On pathlength and energy straggling of megavoltage electrons slowing down

Purposeto elucidate the effects of multiple scattering and energy-loss straggling on electron beams slowing down in materials.MethodsEGSnrc Monte Carlo simulations are done using a purpose-written user-code.ResultsPlots are presented of the primary electron’s energy as a function of pathlength for 20 MeV electrons incident on water and tantalum as are plots of the overall distribution of pathlengths as the 20 MeV electrons slow down under various Monte Carlo scenarios in water and tantalum. The distributions range from 1 % to 135 % of the CSDA range in water and from 1 % to 186 % in tantalum. The effects of energy-loss straggling on energy spectra at depth and electron fluence at depth are also presented.ConclusionsThe role of energy-loss straggling and multiple scattering are shown to play a significant role in the range straggling which determines the dose fall-off region in electron beam dose vs depth curves and a significant role in the energy distributions as a function of depth.     

Measurement of the restricted dose mean LET outside the primary beam of a 60Co radiotherapy unit

A recently developed method for the direct measurement of the restricted dose mean LET (cutoff energy = 500 eV) of an unspecified photon or electron radiation field with the high-pressure ionization chamber has been utilized to investigate the variation of this radiobiologically important parameter outside the primary beam of a clinical 60Co unit. A small high-pressure tissue-equivalent ionization chamber was used, and its characteristics and experimental considerations for the present investigation are reported. Measurement of the restricted dose mean LET at the examined points outside the primary 60Co beam showed an increase of 50% with respect to the restricted dose mean LET of the uncollimated 60Co beam. No significant variation was noted with off-central axis distance, field size, wedge filter, or depth below Perspex slabs. Dose rates at the points of measurement outside the primary 60Co beam were 1-5% of the dose rate in the primary beam.     

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.     

Spatial distributions of inelastic events produced by electrons in gaseous and liquid water

The spatial distributions of ionizations and other inelastic events in charged-particle tracks are important quantities that influence the final outcome of radiation interaction. Calculations of such distributions are presented for the tracks of electrons in the energy range 100 eV to 10 keV in liquid water and water vapor, and the results are compared. The distributions include the frequency of nearest-neighbor distances for all inelastic events, the mean nearest-neighbor distances for ionizations and for all inelastic events as a function of electron energy, the frequency of distances between all ionizations and all inelastic events, and the farthest distances between all inelastic events in electron tracks. The physical differences between liquid water and water vapor are discussed in terms of the respective inverse mean free paths, the collision spectra, and the nonlocalization of energy losses that are likely to occur in the liquid.     

Concentration modulated skin marker for radiotherapy treatment planning process

Background and purposeFor conformal radiotherapy, it is feasible to achieve high accuracy in contouring the outline of the target volume in treatment planning process. In contouring process, target volume is occasionally defined by means of either surgical clips or skin marker during patient anatomical data acquisition. Treatment planning systems are predicting invalid radiation dose distributions by using surgical clips and skin marker within the patient. Purpose of this study is the production of new skin marker which affects less dose distributions of electron beam.Materials and methodsThe influences of lead and commercial markers on dose calculations in a 3D treatment planning systems were investigated in terms of electron beam energy and dose profile depth. Dose deviation with commercial marker was observed to smaller than lead marker. However this dose deviation was still at big value. In order to reduce of this value, barium sulfate suspension and ultrasound gel were mixed with different volumetric ratio. With the purpose of acception the most suitable marker for radiation therapy, obtained new suspensions were investigated in terms of visibility and dose deviation.ResultsB:G/1:10 marker was determined to cause optimum visibility and the lowest dose deviation on dose calculations in terms of electron beam energy and dose profile depth.ConclusionsAppropriate marker, mixture of substances such as barium sulfate suspension and ultrasound gel can be produced. This marker is both ease of usage and practical and economical. Each clinic can prepare marker which is peculiar to suspension with different concentration of substance for specific visibility. But, it should be taken into account resultant dose deviation to beam calculation depending on barium sulfate concentration.     

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.     

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.     

Parameterization of electron beam output factor

Electron beam dose distribution is dependent on the beam energy and complicated trajectory of particles. Recent treatment planning systems using Monte Carlo calculation algorithm provide accurate dose calculation. However, double check of monitor units (MUs) based on an independent algorithm is still required. In this study, we have demonstrated single equation that reproduces the measured relative output factor (ROF) that can be used for MU calculation for electron radiotherapy. Electron beams generated by an iX (Varian Medical Systems) and a PRIMUS (Siemens) accelerator were investigated. For various energies of electron beams, the ROF at respective d_max were measured using diode detector in a water phantom at SSD of 100 cm. Curve fitting was performed with an exponential generalized equation ROF = α(β – e^−γR) including three variables (α, β, γ) as a function of field radius and electron energy. The correlation coefficients between the ROF measured and that calculated by the equation were greater than 0.998. For ROF of Varian electron beams, the average values of all fitting formulas were applied for two of the constants; α and β. The parameter γ showed good agreement with the quadratic approximation as a function of mean energy at surface (E₀). The differences between measured and calculated ROF values were within ±3% for beams with cutout radius of ≥1.5 cm for electron beams with energies from 6 MeV to 15 MeV. The proposed formula will be helpful for double-check of MUs, as it requires minimal efforts for MU calculation.     

Establishing the impact of temporary tissue expanders on electron and photon beam dose distributions

PurposeThis study investigates the effects of temporary tissue expanders (TTEs) on the dose distributions in breast cancer radiotherapy treatments under a variety of conditions.MethodsUsing EBT2 radiochromic film, both electron and photon beam dose distribution measurements were made for different phantoms, and beam geometries. This was done to establish a more comprehensive understanding of the implant's perturbation effects under a wider variety of conditions.ResultsThe magnetic disk present in a tissue expander causes a dose reduction of approximately 20% in a photon tangent treatment and 56% in electron boost fields immediately downstream of the implant. The effects of the silicon elastomer are also much more apparent in an electron beam than a photon beam.ConclusionsEvidently, each component of the TTE attenuates the radiation beam to different degrees. This study has demonstrated that the accuracy of photon and electron treatments of post-mastectomy patients is influenced by the presence of a tissue expander for various beam orientations. The impact of TTEs on dose distributions establishes the importance of an accurately modelled high-density implant in the treatment planning system for post-mastectomy patients.     

Fundamental parameters of a relativistic runaway electron avalanche in air

A relativistic runaway electron avalanche in air is simulated numerically by the Monte Carlo method with allowance for a large number of elementary processes involving electrons, positrons, and photons. The characteristic time scale of the avalanche amplification is calculated as a function of the overvoltage δ relative to the minimum value of the drag force between the electrons and the atomic particles of the medium. The dynamics of the formation of the electron energy distribution is investigated. The steady-state mean electron energy depends weakly on δ. Over a wide range of δ values, there exists a universal electron energy distribution, which is essentially independent of δ. The angular distributions of electrons integrated over energies, as well as the angular distributions for different energy groups, are calculated. Analytic approximations for the energy and angular distributions are obtained.     

A beam model for focused proton pencil beams

IntroductionWe present a beam model for Monte Carlo simulations of the IBA pencil beam scanning dedicated nozzle installed at the Skandion Clinic. Within the nozzle, apart from entrance and exit windows and the two ion chambers, the beam traverses vacuum, allowing for a beam that is convergent downstream of the nozzle exit.Materials and methodsWe model the angular, spatial and energy distributions of the beam phase space at the nozzle exit with single Gaussians, controlled by seven energy dependent parameters. The parameters were determined from measured profiles and depth dose distributions. Verification of the beam model was done by comparing measured and GATE acquired relative dose distributions, using plan specific log files from the machine to specify beam spot positions and energy.ResultsGATE-based simulations with the acquired beam model could accurately reproduce the measured data. The gamma index analysis comparing simulated and measured dose distributions resulted in >95% global gamma index pass rates (3%/2 mm) for all depths.ConclusionThe developed beam model was found to be sufficiently accurate for use with GATE e.g. for applications in quality assurance (QA) or patient motion studies with the IBA pencil beam scanning dedicated nozzles.     

Low-LET microbeam investigation of the track-end dependence of electron-induced damage in normal human diploid fibroblasts

Using a pulsed electron beam, we investigated the dependence of micronucleus formation on the incident electron energy in AG01522 human diploid fibroblasts after nontargeted irradiations at 25 and 80 keV. Examining the dose response, we found that 25 keV electrons are more effective than 80 keV electrons at producing biological damage for a given dose. Our results demonstrating the induction of micronuclei as a function of incident electron energy offer direct support for the hypothesis that the electron track end is responsible for the biological damage occurring in the cell.     

Multiple-source models for electron beams of a medical linear accelerator using BEAMDP computer code

AimThe aim of this work was to develop multiple-source models for electron beams of the NEPTUN 10PC medical linear accelerator using the BEAMDP computer code.BackgroundOne of the most accurate techniques of radiotherapy dose calculation is the Monte Carlo (MC) simulation of radiation transport, which requires detailed information of the beam in the form of a phase-space file. The computing time required to simulate the beam data and obtain phase-space files from a clinical accelerator is significant. Calculation of dose distributions using multiple-source models is an alternative method to phase-space data as direct input to the dose calculation system.Materials and methodsMonte Carlo simulation of accelerator head was done in which a record was kept of the particle phase-space regarding the details of the particle history. Multiple-source models were built from the phase-space files of Monte Carlo simulations. These simplified beam models were used to generate Monte Carlo dose calculations and to compare those calculations with phase-space data for electron beams.ResultsComparison of the measured and calculated dose distributions using the phase-space files and multiple-source models for three electron beam energies showed that the measured and calculated values match well each other throughout the curves.ConclusionIt was found that dose distributions calculated using both the multiple-source models and the phase-space data agree within 1.3%, demonstrating that the models can be used for dosimetry research purposes and dose calculations in radiotherapy.     

Frequency-dependent variation in the two-dimensional beam pattern of an echolocating dolphin

Recent recordings of dolphin echolocation using a dense array of hydrophones suggest that the echolocation beam is dynamic and can at times consist of a single dominant peak, while at other times it consists of forward projected primary and secondary peaks with similar energy, partially overlapping in space and frequency bandwidth. The spatial separation of the peaks provides an area in front of the dolphin, where the spectral magnitude slopes drop off quickly for certain frequency bands. This region is potentially used to optimize prey localization by directing the maximum pressure slope of the echolocation beam at the target, rather than the maximum pressure peak. The dolphin was able to steer the beam horizontally to a greater extent than previously described. The complex and dynamic sound field generated by the echolocating dolphin may be due to the use of two sets of phonic lips as sound sources, or an unknown complexity in the sound propagation paths or acoustic properties of the forehead tissues of the dolphin.     

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.     

Energy characteristics of beam-plasma interaction in a closed volume

Energy exchange between an electron beam and plasma during a beam-plasma discharge in a closed cavity excited by the electron beam is analyzed using computer simulations by the KARAT code. A method allowing one to analyze the beam-plasma interaction in the quasi-steady stage of the discharge is proposed. Qualitative characteristics of energy exchange (such as beam energy losses and the energy distributions of beam electrons and plasma particles leaving the discharge) both during spontaneous discharge excitation and in the presence of initial beam modulation by regular or noiselike signals are determined. The results obtained enable one to estimate the energy characteristics of a plasma processing reactor based on a beam-plasma discharge.     

Clinical application of a gantry-attachable plastic scintillating plate dosimetry system in pencil beam scanning proton therapy beam monitoring

PurposeThe entrance beam fluence of therapeutic proton scanning beams can be monitored using a gantry-attachable plastic scintillating plate (GAPSP). This study evaluated the clinical application of the GAPSP using a method that measures intensity modulated proton therapy (IMPT) beams for patient treatment.MethodsIMPT beams for the treatment of nine patients, at sites that included the spine, head and neck, pelvis, and lung, were measured using the GAPSP, composed of an EJ-212 plastic scintillator and a CMOS camera. All energy layers distinguished by the GAPSP were accumulated to determine the dose distribution of the treatment field. The evaluated fields were compared with reference dose maps verified by quality assurance.ResultsComparison of dose distributions of evaluation treatment fields with reference dose distributions showed that the 3%/1 mm average gamma passing rate was 96.4%, independent of the treatment site, energy range and field size. When dose distributions were evaluated using the same criteria for each energy layer, the average gamma passing rate was 91.7%.ConclusionsThe GAPSP is a suitable, low-cost method for monitoring pencil beam scanning proton therapy, especially for non-spot scanning or additional collimation. The GAPSP can also estimate the treatment beam by the energy layer, a feature not common to other proton dosimetry tools.     

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.     

Condensed-history Monte Carlo simulation of the dosimetric distribution of electron microbeam

To evaluate the dose distributions of an electron microbeam and to help optimization of its design, the condensed-history (CH) Monte Carlo simulation algorithm implemented in the Geant4 toolkit was selected as an alternative to the conventionally used analog algorithm. Compared to the analog algorithm, the CH algorithm is cheaper and less limited by the lack of cross-sections. And, with a properly chosen production cut for secondaries, its accuracy for the problems of microdosimetry is satisfactory. In this work, calculations of the single-event (imparted energy ɛ) size distribution f ₁(ɛ) is described, for compartments in the Orlando electron micro beam. The results agree well with those obtained by use of the analog algorithm and reported in the literature. It is shown that substituting tissue with water in HeLa cells, and replacing Mylar with water of the same mass stopping power in the substrate, makes little difference. Additionally, the neighbor-to-target ratio of average event size R _NT has been calculated as a function of the incident energy of the electrons. Comparison with analog results reported in the literature suggests that the average event size in neighbors, and hence the neighbor-to-target ratio, is sensitive to the selection of the energy threshold. Finally, the effect of finite beam radius on the event size distribution and the neighbor-to-target ratio has also been studied. All results presented suggest the condensed-history technique to provide an efficient and valuable alternative tool in the design of electron microbeams.