Electron spectra derived from depth dose distributions

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

Determining clinical photon beam spectra from measured depth dose with the Cimmino algorithm

A method to determine the spectrum of a clinical photon beam from measured depth-dose data is described. At shallow depths, where the range of Compton-generated electrons increases rapidly with photon energy, the depth dose provides the information to discriminate the spectral contributions. To minimize the influence of contaminating electrons, small (6 x 6 cm2) fields were used. The measured depth dose is represented as a linear combination of basis functions, namely the depth doses of monoenergetic photon beams derived by Monte Carlo simulations. The weights of the basis functions were obtained with the Cimmino feasibility algorithm, which examines in each iteration the discrepancy between predicted and measured depth dose. For 6 and 15 MV photon beams of a clinical accelerator, the depth dose obtained from the derived spectral weights was within about 1% of the measured depth dose at all depths. Because the problem is ill conditioned, solutions for the spectrum can fluctuate with energy. Physically realistic smooth spectra for these photon beams appeared when a small margin (about +/- 1%) was attributed to the measured depth dose. The maximum energy of both derived spectra agreed with the measured energy of the electrons striking the target to within 1 MeV. The use of a feasibility method on minimally relaxed constraints provides realistic spectra quickly and interactively.     

Monte Carlo studies of the exit photon spectra and dose to a metal/phosphor portal imaging screen

The energy spectra and the dose to a Cu plate/Gd2O2S phosphor portal imaging detector were investigated for monoenergetic incident beams of photons (1.25, 2, and 5 MeV). The Monte Carlo method was used to characterize the influence of the patient/detector geometry, detector material and design, and incident beam energy on the spectral distribution and the dose, at the imaging detector plane, of a photon beam scattered from a water phantom. The results show that radiation equilibrium is lost in the air gap and that, for the geometries studied, this effect led to a reduction in the exit dose of up to 40%. The finding that the effects of the air gap and field size are roughly complementary has led to the hypothesis that an equivalent field size concept may be used to account for intensity and spectral changes arising from air gap variations. The copper plate preferentially attenuates the low-energy scattered photons incident on it, while producing additional annihilation, bremsstrahlung, and scattered photons. As a result, the scatter spectra at the copper surface entrance of the detector differs significantly from that at the Cu/phosphor interface. In addition, the mean scattered photon energy at the interface was observed to be roughly 0.4 MeV higher than the corresponding effective energy for 2 MeV incident beams. A comparison of the dose to various detector materials showed that exit dosimetry errors of up to 24% will occur if it is assumed that the Cu plate/Gd2O2S phosphor detector is water equivalent.     

Finding mechanisms responsible for the spectral distribution of electron beams produced by a linear accelerator

The measured electron spectra of linear accelerators from several manufacturers differ in comparison to the spectral form and width. As part of our investigations of linac performance and stability, we analyzed the electron spectra of our linacs. After building a spectrometer the electron spectra were measured. The measured spectral widths were comparable with the results published in the literature. It appeared that the phase of the recycled radio pulse in combination with the limited bandwidth of the bending magnet are responsible for unusual (multipeak) electron spectra. The scatter filters only have a relatively small widening effect on the spectrum. There was no indication that multipeak or wide spectra are related to linac instabilities.     

Benchmarking of Monte Carlo simulation of bremsstrahlung from thick targets at radiotherapy energies

Several Monte Carlo systems were benchmarked against published measurements of bremsstrahlung yield from thick targets for 10-30 MV beams. The quantity measured was photon fluence at 1 m per unit energy per incident electron (spectra), and total photon fluence, integrated over energy, per incident electron (photon yield). Results were reported at 10-30 MV on the beam axis for Al and Pb targets and at 15 MV at angles out to 90 degrees for Be, Al, and Pb targets. Beam energy was revised with improved accuracy of 0.5% using an improved energy calibration of the accelerator. Recently released versions of the Monte Carlo systems EGSNRC, GEANT4, and PENELOPE were benchmarked against the published measurements using the revised beam energies. Monte Carlo simulation was capable of calculation of photon yield in the experimental geometry to 5% out to 30 degrees, 10% at wider angles, and photon spectra to 10% at intermediate photon energies, 15% at lower energies. Accuracy of measured photon yield from 0 to 30 degrees was 5%, 1 s.d., increasing to 7% for the larger angles. EGSNRC and PENELOPE results were within 2 s.d. of the measured photon yield at all beam energies and angles, GEANT4 within 3 s.d. Photon yield at nonzero angles for angles covering conventional field sizes used in radiotherapy (out to 10 degrees), measured with an accuracy of 3%, was calculated within 1 s.d. of measurement for EGSNRC, 2 s.d. for PENELOPE and GEANT4. Calculated spectra closely matched measurement at photon energies over 5 MeV. Photon spectra near 5 MeV were underestimated by as much as 10% by all three codes. The photon spectra below 2-3 MeV for the Be and Al targets and small angles were overestimated by up to 15% when using EGSNRC and PENELOPE, 20% with GEANT4. EGSNRC results with the NIST option for the bremsstrahlung cross section were preferred over the alternative cross section available in EGSNRC and over EGS4. GEANT4 results calculated with the "low energy" physics list were more accurate than those calculated with the "standard" physics list.     

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 significance of electron binding corrections in Monte Carlo photon transport calculations

Many Monte Carlo simulations ignore coherent scattering events and utilise the Klein-Nishina free electron distribution, rather than the incoherent differential cross-section, for choosing the trajectories of incoherently scattered photons. We assess the accuracy of this model by comparing its results with those of the complete bound electron model (form factor approach), which simulates coherent scattering events, and uses the appropriate bound electron angular scattering distributions. Both analytic and Monte Carlo calculations demonstrate that use of the free electron scattering distributions significantly underestimates the angular distribution of scattered photon energy resulting from low and medium energy photons incident upon carbon, iron, and platinum barriers. In using the free electron approximations to calculate barrier transmission, significant errors occur only for primary photon energies below 100 keV. Implementation of the complete bound electron model reduces the computational efficiency of our Monte Carlo code by only 10-25%.     

Dosimetric characteristics of dynamic wedged fields: a Monte Carlo study.

We have developed a Monte Carlo (MC) technique using the EGS4/BEAM system to calculate dosimetric characteristics of dynamic wedges (DW) for photon beam radiotherapy. The simulation of DW was accomplished by weighting the history numbers of the electrons, which are incident on the target in accordance with the segmented treatment table. Calculations were performed for DW with wedge angles ranging from 15 degrees to 60 degrees as well as for open fields with different field sizes for both degrees 6 and 18 MV beams. The MC-calculated percentage depth dose (PDD) and beam profiles agreed with the measurements within +/- 2% (of the dose maximum along the beam axis) or +/- 2 mm in high dose gradient region. The DW slightly affects energy spectra of photons and contaminating electrons. These slight changes have no significant effects on PDD as compared to the open field. The MC-calculated dynamic wedge factors agree with the measurements within +/- 2%. The MC method enables us to provide more detailed beam characteristics for DW fields than a measurement method. This beam characteristic includes photon energy spectra, mean energy, spectra of contaminating electrons and effects of moving jaw on off-axis beam quality. These data are potentially important for treatment planning involving dynamic wedges.     

Absolute dose measurements by means of a small cylindrical ionization chamber for very high dose per pulse high energy electron beams

Very high dose per pulse (3-13 cGy/pulse) high energy electron beams are currently produced by special linear accelerators (linac) dedicated to Intra Operative Radiation Therapy (IORT). The electron beams produced by such linacs are collimated by special Perspex applicators of various size and cylindrically shaped. The biggest problems from the dosimetric point of view are caused by the high dose-per-pulse values and the use of inclined applicators. In this work measurements of absolute dose for the inclined applicators were done by using a small cylindrical ionization chamber, type CC01 (Wellhofer), a parallel plane ionization chamber type Markus (PTW 23343) and radiochromic films type EBT. We show a method which allows calculating the quality correction factors for CC01 chamber with an uncertainty of 1% and the absolute dose value for the inclined applicators using CC01 with an uncertainty of 3.1% for electron beams of energy of 6 and 7 MeV produced by the linac dedicated to IORT Novac7.     

A standard timing benchmark for EGS4 Monte Carlo calculations.

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

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.     

正交电子束和X射线照射野衔接的剂量学分析

正交电子野和光子野衔接区域,一定会有剂量热点和冷点出现,剂量分布不均匀程度与治疗机的物理参数直接相关.本文通过测量了Elekta Precise 治疗机和Elekta Synergy 治疗机X射线和电子线的部分剂量学参数,对正交电子束和X(γ)射线照射野的衔接区域内的剂量分布的不均匀程度进行了定量分析,提出用扩展光子野半影的方法来降低剂量分布的不均匀程度,比较了不同治疗机条件下衔接区域内的剂量分布.结果表明,无论是在未扩展光子野半影的情况下,还是在扩展了光子野半影的情况下,与使用Elekta Precise 治疗机相比,使用光子射野半影较小的Elekta Synergy 治疗机,电子野与光子野衔接区域内的剂量不均匀程度更强.     

Fast modelling of spectra and stopping-power ratios using differentiated fluence pencil kernels

Modern radiotherapy steadily utilizes more of the available degrees of freedom provided by radiotherapy equipment, raising the need for the dosimetric methods to deliver reliable measurements for situations where the spectral properties of the radiation field may also vary. A kernel-based superposition method is presented for which the spectra from any field modulation can be instantly calculated, thus facilitating the determination of dosimetric quantities at arbitrary locations. A database of fluence pencil kernels describing the fluence resulting from point monodirectional monoenergetic beams incident onto a water phantom has been calculated with the PENELOPE-2005 Monte Carlo package. Spectra calculated by means of the kernels are presented for various 6 MV fields. The spectra have been used to investigate depth and lateral variations of water-to-air stopping-power ratios. Results show that the stopping-power ratio decreases with depth, and that this effect is more pronounced for small fields. These variations are clearly connected to spectral variations. For a 10 x 10 cm(2) field, the difference between the stopping-power ratio at 2.5 cm depth and 30 cm depth is less than 0.3% while for a 0.3 x 0.3 cm(2) field this difference is 0.7%. Ratios outside the field were found to be sensitive to the collimator leakage spectral variations.     

Dosimetric study of the new Intersource125 iodine seed.

The use of low energy photon emitters for brachytherapy applications, as in the treatment of the prostate or of eye tumors, has significantly increased these last few years. New seed models for 125I have been recently introduced. The aim of this study is to determine the dosimetric parameters as recommended by the AAPM in the TG43 formalism for a new iodine seed design: the InterSource125 (Furnished by IBt, Seneffe, Belgium). Measurements are made with LiF thermoluminescent dosimeters (size of 1 mm3) in solid water phantoms to obtain the dose constant, the radial dose function, and the anisotropy function. The TLDs were calibrated at 6 MV and an energy correction factor of 1.41 has been applied. The same dose parameters are also obtained by Monte Carlo calculations (MCNP4B) in solid water and in liquid water. The radial function was measured at 1, 1.5, 2, 3, 4, 5, 6, and 7 cm and calculated between 0.3 and 7 cm. The anisotropy functions were measured at 2, 3, and 5 cm and calculated between 0.3 and 7 cm. The calculated and the measured TG43 functions for solid water are in excellent agreement. We have then calculated these functions in liquid water to obtain the dosimetric information for clinical applications as per TG43 recommendations. In WTI, the calculated dose rate constant is 0.98+/-1% and the measured value is 1.03 +/- 7 %. The calculated value for water is 1.02+/- 1 %. In conclusion, the dosimetric functions for the new iodine seed InterSource125 have been determined. They are quite different from the data of the well-known model 6711 from Amersham due to the absence of silver in the new seed. The characteristics are very similar to those of model 6702.     

Monte Carlo study of Siemens PRIMUS photoneutron production

Neutron production in radiotherapy facilities has been studied from the early days of modern linacs. Detailed studies are now possible using photoneutron capabilities of general-purpose Monte Carlo codes at energies of interest in medical physics. The present work studies the effects of modelling different accelerator head and room geometries on the neutron fluence and spectra predicted via Monte Carlo. The results from the simulation of a 15 MV Siemens PRIMUS linac show an 80% increase in the fluence scored at the isocentre when, besides modelling the components necessary for electron/photon simulations, other massive accelerator head components are included. Neutron fluence dependence on inner treatment room volume is analysed showing that thermal neutrons have a 'gaseous' behaviour and then a 1/V dependence. Neutron fluence maps for three energy ranges, fast (E > 0.1 MeV), epithermal (1 eV < E < 0.1 MeV) and thermal (E < 1 eV), are also presented and the influence of the head components on them is discussed.     

Photon scatter in portal images: physical characteristics of pencil beam kernels generated using the EGS Monte Carlo code

Pencil beam kernels describing scattered photon fluence behind homogeneous water slabs at various air gap distances were generated using the EGS Monte Carlo code. Photon scatter fluence was scored in separate bins based on the particle's history: singly scattered, multiply scattered, and bremsstrahlung and positron annihilation photons. Simultaneously, the mean energy and mean angle with respect to the incident photon pencil beam were tallied. Kernels were generated for incident photon pencil beams exhibiting monoenergetic spectra of 2.0 and 10.0 MeV, and polyenergetic spectra representative of 6 and 24 MV beams. Reciprocity was used to generate scatter fractions on the central axis for various field sizes, phantom thicknesses, and air gaps. The scatter kernels were further characterized by full width at half-maximum estimates. Modulation transfer functions were calculated, providing theoretical estimates of the limit of performance of portal imaging systems due to the intrinsic scattering of photon radiation through the patient.     

Compton-scattering measurement of diagnostic x-ray spectrum using high-resolution Schottky CdTe detector

The analysis of x-ray spectra is important for quality assurance (QA) and quality control (QC) of radiographic systems. The aim of this study is to measure the diagnostic x-ray spectra under clinical conditions using a high-resolution Schottky CdTe detector. Under clinical conditions, the direct measurement of a diagnostic spectrum is difficult because of the high photon fluence rates that cause significant detector photon pile-up. An alternative way of measuring the output spectra from a tube is first to measure the 90 deg Compton scattered photons from a given sample. With this set-up detector, pile-up is not a problem. From the scattered spectrum one can then use an energy correction and the Klein-Nishina function to reconstruct the actual spectrum incident upon the scattering sample. The verification of whether our spectra measured by the Compton method are accurate was accomplished by comparing exposure rates calculated from the reconstructed spectra to those measured with an ionization chamber. We used aluminum (Al) filtration ranging in thickness from 0 to 6 mm. The half value layers (HVLs) obtained for a 70 kV beam were 2.78 mm via the ionization chamber measurements and 2.93 mm via the spectral measurements. For a 100 kV beam we obtained 3.98 and 4.32 mm. The small differences in HVLs obtained by both techniques suggest that Compton scatter spectroscopy with a Schottky CdTe detector is suitable for measuring the diagnostic x-ray spectra and useful for QA and QC of clinical x-ray equipment.     

Dosimetric discrepancies caused by differing MLC parameters for dynamic IMRT

Radiotherapy patients will from time to time be treated on another linac than originally planned due to service or logistical challenges. For patients treated with dynamic intensity modulated radiotherapy (IMRT), extra care should be taken to make sure the delivered dose remains as planned. Four linacs with the same type of dynamic multileaf collimator (MLC) were compared to find a general prediction of the potential dosimetric error caused by treating IMRT patients on another linac without recalculating the treatment plan. The MLC parameters, transmission and dosimetric leaf separation (DLS) were measured for all four linacs. The dynamic fields that were measured to find the DLS value were imported into the treatment planning system to compare the calculated and measured doses. Measured values of transmission and DLS were used directly in the calculations to obtain dose differences of less than 1% between the calculated and measured doses at the reference setup. The dosimetric discrepancy between the linacs was acceptable for all but one linac. Recalculation of the treatment plan therefore remains as standard procedure for this linac when a planned patient must switch linac during the course of treatment. The depth and field size dependences of the MLC parameters were also tested, finding dose differences of up to 4%.     

A robust method for determining the absorbed dose to water in a phantom for low-energy photon radiation

The application of more and more low-energy photon radiation in brachytherapy-either in the form of low-dose-rate radioactive seeds such as Pd-103 or I-125 or in the form of miniature x-ray tubes-has induced greater interest in determining the absorbed dose to water in water in this energy range. As it seems to be hardly feasible to measure the absorbed dose with calorimetric methods in this low energy range, ionometric methods are the preferred choice. However, the determination of the absorbed dose to water in water by ionometric methods is difficult in this energy range. With decreasing energy, the relative uncertainty of the photon cross sections increases and as the mass energy transfer coefficients show a steep gradient, the spectra of the radiation field must be known precisely. In this work two ionometric methods to determine the absorbed dose to water are evaluated with respect to their sensitivity to the uncertainties of the spectra and of the atomic database. The first is the measurement of the air kerma free in air and the application of an MC-based conversion factor to the absorbed dose to water. The second is the determination of the absorbed dose to water by means of an extrapolation chamber as an integral part of a phantom. In the complementing MC-calculations, two assortments of spectra each of which is based on a separate unfolding procedure were used as well as two kinds of databases: the standard PEGS and the recently implemented NIST database of EGSnrc. Experimental results were obtained by using a parallel-plate graphite extrapolation chamber and a free-air chamber. In the case when the water kerma in a phantom is determined from the measurements of air kerma free in air, differences in the order of 10% were found, according to which the database or the kind of spectrum is used. In contrast to this, for the second method, the differences found were about 0.5%.     

Dynamic wedge versus physical wedge: a Monte Carlo study

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.