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1.
Accurate simulation of large electron fields may lead to improved accuracy in Monte Carlo treatment planning while simplifying the commissioning procedure. We have used measurements made with wide-open jaws and no electron applicator to adjust simulation parameters. Central axis depth dose curves and profiles of 6-21 MeV electron beams measured in this geometry were used to estimate source and geometry parameters, including those that affect beam symmetry: incident beam direction and offset of the secondary scattering foil and monitor chamber from the beam axis. Parameter estimation relied on a comprehensive analysis of the sensitivity of the measured quantities, in the large field, to source and geometry parameters. Results demonstrate that the EGS4 Monte Carlo system is capable of matching dose distributions in the largest electron field to the least restrictive of 1 cGy or 1 mm, with D(max) of 100 cGy, over the full energy range. This match results in an underestimation of the bremsstrahlung dose of 10-20% at 15-21 MeV, exceeding the combined experimental and calculational uncertainty in this quantity of 3%. The simulation of electron scattering at energies of 15-21 MeV in EGS4 may be in error. The recently released EGSnrc/BEAMnrc system may provide a better match to measurement.  相似文献   

2.
Wang LL  Rogers DW 《Medical physics》2007,34(5):1734-1742
Silicon semiconductor diodes measure almost the same depth-dose distributions in both photon and electron beams as those measured by ion chambers. A recent study in ion chamber dosimetry has suggested that the wall correction factor for a parallel-plate ion chamber in electron beams changes with depth by as much as 6%. To investigate diode detector response with respect to depth, a silicon diode model is constructed and the water/silicon dose ratio at various depths in electron beams is calculated using EGSnrc. The results indicate that, for this particular diode model, the diode response per unit water dose (or water/diode dose ratio) in both 6 and 18 MeV electron beams is flat within 2% versus depth, from near the phantom surface to the depth of R50 (with calculation uncertainty <0.3%). This suggests that there must be some other correction factors for ion chambers that counter-balance the large wall correction factor at depth in electron beams. In addition, the beam quality and field-size dependence of the diode model are also calculated. The results show that the water/diode dose ratio remains constant within 2% over the electron energy range from 6 to 18 MeV. The water/diode dose ratio does not depend on field size as long as the incident electron beam is broad and the electron energy is high. However, for a very small beam size (1 X 1 cm(2)) and low electron energy (6 MeV), the water/diode dose ratio may decrease by more than 2% compared to that of a broad beam.  相似文献   

3.
Buckley LA  Rogers DW 《Medical physics》2006,33(6):1788-1796
The EGSnrc Monte Carlo user-code CSnrc is used to calculate wall correction factors, Pwall,, for parallel-plate ionization chambers in photon and electron beams. A set of Pwall values, computed at the reference depth in water, is presented for several commonly used parallel-plate chambers. These values differ from the standard assumption of unity used by dosimetry protocols by up to 1.7% for clinical electron beams. Calculations also show that Pwall is strongly dependent on the depth of measurement and can vary by as much as 6% for a 6 MeV beam in moving from a depth of dref to a depth of R50. In photon beams, where there is limited information available regarding Pwall for parallel-plate chambers, CSnrc calculations show Pwall values of up to 2.4% at the reference depth over a range of photon energies. The Pwall values for photon beams are in good agreement with previous estimates of the wall correction but have much lower statistical uncertainties and cover a wider range of photon beam energies.  相似文献   

4.
The impact of the oblique electron beam on the lateral buildup ratio (LBR), used in the electron pencil beam model to predict the per cent depth dose (PDD) and dose per monitor unit (MU) for an irregular electron field, was examined using Monte Carlo simulation. The EGSnrc-based Monte Carlo code was used to model electron beams produced by a Varian 21 EX linear accelerator for different beam energies, angles of obliquity and field sizes. The Monte Carlo phase space model was verified by measurements using electron diode and radiographic film. For PDDs of oblique electron beams, it is found that the depth of maximum dose (d(m)) shifts towards the surface as the beam obliquity increases. Moreover, for increasing the beam angle of obliquity, the depth doses just beyond d(m) decrease with depth. The depth doses then increase eventually in a deeper depth close to the practical range. The LBRs and pencil beam radial spread function, calculated using PDDs with different field sizes, are found varying with electron beam energies, angles of obliquity and cutout diameters. It is found that LBR increases along the normalized depth when the beam angle of obliquity increases. This results in a decrease of the radial spread function with an increase of beam obliquity. When the size of the electron field increases, the variation of LBR with beam angle of obliquity decreases. It should be noted that when calculating dose per MU for an oblique electron beam with an irregular field misunderstanding and neglecting the effect of beam obliquity would lead to a significant deviation. A database of LBRs for oblique electron beams can be created using Monte Carlo simulation conveniently and is recommended when an oblique beam is used in electron radiotherapy.  相似文献   

5.
Depth-ionization measurements have been obtained with an air-filled Nordic Association of Clinical Physicists (NACP) design parallel-plate ionization chamber in a water phantom for ten foil-scattered electron beams from two different machines with nominal energies between 6 and 20 MeV and field sizes from 6 X 6 to 25 X 25 cm2. Depths of 50% ionization and practical range have been determined from least-squares fits to both the raw data and values corrected to parallel-beam geometry using measured virtual source distances. Depths of 50% dose have also been obtained from fits to divergence-corrected depth-dose measurements performed under identical conditions using, a p-type silicon diode detector. Utilizing accepted conversion factors between mean incident energy (E0) and depth of 50% dose for parallel incident beams, and taking advantage of the fact that p-type silicon diode detector readings are nearly directly indicative of relative dose, conversion factors between E0 and depth of 50% ionization for divergence-corrected and raw, uncorrected finite source-surface distance depth-ionization data are empirically determined. Those values, obtained using the results of both ETRAN and EGS4 dose calculations as base lines, are compared to values currently recommended for use in clinical dosimetry.  相似文献   

6.
The IPEM Code of Practice (IPEM 2003) for electron dosimetry for radiotherapy beams recommends design requirements for parallel-plate ionization chambers used to determine absorbed dose to water in an electron beam. The Classic Markus design has been found not to meet these requirements. The Advanced Markus ionization chamber has been designed to rectify the problems associated with the Classic Markus ionization chamber. The response of three Advanced Markus ionization chambers was investigated and compared to the designated chamber types. Absorbed dose to water calibration factors were derived at the National Physical Laboratory (NPL) for each ionization chamber at seven electron energies in the range nominally 4-19 MeV. Investigations were carried out into chamber settling, polarity effects, ion recombination and the chamber perturbation. The response of the ionization chambers in a clinical beam was also investigated. In general all three Advanced Markus ionization chambers showed the same energy response. The magnitude of the polarity effect was typically 5% at a nominal energy of 4 MeV. There was discrepancy between the polarity measurements made at the NPL and in the clinic. The recommendation of this study is that this chamber type is not suitable for reference dosimetry in electron beams.  相似文献   

7.
The aim of the present study was to investigate three different detector types (a parallel-plate ionization chamber, a p-type silicon diode and a diamond detector) with regard to output factor measurements in degraded electron beams, such as those encountered in small-electron-field radiotherapy and intraoperative radiation therapy (IORT). The Monte Carlo method was used to calculate mass collision stopping-power ratios between water and the different detector materials for these complex electron beams (nominal energies of 6, 12 and 20 MeV). The diamond detector was shown to exhibit excellent properties for output factor measurements in degraded beams and was therefore used as a reference. The diode detector was found to be well suited for practical measurements of output factors, although the water-to-silicon stopping-power ratio was shown to vary slightly with treatment set-up and irradiation depth (especially for lower electron energies). Application of ionization-chamber-based dosimetry, according to international dosimetry protocols, will introduce uncertainties smaller than 0.3% into the output factor determination for conventional IORT beams if the variation of the water-to-air stopping-power ratio is not taken into account. The IORT system at our department includes a 0.3 cm thin plastic scatterer inside the therapeutic beam, which furthermore increases the energy degradation of the electrons. By ignoring the change in the water-to-air stopping-power ratio due to this scatterer, the output factor could be underestimated by up to 1.3%. This was verified by the measurements. In small-electron-beam dosimetry, the water-to-air stopping-power ratio variation with field size could mostly be ignored. For fields with flat lateral dose profiles (>3 x 3 cm2), output factors determined with the ionization chamber were found to be in close agreement with the results of the diamond detector. For smaller field sizes the lateral extension of the ionization chamber hampers its use. We therefore recommend that the readily available silicon diode detector should be used for output factor measurements in complex electron fields.  相似文献   

8.
Total skin electron irradiation (TSEI) with single fields requires large electron beams having good dose uniformity, dmax at the skin surface, and low bremsstrahlung contamination. To satisfy these requirements, energy degraders and scattering foils have to be specially designed for the given accelerator and treatment room. We used Monte Carlo (MC) techniques based on EGS4 user codes (BEAM, DOSXYZ, and DOSRZ) as a guide in the beam modifier design of our TSEI system. The dosimetric characteristics at the treatment distance of 382 cm source-to-surface distance (SSD) were verified experimentally using a linear array of 47 ion chambers, a parallel plate chamber, and radiochromic film. By matching MC simulations to standard beam measurements at 100 cm SSD, the parameters of the electron beam incident on the vacuum window were determined. Best match was achieved assuming that electrons were monoenergetic at 6.72 MeV, parallel, and distributed in a circular pattern having a Gaussian radial distribution with full width at half maximum = 0.13 cm. These parameters were then used to simulate our TSEI unit with various scattering foils. Two of the foils were fabricated and experimentally evaluated by measuring off-axis dose uniformity and depth doses. A scattering foil, consisting of a 12 x 12 cm2 aluminum plate of 0.6 cm thickness and placed at isocenter perpendicular to the beam direction, was considered optimal. It produced a beam that was flat within +/-3% up to 60 cm off-axis distance, dropped by not more than 8% at a distance of 90 cm, and had an x-ray contamination of <3%. For stationary beams, MC-computed dmax, Rp, and R50 agreed with measurements within 0.5 mm. The MC-predicted surface dose of the rotating phantom was 41% of the dose rate at dmax of the stationary phantom, whereas our calculations based on a semiempirical formula in the literature yielded a drop to 42%. The MC simulations provided the guideline of beam modifier design for TSEI and estimated the dosimetric performance for stationary and rotational irradiations.  相似文献   

9.
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   

10.
We investigated the use of magnetically collimated electron beams together with metal filters for electron fluence and range modulation. A longitudinal magnetic field collimation method was developed to reduce skin dose and to improve the electron beam penumbra. Thin metal foils were used to adjust the energies of magnetically collimated electrons. The effects for different types of foils such as Al, Be, Cu, Pb, and Ti were studied using Monte Carlo calculations. An empirical pencil beam dose calculation model was developed to calculate electron dose distributions under magnetic collimation and foil modulation. An optimization method was developed to produce conformal dose distributions for simulated targets such as a horseshoe-shaped target. Our results show that it is possible to produce an electron depth dose enhancement peak using similar techniques of producing a spread-out Bragg peak. In conclusion, our study demonstrates new aspects of using magnetic collimation and foil filtration for producing fluence and range modulated electron dose distributions.  相似文献   

11.
This report contains the recommendations of the Electron Dosimetry Working Party of the UK Institute of Physics and Engineering in Medicine (IPEM). The recommendations consist of a code of practice for electron dosimetry for radiotherapy beams of initial energy from 4 to 25 MeV. The code is based on the absorbed dose to water calibration service for electron beams provided by the UK standards laboratory, the National Physical Laboratory (NPL). This supplies direct N(D,w) calibration factors, traceable to a calorimetric primary standard, at specified reference depths over a range of electron energies up to approximately 20 MeV. Electron beam quality is specified in terms of R(50,D), the depth in water along the beam central axis at which the dose is 50% of the maximum. The reference depth for any given beam at the NPL for chamber calibration and also for measurements for calibration of clinical beams is 0.6R(50.D) - 0.1 cm in water. Designated chambers are graphite-walled Farmer-type cylindrical chambers and the NACP- and Roos-type parallel-plate chambers. The practical code provides methods to determine the absorbed dose to water under reference conditions and also guidance on methods to transfer this dose to non-reference points and to other irradiation conditions. It also gives procedures and data for extending up to higher energies above the range where direct calibration factors are currently available. The practical procedures are supplemented by comprehensive appendices giving discussion of the background to the formalism and the sources and values of any data required. The electron dosimetry code improves consistency with the similar UK approach to megavoltage photon dosimetry, in use since 1990. It provides reduced uncertainties, approaching 1% standard uncertainty in optimal conditions, and a simpler formalism than previous air kerma calibration based recommendations for electron dosimetry.  相似文献   

12.
目的:比较分析半导体探头和电离室探头在三维水箱测量中的差异,为能够提高数据测量精度从而实现治疗计划系统建立准确的计算模型提供依据:方法:在加速器8MV光子线下,使用0.13cm^3的指形电离室和半导体探头在三维水箱中分别测量照射野1cm×lcm,2cm×2cm,3cm×3cm,4cm×4cm,5cm×5cm,6cm×6cm,8cm×8cm,10cm×l0cm的总散射因子、百分深度剂量曲线、离轴比曲线,对测量结果进行比较和分析;结果:对于总散射因子,在较大照射野测量时结果一致,在小野测量时存在差异,1cm×lcm照射野的两者测量结果偏差15.32%;对于百分深度曲线,在建成区差异最大,各照射野的在水面处的测量结果均偏差10%以上:对于离轴比曲线,在半影区存在显著差异.半导体探头在最大剂量点深度测量的射野大小均小明显小于电离室测量的结果。结论:总散射因子,小照射野测量时建议使用半导体探头或者较小体积的电离室;百分深度剂量曲线,建议使用电离室探头;离轴比曲线,使用半导体探头可测量到较好的射野半影区。  相似文献   

13.
Recent work has shown that there is significant uncertainty in measuring build-up doses in mega-voltage photon beams especially at high energies. In this present investigation we used a phantom-embedded extrapolation chamber (PEEC) made of Solid Water to validate Monte Carlo (MC)-calculated doses in the dose build-up region for 6 and 18 MV x-ray beams. The study showed that the percentage depth ionizations (PDIs) obtained from measurements are higher than the percentage depth doses (PDDs) obtained with Monte Carlo techniques. To validate the MC-calculated PDDs, the design of the PEEC was incorporated into the simulations. While the MC-calculated and measured PDIs in the dose build-up region agree with one another for the 6 MV beam, a non-negligible difference is observed for the 18 MV x-ray beam. A number of experiments and theoretical studies of various possible effects that could be the source of this discrepancy were performed. The contribution of contaminating neutrons and protons to the build-up dose region in the 18 MV x-ray beam is negligible. Moreover, the MC calculations using the XCOM photon cross-section database and the NIST bremsstrahlung differential cross section do not explain the discrepancy between the MC calculations and measurement in the dose build-up region for the 18 MV. A simple incorporation of triplet production events into the MC dose calculation increases the calculated doses in the build-up region but does not fully account for the discrepancy between measurement and calculations for the 18 MV x-ray beam.  相似文献   

14.
This paper compares the characteristics of three types of commercial p-type electron diodes specially designed for in vivo dosimetry (Scanditronix EDD2, Sun Nuclear QED 111200-0 and PTW T60010E diodes coupled with a Therados DPD510 dosimeter) in electron fields with energies from 4.5 to 21 MeV, and in conditions similar to those encountered in radiotherapy. In addition to the diodes, a NACP plane parallel ionization chamber and film dosimeters have been used in the experiments. The influence of beam direction on the diode responses (directional effect) was investigated. It was found to be the greatest for the lowest electron beam energy. At 12 MeV and an incidence of +/- 30 degrees, the variation was found to be less than 1% for the Scanditronix and Sun Nuclear diodes and less than 3% for the PTW one. The three diodes exhibited a variation in sensitivity with dose-per-pulse of less than 1% over the range 0.18-0.43 mGy/pulse. The temperature dependence was also studied. The response was linear for the three diodes between 22.2 and 40 degrees C and the sensitivity variations with temperature were (0.25+/-0.01)%/degree C, (0.28+/-0.01)%/degree C, and (0.02 +/-0.01)%/degree C for Scanditronix, Sun Nuclear, and PTW diodes, respectively. Finally the perturbation to the irradiation field induced by the presence of diodes placed at the surface of a homogeneous phantom was investigated and found to be significant, both at the surface and at the depth of maximum dose (several tens of percent) for all three diode types. There is an increase of dose right underneath the diode (close to the surface) and a dose shadow at the depth of maximum. The study shows that electron diodes can be used for in vivo dosimetry provided their characteristics are carefully established before use and taken into consideration at the time of interpretation of the results.  相似文献   

15.
Understanding the limitations of Monte Carlo codes is essential in order to avoid systematic errors in simulations, and to suggest further improvement of the codes. MCNP and EGS4, Monte Carlo codes commonly used in medical physics, were compared and evaluated against electron depth dose data and experimental backscatter results obtained using clinical radiotherapy beams. Different physical models and algorithms used in the codes give significantly different depth dose curves and electron backscattering factors. The default version of MCNP calculates electron depth dose curves which are too penetrating. The MCNP results agree better with experiment if the ITS-style energy-indexing algorithm is used. EGS4 underpredicts electron backscattering for high-Z materials. The results slightly improve if optimal PRESTA-I parameters are used. MCNP simulates backscattering well even for high-Z materials. To conclude the comparison, a timing study was performed. EGS4 is generally faster than MCNP and use of a large number of scoring voxels dramatically slows down the MCNP calculation. However, use of a large number of geometry voxels in MCNP only slightly affects the speed of the calculation.  相似文献   

16.
The characteristics of very small fields, 1 X 1 and 2 X 2 cm, of electron beams of nominal energies, 5, 7, 10, 12, 15, and 18 MeV have been studied and compared to a 10 X 10 cm field. A parallel-plate ion chamber and film have been used to obtain various dose parameters. The central axis depth dose measurements, field flatness, uniformity index, and relative output factors are presented. It was found that satisfactory results for determining the relative output factor can be obtained from film data using a scanning densitometer. It is our conclusion that film dosimetry is acceptable in determining the necessary clinical parameters needed to treat patients with fields as small as 2 X 2 cm. For the 1 X 1 cm field size and for the electron energies greater than 10 MeV, there was substantial disagreement between the ion chamber and film data in the buildup region as well as the regions beyond the depth of maximum dose to the depth of 90% dose.  相似文献   

17.
Abutment of unmodified electron fields to irradiate large areas can lead to significant dose inhomogeneities in the region of junction of the fields. In this paper we describe the design and dosimetric characteristics of a device developed to broaden the electron beam penumbra and thereby to improve the dose uniformity in the overlap region. The device is a high-density triangular-toothed comb capable of reducing the beam intensity without seriously degrading the beam energy. The effect of the comb is such that a single device will generate a beam penumbra which is broad and very nearly linear at all depths for all clinically used beam energies. Results are shown for various field configurations and energies. With a gap of 5.0 cm between the treatment cone and phantom surface the dose "ripple" in the region beneath the teeth was found not to exceed +/- 5% at 0.5-cm depth.  相似文献   

18.
X A Li  J C Chu  W Chen  T Zusag 《Medical physics》1999,26(7):1245-1251
The purpose of this work is to study the dose enhancement by a thin foil (thickness of 0.2-4 mm) of high-Z material in a water phantom, irradiated by high-energy photon beams. EGS4 Monte Carlo technique was used. Perturbations on the beam spectra due to the presence of the foils, and dose enhancement dependence of photon-beam quality, beam incident angle, atomic number (Z), the thickness and size of the foil, and the depth of the foil situated in the phantom were studied. Analysis of photon and secondary-electron spectra indicates that the dose enhancement near an inhomogeneity interface is primarily due to secondary electrons. A calculation for 1-mm-thick planar lead foil in a water phantom shows that the dose enhancements at 0.25, 1, 2 and 3 mm away from the foil in the backward region were 58%, 37%, 24% and 17%, respectively, for a 15 MV beam. Calculations for a variety of planar foils and photon beams show that dose enhancement: (a) increases with Z; (b) decreases with decreasing foil thickness when the foils are thinner than a certain value (1 mm for lead foil for 15 MV); (c) decreases with decreasing incident photon-beam energies; (d) changes slightly for beam incident angles less than 45 degrees and more prominently for larger angles; (e) increases with size of foil; and (f) is almost independent of the depth at which the foil is situated when the foil is placed beyond the range of secondary electrons. The dose enhancement calculation is also performed for a cylindrically shaped lead foil irradiated by a four-field-box. The dose enhancement of 34%/13% was obtained at 0.25/2 mm away from the cylindrical outer interface for a 15 MV four-field-box.  相似文献   

19.
Given that laser wakefield acceleration (LWFA) has been demonstrated experimentally to accelerate electron beams to energies beyond 25 MeV, it is reasonable to assess the ability of existing LWFA technology to compete with conventional radiofrequency linear accelerators in producing electron and x-ray beams for external-beam radiotherapy. We present calculations of the dose distributions (off-axis dose profiles and central-axis depth dose) and dose rates of x-ray beams that can be produced from electron beams that are generated using state-of-the-art LWFA. Subsets of an LWFA electron energy distribution were propagated through the treatment head elements (presuming an existing design for an x-ray production target and flattening filter) implemented within the EGSnrc Monte Carlo code. Three x-ray energy configurations (6 MV, 10 MV and 18 MV) were studied, and the energy width deltaE of the electron-beam subsets varied from 0.5 MeV to 12.5 MeV. As deltaE increased from 0.5 MeV to 4.5 MeV, we found that the off-axis and central-axis dose profiles for x-rays were minimally affected (to within about 3%), a result slightly different from prior calculations of electron beams broadened by scattering foils. For deltaE of the order of 12 MeV, the effect on the off-axis profile was of the order of 10%, but the central-axis depth dose was affected by less than 2% for depths in excess of about 5 cm beyond d(max). Although increasing deltaE beyond 6.5 MeV increased the dose rate at d(max) by more than 10 times, the absolute dose rates were about 3 orders of magnitude below those observed for LWFA-based electron beams at comparable energies. For a practical LWFA-based x-ray device, the beam current must be increased by about 4-5 orders of magnitude.  相似文献   

20.
Treating shallow tumors with a homogeneous dose while simultaneously minimizing the dose to distal critical organs remains a challenge in radiotherapy. One promising approach is modulated electron radiotherapy (MERT). Due to the scattering properties of electron beams, the commercially provided secondary and tertiary photon collimation systems are not conducive for electron beam delivery when standard source-to-surface distances are used. Also, commercial treatment planning systems may not accurately model electron-beam dose distributions when collimated without the standard applicators. However, by using the photon multileaf collimators (MLCs) to create segments to modulate electron beams, the quality of superficial tumor dose distributions may improve substantially. The purpose of this study is to develop and evaluate calculations for the narrow segments needed to modulate megavoltage electron beams using photon beam multileaf collimators. Modulated electron radiotherapy (MERT) will be performed with a conventional linear accelerator equipped with a 120 leaf MLC for 6-20 MeV electron beam energies. To provide a sharp penumbra, segments were delivered with short SSDs (70-85 cm). Segment widths (SW) ranging from 1 to 10 cm were configured for delivery and planning, using BEAMnrc Monte Carlo (MC) code, and the DOSXYZnrc MC dose calculations. Calculations were performed with voxel size of 0.2 x 0.2 x 0.1 cm3. Dosimetry validation was performed using radiographic film and micro- or parallel-plate chambers. Calculated and measured data were compared using technical computing software. Beam sharpness (penumbra) degraded with decreasing incident beam energy and field size (FS), and increasing SSD. A 70 cm SSD was found to be optimal. The PDD decreased significantly with decreasing FS. The comparisons demonstrated excellent agreement for calculations and measurements within 3%, 1 mm. This study shows that accurate calculations for MERT as delivered with existing photon MLC are feasible and allows the opportunity to take advantage of the dynamic leaf motion capabilities and control systems, to provide conformal dose distributions.  相似文献   

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