Determination of initial electron parameters by means of Monte Carlo simulations for the Siemens Artiste Linac 6 MV photon beam

AimIn this study, we investigated initial electron parameters of Siemens Artiste Linac with 6 MV photon beam using the Monte Carlo method.BackgroundIt is essential to define all the characteristics of initial electrons hitting the target, i.e. mean energy and full width of half maximum (FWHM) of the spatial distribution intensity, which is needed to run Monte Carlo simulations. The Monte Carlo is the most accurate method for simulation of radiotherapy treatments.Materials and methodsLinac head geometry was modeled using the BEAMnrc code. The phase space files were used as input file to DOSXYZnrc simulation to determine the dose distribution in a water phantom. We obtained percent depth dose curves and the lateral dose profile. All the results were obtained at 100 cm of SSD and for a 10 × 10 cm² field.ResultsWe concluded that there existed a good conformity between Monte Carlo simulation and measurement data when we used electron mean energy of 6.3 MeV and 0.30 cm FWHM value as initial parameters. We observed that FWHM values had very little effect on PDD and we found that the electron mean energy and FWHM values affected the lateral dose profile. However, these effects are between tolerance values.ConclusionsThe initial parameters especially depend on components of a linac head. The phase space file which was obtained from Monte Carlo Simulation for a linac can be used as calculation of scattering, MLC leakage, to compare dose distribution on patients and in various studies.     

An inhomogeneous most likely path formalism for proton computed tomography

PurposeMultiple Coulomb scattering (MCS) poses a challenge in proton CT (pCT) image reconstruction. The assumption of straight paths is replaced with Bayesian models of the most likely path (MLP). Current MLP-based pCT reconstruction approaches assume a water scattering environment. We propose an MLP formalism based on accurate determination of scattering moments in inhomogeneous media.MethodsScattering power relative to water (RScP) was calculated for a range of human tissues and investigated against relative stopping power (RStP). Monte Carlo simulation was used to compare the new inhomogeneous MLP formalism to the water approach in a slab geometry and a human head phantom. An MLP-Spline-Hybrid method was investigated for improved computational efficiency.ResultsA piecewise-linear correlation between RStP and RScP was shown, which may assist in iterative pCT reconstruction. The inhomogeneous formalism predicted Monte Carlo proton paths through a water cube with thick bone inserts to within 1.0 mm for beams ranging from 210 to 230 MeV incident energy. Improvement in accuracy over the conventional MLP ranged from 5% for a 230 MeV beam to 17% for 210 MeV. There was no noticeable gain in accuracy when predicting 200 MeV proton paths through a clinically relevant human head phantom. The MLP-Spline-Hybrid method reduced computation time by half while suffering negligible loss of accuracy.ConclusionsWe have presented an MLP formalism that accounts for material composition. In most clinical cases a water scattering environment can be assumed, however in certain cases of significant heterogeneity the proposed algorithm may improve proton path estimation.     

Comparison between an event-by-event Monte Carlo code,NOREC, and ETRAN for electron scaled point kernels between 20 keV and 1 MeV

An event-by-event Monte Carlo code called NOREC, a substantially improved version of the Oak Ridge electron transport code (OREC), was released in 2003, after a number of modifications to OREC. In spite of some earlier work, the characteristics of the code have not been clearly shown so far, especially for a wide range of electron energies. Therefore, NOREC was used in this study to generate one of the popular dosimetric quantities, the scaled point kernel, for a number of electron energies between 0.02 and 1.0 MeV. Calculated kernels were compared with the most well-known published kernels based on a condensed history Monte Carlo code, ETRAN, to show not only general agreement between the codes for the electron energy range considered but also possible differences between an event-by-event code and a condensed history code. There was general agreement between the kernels within about 5% up to 0.7 r/r ₀ for 100 keV and 1 MeV electrons. Note that r/r ₀ denotes the scaled distance, where r is the radial distance from the source to the dose point and r ₀ is the continuous slowing down approximation (CSDA) range of a mono-energetic electron. For the same range of scaled distances, the discrepancies for 20 and 500 keV electrons were up to 6 and 12%, respectively. Especially, there was more pronounced disagreement for 500 keV electrons than for 20 keV electrons. The degree of disagreement for 500 keV electrons decreased when NOREC results were compared with published EGS4/PRESTA results, producing similar agreement to other electron energies.     

Radial secondary electron dose profiles and biological effects in light-ion beams based on analytical and Monte Carlo calculations using distorted wave cross sections

To speed up dose calculation, an analytical pencil-beam method has been developed to calculate the mean radial dose distributions due to secondary electrons that are set in motion by light ions in water. For comparison, radial dose profiles calculated using a Monte Carlo technique have also been determined. An accurate comparison of the resulting radial dose profiles of the Bragg peak for (1)H(+), (4)He(2+) and (6)Li(3+) ions has been performed. The double differential cross sections for secondary electron production were calculated using the continuous distorted wave-eikonal initial state method (CDW-EIS). For the secondary electrons that are generated, the radial dose distribution for the analytical case is based on the generalized Gaussian pencil-beam method and the central axis depth-dose distributions are calculated using the Monte Carlo code PENELOPE. In the Monte Carlo case, the PENELOPE code was used to calculate the whole radial dose profile based on CDW data. The present pencil-beam and Monte Carlo calculations agree well at all radii. A radial dose profile that is shallower at small radii and steeper at large radii than the conventional 1/r(2) is clearly seen with both the Monte Carlo and pencil-beam methods. As expected, since the projectile velocities are the same, the dose profiles of Bragg-peak ions of 0.5 MeV (1)H(+), 2 MeV (4)He(2+) and 3 MeV (6)Li(3+) are almost the same, with about 30% more delta electrons in the sub keV range from (4)He(2+)and (6)Li(3+) compared to (1)H(+). A similar behavior is also seen for 1 MeV (1)H(+), 4 MeV (4)He(2+) and 6 MeV (6)Li(3+), all classically expected to have the same secondary electron cross sections. The results are promising and indicate a fast and accurate way of calculating the mean radial dose profile.     

Estimation and correction of Cerenkov-light on luminescence image of water for carbon-ion therapy dosimetry

PurposeThe luminescence images of water during the irradiation of carbon-ions provide useful information such as the ranges and the widths of carbon-ion beams. However, measured luminescence images show higher intensities in shallow depths and wider lateral profiles than those of the dose distributions. These differences prevent the luminescence imaging of water from being applied to a quality assurance for carbon-ion therapy. We assumed that the differences were due to the contaminations of Cerenkov-light from the secondary electrons of carbon-ions as well as the prompt gamma photons in the measured image. In this study, we applied a correction method to a luminescence image of water during the irradiation of carbon-ion beams.MethodsWe estimated the distribution of the Cerenkov-light in water during the irradiation of carbon-ions by Monte Carlo simulation and subtracted the simulated Cerenkov-light from the depth and lateral profiles of the measured luminescence image for 241.5 MeV/u-carbon-ions.ResultsWith these corrections, we successfully obtained depth and lateral profiles whose distributions are almost identical to the dose distributions of carbon-ions. The high intensities in the shallow depth areas decreased and the Bragg peak intensity increased. The beam widths of the measured images approached those of the ionization chamber.ConclusionsThese results indicate that the luminescence imaging of water with our proposed correction has potential to be used for dose distribution measurements for carbon-ion therapy dosimetry.     

Calculation of the proximity function of electrons

A new semianalytical method to calculate the proximity function for electrons is proposed. An integral equation for the proximity function that can be solved by using information on the spatial dose distributions is obtained. The proximity function for electrons in the energy range from 10 eV to 10 keV is calculated by solving the equation numerically, using a set of electron collision cross sections for water vapor. The results are in good agreement with those obtained using the Monte Carlo method. The proposed method can be used for electrons of high energies much more efficiently than the Monte Carlo method.     

Monte Carlo calculations of energy deposition distributions of electrons below 20 keV in protein

The distributions of energy depositions of electrons in semi-infinite bulk protein and the radial dose distributions of point-isotropic mono-energetic electron sources [i.e., the so-called dose point kernel (DPK)] in protein have been systematically calculated in the energy range below 20 keV, based on Monte Carlo methods. The ranges of electrons have been evaluated by extrapolating two calculated distributions, respectively, and the evaluated ranges of electrons are compared with the electron mean path length in protein which has been calculated by using electron inelastic cross sections described in this work in the continuous-slowing-down approximation. It has been found that for a given energy, the electron mean path length is smaller than the electron range evaluated from DPK, but it is large compared to the electron range obtained from the energy deposition distributions of electrons in semi-infinite bulk protein. The energy dependences of the extrapolated electron ranges based on the two investigated distributions are given, respectively, in a power-law form. In addition, the DPK in protein has also been compared with that in liquid water. An evident difference between the two DPKs is observed. The calculations presented in this work may be useful in studies of radiation effects on proteins.     

Energy loss of hydrogen- and helium-ion beams in DNA: calculations based on a realistic energy-loss function of the target

We have calculated the electronic energy loss of proton and α-particle beams in dry DNA using the dielectric formalism. The electronic response of DNA is described by the MELF-GOS model, in which the outer electron excitations of the target are accounted for by a linear combination of Mermin-type energy-loss functions that accurately matches the available experimental data for DNA obtained from optical measurements, whereas the inner-shell electron excitations are modeled by the generalized oscillator strengths of the constituent atoms. Using this procedure we have calculated the stopping power and the energy-loss straggling of DNA for hydrogen- and helium-ion beams at incident energies ranging from 10 keV/nucleon to 10 MeV/nucleon. The mean excitation energy of dry DNA is found to be I = 81.5 eV. Our present results are compared with available calculations for liquid water showing noticeable differences between these important biological materials. We have also evaluated the electron excitation probability of DNA as a function of the transferred energy by the swift projectile as well as the average energy of the target electronic excitations as a function of the projectile energy. Our results show that projectiles with energy ?100 keV/nucleon (i.e., around the stopping-power maximum) are more suitable for producing low-energy secondary electrons in DNA, which could be very effective for the biological damage of malignant cells.     

The application of track calculations to radiobiology. II. Calculations of microdosimetric quantities

In this second paper of a series, Monte Carlo-simulated proton tracks in water vapor are analyzed to yield a range of quantities that are of radiobiological interest. These include proximity functions of energy deposition, lineal energy distributions in micrometer and nanometer site sizes, and radial energy distributions. Many of these quantities cannot be measured with current experimental techniques. Some results are compared with those from analytic calculations. Also the effect on such quantities of the uncertainties in cross-sectional data used in the original Monte Carlo calculations is assessed, as is the effect of including nonionizing energy-loss events for analysis in the calculation.     

A semi-analytical model for calculating the penetration depth of a high energy electron beam in a water phantom with a magnetic field

PurposeAs an electron beam is incident on a uniform water phantom in the presence of a lateral magnetic field, the depth-dose distribution of the electron beam changes significantly and forms the well-known ‘Bragg peak’, with a depth-dose distribution similar to that of heavy ions. This phenomenon has pioneered a new field in the clinical application of electron beams. For such clinical applications, evaluating the penetration depth of electron beams quickly and accurately is the critical problem.MethodsThis paper describes a model for calculating the penetration depth of an electron beam rapidly and correctly in a water phantom under the influence of a magnetic field. The model was used to calculate the penetration depths under different conditions: the energies of electron beams of 6, 8, 12 and 15 MeV and the magnetic induction intensities of 0.75, 1.0, 1.5, 2.0 and 3.0 T. In addition, the calculation results were compared with the results of a Monte Carlo simulation.ResultsThe comparison results indicate that the difference between the two calculation methods was less than 0.5 cm. Moreover, the computing time of the calculation model was less than a second.ConclusionsThe semi-analytical model proposed in the present study enables the penetration depth of the electron beam in the presence of a magnetic field to be obtained with a computational efficiency higher than that of the Monte Carlo approach; thus, the proposed model has high potential for application.     

Monte Carlo simulation and measurement of radiation leakage from applicators used in external electron radiotherapy

External electron radiotherapy is performed using a cone or applicator to collimate the beam. However, because of a trade-off between collimation and scattering/bremsstrahlung X-ray production, applicators generate a small amount of secondary radiation (leakage). We investigate the peripheral dose outside the radiation field of a Varian-type applicator. The dose and fluence outside the radiation field were analyzed in a detailed Monte Carlo simulation. The differences between the calculation results and data measured in a water phantom in an ionization chamber were less than ±1% in regions more than 3 mm below the surface of the phantom and at the depth of dose maximum. The calculated fluence was analyzed inside and outside the radiation field on a plane just above the water phantom surface. Changing the electron energy affected the off-axis fluence distribution outside the radiation field; however, the size of the applicator had little effect on this distribution. For each energy, the distributions outside the radiation field were similar to the dose distribution at shallow depths in the water phantom. The effect of secondary electrons generation by photon transmission through the alloy making up the lowest scraper was largest in the region from the field edge to directly below the cutout and at higher beam energies. The results of the Monte Carlo simulation confirm that the peripheral dose outside the field is significantly affected by radiation scattered or transmitted from the applicator, and the effect increases with the electron energy.     

The determination of a dose deposited in reference medium due to (p,n) reaction occurring during proton therapy

AimThe aim of the investigation was to determine the undesirable dose coming from neutrons produced in reactions (p,n) in irradiated tissues represented by water.BackgroundProduction of neutrons in the system of beam collimators and in irradiated tissues is the undesirable phenomenon related to the application of protons in radiotherapy. It makes that proton beams are contaminated by neutrons and patients receive the undesirable neutron dose.Materials and methodsThe investigation was based on the Monte Carlo simulations (GEANT4 code). The calculations were performed for five energies of protons: 50 MeV, 55 MeV, 60 MeV, 65 MeV and 75 MeV. The neutron doses were calculated on the basis of the neutron fluence and neutron energy spectra derived from simulations and by means of the neutron fluence–dose conversion coefficients taken from the ICRP dosimetry protocol no. 74 for the antero-posterior irradiation geometry.ResultsThe obtained neutron doses are much less than the proton ones. They do not exceed 0.1%, 0.4%, 0.5%, 0.6% and 0.7% of the total dose at a given depth for the primary protons with energy of 50 MeV, 55 MeV, 60 MeV, 65 MeV and 70 MeV, respectively.ConclusionsThe neutron production takes place mainly along the central axis of the beam. The maximum neutron dose appears at about a half of the depth of the maximum proton dose (Bragg peak), i.e. in the volume of a healthy tissue. The doses of neutrons produced in the irradiated medium (water) are about two orders of magnitude less than the proton doses for the considered range of energy of protons.     

Monte Carlo simulation of the spatial distribution of energy deposition for an electron microbeam

Dosimetry calculations characterizing the spatial variation of the energy deposited by the slowing and stopping of energetic electrons are reported and compared with experimental measurements from an electron microbeam facility. The computations involve event-by-event, detailed-histories Monte Carlo simulations of low-energy electrons interacting in water vapor. Simulations of electron tracks with starting energies from 30 to 80 keV are used to determine energy deposition distributions in thin cylindrical rings as a function of penetration and radial distance from a beam source. Experimental measurements of the spatial distribution of an electron microbeam in air show general agreement with the density-scaled simulation results for water vapor at these energies, yielding increased confidence in the predictions of Monte Carlo track-structure simulations for applications of the microbeam as a single-cell irradiator.     

Integration of the M6 Cyberknife in the Moderato Monte Carlo platform and prediction of beam parameters using machine learning

PurposeThis work describes the integration of the M6 Cyberknife in the Moderato Monte Carlo platform, and introduces a machine learning method to accelerate the modelling of a linac.MethodsThe MLC-equipped M6 Cyberknife was modelled and integrated in Moderato, our in-house platform offering independent verification of radiotherapy dose distributions. The model was validated by comparing TPS dose distributions with Moderato and by film measurements. Using this model, a machine learning algorithm was trained to find electron beam parameters for other M6 devices, by simulating dose curves with varying spot size and energy. The algorithm was optimized using cross-validation and tested with measurements from other institutions equipped with a M6 Cyberknife.ResultsOptimal agreement in the Monte Carlo model was reached for a monoenergetic electron beam of 6.75 MeV with Gaussian spatial distribution of 2.4 mm FWHM. Clinical plan dose distributions from Moderato agreed within 2% with the TPS, and film measurements confirmed the accuracy of the model. Cross-validation of the prediction algorithm produced mean absolute errors of 0.1 MeV and 0.3 mm for beam energy and spot size respectively. Prediction-based simulated dose curves for other centres agreed within 3% with measurements, except for one device where differences up to 6% were detected.ConclusionsThe M6 Cyberknife was integrated in Moderato and validated through dose re-calculations and film measurements. The prediction algorithm was successfully applied to obtain electron beam parameters for other M6 devices. This method would prove useful to speed up modelling of new machines in Monte Carlo systems.     

Influence of energy straggling on the shape of neutron-produced single event spectra

Summary The influence of energy straggling on the shape of single event spectra produced by neutrons in volumes equivalent to very small spherical biological systems was investigated by simulation of the interaction processes with a Monte Carlo calculation.The results show that the effect of energy straggling already becomes noticeable for fast neutrons of 6 MeV at equivalent sphere diameters of 1.0 m and increases in importance with decreasing volume size.     

Towards MR-guided electron therapy: Measurement and simulation of clinical electron beams in magnetic fields

PurposeIn the current era of MRI-linac radiotherapy, dose optimization with arbitrary dose distributions is a reality. For the first time, we present new and targeted experiments and modeling to aid in evaluating the potential dose improvements offered with an electron beam mode during MRI-linac radiotherapy.MethodsSmall collimated (1 cm diameter and 1.5 × 1.5 cm² square) electron beams (6, 12 and 20 MeV) from a clinical linear accelerator (Varian Clinac 2100C) are incident perpendicular and parallel to the strong and localized magnetic fields (0–0.7 T) generated by a permanent magnet device. Gafchromic EBT3 film is placed inside a slab phantom to measure two-dimensional dose distributions. A benchmarked and comprehensive Monte Carlo model (Geant4) is established to directly compare with experiments.ResultsWith perpendicular fields a 5% narrowing of the beam FWHM and a 10 mm reduction in the 15% isodose penetration is seen for the 20 MeV beam. In the inline setup the penumbral width is reduced by up to 20%, and a local central dose enhancement of 100% is observed. Monte Carlo simulations are in agreement with the measured dose distributions (2% or 2 mm).ConclusionA new range of experiments have been performed to offer insight into how an electron beam mode could offer additional choices in MRI-linac radiotherapy. The work extends on historic studies to bring a successful unified experimental and Monte Carlo modeling approach for studying small field electron beam dosimetry inside magnetic fields. The results suggest further work, particularly on the inline magnetic field scenario.     

Low-energy electron penetration range in liquid water

Monte Carlo simulations of electron tracks in liquid water are performed to calculate the energy dependence of the electron penetration range at initial electron energies between 0.2 eV and 150 keV, including the subexcitation electron region (<7.3 eV). Our calculated electron penetration distances are compared with available experimental data and earlier calculations as well as with the results of simulations using newly reported amorphous ice electron scattering cross sections in the range approximately 1-100 eV.     

Analytical theory for the fluence,planar fluence,energy fluence,planar energy fluence and absorbed dose of primary particles and their fragments in broad therapeutic light ion beams

The purpose of the present work is to develop analytical expressions for the depth variation of the fluence, planar fluence, the energy fluence, planar energy fluence, the mean energy and absorbed dose of primary ions and their associated fragments in tissue-like media with ranges of clinical interest. The analytical expressions of the primary ions and associated fragments take into account nuclear interactions, energy losses, range straggling and multiple scattering. The analytical models of the radiation field quantities were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT₊. The results show that the shape of the depth absorbed dose distribution of the primary particles is characterized by an increasingly steep exponential fluence decrease with depth as the charge and atomic weight increase. This is accompanied by a compensating increased energy loss towards the Bragg peak as the charge of the ion increases. These largely compensating mechanisms are the main reason that the depth absorbed dose curve of all light ions is surprisingly similar. In addition, a rather uniform dose in the plateau region is obtained since the increasing fragment production almost precisely compensates the loss of primaries. The dominating light fragments such as protons and alpha particles are characterized by longer ranges than the primaries and their depth dose curves to some extent coincide well with the depth fluence curves due to a rather slow variation of mean stopping powers. In contrast, the heavier fragments are characterized by the build up of a slowing down spectrum similar to that of the primaries but with initially slightly shorter or longer ranges depending on their mass to atomic number ratio. The presented analytical theory for the light ion penetration in matter agree quite well with the MC and experimental data and may be very useful for fast analytical calculations of quantities like mean energy, fluence, energy fluence, absorbed dose, and LET.     

Model for radial dependence of frequency distributions for energy imparted in nanometer volumes from HZE particles

This paper develops a deterministic model of frequency distributions for energy imparted (total energy deposition) in small volumes similar to DNA molecules from high-energy ions of interest for space radiation protection and cancer therapy. Frequency distributions for energy imparted are useful for considering radiation quality and for modeling biological damage produced by ionizing radiation. For high-energy ions, secondary electron (delta-ray) tracks originating from a primary ion track make dominant contributions to energy deposition events in small volumes. Our method uses the distribution of electrons produced about an ion's path and incorporates results from Monte Carlo simulation of electron tracks to predict frequency distributions for ions, including their dependence on radial distance. The contribution from primary ion events is treated using an impact parameter formalism of spatially restricted linear energy transfer (LET) and energy-transfer straggling. We validate our model by comparing it directly to results from Monte Carlo simulations for proton and alpha-particle tracks. We show for the first time frequency distributions of energy imparted in DNA structures by several high-energy ions such as cosmic-ray iron ions. Our comparison with results from Monte Carlo simulations at low energies indicates the accuracy of the method.     

Analysis of low-energy electron track structure in liquid water

An implementation is presented of interaction cross sections for non-relativistic electron track structure simulations. The model, incorporating liquid-phase cross sections for inelastic interactions and improved algorithms for elastic scattering, is applied to Monte Carlo simulation of the track structure of low-energy electrons. Benchmark distributions and mean values are presented for several measures of penetration distances that characterize the general physical extent of the track structure. The results indicate that, except for the last approximately 500 eV of energy loss, electron tracks have a quasi-linear character; this suggests that a major part of an electron track may be reasonably described by a lineal-energy-like characterization.