Influence of initial electron beam parameters on Monte Carlo calculated absorbed dose distributions for radiotherapy photon beams

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.     

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.     

Using a photon phase-space source for convolution/superposition dose calculations in radiation therapy

For a given linac design, the dosimetric characteristics of a photon beam are determined uniquely by the energy and radial distributions of the electron beam striking the x-ray target. However, in the usual commissioning of a beam from measured data, a large number of variables can be independently tuned, making it difficult to derive a unique and self-consistent beam model. For example, the measured dosimetric penumbra in water may be attributed in various proportions to the lateral secondary electron range, the focal spot size and the transmission through the tips of a non-divergent collimator; the head-scatter component in the tails of the transverse profiles may not be easy to resolve from phantom scatter and head leakage; and the head-scatter tails corresponding to a certain extra-focal source model may not agree self-consistently with in-air output factors measured on the central axis. To reduce the number of adjustable variables in beam modelling, we replace the focal and extra-focal sources with a single phase-space plane scored just above the highest adjustable collimator in a EGS/BEAM simulation of the linac. The phase-space plane is then used as photon source in a stochastic convolution/superposition dose engine. A photon sampled from the uncollimated phase-space plane is first propagated through an arbitrary collimator arrangement and then interacted in the simulation phantom. Energy deposition kernel rays are then randomly issued from the interaction points and dose is deposited along these rays. The electrons in the phase-space file are used to account for electron contamination. 6 MV and 18 MV photon beams from an Elekta SL linac are used as representative examples. Except for small corrections for monitor backscatter and collimator forward scatter for large field sizes (<0.5% with <20 x 20 cm2 field size), we found that the use of a single phase-space photon source provides accurate and self-consistent results for both relative and absolute dose calculations.     

Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code

A recent paper analyzed the sensitivity to various simulation parameters of the Monte Carlo simulations of nine beams from three major manufacturers of commercial medical linear accelerators, ranging in energy from 4-25 MV. In this work the nine models are used: to calculate photon energy spectra and average energy distributions and compare them to those published by Mohan et al. [Med. Phys. 12, 592-597 (1985)]; to separate the spectra into primary and scatter components from the primary collimator, the flattening filter and the adjustable collimators; and to calculate the contaminant-electron fluence spectra and the electron contribution to the depth-dose curves. Notwithstanding the better precision of the calculated spectra, they are similar to those calculated by Mohan et al. The three photon spectra at 6 MV from the machines of three different manufacturers show differences in their shapes as well as in the efficiency of bremsstrahlung production in the corresponding target and filter combinations. The contribution of direct photons to the photon energy fluence in a 10 x 10 field varies between 92% and 97%, where the primary collimator contributes between 0.6% and 3.4% and the flattening filter contributes between 0.6% and 4.5% to the head-scatter energy fluence. The fluence of the contaminant electrons at 100 cm varies between 5 x 10(-9) and 2.4 x 10(-7) cm(-2) per incident electron on target, and the corresponding spectrum for each beam is relatively invariant inside a 10 x 10 cm2 field. On the surface the dose from electron contamination varies between 5.7% and 11% of maximum dose and, at the depth of maximum dose, between 0.16% and 2.5% of maximum dose. The photon component of the percentage depth-dose at 10 cm depth is compared with the general formula provided by AAPM's task group 51 and confirms the claimed accuracy of 2%.     

The flatness of Siemens linear accelerator x-ray fields

The primary definer for Siemens MXE and MDX linear accelerators projects a circular opening with a radius of 25 cm at 100 cm from the target. Our measurements of photon beam profiles, however, indicate that the photon fluence drops to 95% of the central axis value at a radius of 18 cm. The flattening filter for these machines projects a flattened field size that is much smaller than the primary definer would allow. The clinical implications of this mismatch for large rectangular fields and for fields defined by asymmetric jaws are discussed and solutions are considered. A large field flattener was designed for our Siemens MXE 6 MV beam using Monte Carlo simulation of the treatment head and water phantom. The accuracy required of source and geometry details for dose distributions calculation is presented. The key parameters are the mean energy and focal spot size of the electron beam incident on the exit window, the material composition, and thickness profile of the exit window, target, flattener, and primary collimator, and the position of the primary collimator relative to the target. Profiles were more sensitive than central axis depth doses to simulation details. The beam energy and primary collimator position were selected to achieve good agreement between measured and calculated dose distributions. The flattener we designed with Monte Carlo was machined from brass and mounted on our MXE treatment unit. Measurements demonstrate that the large field flattener extends the useful radius of the field out to 22 cm, right into the penumbra cast by the primary collimator.     

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.     

A Monte Carlo study of a flattening filter-free linear accelerator verified with measurements

A Monte Carlo model of an Elekta Precise linear accelerator has been built and verified by measured data for a 6 and 10 MV photon beam running with and without a flattening filter in the beam line. In this study the flattening filter was replaced with a 6 mm thick copper plate, provided by the linac vendor, in order to stabilize the beam. Several studies have shown that removal of the filter improves some properties of the photon beam, which could be beneficial for radiotherapy treatments. The investigated characteristics of this new beam included output, spectra, mean energy, half value layer and the origin of scattered photons. The results showed an increased dose output per initial electron at the central axis of 1.76 and 2.66 for the 6 and 10 MV beams, respectively. The number of scattered photons from the accelerator head was reduced by (31.7 ± 0.03)% (1 SD) for the 6 MV beam and (47.6 ± 0.02)% for the 10 MV beam. The photon energy spectrum of the unflattened beam was softer compared to a conventional beam and did not vary significantly with the off-axis distance, even for the largest field size (0-20 cm off-axis).     

Commissioning of a medical accelerator photon beam Monte Carlo simulation using wide-field profiles

A method for commissioning an EGSnrc Monte Carlo simulation of medical linac photon beams through wide-field lateral profiles at moderate depth in a water phantom is presented. Although depth-dose profiles are commonly used for nominal energy determination, our study shows that they are quite insensitive to energy changes below 0.3 MeV (0.6 MeV) for a 6 MV (15 MV) photon beam. Also, the depth-dose profile dependence on beam radius adds an additional uncertainty in their use for tuning nominal energy. Simulated 40 cm x 40 cm lateral profiles at 5 cm depth in a water phantom show greater sensitivity to both nominal energy and radius. Beam parameters could be determined by comparing only these curves with measured data.     

Reference dosimetry condition and beam quality correction factor for CyberKnife beam

This article is intended to improve the certainty of the absorbed dose determination for reference dosimetry in CyberKnife beams. The CyberKnife beams do not satisfy some conditions of the standard reference dosimetry protocols because of its unique treatment head structure and beam collimating system. Under the present state of affairs, the reference dosimetry has not been performed under uniform conditions and the beam quality correction factor kQ for an ordinary 6 MV linear accelerator has been temporally substituted for the kQ of the CyberKnife in many sites. Therefore, the reference conditions and kQ as a function of the beam quality index in a new way are required. The dose flatness and the error of dosimeter reading caused by radiation fields and detector size were analyzed to determine the reference conditions. Owing to the absence of beam flattening filter, the dose flatness of the CyberKnife beam was inferior to that of an ordinary 6 MV linear accelerator. And if the absorbed dose is measured with an ionization chamber which has cavity length of 2.4, 1.0 and 0.7 cm in reference dosimetry, the dose at the beam axis for a field of 6.0 cm collimator was underestimated 1.5%, 0.4%, and 0.2% on a calculation. Therefore, the maximum field shaped with a 6.0 cm collimator and ionization chamber which has a cavity length of 1.0 cm or shorter were recommended as the conditions of reference dosimetry. Furthermore, to determine the kQ for the CyberKnife, the realistic energy spectrum of photons and electrons in water was simulated with the BEAMnrc. The absence of beam flattening filter also caused softer photon energy spectrum than that of an ordinary 6 MV linear accelerator. Consequently, the kQ for ionization chambers of a suitable size were determined and tabulated as a function of measurable beam quality indexes in the CyberKnife beam.     

Monte Carlo simulation and dosimetric verification of radiotherapy beam modifiers.

Monte Carlo simulation of beam modifiers such as physical wedges and compensating filters has been performed with a rectilinear voxel geometry module. A modified version of the EGS4/DOSXYZ code has been developed for this purpose. The new implementations have been validated against the BEAM Monte Carlo code using its standard component modules (CMs) in several geometrical conditions. No significant disagreements were found within the statistical errors of 0.5% for photons and 2% for electrons. The clinical applicability and flexibility of the new version of the code has been assessed through an extensive verification versus dosimetric data. Both Varian multi-leaf collimator (MLC) wedges and standard wedges have been simulated and compared against experiments for 6MV photon beams and different field sizes. Good agreement was found between calculated and measured depth doses and lateral dose profiles along both wedged and unwedged directions for different depths and focus-to-surface distances. Furthermore, Monte Carlo-generated output factors for both open and wedged fields agreed with linac commissioning beam data within statistical uncertainties of the calculations (<3% at largest depths). Compensating filters of both low-density and high-density materials have also been successfully simulated. As a demonstration, a wax compensating filter with a complex three-dimensional concave and convex geometry has been modelled through a CT scan import. Calculated depth doses and lateral dose profiles for different field sizes agreed well with experiments. The code was used to investigate the performance of a commercial treatment planning system in designing compensators. Dose distributions in a heterogeneous water phantom emulating the head and neck region were calculated with the convolution-superposition method (pencil beam and collapsed cone implementations) and compared against those from the MC code developed herein. The new technique presented in this work is versatile, DICOM-RT compliant and accurate in the simulation of beam modulators. This paper addresses the need to reduce the sources of error in the modelling of beam modifiers since they remain a viable alternative to the MLC technique in the delivery of IMRT beams.     

Determination of the initial beam parameters in Monte Carlo linac simulation

For Monte Carlo linac simulations and patient dose calculations, it is important to accurately determine the phase space parameters of the initial electron beam incident on the target. These parameters, such as mean energy and radial intensity distribution, have traditionally been determined by matching the calculated dose distributions with the measured dose distributions through a trial and error process. This process is very time consuming and requires a lot of Monte Carlo simulation experience and computational resources. In this paper, we propose an easy, efficient, and accurate method for the determination of the initial beam parameters. We hypothesize that (1) for one type of linacs, the geometry and material of major components of the treatment head are the same; the only difference is the phase space parameters of the initial electron beam incident on the target, and (2) most linacs belong to a limited number of linac types. For each type of linacs, Monte Carlo treatment planning system (MC-TPS) vendors simulate the treatment head and calculate the three-dimensional (3D) dose distribution in water phantom for a grid of initial beam energies and radii. The simulation results (phase space files and dose distribution files) are then stored in a data library. When a MC-TPS user tries to model their linac which belongs to the same type, a standard set of measured dose data is submitted and compared with the calculated dose distributions to determine the optimal combination of initial beam energy and radius. We have applied this method to the 6 MV beam of a Varian 21EX linac. The linac was simulated using EGSNRC/BEAM code and the dose in water phantom was calculated using EGSNRC/DOSXYZ. We have also studied issues related to the proposed method. Several common cost functions were tested for comparing measured and calculated dose distributions, including chi2, mean absolute error, dose difference at the penumbra edge point, slope of the dose difference of the lateral profile, and the newly proposed Kappaalpha factor (defined as the fraction of the voxels with absolute dose difference less than alpha%). It was found that the use of the slope of the lateral profile difference or the difference of the penumbra edge points may lead to inaccurate determination of the initial beam parameters. We also found that in general the cost function value is very sensitive to the simulation statistical uncertainty, and there is a tradeoff between uncertainty and specificity. Due to the existence of statistical uncertainty in simulated dose distributions, it is practically impossible to determine the best energy/radius combination; we have to accept a group of energy/radius combinations. We have also investigated the minimum required data set for accurate determination of the initial beam parameters. We found that the percent depth dose curves along or only a lateral profile at certain depth for a large field size is not sufficient and the minimum data set should include several lateral profiles at various depths as well as the central axis percent depth dose curve for a large field size.     

有无均整器模式下臂架与准直器不同角度条件下的剂量学比较

目的:探讨臂架或准直器角度的改变对均整（FF）与非均整（FFF）两种模式的射线剂量的影响。方法:选用Versa HD直线加速器配备的6 MV/10 MV光子束FF/FFF模式4档能量在设定好九点位置的10 cm×10 cm标准射野内进行实验。首先,借助IMF等中心夹具将Mapcheck2固定于治疗机机头,并用Mapcheck2测量相同臂架与准直器角度条件下4种光子束输出的平面剂量值;其次,用Mapcheck2测量在相同臂架角度、不同准直器角度与相同准直器角度、不同臂架角度两种条件下4种光子束的中心轴剂量值;最后,固定准直器为0°,设立两组臂架对穿射野（0°与180°,90°与270°）。拆除Mapcheck2,采用固体水和FC65-G电离室建立一个测量模体来测量4种光子束在两组等中心对穿野的剂量。运用SPSS统计软件对该实验收集到的数据进行对比分析。结果:在相同臂架与准直器角度条件下,4种光子束辐照9个点的平面剂量之间均存在明显统计学差异（P6 MV FF =0.020, P6 MV FFF=0.017, P10 MV FF =0.030, P10 MV FFF=0.016）;而不同臂架角度或不同准直器角度条件下,4种能量光子束的中心轴点剂量值均无统计学差异。在0°与180°的对穿野,4种能量光子束的输出剂量存在统计学差异（P6 MV FF =0.001, P6 MV FFF=0.002, P10 MV FF =0.003, P10 MV FFF=0.001）,而在90°与270°的对穿野无统计学差异。结论:Versa HD直线加速器拥有优良的机械等中心性能。在实际工作时,臂架和准直器的旋转,均不影响光子束的中心轴剂量的准确输出。在FF模式下,射线能量越高,受治疗床影响越小;FFF模式射线由于射线质软,能量越高,更易受到治疗床的衰减作用,在实际中应引起重视。     

Monte Carlo study of photon fields from a flattening filter-free clinical accelerator

In conventional clinical linear accelerators, the flattening filter scatters and absorbs a large fraction of primary photons. Increasing the beam-on time, which also increases the out-of-field exposure to patients, compensates for the reduction in photon fluence. In recent years, intensity modulated radiation therapy has been introduced, yielding better dose distributions than conventional three-dimensional conformal therapy. The drawback of this method is the further increase in beam-on time. An accelerator with the flattening filter removed, which would increase photon fluence greatly, could deliver considerably higher dose rates. The objective of the present study is to investigate the dosimetric properties of 6 and 18 MV photon beams from an accelerator without a flattening filter. The dosimetric data were generated using the Monte Carlo programs BEAMnrc and DOSXYZnrc. The accelerator model was based on the Varian Clinac 2100 design. We compared depth doses, dose rates, lateral profiles, doses outside collimation, total and collimator scatter factors for an accelerator with and without a flatteneing filter. The study showed that removing the filter increased the dose rate on the central axis by a factor of 2.31 (6 MV) and 5.45 (18 MV) at a given target current. Because the flattening filter is a major source of head scatter photons, its removal from the beam line could reduce the out-of-field dose.     

Calculating photon beam characteristics with Monte Carlo techniques.

This study describes the results from a simulation of a 10 MV photon beam from a medical linac using the BEAM code. To check the quality of the generated photon beam, the characteristics of this beam (depth dose curve, cross profiles, and output factors) have been calculated and compared to measured data. By splitting up the radiation head in two parts, the target section and the collimator section calculation times were long, but acceptable when aiming at phase space files containing some 5 million particles. Given the number of particles evaluated, the accuracy of all data was around 2%. Analysis of the phase space files for different field size supports results from previous studies about contaminant particles and sources for scattered radiation for photon beams from medical linacs. The total scatter output factor Scp as well as the collimator scatter output factor Sc have been calculated within 2% of measurements. Also, the ratio between dose at a reference point for the full scatter situation and the no-scatter situation has been calculated correctly. All depth dose curves and cross profiles have also been calculated correctly, although with only moderate statistics. Improvements are possible by increasing the number of particles in the simulations (up to 50 million for the largest field size) at least 4-8 times, although calculation times will increase with the same factor. Nevertheless, the method proved itself as reliable. Still, the accuracy should be improved to 1% or better. This is necessary as we plan to use Monte Carlo simulations to benchmark three-dimensional radiotherapy planning systems. By increasing the number of particles in the phase space files and subsequently increasing the number of particles in each simulation, this 1% accuracy will be achieved. The easy way to increase the number of particles in a simulation by increasing the number of times phase space files, which were already recycled ten times, are reused from ten times (this study) to 40 times or more will not work, as it introduces artifacts, especially in the cross profiles.     

Characteristics of the high-energy photon beam of a 25-MeV accelerator

The CGR Saturne 25 is an isocentrically mounted standing wave medical linear accelerator that produces dual-energy photon beams and a scanned electron beam with six selectable energies between 4 and 25 MeV. The highest energy photon beam is nominally referred to as 23 MV. For this beam the mean energy of the accelerated electron beam on the 1.3 radiation length (4 mm) tungsten x-ray target is found to be approximately 21 MeV, with the energy acceptance stated to be +/- 5%. The electron beam traverses a 270 degrees bending magnet upstream of the x-ray production target. The resulting bremsstrahlung beam passes through a combination steel and lead flattening filter, 4-cm maximum thickness. Dosimetric data for the 23-MV beam are presented with respect to rectangular field output factor, depth of maximum dose as a function of field size, surface and buildup dose, central axis percent depth dose, tissue-phantom ratios, beam profile, applicability of inverse square, and block transmission. Some data are also presented on the effect of different flattening filter designs on apparent beam energy.     

An MCNP-based model of a linear accelerator x-ray beam.

The Monte Carlo N-Particle radiation transport computer code (MCNP) has been employed on a personal computer to develop a simple model simulating the major components within the beam path of a linear accelerator radiation head, namely the electron target, primary conical collimator, beam flattening filter, wedge filter and the secondary collimators. The model was initially used to calculate the energy spectra and angular distributions of the x-ray beam for the Philips SL 75/5 linear accelerator, in a plane immediately beneath the flattening filter. These data were subsequently used as a 'source' of x-rays at the target position, to assess the emergent beam from the secondary collimators. The depth dose distributions and dose profiles at constant depth for various field sizes have been calculated for a nominal operating potential of 4 MV and found to be within acceptable limits. It is concluded that the technique may be used to calculate the energy spectra of any linear accelerator upon specification of the component dimensions, materials and nominal accelerating potential. It is anticipated that this work will serve as the basis of a quality control tool for linear accelerators and treatment planning systems.     

Peripheral dose from a linear accelerator equipped with multileaf collimation

In radiation therapy, knowledge of the peripheral dose is important when anatomical structures with very low dose tolerances might be involved. Two of the major sources of peripheral dose, leakage from the linac head, and scatter from secondary collimators, depend strongly on the configuration of the linac head and therefore might be affected by the presence of a multileaf collimator (MLC). In this study, peripheral dose was measured at two depths and two field sizes for 6 and 18 MV photons from a linac with a MLC. The MLC was configured both with leaves fully retracted and with leaves positioned at the field edges defined by the secondary collimator jaws. Comparative measurements were also made for 6 MV photons from a linac without MLC. Peripheral dose was determined as a percentage of the central axis dose for the same energy, field size, and depth using diode detectors in solid phantom material. The data for the 6 MV without MLC agreed with those for the beam with MLC leaves retracted. For both energies at all depths and distances from the field edge, configuring the MLC leaves at the field edge yielded a reduction in peripheral dose of 6%-50% compared to MLC leaves fully retracted.     

Photon-beam subsource sensitivity to the initial electron-beam parameters

One limitation to the widespread implementation of Monte Carlo (MC) patient dose-calculation algorithms for radiotherapy is the lack of a general and accurate source model of the accelerator radiation source. Our aim in this work is to investigate the sensitivity of the photon-beam subsource distributions in a MC source model (with target, primary collimator, and flattening filter photon subsources and an electron subsource) for 6- and 18-MV photon beams when the energy and radial distributions of initial electrons striking a linac target change. For this purpose, phase-space data (PSD) was calculated for various mean electron energies striking the target, various normally distributed electron energy spread, and various normally distributed electron radial intensity distributions. All PSD was analyzed in terms of energy, fluence, and energy fluence distributions, which were compared between the different parameter sets. The energy spread was found to have a negligible influence on the subsource distributions. The mean energy and radial intensity significantly changed the target subsource distribution shapes and intensities. For the primary collimator and flattening filter subsources, the distribution shapes of the fluence and energy fluence changed little for different mean electron energies striking the target, however, their relative intensity compared with the target subsource change, which can be accounted for by a scaling factor. This study indicates that adjustments to MC source models can likely be limited to adjusting the target subsource in conjunction with scaling the relative intensity and energy spectrum of the primary collimator, flattening filter, and electron subsources when the energy and radial distributions of the initial electron-beam change.     

On the existence of low-energy photons (<150 keV) in the unflattened x-ray beam from an ordinary radiotherapeutic target in a medical linear accelerator

Low-energy photons (<150 keV) are essential for obtaining high quality x-ray radiographs. These photons are usually produced in the accelerator target, but are effectively absorbed by the flattening filter and, at least partially, by the target itself. Experimental proof is presented for the existence of low-energy photons in the unflattened x-ray beam produced by a 6 MeV electron beam normally incident on the thinner of the two existing ports of the all-Cu radiotherapeutic target of a Clinac 18 (Varian Associates) linear accelerator. A number of one-shot absorption measurements were carried out with 12 foils of Pb absorbers with thicknesses varying from 0.25 to 3 mm in steps of 0.25 mm arranged symmetrically around the central axis on a 7.2 cm radius circumference. A Kodak ECL film-screen-cassette combination was used as a detector in the absorption measurements, in which optical density was measured as a function of the thickness of the Pb absorbers. Two sets of absorption measurements were carried out: the first one with the Clinac 18 6 MV unflattened beam and the second one with the Clinac 600C 6 MV therapeutic counterpart beam. There is a striking difference between the two sets: the optical density versus Pb-absorber thickness curve shows a sharp increase in optical density at small absorber thicknesses in the case of the unflattened 6 MV x-ray beam as compared with a gently sloping dependence in the case of the 6 MV therapeutic beam. A semi-quantitative assessment of the low-energy photon contribution to the whole optical density/contrast is presented. A 0.85 mm thick Pb absorber intercepting the 6 MV unflattened x-ray beam eliminates almost totally the sharp peak in the optical density curve at small Pb-absorber thicknesses. This constitutes additional evidence for the existence of low-energy photons (<150 keV) in the unflattened 6 MV beam from the Cu therapeutic target.     

An empirical model for megavoltage x-ray output factors

An empirical model of the factors that determine the central axis dose at 10 cm depth in water for 4 MV, 6 MV and 18 MV photon beams is presented. Backscattering from the variable collimators into the dose monitoring ionization chamber can cause a variation of -0.5% to +1.8% in the dose per monitor unit in accelerators with an electron facility. Forward emission towards the isocentre from the beam flattening filter and upper collimators is more dependent on the position of the upper variable collimator blades than the lower blades, so that they are not interchangeable in determining output factors, which can differ by up to 2%. The model includes the product of the monitor backscatter factor, normalized phantom scatter factor, normalized head scatter factor and inverse square law, corrected for the displacement of the virtual x-ray focus from the target. It can predict the dose to -/+0.83% for 4 MV, -/+0.80% for 6 MV photons and -/+0.82% for 18 MV photons. The normalized head scatter factor is a second-order polynomial of the modified equivalent square collimator, whose coefficients do not vary significantly with x-ray energy. The model was tested by comparison with independent measurements of output factor and generally agreed to around 1%.