Photon dose calculation based on electron multiple-scattering theory: primary dose deposition kernels.

The transport of the secondary electrons resulting from high-energy photon interactions is essential to energy redistribution and deposition. In order to develop an accurate dose-calculation algorithm for high-energy photons, which can predict the dose distribution in inhomogeneous media and at the beam edges, we have investigated the feasibility of applying electron transport theory [Jette, Med. Phys. 15, 123 (1988)] to photon dose calculation. In particular, the transport of and energy deposition by Compton electron and electrons and positrons resulting from pair production were studied. The primary photons are treated as the source of the secondary electrons and positrons, which are transported through the irradiated medium using Gaussian multiple-scattering theory [Jette, Med. Phys. 15, 123 (1988)]. The initial angular and kinetic energy distribution(s) of the secondary electrons (and positrons) emanating from the photon interactions are incorporated into the transport. Due to different mechanisms of creation and cross-section functions, the transport of and the energy deposition by the electrons released in these two processes are studied and modeled separately based on first principles. In this article, we focus on determining the dose distribution for an individual interaction site. We define the Compton dose deposition kernel (CDK) or the pair-production dose deposition kernel (PDK) as the dose distribution relative to the point of interaction, per unit interaction density, for a monoenergetic photon beam in an infinite homogeneous medium of unit density. The validity of this analytic modeling of dose deposition was evaluated through EGS4 Monte Carlo simulation. Quantitative agreement between these two calculations of the dose distribution and the average energy deposited per interaction was achieved. Our results demonstrate the applicability of the electron dose-calculation method to photon dose calculation.     

Modelling of electron contamination in clinical photon beams for Monte Carlo dose calculation

The purpose of this work is to model electron contamination in clinical photon beams and to commission the source model using measured data for Monte Carlo treatment planning. In this work, a planar source is used to represent the contaminant electrons at a plane above the upper jaws. The source size depends on the dimensions of the field size at the isocentre. The energy spectra of the contaminant electrons are predetermined using Monte Carlo simulations for photon beams from different clinical accelerators. A 'random creep' method is employed to derive the weight of the electron contamination source by matching Monte Carlo calculated monoenergetic photon and electron percent depth-dose (PDD) curves with measured PDD curves. We have integrated this electron contamination source into a previously developed multiple source model and validated the model for photon beams from Siemens PRIMUS accelerators. The EGS4 based Monte Carlo user code BEAM and MCSIM were used for linac head sinulation and dose calculation. The Monte Carlo calculated dose distributions were compared with measured data. Our results showed good agreement (less than 2% or 2 mm) for 6, 10 and 18 MV photon beams.     

Monte Carlo study of correction factors for Spencer-Attix cavity theory at photon energies at or above 100 keV

To develop a primary standard for 192Ir sources, the basic science on which this standard is based, i.e., Spencer-Attix cavity theory, must be established. In the present study Monte Carlo techniques are used to investigate the accuracy of this cavity theory for photons in the energy range from 20 to 1300 keV, since it is usually not applied at energies below that of 137Cs. Ma and Nahum [Phys. Med. Biol. 36, 413-428 (1991)] found that in low-energy photon beams the contribution from electrons caused by photons interacting in the cavity is substantial. For the average energy of the 192Ir spectrum they found a departure from Bragg-Gray conditions of up to 3% caused by photon interactions in the cavity. When Monte Carlo is used to calculate the response of a graphite ion chamber to an encapsulated 192Ir source it is found that it differs by less than 0.3% from the value predicted by Spencer-Attix cavity theory. Based on these Monte Carlo calculations, for cavities in graphite it is concluded that the Spencer-Attix cavity theory with delta = 10 keV is applicable within 0.5% for photon energies at 300 keV or above despite the breakdown of the assumption that there is no interaction of photons within the cavity. This means that it is possible to use a graphite ion chamber and Spencer-Attix cavity theory to calibrate an 192Ir source. It is also found that the use of delta related to the mean chord length instead of delta = 10 keV improves the agreement with Spencer-Attix cavity theory at 60Co from 0.2% to within 0.1% of unity. This is at the level of accuracy of which the Monte Carlo code EGSnrc calculates ion chamber responses. In addition, it is shown that the effects of other materials, e.g., insulators and holders, have a substantial effect on the ion chamber response and should be included in the correction factors for a primary standard of air kerma.     

EGS4 Monte Carlo determination of the beta dose kernel in water

The EGS4 Monte Carlo code has been used to simulate the emission and energy deposition in H2O about point sources of monoenergetic electrons and radionuclides of potential use in radioimmunotherapy. The radiations studied were 0.05, 0.1, 0.5, 1.0, 2.0, and 3.0 MeV monoenergetic electrons and 32P, 67Cu, 90Y, 105Rh, 131I, 153Sm, 186Re, and 188Re beta particles and conversion and Auger electrons. Ten batches of 10,000 electrons (or 10,000 radionuclide decays) each were started isotropically at a point in an infinite homogeneous H2O phantom. The parameter-reduced electron-step transport algorithm (PRESTA) version of the EGS4 Monte Carlo code was used to follow these and their progeny, scoring the energy deposited in thin spherical shells. The scaled dose kernels are calculated and compared to kernels available in the literature. These previously published kernels either completely ignore secondary electrons or are based on a Monte Carlo code which improperly sampled the Landau energy straggling distribution.     

Interface effects in the Monte Carlo simulation of electron tracks

An analog of Fano's theorem for ionization in cavities is shown to hold for the stepwise representation of electron paths used in Monte Carlo computer models of electron transport. This brings to light an error in the distribution of electron paths and hence energy deposition which is induced by interrupting steps which cross the interface between media of different densities. The magnitude of the error depends on the shape of the cavity and its size relative to the electron path length in the cavity gas. In a typical calculation of a cylindrical chamber exposed to 60Co radiation, if the electron step size is taken as 10% of the remaining path, then a 3% energy deficit in the cavity results. An algorithm for crossing an interface is described which does not produce this error.     

Monte Carlo simulation on a gold nanoparticle irradiated by electron beams

This study investigated the secondary electron production from a gold nanoparticle (GNP) irradiated by monoenergetic electron beams using Monte Carlo (MC) simulation. Spherical GNPs with diameters of 2, 50 and 100 nm in water were irradiated by monoenergetic electron beams with energies equal to 50 keV, 250 keV, 1 MeV and 4 MeV. MC simulations were performed using the Geant4 toolkit to determine the energy of the secondary electrons emitted from the GNPs. The mean effective range and deflection angle of the secondary electrons were tracked. Energy depositions inside and outside the nanoparticles due to the secondary electrons were also calculated. For comparisons, simulations were repeated by replacing the GNPs with water. Our results show that the mean effective range of secondary electrons increased with an increase of the GNP size and electron beam energy. For the electron beam energy and GNP size used in this study, the mean effective range was 0.5-15 μm outside the nanoparticle, which is approximately within the dimension of a living cell. The mean deflection angles varied from 78 to 83 degrees as per our MC results. The proportion of energy deposition inside the GNP versus that outside increased with the GNP size. This is different from the results obtained from a previous study using photon beams. The secondary electron energy deposition ratio (energy deposition for GNP/energy deposition for water) was found to be highest for the smallest GNP of 2 nm diameter in this study. For the energy deposited by the secondary electron, we concluded that the addition of GNPs can increase the secondary electron energy deposition in water, though most of the energy was self-absorbed by the large nanoparticles (50 and 100 nm). In addition, an electron source in the presence of GNPs does not seem to be better than photons as the yield of secondary electrons per unit mass of gold is less than water.     

The energy-dependent electron loss model: backscattering and application to heterogeneous slab media

Electron backscattering has been incorporated into the energy-dependent electron loss (EL) model and the resulting algorithm is applied to predict dose deposition in slab heterogeneous media. This algorithm utilizes a reflection coefficient from the interface that is computed on the basis of Goudsmit-Saunderson theory and an average energy for the backscattered electrons based on Everhart's theory. Predictions of dose deposition in slab heterogeneous media are compared to the Monte Carlo based dose planning method (DPM) and a numerical discrete ordinates method (DOM). The slab media studied comprised water/Pb, water/Al, water/bone, water/bone/water, and water/lung/water, and incident electron beam energies of 10 MeV and 18 MeV. The predicted dose enhancement due to backscattering is accurate to within 3% of dose maximum even for lead as the backscattering medium. Dose discrepancies at large depths beyond the interface were as high as 5% of dose maximum and we speculate that this error may be attributed to the EL model assuming a Gaussian energy distribution for the electrons at depth. The computational cost is low compared to Monte Carlo simulations making the EL model attractive as a fast dose engine for dose optimization algorithms. The predictive power of the algorithm demonstrates that the small angle scattering restriction on the EL model can be overcome while retaining dose calculation accuracy and requiring only one free variable, chi, in the algorithm to be determined in advance of calculation.     

Comparison of Monte Carlo calculated electron slowing-down spectra generated by 60Co gamma-rays,electrons, protons and light ions

When analysing the factors affecting the relative biological effectiveness (RBE) of different radiation qualities, it is essential to consider particularly the low-energy slowing-down electrons (around 100 eV to 1 keV) since they have the potential of inflicting severe damage to the DNA. We present a modified and extended version of the Monte Carlo code PENELOPE that enables scoring of slowing-down spectra. mean local energy imparted spectra and average intra-track nearest-neighbour energy deposition distances of the secondary electrons generated by different radiation qualities, such as electrons, photons, protons and light ions in general. The resulting spectra show that the low-linear energy transfer (LET) beams, 60Co gamma-rays and electrons with initial energies of 0.1 MeV and higher, have as expected approximately the same electron slowing-down fluence per unit dose in the biologically important low-energy interval. Consistent with the general behaviour of the RBE of low-energy electrons, protons and light ions, the low-energy electron slowing-down fluence per unit dose is larger than for low-LET beams, and it increases with decreasing initial projectile energy.     

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.     

Electron spectra derived from depth dose distributions

The technique of extracting electron energy spectra from measured distributions of dose along the central axis of clinical electron beams is explored in detail. Clinical spectra measured with this simple spectroscopy tool are shown to be sufficient in accuracy and resolution for use in Monte Carlo treatment planning. A set of monoenergetic depth dose curves of appropriate energy spacing, precalculated with Monte Carlo for a simple beam model, are unfolded from the measured depth dose curve. The beam model is comprised of a point electron and photon source placed in vacuum with a source-to-surface distance of 100 cm. Systematic error introduced by this model affects the calculated depth dose curve by no more than 2%/2 mm. The component of the dose due to treatment head bremsstrahlung, subtracted prior to unfolding, is estimated from the thin-target Schiff spectrum within 0.3% of the maximum total dose (from electrons and photons) on the beam axis. Optimal unfolding parameters are chosen, based on physical principles. Unfolding is done with the public-domain code FERDO. Comparisons were made to previously published spectra measured with magnetic spectroscopy and to spectra we calculated with Monte Carlo treatment head simulation. The approach gives smooth spectra with an average resolution for the 27 beams studied of 16+/-3% of the mean peak energy. The mean peak energy of the magnetic spectrometer spectra was calculated within 2% for the AECL T20 scanning beam accelerators, 3% for the Philips SL25 scattering foil based machine. The number of low energy electrons in Monte Carlo spectra is estimated by unfolding with an accuracy of 2%, relative to the total number of electrons in the beam. Central axis depth dose curves calculated from unfolded spectra are within 0.5%/0.5 mm of measured and simulated depth dose curves, except near the practical range, where 1%/1 mm errors are evident.     

Angular correction in reconstruction of electron spectra from depth dose distributions

Techniques for reconstruction of electron spectra from the depth-dose curves used to date have ignored the angular distribution of incident electrons scattered at large angles. The approximation adopted is to employ a database of monoenergetic depth-dose curves generated for normal incidence of electrons at the surface. This approximation is acceptable for direct electrons with small angular spread. However, electrons scattered from the treatment head and collimating system may have large average angles of incidence which affects the depth-dose distribution significantly at shallow depths by increasing energy deposition close to the surface. We show that ignoring the electron incident angular distribution leads to systematic errors in the low energy region of reconstructed electron spectra. We propose a simple 1-D model to correct for these systematic errors using only electron angular distribution at the central beam axis. This model provides reconstructed spectra in excellent agreement with Monte Carlo simulation in the low energy region.     

A new approach to the determination of air kerma using primary-standard cavity ionization chambers

A consistent formalism is presented using Monte Carlo calculations to determine the reference air kerma from the measured energy deposition in a primary-standard cavity ionization chamber. A global approach avoiding the use of cavity ionization theory is discussed and its limitations shown in relation to the use of the recommended value for W. The role of charged-particle equilibrium is outlined and the consequent requirements placed on the calculations are detailed. Values for correction factors are presented for the BIPM air-kerma standard for 60Co, making use of the Monte Carlo code PENELOPE, a detailed geometrical model of the BIPM 60Co source and event-by-event electron transport. While the wall correction factor k(wall) = 1.0012(2) is somewhat lower than the existing value, the axial non-uniformity correction k(an) = 1.0027(3) is significantly higher. The use of a point source in the evaluation of k(an) is discussed. A comparison is made of the calculated dose ratio with the Bragg-Gray and Spencer-Attix stopping-power ratios, the results indicating a preference for the Bragg-Gray approach in this particular case. A change to the recommended value for W of up to 2 parts in 10(3) is discussed. The uncertainties arising from the geometrical models, the use of phase-space files, the radiation transport algorithms and the underlying radiation interaction coefficients are estimated.     

An EGSnrc investigation of cavity theory for ion chambers measuring air kerma

The EGSnrc system is used to compare the response of an aluminum-walled thimble chamber to that of a graphite-walled thimble chamber for a 60Co beam. When compared to previous experimental results, the EGSnrc values of the ratios of chamber response differ by as much as 0.7% from the experiment. However, it is shown that this difference can be more than accounted for by switching from using the graphite mean excitation energy of 78 eV used in dosimetry protocols to the value of 86.8 eV suggested by more recent stopping-power experiments. This suggests that the uncertainty analysis of Monte Carlo results must be done more carefully, by taking into account uncertainties in the underlying basic data such as the electron and photon cross sections. In comparison to Spencer-Attix cavity theory for a thick-walled ion chamber, the Monte Carlo calculated values of the chamber response differ from the expected ones by 0.15% and 0.01% for the graphite and aluminum chambers, respectively, which are comparable to previously reported values for the Spencer-Attix correction factors. EGSnrc is also used to investigate the effect on the chamber response of thin dag layers on the inside of the aluminum wall. There is good agreement between the calculated and measured changes in chamber response versus the thickness of the dag. The results are compared to the predictions of the Almond-Svensson extension of cavity theory and show that the theory does not correctly predict the chamber response in the presence of thin dag layers. This finding is in agreement with previously reported experimental results. It is demonstrated that the values of alpha, the fraction of ionizations in the gas arising from electrons generated in the dag layer, used in the theory, are not the source of the disagreement.     

The energy dependence of lithium formate EPR dosimeters for clinical electron beams

The objective of this study was to investigate the potential of using polycrystalline lithium formate for EPR (electron paramagnetic resonance) dosimetry of clinical electron beams, with the main focus on the dose-to-water energy response. Lithium formate dosimeters were irradiated using (60)Co gamma-rays and 6-20 MeV electrons in a PMMA phantom to doses in the range of 3-9 Gy. A plane-parallel ion chamber was used for water-based absolute dosimetry. In addition, the electron/photon transport was simulated using the EGSnrc Monte Carlo code. From the EPR measurements, the standard deviation of single dosimeter readings was 1.2%. The experimental energy response (the lithium formate dosimeter reading per absorbed dose to water for electrons relative to that for (60)Co gamma rays) was nearly independent of the electron energy and on average 0.99 +/- 0.03. The Monte Carlo calculated energy response was on average 0.5% higher than the experimental energy response, the difference being not significant. Simulations with water and polystyrene as irradiation media indicated that the energy response of lithium formate dosimeters was nearly independent of the phantom materials. In conclusion, lithium formate EPR dosimetry of clinical electron beams provides precise dose measurements with low dependence on the electron energy.     

A theoretical re-examination of Spencer-Attix cavity theory

The aim of radiation dosimetry is to evaluate, under specific conditions, absorbed dose in a medium of interest using a detection device. In comparison to what is meant to be evaluated, the distinctive composition of the detector causes particle fluence perturbation and shifted absorbed-dose response, both effects depending on beam quality. For electron and megavoltage photon beams, Spencer-Attix cavity theory further adapted by Nahum remains the accepted standard method used to convert absorbed dose in a wall-less detector to absorbed dose in the medium of interest. For several decades, the approach has been widely used in protocols to generate data for ionization chamber dosimetry. As a considerable effort was made towards accurate Monte Carlo methods, computation techniques are nowadays available to determine absorbed dose accurately in complex geometries, including radiation detectors. In the development of nonstandard beam protocols, direct Monte Carlo dose calculations using realistic models are being suggested and used to generate data for ionization chamber dosimetry. This indicates that for a general dosimetric context, including nonstandard beams, a more general cavity theory in agreement with what is currently being done could be adopted. Not only this could be of interest in the dosimetry standards community, but also for educational purposes. This paper re-examines Spencer-Attix theory from first principles, using a new general cavity theory rigorously derived from radiation transport equations. The approach is based on the same schematization as for Spencer-Attix's (i.e. groups of slow and fast electrons) and yields a general expression of absorbed dose for suitably implemented Monte Carlo methods. The Spencer-Attix-Nahum formulation is shown to be a special case of the presented model, outlining specific issues of the standard method. By providing an expression of absorbed dose which reflects the gold standard calculation method (i.e. Monte Carlo), the proposed theory could be adopted by the radiation dosimetry community.     

Measurement of absorbed dose with a bone-equivalent extrapolation chamber

A hybrid phantom-embedded extrapolation chamber (PEEC) made of Solid Water and bone-equivalent material was used for determining absorbed dose in a bone-equivalent phantom irradiated with clinical radiation beams (cobalt-60 gamma rays; 6 and 18 MV x rays; and 9 and 15 MeV electrons). The dose was determined with the Spencer-Attix cavity theory, using ionization gradient measurements and an indirect determination of the chamber air-mass through measurements of chamber capacitance. The collected charge was corrected for ionic recombination and diffusion in the chamber air volume following the standard two-voltage technique. Due to the hybrid chamber design, correction factors accounting for scatter deficit and electrode composition were determined and applied in the dose equation to obtain absorbed dose in bone for the equivalent homogeneous bone phantom. Correction factors for graphite electrodes were calculated with Monte Carlo techniques and the calculated results were verified through relative air cavity dose measurements for three different polarizing electrode materials: graphite, steel, and brass in conjunction with a graphite collecting electrode. Scatter deficit, due mainly to loss of lateral scatter in the hybrid chamber, reduces the dose to the air cavity in the hybrid PEEC in comparison with full bone PEEC by 0.7% to approximately 2% depending on beam quality and energy. In megavoltage photon and electron beams, graphite electrodes do not affect the dose measurement in the Solid Water PEEC but decrease the cavity dose by up to 5% in the bone-equivalent PEEC even for very thin graphite electrodes (<0.0025 cm). In conjunction with appropriate correction factors determined with Monte Carlo techniques, the uncalibrated hybrid PEEC can be used for measuring absorbed dose in bone material to within 2% for high-energy photon and electron beams.     

Electron fluence perturbation correction factors for solid state detectors irradiated in megavoltage electron beams

The perturbation correction factor gamma(p) is defined as the deviation of the absorbed dose in the medium from that predicted by the Spencer-Attix extension of the Bragg-Gray cavity theory where the medium occupies exactly the same volume as the solid state cavity and the electron fluence energy spectrum in the cavity is identical in shape, but not necessarily in magnitude, to that in the medium. The value of gamma(p) has been examined for TL detectors irradiated in megavoltage electron beams (5-20 MeV) using the EGS4 Monte Carlo code. LiF and CaF2 solid state detectors simulated were standard size discs of thickness 1 mm and diameter 3.61 mm irradiated in a water phantom with their centres at d(max) or close to it. Values of gamma(p) for LiF ranged from 0.998 +/- 0.005 to 0.994 +/- 0.005 for electron beams with initial energies of 5 and 20 MeV respectively. For CaF2 the corresponding values were 0.956 +/- 0.006 to 0.989 +/- 0.006 for the same size cavities irradiated at the same depth. EGS4 Monte Carlo simulations demonstrate that the total electron fluence (primary electrons and delta-rays) in these solid state detector materials is significantly different from that in water for the same incident electron energy and depth of irradiation. Thus the Spencer-Attix assumption that the electron fluence energy spectrum in the cavity is identical in shape to that in the medium is violated. Differences in the total electron fluence give rise to electron fluence perturbation correction factors which were up to 5% less than unity for CaF2, indicating a strong violation in this case, but were generally less than 1% for LiF. It is the density of the cavity which perturbs the electron fluence, but it is actually the atomic number differences between the medium and cavity that are responsible for the large electron fluence perturbation correction factors for detectors irradiated close to d(max) because the atomic number affects the change in stopping power with energy. When correction is made for the difference between the electron fluence spectrum in the uniform water phantom and the solid state cavity, the Spencer-Attix cavity equation predicts the dose to water within 0.3% in both clinical and monoenergetic electron beams. Harder's formulation for computing the average mass collision stopping power of water to calcium fluoride, surprisingly, requires perturbation correction factors that are closer to unity than those determined using the Spencer-Attix integrals at depths close to d(max).     

Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy

Degraded electron beams, as used for intraoperative radiation therapy (IORT) or similar complicated dosimetric situations, have different characteristics compared to conventional electron therapy beams. If international dosimetry protocols are applied in a direct manner to such degraded beams, uncertainties will be introduced in the absorbed dose determination. The Monte Carlo method has been used to verify experimentally determined relative absorbed dose distributions and output factors in an IORT geometry. Monte Carlo generated dose distributions are mostly within +/-2% or +/-2 mm of measured data. The simulated output variation between the IORT cones (relative output factors) are mostly within 2% of measured values. By comparing IORT and conventional electron beam characteristics (e.g. energy spectra, angular distributions and the contributions of different system components to these quantities) limitations and uncertainties of commonly used dosimetric techniques in IORT electron fields are quantified. The intraoperative treatment field contains a larger amount of scattered electrons, which leads to a broader energy spectrum as well as a wider angular distribution of electrons at the phantom surface. The dose from the scattered electrons can contribute up to 40% of the total dose at a depth of dose maximum, compared to approximately 10% for standard beams. A study of the energy spectra at the reference depth reveals that an uncertainty of the order of 1% can be introduced if ionization chamber based dosimetry is used to determine output factors for the investigated IORT system. We recommend that relative absorbed dose distributions and output factors in IORT electron beams and for similar complicated dosimetric situations should be determined with detectors having a small energy and angular dependence (e.g. diamond detectors or p-Si diodes).     

A standard timing benchmark for EGS4 Monte Carlo calculations.

A Fortran 77 Monte Carlo source code built from the EGS4 Monte Carlo code system has been used for timing benchmark purposes on 29 different computers. This code simulates the deposition of energy from an incident electron beam in a 3-D rectilinear geometry such as one would employ to model electron and photon transport through a series of CT slices. The benchmark forms a standalone system and does not require that the EGS4 system be installed. The Fortran source code may be ported to different architectures by modifying a few lines and only a moderate amount of CPU time is required ranging from about 5 h on PC/386/387 to a few seconds on a massively parallel supercomputer (a BBN TC2000 with 512 processors).     

Mean energy in electron beams

The mean energy of the energy spectrum is an essential parameter for the dosimetry of therapeutic electron beams. Frequently it is assumed that the mean energy of such beams remains constant across the beam and only its degradation with depth is considered. The present work analyzes the variation of the mean energy of primary electrons with depth and lateral position in an electron beam using the Monte Carlo method. Results are compared with relations commonly employed for determination of mean energy at a depth. For the variation of the mean electron energy with depth in broad beams, good agreement was found between Monte Carlo results and an analytic continuous slowing down expression, which takes the variation of radiation stopping power with depth into account. Due to the calculated lateral variation of the mean energy, the relative absorbed dose profile determined with an air ionization chamber in a clinical beam should differ by less than 1% from the measured ionization profile.