2$, both IRT and IRT-sync produce higher G-values (about 1.3 and 2 times higher, respectively) at the start of the chemical stage when compared to SBS. After that, the difference decreases with time. In the case of $e_{aq}^-$, IRT produces similar results to SBS within approximately 0.1 ns from the start of the
<figure><img src="image_92.png" /><figcaption>**FIGURE 37** G-values of $e_{aq}^-$, $H_2O_2$, and $\cdot OH$ species calculated with the chemistry test, using the SBS, *IRT-sync*, and *IRT* models. Results obtained with Geant4 11.1. The error bars of the simulation results are within the symbols.</figcaption></figure>

<figure><img src="image_93.png" /><figcaption>**FIGURE 38** Ratio of G-values (plotted in Figure 37) obtained with *IRT-sync* and *IRT* models, when compared to SBS. The shadowed area indicates an agreement within 5%.</figcaption></figure>

chemical stage. After that, it produces lower G-values with a MD of about 5% at 1 µs. *IRT-sync* underestimates the $e_{aq}^-$ G-values of about 1%–5% with respect to the SBS. In the case of $\cdot OH$ G-values, both *IRT* and *IRT-sync* produce consistently lower G-values (differences up to approximately 4 and 6%, respectively, when compared to SBS).

Figure 39 reports the ratio of the results obtained with Geant4 11.1 and the reference experimental data.<sup>122–124</sup> The three chemistry models of Geant4 agree with the reference data within $2\sigma$, apart from the case of $\cdot OH$ around 400 ns to 1 µs, where Geant4 tends to overestimate the G-value. Nevertheless, provided the few experimental data, it is difficult
<figure><img src="image_94.png" /><figcaption>**FIGURE 39** Ratio of G-values obtained with SBS, IRT, and IRT-sync (Geant4 11.1) and experimental data.<sup>122–124</sup> The shadowed area indicates an agreement within 5%.</figcaption></figure>

to draw any conclusion, more reference data are needed.

# 7 | COMPUTING PERFORMANCE TEST

The aim of this part of the project is to benchmark the execution times of the main Geant4 physics constructors and lists used within the G4-Med suite. This is achieved using a simplified Geant4 simulation, described in Section 7.1.

Each simulation configuration of the Geant4 application is executed in sequential mode (i.e., single threaded) on a dedicated computing server, a 2.30 GHz Intel Xeon E5-2650v3-based machine maintained by the Centre for Medical and Radiation Physics, University of Wollongong, Australia. Each simulation configuration is repeated 10 times with different random seeds. Then, the average and standard deviation of the execution times are calculated. The computing performance $\epsilon$ is then calculated as $\epsilon = \frac{T}{T_{ref}}$, where T and $T_{ref}$ are the execution times of the Geant4 simulation for a particular physics lists/constructor and a reference list/constructor, respectively.

## 7.1 | Geant4 simulation set-up

The Geant4 simulation consists of a 30-cm water cube, a pencil beam is generated at the center of one of the face's surface, just inside the water medium. No particle track information or other physical quantities (for example, energy deposition) are retrieved or stored. The simulation only generates primary particles with a defined energy and direction, and tracks them in the water phantom. The execution time from the start of the first event to the end of the last event is stored. This is

to minimize the contribution to the computational time deriving from components other than the physics modeling, for example, geometry operations, retrieval and storage of track and stepping information in Geant4 User Actions. An “event” is the generation of a single primary particle within the simulation geometry and tracking this primary particle as it interacts in the geometry. The end of an event occurs once the primary particle and all secondary particles it creates either exit the simulation’s geometry or lose all their kinetic energy. The total number of events chosen by the user is referred to as a “run.”

The quantity compared for these execution times is the *execution time per event*, obtained from dividing the recorded runtime of all the events by the number of events. Configuration runtimes were averaged over 10 separate runs using different seeds, with the standard deviation of the 10 runs used as the uncertainty. The number of primaries generated for each configuration (run 10 times) was chosen such that the runtime would be at least 1000 s and are summarized in Table 11.

### 7.1.1 | Electromagnetic settings

Mono-energetic electron beams are generated to compare the execution times of both Geant4-DNA track structure (Geant4-DNA-Opt2, Geant4-DNA-Opt4, and Geant4-DNA-Opt6) and Geant4 CH EM constructors (Opt3, Opt4, Livermore, and Penelope).

The energy of the primary electron beams are as follows: 1, 10, 100, $10^3$, $10^4$ keV. All the Geant4 CH EM physics constructors have a cut of 1 µm and a threshold production of 1 keV, which corresponds to an electron range in water of ~1 µm. The choice of a 1 keV production threshold is dictated by the fact that this is the minimum recommended energy of the Geant4 EM Opt3 constructor.
<table><caption>**TABLE 11** Number of primary particles (events) generated for each computation configuration, used to compare the computing performance of Geant4-DNA physics lists, Geant4 EM physics constructors based on condensed history approach and Geant4 physics lists (with both EM and hadronic physics processes).</caption><thead><tr><th>Configuration</th><th>Number of primary particles</th></tr></thead><tbody><tr><td colspan="2"><strong>Geant4-DNA physics lists</strong></td></tr><tr><td>1 keV e<sup>-</sup></td><td>10<sup>6</sup></td></tr><tr><td>10 keV e<sup>-</sup></td><td>10<sup>5</sup></td></tr><tr><td colspan="2"><strong>Geant4 EM physics constructors</strong></td></tr><tr><td>10 keV e<sup>-</sup></td><td>10<sup>8</sup></td></tr><tr><td>100 keV e<sup>-</sup></td><td>10<sup>7</sup></td></tr><tr><td>1 MeV e<sup>-</sup></td><td>10<sup>7</sup></td></tr><tr><td>10 MeV e<sup>-</sup></td><td>10<sup>6</sup></td></tr><tr><td colspan="2"><strong>Geant4 EM physics lists (EM + hadronic processes)</strong></td></tr><tr><td>150-MeV protons, 0.1 mm cut</td><td>10<sup>7</sup></td></tr><tr><td>150-MeV protons, 1 m cut</td><td>10<sup>7</sup></td></tr><tr><td>290-MeV/u <sup>12</sup>C ions, 0.1 mm cut</td><td>10<sup>5</sup></td></tr><tr><td>290-MeV/u <sup>12</sup>C ions, 1 m cut</td><td>10<sup>6</sup></td></tr></tbody></table>

Note: Each configuration was run 10 times for statistical calculations, meaning that the total number of primary particles generated is 10 times larger than the ones reported in this table.

Until version 11.0, simulations with the Geant4-DNA physics constructors were performed for primary energies of 1 and 10 keV only, due to Geant4-DNA-Opt4 and Geant4-DNA-Opt6 having maximum electron ionization energies of 10 and 255 keV, respectively. Since version 11.1, a combination with Born models (ionization and excitation) extends the maximum energies up to 1 MeV for Geant4-DNA-Opt4 and Geant4-DNA-Opt6. Conversely, Geant4 CH EM physics constructors are executed only for electron energies of 10 keV and higher due the adoption of the 1-keV cut.

### 7.1.2 | Hadronic settings

The execution times of the prebuilt Geant4 physics lists for hadronic interactions are compared using a 150 MeV proton and a 290 MeV/u <sup>12</sup>C ion beam incident on the 30 cm water cube. In the case of the proton beam, the QGSP_BIC HP, QGSP_BIC AllHP and QGSP BERT HP physics lists are compared. In the case of an incident <sup>12</sup>C ion beam, the QGSP_BIC HP is adopted. The ion fragmentation is modeled alternatively with BIC, QMD, and INCL. Opt4 is chosen in all the Geant4 physics lists under study to describe EM physics interactions, as it is deemed to be the most accurate for bio-medical applications.

Both the proton and <sup>12</sup>C ion simulations are executed with a 0.1 mm and a 1 m cut. The 0.1 mm value represents a more clinically relevant description of the generation of delta electrons in the simulation. The 1 m cut has instead been chosen to minimize the con-

tribution of the EM physics interactions (no generation of delta electrons), to compare the effect of different hadronic physics models in the execution times.

## 7.2 | Results and discussion

Execution times using Geant4-DNA physics constructors, for electron beams with energies 1 and 10 keV in water, are shown in Table 12. For 1 keV electron beams, Geant4-DNA-Opt4 is about 12% slower than Geant4-DNA-Opt2, while Geant4-DNA-Opt6 is ~15% faster. At 10 keV, Geant4-DNA-Opt4 becomes significantly more computationally intensive than Geant4-DNA-Opt2, with ~70% longer execution time, with Geant4-DNA-Opt6 maintaining a similar ratio with Geant4-DNA-Opt2 at both 10 and 1 keV cases.

The execution times obtained with the Geant4 EM CH approach constructors when simulating electron beams with energy between 10 and 10 MeV are shown in Table 13. For the case of 10 keV electrons in water, Opt4, Livermore, and Penelope have the same computing performance and are about twice slower than Opt3. When considering 100 keV electrons, Opt4 and Penelope are about three times slower than Opt3, while Livermore is about 3.7 times slower. At higher electron beam energies, 1 MeV and above, Penelope becomes significantly slower than Opt4 and Livermore. At these higher energies, Opt4 and Livermore's execution time ratios reduce to ~2.5× and ~2.2× at 1 and 10 MeV, respectively, when compared to Opt3, while Penelope is about four times slower than Opt3 for both electron energies.

Table 14 show the execution times per event obtained in the case of a 150 MeV proton beam, with the different Geant4 physics lists under study and two different cuts (0.1 mm and 1 m). For both cut sizes, the BIC HP and BERT HP have very similar execution times. QGSP_BIC AllHP is characterized by significantly shorter execution times than QGSP_BIC HP and QGSP BERT HP.

Comparison of execution times per event obtained with QGSP_BIC HP and changing the ion fragmentation model are shown in Table 15, for a 290 MeV/u <sup>12</sup>C ion beam in water. The simulations with BIC and INCL have similar execution times. In the case of the smaller 0.1 mm cut, the execution time obtained with the QMD fragmentation model is about 40% longer than in the case of BIC and INCL. In the case of the higher cut of 1 m, the execution time obtained with QMD is about four times longer than BIC and INCL. Both BIC and QMD model the interaction of projectile and target nucleons as Gaussian wave functions. However, the reason for the significantly longer QMD execution times is that, compared to BIC, QMD produces wave functions for all target and projectile nucleons in the interaction, while BIC only produce wave functions for participating nucleons. Additionally, QMD is time-dependent while BIC is
<table><caption>**TABLE 12** Execution time per event calculated with incident electrons, with energy 1 and 10 keV, in a water phantom, for the Geant4-DNA physics constructors studied in this work.</caption><thead><tr><th>Energy (keV)</th><th>EM Physics constructor</th><th>Execution time per event (µs)</th><th>G4EMconstructor<br>Geant4 - DNA - Opt2</th></tr></thead><tbody><tr><td rowspan="3">1 keV</td><td>Geant4-DNA-Opt2</td><td>(414. ± 3.)·10</td><td>1</td></tr><tr><td>Geant4-DNA-Opt4</td><td>(466. ± 3.)·10</td><td>1.12 ± 0.01</td></tr><tr><td>Geant4-DNA-Opt6</td><td>(353. ± 2.)·10</td><td>0.85 ± 0.01</td></tr><tr><td rowspan="3">10 keV</td><td>Geant4-DNA-Opt2</td><td>(430. ± 2.)·10<sup>2</sup></td><td>1</td></tr><tr><td>Geant4-DNA-Opt4</td><td>(744. ± 4.)·10<sup>2</sup></td><td>1.73 ± 0.01</td></tr><tr><td>Geant4-DNA-Opt6</td><td>(357. ± 4.)·10<sup>2</sup></td><td>0.83 ± 0.01</td></tr></tbody></table>

Note: Results obtained with Geant4 11.1.

<table><caption>**TABLE 13** Execution times per event obtained with the simulations modeling 0.10, 0.1, 1, and 10 MeV electron beams in water.</caption><thead><tr><th>Energy (MeV)</th><th>Model</th><th>Execution time per event (µs)</th><th>G4EMConstructor<br>Opt3</th></tr></thead><tbody><tr><td rowspan="4">0.01</td><td>Opt3</td><td>23. ± 1.</td><td>1</td></tr><tr><td>Opt4</td><td>45. ± 2.</td><td>(2.0 ± 0.2)</td></tr><tr><td>Penelope</td><td>46. ± 3.</td><td>(2.0 ± 0.2)</td></tr><tr><td>Livermore</td><td>48. ± 1.</td><td>(2.1 ± 0.1)</td></tr><tr><td rowspan="4">0.1</td><td>Opt3</td><td>48. ± 3.</td><td>1</td></tr><tr><td>Opt4</td><td>143. ± 2.</td><td>3.0 ± 0.2</td></tr><tr><td>Penelope</td><td>145. ± 7.</td><td>3.0 ± 0.2</td></tr><tr><td>Livermore</td><td>178. ± 3.</td><td>3.7 ± 0.2</td></tr><tr><td rowspan="4">1</td><td>Opt3</td><td>(30. ± 1.)·10</td><td>1</td></tr><tr><td>Opt4</td><td>(75. ± 3.)·10</td><td>2.5 ± 0.1</td></tr><tr><td>Penelope</td><td>(120. ± 10.)·10</td><td>3.9 ± 0.4</td></tr><tr><td>Livermore</td><td>(74 ± 3)·10</td><td>2.5 ± 0.1</td></tr><tr><td rowspan="4">10</td><td>Opt3</td><td>(27. ± 1.)·10<sup>2</sup></td><td>1</td></tr><tr><td>Opt4</td><td>(58. ± 3.)·10<sup>2</sup></td><td>2.2 ± 0.1</td></tr><tr><td>Penelope</td><td>(109. ± 4.)·10<sup>2</sup></td><td>4.1 ± 0.2</td></tr><tr><td>Livermore</td><td>(59. ± 1.)·10<sup>2</sup></td><td>2.2 ± 0.1</td></tr></tbody></table>

Note: Results shown for the Geant4 condensed history EM physics constructors under study, with Geant4 11.1.

time-independent. The INCL model instead describes the wave functions of the interacting nucleons as free Fermi gas in a static potential well, which shows to be computationally similar to the BIC.

# 8 | DISCUSSION OF THE RESULTS

## 8.1 | Electromagnetic physics tests

Three new EM physics tests have been introduced in the G4-Med benchmarking system since our first work documented in Arce et al.¹³ to extend the validation of Geant4 to low-dose-rate brachytherapy, MV x-ray external radiotherapy and electron FLASH radiotherapy,

extending the coverage of the G4-Med benchmarking system to more medical physics application scenarios.

The electromagnetic physics tests of the G4-Med benchmarking system showed some significant differences between Geant4 10.5 and 11.1 in Opt3 due to differences in the multiple scattering, documented in Section 3.1. While Opt3 in Geant4 11.1 provides a better description of electron backscattering (see Section 3.5.1), it is less accurate to describe the transmission of electrons in the forward direction, when compared to *Livermore*, *Penelope*, and *Opt4* (see Section 3.5.2), which then translates in a less accurate calculation of dose (see Section 3.4). Because of this finding, a patch of Geant4 has been released (11.2.1) where the multiple scattering parameters of Opt3 have been reverted to those of Geant4 10.5. Thanks to this change, the electron transmission and dose calculations with Opt3 show to improve, but our results indicate that the agreement achieved with Geant4 10.5 cannot still be fully reproduced. Work is under way to understand the source of the observed behavior.

The MV x-ray radiotherapy test (Section 3.3) shows some significant differences in the implementation of the bremsstrahlung model between *Penelope* and *Opt4*, which will be the subject of a detailed investigation.

Based on our findings in the electron backscattering, MV x-ray radiotherapy, Electron FLASH radiotherapy, 13 MeV electron forward scatter and Bremsstrahlung from thick targets tests, it is recommended to use the EM constructor *Opt4*, which shows to be—overall—the most adequate choice among the available EM constructors for different medical physics application scenarios.

## 8.2 | Hadronic physics tests

Three hadronic inelastic scattering tests are currently included in the G4-Med benchmarking suite.

The regression testing showed that the nucleus-nucleus hadronic inelastic scattering cross sections of incident protons on ¹²C, ¹⁶O, ²⁷Al, and ⁴⁰Ca targets changes between Geant4 10.5 and 11.1 for energies below 10 MeV (see Section 4.1.1). This change is due
<table><caption>TABLE 14 Execution times per event of the Geant4 physics lists used in this work, for a 150-MeV proton beam in a water phantom.</caption><thead><tr><th>Cut</th><th>Geant4 physics list</th><th>Execution time per event (µs)</th><th>Geant4PhysicsList<br/>QGSP_BIC_HP</th></tr></thead><tbody><tr><td rowspan="3">0.1 mm</td><td>QGSP_BIC_HP</td><td>(133. ± 8.)·10</td><td>1</td></tr><tr><td>QGSP_BIC_AIIHP</td><td>(31. ± 1.)·10</td><td>0.23 ± 0.02</td></tr><tr><td>QGSP_BERT_HP</td><td>(131. ± 6.)·10</td><td>0.99 ± 0.07</td></tr><tr><td rowspan="3">1 m</td><td>QGSP_BIC_HP</td><td>425. ± 9.</td><td>1</td></tr><tr><td>QGSP_BIC_AIIHP</td><td>47. ± 2.</td><td>0.11 ± 0.01</td></tr><tr><td>QGSP_BERT_HP</td><td>391. ± 9.</td><td>0.92 ± 0.03</td></tr></tbody></table>

Note: Results obtained with Geant4 11.1.

<table><caption>TABLE 15 Execution times of the Geant4 ion fragmentation models, BIC, INCL, and QMD, for a 290 MeV/u <sup>12</sup>C ion beam in water.</caption><thead><tr><th rowspan="2">Cut</th><th rowspan="2">Geant4 ion<br/>fragmentation<br/>model</th><th rowspan="2">Execution time<br/>per event (µs)</th><th>Geant4PhysicsList</th></tr><tr><th>BIC</th></tr></thead><tbody><tr><td rowspan="3">0.1 mm</td><td>BIC</td><td>(332. ± 9.)·10<sup>2</sup></td><td>1</td></tr><tr><td>QMD</td><td>(469. ± 8.)·10<sup>2</sup></td><td>1.41 ± 0.05</td></tr><tr><td>INCL</td><td>(321. ± 8.)·10<sup>2</sup></td><td>0.97 ± 0.04</td></tr><tr><td rowspan="3">1 m</td><td>BIC</td><td>(47.0 ± 0.8)·10<sup>2</sup></td><td>1</td></tr><tr><td>QMD</td><td>(188. ± 1.)·10<sup>2</sup></td><td>4.01 ± 0.07</td></tr><tr><td>INCL</td><td>(44. ± 2.)·10<sup>2</sup></td><td>0.94 ± 0.04</td></tr></tbody></table>

Note: Results obtained with Geant4 11.1.

to the change of the Coulomb barrier parameterization in the cross section computation. Geant4 11.1 hadronic cross sections are deemed to be more accurate as they are obtained from tabulation of ParticleHP evaluated data based on the best known experimental data and at higher energies on the Glauber–Gribov theory.³

The 300 MeV/u <sup>12</sup>C ion charge-changing cross section test (Section 4.1.3) shows significant differences between Geant4 10.5 and 11.1 in the calculation of the fragmentation yields. Geant4 11.1 describes significantly better the B isotopes yield, with approximately a 20% agreement with the reference data, when compared to Geant4 10.5. Nevertheless, this improvement is accompanied by a worsening of the results for Be production of about 10%–15%. The change in the fragmentation yields may be due to the change of de-excitation channels of the Fermi Break-Up model, nevertheless more tailored tests should be performed to confirm this hypothesis. Among the three fragmentation models under study (BIC, QMD and INCL), BIC produces overall the best agreement with the reference data. The results of the 300 MeV/u <sup>12</sup>C ion charge-changing cross section test (Section 4.1.3) are coherent with the results of the 62 MeV/u <sup>12</sup>C fragmentation test (Section 4.1.2).

In summary, the results show that it is paramount to execute the G4-Med nuclear fragmentation tests whenever there is a new development in the hadronic physics of Geant4 to monitor closely the evolution of its physics models. In addition, more tests need to be included in

the G4-Med suite to benchmark individual models (e.g. the Fermi Break-Up model), to cover a wider energy range of carbon ions of interest for hadron therapy, to include more cross sections of interest, for example for accelerator-based Boron Neutron Capture Therapy, and neutron radiation fields.

## 8.3 Electromagnetic and hadronic physics tests

Two new tests have been included in the G4-Med benchmarking suite covering two new application scenarios of interest for hadrontherapy, experimental, microdosimetry (Section 5.2) and in vivo PET (Section 5.3).

When considering the G4-Med tests of interest for proton therapy, the following observations can be made. QGSP_BIC_HP, QGSP_BIC_AIIHP, and QGSP_BERT_HP produce the same results when calculating the track-averaged LET of a 62 MeV SOBP proton beam in water. The agreement with reference data is within 15% (Hadrontherapy test, Section 5.2).

The regression testing of 67.5 MeV proton Bragg curves in water (Section 5.4.1) shows a slight improvement in Geant4 11.1 in terms of spread of a Gaussian describing the width of the Bragg peak, while the results of the Light Ion Bragg Peak curves test show that the R<sub>82</sub> of protons with energy up to 200 MeV in water improves of approximately 0.2 mm in Geant4 11.1. These improvements are ascribed to the ICRU90 adoption to calculate the low energy proton stopping powers in water in Geant4 11.1.

The Neutron yield of protons with energy 113 and 256 MeV test (Section 5.4.3) reports that QGSP_BIC_HP in Geant4 11.1 produces a higher yield of neutrons (up to approximately 20%) with energy below 10 MeV for protons with 113 and 256 MeV energies, incident on a Fe target. No difference between Geant4 10.5 and 11.1 is found for the lighter targets considered (C and Al) in the irradiation scenarios under study.

When considering the G4-Med tests of interest for heavy ion therapy, the in vivo PET test (Section 5.3) shows that BIC and QMD are more adequate than INCL to describe the positron yield for incident <sup>12</sup>C and <sup>16</sup>O beams in the targets under study (gelatin, PMMA, and
polyethylene). Overall, BIC provides better description of the positron yields in the Bragg peak region, while QMD outperforms BIC after the distal edge of the Bragg peak.

The regression testing of the *Light Ion Bragg Peak* curves test show that the R<sub>82</sub> in water changes between Geant4 10.5 and 11.1 due to the introduction of the Lindhard-Sorensen ion model, available in Geant4 since version 11.0. When compared to Geant4 10.5, Geant4 11.1 produces R<sub>82</sub> closer to the reference data for <sup>12</sup>C ions with energies up to 250 MeV/u (within 0.3 and 0.6 mm for Geant4 11.1 and 10.5, respectively). Instead, in the case of 400 MeV/u <sup>12</sup>C ions, which is the largest energy of the carbon ion beam under study, the difference in the calculation of R<sub>82</sub> between Geant4 simulation results and experimental data is about 0.85 and 1.0 mm, for Geant4 10.5 and 11.1, respectively.

The *Neutron yield of carbon ions with energy 290 MeV/u* test did not report any change in the neutron production yield of 290 MeV/u <sup>12</sup>C ions in water between Geant4 10.5 and 11.1.

The *Fragmentation of a 400 MeV/u <sup>12</sup>C ion beam in water* test shows a higher production of the boron fragment, leading to a better agreement with the reference data. This result is consistent with the results of the 300-MeV/u <sup>12</sup>C ion charge-changing cross section test (Section 4.1.3).

Arce et al.<sup>13</sup> recommended for hadrontherapy simulations the use of *QGSP\_BIC\_HP* with *Opt4* (*Opt4* is the default EM constructor in *QGSP\_BIC\_HP* since Geant4 11.0) to describe the EM physics component, as this physics list provides an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. The same recommendation is given here based on the results of the G4-Med tests documented in this special report.

To note, for nuclear fragmentation, a novel QMD model<sup>125</sup> has been introduced in Geant4 11.2, called LiQMD, whose model parameters have been improved for carbon ion therapy. This model will be included in the next future in the G4-Med benchmarking activity as first results showed a better agreement with experimental reference data for nuclear fragmentation.<sup>125</sup>

It should be noted that the provided recommendations in terms of Geant4 physics list do have some limitations. Only few physical quantities (position and spread of the Bragg peak, neutron yields and fragment yields) in specific irradiation scenarios have been considered. Despite our effort to increase the number of hadronic physics tests (two new tests have been included since Arce et al.<sup>13</sup>), more tests should be added to extend the benchmark further for nuclear fragmentation and to test neutron production and interactions.

The hadronic physics of Geant4 is an active domain of development and the results of the G4-Med benchmarking system highlight the need to perform regression testing whenever there is a change in the hadronic physics of Geant4 to monitor the evolution of this Monte Carlo simulation code.

## 8.4 | Geant4-DNA tests

Three tests have been introduced in the G4-Med suite to perform Geant4-DNA regression testing: the *Low energy electron Dose Point Kernels, microdosimetry*, and *chemistry* tests. In summary, the *Low energy electron Dose Point Kernels and microdosimetry* tests show that *Geant4-DNA-Opt2* and *Geant4-DNA-Opt4* produce slightly different results in the physical quantities under study, while more significant differences can be found when these two physics constructors are compared to *Geant4-DNA-Opt6*. Differences between Geant4-DNA physics constructors in dose-mean lineal energy tend to increase for sensitive volume sizes below 100 nm and move toward the smallest differences for the 1 micron volume diameter due to the absorption of most of the sub-kilo-electron-volt electrons within the scoring site. In general, the different cross sections contained in the three different physics constructors are more likely to affect studies concerning subkilo-electron-volt energies and smaller scoring volumes as it has already been shown in previous relevant studies, that is, Refs. 117, 119, 126.

The *chemistry* test shows that the *SBS*, *IRT*, and *IRT-sync* can produce different *G*-values, depending on the chemical species under study and considered time interval after the start of the chemical stage.

More Geant4-DNA tests will be added to future versions of the G4-Med suite for regression testing of physics and chemistry models and for easier comparison to other simulation data or measurements.

## 8.5 | Execution times test

Differences in physics models (e.g., analytical or based on data), parameters and data extrapolation techniques have an impact on simulation execution times. Therefore, a test has been added to the G4-Med benchmarking suite to compare different Geant4 EM physics constructors and physics lists in terms of execution times, in a very simple simulation configuration.

In summary, the results show that, in general, *Geant4-DNA-Opt6* is the fastest when compared to *Geant4-DNA-Opt2* and *Geant4-DNA-Opt4*. When considering Geant4 EM CH approach models under study, in the case of electron beams incident in water with energy from 10 keV to 10 MeV, *Opt3* showed globally to be the fastest Geant4 EM constructor under study, followed by *Opt4* and *Livermore* and, finally, by *Penelope*.

The benchmarking of the execution times of the test with a 150 MeV proton beam in water, of interest for proton therapy, shows that *QGSP\_BIC\_AllHP* is the fastest Geant4 physics list for proton therapy and that *QGSP\_BIC\_HP* and *QGSP\_BERT\_HP* have similar execution times in the specific test under study. In the case of an incident 290 MeV/u <sup>12</sup>C ion beam, BIC and INCL ion fragmentation models show
similar execution times, while the QMD is significantly slower.

9 | CONCLUSIONS

The G4-Med benchmarking suite was born in 2014 from the effort of an international collaboration, the Geant4 Medical Simulation Benchmarking Group, to validate Geant4 and monitor its evolution for bio-medical applications. The G4-Med system was first documented in Arce et al.,<fnref n="13" /> where the results of the tests were reported for Geant4 10.5. In this special report, we describe the evolution of the project in terms of novel tests included in the G4-Med testing system and the results of the regression testing between Geant4 10.5 and 11.1.

In summary, new tests have been included to benchmark Geant4-DNA physics models and the capability of Geant4 for external x-ray and electron FLASH radiotherapy. New hadron therapy tests include Geant4 applications in experimental microdosimetry and in vivo PET.

Overall, the regression testing results showed the importance of the G4-Med benchmarking system to maintain and improve Geant4 for bio-medical physics applications. For example, thanks to this project, it was possible to identify problems in the implementation of the multiple scattering of the Geant4 EM constructor *Opt3* in Geant4 11.1 (which was then revised in Geant4 11.2.1). It was then possible to check the impact of novel proton and ion ionizations models in results of interest for hadron therapy and to monitor the evolution of hadronic inelastic cross sections.

The MRE, the NMAE and the MD, which could be applied transparently to any tested physical quantity of the G4-Med testing suite, proved to be adequate metrics for the regression testing and they provided a consistent analysis of the results.

The regression testing study showed that there can be significant differences between different Geant4 versions, therefore it is recommended to perform in-house regression testing for the specific application scenario of interest, when moving from an older to a more recent version of Geant4.

For the first time, we reported a comparison of the Geant4 EM physics constructors and physics lists under study in terms of computational times. A simple Geant4 simulation was developed for this purpose, which will be executed for future Geant4 releases.

The following areas of future development of the G4-Med benchmarking system arose from this work. While the execution of the tests in geant-val is automatized, the code maintenance, the inclusion of the results in the geant-val web interface, and the analysis of the results are manual. In order to speed-up the G4-Med system and be able to use it more efficiently to monitor the evolution of the Geant4 physics lists frequently

(e.g., three/four times per year), the entire G4-Med system needs to be automatized, from the execution of the individual tests to the analysis of the regression testing results in terms of MRE, NMAE, and MD. This development would allow to monitor more efficiently the evolution of Geant4 and to perform swiftly regression testing studies few times per year before the public release of Geant4, while now, provided our current resources and the status of the developed software tools used in the project, we are able to perform regression testing only with public releases of Geant4 (in other words, one Geant4 release per year). An extensive effort is under way to achieve this goal.

The regression testing showed that the hadronic physics component of Geant4 can change significantly from a Geant4 release to the next one and needs particular attention. Provided the complexity of this physics component, there is a need to extend the G4-Med system to a wider set of tests dedicated to fundamental physics quantities (e.g., hadronic cross sections and final states of individual interactions). In addition, more tests should be included in the G4-Med benchmarking system, especially for radioactivity, nuclear medicine, and neutron production and interactions.

## AFFILIATIONS

<footnote n="1">¹CIEMAT, Madrid, Spain</footnote>

<footnote n="2">²Centre for Medical Radiation Physics, University of Wollongong, Wollongong, New South Wales, Australia</footnote>

<footnote n="3">³Sapienza, University of Rome, Rome, Italy</footnote>

<footnote n="4">⁴INFN, Roma1 Section, Rome, Italy</footnote>

<footnote n="5">⁵Lebedev Physical Institute, Moscow, Russia</footnote>

<footnote n="6">⁶Swinburne University of Technology, Melbourne, Victoria, Australia</footnote>

<footnote n="7">⁷Istituto Superiore di Sanità, Rome, Italy</footnote>

<footnote n="8">⁸Australian Nuclear Science and Technology Organisation, Lucas Heights, New South Wales, Australia</footnote>

<footnote n="9">⁹INFN LNS, Catania, Italy</footnote>

<footnote n="10">¹⁰Centro Siciliano di Fisica Nucleare e Struttura della Materia, Catania, Italy</footnote>

<footnote n="11">¹¹Universidad de Sevilla, Sevilla, Spain</footnote>

<footnote n="12">¹²SWHARD srl, Genova, Italy</footnote>

<footnote n="13">¹³SLAC National Accelerator Laboratory, Stanford, California, USA</footnote>

<footnote n="14">¹⁴University of California, San Francisco, California, USA</footnote>

<footnote n="15">¹⁵Nuclear Research and Consultancy Group (NRG), LE Petten, The Netherlands</footnote>

<footnote n="16">¹⁶Tokushima University, Tokushima, Japan</footnote>

<footnote n="17">¹⁷CNRS, Univ. Bordeaux, LP21 Bordeaux, UMR5797, Gradignan, France</footnote>

<footnote n="18">¹⁸Tomsk State Research University, Tomsk, Russia</footnote>

<footnote n="19">¹⁹University of Virginia, Charlottesville, Virginia, USA</footnote>

<footnote n="20">²⁰Ioannina University, Ioannina, Greece</footnote>

<footnote n="21">²¹LAPP, IN2P3, Annecy, France</footnote>

<footnote n="22">²²Medical Imaging Department, Nepean Blue Mountains LHD, Sydney, New South Wales, Australia</footnote>

<footnote n="23">²³INFN Catania Division, Catania, Italy</footnote>

<footnote n="24">²⁴CERN, Geneva, Switzerland</footnote>

<footnote n="25">²⁵Nagoya Proton Therapy Center, Nagoya, Japan</footnote>
## ACKNOWLEDGMENTS

J. W. Archer and C. White were financially supported by the Australian Government Research Training Program Scholarship. A. Bagulya and V. Ivanchenko were supported by the Government Grant 075-15-2024-667. Z. Li's PhD at the University of Bordeaux, France, was financially supported by China Scholarship Council, through a 4-year funding (No. 201906680103), in collaboration with Fudan University, Shanghai. LP2I Bordeaux also thanks CNRS/IN2P3 for providing support to the Geant4 project (http://geant4.in2p3.fr). M. A. Cortés-Giraldo and J. M. Quesada were financially supported by Grant PID2021-1238790B-C21 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe." S. Guatelli and A. B. Rosenfeld acknowledge the financial support of the NHMRC Idea Grant ID2028435 and ARC Discovery Project DP230103091. G. Milluzzo acknowledges the financial support of the National Plan for NRRP Complementary Investments project n. PNC0000003—AdvaNced Technologies for Human-centrEd Medicine (project acronym: ANTHEM). We also thank Fondazione Pisa for funding CPFR with the grant prog. n. 134/2021 for providing the experimental data used in the paper. F. Romano is funded through the Programma di ricerca CN00000013 "National Centre for HPC, Big Data and Quantum Computing," funded by the Decreto Direttoriale di concessione del finanziamento n.1031 del 17.06.2022 a valere sulle risorse del PNRR-M4C2—Investimento 1.4—Avviso "Centri Nazionali"—D.D. n. 3138 del 16 dicembre 2021.

## CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

## ORCID

Pedro Arce ID https://orcid.org/0000-0003-3009-0484

Jay W. Archer ID

https://orcid.org/0009-0008-5248-5739

Lorenzo Arsini ID

https://orcid.org/0000-0002-3922-2052

Alexander Bagulya ID

https://orcid.org/0000-0001-9246-1952

David Bolst ID https://orcid.org/0000-0002-0257-1267

Jeremy M. C. Brown ID

https://orcid.org/0000-0001-9508-6190

Barbara Caccia ID

https://orcid.org/0000-0002-8729-3533

Andrew Chacon ID

https://orcid.org/0000-0003-3939-0862

Giuseppe Antonio Pablo Cirrone ID

https://orcid.org/0000-0001-5733-9281

Miguel Antonio Cortés-Giraldo ID

https://orcid.org/0000-0002-3646-1015

Giacomo Cutrone ID

https://orcid.org/0000-0002-9534-4855

Paolo Dondero ID

https://orcid.org/0000-0002-9185-9413

Andrea Dotti ID https://orcid.org/0000-0001-6697-608X

Bruce Faddegon ID

https://orcid.org/0000-0002-4573-1582

Serena Fattori ID

https://orcid.org/0000-0002-9381-7620

Christian Fedon ID

https://orcid.org/0000-0002-5998-453X

Susanna Guatelli ID

https://orcid.org/0000-0002-9289-7956

Akihiro Haga ID https://orcid.org/0000-0002-6717-2726

Sebastien Incerti ID

https://orcid.org/0000-0002-0619-2053

Vladimir Ivanchenko ID

https://orcid.org/0000-0002-1844-5433

Dmitri Konstantinov ID

https://orcid.org/0000-0001-6673-7273

Ioanna Kyriakou ID

https://orcid.org/0000-0003-2105-4078

Zhuxin Li ID https://orcid.org/0000-0001-9165-0372

Alessandra Malaroda ID

https://orcid.org/0000-0003-2127-146X

Carlo Mancini-Terracciano ID

https://orcid.org/0000-0001-8849-0259

Alfonso Mantero ID

https://orcid.org/0000-0002-5741-3397

Claire Michelet ID

https://orcid.org/0000-0002-4947-5520

Giuliana Milluzzo ID

https://orcid.org/0000-0001-5110-0659

Francesca Nicolanti ID

https://orcid.org/0000-0002-9614-3174

Mihaly Novak ID

https://orcid.org/0009-0005-1970-2613

Luciano Pandola ID

https://orcid.org/0000-0003-2867-0121

Jake Harold Pensavalle ID

https://orcid.org/0000-0002-2972-6265

Álvaro Perales ID

https://orcid.org/0000-0002-8035-2094

Yann Perrot ID https://orcid.org/0000-0001-9043-5857

Giada Petringa ID

https://orcid.org/0000-0002-2854-8436

<footnote n="26">²⁶Azienda Ospedaliera Universitaria Pisa, Pisa, Italy</footnote>

<footnote n="27">²⁷Hospital Universitario Puerta de Hierro, Majadahonda, Spain</footnote>

<footnote n="28">²⁸IRSN, Fontenay-aux-Roses, France</footnote>

<footnote n="29">²⁹Osaka University, Osaka, Japan</footnote>

<footnote n="30">³⁰Department of Physics, Lund University, Lund, Sweden</footnote>

<footnote n="31">³¹KEK, Tsukuba, Japan</footnote>

<footnote n="32">³²Radboud University Medical Center, Nijmegen, The Netherlands</footnote>

<footnote n="33">³³Dutch Expert Center for Screening (LRCB), Nijmegen, The Netherlands</footnote>

<footnote n="34">³⁴Department of Nuclear Physics and Accelerator Applications, Research School of Physics, Australian National University, Canberra, Australia</footnote>

<footnote n="35">³⁵Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil</footnote>
Silvia Pozzi https://orcid.org/0000-0002-8405-2275

José Manuel Quesada

https://orcid.org/0000-0002-2038-2814

José Ramos-Méndez

https://orcid.org/0000-0002-8106-5142

Francesco Romano

https://orcid.org/0000-0002-1865-6396

Anatoly B. Rosenfeld

https://orcid.org/0000-0001-5116-6308

Mitra Safavi-Naeini

https://orcid.org/0000-0002-6975-9563

Dousatsu Sakata

https://orcid.org/0000-0002-8398-3334

Luis G. Sarmiento

https://orcid.org/0000-0001-7600-2772

Takashi Sasaki

https://orcid.org/0000-0003-1591-7252

Alberto Sciuto

https://orcid.org/0000-0002-9176-9733

Ioannis Sechopoulos

https://orcid.org/0000-0001-9615-8205

Edward C. Simpson

https://orcid.org/0000-0001-9364-0768

Alessandra Tomal

https://orcid.org/0000-0003-3744-074X

Toshiyuki Toshito

https://orcid.org/0000-0002-6762-0015

Hoang Ngoc Tran

https://orcid.org/0000-0002-9243-6842

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**How to cite this article:** Arce P, Archer JW, Arsini L, et al. Results of a Geant4 benchmarking study for bio-medical applications, performed with the G4-Med system. *Med Phys*. 2025;52:2707–2761.
https://doi.org/10.1002/mp.17678