Stopping-power ratios and their uncertainties for clinical electron beam dosimetry

Evaluation of latent variances in Monte Carlo dose calculations with Varian TrueBeam photon phase-spaces used as a particle source

The purpose of this study was to evaluate the latent variance (LV) of Varian TrueBeam photon phase-space files (PSF) for open 10  ×  10 cm² and small stereotactic fields and estimate the number of phase spaces required to be summed up in order to maintain sub-percent LV in Monte Carlo (MC) dose calculations. BEAMnrc/DOSXYZnrc software was used to transport particles from Varian phase-space files (PSF_A) through the secondary collimators. Transported particles were scored into another phase-space located under the jaws (PSF_B), or transported further through the cone collimators and scored straight below, forming PSF_C. Phase-space files (PSF_B) were scored for 6 MV-FFF, 6 MV, 10 MV-FFF, 10 MV and 15 MV beams with 10  ×  10 cm² field size, and PSF_C were scored for 6 MV beam under circular cones of 0.13, 0.25, 0.35, and 1 cm diameter. Both PSF_B and PSF_C were transported into a water phantom with particle recycling number ranging from 10 to 1000. For 10  ×  10 cm² fields 0.5  ×  0.5  ×  0.5 cm³ voxels were used to score the dose, whereas the dose was scored in 0.1  ×  0.1  ×  0.5 cm³ voxels for beams collimated with small cones. In addition, for small 0.25 cm diameter cone-collimated 6 MV beam, phantom voxel size varied as 0.02  ×  0.02  ×  0.5 cm³, 0.05  ×  0.05  ×  0.5 cm³ and 0.1  ×  0.1  ×  0.5 cm³. Dose variances were scored in all cases and LV evaluated as per Sempau et al. For the 10  ×  10 cm² fields calculated LVs were greatest at the phantom surface and decreased with depth until they reached a plateau at 5 cm depth. LVs were found to be 0.54%, 0.96%, 0.35%, 0.69% and 0.57% for the 6 MV-FFF, 6 MV, 10 MV-FFF, 10 MV and 15 MV energies, respectively at the depth of 10 cm. For the 6 MV phase-space collimated with cones of 0.13, 0.25, 0.35, 1.0 cm diameter, the LVs calculated at 1.5 cm depth were 75.6%, 25.4%, 17.6% and 8.0% respectively. Calculated LV for the 0.25 cm cone-collimated 6 MV beam were 61.2%, 40.7%, 22.5% in 0.02  ×  0.02  ×  0.5 cm³, 0.05  ×  0.05  ×  0.5 cm³ and 0.1  ×  0.1  ×  0.5 cm³ voxels respectively. In order to achieve sub-percent LV in open 10  ×  10 cm² field MC simulations a single PSF can be used, whereas for small SRS fields (0.13-1.0 cm) more PSFs (66-8 PSFs) would have to be summed.

Advances in the determination of absorbed dose to water in clinical high-energy photon and electron beams using ionization chambers

During the last two decades, absorbed dose to water in clinical photon and electron beams was determined using dosimetry protocols and codes of practice based on radiation metrology standards of air kerma. It is now recommended that clinical reference dosimetry be based on standards of absorbed dose to water. Newer protocols for the dosimetry of radiotherapy beams, based on the use of an ionization chamber calibrated in terms of absorbed dose to water, N(D,w), in a standards laboratory's reference quality beam, have been published by several national or regional scientific societies and international organizations. Since the publication of these protocols multiple theoretical and experimental dosimetry comparisons between the various N(D,w) based recommendations, and between the N(D,w) and the former air kerma (NK) based protocols, have been published. This paper provides a comprehensive review of the dosimetry protocols based on these standards and of the intercomparisons of the different protocols published in the literature, discussing the reasons for the observed discrepancies between them. A summary of the various types of standards of absorbed dose to water, together with an analysis of the uncertainties along the various steps of the dosimetry chain for the two types of formalism, is also included. It is emphasized that the NK-N(D,air) and N(D,w) formalisms have very similar uncertainty when the same criteria are used for both procedures. Arguments are provided in support of the recommendation for a change in reference dosimetry based on standards of absorbed dose to water.

Influence of initial electron beam characteristics on monte carlo calculated absorbed dose distributions for linear accelerator electron beams

The least known parameters in a Monte Carlo simulation of a linear accelerator treatment head are often the properties of the initial electron beam directed onto the exit vacuum window. Several initial beams with different spatial fluence distributions, angular divergences and energy spectra have been transported through the geometry of a scattering foil accelerator. The electron beam characteristics (energy spectrum and angular distribution) at the phantom surface and the subsequent relative absorbed dose distribution in a water phantom were calculated. The dose distribution was found to be insensitive to the geometrical properties of the initial beam. Furthermore, the lateral dose profiles are unaffected by the energy spectrum of the initial beam. The effect on the depth-dose curve is negligible if the initial energy spectrum is symmetric (e.g., Gaussian shaped) and its full width at half maximum (FWHM) is less than approximately 10% of the most probable energy. A larger FWHM will decrease the normalized dose gradient, but will not affect the dose in the build-up region. An asymmetric wedge shaped spectrum with a low-energy extension simultaneously increases the dose in the build-up region and decreases the dose gradient. The relationship between the energy spectral width and the normalized dose gradient is, however, smaller than published analytical expressions indicate. Some well-established energy-range relationships were shown to be accurate for most of the initial beams studied. The energy spectrum at the phantom surface was also derived from a measured depth-dose curve through different methods. The extracted spectrum depends on the beam model and the spectral reconstruction algorithm. Even though the depth-dose curve is fairly independent of initial beam characteristics, a correct description of the low-energy tail of the energy spectrum is important to obtain good agreement between measured and Monte Carlo calculated doses in the build-up region.

Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy

Degraded electron beams, as used for intraoperative radiation therapy (IORT) or similar complicated dosimetric situations, have different characteristics compared to conventional electron therapy beams. If international dosimetry protocols are applied in a direct manner to such degraded beams, uncertainties will be introduced in the absorbed dose determination. The Monte Carlo method has been used to verify experimentally determined relative absorbed dose distributions and output factors in an IORT geometry. Monte Carlo generated dose distributions are mostly within +/-2% or +/-2 mm of measured data. The simulated output variation between the IORT cones (relative output factors) are mostly within 2% of measured values. By comparing IORT and conventional electron beam characteristics (e.g. energy spectra, angular distributions and the contributions of different system components to these quantities) limitations and uncertainties of commonly used dosimetric techniques in IORT electron fields are quantified. The intraoperative treatment field contains a larger amount of scattered electrons, which leads to a broader energy spectrum as well as a wider angular distribution of electrons at the phantom surface. The dose from the scattered electrons can contribute up to 40% of the total dose at a depth of dose maximum, compared to approximately 10% for standard beams. A study of the energy spectra at the reference depth reveals that an uncertainty of the order of 1% can be introduced if ionization chamber based dosimetry is used to determine output factors for the investigated IORT system. We recommend that relative absorbed dose distributions and output factors in IORT electron beams and for similar complicated dosimetric situations should be determined with detectors having a small energy and angular dependence (e.g. diamond detectors or p-Si diodes).

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.

Monte Carlo modelling of electron beams from medical accelerators

Monte Carlo simulation of radiation transport is considered to be one of the most accurate methods of radiation therapy dose calculation. With the rapid development of computer technology, Monte Carlo based treatment planning for radiation therapy is becoming practical. A basic requirement for Monte Carlo treatment planning is a detailed knowledge of the radiation beams from medical accelerators. A practical approach to obtain the above is to perform Monte Carlo simulation of radiation transport in the medical accelerator. Additionally, Monte Carlo modelling of the treatment machine head can also improve our understanding of clinical beam characteristics, help accelerator design and improve the accuracy of clinical dosimetry by providing more realistic beam data. This paper summarizes work over the past two decades on Monte Carlo simulation of clinical electron beams from medical accelerators.

Stopping-power ratios for clinical electron beams from a scatter-foil linear accelerator

Restricted mass collision stopping-power ratios for electron beams from a scatter-foil medical linear accelerator (Varian Clinac 2100C) were calculated for various combinations of beams, phantoms and detector materials using the Monte Carlo method. The beams were of nominal energy 6, 12 or 20 MeV, with square dimensions 1 x 1 cm2 to 10 x 10 cm2. They were incident at nominal SSDs of 100 or 120 cm and inclined at 90 degrees or 30 degrees to the surface of homogeneous water phantoms or water phantoms interspersed with layered lung or bone-like materials. The broad beam water-to-air stopping-power ratios were within 1.3% of the AAPM TG21 protocol values and consistent with the results of Ding et al to within 0.2%. On the central axis the stopping-power ratio variations for narrow beams compared with normally incident broad beams were 0.1% or less for water-to-LiF-100, graphite, ferrous sulfate dosimeter solution, polystyrene and PMMA, 0.5% for water-to-silicon and 1% for water-to-air and water-to-photographic-film materials. The transverse variations of the stopping-power ratios were up to 4% for water-to-silicon, 7% for water-to-photographic-film materials and 10% for water-to-air in the penumbral regions (where the dose was 10% of the global dose maximum) at shallow depths compared with the values at the same depths on the central axis. In the inhomogeneous phantoms studied, the stopping-power ratio correction factors varied more significantly for air, followed by photographic materials and silicon, at various depths on the central axis in the heterogeneous regions. For the simple layered phantoms studied, the estimation of the stopping-power ratio correction factors based on the relative electron-density derived effective depth approach yielded results that were within 0.5% of the Monte Carlo derived values for all the detector materials studied.

An algorithm to include the bremsstrahlung contamination in the determination of the absorbed dose in electron beams

None of the existing protocols or codes of practice for high-energy electron dosimetry take any account of the accelerator-generated bremsstrahlung always present in electron beams. This results in a systematic error in the derivation of the absorbed dose. The purpose of this study is to draw attention to this omission which affects the absorbed dose calibration. A method based on available experimental data is presented for dealing with this deficiency in electron dosimetry. A re-defined algorithm for absorbed dose derivation accounting for this bremsstrahlung component is proposed. The question of omission of the bremsstrahlung contamination is important in comparing ionization methods with other dosimetric methods such as calorimetry or the use of ferrous sulphate.

Measurement of Prepl Pwall factors in electron beams and in a 60Co beam for plane-parallel chambers

This paper describes a method to measure the product of Prepl Pwall correction factors for ionization chambers and presents our measured values of Prepl Pwall for Markus plane-parallel chambers in electron beams. It is shown that the measured values of Prepl Pwall can be fitted to an equation, Prepl Pwall = c1 + c2 R50 + c3 (R50)2, for Markus chambers at the new reference depth for electron beams (6 MeV < or = nominal energy E < or = 20 MeV). We also present our measured values of Prepl Pwall for NACP and Markus chambers in a water phantom irradiated in a 60Co beam.

Improvements in absorbed dose measurements for external radiation therapy using ferrous dosimeter gel and MR imaging (FeMRI)

A ferrous gel, based on ferrous (Fe) sulphate and agarose, was used with a clinical magnetic resonance imaging (MRI) scanner to obtain relative dose distribution data from therapeutic photon and electron beams. The FeMRI gel was scanned using a new MRI acquisition protocol optimized for T1 measurements. Thorough comparisons with silicon semiconductor detector and ionization chamber measurements, as well as with Monte Carlo calculations, were performed in order to quantify the improvements obtained using FeMRI for dose estimations. Most of the relative doses measured with FeMRI were within 2% of the doses measured with other methods. The larger discrepancies (2-4%) found at shallow depths are discussed. The uncertainty in relative dose measurements using FeMRI was significantly improved compared with previously reported results (5-10%, one standard deviation, 1 SD), and is today between 1.6% and 3.3% (depending on dose level, 2 SD). This corresponds to an improvement in the minimum detectable dose (3 SD above background) from approximately 2 Gy to better than 0.6 Gy. The results obtained in this study emphasize the importance of obtaining basic FeMRI dose data before the method is extended to complicated treatment regimes.

Experimental determination of fluence correction factors at depths beyond dmax for a Farmer type cylindrical ionization chamber in clinical electron beams

Recently, it has been recommended that electron beam calibrations be performed at a new reference depth [Burns et al., Med. Phys. 23, 383 (1996)] given by dref = 0.6R50-0.1 cm, where R50 is the depth of 50% depth dose. In order to calibrate electron beams at dref with a Farmer type cylindrical ionization chamber, the values of the perturbation correction factors Pwall and Pfl at dref are required. Using a parallel plate Holt chamber as a reference chamber, the product PwallPfl has been determined for a 6.1-mm-diameter PTW cylindrical ionization chamber at dref as a function of R50 of clinical electron beams (6 < or = nominal energy E < or = 22 MeV). Assuming that Pwall for the PTW chamber is unity in electron beams, the measured Pfl values ranged from 0.96 to 0.98 as the energy is increased. These results are in close agreement with recently reported calculated values. Determination of dref requires the knowledge of R50. A relation between I50 and R50 is given in the IAEA Protocol [TRS No. 277 (IAEA, Vieńna, 1987), pp. 1-98] for broad beams at SSD = 100 cm. It has been shown experimentally that the equation R50 = 1.029 x I50-0.063 cm, derived by Ding et al. [Med. Phys. 22, 489 (1995)] from Monte Carlo simulations of realistic clinical electron beams, can be used satisfactorily to obtain R50 from I50, where I50 is the depth of 50% ionization. The largest difference between the measured value of R50 and that calculated by using the above equation has been found to be about 1 mm at 22 MeV.

Accurate characterization of Monte Carlo calculated electron beams for radiotherapy

Monte Carlo studies of dose distributions in patients treated with radiotherapy electron beams would benefit from generalized models of clinical beams if such models introduce little error into the dose calculations. Methodology is presented for the design of beam models, including their evaluation in terms of how well they preserve the character of the clinical beam, and the effect of the beam models on the accuracy of dose distributions calculated with Monte Carlo. This methodology has been used to design beam models for electron beams from two linear accelerators, with either a scanned beam or a scattered beam. Monte Carlo simulations of the accelerator heads are done in which a record is kept of the particle phase-space, including the charge, energy, direction, and position of every particle that emerges from the treatment head, along with a tag regarding the details of the particle history. The character of the simulated beams are studied in detail and used to design various beam models from a simple point source to a sophisticated multiple-source model which treats particles from different parts of a linear accelerator as from different sub-sources. Dose distributions calculated using both the phase-space data and the multiple-source model agree within 2%, demonstrating that the model is adequate for the purpose of Monte Carlo treatment planning for the beams studied. Benefits of the beam models over phase-space data for dose calculation are shown to include shorter computation time in the treatment head simulation and a smaller disk space requirement, both of which impact on the clinical utility of Monte Carlo treatment planning.

The IPEMB code of practice for electron dosimetry for radiotherapy beams of initial energy from 2 to 50 MeV based on an air kerma calibration. Institution of Physics and Engineering in Medicine and Biology

This report contains the recommendations of the Electron Dosimetry Working Party of the UK Institution of Physics and Engineering in Medicine and Biology (IPEMB). The recommendations consist of a code of practice for electron dosimetry for radiotherapy beams of initial energy from 2 to 50 MeV. The code is based on the 2 MV (or 60Co) air kerma calibration of the NE 2561/2611 chamber, which is used as the transfer instrument between national standards laboratory and hospitals in the UK. The code utilizes an ND.air approach. Designated chambers are the NE 2571 (graphite-walled Farmer chamber), to be calibrated against the transfer instrument in a megavoltage photon beam, and three parallel-plate chambers, to be calibrated against the NE 2571 in a higher-energy electron beam. The practical code is supplemented by comprehensive discussion of the theoretical background and the sources and values of included data.

MMC--a high-performance Monte Carlo code for electron beam treatment planning

The macro Monte Carlo (MMC) method has been developed to improve the speed of traditional Monte Carlo (MC) high-energy electron transport calculations without loss in accuracy. The MMC algorithm uses results derived from conventional MC simulations of electron transport through macroscopic spheres of various radii and consisting of a variety of media. Based on these results, electrons are transported in macroscopic steps through the absorber. The absorber geometry is represented by a three-dimensional (3D) density matrix, typically derived from computer tomographic (CT) data. Energy lost by the electrons along their paths through the absorber is scored in a 3D dose matrix. Transport of secondary electrons and bremsstrahlung photons is taken into account. Major modifications of the original implementation of the MMC algorithm have resulted in an improved version of the code, resolving earlier problems with electron transport across interfaces of different materials, and running at a substantially higher speed. Furthermore, the code has been integrated into a clinical 3D treatment planning system. MMC results are in good agreement with results from conventional MC codes and are obtained with a speed gain of about one order of magnitude for clinically relevant irradiation situations. Calculation times to obtain a relative statistical accuracy of 2% per dose grid voxel for small electron field sizes are short enough to be routinely useful in radiotherapy clinics on present day affordable workstation computers. Considering speed, accuracy and memory requirements, MMC is a promising alternative to currently available electron dose planning algorithms.

The application of correlated sampling to the computation of electron beam dose distributions in heterogeneous phantoms using the Monte Carlo method

Although the Monte Carlo method is capable of computing the dose distribution in heterogeneous phantoms directly, there are some advantages to computing a heterogeneity correction factor. If this approach is adopted there are savings in time using correlated sampling. This technique forces histories to have the same energy, position, direction and random number seed as incident on both the heterogeneous and homogeneous water phantom. This ensures that a history that has, by chance, travelled through only water in the heterogeneous phantom will have the same path as it would have through the homogeneous phantom, resulting in a reduced variance when a ratio of heterogeneous dose to homogeneous dose is formed. Metrics to describe the distributions of uncertainty, efficiency, and degree of correlation are defined. EGS4 Monte Carlo calculation of the dose distribution from a 20 MeV electron beam on water phantoms containing aluminum or air slab heterogeneities illustrate that this technique is the most efficient when the heterogeneity is deep within the phantom, but that improved efficiency can be realized even when the heterogeneity is at or near the surface. This is because some correlation between the two histories is retained despite passage through the heterogeneity.

The status of high-energy photon and electron beam dosimetry five years after the implementation of the IAEA Code of Practice in the Nordic countries

The status of the dosimetry of high-energy photon and electron beams is analysed, taking into account the main developments in the field since the implementation of the IAEA Code of Practice in the Nordic countries. In electron beam dosimetry, energy-range relationships are discussed; Monte-Carlo results with different codes are compared with the experimentally derived empirical expression used in most protocols. Updated calculations of water-to-air stopping-power ratios following the changes in the Monte-Carlo code used to compute actual Sw,air values are compared with the data included in most dosimetry protocols. The validity of the commonly used procedure to select stopping-power ratios for a clinical beam from the mean energy at the phantom surface and the depth of measurement, is analysed for 'realistic' electron beams. In photon beam dosimetry, calculated correction factors including the effect of the wall plus waterproofing sleeve and existing data on the shift of the effective point of measurement of an ionization chamber, are discussed. New calculations of medium-to-air stopping-power ratios and their correlation with the quality of the beam obtained from the convolution of Monte-Carlo kernels are presented together with their possible practical implications in dosimetry. Trends in Primary Standard Dosimetry Laboratories towards implementing calibrations in terms of absorbed dose to water are presented, emphasizing controversial proposals for the specification of photon beam qualities. Plane-parallel ionization chambers are discussed regarding aspects that affect determinations of absorbed dose, either through the different methods used for the calibration of these chambers or by means of correction factors. Recent studies on the effect of the central electrode in Farmer-type cylindrical chambers are described.

Determination of absorbed dose in high-energy electron and photon radiation by means of an uncalibrated ionization chamber

The aim of this study was to develop a dosimetric method based on an ionization chamber which has an uncalibrated sensitive volume but which behaves as a Bragg-Gray cavity in high-energy radiation. The new type of chamber developed in the course of this study has a variable volume and is constructed from water-similar materials. It can be used in a water phantom directly in a beam of a therapy megavoltage machine under clinical conditions. The chamber allows absorbed dose to be determined from first principles, overcoming many of the problems encountered with conventional dosimetry based on calibrated chambers. The study involved an intercomparison of the performance of the new chamber in high-energy electron and photon radiation with the conventional calibrated chambers employed according to the established dosimetry protocols. Good agreement was found between these dosimetric methods and it may therefore be concluded that the method developed in this work can be successfully employed for absolute dosimetry. The new chamber is a promising device for research in various aspects of dosimetry.

The role of Monte Carlo simulation of electron transport in radiation dosimetry

A brief overview is given of the role in radiation dosimetry of electron transport simulations using the Monte Carlo technique. Two areas are discussed in some detail. The first is the calculation of stopping-power ratios for use in ion chamber dosimetry. The uncertainty in stopping-power ratios is discussed with attention being drawn to the fact that the relative uncertainty in restricted collision stopping powers is greater than that in unrestricted stopping powers if the major source of uncertainty is the density effect correction. Using ICRU Report 37 stopping powers and electron spectra calculated in a small cylinder of graphite, the value of the Spencer-Attix graphite to air stopping-power ratio in a 60Co beam is found to be 1.0021 for an assumed graphite density of 1.70 g/cm(3) and 0.23% less for an assumed density of 2.26 g/cm(3). The second area discussed is the feasibility of using Monte Carlo techniques to calculate dose patterns in a patient undergoing electron beam radiotherapy.

Uncertainties in dosimetric data and beam calibration

Recent studies indicate that the calibration of therapeutic beams is one of the main sources of uncertainty in the mean absorbed dose to the target volume in radiotherapy. Interaction coefficients and data used through the different steps in the calibration are pointed out as the main contribution to this uncertainty. Procedures used to select dosimetric data, that is, input parameters used in the specification of the quality of the beam, cause another contribution. In this paper the actual status of the data used for the dosimetry of photon and electron beams is introduced first. Uncertainties along the dosimetric chain are analyzed according to the procedure and data used in recent publications. Uncertainties in stopping-power ratios, considered the main contribution, are discussed in detail starting from the basic electron stopping-power data. Overall uncertainties in the presently available set of stopping-power ratios are analyzed. Recent developments in the dosimetry of electron beams, related to the effect of energy and angular spread and electron and photon contamination, are discussed in connection with the procedure to select stopping-power ratios for clinical dosimetry. Uncertainties along the dosimetric chain are evaluated in terms of the present knowledge of error sources.