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.     

A Monte Carlo program for the analysis of low-energy electron tracks in liquid water

A Monte Carlo code for the event-by-event simulation of electron transport in liquid water is presented. The code, written in C++, can accommodate different interaction models. Currently it implements cross sections for ionizing collisions calculated with the model developed by Dingfelder et al (1998 Radiat. Phys. Chem. 53 1-18, 2008 Radiat. Res. 169 584-94) and cross sections for elastic scattering computed within the static-exchange approximation (Salvat et al 2005 Comput. Phys. Commun. 165 157-90). The latter cross sections coincide with those recommended in ICRU Report 77 (2007). Other included interaction mechanisms are excitation by electron impact and dissociative attachment. The main characteristics of the code are summarized. Various track penetration parameters, including the detour factor, are defined as useful tools to quantify the geometrical extent of electron tracks in liquid water. Results obtained with the present microdosimetry code are given in the form of probability density functions for initial electron kinetic energies ranging from 0.1 to 10 keV. The sensitivity of the simulated distributions to the choice of alternative physics models has been briefly explored. The discrepancies with equivalent simulations reported by Wilson et al (2004 Radiat. Res. 161 591-6) stem from the adopted cross sections for elastic scattering, which determine largely the spatial evolution of low-energy electron tracks.     

Radiological characterization and water equivalency of genipin gel for x-ray and electron beam dosimetry

The genipin radiochromic gel offers enormous potential as a three-dimensional dosimeter in advanced radiotherapy techniques. We have used several methods (including Monte Carlo simulation), to investigate the water equivalency of genipin gel by characterizing its radiological properties, including mass and electron densities, photon interaction cross sections, mass energy absorption coefficient, effective atomic number, collisional, radiative and total mass stopping powers and electron mass scattering power. Depth doses were also calculated for clinical kilovoltage and megavoltage x-ray beams as well as megavoltage electron beams. The mass density, electron density and effective atomic number of genipin were found to differ from water by less than 2%. For energies below 150 keV, photoelectric absorption cross sections are more than 3% higher than water due to the strong dependence on atomic number. Compton scattering and pair production interaction cross sections for genipin gel differ from water by less than 1%. The mass energy absorption coefficient is approximately 3% higher than water for energies <60 keV due to the dominance of photoelectric absorption in this energy range. The electron mass stopping power and mass scattering power differ from water by approximately 0.3%. X-ray depth dose curves for genipin gel agree to within 1% with those for water. Our results demonstrate that genipin gel can be considered water equivalent for kilovoltage and megavoltage x-ray beam dosimetry. For megavoltage electron beam dosimetry, however, our results suggest that a correction factor may be needed to convert measured dose in genipin gel to that of water, since differences in some radiological properties of up to 3% compared to water are observed. Our results indicate that genipin gel exhibits greater water equivalency than polymer gels and PRESAGE formulations.     

Optimizing SHIELD-HIT for carbon ion treatment

The SHIELD-HIT Monte Carlo transport code has been widely used in particle therapy, but has previously shown some discrepancies, when compared with experimental data. In this work, the inelastic nuclear cross sections of SHIELD-HIT are calibrated to experimental data for carbon ions. In addition, the models for nuclear fragmentation were adjusted to experiments, for the partial charge-changing cross section of carbon ions in water. Comparison with fragmentation yield experiments for carbon and neon primaries were made for validation. For carbon primaries, excellent agreement between simulation and experiment was observed, with only minor discrepancies. For neon primaries, the agreement was also good, but larger discrepancies were observed, which require further investigation. In conclusion, the current version SHIELD-HIT10A is well suited for simulating problems arising in particle therapy for clinical ion beams.     

Monte Carlo simulation and analysis of proton energy-deposition patterns in the Bragg peak

The spatial pattern of energy depositions is crucial for understanding the mechanisms that modify the relative biological effectiveness of different radiation qualities. In this paper, we present data on energy-deposition properties of mono-energetic protons (1-20 MeV) and their secondary electrons in liquid water. Proton-impact ionization was described by means of the Hansen-Kocbach-Stolterfoht doubly differential cross section (DDCS), thus modelling both the initial energy and angle of the emitted electron. Excitation by proton impact was included to account for the contribution of this interaction channel to the electronic stopping power of the projectile. Proton transport was implemented assuming track-segment conditions, whereas electrons were followed down to 50 eV by the Monte Carlo code PENELOPE. Electron intra-track energy-deposition properties, such as slowing-down and energy-imparted spectra of electrons, were calculated. Furthermore, the use of DDCSs enabled the scoring of electron inter-track properties. We present novel results for 1, 5 and 20 MeV single-proton-track frequencies of distances between the nearest inter- (e(-)-e(-), e(-)-H+) and intra-track (e(-)-e(-), e(-)-H+, H+-H+) energy-deposition events. By setting a threshold energy of 17.5 eV, commonly employed as a surrogate to discriminate for elementary damage in the DNA, the variation in these frequencies was studied as well. The energy deposited directly by the proton represents a large amount of the total energy deposited along the track, but when an energy threshold is adopted the relative contribution of the secondary electrons becomes larger for increasing energy of the projectile. We found that the frequencies of closest energy-deposition events per nanometre decrease with proton energy, i.e. for lower proton energies a denser ionization occurs, following the trend of the characteristic LET curves. In conclusion, considering the energy depositions due to the delta electrons and at the core of the track, 1 MeV protons have an intrinsic capability of generating about five times more dual depositions within the characteristic 2 nm of the DNA-chain structure than 20 MeV protons.     

A Monte Carlo study of absorbed dose distributions in both the vapor and liquid phases of water by intermediate energy electrons based on different condensed-history transport schemes

Monte Carlo transport calculations of dose point kernels (DPKs) and depth dose profiles (DDPs) in both the vapor and liquid phases of water are presented for electrons with initial energy between 10 keV and 1 MeV. The results are obtained by the MC4 code using three different implementations of the condensed-history technique for inelastic collisions, namely the continuous slowing down approximation, the mixed-simulation with delta-ray transport and the addition of straggling distributions for soft collisions derived from accurate relativistic Born cross sections. In all schemes, elastic collisions are simulated individually based on single-scattering cross sections. Electron transport below 10 keV is performed in an event-by-event mode. Differences on inelastic interactions between the vapor and liquid phase are treated explicitly using our recently developed dielectric response function which is supplemented by relativistic corrections and the transverse contribution. On the whole, the interaction coefficients used agree to better than approximately 5% with NIST/ICRU values. It is shown that condensed phase effects in both DPKs and DDPs practically vanish above 100 keV. The effect of delta-rays, although decreases with energy, is sizeable leading to more diffused distributions, especially for DPKs. The addition of straggling for soft collisions is practically inconsequential above a few hundred keV. An extensive benchmarking with other condensed-history codes is provided.     

Inactivation cross section of ions for dry enzymes and viruses

In this note, a semi-empirical analytical formula for the inactivation cross section of ions for dry enzymes and viruses is developed based on the delta-ray theory of track structure. Using the experimental characteristic dose of gamma rays, the cross sections are calculated and compared with experimental results. The average ratio of the experimental to the calculated cross section is 0.96 +/- 0.17.     

Single and multiple cross sections for ionizing processes of biological molecules by protons and alpha-particle impact: a classical Monte Carlo approach

A classical trajectory model has been used to predict total cross sections of single and double ionizing processes (including capture processes) for several ion-biological molecule collisional systems in the intermediate and high energy range. In this work, the systems studied are water, adenine or cytosine targets ionized by protons and alpha-particles with kinetic energies ranging from 25 keV amu(-1) to 3000 keV amu(-1). In our approach, we have combined several features of two classical methods namely the classical trajectory Monte Carlo (CTMC) and the classical over-barrier (COB) models. For the water target, our results are compared, for high kinetic energies of incident particles, to the available experimental and theoretical results, and reasonable agreement are generally observed especially for the single ionization (liberated electron moves freely after the collision) and the single capture (liberated electron captured by the projectile), both processes representing ionizing processes. Considering the double ionizing processes which have been largely less studied, the unique comparison concerns the double capture process for alpha+H(2)O collision for which we reproduce the experiment reasonably well. Finally, we present total cross sections of single and double ionizing processes for biological targets such as adenine and cytosine where no experimental results exist till now.     

Experimental determination of beam quality conversion factors k(Q) in clinical photon beams using ferrous sulphate (Fricke) dosimetry

The implementation of protocols based on absorbed dose to water standards requires beam quality conversion factors, k(Q). Calculated values of k(Q) are available for ionization chambers used for reference dosimetry. Ideally, k(Q) should be experimentally determined at the same beam qualities as that of the user. In this work we measure k(Q) factors in clinical photon beams and compare them with calculated and measured values. Beam quality conversion factors are determined for clinical photon beams of nominal energies 4 MV, 6 MV, 15 MV, and 25 MV, for commonly used cylindrical ionization chambers. Twelve chambers of eight different types are used. For three of them, no experimental data have previously been available. The experimental procedure is based on measurements with ionization chambers and Fricke dosimetry in the reference beam (60Co gamma radiation) and in clinical linear accelerator beams. The k(Q) values determined in this work generally agree within 0.5% with previously reported experimental values both when %dd(10)x and TPR2010 are used for beam quality specification. The agreement with calculated data is generally within 0.5%, except for the 15 MV beam. For this beam the measured values are usually between 0.5% and 1% lower than the data taken from the TG-51 protocol or the TRS-398 code of practice. For three NE2571 chambers and three NE2581 chambers, the maximum observed deviation of individual k(Q) values is 0.2% and 0.4%, respectively.     

Quantitative measurement of small-angle gamma ray scattering from water, nylon, and Lucite

The small-angle (2 degrees-10 degrees) total-differential-scattering cross sections of water, methyl methacrylate, and nylon 6 have been measured at a photon energy of 59.54 keV. An annular target geometry has been used with an acceptance of +/- 0.5 degrees and an experimental uncertainty of approximately 4% achieved. The experimental methods and data corrections necessary to obtain this accuracy are discussed in detail. The results demonstrate clearly the contribution of intermolecular effects to the scattering process and allow critical comparison with calculations using molecular form factors for water obtained from interpolated x-ray diffractometer data; agreement is obtained within the experimental uncertainties. They also support earlier Monte Carlo predictions of scattering in water at angles of the order of 2 degrees which are in disagreement with certain published experimental data.     

Comparison of nanodosimetric parameters of track structure calculated by the Monte Carlo codes Geant4-DNA and PTra

The concept of nanodosimetry is based on the assumption that initial damage to cells is related to the number of ionizations (the ionization cluster size) directly produced by single particles within, or in the close vicinity of, short segments of DNA. The ionization cluster-size distribution and other nanodosimetric quantities, however, are not directly measurable in biological targets and our current knowledge is mostly based on numerical simulations of particle tracks in water, calculating track structure parameters for nanometric target volumes. The assessment of nanodosimetric quantities derived from particle-track calculations using different Monte Carlo codes plays, therefore, an important role for a more accurate evaluation of the initial damage to cells and, as a consequence, of the biological effectiveness of ionizing radiation. The aim of this work is to assess the differences in the calculated nanodosimetric quantities obtained with Geant4-DNA as compared to those of the ad hoc particle-track Monte Carlo code 'PTra' developed at Physikalisch-Technische Bundesanstalt (PTB), Germany. The comparison of the two codes was made for incident electrons of energy in the range between 50 eV and 10 keV, for protons of energy between 300 keV and 10 MeV, and for alpha particles of energy between 1 and 10 MeV as these were the energy ranges available in both codes at the time this investigation was carried out. Good agreement was found for nanodosimetric characteristics of track structure calculated in the high-energy range of each particle type. For lower energies, significant differences were observed, most notably in the estimates of the biological effectiveness. The largest relative differences obtained were over 50%; however, generally the order of magnitude was between 10% and 20%.     

Experimental partial and total kerma coefficients for aluminium at incident neutron energies from reaction thresholds to 65 MeV

For nine incident neutron energies in the range 25 to 65 MeV, the double-differential cross sections (energy spectra) for the (n, px), (n, dx), (n, tx) and (n, alpha x) reactions on aluminium have been measured at lab angles between 20 degrees and 160 degrees in steps of 10 degrees. The partial and total kerma coefficients have been determined from the experimental energy-differential cross sections. The resulting partial kerma coefficients for the incident neutron energy range of 25-65 MeV are extrapolated to the threshold energy of each registered reaction product type. Only illustrative results of the experimental double-differential, energy-differential and total cross sections are presented. The deduced partial and total kerma coefficients of the present work are compared with results of previous integral measurements and theoretical predictions.     

Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac

We have benchmarked photon beam simulations with the EGS4 user code BEAM [Rogers et al., Med. Phys. 22, 503-524 (1995)] by comparing calculated and measured relative ionization distributions in water from the 10 and 20 MV photon beams of the NRC linac. Unlike previous calculations, the incident electron energy is known independently to 1%, the entire extra-focal radiation is simulated, and electron contamination is accounted for. The full Monte Carlo simulation of the linac includes the electron exit window, target, flattening filter, monitor chambers, collimators, as well as the PMMA walls of the water phantom. Dose distributions are calculated using a modified version of the EGS4 user code DOSXYZ which additionally allows scoring of average energy and energy fluence in the phantom. Dose is converted to ionization by accounting for the (L/rho)water(air) variation in the phantom, calculated in an identical geometry for the realistic beams using a new EGS4 user code, SPRXYZ. The variation of (L/rho)water(air) with depth is a 1.25% correction at 10 MV and a 2% correction at 20 MV. At both energies, the calculated and the measured values of ionization on the central axis in the buildup region agree within 1% of maximum ionization relative to the ionization at 10 cm depth. The agreement is well within statistics elsewhere. The electron contamination contributes 0.35(+/- 0.02) to 1.37(+/- 0.03)% of the maximum dose in the buildup region at 10 MV and 0.26(+/- 0.03) to 3.14(+/- 0.07)% of the maximum dose at 20 MV. The penumbrae at 3 depths in each beam (in g/cm2), 1.99 (dmax, 10 MV only), 3.29 (dmax, 20 MV only), 9.79 and 19.79, agree with ionization chamber measurements to better than 1 mm. Possible causes for the discrepancy between calculations and measurements are analyzed and discussed in detail.     

Modification and benchmarking of MCNP for low-energy tungsten spectra

The MCNP Monte Carlo radiation transport code was modified for diagnostic medical physics applications. In particular, the modified code was thoroughly benchmarked for the production of polychromatic tungsten x-ray spectra in the 30-150 kV range. Validating the modified code for coupled electron-photon transport with benchmark spectra was supplemented with independent electron-only and photon-only transport benchmarks. Major revisions to the code included the proper treatment of characteristic K x-ray production and scoring, new impact ionization cross sections, and new bremsstrahlung cross sections. Minor revisions included updated photon cross sections, electron-electron bremsstrahlung production, and K x-ray yield. The modified MCNP code is benchmarked to electron backscatter factors, x-ray spectra production, and primary and scatter photon transport.     

Parameter dependence of the MCNP electron transport in determining dose distributions

In this paper, a detailed study of the electron transport in MCNP is performed, separating the effects of the energy binning technique on the energy loss rate, the scattering angles, and the sub-step length as a function of energy. As this problem is already well known, in this paper we focus on the explanation as to why the default mode of MCNP can lead to large deviations. The resolution dependence was investigated as well. An error in the MCNP code in the energy binning technique in the default mode (DBCN 18 card = 0) was revealed, more specific in the updating of cross sections when a sub-step is performed corresponding to a high-energy loss. This updating error is not present in the ITS mode (DBCN 18 card = 1) and leads to a systematically lower dose deposition rate in the default mode. The effect is present for all energies studied (0.5-10 MeV) and depends on the geometrical resolution of the scoring regions and the energy grid resolution. The effect of the energy binning technique is of the same order of that of the updating error for energies below 2 MeV, and becomes less important for higher energies. For a 1 MeV point source surrounded by homogeneous water, the deviation of the default MCNP results at short distances attains 9% and remains approximately the same for all energies. This effect could be corrected by removing the completion of an energy step each time an electron changes from an energy bin during a sub-step. Another solution consists of performing all calculations in the ITS mode. Another problem is the resolution dependence, even in the ITS mode. The higher the resolution is chosen (the smaller the scoring regions) the faster the energy is deposited along the electron track. It is proven that this is caused by starting a new energy step when crossing a surface. The resolution effect should be investigated for every specific case when calculating dose distributions around beta sources. The resolution should not be higher than 0.85*(1-EFAC)*CSDA, where EFAC is the energy loss per energy step and CSDA a continuous slowing down approximation range. This effect could as well be removed by determining the cross sections for energy loss and multiple scattering at the average energy of an energy step and by sampling the cross sections for each sub-step. Overall, we conclude that MCNP cannot be used without a caution due to possible errors in the electron transport. When care is taken, it is possible to obtain correct results that are in agreement with other Monte Carlo codes.     

Accurate Monte Carlo calculations of the combined attenuation and build-up factors, for energies (20-1500 keV) and distances (0-10 cm) relevant in brachytherapy

The combined build-up and attenuation factor, B exp (-mu r), of point isotropic photon sources in a water medium has been calculated using the Monte Carlo method, for energies (20-1500 keV) and distances (1-10 cm) relevant in brachytherapy. For the transport of photons and electrons, up-to-date and self-consistent total, partial and differential cross sections were used. The influence of coherent (Rayleigh) and incoherent (Compton) scattering, as well as the effects of the source and medium geometries on the calculations, were investigated in detail and it was found that these effects can lead to significant deviations from published data, especially at low energies and/or large distances from the sources. Our results can be used for any mono- or multi-energetic photon source in the energy range 20-1500 keV with uncertainties of the order of 2-3%, and they may influence treatment planning especially in the case of organs at risk which are usually near the edge of the body.     

In-phantom dosimetry for the 13C(d,n)14N reaction as a source for accelerator-based BNCT

The use of the 13C(d,n) 14N reaction at Ed=1.5 MeV for accelerator-based boron neutron capture therapy (AB-BNCT) is investigated. Among the deuteron-induced reactions at low incident energy, the 3C(d,n)14N reaction turns out to be one of the best for AB-BNCT because of beneficial materials properties inherent to carbon and its relatively large neutron production cross section. The deuteron beam was produced by a tandem accelerator at MIT's Laboratory for Accelerator Beam Applications (LABA) and the neutron beam shaping assembly included a heavy water moderator and a lead reflector. The resulting neutron spectrum was dosimetrically evaluated at different depths inside a water-filled brain phantom using the dual ionization chamber technique for fast neutrons and photons and bare and cadmium-covered gold foils for the thermal neutron flux. The RBE doses in tumor and healthy tissue were calculated from experimental data assuming a tumor 10B concentration of 40 ppm and a healthy tissue 10B concentration of 11.4 ppm (corresponding to a reported ratio of 3.5:1). All results were simulated using the code MCNP, a general Monte Carlo radiation transport code capable of simulating electron, photon, and neutron transport. Experimental and simulated results are presented at 1, 2, 3, 4, 6, 8, and 10 cm depths along the brain phantom centerline. An advantage depth of 5.6 cm was obtained for a treatment time of 56 min assuming a 4 mA deuteron current and a maximum healthy tissue dose of 12.5 RBE Gy.     

Microdosimetric properties of ionizing electrons in water: a test of the PENELOPE code system

The ability to simulate the tortuous path of very low-energy electrons in condensed matter is important for a variety of applications in radiobiology. Event-by-event Monte Carlo codes such as OREC, MOCA and PITS represent the preferred method of computing distributions of microdosimetric quantities. However, event-by-event Monte Carlo is computationally expensive, and the cross sections needed to transport simulations to this level of detail are usually only available for water. In the recently developed PENELOPE code system, 'hard' electron and positron interactions are simulated in a detailed way while soft' interactions are treated using multiple scattering theory. Using this mixed simulation algorithm, electrons and positrons can be transported down to energies as low as 100 eV. To our knowledge, PENELOPE is the first widely available, general purpose Monte Carlo code system capable of transporting electrons and positrons in arbitrary media down to such low energies. The ability to transport electrons and positrons to such low energies opens up the possibility of using a general purpose Monte Carlo code system for microdosimetry. This paper presents the results of a code intercomparison study designed to test the applicability of the PENELOPE code system for microdosimetry applications. For sites comparable in size to a mammalian cell or cell nucleus, single-event distributions, site-hit probabilities and the frequency-mean specific energy per event are in reasonable agreement with those predicted using event-by-event Monte Carlo. Site-hit probabilities and the mean specific energy per event can be estimated to within about 1-10% of those predicted using event-by-event Monte Carlo. However, for some combinations of site size and source-target geometry, site-hit probabilities and the mean specific energy per event may only agree to within 25-60%. The most problematic source-target geometry is one in which the emitted electrons are very close to the tally site (e.g., a point source on the surface of a cell). Although event-by-event Monte Carlo will continue to be the method of choice for microdosimetry, PENELOPE is a useful, computationally efficient tool for some classes of microdosimetry problem. PENELOPE may prove particularly useful for applications that involve radiation transport through materials other than water or for applications that are too computationally intensive for event-by-event Monte Carlo, such as in vivo microdosimetry of spatially complex distributions of radioisotopes inside the human body.