C. Champion

THE Geant4-DNA project

The Geant4-DNA project proposes to develop an open-source simulation software based and fully included in the general-purpose Geant4 Monte-Carlo simulation toolkit. The main objective of this software is to simulate biological damages induced by ionizing radiations at the cellular and sub-cellular scale. This project was originally initiated by the European Space Agency for the prediction of the deleterious effects of radiations that may affect astronauts during future long duration space exploration missions. In this paper, the Geant4-DNA collaboration presents an overview of the whole on-going project, including its most recent developments that are available in the Geant4 toolkit since December 2009 (release 9.3), as well as an illustration example simulating the direct irradiation of a biological chromatin fiber. Expected extensions involving several research domains, such as particle physics, chemistry and cellular and molecular biology, within a fully interdisciplinary activity of the Geant4 collaboration are also discussed.

Theoretical cross sections for electron collisions in water: structure of electron tracks

To understand what happens when biological matter is irradiated needs a detailed knowledge of the microscopic distribution of interactions and especially of the energy deposited in irradiated matter. Monte Carlo event-by-event simulations are particularly suitable for this task. However, the development of these track-structure codes necessitates accurate interaction cross sections for all the electronic processes: ionization, excitation and elastic scattering. In these conditions, we have recently developed a Monte Carlo code for electrons in water, this latter being commonly used to simulate the biological medium. All the electronic processes are studied in detail via theoretical differential and total cross-section calculations. The purpose of this work is to make an inter-comparison of our cross sections with those used in the electron track-structure codes developed in the literature, and to compare macroscopic quantities such as stopping powers and mean energy transfer distributions to available experimental data and/or to theoretical predictions in liquid water.

Positron follow-up in liquid water: II. Spatial and energetic study for the most important radioisotopes used in PET

With the increasing development of positron emission tomography (PET), beta(+)-emitters are more and more regularly used in nuclear medicine. Therefore, today it is of prime importance to have a reliable description of their behavior in living matter in order to quantify the full spectra of the molecular damages potentially radio-induced and then to access a cellular dosimetry. In this work, we present a detailed inter-comparison of the main isotopes commonly used in PET: (18)F, (11)C, (13)N, (15)O, (68)Ga and (82)Rb. We have used an event-by-event Monte Carlo code recently developed for positron tracking in water (Champion and Le Loirec 2006 Phys. Med. Biol. 51 1707-23) which consists in simulating step-by-step, interaction after interaction, the history of each ionizing particle created during the irradiation of the biological matter. This simulation has been finally adapted for describing the decays of medically important positron emitters. Quantitative information about positron penetrations, Positronium formation, annihilation event distributions, energy deposit patterns and dose profiles is then accessible and compared to published measurements and/or calculations.

CELLDOSE: A Monte Carlo Code to Assess Electron Dose Distribution—S Values for 131I in Spheres of Various Sizes

Monte Carlo simulation can be particularly suitable for modeling the microscopic distribution of energy received by normal tissues or cancer cells and for evaluating the relative merits of different radiopharmaceuticals. We used a new code, CELLDOSE, to assess electron dose for isolated spheres with radii varying from 2,500 μm down to 0.05 μm, in which 131I is homogeneously distributed. Methods: All electron emissions of 131I were considered, including the whole β− 131I spectrum, 108 internal conversion electrons, and 21 Auger electrons. The Monte Carlo track-structure code used follows all electrons down to an energy threshold Ecutoff = 7.4 eV. Results: Calculated S values were in good agreement with published analytic methods, lying in between reported results for all experimental points. Our S values were also close to other published data using a Monte Carlo code. Contrary to the latter published results, our results show that dose distribution inside spheres is not homogeneous, with the dose at the outmost layer being approximately half that at the center. The fraction of electron energy retained within the spheres decreased with decreasing radius (r): 87.1% for r = 2,500 μm, 8.73% for r = 50 μm, and 1.18% for r = 5 μm. Thus, a radioiodine concentration that delivers a dose of 100 Gy to a micrometastasis of 2,500 μm radius would deliver 10 Gy in a cluster of 50 μm and only 1.4 Gy in an isolated cell. The specific contribution from Auger electrons varied from 0.25% for the largest sphere up to 76.8% for the smallest sphere. Conclusion: The dose to a tumor cell will depend on its position in a metastasis. For the treatment of very small metastases, 131I may not be the isotope of choice. When trying to kill isolated cells or a small cluster of cells with 131I, it is important to get the iodine as close as possible to the nucleus to get the enhancement factor from Auger electrons. The Monte Carlo code CELLDOSE can be used to assess the electron map deposit for any isotope.

Estimation of the β+ Dose to the Embryo Resulting from 18F-FDG Administration During Early Pregnancy

Although 18F-FDG examinations are widely used, data are lacking on the dose to human embryo tissues in cases of exposure in early pregnancy. Although the photon component can easily be estimated from available data on the pharmacokinetics of 18F-FDG in female organs and from phantom measurements (considering the uterus as the target organ), the intensity of embryo tissue uptake, which is essential for deriving the β+ dose, is not known. We report the case of a patient who underwent 18F-FDG PET/CT for tumor surveillance and who was later found to have been pregnant at the time of the examination (embryo age, 8 wk). Methods: The patient received 320 MBq of 18F-FDG. Imaging started with an unenhanced CT scan 1 h after the injection, followed by PET acquisition. PET images were used to compute the total number of β+ emissions in embryo tissues per unit of injected activity, from standardized uptake value (SUV) measurements corrected for partial-volume effects. A Monte Carlo track structure code was then used to derive the β+ self-dose and the β+ cross-dose from amniotic fluid. The photon and CT doses were added to obtain the final dose received by the embryo. Results: The mean SUV in embryo tissues was 2.7, after correction for the partial-volume effect. The mean corrected SUV of amniotic fluid was 1.1. Monte Carlo simulation showed that the β+ dose to the embryo (self-dose plus cross-dose from amniotic fluid) was 1.8E−2 mGy per MBq of injected 18F-FDG. Based on MIRD data for the photon dose to the uterus, the estimated photon dose to the embryo was 1.5E−2 mGy/MBq. Thus, the specific 18F-FDG dose to the embryo was 3.3E−2 mGy/MBq (10.6 mGy in this patient). The CT scan added a further 8.3 mGy. Conclusion: The dose to the embryo is 3.3E−2 mGy/MBq of 18F-FDG. The β+ dose contributes 55% of the total dose. This value is higher than previous estimates in late nonhuman-primate pregnancies.

Monte Carlo simulation of energy-deposit clustering for ions of the same LET in liquid water.

This work presents a Monte Carlo study of energy depositions due to protons, alpha particles and carbon ions of the same linear-energy-transfer (LET) in liquid water. The corresponding track structures were generated using the Geant4-DNA toolkit, and the energy deposition spatial distributions were analyzed using an adapted version of the DBSCAN clustering algorithm. Combining the Geant4 simulations and the clustering algorithm it was possible to compare the quality of the different radiation types. The ratios of clustered and single energy depositions are shown versus particle LET and frequency-mean lineal energies. The estimated effect of these types of radiation on biological tissues is then discussed by comparing the results obtained for different particles with the same LET.

Positron follow-up in liquid water: I. A new Monte Carlo track-structure code

When biological matter is irradiated by charged particles, a wide variety of interactions occur, which lead to a deep modification of the cellular environment. To understand the fine structure of the microscopic distribution of energy deposits, Monte Carlo event-by-event simulations are particularly suitable. However, the development of these track-structure codes needs accurate interaction cross sections for all the electronic processes: ionization, excitation, positronium formation and even elastic scattering. Under these conditions, we have recently developed a Monte Carlo code for positrons in water, the latter being commonly used to simulate the biological medium. All the processes are studied in detail via theoretical differential and total cross-section calculations performed by using partial wave methods. Comparisons with existing theoretical and experimental data in terms of stopping powers, mean energy transfers and ranges show very good agreements. Moreover, thanks to the theoretical description of positronium formation, we have access, for the first time, to the complete kinematics of the electron capture process. Then, the present Monte Carlo code is able to describe the detailed positronium history, which will provide useful information for medical imaging (like positron emission tomography) where improvements are needed to define with the best accuracy the tumoural volumes.

Electron impact ionization of water molecule

In the present paper, differential and total cross sections are calculated for the interaction of electrons with a water molecule. The calculations are performed in the distorted wave Born approximation framework where the incident and scattered (fast) electrons are described by a plane wave function, whereas the ejected (slow) electron is described by a distorted wave function. From the fivefold differential cross sections, triply and singly differential cross sections have been calculated by successive integrations. In these conditions, very good agreement is found with available experimental measurements essentially limited to triply and singly ionization cross sections. Finally, a comparison of our results with a large set of experimental data of total ionization cross sections exhibits very good agreement.

Differential and total (e,2e) cross sections of simple polyatomic molecules

In this paper, we present a theoretical approach to calculate differential and total ionization cross sections of polyatomic molecules by fast electron impact. More exactly, we have studied the ionization of ammonia (NH(3)) and methane (CH(4)) molecules, and previous results concerning the H(2)O molecule ionization are reported for comparison. The calculations are performed in the distorted wave Born approximation without exchange by employing the independent electron model. The molecular target wave functions are described by linear combinations of atomic orbitals. To describe the interaction between the inactive target electrons and the slow ejected electron, we have introduced a distortion via an effective potential calculated for each molecular orbital. The present theoretical calculations agree well with a large set of existing experimental data in terms of multiple differential and total cross sections.

EPOTRAN: a full-differential Monte Carlo code for electron and positron transport in liquid and gaseous water.

Abstract Purpose: We describe here a novel full-differential Monte Carlo (MC) event-by-event simulation, for modelling electron and positron histories in liquid and gaseous water, with impact energies ranging from the water excitation threshold (7.4 eV) to 10 keV. This new track-structure code is named EPOTRAN, an acronym for Electron and POsitron TRANsport in water. Material and methods: All the processes induced by both electrons and positrons are studied in detail via theoretical differential and total cross sections, calculated within the quantum mechanical framework by using the partial-wave method. Elastic and inelastic interactions are then successively reviewed, including in particular an original description of the positron-induced capture process leading to Positronium formation. Results: Total and differential cross sections are reported and compared with a large set of existing measurements. Rather good agreement is generally observed over the considered energy range. Conclusions: This work reports the theoretical cross sections used in a special purpose Monte Carlo simulation suitable for electron and positron transport in gaseous and liquid water. This MC code should represent an accurate tool for dose calculation at the nanometric scale, by providing a detailed spatial distribution of energy deposits. Furthermore, positron trajectory studies made possible by this approach should prove useful for evaluating the real contribution of the positron range on the overall spatial resolution of PET (Positron Emission Tomography) imaging.