E. S. M. Ali

Benchmarking EGSnrc in the kilovoltage energy range against experimental measurements of charged particle backscatter coefficients

This study benchmarks the EGSnrc Monte Carlo code in the energy range of interest to kilovoltage medical physics applications (5-140 keV) against experimental measurements of charged particle backscatter coefficients. The benchmark consists of experimental data from 20 different published experiments (1954-2007) covering 35 different elements (4<or=Z<or=92), electron and positron backscatter, normal and oblique incidence, and backscatter from thin films. EGSnrc simulation results show excellent agreement with the vast majority of the experimental data. Possible experimental and computational uncertainties explaining the few noted discrepancies are discussed. This study concludes that for the energy range of interest to kilovoltage medical physics application, EGSnrc produces backscatter results within approximately 4% of the average of the majority of published experimental data. A documented EGSnrc user-code customized for backscatter calculations is available from the authors at http://www.physics.carleton.ca/clrp/backscatter.

Efficiency improvements of x-ray simulations in EGSnrc user-codes using bremsstrahlung cross-section enhancement (BCSE)

This paper presents the implementation of the bremsstrahlung cross-section enhancement (BCSE) variance-reduction technique into the EGSnrc/BEAMnrc system. BCSE makes the simulation of x-ray production from bremsstrahlung targets more efficient; it does so by artificially making the rare event of bremsstrahlung emission more abundant, which increases the number of statistically-independent photons that contribute to reducing the variance of the quantity of interest without increasing the CPU time appreciably. BCSE does not perturb the charged-particle transport in EGSnrc and it is made compatible with all other variance-reduction techniques already used in EGSnrc and BEAMnrc, including range rejection, uniform bremsstrahlung splitting, and directional bremsstrahlung splitting. When optimally combining BCSE with splitting to simulate typical situations of interest in medical physics research and in clinical practice, efficiencies can be up to five orders of magnitude larger than those obtained with analog simulations, and up to a full order of magnitude larger than those obtained with optimized splitting alone (which is the state-of-the-art of the EGSnrc/BEAMnrc system before this study was carried out). This study recommends that BCSE be combined with the existing splitting techniques for all EGSnrc/BEAMnrc simulations that involve bremsstrahlung targets, both in the kilovoltage and megavoltage range. Optimum crosssection enhancement factors for typical situations in diagnostic x-ray imaging and in radiotherapy are recommended, along with an easy algorithm for simulation optimization.

Functional forms for photon spectra of clinical linacs

Specifying photon spectra of clinical linacs using a functional form is useful for many applications, including virtual source modelling and spectral unfolding from dosimetric measurements such as transmission data or depth-dose curves. In this study, 11 functional forms from the literature are compiled and quantitatively compared. A new function is proposed which offers improvements over existing ones. The proposed function is simple, physics-based and has four free parameters, one of which is the mean incident electron kinetic energy. A comprehensive benchmark set of validated, high-precision Monte Carlo spectra is generated and used to evaluate the strengths and limitations of different functions. The benchmark set has 65 spectra (3.5-30 MV) from Varian, Elekta, Siemens, Tomotherapy, Cyberknife and research linacs. The set includes spectra on- and off-axis from linacs with and without a flattening filter, and in treatment and imaging modes. The proposed function gives the lowest spectral deviations among all functions. It reproduces the energy fluence values in each bin for the benchmark set with a normalized root-mean-square deviation of 1.7%. The mean incident electron kinetic energy, maximum photon energy, most-probable energy and average energy are reproduced, on average, within 1.4%, 4.3%, 3.9% and 0.6% of their true values, respectively. The proposed function is well behaved when used for spectral unfolding from dosimetric data. The contribution of the 511 keV annihilation peak and the energy spread of the incident electron beam can be added as additional free parameters.

An improved physics-based approach for unfolding megavoltage bremsstrahlung spectra using transmission analysis

PURPOSE To develop a physics-based approach to improve the accuracy and robustness of the ill-conditioned problem of unfolding megavoltage bremsstrahlung spectra from transmission data. METHODS Spectra are specified using a rigorously-benchmarked functional form. Since ion chambers are the typical detector used in transmission measurements, the energy response of a Farmer chamber is calculated using the EGSnrc Monte Carlo code, and the effect of approximating the energy response on the accuracy of the unfolded spectra is studied. A proposal is introduced to enhance spectral sensitivity by combining transmission data measured with multiple detectors of different energy response and by combining data from multiple attenuating materials. Monte Carlo methods are developed to correct for nonideal exponential attenuation (e.g., scatter effects and secondary attenuation). The performance of the proposed methods is evaluated for a diverse set of validated clinical spectra (3.5-25 MV) using analytical transmission data with simulated experimental noise. RESULTS The approximations commonly used in previous studies for the ion-chamber energy response lead to significant errors in the unfolded spectra. Of the configurations studied, the one with best spectral sensitivity is to measure four full transmission curves using separate low-Z and high-Z attenuators in conjunction with two detectors of different energy response (the authors propose a Farmer-type ion chamber, once with a low-Z, and once with a high-Z buildup cap material), then to feed the data simultaneously to the unfolding algorithm. Deviations from ideal exponential attenuation are as much as 1.5% for the smallest transmission signals, and the proposed methods properly correct for those deviations. The transmission data with enhanced spectral sensitivity, combined with the accurate and flexible spectral functional form, lead to robust unfolding without requiring a priori knowledge of the spectrum. Compared with the commonly-used methods, the accuracy is improved for the unfolded spectra and for the unfolded mean incident electron kinetic energy by at least factors of three and four, respectively. With simulated experimental noise and a lowest transmission of 1%, the unfolded energy fluence spectra agree with the original spectra with a normalized root-mean-square deviation, %Δ(ψ), of 2.3%. The unfolded mean incident electron kinetic energies agree, on average, with the original values within 1.4%. A lowest transmission of only 10% still allows unfolding with %Δ(ψ) of 3.3%. CONCLUSIONS In the presence of realistic experimental noise, the proposed approach significantly improves the accuracy and robustness of the spectral unfolding problem for all therapy and MV imaging beams of clinical interest.

Energy spectra and angular distributions of charged particles backscattered from solid targets

In this study, the EGSnrc (Electron Gamma Shower) Monte Carlo radiation transport code is used to simulate the energy spectra and the angular distributions of charged particles backscattered from solid targets. The study covers the energy range 10–70 keV, which is of interest to applied physics fields such as scanning electron microscopy, microprobe analysis and x-ray imaging. Simulation results are compared with experimental data from 11 different published experiments (1954–2002). Comparisons include electrons and positrons, low- and high-Z targets, normal and oblique incidence, different backscatter angles and backscatter planes, and backscatter from thin films. EGSnrc simulation results show excellent agreement with the majority of the published experimental data. Possible experimental and computational uncertainties explaining the few noted discrepancies are discussed. This study concludes that EGSnrc produces accurate backscatter data in the kilovoltage energy range. A documented EGSnrc user-code customized for backscatter calculations is available from the authors at http://www.physics.carleton.ca/clrp/backscatter.

Quantifying the effect of off-focal radiation on the output of kilovoltage x-ray systems.

In a typical x-ray tube, off-focal radiation is mainly generated by the backscattered electrons that reenter the anode outside the focal spot. In this study, BEAMnrc (an EGSnrc user-code) is modified to simulate off-focal radiation. The modified BEAMnrc code is used to study the characteristics of electrons that backscatter from the anode, and to quantify their effect on the output of typical x-ray systems. Results show that the first generation backscatter coefficient is ∼50% for tungsten anodes at diagnostic energies, and ∼38% for molybdenum anodes at mammography energies. Second and higher generations of backscatter have a relatively minor contribution. At the patient plane, our simulation results are in excellent agreement with experimental measurements in the literature for the spectral shape of both the primary and the off-focal components, and also for the integral off-focal-to-primary ratio. The spectrum of the off-focal component at the patient plane is softer than the primary, which causes a slight softening in the overall spectrum. For typical x-ray systems, the off-focal component increases patient exposure (for a given number of incident primary electrons) by up to 11% and reduces the half-value layer and the effective energy of the average spectrum by up to 7% and 3%, respectively. The larger effects are for grounded cathode tubes, smaller interelectrode distance, higher tube voltage, lighter filtration, and less collimation. Simulation time increases by ∼30% when the off-focal radiation is included, but the overall simulation time remains of the order of a few minutes. This study concludes that the off-focal radiation can have a non-negligible effect on the output parameters of x-ray systems and that it should be included in x-ray tube simulations for more realistic modeling of these systems.

Unfolding linac photon spectra and incident electron energies from experimental transmission data, with direct independent validation

PURPOSE In a recent computational study, an improved physics-based approach was proposed for unfolding linac photon spectra and incident electron energies from transmission data. In this approach, energy differentiation is improved by simultaneously using transmission data for multiple attenuators and detectors, and the unfolding robustness is improved by using a four-parameter functional form to describe the photon spectrum. The purpose of the current study is to validate this approach experimentally, and to demonstrate its application on a typical clinical linac. METHODS The validation makes use of the recent transmission measurements performed on the Vickers research linac of National Research Council Canada. For this linac, the photon spectra were previously measured using a NaI detector, and the incident electron parameters are independently known. The transmission data are for eight beams in the range 10-30 MV using thick Be, Al and Pb bremsstrahlung targets. To demonstrate the approach on a typical clinical linac, new measurements are performed on an Elekta Precise linac for 6, 10 and 25 MV beams. The different experimental setups are modeled using EGSnrc, with the newly added photonuclear attenuation included. RESULTS For the validation on the research linac, the 95% confidence bounds of the unfolded spectra fall within the noise of the NaI data. The unfolded spectra agree with the EGSnrc spectra (calculated using independently known electron parameters) with RMS energy fluence deviations of 4.5%. The accuracy of unfolding the incident electron energy is shown to be ∼3%. A transmission cutoff of only 10% is suitable for accurate unfolding, provided that the other components of the proposed approach are implemented. For the demonstration on a clinical linac, the unfolded incident electron energies and their 68% confidence bounds for the 6, 10 and 25 MV beams are 6.1 ± 0.1, 9.3 ± 0.1, and 19.3 ± 0.2 MeV, respectively. The unfolded spectra for the clinical linac agree with the EGSnrc spectra (calculated using the unfolded electron energies) with RMS energy fluence deviations of 3.7%. The corresponding measured and EGSnrc-calculated transmission data agree within 1.5%, where the typical transmission measurement uncertainty on the clinical linac is 0.4% (not including the uncertainties on the incident electron parameters). CONCLUSIONS The approach proposed in an earlier study for unfolding photon spectra and incident electron energies from transmission data is accurate and practical for clinical use.

Detailed high-accuracy megavoltage transmission measurements: A sensitive experimental benchmark of EGSnrc

PURPOSE There are three goals for this study: (a) to perform detailed megavoltage transmission measurements in order to identify the factors that affect the measurement accuracy, (b) to use the measured data as a benchmark for the EGSnrc system in order to identify the computational limiting factors, and (c) to provide data for others to benchmark Monte Carlo codes. METHODS Transmission measurements are performed at the National Research Council Canada on a research linac whose incident electron parameters are independently known. Automated transmission measurements are made on-axis, down to a transmission value of ∼1.7%, for eight beams between 10 MV (the lowest stable MV beam on the linac) and 30 MV, using fully stopping Be, Al, and Pb bremsstrahlung targets and no fattening filters. To diversify energy differentiation, data are acquired for each beam using low-Z and high-Z attenuators (C and Pb) and Farmer chambers with low-Z and high-Z buildup caps. Experimental corrections are applied for beam drifts (2%), polarity (2.5% typical maximum, 6% extreme), ion recombination (0.2%), leakage (0.3%), and room scatter (0.8%)-the values in parentheses are the largest corrections applied. The experimental setup and the detectors are modeled using EGSnrc, with the newly added photonuclear attenuation included (up to a 5.6% effect). A detailed sensitivity analysis is carried out for the measured and calculated transmission data. RESULTS The developed experimental protocol allows for transmission measurements with 0.4% uncertainty on the smallest signals. Suggestions for accurate transmission measurements are provided. Measurements and EGSnrc calculations agree typically within 0.2% for the sensitivity of the transmission values to the detector details, to the bremsstrahlung target material, and to the incident electron energy. Direct comparison of the measured and calculated transmission data shows agreement better than 2% for C (3.4% for the 10 MV beam) and typically better than 1% for Pb. The differences can be explained by acceptable photon cross section changes of ≤0.4%. CONCLUSIONS Accurate transmission measurements require accounting for a number of influence quantities which, if ignored, can collectively introduce errors larger than 10%. Accurate transmission calculations require the use of the most accurate data and physics options available in EGSnrc, particularly the more accurate bremsstrahlung angular sampling option and the newly added modeling of photonuclear attenuation. Comparison between measurements and calculations implies that EGSnrc is accurate within 0.2% for relative ion chamber response calculations. Photon cross section uncertainties are the ultimate limiting factor for the accuracy of the calculated transmission data (Monte Carlo or analytical).

Sci—Thur PM: YIS — 02: A validated approach for clinical linacs to accurately determine the photon spectra and the incident electron energy

In clinical photon beams, independent determination of the photon spectra and the incident electron energy is useful for beam (re)commissioning and for detector response modelling. In this study, an approach is developed for that purpose, and validated on a research linac whose photon spectra and electron beams are directly and independently known. In this approach, an optimized combination of transmission curves is measured using multiple attenuators and detectors to maximize energy differentiation. For validation, transmission measurements are made for 8 beams from 10-30 MV, with bremsstrahlung targets from Be to Pb. A protocol is established to account for many influence quantities including linac drifts (2%), polarity (6%), ion recombination (0.2%), leakage (0.3%), room scatter (0.8%), non-ideal attenuation (1.5%), attenuator mass thickness (4%), and photonuclear effect (5.6%). The experimental accuracy on the smallest signals is 0.4%. EGSnrc is upgraded to model photonuclear attenuation (without tracking secondary particles), and then used to model the full experiment. For direct transmission comparisons, the agreement is 2%. This allows for an estimate of 0.5% on the upper limit of photon cross section uncertainties, which is much better than the current estimate of 1-2%. The unfolded spectra agree with the benchmark ones within 4.5%. The incident electron energy is accurate within 5%, with 95% confidence. The overall improvement over the commonly used methods is a factor of 3. This transmission study is the first to independently determine the incident electron energy, and to recognize the significant role of the photonuclear effect at higher energies.

TH‐E‐BRC‐09: Beyond Self‐Consistency in Beam Commissioning: Determination of True Linac Spectra

Purpose: To develop a method for reliably unfolding the true spectra of clinical photonbeams using simple depth‐ionization measurements, and to validate the method using other independent spectral measurements. Methods and Materials: An accurate and flexible functional form to represent photon spectra is developed and benchmarked against a comprehensive set of 68 realistic spectra. A monoenergetic depth‐ionization kernel is generated using EGSnrc. Electron contamination is included using a validated one‐parameter model. Depth‐ionization measurements are performed on a Vickers research linac for three energies (10, 15, 20 MV) and three targets (Be, Al, Pb). The Vickers electron beam parameters are independently known to 0.4%, and its spectra have been previously measured using a NaI detector (i.e. the true spectra are known). Measurements are also performed on clinical beams (Elekta Precise 6, 10 and 25 MV) both on‐ and off‐axis to extract off‐axis softening. Independent transmission measurements are performed on the same two machines using multiple detectors with different energy responses and multiple attenuating materials to improve energy differentiation. Experimental and Monte Carlo methods are used to correct for attenuator scatter, polarity and beam instabilities. Results: Spectra unfolded from depth‐ionization data agree well with those unfolded from transmission data and with previous NaI measurements. Electron contamination is reproduced within 1% of the maximum dose. Photon spectra from electron beams with more than 5% mean energy difference are resolvable. Off‐axis softening can be extracted. Conclusions: Despite the ill‐conditioned nature of spectral unfolding, this study shows that when the full potential of the new approach is used, it is possible to unfold the true photon spectra from basic clinical measurements without prior knowledge of the linac head or incident electron beam. The proposed method is a significant improvement over the ‘self‐tuning’ approach that is currently being used in beam commissioning. E. Ali acknowledges the funding from an NSERC Vanier CGS. D. Rogers acknowledges the funding from CRC, CFI and OIT.