Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit.

ARTICLE IN PRESS Physica Medica ■■ (2015) ■■–■■

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Review Paper

Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit M.A. Bernal a, M.C. Bordage b,c, J.M.C. Brown d,e, M. Davídková f, E. Delage g, Z. El Bitar h, S.A. Enger i, Z. Francis j, S. Guatelli k, V.N. Ivanchenko l,m, M. Karamitros n, I. Kyriakou o, L. Maigne g, S. Meylan p, K. Murakami q, S. Okada q, H. Payno g, Y. Perrot g, I. Petrovic r, Q.T. Pham g, A. Ristic-Fira r, T. Sasaki q, V. Šteˇpán f, H.N. Tran s,t, C. Villagrasa p, S. Incerti s,t,u,v,* a

Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP, Brazil CRCT, UMR 1037 INSERM, Université Paul Sabatier, Toulouse, France c UMR 1037, CRCT, Univ. Toulouse III-Paul Sabatier, F-31000 Toulouse, France d School of Physics and Astronomy, Monash University, Melbourne, Australia e School of Mathematics and Physics, Queen’s University Belfast, Belfast, UK f Department of Radiation Dosimetry, Nuclear Physics Institute of the CAS, Praha, Czech Republic g CNRS/IN2P3, Laboratoire de Physique Corpusculaire, Clermont Université, UMR6533 Aubière, France h Institut Pluridisciplinaire Hubert Curien, Strasbourg, France i Medical Physics Unit, Department of Oncology, McGill University, Montreal, QC, Canada j Department of Physics, Faculty of Sciences, Université Saint Joseph, Beirut, Lebanon k Centre for Medical Radiation Physics, University of Wollongong, NSW, Australia l Geant4 Associates International Ltd, United Kingdom m Ecoanalytica, 119899 Moscow, Russia n Notre Dame Radiation Laboratory, University of Notre Dame, Notre Dame, IN, United States o Medical Physics Laboratory, University of Ioannina Medical School, Ioannina 45110, Greece p IRSN, Institut de Radioprotection et de Sureté Nucléaire, BP17, 92962 Fontenay-aux-Roses, France q KEK, Tsukuba, Ibaraki, Japan r Vinc ˇ a Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia s Division of Nuclear Physics, Ton Duc Thang University, Ho Chi Minh City, Viet Nam t Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, Viet Nam u Univ. Bordeaux, CENBG, UMR 5797, F-33170 Gradignan, France v CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan, France b

A R T I C L E

I N F O

Article history: Received 27 July 2015 Received in revised form 28 September 2015 Accepted 7 October 2015 Available online Keywords: Monte Carlo Geant4-DNA Radiolysis Radiobiology Ionizing radiation

A B S T R A C T

Understanding the fundamental mechanisms involved in the induction of biological damage by ionizing radiation remains a major challenge of today’s radiobiology research. The Monte Carlo simulation of physical, physicochemical and chemical processes involved may provide a powerful tool for the simulation of early damage induction. The Geant4-DNA extension of the general purpose Monte Carlo Geant4 simulation toolkit aims to provide the scientific community with an open source access platform for the mechanistic simulation of such early damage. This paper presents the most recent review of the Geant4DNA extension, as available to Geant4 users since June 2015 (release 10.2 Beta). In particular, the review includes the description of new physical models for the description of electron elastic and inelastic interactions in liquid water, as well as new examples dedicated to the simulation of physicochemical and chemical stages of water radiolysis. Several implementations of geometrical models of biological targets are presented as well, and the list of Geant4-DNA examples is described. © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

The authors are members of the Geant4-DNA Collaboration. * Corresponding author. CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan, France. Tel.: +33 5 57 12 08 89; fax: +33 5 57 12 08 01. E-mail address: [email protected]; [email protected] (S. Incerti). http://dx.doi.org/10.1016/j.ejmp.2015.10.087 1120-1797/© 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Please cite this article in press as: M.A. Bernal, et al., Track structure modeling in liquid water: A review of the Geant4-DNA very low energy extension of the Geant4 Monte Carlo simulation toolkit, Physica Medica (2015), doi: 10.1016/j.ejmp.2015.10.087

ARTICLE IN PRESS M.A. Bernal et al./Physica Medica ■■ (2015) ■■–■■

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Introduction Monte Carlo (MC) track structure codes play a fundamental role in the investigation of radiation effects at the micro- and nanoscales, in biological media, with applications spanning from radiotherapy to radiation protection [1–3]. For example, in heavy ion therapy, track structure codes can be used to calculate the dose distribution of particle tracks with nanoscale resolution. Radiobiological models, such as the local effect model or the microdosimetric kinetic model [4], can then be appropriately applied to the simulation results to estimate the relative biological effectiveness as input to the clinical Treatment Planning System. Track structure codes can be adopted as investigation tool when studying radionuclide targeted techniques, such as targeted alpha and Auger electron therapies, as they allow studying the effect of radiation at cellular and sub-cellular levels [5]. Also novel, currently proposed methods such as the use of high atomic number nanoparticles (NPs) in radiotherapy require track structure codes to investigate the dose enhancement produced by the NPs in the target tumor (e.g. [6,7]). As an example of application in radiation protection, track structure codes can be used to investigate the radiobiological effect of heavy ions which is paramount for the human exploration of the Solar System, for the determination of the crew radiation risks and for the optimization of shielding solutions [8]. Geant4 is a general MC simulation toolkit [9,10] utilized in a wide variety of applications spanning high energy particle to aerospace and medical physics, which contains the Geant4-DNA extension aimed at describing the interactions of particles down to ~eV scale in liquid water [11,12]. This very low energy extension was first publicly released in Geant4 version 9.1 in 2007 [13]. Since then, we have observed an increasing use of Geant4-DNA by Geant4 users [14]. Geant4-DNA has since been further extended to model the physical, the physicochemical and the chemical stages of radiation interactions with liquid water. Geometrical models down to the size of the DNA double helix are also provided in dedicated examples. This paper reviews the current status of the Geant4-DNA extension available to Geant4 users and discusses its future developments.

Physics stage Default models for liquid water The Geant4-DNA extension provides a complete set of models describing the step-by-step physical electromagnetic interactions of particles (electrons, protons and neutral hydrogen atoms, alpha particles including their charge states, and a few ions – Li, Be, B, C, N, O, Si, Fe) with liquid water, the main component of biological systems. These models describe both the cross sections and the final states of the physical interactions, with a full description of the interaction products, taking into account the molecular structure of liquid water. This is not the case for the rest of Geant4 electromagnetic models available in the Geant4 “Low energy” and “Standard” categories of electromagnetic interactions, which are applicable to atomic constituents only1 [16]. Geant4-DNA is able to simulate the physical interaction processes of the following particle types with liquid water:

•

electrons: elastic scattering, electronic excitation, vibrational excitation, ionization and molecular attachment in the 7.4 eV– 1 MeV kinetic energy range;

1 Note one exception: Geant4 also proposes a set of electromagnetic models for the transport of electrons and ions in condensed Silicon, the so-called “MicroElec” models, which are adapted to microelectronics applications [15].

• • •

protons and neutral hydrogen atoms: elastic scattering, electronic excitation, ionization, and electron capture or loss in the 100 eV–100 MeV range; helium atoms and their charge states: elastic scattering, electronic excitation, ionization and charge exchange in the 1 keV– 400 MeV range; other ions: ionization only in the 0.5 MeV/u–106 MeV/u range.

Further information on these models developed by the Geant4DNA collaboration is outlined in [12,17–19]. How to activate the Geant4 DNA physics in a Geant4 user application As in any other Geant4 application, users specify the list of particles “processes” and “models” needed for their simulation. A physics “process” fully describes a physical interaction (such as ionization, elastic scattering…) and can evoke several “models”, usually obtained from the literature (they can be fully theoretical, semiempirical…). In addition, some models are “complementary” (applicable to different energy ranges) whereas others are “alternative” (applicable to identical energy ranges). Such models are responsible for the computation of the physical interaction total cross section and full description of the final state of the colliding system, which includes the production of secondary particles, energy loss and emission angles. A detailed description of the corresponding software design is presented elsewhere [12]. For an easier use of physics processes and models, Geant4 provides pre-built C++ classes – called “physics constructors” – which contain the whole list of particles, processes and models for a variety of application domains. Among them, a default physics constructor, named “G4EmDNAPhysics”, is provided to users for the development of applications employing the Geant4-DNA extension. This constructor also includes processes and models for the transport of photons (photoelectric effect, Compton and Rayleigh scattering, pair production) based on the “Livermore” library of the Geant4 “Low energy” electromagnetic physics category [20] and positrons (multiple scattering, ionization, annihilation and bremsstrahlung) available in the Geant4 “Standard” electromagnetic physics category. Atomic de-excitation processes can be simulated through the universal atomic deexcitation interface available in Geant4 [21]. The step-by-step simulation of physical interactions can be significantly time consuming, especially for high linear energy transfer radiation and/or in large volumes; therefore, users have now the possibility to select a faster simulation of ionization for electrons and protons (above 500 keV) by using cumulated single differential cross sections (SDCS) instead of a classical rejection method directly based on SDCS [22]. This feature is available in an alternative physics constructor named “G4EmDNAPhysics_option2”. Finally, a second alternative physics constructor, named “G4EmDNAPhyiscs_option3”, was released in Geant4 10.2 Beta version (June 2015) that employs Tran et al. [19] algorithms for simulating the elastic scattering of photons and alpha particles. Benchmarking the Geant4-DNA models The Geant4-DNA physics models have been benchmarked against experimental measurements performed in water vapor as a suitable set of liquid water measurements does not exist for full validation stricto senso [12]. Simulated dose point kernel distributions for incident electrons in the 10 keV–100 keV range and in 120 nanometer-sized spherical shells showed to be compatible with the results of other MC codes [23]. Similarly, Geant4-DNA simulations of S-values for monoenergetic electrons in the 100 eV–20 keV range in nanometer-sized spheres and electron spectra emitted by iodine isotopes (131I, 132I, 133I, 134I and 135I) in micrometer-sized spheres in the context of thyroid targeted radio-immunotherapy are also com-



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Table 1 Overview of physical quantities simulated in liquid water using Geant4-DNA taken from the literature and compared to other reference data. Incident particles are given as well as main result and corresponding references. Readers are invited to refer to the cited references for more details. “MC” stands for Monte Carlo. Quantity

Incident particle

Main result

References

Cross sections

Frequency of energy deposition Ionization cluster size

Electron, proton, alpha particle Electron

Mean lineal energy Mean energy deposition

Proton Proton

Radial doses

General agreement compared to ICRU (>keV)

[19,29]

S-values

Proton, alpha particle, ions Electron, proton, alpha particle Electron

Qualitative global plausibility of Geant4-DNA cross sections for liquid water compared to experimental data in the gas phase Accurate simulation of dose point kernels in the 10 keV–100 keV energy range compared to a variety of other MC codes Similar tendencies of frequencies of energy deposition with nevertheless slight differences between Geant4-DNA and the the MOCA series of MC codes Reasonably good agreement but differences are observed between Geant4-DNA and the PTB MC code for large cluster sizes General good agreement with experimental data and TRIOL simulations General good agreement with experimental data and TRIOL simulations, but significant differences with ICRU Good agreement with literature data (calculations, MC simulations and experimental data)

[12]

Dose point kernels

Electron, proton, alpha particle Electron

[24,30,31]

Slowing down spectrum Stopping power or stopping cross section W-values to form an ion pair

Electron Electron, proton, alpha particle, C, O, Si, Fe Electron

Simulations are statistically compatible with a selection of MC codes. Significant differences observed compared to MIRD recommendations. General good agreement with literature data (>keV) General agreement with international recommendations (>few 100 eV for electrons, > few keV for protons and alpha particles, > 1 MeV/amu for heavier ions) Underestimation of W-values by default Geant4-DNA models compared to literature data (MC and experimental), but better agreement using the recently added models developed at Ioannina U., Greece

Range

patible with other MC simulations [24]. Furthermore, it has been shown that the absorbed radial doses by incident ions are in agreement with a variety of other MC codes and experimental data [25]. Table 1 summarizes the physical quantities simulated using the Geant4-DNA physics processes as available in the literature, published by the Geant4-DNA Collaboration or by other research groups, and compared to reference data. From these results it can be inferred that the Geant4-DNA extension is reliable for nano- and microdosimetry applications in medical physics, and possesses overall comparable physics accuracy with respect to other MC track structure codes. Nevertheless, some limitations have been recently reported for the simulation of the transport of electrons with the Geant4-DNA extension, such as lower cross section values for electronic excitation (see for example fig. 4 in [12]) or too low mean energy values W to form an ion pair (see for example fig. 4 in [32]), when compared to a collection of experimental measurements in gas and to other MC codes. To overcome these limitations, new physics models have been proposed to be included in the Geant4-DNA. Users are now able to select these new models in their Geant4 application, substituting the default ones, if needed for their specific research application. These models are described in the next section, keeping in mind that Geant4-DNA adopts a modular approach for the modeling of physical interactions, just as the rest of Geant4 electromagnetic physics: Geant4-DNA offers a variety of alternative sets of models to the users according to their needs. Improvements for liquid water: dielectric function, Born corrections, and elastic scattering In the current Geant4-DNA electron models, the calculation of ionization and excitation cross sections is based on the Emfietzoglou model [35] of the dielectric function of liquid water. The dielectric function approach is currently the state-of-the-art for modeling the energy-loss of low-energy electrons in the condensed phase [36] and it is used in most major MC track structure codes, such as OREC/ NOREC [37], PARTRAC [38], PITS [39], KURBUC [40], MC4 [41], RETRACKS [42], and SEICS [43]. Recently, the Dingfelder model [44] for the dielectric function has been implemented into the generalpurpose code PENELOPE for improving electron transport in the lowenergy range [45].

[23] [26] [27] [17] [17] [25,28]

[32] [12,19,29,33] [32,34]

An alternative set of ionization and excitation cross sections in Geant4-DNA, effective at sub-keV electron energies, was recently implemented in the Geant4 10.2 Beta release. This new set of cross sections, developed by Kyriakou at the University of Ioannina (Greece), is based on an improved implementation of the Emfietzoglou model of the dielectric function and includes refinements made on the low-energy Born corrections [34]. It includes a truncation algorithm for the dielectric function that accounts for the vanishing contribution of ionizations below the binding energies and an exponential smoothing around the ionization thresholds. This algorithm essentially re-distributes the imaginary part of the dielectric function (or oscillator strength) to the different ionization shells and excitation levels in an f-sum-rule conserving manner without affecting the original fit to the experimental data. In the context of the dielectric function approach, non-Born effects (e.g. exchange), which are important for low-energy electron transport, can be considered at different levels of sophistication [46–48]. In the existing Geant4-DNA model, corrections for the deficiencies of the Born approximation are made through Mott-like exchange and interference terms and a kinematic Coulomb-field correction [12]. Improvements in the existing implementation have now been made [34] following the work of Emfietzoglou and Nikjoo [47]. This includes the extension of the Coulomb-field correction to both ionizations and excitations, and the elimination of a pre-factor in the interference term, which is a source of unphysical results at verylow energies. The above developments are assembled into the two model classes “G4DNAEmfietzoglouIonizationModel” and “G4DNAEmfietzoglouExcitationModel”. The models are available in Geant4 from 10.2 Beta release [34]. The new energy-loss model provides ionization and excitation cross sections that are significantly different from those of existing Geant4-DNA models below a few hundred eVs. Simulations by Geant4 using both the existing and new model show that electron penetration and dose-point-kernel results are in good agreement for electron energies above 1 keV, in moderate agreement for electron energies down to ~500 eV, and in rather poor agreement at even lower energies (see fig. 4 in [34]). In addition, the new W-values are higher by several eVs and in better agreement with other liquidwater track-structure codes [34]. Differences in the simulation results between the existing and new models are mainly due to the different partitioning of the dielectric function to excitations and


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ionizations in the new implementation. This results in a significant increase in excitation cross section and concomitant enhancement of the ratio of excitations to ionizations, which leads to an increase of W. Elastic interactions, although they do not lead (practically) to energy loss, are very important for the spatial distribution of energy deposition. In Geant4-DNA [12], elastic scattering is computed either by a screened Rutherford (SR) model or by a partial wave (PW) model, the latter being the Geant4-DNA default model for elastic scattering. The SR model is particularly convenient because both the differential and the total elastic scattering cross sections can be expressed analytically. The limitation of this model is that it is practically limited to high electron energies (>1–10 keV for low-Z materials) due to the general restrictions of the first Born approximation upon which it is based. Therefore, it is customary to extend the applicability of the SR model to low electron energies by determining the screening parameter in an empirical manner, at least for those materials where experimental scattering data are available (like water). In the existing Geant4DNA SR model the Grosswendt–Waibel screening parameter implemented is based on experimental data on nitrogen gas [49]. In the new release we have also implemented the screening parameter of Uehara et al. [50] that is based on experimental measurements of gaseous water. It is implemented in the socalled “G4DNAUeharaScreenedRutherfordElasticModel” class. These three new models (for excitation, ionization and elastic processes) are now available in a dedicated physics constructor called “G4EmDNAPhysics_option4” (or “G4EmDNAPhysics_option5” if the use of cumulated differential cross sections is preferred).

The CPA100 Monte Carlo code for electrons in liquid water To include a variety of alternative physics models in Geant4DNA, the porting of the CPA100 Monte Carlo code into the Geant4DNA extension recently began at Paul Sabatier University/CNRS/ INSERM, Toulouse (France). The CPA100 code is a track structure code for particle transport (electrons and photons) developed by Terrissol (Toulouse, France) for understanding the fundamental aspects of radiation interactions [51]. It simulates transport in liquid water, complex DNA targets and higher order DNA organization structures [52] for particles with initial energy lower than 250 keV. CPA100 can generate all the electronic and photonic cascades (Auger electrons, X-rays and atomic reorganization) and can simulate the physical, physicochemical and chemical stages during the early passage of particles in matter up to one microsecond to evaluate early DNA damage. Excitation cross sections for five discrete levels are based on differential oscillator strengths with dielectric response coming from Dingfelder et al. [44]. In its last version [53], to better take into account the molecular structure of targets, CPA100 implemented the Binary Encounter Bethe (BEB) [54] model for the evaluation of ionization energy single differential and total cross sections for each molecular subshell. The BEB analytical expression does not require empirical parameters, only the binding and mean kinetic energy for individual orbital and the number of electrons in each subshell. In the case of elastic scattering, the differential cross sections above 50 eV are determined using the independent atom model (IAM) by taking into account the scattering amplitude of each atom and their separation [55]. Below this energy threshold the differential elastic scattering cross sections are taken directly from experimental measurement of a solid water target [56]. These CPA100 cross-sections have been implemented into three new Geant4-DNA classes, namely “G4DNACPA100ElasticModel”, “G4DNACPA100ExcitationModel” and “G4DNACPA100IonisationModel”, and will be publicly released soon.

Figure 1. Total electron elastic scattering cross sections in liquid water showing the model adopted in CPA100 (“CPA100” – dash dot black line), the Screened Rutherford model proposed by Uehara et al. (“Uehera SR” – full red line) and the two alternative default Geant4-DNA models (blue lines) as a function of electron incident energy. The two models available in default Geant4-DNA are shown: the Screened Rutherford model (“Geant4-DNA SR” – short dash blue line) and the partial wave model (“Geant4-DNA PW” – long dash blue line). A collection of available experimental data in gaseous water is also shown. These data are fully referenced in [12]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The CPA100 cross sections for liquid water, compared to default cross sections available in Geant4-DNA and models presented in the previous section, are shown in Figs. 1–3 for elastic scattering, excitation and ionization processes, respectively. In these figures, the models are compared to a collection of experimental data in the gaseous phase (since data in the liquid phase are not available). As it has been extensively discussed in the literature (see [47] and references therein), inelastic cross sections in water in the liquid phase are expected to be significantly lower than those in the gaseous phase. This is because polarization and screening effects in the condensed phase reduce the strength of electron–matter interaction leading to larger inelastic mean free path (or lower inelastic cross sections). For example, Emfietzoglou and Nikjoo [47] have shown that the inelastic cross section of 100 eV electrons in water vapor, when scaled to the same density, is 1.7 times larger than the corresponding value in liquid water, with the difference increasing further at lower energies. Thus, the experimental data for the gas phase depicted in Figs. 2 and 3 provide limited insight in the present context, other than representing an upper bound for models of electron scattering in the liquid phase. In Fig. 4 we present a comparison of the total inelastic cross sections (excitation + ionization) for all models implemented in Geant4-DNA (described above) with two sets of experimental data provided by Michaud et al. [58] in amorphous ice, which has a similar molecular lay-out with liquid water. These data, which cover a limited energy range (1–100 eV) and possess a large experimental uncertainty (40%), represent the only available data for water in the condensed phase. Evidently, the experimental data in Fig. 4 confirm the theoretical expectation of much lower inelastic cross sections in the condensed phase compared to the gas phase. Thus, we can observe that whereas the CPA100 models are in better agreement with the gaseous data (see Figs. 2 and 3), they are in worse agreement with the ice data, compared to the other models. It is also evident that the new implementation of the Emfietzoglou model “corrects” the default model downwards, consistent with the lower values of the ice data. Furthermore, the strong enhancement of the excitation cross section, effective below ~20 eV, in the new implementation of the Emfietzoglou model yields



Figure 2. Total electron impact excitation cross sections implemented in CPA100 (full black line), default Geant4-DNA (full blue line with squares) and the alternative model of Emfietzoglou (full red line with disks) in liquid water. The experimental data of Munoz et al. [57] in the gaseous phase (green squares) are also shown. An uncertainty of 40% has been assigned to the plotted values as suggested by their authors. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

a less steep decrease of the inelastic cross section, which appears to be in good agreement with the ice data (and contrary to the sharp decrease predicted by the default and CPA100 models). This gradual population of inelastic channels with increasing electron energy is a direct consequence of the many-body character of the excitations in the condensed phase, which results in the broadening of states due to a strong damping mechanism (shorter excitation lifetimes) that is entirely absent in the gas phase [59]. Nevertheless, CPA100 cross section models have been calculated for a variety of other target materials of biological interest (such as DNA bases and sugar-phosphate groups), which will also be included in Geant4-DNA. In addition, CPA100 is capable of simulating

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Figure 4. Comparison of inelastic cross sections (excitation + ionization) calculated by the Geant4-DNA (default, full blue line), Emfietzoglou (full red line), and CPA100 (full black line) models against two sets of data in amorphous ice provided by Michaud et al. (symbols, see Table 1 – “Total inelastic σT,i” column – and Table 3 – “Others” column – of [58]) up to 100 eV. An error of 40% has been associated to all data, as suggested by their authors. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

water radiolysis and will be useful for the verification of Geant4DNA simulation accuracy of the physico-chemical and chemical stages presented in the next section.

The physicochemical and chemical stages The Geant4-DNA extension proposes to users a set of features for the simulation of water radiolysis by ionizing radiation. Since the 10.1 release (December 2014), Geant4 includes a framework prototype to model the response of non-inert media, models for liquid water radiolysis, and examples demonstrating use and customizations of the chemistry modules [60]. Radiation action in liquid water is conventionally described in three consecutive stages. During the physical stage, handled by the physics models described earlier, the incident radiation transfers its energy to the medium in a series of elementary physical interactions. In liquid water, these generate "ionized or excited" water molecules, as well as water "anions" through the dissociative attachment process. The electronic modifications undergone by the water molecules can trigger radiative or/and dissociative deexcitation. These electronic and atomic rearrangements take place in the so-called physicochemical stage that is assumed to be very short from femtoseconds to a few picoseconds. The outcome of this stage is the generation of new chemical species that can diffuse within the aqueous medium, react one with another or with other species already present in the biological medium before irradiation. This is the so-called chemical stage.

Principles

Figure 3. Total electron impact ionization cross sections implemented CPA100 (full black line), default Geant4-DNA (full blue line with squares) and the alternative model of Emfietzoglou (full red line with disks) in liquid water. A collection of available experimental data in gaseous water is also shown. These data are fully referenced in [12]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Representations When modeling a system, one has to choose the granularity at which the system will be described. We refer to the levels of granularity as “representations”. Models for chemical systems have been developed in various representations. Among them, we can mention the following representations:



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Table 2 Dissociation schemes used in Geant4-DNA 10.1 (December 2014) and 10.2 Beta (June 2015). AI stands for Auto-Ionization. Electronic state of water molecule

Dissociation channels

Fraction (%)

All single ionization states: H2O+ Excitation state A1B1: (1b1) → (4a1/3s)

H3O+ + •OH •OH + H• H2O + ΔE H3O+ + •OH + e−aq (AI) •OH + •OH + H2 H2O + ΔE H3O+ + •OH + e−aq (AI) H2O + ΔE •OH + OH− + H2

100 65 35 55 15 30 50 50 100

Excitation state B1A1: (3a1) → (4a1/3s)

Excitation state: Rydberg, diffusion bands Dissociative attachment: H2O−

1. Atomistic, describing part or all of the atoms’ motion of the system; 2. Particle-continuum or particle-based, which describes only the motion of "species" of interest represented as point-like objects diffusing in a continuous medium; 3. Compartment-based or continuum-based, which describes the time-evolution of the number of chemical species in one or many compartments without explicitly describing individual trajectories. Therefore, the main observables of this representation are the concentrations of chemical species in the considered compartments; 4. The last class of representation is purely qualitative and does not consider the trajectories of molecules, reaction rates, any quantitative observable of the system such as concentrations. It is mostly known through the Boolean network model, which is used to describe the qualitative temporal behavior of large-scale systems to test hypotheses and study the effect of perturbations on the overall system. Modelers choose one of these representations depending on the time and space scales of their study. It is in the context of the selected representation that models are then developed. The models currently implemented in Geant4-DNA use the particle-continuum representation, where only the "species" of interest are modeled explicitly, as spheres or point-like objects diffusing through Brownian motion, while the rest of the medium’s content is treated as continuum. Refer to Karamitros et al. [60] for an in-depth discussion, including comparison of simulated radiochemical yields using Geant4-DNA with published data. Physicochemical stage The main event of this stage is the dissociation or relaxation of the water ions and molecules. Traditionally, to model this stage, a dissociation channel is selected in respect to the type of electronic modifications undergone by the water molecule and corresponding branching ratios predefined by the user. Geant4-DNA follows the same approach. However, these branching ratios are not directly observed and are usually chosen so that the long-term dynamic of the chemical stage will remain close to experimental observables. The most challenging part is the time-space placement of the dis-

sociation products right after dissociation. Geant4-DNA follows the description used in the PARTRAC software [61]. Table 2 presents the dissociation scheme implemented in the so-called “G4EmDNAChemistry” chemistry constructor of Geant4-DNA, a class that gathers all necessary parameters for the simulation of water radiolysis. If needed, the users may tune these parameters. The class responsible for the placement of the radiolytic products is named “G4DNAWaterDissociationDisplacer”. Table 3 summarizes the parameters implemented in this class; they are used by the process“G4DNAMolecularDissociation”. This table intro duces vectors R (rrms ) and Re to place the new radiolytic products:

•

R (rrms ) is a random vector defined as: R (rrms ) = rˆ (rrms ) ⋅ uR

rrms and 3 rˆ (rrms ) is a random variable sampled from using the density probability [61]: where rrms is the root mean square displacement, σ (rrms ) =

⎡ 1

fr (rms ) =

•

r2

⎤

r2 2 ⎢⎣− 2 σ 2(rrms ) ⎥⎦ e σ 3 (rrms ) π

Re is a random vector defined as: Re = rê ⋅ uR

where rê is a random variable sampled from fre = 4re −2r [61] (for another parameterization, see also [51]). This density probability is an adjustment to the results obtained with full MC simulations of low energy electrons down to thermal energy. This is used to place the solvated electrons after dissociation of excited water molecules. In this modeling approach, in case of ionization, before dissociation may happen, the hole created from the removal of an electron is assumed to be able to hop in a series of fast charge transfers, as summarized in Table 3. Our modeling of the physicochemical stage remains quite approximate. To the best of our knowledge, all radiation chemistry simulation platforms use a similar rough MC description of the physicochemical stage. This remains an important point to be improved and studied as new coarse-grained simulation techniques have emerged [62,63]. Chemical stage The method and mathematical background of the chemical stage have been extensively described elsewhere [60]. Briefly, in Geant4DNA, the description of Brownian motion of the chemical species is based on the Smoluchowski model. This model assumes that the Brownian particles being diffused have reached thermal equilibrium. The time steps used for diffusing Brownian particles must then be greater than the relaxation time of the velocity of the particles in the medium. The diffusion is done on a step-by-step basis. Given a time step, all species are diffused along this time step and are then placed at a new position. Thus, the species do not travel in a rectilinear motion but by jumping from one position to another. Their position at a given time is then evaluated in terms of probability, in contrast with the standard transportation of Geant4 for which

Table 3 Placement of dissociation products used in Geant4-DNA 10.1 (December 2014) and 10.2 Beta(June 2015) releases [61]. The star * indicates that the placement between two products may be interchanged randomly by coin-toss. The values of the random vectors R and Re are detailed in the text.

H3O+ + •OH H3O+ + •OH + e−aq (AI) •OH + H• H2+ •OH + •OH H2+ •OH + OH−

Hole hopping R (2 nm) (charge transfer) R (2 nm) (charge transfer) 0 0 0

Product 1 0* 0* − 1 18 × R(2.4 nm) − 2 18 × R (0.8 nm) − 2 18 × R (0.8 nm)

Product 2 R (0.8 nm) * R (0.8 nm )* 17 18 × R (2.4 nm) 16 18 × R (0.8 nm) + 1 2 × R (1.1 nm) 16 18 × R (0.8 nm) + 1 2 × R (1.1 nm)

Product 3 — Re — 16 18 × R (0.8 nm) − 1 2 × R (1.1 nm) 16 18 × R (0.8 nm) − 1 2 × R (1.1 nm)



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the position and velocity of a given particle are well established at any time along a step. For now, the reactions modeled in Geant4-DNA must be diffusioncontrolled. This means that a reaction happens as soon as two reactants encounter, i.e. their separation distance is less than a certain threshold, in other words, a reaction radius. Therefore, the criterion for deciding whether a reaction takes place is the separation distance between two Brownian particles. Since the chemical species are subject to Brownian motion, the knowledge of whether two reactants are separated by less than a reaction radius can be obtained either by (1) checking after a step the separation distance between reactants or (2) along the jumps by using a probabilistic technique called Brownian Bridge. The Brownian Bridge tries to answer the following question: “Knowing the jumping positions – initial and final positions – of two reactants, what is the probability that they have been separated by less than a given distance during a given time step?” In Geant4-DNA, we combined (1) and (2) by selecting the time step dynamically for point (1). The time step is dynamically computed using the method proposed by Michalik et al. [64,65] (also implemented in the RADAMOL software [65]) which tries to answer the following question: “Knowing the initial separation distance between two Brownian particles, at what time the particles may be separated by less than a given distance with a probability of 4–5%?” Compared to a standard step-by-step simulation, this method is much faster. However, the main drawback with this technique is that it leads to time steps that are smaller and smaller before a reaction can happen. Indeed, a 4–5% encounter probability is a very small fraction. Therefore, to speed up the simulation, we introduced a minimum time threshold on the allowed time steps. If the dynamically computed time step falls below the threshold, the value of the threshold is used as the next time step (instead of the dynamically computed one) and the corresponding pair of reactants is selected. Then, we diffuse all the chemical species. At this point, two cases may happen. First, if the dynamically computed time step is greater than the threshold, then only the separation distance between the reactants is checked and used as criterion to trigger or not the reaction. Otherwise, the probability of encounter for the pre-selected pair (along the time step which in this case would correspond to the selected threshold value on the minimum time step) is computed using the Brownian Bridge technique. Note that the minimum thresholds may vary along the virtual time. Indeed, when the simulation starts, just after the water species have dissociated, the radiolytic products are very close to one another and are more likely to react at longer times. Therefore, as the virtual time increases, the thresholds may be made progressively larger. It is up to the user to select the threshold values. For now, the Brownian Bridge technique, as implemented in Geant4-DNA, is a 1D approximation. Although the implemented method does not uncouple diffusion and reactions, it remains less efficient than the independent reaction time technique [66,67] widely used in radiation chemistry and implemented in Geant4-DNA for a future release. As an illustration, Fig. 5 shows the evolution of a single 1 keV electron track during physical, physicochemical and chemical stages in a sphere of liquid water, as simulated using Geant4-DNA.

particle. This starting time is rather arbitrary and, for a given irradiated sample, choosing 1 picosecond as the start time to diffuse all radiolytic products may be too approximate. For example, it can be observed in the animations constructed by Šteˇpán [69–71] that in certain circumstance the physical stage may not have ended yet after 1 picosecond. The physical picture of the physicochemical stage may then involve an overlap in time between the transport of the physical tracks, the dissociation of water species and the early diffusion of radiolytic products. In MC simulations, the initial energy of these radiolytic products is not taken into account. At 1 picosecond after initiating the simulation of the primary particle, the radiolytic products are assumed to have already thermalized. Then, in the chemical stage, the Smoluchowski diffusion that only considers Brownian diffusion at thermal equilibrium is applied. This assumption should be studied carefully. Finally, in ion beam irradiation, energy dissipation may generate thermal and pressure waves in the vicinity of the Bragg peak [72] that could also cause indirect DNA damage without the need of radicals entering in the play. These waves could also affect the motion and diffusion coefficients of the radiolytic products as well as the reaction rates. According to the authors [72], the characteristic times of the heat transfer could go up to the nanosecond. If a better description of the physicochemical stage could be provided, it would imply a reliable description of water dissociation and placement of the radiolytic products.

Limitations of the modeling of the physicochemical stage and early chemical stage

Geant4-DNA example applications

In the physicochemical stage, dissociation of the water species and the placement of the radiolytic products take place. This stage is of high importance. Indeed, the initial placement of the chemical species conditions the time evolution of the chemical stage. In the current version of Geant4-DNA, the chemical stage is assumed to start at 1 picosecond after initiating the simulation of the primary

Limitations of the modeling of the chemical stage and biological stage The initial goal of Geant4-DNA is to be able to compute early DNA damage using various representations of the DNA molecule. The DNA representations can be coarse-grained (as introduced in the “extended/medical/dna/wholeNuclearDNA” and “extended/medical/ dna/pdb4dna” example applications – see next section) or continuum. The chemistry is usually followed up to 1 microsecond. Beyond this time, when one is interested in irradiation of biological matter, it is considered that the repair mechanisms enter into play. The repair kinetics is then usually modeled using deterministic approaches [73–77]. The current released versions of the chemical stage are not fitted to tackle reactions between reactants at high concentration. However, new developments are enabling a smooth transition to a high concentration regime and so to the biochemical stage. There are a few important differences between inert, lifeless irradiated media and biological irradiated matter. The chemical content of biological samples is hard to control and sometime to determine. An emergent modeling approach, referred to as “whole cell modeling”, has been concretized with the first modeling of the human parasite “Mycoplasma genitalium” [78]. This parasite is known as being the simplest living organism with ~525 kbp deprived of a nucleus. The goal of this work was to numerically reproduce the life cycle of the parasite by accounting for its internal chemical network. Modeling simpler living organisms than human cells is a strategy that modelers interested in radiobiology could consider. Various studies are being undertaken on plasmid irradiation and could somehow be merged with the work of the whole cell modeling community.

Geant4-DNA comes with examples that demonstrate its functionality for the simulation of physical, physicochemical and chemical interactions in liquid water. Some of these examples also demonstrate the implementation of specific biological target geometries for direct damage estimation. The following sub-section describes these examples and an accompanying summary can be found in Table 4.



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Figure 5. Illustration at different times of the physical, physicochemical and chemical processes induced by a single 1 keV electron shot from the center of a 150 nm-diameter sphere of liquid water (top left: 0.01 ps, top right: 10 ns, bottom left: 50 ns, bottom right: 100 ns). Color trails in frames 2–4 show tracks of chemical species during a sliding time window. The corresponding movie is available online at [68]. Red segments on the top-left plot show the electron trajectory and yellow vertices show the location of physical interactions. On the three other plots, a colored code is used for the representation of molecular species: magenta for •OH, yellow for H3O+, blue for solvated electrons, green for H2O2 and white for H• and H2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Table 4 List of examples provided in Geant4 (from release 10.2 Beta, June 2015), which illustrates Geant4-DNA functionality for the simulation of physics, radiolysis and geometrydamage estimation in simplified biological targets. Example name, purpose of example and main reference are given. Example name Examples demonstrating physics simulation capabilities extended/medical/dna/dnaphysics extended/medical/dna/microdosimetry extended/electromagnetic/TestEm12 extended/medical/dna/svalue extended/medical/dna/wvalue Examples demonstrating radiolysis simulation capabilities extended/medical/dna/chem1 extended/medical/dna/chem2 extended/medical/dna/chem3 Examples demonstrating geometrical and damage simulation capabilities extended/medical/dna/wholeNuclearDNA extended/medical/dna/pdb4dna extended/medical/dna/clustering

Purpose

Reference

Use of Geant4-DNA physics Combination of Geant4-DNA physics and Geant4 electromagnetic physics Dose point kernel S-values in spheres Calculation of W

[11] [79] [23] New for Geant4 10.2 Beta [24] To be released

Geant4-DNA physicochemistry and chemistry Geant4-DNA physicochemistry and chemistry Geant4-DNA physicochemistry and chemistry

[60] [60] [60]

Geometry of the DNA contained in a eukaryotic cell nucleus Interface to the Protein Data Bank© for the implementation of realistic molecular geometries Pattern of energy deposition

[80] [81], http://pdb4dna.in2p3.fr To be released



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Physics stage examples

Geometries of biological targets and damage examples

Four Geant4 extended examples are dedicated to the modeling of physical interactions using Geant4-DNA processes and models.

The Geant4-DNA models and features for physics, physicochemistry and chemistry have been implemented in Geant4 with the main objective of offering tools allowing the simulation of early biological effects induced by ionizing radiation at subcellular scale. Among those radiation-induced biological effects, double strand breaks of the DNA molecule (DSB) are considered to be critical lesions because they can lead to improper repair and induce chromosomal aberrations or cell death. A DSB is defined as two breaks in the sugar-phosphate moiety of the DNA structure placed in opposite bands and separated by less than ten base pairs [80]. Because the typical distances between ionizations (and other energy depositions) in a track are of the same order of the distances between the base pairs on the DNA molecule (2–3 nm), a detailed and realistic geometrical description of the target is needed at the level of its molecular composition [82]. This is the reason why, for several years, the Geant4-DNA Collaboration has been working on different models of the DNA double helix and other cellular structures of interest. First attempts to combine Geant4-DNA simulations with geometrical models of biological targets are described in Bernal et al. [83]. The authors developed a B-DNA geometrical model with atomic resolution (see Fig. 6). This model accounts for the explicit position of every atom in DNA and includes five organization levels of the genetic material: nucleotide pairs, double helix, nucleosomes and the 10- and 30-nm chromatin fibers. A base pair (bp) is used as the brick to construct the whole model. Nucleosomes are built by wrapping two turns of the DNA double helix around virtual histones. Two adjacent nucleosomes are linked by a DNA fragment containing 46 bp. With 154 bp wrapped around the histone core, there are 200 bp per nucleosome in this model. This model was validated through the comparison of the packing ratio and dimensions of the nucleosome with experimental values. An algorithm that is able to find the closest atom to an arbitrary point in space was also present in this publication [83]. This enables the determination of which atom in the DNA is closest to a given energy deposition site that has been previously calculated using Geant4-DNA track structure simulations. Successful consistency tests were carried out by comparing the site-hit probabilities determined theoretically (as a volume ratio) and by uniformly irradiating the geometrical model. In these calculations, the volume defined as the union of all atoms forming the sugar-phosphate group is taken as target (see [83] for details). In parallel, geometrical models of biological targets have been implemented directly as a Geant4 geometry and have been provided to users. The Geant4 extended example called “extended/medical/ dna/wholeNuclearDNA” was the first example of direct implementation of such geometry in Geant4 (it was previously named as “dnageometry” and it was located in the Geant4 advanced examples category before Geant4 release 10). This example contains a simple model of the whole DNA content of a cell nucleus. In this model [80], the cell nucleus is based on the chromosome territory – interchromatin compartment model [84] – where the chromatin is organized in 0.5 Mbp “rosettes” of small loops which are in contact with the inter chromatin domains; the nucleus has been represented as an ellipsoid that contains 6 ·109 base pairs organized in 5 compaction levels (see Fig. 7):

•

•

•

•

“extended/medical/dna/dnaphysics” demonstrates how to record step-by-step physical information, such as occurrences of physical process, position of steps in space and energy deposition. It is the simplest Geant4-DNA example and it uses the default Geant4-DNA physics constructor. “extended/medical/dna/microdosimetry” is a more advanced example which explains how to combine Geant4 electromagnetic physics processes and models with Geant4-DNA processes and models in two different volumes with various energy ranges. This allows users to restrict Geant4-DNA simulations to small volumes where accuracy in space and energy is required (inevitably requiring more computing performance), while maintaining computing performance outside such volumes. “extended/electromagnetic/TestEm12” is not specific to Geant4DNA. It is dedicated to the simulation of dose point kernels as a function of radial distance from the emission point in selected materials. This example can be utilized with Geant4DNA physics constructors for the simulation of electron dose point kernels in liquid water. “extended/medical/dna/svalue” was added to the Geant4 10.2 Beta release for the simulation of s-values for incident electrons, linking source activity to absorbed dose in spherical targets of liquid water.

In addition we expect to release a new example in the next Geant4 release (10.2), “extended/medical/dna/wvalue”, that illustrates how to calculate the mean energy value W, the mean energy required to form an ion pair in liquid water, which is often used to quantify the performance of track structure codes [34].

Physicochemical and chemical stage examples Regarding physicochemical and chemical interactions, three additional examples explain how to enable and use the chemical module of Geant4-DNA. These examples are presented below by order of complexity:

•

•

•

“extended/medical/dna/chem1” demonstrates the simplest activation of the chemical module of Geant4-DNA. In addition to the implementation of all required particles, physics processes and models for the simulation of the physical stage, a new constructor named “G4EmDNAChemistry” is added; this constructor defines all the default parameters used in the physicochemistry and chemistry stage simulation. Once all the particles have been tracked in the physics stage, the Geant4DNA chemical module manages the chemical reactions involving the molecular species. “extended/medical/dna/chem2” introduces new features for a more advanced interaction with the chemical module. These features include the selection of the minimum duration of time steps, access to information before and after each time step, access to each chemical reaction to occur and access to pre/post-processing of the entire physicochemical and chemical stage simulation. “extended/medical/dna/chem3” is the most advanced example, proposing extended interactivity with the simulation of the physicochemical and chemical stages of the simulation, such as visualization of molecular species.

• • •

DNA double helix: containing the amino basis as spheres of radius 0.17 nm and the backbone region, the nucleosome, formed by a histone protein core (cylinder) wrapped by two turns of the DNA double helix (equivalent to 200 bp), chromatin fibers, composed of 90 nucleosomes placed on an helix,


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Figure 6. Nucleosome (top) and 30-nm chromatin fiber (bottom) of the B-DNA atomistic model (see [83] for more details).

• •

chromatin fiber loops, “rosette” loops composed of 28 chromatin fibers, chromosome territories, with volumes proportional to the number of base pairs composing the chromosome. The position of the flower loops for each chromosome territory is given in the provided “chromosome+number.dat” files and they are repeated to fill up the chromosome territory volumes.

In this example, the ionizations that take place in the volumes of the geometry corresponding to the backbone region are recorded (in the ROOT [85] n-tuple form) to be analyzed afterwards as possible candidates to break by direct effect the DNA structure and thus participate to the formation of DSB. One advantage of this geometrical configuration is that different material compositions can be used in different volumes of the target. Indeed, until now, the cross-sections used by the Geant4-DNA physics pro-

cesses are only valid for liquid water. Nevertheless, new crosssection data for DNA-like materials are being integrated in the code and will be released soon in Geant4-DNA. However, the geometrical model described in this example imposes some limitations when trying to calculate direct strand breaks from the energy transfer points located in the backbone region. The main problem concerns the fact that the sugar-phosphate groups of the DNA fiber in a given nucleosome (~200 bp) are defined as a unique volume. Thus, it is not possible to separate the different nucleotides in the same nucleosome. This limitation, as well as other considerations, was solved in a new model that has been recently developed at IRSN, France, in which the different volumes are defined for each molecule in a nucleotide, including a water hydration shell of 12 molecules/nucleotide. In this new geometry (that will also be released in Geant4-DNA) nucleosomes are now linked and the fiber is built using a solenoid form with an interrupted DNA chain. From this description of the DNA fiber, the users will be free of building their own chromatin folding (not only using rosettes loops) to fill the chromosome domains and territories. For illustration purpose, Fig. 8 shows two nucleosomes of this new geometry that are linked by the DNA double helix. Double Strand Breaks and other radiation-induced damages of the DNA are produced either by direct or indirect effects. The geometry presented in Fig. 8 has also been developed to offer the required detail (molecular level) to be used in the simulation of the chemical stage. To do so, reaction rate constants between the reactive oxygen species and the DNA molecules must be included in the simulation. In addition to the “extended/medical/dna/wholeNuclearDNA” example, another example called “extended/medical/dna/pdb4dna” developed at LPC Clermont, France [81], has been proposed in the 10.1 release of Geant4 (December 2014). In this example, the DNA geometry is constructed from information extracted from Protein Data Bank© (PDB) files (http://rcsb.org) [86]. As an illustration, “pdb4dna” translates the provided PDB “1ZBB.PDB” file, describing a short complex of four nucleosomes [87], to work with a dinucleosome, as shown in Fig. 9. A dedicated algorithm is in charge of finding the closest atom to each energy deposition by associating the coordinates of an interaction to the coordinates of the atoms read from the PDB file. If a match is found the algorithm returns the DNA strand, the nucleotide identifier and the group identifier (base, phosphate or sugar group) allowing the evaluation of DNA strand breaks. An example of direct strand break estimation from monoenergetic proton irradiation of such a nucleosome can be found in fig. 9 of [81]. The previously-described developments are driven by the need to assess early biological effects of ionizing radiation by combining the physical, physicochemical and chemical stages with advanced geometrical models of biological targets. This mechanistic approach may not always be suitable for immediate applications and, as such, clustering algorithms may offer an interesting alternative. These algorithms analyze the pattern of energy deposition and are tuned to reproduce experimental data. Using Geant4, Francis et al. proposed a strategy of randomly selecting points and then run an adaption of the “Density-Based Spatial Clustering of Applications with Noise” (DBSCAN) algorithm described by Ester et al. [88] to form clusters [89]. The main idea behind this approach consists of sampling physical interaction points able to induce DNA damage, according to their location in space and to the associated local energy deposition. Then, the algorithm tries to merge the selected points to form clusters according to a distance criterion. More details can be found in the paper of Francis et al. [89]. However, the algorithm by Francis et al. is not publicly available. For this reason, a new clustering algorithm adapted from DBSCAN has been developed by Perrot and Payno at Blaise Pascal University, ClermontFerrand, France, with the goal to be released as a Geant4-DNA



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Figure 7. The 5-compaction levels of the DNA molecule description used in the example “extended/medical/dna/wholeNuclearDNA”: double helix around the histone protein (nucleosome) (two views on top row), B-type chromatin fiber (center row), chromatin loops (bottom left row) and chromosome territories within an ellipsoidal cell nucleus (bottom right row). Geometry implementation is further described in [80].

user example, named “extended/medical/dna/clustering”. To check the consistency of this new clustering algorithm, results of simulations performed under the same conditions as those of Francis et al. are presented. A box of 1 μm × 1 μm × 0.5 μm made of liquid water is irradiated with protons with energy ranging from 500 keV to 50 MeV. Simulations are performed using the default “G4EmDNAPhysics” physics constructor. The probability that an in-

Figure 8. Two linked nucleosomes in a newly developed Geant4 geometry of the DNA molecule.

teraction point falls within a sensitive region is fixed to 0.2 (Francis et al. have used a value of 0.16), and the probability that the energy deposit induces a damage varies linearly between 5 eV and 37.5 eV (as in Francis et al.). The maximum limit distance to merge points was tuned to reproduce the DSB/SSB ratio published for DBSCAN [89] and PARTRAC [90]. We found that this distance could be set at 3.3 nm to reproduce published data, as presented in Fig. 10a, whereas Francis et al. used 3.2 nm. These differences may be attributed to the difference between physical models as we found that the distance criterion in our algorithm was dependent on the elastic scattering model. In addition to the number of single, complex single and double strand breaks, our clustering user application stores the cluster size distribution corresponding to the result of the merging procedure as presented in Fig. 10b.

Figure 9. Rendering of the atomistic view of a dinucleosome irradiated by a single 100 keV proton using the “extended/medical/dna/pdb4dna” Geant4-DNA example (see details in [81]).


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etries, developments to handle the simulation of multiple system representations, a better description of the processes taking place during the physicochemical stage, and models for non diffusioncontrolled reactions. Third, continuous geometrical modeling of genome of bacteria or cells needs to be undertaken, ensuring in particular the possibility to combine the simulation of the physicochemical and chemical stages of Geant4-DNA with such geometries for the simulation of early biological damage. This will be a requirement for future implementation of biological repair processes, extending well beyond the microsecond scale [95]. Overall, the porting of the whole Geant4-DNA extension, including physicochemical and chemical processes, to high efficiency computing systems (such as GPGPU – see the recent work of Okada et al. [96] describing for the first time the porting of Geant4-DNA to GPGPU) is another challenge to face, which will certainly further encourage the use of the Geant4-DNA extension. All these developments require continuous verification – with other codes and models – and validation – with experimental data. In particular, we expect that the availability of state-of-the-art imaging techniques, such as confocal microscopy, immunofluorescence staining and videomicroscopy, combined with targeted irradiation of cells and multicellular organisms will bring quantitative validation information on damage induction and repair up to a few minutes after irradiation [97].

Acknowledgements

Figure 10. Example of results obtained using the new clustering algorithm for monoenergetic protons in liquid water: (a) DSB/SSB ratio compared with PARTRAC and DBSCAN by Francis et al. [89], (b) cluster size distribution.

We would like to acknowledge Pr Paolo Russo for kindly inviting us to submit this review to the “Physica Medica – European Journal of Medical Physics”. M.A. Bernal thanks the FAPESP foundation in Brazil for financing his research activities through the 2011/ 51594-2 project. Geant4-DNA receives funding from the European Space Agency through the BioRadII contract (contract number: 4000107387/12/NL/AK).

References Conclusion and perspectives The Geant4-DNA extension of the open source and general purpose Geant4 MC simulation toolkit provides features for the modeling of physical, physicochemical and chemical processes up to the microsecond scale after incident ionizing particles interact with liquid water, the main component of biological medium. In addition, Geant4-DNA proposes to users several applications illustrating such features, including the realistic geometrical modeling of biological target geometries, from the size of the DNA up to cellular nucleus. Being delivered in free access to the community, they become accessible to highly popular external software based on Geant4, such as the TOPAS MC system [91], primarily aimed at proton therapy simulations, or the GATE platform [92,93] for medical imaging and radiotherapy, possibly extending their application domain down to micro- and nano-dosimetry applications. However, to propose to the community a sound and realistic mechanistic simulation platform for nano-scale modeling in radiobiology, there is still a strong need for deeper developments. First, the set of physics models available in Geant4-DNA needs to be further extended not only for new target materials such as biological targets (like DNA bases and amino acids) instead of liquid water only, but also for high-Z materials (such as metals) in particular for the simulation of processes possibly involved in metal nanoparticle radiosensitization effects [94] and for gas materials used in nanodosimetry. Second, the prototype developments of Geant4DNA for modeling physicochemistry and chemistry require improving the management of many-tracks navigation in complex geom-

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Monte Carlo simulation of laser beams interaction with the human eye using Geant4.

Analysis of the track- and dose-averaged LET and LET spectra in proton therapy using the geant4 Monte Carlo code.

Cross-section scaling for track structure simulations of low-energy ions in liquid water.

The liquid structure of tetrachloroethene: molecular dynamics simulations and reverse Monte Carlo modeling with interatomic potentials.

Evaluation of the dose perturbation around gold and steel fiducial markers in a medical linac through Geant4 Monte Carlo simulation.

Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo.

Monte Carlo simulation of the water in a channel with charges.

Noise-Parameter Uncertainties: A Monte Carlo Simulation.

On the consistency of Monte Carlo track structure DNA damage simulations.

Monte Carlo simulation of skull and knee voxel phantoms for the assessment of skeletal burden of low-energy photon emitters.

Atomistic Monte Carlo simulation of lipid membranes.

Thermal neutron response of a boron-coated GEM detector via GEANT4 Monte Carlo code.

Coherent scatter imaging Monte Carlo simulation.

Optimizing staff scheduling by Monte-Carlo simulation.

Monte Carlo modeling of the Siemens Optifocus multileaf collimator.

Reverse Monte Carlo modeling in confined systems.

Hydration of uracil and thymine methylderivatives: a Monte Carlo simulation.

Monte Carlo simulation and SAFT modeling study of the solvation thermodynamics of dimethylformamide, dimethylsulfoxide, ethanol and 1-propanol in the ionic liquid trimethylbutylammonium bis(trifluoromethylsulfonyl)imide.

Quantum Monte Carlo Study of the Protonated Water Dimer.

A scatter correction method for dual-energy digital mammography: Monte Carlo simulation.

Colloidal nanoparticles trapped by liquid-crystal defect lines: a lattice Monte Carlo simulation.

Modeling of vision loss due to vitreous hemorrhage by Monte Carlo simulation.

The role of cell death in the growth of preneoplastic lesions: a Monte Carlo simulation model.

Monte Carlo-quantum mechanics study of magnetic properties of hydrogen peroxide in liquid water.