First published online July 19, 2006
British Journal of Radiology (2006) 79, 912-917
© 2006 British Institute of Radiology
doi: 10.1259/bjr/94993761
Scatter from radiotherapy beams emerging from primary barriers: an aid to bunker design
D C Benito, MSc1 and
A L McKenzie, DSc2
1 H H Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, 2 Department of Medical Physics and Bioengineering, Bristol Haematology and Oncology Centre, Horfield Road, Bristol BS2 8ED, UK
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Abstract
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Charts to assist in linear accelerator bunker design have been produced using the Monte Carlo framework, Geant4. These charts assess the amount of forward scatter produced at different angles to the beam axis by concrete and steel barriers irradiated by 6 MV and 10 MV photon beams at normal incidence. These new charts complement existing charts of broad-beam transmission through walls. This is because the existing charts give no indication of the amount of scatter emerging at large angles from the beam axis, for example, towards the maze entrance.
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Introduction
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Designers of linear accelerator bunkers commonly refer to charts such as those given in references [1, 2]. These plot primary beam attenuation against wall thickness at given X-ray energies. Experience shows that such charts are sufficiently accurate for design purposes.
The relative intensity of back-scatter from the bunker walls may also be determined from charts in the above publications to a level of accuracy that is sufficient for radiation protection calculations. Such back-scatter may be used to estimate dose rates at maze entrances, provided that the linear accelerator is not orientated in the room in such a way that the primary beam can be aimed at the inner maze wall. In such cases, if the inner maze wall has been designed insufficiently thick, the dose rate from wide-angle scatter from the X-ray beam emerging from the wall can be more than an order of magnitude greater than the dose rates, typically a few µGy h–1, arising from the multiple-order scatter that eventually finds its way down the maze (Figure 1
). An example is discussed later.
Surprisingly, perhaps, no charts have been published to cater for this situation. While primary-beam charts can be used to calculate the intensity of broad-beam transmission through an inner maze wall, no charts exist to show the level of scatter that may emerge at discrete angles and contribute to the dose at the maze entrance (Figure 1
).
Designers who have access to software packages based on Monte Carlo programs may use these to find the scatter from such beam configurations. However, such packages are not widely available, and require a period of training and familiarization. For those who do not design bunkers regularly, these inconveniences militate against their use.
In attempting to provide a simple, practical solution to what is a relatively common problem we have calculated a series of plots, illustrated in Figures 2–5. These show the intensity of radiation scattered at different angles from a primary beam as it emerges from a wall made of concrete or steel. The data are plotted as ratios of scattered dose rate at 1 m from the exit point relative to the dose rate of the primary beam as it enters the wall, where it is assumed to have an area of 100 cm2.
In practical use, the bunker designer will need to know the scatter not at 1 m, but at several metres from the centre of the area of the beam as it emerges from the wall. This distance would typically be the distance to the maze entrance. The dose rate there will be found by applying the inverse-square law. The inaccuracies of using a distance measured from a single point in the centre of a finite beam area are minimized because the distance to the maze entrance is generally significantly greater than the size of the exit beam.
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Method
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In order to calculate the scatter charts, we used the Geant4 Monte Carlo framework code [3] to simulate scattering within the wall. We chose 6 MV and 10 MV spectra [4] from Elekta (Elekta; Elekta Ltd, Crawley, West Sussex, UK) and Varian (Varian; Varian Medical Systems UK Ltd, Crawley, West Sussex, UK) linear accelerators to create beams incident on concrete of density 2.35 tonnes m–3 and steel of density 7.85 tonnes m–3. These materials are commonly used in bunker walls.
Where practicable, we checked that our use of the code generated results that were consistent with our experiments or with published charts. Comparison with existing charts was only indirect, since no charts of the kind we have produced were previously available. Experimental verification was similarly not without difficulty, because dose rates were generally low and the level of background leakage and scatter tended to be of the same order as that of scatter from the maze wall. This is discussed in more detail below.
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Plots
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The calculated plots are shown in Figures 2–5. The statistics were such that the plots were smooth, apart from data points at the largest barrier thicknesses at the greatest scatter angles where random deviations from smoothed data were in the order of 30%. Because of this, some plots have been replaced with the best fitting (exponential) dotted line. The position of the calculated data points indicates the closeness of fit.
All four charts show the expected decrease in scatter dose rate with increasing wall thickness at given angles of scatter. The agreement between the gradients of these charts and those of primary attenuation is striking. For instance, referring to Figure 2, for 6 MV radiation through concrete, the gradient of the intensity of scatter exiting at 60° is three decades per metre of concrete. This is the same as the gradient found in published charts [1, 2] of the attenuation of primary 6 MV radiation through concrete.
Similarly, for 6 MV radiation through steel (Figure 3), the gradient of the intensity of scatter exiting at 60° is three decades for approximately 300 mm of steel. After correcting for the relative densities of steel and concrete, this is essentially the same as the gradient in Figure 2 for 6 MV radiation through concrete.
Consideration of the physics shows that the similarity of the gradients of scatter and primary plots is to be expected. Suppose that the intensity of 60° scatter exiting a concrete wall of thickness 0.2 m is measured. Suppose that an extra metre of concrete is now added "upstream", making a total thickness of 1.2 m. Any scatter from this extra metre will be so attenuated by the final 0.2 m when it exits the wall that it will contribute a negligible amount to the measured scatter, relative to that arising from the 0.2 m nearest the detector. However, after the primary beam has travelled the added metre and enters the final 0.2 m, it is diminished in intensity by three decades. Therefore, the scatter arising within the final 0.2 m will also have diminished by three decades. This, in broad terms, explains why plots of both the exit scatter and primary attenuation have the same gradient.
An example will serve to illustrate the use of the charts.
Suppose that the inner maze wall in Figure 1 is made of concrete of density 2.35 tonnes m–3 and is 0.6 m thick. This was a common thickness for secondary barriers in bunkers designed for cobalt treatment. Suppose that a 6 MV linear accelerator is to be installed in the bunker. Assuming an instantaneous dose rate of 4 Gy min–1 at the isocentre, the dose rate at the entrance to the maze wall, 4 m from the source, is 15 Gy h–1. For a collimator setting of 10 cmx10 cm, the area at the wall is 1600 cm2.
Using Figure 2, the dose rate scattered at 60° to 1 m from the centre of the exit beam is 5x10–6x15 Gy h–1x16 = 1200 µGy h–1. The factor 16 arises because the charts are presented for a beam area of 100 cm2 on entry to the wall. Using the inverse-square law to find the dose at the maze entrance, which also happens to be 4 m from the centre of the exit beam, and using a factor of unity to convert whole-body dose to effective dose, the effective dose rate at the maze entrance is then 75 µSv h–1.
Such a calculation shows that additional protection might be needed for the inner maze wall in this case, possibly provided by steel. From the discussion above, the same Figure 2 could be used to determine the scatter exiting from a wall of concrete and steel by finding the equivalent thickness of an all-concrete wall.
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Comparison with measurement
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Before these plots can be used with confidence to design bunkers, the level of scattered dose that they predict must be compared with measurement. The reason why direct comparison with experiment is difficult is explained below. We were able to check that elements of our implementation of the Geant4 code were in accordance with existing charts by comparing our predictions of backscatter with those of the experimental data summarized in Figure 19 of Reference [2]. The middle column of Table 1 shows our Geant4 estimates of the intensity of 6 MV radiation back-scattered to 1 m from a concrete barrier irradiated by a 100 cm2 beam. The figures are shown relative to the intensity of the incident beam.
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Table 1. Comparison between the Geant 4 simulation and data from reference[2] for back-scattered doses for three different scattering angles
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The statistical uncertainties in the Monte-Carlo results are indicated by two standard deviations. The estimates agree with published data to within about 10%, which suggests that the code was functioning as intended, as far as could be tested using results for back-scatter.
The difficulty in verifying the plots by direct experiment is that (1) any barrier from which oblique scatter is measured will also transmit head leakage from the linear accelerator into the detector and (2) back-scatter from the barrier tends to be multipally scattered around the barrier, and again adds to the signal due to the oblique scatter. The intensity of both the leakage and the multiple scatter are generally of the same order as, or greater than, that of the oblique scatter, and it is difficult to identify the individual components in the detected signal. This neutralizes the effectiveness of building temporary barriers within a linear accelerator room in order to test the oblique-scatter plots.
Experiments based on bunkers in clinical use run into difficulty because dose rates from scatter from inner maze walls in existing installations tend to be very low. Inner maze walls may well be over-protected: maze walls that were inadvertently designed too thin would have had extra protection added at the first opportunity. These low dose rates are not only of the same order as the background from leakage and multiple scatter, but they are also at the detection limit of most readily available ionization chambers.
It might be perceived that the presence of head leakage and multiple scatter down a maze would detract from the usefulness of oblique-scatter plots. However, in practice, it is the dose beyond the maze entrance that is of interest, where the head leakage is insignificant because of attenuation by the outside secondary wall, and where the multiple scattered radiation has diminished with distance down the maze and can, in any case, be estimated from existing charts. It is here, beyond the maze entrance, that the oblique-scatter plots should prove useful in ensuring that scatter from the inner maze wall to the outside is kept to acceptably low levels.
Instead of building barriers inside the linear accelerator bunker, another way to test the plots is to measure the dose rate beyond the maze entrance where the detector is protected from head leakage by the outside secondary wall. The detector should be positioned slightly to one side of the maze barrier, so that it can "see" the area where the primary beam exits the inner maze wall, but not the far end of the maze, which is a source of multiple scatter.
There is only one linear accelerator bunker in our radiotherapy centre where the primary beam can be directed at the inner maze wall. This wall consists of a 0.6 m concrete barrier to which has been added 0.25 m of steel on the inside of the room. A Southern Scientific RO-10 survey meter using a 400 cm3 ionization chamber was placed outside the end of the maze, and slightly to one side of it, in order to minimize the level of multiple scatter entering the detector. The instrument had been calibrated less than 2 months previously in accordance with the laboratory accreditation requirements of the UK Accreditation Service. This detector was 4.43 m from the centre of the linear accelerator beam at the point where it exited the inner maze wall. The scatter angle from the centre of the beam to the detector was 62.5°.
The primary beam of the linear accelerator was aimed at normal incidence onto the inner maze wall, and set to deliver a 40 cmx20 cm beam as defined at a target distance of 1 m. The beam was narrower in the horizontal direction so that the oblique scatter entering the detector would be confined within a smaller range of scatter angles. The measured dose rate was 0.7 µGy h–1. When the detector was moved out of the line of sight of the exit beam, the measured dose rate fell to between 0.1 µGy h–1 and 0.2 µGy h–1. This is representative of the dose rate from multiple scatter reaching the detector even although it was within the "shadow" of the main component of multiple scatter from the far end of the maze. Hence the dose rate attributable to oblique scatter from the inner maze wall was in the order of 0.5 µGy h–1.
This dose rate has to be compared with that predicted by the plots. We accounted for the two-component nature of our maze wall by multiplying by the ratio of the densities of steel and concrete to estimate the thickness of an equivalent wall built either entirely of concrete or entirely of steel. The calculated thicknesses are 1.435 m and 0.43 m, respectively. For an oblique angle of 62.5°, the charts in Figures 2 and 3 predict a relative scattered dose rate of 2.1x10–8 and 1.2x10–8, respectively. Using the linear accelerator output of 240 Gy h–1 at 1 m from the source, and taking care to estimate the incident beam size at the same distance from the source as that at which the output is calculated, the predicted dose rates at the detector are 1.1 µGy h–1 or 1.9 µGy h–1 depending upon whether an all-concrete or an all-steel wall is assumed.
Hence, in comparison with the measured rate of 0.5 µGy h–1, the plots predict between two and four times the actual dose rate. Several uncertainties attend this conclusion, however. The measured dose rates were at the very limits of detection of the instrument. In addition to the concrete and steel composition of the wall, there is a layer of plaster of indeterminate thickness, but which will reduce the measured dose rate. The predicted dose rates had to be made using a calculated effective thickness, which turned out to be so large that the plots even had to be extrapolated slightly to determine the relative scattered dose.
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Conclusion
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The charts presented here are for calculating the intensity of radiation emerging from a wall and scattered in different directions, and are particularly helpful in designing bunkers where a primary beam is directed at a maze wall.
A ratio of between two and four between the predicted and the measured dose rate is equivalent to an uncertainty of 100–200 mm concrete or 30–60 mm steel. The lower values in these ranges may be acceptable, particularly since the plots appear to be conservative, that is, a design based on the plots might tend to overestimate the protection required. The discrepancy may arise because of the very low dose rates that are available and because of the uncertainty of the effect of the additional plaster layer to the wall which would reduce the amount of the discrepancy.
In the light of the remaining uncertainties, we should welcome experimental verification by other centres who may happen to have thinner maze walls, ideally of uniform composition. Such independent corroboration would lend weight to these plots as a primary tool in room design.
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Acknowledgments
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We are grateful for the assistance of Paul Stevens and Henry Lawrence in implementing the Geant4 code.
Received for publication January 10, 2006.
Revision received May 24, 2006.
Accepted for publication May 30, 2006.
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References
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- Handbook of Radiological Protection. Part 1: Data. SBN 11 360079 8. London, UK: HMSO, 1971
- Recommendation for Data on Shielding from Ionizing Radiation, Part 2 Shielding from X-radiation. British Standards: BS4094. ISBN 058006522-7. London, UK: British Standards Institution, 1971
- GEANT4 (Agostinelli S, Allison J, Amako K, Apostolakis J, Araujo H, Arce P, et al), http://cern.ch/geant4 [Accessed 18 September 2006]
- Sheikh-Bagheri D, Rogers DW. Monte Carlo calculations of nine megavoltage photon beam spectra using the BEAM code. Med Phys 2002;29:391–402.[CrossRef][Medline]
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Abstract
Introduction
