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1.
This study presents measured neutron dose using a neutron dosimeter in a water phantom and investigates a hypothesis that neutrons in a high-energy photon beam may be responsible for the reported significant dose discrepancies between Monte Carlo calculations and measurements at the build-up region in large fields. Borated polyethylene slabs were inserted between the accelerator head and the phantom in order to remove neutrons generated in the accelerator head. The thickness of the slab ranged from 2.5 cm to 10 cm. A lead slab of 3 mm thickness was also used in the study. The superheated drop neutron dosimeter was used to measure the depth-dose curve of neutrons in a high-energy photon beam and to verify the effectiveness of the slab to remove these neutrons. Total dose measurements were performed in water using a WELLHOFER WP700 beam scanner with an IC-10 ionization chamber. The Monte Carlo code BEAM was used to simulate an 18 MV photon beam from a Varian Clinac-2100EX accelerator. Both EGS4/DOSXYZ and EGSnrc/DOSRZnrc were used in the dose calculations. Measured neutron dose equivalents as a function of depth per unit total dose in water were presented for 10 x 10 and 40 x 40 cm2 fields. The measured results have shown that a 5-10 cm thick borated polyethylene slab can reduce the neutron dose by a factor of 2 when inserted between the accelerator head and the detector. In all cases the measured neutron dose equivalent was less than 0.5% of the photon dose. In order to study if the ion chamber was highly sensitive to the neutron dose, we have investigated the disagreement between the Monte Carlo calculated and measured central-axis depth-dose curves in the build-up region when different shielding materials were used. The result indicated that the IC-10 chamber was not highly sensitive to the neutron dose. Therefore, neutrons present in a high-energy photon beam were unlikely to be responsible for the reported discrepancies in the build-up region for large fields.  相似文献   

2.
Our aim in the present study was to investigate the effects of initial electron beam characteristics on Monte Carlo calculated absorbed dose distribution for a linac 6 MV photon beam. Moreover, the range of values of these parameters was derived, so that the resulted differences between measured and calculated doses were less than 1%. Mean energy, radial intensity distribution and energy spread of the initial electron beam, were studied. The method is based on absorbed dose comparisons of measured and calculated depth-dose and dose-profile curves. All comparisons were performed at 10.0 cm depth, in the umbral region for dose-profile and for depths past maximum for depth-dose curves. Depth-dose and dose-profile curves were considerably affected by the mean energy of electron beam, with dose profiles to be more sensitive on that parameter. The depth-dose curves were unaffected by the radial intensity of electron beam. In contrast, dose-profile curves were affected by the radial intensity of initial electron beam for a large field size. No influence was observed in dose-profile or depth-dose curves with respect to energy spread variations of electron beam. Conclusively, simulating the radiation source of a photon beam, two of the examined parameters (mean energy and radial intensity) of the electron beam should be tuned accurately, so that the resulting absorbed doses are within acceptable precision. The suggested method of evaluating these crucial but often poorly specified parameters may be of value in the Monte Carlo simulation of linear accelerator photon beams.  相似文献   

3.
In this study, a Monte Carlo (MC)-based beam model for an ELEKTA linear accelerator was established. The beam model is based on the EGSnrc Monte Carlo code, whereby electron beams with nominal energies of 10, 12 and 15?MeV were considered. For collimation of the electron beam, only the integrated photon multi-leaf-collimators (MLCs) were used. No additional secondary or tertiary add-ons like applicators, cutouts or dedicated electron MLCs were included. The source parameters of the initial electron beam were derived semi-automatically from measurements of depth-dose curves and lateral profiles in a water phantom. A routine to determine the initial electron energy spectra was developed which fits a Gaussian spectrum to the most prominent features of depth-dose curves. The comparisons of calculated and measured depth-dose curves demonstrated agreement within 1%/1?mm. The source divergence angle of initial electrons was fitted to lateral dose profiles beyond the range of electrons, where the imparted dose is mainly due to bremsstrahlung produced in the scattering foils. For accurate modelling of narrow beam segments, the influence of air density on dose calculation was studied. The air density for simulations was adjusted to local values (433?m above sea level) and compared with the standard air supplied by the ICRU data set. The results indicate that the air density is an influential parameter for dose calculations. Furthermore, the default value of the BEAMnrc parameter 'skin depth' for the boundary crossing algorithm was found to be inadequate for the modelling of small electron fields. A higher value for this parameter eliminated discrepancies in too broad dose profiles and an increased dose along the central axis. The beam model was validated with measurements, whereby an agreement mostly within 3%/3?mm was found.  相似文献   

4.
For 1-50 MeV electrons incident on a water phantom there are systematic differences in the depth-dose curves calculated by the Monte Carlo codes EGS and ETRAN (and its descendants SANDYL, CYLTRAN, ACCEPT, and the ITS system). Compared to ETRAN, the EGS code calculates a higher surface dose and a slightly slower dose falloff past the dose maximum. The discrepancy in the surface dose is shown to exist because the modified Landau energy-loss straggling distribution used in ETRAN underestimates the mean energy loss by about 10% since it underestimates the number of large energy-loss events. Comparison to experimental data shows a preference for the EGS depth-dose curves at 10 and 20 MeV. Since various dosimetry protocols assign electron beam energies based on measured depth-dose curves in water, formulas based on these more accurate EGS4 calculations are presented: relating the mean energy of an incident electron beam to R50, the depth at which the dose in a water phantom falls to 50% of its maximum value; and relating the most probable energy of the incident beam to the projected range of the depth-dose curve. A study is presented of the effects of the incident electron spectrum on the calculated depth-dose curve.  相似文献   

5.
The purpose of this investigation is to study the feasibility of using an alternative method to commission stereotactic radiosurgery beams shaped by micro multi-leaf collimators by using Monte Carlo simulations to obtain beam characteristics of small photon beams, such as incident beam particle fluence and energy distributions, scatter ratios, depth-dose curves and dose profiles where measurements are impossible or difficult. Ionization chambers and diode detectors with different sensitive volumes were used in the measurements in a water phantom and the Monte Carlo codes BEAMnrc/DOSXYZnrc were used in the simulation. The Monte Carlo calculated data were benchmarked against measured data for photon beams with energies of 6 MV and 10 MV produced from a Varian Trilogy accelerator. The measured scatter ratios and cross-beam dose profiles for very small fields are shown to be not only dependent on the size of the sensitive volume of the detector used but also on the type of detectors. It is known that the response of some detectors changes at small field sizes. Excellent agreement was seen between scatter ratios measured with a small ion chamber and those calculated from Monte Carlo simulations. The values of scatter ratios, for field sizes from 6 x 6 mm2 to 98 x 98 mm2, range from 0.67 to 1.0 and from 0.59 to 1.0 for 6 and 10 MV, respectively. The Monte Carlo calculations predicted that the incident beam particle fluence is strongly affected by the X-Y-jaw openings, especially for small fields due to the finite size of the radiation source. Our measurement confirmed this prediction. This study demonstrates that Monte Carlo calculations not only provide accurate dose distributions for small fields where measurements are difficult but also provide additional beam characteristics that cannot be obtained from experimental methods. Detailed beam characteristics such as incident photon fluence distribution, energy spectra, including composition of primary and scattered photons, can be independently used in dose calculation models and to improve the accuracy of measurements with detectors with an energy-dependent response. Furthermore, when there are discrepancies between results measured with different detectors, the Monte Carlo calculated values can indicate the most correct result. The data set presented in this study can be used as a reference in commissioning stereotactic radiosurgery beams shaped by a BrainLAB m3 on a Varian 2100EX or 600C accelerator.  相似文献   

6.
Ding GX 《Medical physics》2002,29(11):2459-2463
This study investigates a possible cause of reported significant dose discrepancies between Monte Carlo calculations and measurements in the buildup region for high-energy photon beams in large fields. A proposed hypothesis was that the discrepancy was caused by a source of electrons in the accelerator head that was not fully accounted for in the treatment head simulation. In this investigation, a lead foil is added just below the accelerator head in order to study this hypothesis. The lead foil effectively removes charged particles generated inside the accelerator head. The charged particles generated by the lead foil can be accounted for fully because the simple geometry can be simulated accurately. An 18 MV photon beam from a Varian Clinac-2100EX is measured using a WELLHOFER WP700 beam scanner with an IC-10 ionization chamber (cavity radius=3 mm). The BEAM Monte Carlo code is used in the incident beam simulations. Both EGS4/DOSXYZ and EGSnrc/DOSRZnrc are used in the dose calculations in a water phantom. The Monte Carlo calculated depth-dose curve is scaled so that it has the same values at 10 cm depth as the measured curve. It is found that the discrepancies between Monte Carlo calculations and measurements remain significant in the buildup region even after applying necessary corrections to the measured data. The discrepancies have only been modestly decreased with the lead foil in place compared to the 40 x 40 cm2 open field. At a depth of 1 cm, discrepancies of about 5% are still observed in the buildup region for the field with the lead foil. Therefore a new explanation for the unresolved discrepancy remains to be found.  相似文献   

7.
A method for deriving the electron and photon energy spectra from electron beam central axis percentage depth dose (PDD) curves has been investigated. The PDD curves of 6, 12 and 20 MeV electron beams obtained from the Monte Carlo full phase space simulations of the Varian linear accelerator treatment head have been used to test the method. We have employed a 'random creep' algorithm to determine the energy spectra of electrons and photons in a clinical electron beam. The fitted electron and photon energy spectra have been compared with the corresponding spectra obtained from the Monte Carlo full phase space simulations. Our fitted energy spectra are in good agreement with the Monte Carlo simulated spectra in terms of peak location, peak width, amplitude and smoothness of the spectrum. In addition, the derived depth dose curves of head-generated photons agree well in both shape and amplitude with those calculated using the full phase space data. The central axis depth dose curves and dose profiles at various depths have been compared using an automated electron beam commissioning procedure. The comparison has demonstrated that our method is capable of deriving the energy spectra for the Varian accelerator electron beams investigated. We have implemented this method in the electron beam commissioning procedure for Monte Carlo electron beam dose calculations.  相似文献   

8.
Shih R  Li XA  Chu JC 《Medical physics》2001,28(4):612-619
The purpose of this study is to analyze the characteristics of dynamic wedges (DW) and to compare DW to physical wedges (PW) in terms of their differences in affecting beam spectra, energy fluence, angular distribution, contaminated electrons, and dose distributions. The EGS4/BEAM Monte Carlo codes were used to simulate the exact geometry of a 6 MV beam and to calculate 3-D dose distributions in phantom. The DW was simulated in accordance with the segmented treatment tables (STT). The percentage depth dose curves and beam profiles for PW, DW, and open fields were measured and used to verify the Monte Carlo simulations. The Monte Carlo results were found to agree within 2% with the measurements performed using film and ionizing chambers in a water phantom. The present EGS4 calculation reveals that the effects of a DW on beam spectral and angular distributions, as well as electron contamination, are much less significant than those for a PW. For the 6 MV photon beam, a 45 degrees PW can result in a 30% increase in mean photon energy due to the effect of beam hardening. It can also introduce a 5% dose reduction in the build-up region due to the reduction of contaminated electrons by the PW. Neither this mean-energy increase nor such dose reduction is found for a DW. Compared to a DW, a PW alters the photon-beam spectrum significantly. The dosimetric differences between a DW and a PW are significant and clearly affect the clinical use of these beams. The data presented may be useful for DW commissioning.  相似文献   

9.
This work is intended to investigate the application and accuracy of micro-MOSFET for superficial dose measurement under clinically used MV x-ray beams. Dose response of micro-MOSFET in the build-up region and on surface under MV x-ray beams were measured and compared to Monte Carlo calculations. First, percentage-depth-doses were measured with micro-MOSFET under 6 and 10 MV beams of normal incidence onto a flat solid water phantom. Micro-MOSFET data were compared with the measurements from a parallel plate ionization chamber and Monte Carlo dose calculation in the build-up region. Then, percentage-depth-doses were measured for oblique beams at 0 degrees-80 degrees onto the flat solid water phantom with micro-MOSFET placed at depths of 2 cm, 1 cm, and 2 mm below the surface. Measurements were compared to Monte Carlo calculations under these settings. Finally, measurements were performed with micro-MOSFET embedded in the first 1 mm layer of bolus placed on a flat phantom and a curved phantom of semi-cylindrical shape. Results were compared to superficial dose calculated from Monte Carlo for a 2 mm thin layer that extends from the surface to a depth of 2 mm. Results were (1) Comparison of measurements with MC calculation in the build-up region showed that micro-MOSFET has a water-equivalence thickness (WET) of 0.87 mm for 6 MV beam and 0.99 mm for 10 MV beam from the flat side, and a WET of 0.72 mm for 6 MV beam and 0.76 mm for 10 MV beam from the epoxy side. (2) For normal beam incidences, percentage depth dose agree within 3%-5% among micro-MOSFET measurements, parallel-plate ionization chamber measurements, and MC calculations. (3) For oblique incidence on the flat phantom with micro-MOSFET placed at depths of 2 cm, 1 cm, and 2 mm, measurements were consistent with MC calculations within a typical uncertainty of 3%-5%. (4) For oblique incidence on the flat phantom and a curved-surface phantom, measurements with micro-MOSFET placed at 1.0 mm agrees with the MC calculation within 6%, including uncertainties of micro-MOSFET measurements of 2%-3% (1 standard deviation), MOSFET angular dependence of 3.0%-3.5%, and 1%-2% systematical error due to phantom setup geometry asymmetry. Micro-MOSFET can be used for skin dose measurements in 6 and 10 MV beams with an estimated accuracy of +/- 6%.  相似文献   

10.
The purpose of this study is to provide detailed characteristics of incident photon beams for different field sizes and beam energies. This information is critical to the future development of accurate treatment planning systems. It also enhances our knowledge of radiotherapy photon beams. The EGS4 Monte Carlo code, BEAM, has been used to simulate 6 and 18 MV photon beams from a Varian Clinac-2100EX accelerator. A simulated realistic beam is stored in a phase space data file, which contains details of each particle's complete history including where it has been and where it has interacted. The phase space files are analysed to obtain energy spectra, angular distribution, fluence profile and mean energy profiles at the phantom surface for particles separated according to their charge and history. The accuracy of a simulated beam is validated by the excellent agreement between the Monte Carlo calculated and measured dose distributions. Measured depth-dose curves are obtained from depth-ionization curves by accounting for newly introduced chamber fluence corrections and the stopping-power ratios for realistic beams. The study presents calculated depth-dose components from different particles as well as calculated surface dose and contribution from different particles to surface dose across the field. It is shown that the increase of surface dose with the increase of the field size is mainly due to the increase of incident contaminant charged particles. At 6 MV, the incident charged particles contribute 7% to 21% of maximum dose at the surface when the field size increases from 10 x 10 to 40 x 40 cm2. At 18 MV, their contributions are up to 11% and 29% of maximum dose at the surface for 10 x 10 cm2 and 40 x 40 cm2 fields respectively. However, the fluence of these incident charged particles is less than 1% of incident photon fluence in all cases.  相似文献   

11.
The feasibility is demonstrated of a numerical method to calculate dose deposition by broad high-energy electron beams in homogeneous matter or in heterogeneous matter in which the heterogeneities are arranged in slabs perpendicular to the beam axis. The method is based only on the basic physical interaction processes of high-energy electrons and matter. The method is an extended version of the phase space time evolution method as described by Cordaro and Zucker (1971). The calculated depth-dose curves, energy spectra and angular distributions agree very well with results of the extensive class II Monte Carlo calculations of Andreo and Brahme (1984) and Andreo (1985), but require much less computer time: typically 3 minutes on a VAX 785 with floating point accelerator. This demonstrates the power of a numerical method in comparison with Monte Carlo methods.  相似文献   

12.
This report investigates the buildup region of the depth-dose curve for broad parallel beams of 60Co and lower energy photons incident on slabs of tissue as defined by the International Commission on Radiation Units and Measurements (ICRU) and other materials. The EGS Monte Carlo system was used to simulate the transport of photons and electrons in the materials. Calculated buildup regions of the depth-dose curves are presented for photons incident on ICRU tissue. For 60Co beams, the primary and scatter dose components are presented, both for the buildup region and at depth in the phantom. Effects of beam radius were investigated and found to have only a small effect in the buildup region of the central axis depth-dose curve. The calculated effects of beam radius are larger at depth and in good agreement with experiment. Effects of scatter and attenuation in a small miniphantom of water were investigated as a function of photon energy and were found to cancel within 0.8%. The mean distance of electron transport was calculated for 60Co beams incident on carbon, water, polystyrene, aluminum, and lead.  相似文献   

13.
Electron beam radiotherapy treatment planning systems need to be fed with the characteristics of the high-energy electron beams (4-50 MeV) from the specifically applied accelerator. Beams can be characterized by their mean initial energy, effective initial angular variance, virtual source position and the resulting central axis depth dose distribution in water. This information is the only input to pencil beam dose calculation models. Newer calculation models like macro Monte Carlo, voxel Monte Carlo and phase space evolution require as input the full initial phase space or a parametrization of that initial phase space, generally consisting of a primary beam component and one or more scatter components. This primary beam component is often characterized by initial energy, primary beam initial angular variance and virtual source distance. The purpose of the present investigation was to investigate to what extent standard values can be used both for the effective initial angular variance as input to pencil beam models and for the primary beam initial angular variance. Comprehensive benchmark data were obtained on the initial angular variance of various types of accelerator, for various energies and field sizes. The initial angular variance sigma2theta(x) has been derived from penumbra measurements in air by means of film dosimetry at various distances from the lower collimator. For the types of accelerator used in radiotherapy nowadays the measurements show values for sigma2theta(x)/T(E) of around 13 cm where T(E) is the ICRU-35 linear angular scattering power in air. This value can be chosen as standard value for the primary beam initial angular variance, only slightly compromising the dose calculation accuracy. As input to pencil beam models, an effective sigma2theta(x)/T(E) should be used incorporating the scatter from the lower collimator. For the case that the air gaps between lower collimator and patient are small (5-10 cm) an effective sigma2theata(x)/T(E) of 20 cm has been found and is recommended as the standard input for pencil beam models. Of the accelerators investigated, a different value was found only for the Elekta SL15, i.e. 50% higher for the effective sigma2theta(x)/T(E).  相似文献   

14.
Araki F 《Medical physics》2008,35(9):4033-4040
Recent standard dosimetry protocols recommend that plane-parallel ionization chambers be used in the measurements of depth-dose distributions or the calibration of low-energy electron beams with beam quality R50 <4 g/cm2. In electron dosimetry protocols with the plane-parallel chambers, the wall correction factor, Pwall, in water is assumed to be unity and the replacement correction factor, Prepl, is taken to be unity for well-guarded plane-parallel chambers, at all measurement depths. This study calculated Pwall and Prepl for NACP-02, Markus, and Roos plane-parallel chambers in clinical electron dosimetry using the EGSnrc Monte Carlo code system. The Pwall values for the plane-parallel chambers increased rapidly as a function of depth in water, especially at lower energy. The value around R50 for NACP-02 was about 10% greater than unity at 4 MeV. The effect was smaller for higher electron energies. Similarly, Prepl values with depth increased drastically at the region with the steep dose gradient for lower energy. For Markus Prepl departed more than 10% from unity close to R50 due to the narrow guard ring width. Prepl for NACP-02 and Roos was close to unity in the plateau region of depth-dose curves that includes a reference depth, dref. It was also found that the ratio of the dose to water and the dose to the sensitive volume in the air cavity for the plane-parallel chambers, Dw/[Dair]pp, at d(ref) differs significantly from that assumed by electron dosimetry protocols.  相似文献   

15.
An analytical model is presented to calculate the effective depth in water of cylindrical ionization chambers in clinical proton or heavy ion beams in the presence of modest and linear gradients. This model is compared with Monte Carlo simulations and recommendations in IAEA TRS-398 for all ionization chambers listed in that report. A refinement of the analytical model allows its application for depth-dose curves even in the nonlinear gradient region of the Bragg peak. Combined with information from the Monte Carlo simulations it also allows one to solve the inverse problem of deriving a depth-dose curve in homogeneous water from the depth-dose response obtained with a cylindrical ionization chamber. The results show that the effective depth in water calculated analytically, calculated by Monte Carlo, and derived from experimental literature are in good agreement. The agreement with the IAEA TRS-398 recommendation is good for most ionization chambers but can be wrong by up to 1.5 mm for some ionization chamber types. The agreement between the refined analytical model and Monte Carlo simulations of depth-dose response curves is shown to be good (even in extreme situations of large ionization chambers in low-energy beams). An indication is given of situations in which a simple shift of the entire depth-dose curve is sufficiently accurate. It is demonstrated that it is possible to solve the inverse problem with this method, even for rather noisy data. This is illustrated by successfully applying it to depth-dose measurements with cylindrical ionization chambers taken from the literature.  相似文献   

16.
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.  相似文献   

17.
18.
Earl MA  Ma L 《Medical physics》2002,29(4):484-491
We studied the dose distributions from electron beams subjected to a longitudinal magnetic field applied to them before they reach the phantom. We found that specific combinations of the length and intensity of the magnetic field produced enhancement of the peaks of the central-axis depth-dose distributions. The EGS4 Monte Carlo system was used in this study. In the simulations, a uniform axial magnetic field parallel to the electron beam direction was applied to the air gap between the collimation and the phantom. We extensively studied the simplified case of an 18 MeV electron beam point source. Dose deposition was calculated for various magnetic field strengths, distances through which the magnetic field was applied, collimation sizes, and source to collimation distances. The magnetic field strengths varied from 0 to 3 T, the source-to-collimation distances studied were 50 and 95 cm, the collimation sizes studied were 10 x 10 and 20 x 20 cm2, and the distance through which the field was applied ranged from 10 to 20 cm. Specific combinations of these variables resulted in as much as a 70% enhancement of the peak dose relative to the surface dose. Finally, to determine how the geometry of a real accelerator affects the resulting dose distribution, we performed a full simulation of an Elekta SL20 linear accelerator and compared the results with the ideal case.  相似文献   

19.
Model pencil-beam on slab calculations are used as well as a series of detailed calculations of photon and electron output from commercial accelerators to quantify level(s) of physics required for the Monte Carlo transport of photons and electrons in treatment-dependent beam modifiers, such as jaws, wedges, blocks, and multileaf collimators, in photon teletherapy dose calculations. The physics approximations investigated comprise (1) not tracking particles below a given kinetic energy, (2) continuing to track particles, but performing simplified collision physics, particularly in handling secondary particle production, and (3) not tracking particles in specific spatial regions. Figures-of-merit needed to estimate the effects of these approximations are developed, and these estimates are compared with full-physics Monte Carlo calculations of the contribution of the collimating jaws to the on-axis depth-dose curve in a water phantom. These figures of merit are next used to evaluate various approximations used in coupled photon/electron physics in beam modifiers. Approximations for tracking electrons in air are then evaluated. It is found that knowledge of the materials used for beam modifiers, of the energies of the photon beams used, as well as of the length scales typically found in photon teletherapy plans, allows a number of simplifying approximations to be made in the Monte Carlo transport of secondary particles from the accelerator head and beam modifiers to the isocenter plane.  相似文献   

20.
This work is a report on the commissioning of low energy electron beams of a medical linear accelerator for Monte Carlo dose calculation using NXEGS software (NXEGS version 1.0.10.0, NX Medical Software, LLC). A unique feature of NXEGS is automated commissioning, a process whereby a combination of analytic and Monte Carlo methods generates beam models from dosimetric data collected in a water phantom. This study uses NXEGS to commission 6, 9, and 12 MeV electron beams of a Varian Clinac 2100C using three applicators with standard inserts. Central axis depth-dose, primary axis and diagonal beam profiles, and output factors are the measurements necessary for commissioning of the code. We present a comparison of measured dose distributions with the distributions generated by NXEGS, using confidence limits on seven measures of error. We find that confidence limits are typically less than 3% or 3 mm, but increase with increasing source to surface distance (SSD) and depth at or beyond R(50). We also investigate the dependence of NXEGS' performance on the size and composition of data used to commission the program, finding a weak dependence on number of dose profiles in the data set, but finding also that commissioning data need be measured at only two SSDs.  相似文献   

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