First published online February 15, 2007
British Journal of Radiology (2007) 80, 202-208
© 2007 British Institute of Radiology
doi: 10.1259/bjr/86992777
Electron dosimetry of angular fields
G Davies
M Bidmead
C Lamb
C Nalder
and
J Seco
Royal Marsden NHS Foundation Trust, Fulham Road, London SW3 6JJ, UK
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Abstract
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Shaping electron fields through the use of lead cut-outs may result in there being acute angles in part of the field. Using both experimental techniques and EGSnrc Monte Carlo simulations an investigation was carried out to determine the dosimetric consequences of this. Measurements were made to investigate how the field dose was related to the angle between adjacent sides in the cut-outs. The study involved two electron energies (9 MeV and 12 MeV) and source–skin distances (SSDs) in the range 1000–1100 mm. For angles less than about 120° the dose received in the angular region decreased significantly, the effect being more pronounced at 12 MeV than at 9 MeV, and at longer SSDs. The planar shapes of the Monte Carlo dose distributions agreed with those experimentally determined to within ±1.5 mm at 9 MeV and ±1.0 mm at 12 MeV, demonstrating the validity of using such calculations for this purpose. Graphs are presented which may help in the prospective assessment of the dose reductions likely to be incurred.
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Introduction
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Electron treatment fields are often shaped using cut-outs (manufactured from lead alloys) which are attached to the end of an electron applicator. Such cut-outs may occasionally require very acute angles to be included in part of the field, for example when shielding the base of the brain in neck node treatments.
The International Commission on Radiation Units and Measurements, ICRU 50 [1], states that, for photon beam therapy, the planning target volume should be covered by at least the 95% isodose. However, this dictum cannot be applied to electron beam therapy as this would mean unacceptably large margins around the planning target volume (PTV). The International Atomic Energy Agency, IAEA [2], recommends 85% coverage and the American Association of Physicists in Medicine [3] recommend 90% coverage. The most recent recommendations, ICRU 71 [4], advise that the dose variation within the PTV for an electron treatment should be less than ±10%. At the Royal Marsden Hospital beam energy is chosen such that the 90% isodose line will encompass the planning target volume – this includes a margin of 50–100 mm around the clinical target volume, depending on beam energy and depth of tumour. Individual treatments are normally given at a fixed source to skin distance (SSD) in the range 1000–1100 mm SSD. The longer SSD is sometimes necessary if it is not possible to position the electron applicator closer to the patient, as when the shoulder may prevent treatment of a neck field at 1000 mm SSD.
Monte Carlo simulations provide accurate predictions of electron dose distributions and are especially useful for their ability to model the dose at tissue interfaces [5]. Such simulations can also model the interactions that the electrons undergo within the treatment head of the linear accelerator, allowing the dose at each point in tissue to be broken down into several components, including that from contaminant photons [6]. In this study the Monte Carlo simulations were carried out with the use of the code EGSnrc/BEAM [7, 8] and EGSnrc/DOSXYZNRC [9]. All comparisons with the experimentally determined planar dose distributions were performed at the depth of the 90% dose, corresponding to depths of 28 mm and 40 mm, respectively, for the 9 and 12 MeV electron beams. The cut-outs were evaluated by examining the planar shape of the 90% isodose line.
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Methods and materials
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The experiments
Investigation of cut-outs displaying various angles
Three cut-outs were designed for use with a 100 mmx100 mm electron applicator to investigate how the coverage varies with the size of the sharpest angle. The dimensions of the various cut-outs are illustrated in Figure 1
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In order to characterize the isodose distributions obtained from the films of cut-outs 1, 2 and 3, the angles given by the light field were bisected and the distance along the bisector to the 90% isodose was measured.
Electron cut-out percentage depth dose
The depth of 90% dose is normally determined from percentage depth–dose curves for a 100x100 mm2 electron field and it was necessary to check if such depths were maintained in the cut-outs under investigation. The measurements were made in a Perspex water tank of dimensions 300 mmx300 mmx300 mm at an SSD of 1000 mm which contained a Perspex jig holding a Scanditronix waterproof electron diode (detector volume 0.2–0.3 mm3). The diode was used to obtain readings at depth throughout the open area beneath the cut-outs.
Film dosimetry
Films were used to investigate the treatment field coverage at depth and were positioned at a depth of either 28 mm or 40 mm within a block composed of slabs of WTe solid water. These depths correspond to the depth of 90% of the dmax dose for 9 MeV and 12 MeV, respectively. An example of the experimental set up used for the 9 MeV beam is shown in Figure 2. At 12 MeV, the set up was identical except 40 mm of solid water was placed on top of the film instead of the 28 mm shown in Figure 2. These arrangements were used at both 1000 mm and 1100 mm SSD. The cross wires representing the beam central axis were marked on the film. In order to compare the physical shape of the cut-out with the resultant dose distribution the light field at SSDs of 1028 mm, 1128 mm, 1040 mm and 1140 mm was traced onto graph paper whilst the cut-out was attached to the electron applicator.
The developed films were scanned using a Vidar optical density scanner with an image resolution of the order of 1 mm. The scanner software (RFAplus Version 5.3) was calibrated such that the optical density could be converted to dose. The raw image was firstly corrected for background radiation (using a fog region away from the area of high optical density) and was then normalized to a point at the geometric centre of the cut-out. This normalized image was then used to produce an isodose map showing the coverage of the 102%, 100%, 95%, 90%, 80%, 70%, 50% and 20% isodoses.
Reproducibility of the acquisition of the isodose distributions
The measurements at 1000 mm SSD for 9 MeV were repeated to assess reproducibility. A calibration film was also produced, and this was used to recalibrate the scanner for this particular batch of films.
The Monte Carlo simulation
Modelling of Varian Clinac 2100CD
A Monte Carlo model of the Royal Marsden Varian 2100C linear accelerator had already been developed for a number of electron beam energies [10], using the code EGSnrc/BEAM [7, 8]. In this study the chosen starting energy of the primary electrons incident on the exit window was 13.1 MeV for the 12 MeV beam and 9.9 MeV for the 9 MeV beam. The BLOCK component module was used to simulate the electron cut-outs as this allowed irregular and triangular fields to be modelled through user input of the co-ordinates of the x and y vertices of the cut-out.
As a preliminary check, 100 mmx100 mm fields were modelled for 9 MeV and 12 MeV and the percentage depth–dose and profile curves were determined using simulations with a water phantom in DOSXYZnrc. The Monte Carlo depth–dose curves were compared with the measured depth–doses obtained from the linear accelerator during commissioning. The Monte Carlo values were found to be within 1% of the measured values (see Figure 3).
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Figure 3. Monte Carlo commissioning of the 9 MeV and 12 MeV electron beams: intercomparison of the depth–dose curves and the profiles. The Monte Carlo values were found to be within 1% of the measured values.
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One limitation in using the BLOCK model for the cut-outs is that certain shapes may not be modelled and it was possible only to model cut-out 1 (Figure 1a
). The scoring plane for creation of the phase space file was chosen to be at the exit of the cut-out. Each simulation was started with 2x107 incident particles and resulted in phase space files of 40–100 MB, each containing 1.5–2x106 particles. DOSXYZnrc was then used for dose calculations in a water phantom to look at the resulting planar dose distribution from cut-out 1 at 28 mm for 9 MeV and 40 mm for 12 MeV with a scoring grid of 2 x 2 x 5 mm3. Each simulation took approximately 8 h to complete.
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Results and discussion
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Dosimetry of angular cut-outs
The depth at which the electron treatment dose is prescribed at the Royal Marsden depends on the incident beam energy. For a 9 MeV beam, 90% of dmax is achieved at a depth of 28 mm while for a 12 MeV beam, 90% of dmax is achieved at a depth of 40 mm. Figure 4 shows the results of a film measurement performed with a 9 MeV electron beam in solid water, at the prescribed dose depth, to evaluate the dose distribution obtained by cut-out 1. The measurements were performed at 1000 mm SSD and all isodoses presented are relative to the prescribed dose. Isodoses presented are 20%, 50%, 70%, 80%, 90%, 95% and 100% and these are shown in juxtaposition to the cut-out contour. In the vicinity of any vertex of the cut-out the dose coverage is usually of the order of 40–50%, i.e. very much lower than the 90% requested clinically. This underdosage effect was seen in both the 9 MeV and the 12 MeV beam at both 1000 mm and 1100 mm SSD and clearly could compromise the quality of a clinical electron therapy treatment.
Evaluating set up errors in measuring electron cut-out dose distributions
The reproducibility study provided information regarding the accuracy of the method used to quantitatively analyse the dose distribution. The repeat set of measurements were all in good agreement with the first set, the average difference in the distance to the 90% isodose from the angle vertex being found to be 1.2 mm. Using this information, and considering the errors with the tracing of the light field etc., it was estimated that the net error in the measurement process was approximately ±1.5 mm for both the 9 MeV and 12 MeV beams.
Percentage depth–dose variation with electron cut-out
The depth–doses obtained for cut-outs 1, 2 and 3 were measured and compared with the standard 100 mmx100 mm field for both energies. For the 9 MeVbeam there was a slight discrepancy between the cut-outs 2 and 3 and the standard field at the 90% depth; this difference was of the order of 1–2 mm. This was attributed to set up errors. The depth–dose for cut-out 1 was identical to the standard 100 mmx100 mm field, within experimental error. All results for the 9 MeV beam were therefore considered to have a maximum error of 2 mm. For the 12 MeV beam (see Figure 5) there was no measurable difference between the depth of the 90% isodose of the 100 mmx100 mm reference field and that for the cut-outs.
Results from custom-made cut-outs
Figure 6 shows the distance from the vertex to the 90% isodose as a function of the vertex angle for 9 MeV and 12 MeV, respectively. The results show that the distance increases significantly as the size of the angle decreases, for both SSDs and both energies, with a maximum distance approaching 60 mm at the very acute angle of 35°. The graphs also show that the coverage will be generally worse if the treatment is given at an extended SSD of 1100 mm.
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Figure 6. Comparison of the distance from the angle vertex to 90% isodose for (a) 9 MeV and (b) 12 MeV beam at 1000 mm and 1100 mm SSD.
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Figure 7 directly compares 9 MeV and 12 MeV beams for an SSD of 1000 mm. The distance to the 90% isodose from the vertex is greater at the higher energy, suggesting that tumour coverage will be worse for an angled cut-out as the energy of the electron beam is increased. This result is also observed if the SSD of the treatment is increased from 1000 mm to 1100 mm.
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Figure 7. Comparison of the distance from the angle-vertex to 90% isodose for 9 MeV and 12 MeV beam at 1000 mm SSD.
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Monte Carlo verification of electron cut-out dosimetry
The distances from the vertex to the 90% isodose were then determined from the Monte Carlo results derived for cut-out 1 and the results are presented in Figure 8. The theoretical results match those measured to within the positioning error of 1.25 mm, this being half the length of one of the sides of the scoring cube used in the simulation.
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Figure 8. Comparison between Monte Carlo and measured values of the distance from the angle vertex to 90% isodose for 9 MeV and 12 MeV beams for 1000 mm SSD.
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The maximum differences between the Monte Carlo results and the measured values were observed to be 1.5 mm and 1.0 mm for 9 MeV and 12 MeV, respectively, both at 70° angle. In the case of the 9 MeV, a maximum difference of 1.5 mm was also observed at the 130° angle. However, these differences are all within the combined Monte Carlo and measurement errors, indicating excellent agreement between simulation and measurement.
The Monte Carlo results also predict the correct dependence of the distance to 90% isodose as a function of the vertex angles for both energies. This was verified by comparing the shapes of the measured curves shown in Figure 8 with a best-fit curve through the Monte Carlo results (not shown).
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Conclusions
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Within the region of sharp cut-out angles the dose received may be severely reduced. This can be attributed to the fact that side-scatter equilibrium may not be attained in these regions, the dose decreasing with decreasing vertex angle. At an extended SSD the dose received in such regions is less than if the treatment is given at an SSD of 1000 mm. Through comparison of the distributions produced with 9 MeV and 12 MeV electron beams the dose coverage in the region of the angle has been shown to be worse at higher energies. The experimental results were all satisfactorily emulated by the Monte Carlo simulations and the validity of using a purely theoretical approach to quantify problems such as these has been demonstrated.
This work shows that acute angles in electron cut-outs should be avoided where possible since, for angles less than 120°, the dose within the vicinity of the angle becomes significantly reduced. However, it is usually not practical to put in place restrictions stating that electron cut-outs should not contain angles less than 120° as this would exclude the use of a large number of clinically-necessary cut-outs. We present here a set of results that can be referred to in order to predict the compromises in dose distribution that will likely occur at the depth of 90% dose for particular practical cases. This could be a useful tool and this limited study highlights the clinical dosimetry implications arising from the use of angled electron cut-outs.
Current address for Gemma Davis: Radiation Physics & Radiobiology, Hammersmith Hospitals NHS Trust, London W6 8RF, UK.
Current address for Joao Seco: Department of Radiation Oncology, Francis H. Burr Proton Therapy Center, Massachusetts General Hospital, Harvard Medical School, Boston USA.
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Acknowledgments
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The work presented in this manuscript was carried out as part of Gemma Davies' MSc in Medical and Physics Engineering at King's College London. We would like to thank Dr Cephas Mobata for suggesting the MSc project and also the MSc coorinatar, Dr Slavik Tabakov. We would also like to acknowledge the assistance of the Tim Coles Research Fund in the purchase of some of the equipment used during the project. Professor Roger Dale (Hammersmith Hospitals) is thanked for advice relating to the format of the manuscript.
Received for publication February 3, 2005.
Revision received June 22, 2007.
Accepted for publication July 11, 2006.
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References
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Abstract
Introduction
