Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs

Journal of Radiological Protection PAPER Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs To cite this article: C J Martin et al 2012 J. Radiol. Prot. 32 373 View the article online for updates and enhancements. Related content - Establishment of scatter factors for use in shielding calculations and risk assessment forcomputed tomography facilities H Wallace, C J Martin, D G Sutton et al. - The characterization and transmission of scattered radiation resulting from x-ray beamsfiltered with zero to 0.99 mm copper D G Sutton, C J Martin, D Peet et al. - Application of Gafchromic film in the study of dosimetry methods in CT phantoms C J Martin, D J Gentle, S Sookpeng et al. Recent citations - Monte Carlo Modeling of Computed Tomography Ceiling Scatter for Shielding Calculations Stephen Edwards and Daniel Schick - RADIATION SHIELDING FOR DIAGNOSTIC RADIOLOGY L. T. Dauer This content was downloaded from IP address 46.3.194.4 on 29/11/2017 at 11:22

IOP PUBLISHING JOURNAL OF RADIOLOGICAL PROTECTION J. Radiol. Prot. 32 (2012) 373 396 doi:10.1088/0952-4746/32/4/373 Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs C J Martin 1, D G Sutton 2, J Magee 1, S McVey 2, J R Williams 3 and D Peet 4 1 Health Physics, Gartnavel Royal Hospital, 1055 Great Western Road, Glasgow G12 0XH, UK 2 Medical Physics, Ninewells Hospital and Medical School, Dundee DD1 9SY, UK 3 Medical Physics, Royal Infirmary of Edinburgh, 51 Little France Crescent, Edinburgh EH16 4SA, UK 4 Radiation Protection, Royal Surrey County Hospital, Guildford GU2 7XX, UK Received 21 March 2012, in final form 10 August 2012, accepted for publication 10 August 2012 Published 24 September 2012 Online at stacks.iop.org/jrp/32/373 Abstract Computed tomography (CT) scanning rooms and interventional x-ray facilities with heavy workloads may require the installation of shielding to protect against radiation scattered from walls or ceiling slabs. This is particularly important for the protection of those operating x-ray equipment from within control cubicles who may be exposed to radiation scattered from the ceiling over the top of the protective barrier and round the side if a cubicle door is not included. Data available on the magnitude of this tertiary scatter from concrete slabs are limited. Moreover, there is no way in which tertiary scatter levels can be estimated easily for specific facilities. There is a need for a suitable method for quantification of tertiary scatter because of the increases in workloads of complex x-ray facilities. In this study diagnostic x-ray air kerma levels scattered from concrete and brick walls have been measured to verify scatter factors. The results have been used in a simulation of tertiary scatter for x-ray facilities involving summation of scatter contributions from elements across concrete ceiling slabs. The majority of the ceiling scatter air kerma to which staff behind a barrier will be exposed arises from the area between the patient/x-ray tube and the staff. The level depends primarily on the heights of the ceiling and protective barrier. A method has been developed to allow tertiary scatter levels to be calculated using a simple equation based on a standard arrangement for rooms with different ceiling and barrier heights. Coefficients have been derived for a CT facility and an interventional suite to predict tertiary scatter levels from the workload, so that consideration can be given to the protection options available. 0952-4746/12/040373+24$33.00 c 2012 IOP Publishing Ltd Printed in the UK

374 C J Martin et al 1. Introduction During radiology procedures x-rays are scattered from patients in all directions and there is leakage of radiation from the x-ray tube housing. When designing shielding requirements for radiology facilities protection is provided against all the secondary radiation. For equipment, such as computed tomography (CT) scanners and interventional radiology and cardiology units with heavy workloads, the further tertiary scatter of this radiation from ceilings and walls must also be considered. The information available on factors for determining levels of tertiary scatter from x-ray beams with energies in the diagnostic range is limited. Results from most studies have been derived from experimental data with narrow beams in specific geometries (RSAC 1971) and require further assumptions to be made about radiation fields in order to estimate the levels of scattered radiation to which personnel might be exposed. The information on scatter levels from large concrete slabs such as from the ceilings of many diagnostic x-ray rooms is derived from Monte Carlo simulations using primarily scatter data from the early RSAC report (McVey and Weatherburn 2004, Fog and Cormack 2010). Broad assumptions are usually made about the percentage of radiation that will be scattered and little account is taken of the layout of specific facilities. A study has therefore been undertaken to measure x-ray scatter levels from concrete walls and derive scatter factors that can be used in predicting levels of tertiary scattered air kerma in diagnostic x-ray facilities. The factors derived have then been applied in modelling the effect of different ceiling and barrier configurations on scatter levels in control cubicles and other areas adjacent to x-ray facilities. The aim of the study has been to develop a methodology through which tertiary scatter air kerma levels from higher dose medical exposures can be predicted in order to determine where shielding is required and how much should be used. 2. Materials and methods The factors on which scatter from a concrete slab will depend are the energy of the radiation and the direction of scatter. Since the ceiling in an x-ray room extends for several metres to each side of the x-ray unit, a large area will contribute to the scatter air kerma incident on the operator. Data are available on the dependence of scatter on angle for x-ray beams incident perpendicularly on concrete walls (RSAC 1971, McVey and Weatherburn 2004), but the experimental data available for x-ray beams incident on walls at acute angles, which more closely resemble the situation in practice, are limited. In particular there are no data on the variation of scatter with the angle of emergence of x-rays incident on a surface at an angle of 45 or similar. Measurements have therefore been made to quantify some of these variations with the aim of determining factors that could be applied in summations of scatter contributions from across large slabs of concrete. The secondary scatter radiation that is incident on the ceiling and walls of an x-ray room comprises scatter from the patient and leakage from the x-ray tube. The leakage fluence is lower than the scattered by a factor of more than ten and, despite the spectrum being harder because of transmission through the tube housing containing 2 3 mm of lead, can be neglected without serious error (Sutton et al 2012). The scattered fluence varies with scattering angle (Williams 1996, McVey and Weatherburn 2004, McVey 2006). The spectra of x-rays back scattered from a patient s skin will be softer than that of the primary beam, while that in the forward direction will be harder but of lower fluence (Sutton et al 2012). For CT scans the scattered radiation will be a mixture of scatter from all orientations of the x-ray beam, while for interventional procedures the scattering angle will be predominantly between 0 and 90 on the ceiling and between 45 and 135 on the wall. The spectra of the x-rays scattered from the patient incident

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 375 Figure 1. Experimental arrangement used for measurements of scattered air kerma with the x-ray beam directed horizontally and incident on the wall at an angle θ = 45. (a) Plan view with the chamber positioned to measure scatter emerging from the wall at an angle ϕ = 45, employed for measurements of the dependence on tube potential S(kV). The plan view also relates to the arrangement for measurements with lateral displacement f (x/h), but for this the height of the x-ray tube above the chamber (x) was altered for each measurement as shown in (b). Results are reported in terms of x/h = tan ψ. The distance from the wall (h) was kept constant for these measurements. For assessment of f (ϕ) the arrangement in (a) was used, but the angle of scatter emergence ϕ was varied. on the ceiling will be harder than the primary beam, but that on the wall will not be significantly different from that of a primary beam. Three series of experiments were set up in basement areas in the Western Infirmary, Glasgow and Ninewells Hospital, Dundee to allow scatter levels to be investigated from different concrete walls and provide independent confirmation of results. A plan of the experimental arrangement used in the two centres is shown in figure 1. General electric AMX-4 mobile x-rays units with filtration equivalent to 3 mm of aluminum were used to enable experiments to be performed in basement areas, where suitable concrete walls were located. Areas on the walls being investigated between 0.4 and 0.6 m 2 in size were irradiated to allow information on the distribution of scatter from the irradiated area to be obtained. These field sizes were chosen as they provided sufficient radiation to give a scatter air kerma level that could be measured with reasonable accuracy, while being small enough to enable assessments to be made at different spatial positions. The mobile x-ray units were set up so that the x-ray beams were directed horizontally at the wall and the centre of the beam was incident at an angle of 45 for all experiments. This was chosen as representing the mean angle at which x-rays scattered from the patient near the centre of an examination room ( 3 m from the operator control barrier) would be incident on a ceiling slab ( 3 m above the patient for a 4 m high ceiling). The distance between the tube focus and the cross-wires marking the centre of the x-ray field on the wall was between 0.8 and 1.7 m, and the majority of the measurements were made with a distance over 1 m. The scatter air kerma was measured

376 C J Martin et al with 1800 cm 3 ionisation chambers used with RADCAL 9010 dosemeters with calibrations traceable to a national standard. Lead screens were placed between the x-ray tubes and the ionisation chambers to limit the detection of leakage radiation. The air kerma incident on the wall was quantified in terms of the scatter kerma-area product (SKAP) for all the experiments. The SKAP was used as the amount of radiation incident on a wall or ceiling contributing to tertiary scatter depends on both the air kerma and the area irradiated. The units used were mgy m 2, which was determined either from measurements of air kerma made independently corrected for the inverse square law and multiplied by the area of the beam at the wall (Glasgow), or measured directly by a standard kerma-area product (KAP) meter used for patient dose assessment (Dundee). Measurements of scatter air kerma made with the 1800 cm 3 chambers were used to derive the scatter air kerma (K s ) at 1 m from the centre of the scattering area in order to derive a scatter factor S con for concrete. S con = K s /SKAP. (1) For the purpose of this study, the scatter factor S con has been described in terms of three components set out in the equation: S con = S(kV)f (x/h)f (ϕ) (2) where S(kV) is the value of S con for the reflection geometry where an x-ray beam of tube potential kv is incident on a wall at θ = 45 and the scatter air kerma emerges at an angle ϕ = 45 in a plane perpendicular to the wall (figure 1(a)) and f (x/h) and f (ϕ) are dimensionless correction factors giving the deviation of S con with angle from the standard reflection geometry. Here x is the displacement of the scattering element from the plane perpendicular to that in which the x-rays are incident on the wall, and h is the perpendicular distance from the wall of the point at which the air kerma is measured so that x/h = tan ψ (figure 1(b)) and ϕ is the angle of emergence of the scatter air kerma in the horizontal plane perpendicular to the wall (figure 1(a)). Each factor has been evaluated separately as described below in three sets of experiments. 2.1. Variation with tube potential S(kV) The factor S(kV) describes the scatter as a function of tube potential and was used as the primary quantity as it is considered to reflect more closely the tertiary scatter arrangement in an x-ray room. The ionisation chambers were positioned at the same height as the x-ray tube to detect scatter emerging from the wall at 45 with respect to the centre of the x-ray field. Measurements were made for tube potentials between 60 and 120 kv with the same experimental arrangement. The factor S(kV) derived represents the scattered air kerma relative to the x-ray SKAP incident on the wall in mgy (mgy m 2 ) 1. The error resulting from the precision with which the chamber and x-ray tube could be positioned (±14%) and the accuracy of the ionisation chamber calibration (±15%) is assessed as being ±20%. 2.2. Variation with lateral displacement f (x/h) In an x-ray room scattered radiation will be incident over a large area of the ceiling or wall. Information on how isotropic the scattering may be is important for determining the contributions from scatter for areas of wall or ceiling outside the plane in which the radiation is incident on the wall. Measurements were made to determine the variation with angle of scatter emergence ψ in terms of lateral displacement x, again with the x-ray beam incident on the wall in the horizontal plane at θ = 45 (figure 1(a)). x was taken as the distance of the centre of the scattering area from the zero displacement geometry described in section 2.1 and the

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 377 Figure 2. Sectional diagram showing how the area of ceiling slab (BE) from which exposure to scatter air kerma will occur is defined for simulation. The letters and distances are used in equations (3) (7). For the simulations of scattering from ceiling slabs d pat = 3.0 m, d op = 1.5 m, h pat = 1.0 m, h op = 1.5 m, NL = 2 m and FL = 10 m. variation of scatter was determined by moving the x-ray tube by defined amounts in the vertical direction (figure 1(b)). This arrangement was chosen as it could be set up readily in practice. The measurement of angular variation was made in terms of x divided by the distance of the centre of the chamber from the wall h, so that the results could be incorporated readily into a summation of contributions from across a large concrete slab. The ionisation chamber was positioned initially so that it was in the same horizontal plane as the x-ray tube at between 1.0 and 1.2 m from the wall and was measuring radiation scattered at an angle ϕ = 45. These measurements were made at a fixed tube potential of either 100 or 80 kvp, and the scatter air kerma at 1 m from the centre of the irradiated area determined by application of the inverse square law. The factor f (x/h) represents a dimensionless correction for lateral distance of the detection point from the plane containing the source and scattering element. 2.3. Variation with angle of scatter f(ϕ) Measurements were performed at 100 kvp with an arrangement similar to that shown in figure 1(a) to assess variations in scatter air kerma emerging at different angles ϕ in the same horizontal plane as the x-ray tube and detector. The position of the x-ray tube was again set with the radiation incident at 45 on the wall, but the position of the chamber was moved to measure scatter from the wall over a range of different angles ϕ, including ones where the radiation was scattered back towards the x-ray tube. For these experiments the position of the screen was adjusted to allow measurements of scatter back towards the direction of the tube, care being taken to ensure that the screen did not interfere either with the x-ray beam incident on the wall or the field from which the ionisation chamber would detect scattered radiation. The factor f (ϕ) represents a dimensionless correction for angle of scatter in the plane of the incident air kerma. 2.4. Simulation of tertiary scatter from ceiling slabs Scatter factors were derived from the results of the experimental measurements to represent the dependence on tube potential in the standard 45 reflection geometry S(kV), with corrections for lateral displacement of the scattering element f (x/h) and angle of scatter emergence f (ϕ). In order to investigate the tertiary scatter levels that might be expected in x-ray rooms with different ceiling heights and with barriers of varying height, contributions from elements across a whole ceiling were summed for the arrangement shown as a sectional diagram in figure 2.

378 C J Martin et al Figure 3. Plan illustrating how scatter from elements of ceiling slab to the side of the vertical plane illustrated in figure 2 has been taken into account. The area of the ceiling slab, on which x-rays scattered from the patient at the isocentre of the x-ray unit were incident, was divided up into square elements. Figure 3 is a plan view showing an element on the ceiling contributing to the scatter. The figures illustrate the arrangement simulated for an x-ray unit (interventional unit or CT scanner) with an operator protected by a barrier. The ceiling slab was used for the simulation was 6 m wide and 17 m deep. Distances from the isocentre to the centre of each element and then from the element to an operator behind the barrier were used to make inverse square law corrections to the scatter incident on the ceiling and the scatter from the ceiling incident on the operator. The patient is taken as being at the origin, the distance to the scattering element in the direction of the operator is y (figure 2), and the lateral displacement from the plane containing the x-ray tube and operator is x (figure 3). If the height of the ceiling is h c and the height of the patient is h pat, then the distance D pat from the patient to the scattering element is given by: D pat = y 2 + x 2 + (h c h pat ) 2. (3) If the radiosensitive organs of the operator are at height h op above the floor, the patient is distance d pat from the protective barrier, and the operator a distance d op behind the barrier, then the distance from the scattering element to the operator D op is given by: D op = (d pat + d op y) 2 + x 2 + (h c h op ) 2. (4) Scatter factors derived from the measurements were used to model arrangements with different ceiling and barrier heights in order to investigate their influence on exposure to scattered radiation. The area of the ceiling slab contributing to the scatter is defined by the relative heights of the ceiling h c and the protective barrier h b and can be determined from comparisons of similar triangles in figure 2. From triangles BCG and GHJ, the distance of the near limit (NL) from the origin is given by: so that (d pat NL) d op = (h c h b ) (h b h op ) NL = d pat d op(h c h b ) (h b h op ). (5)

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 379 From triangles ECG and GFI, the distance of the far limit (FL) from the origin is given by: so that (FL d pat ) d pat = (h c h b ) (h b h pat ) FL = d pat + d pat(h c h b ) (h b h pat ). (6) The size of the scattering surface on the patient is substantially smaller than the distance of the patient to the ceiling, and the decline in scatter air kerma with distance from the patient has been shown to approximate to an inverse square law at distances over 0.6 m for CT (Wallace et al 2012). In addition, if the ceiling slab is sub-divided into scattering elements small compared to the distance of the operator from the ceiling, then the decline in scatter from ceiling elements will also be according to an inverse square law. Taking this into account, the scatter air kerma K s can be calculated from a summation over all the elements across the ceiling of the form: y=fl x=+w K s = S(kV)A f (ϕ) x= W y=nl f (x/h) D 2 pat D2 op (7) where A is the area of each scattering element, NL and FL are the near and far limits of the scatter from the ceiling, determined by the heights of the ceiling and the barrier, and +W and W are the lateral limits of the ceiling slab width from which scatter is assumed to contribute. Two independent approaches to the simulation were investigated. Preliminary assessments were made using an Excel spreadsheet with 0.5 m 0.5 m elements. The limits of the scattered radiation incident on the ceiling calculated for each ceiling and barrier height (NL and FL) were entered manually to define the area contributing to the tertiary scatter. Subsequently a program was set up with MATLAB Version R2010a to model the same arrangement with 0.1 m 0.1 m elements and provide a flexible tool for studying the interdependence of the scatter on the independent variables involved. Results for the two methods were within 20%, providing independent confirmation of the relationships derived. All the results presented in this paper were derived using the MATLAB model. Preliminary assessments revealed that the major factors influencing scatter in the scenario under consideration were the height of the ceiling slab from which the x-rays were scattered and the height of the barrier providing protection against the scatter coming directly from the patient. However, other variables such as the distance of the patient, i.e. the source of scatter, from the barrier (d pat ), the distance of personnel exposed behind the barrier (d op ), the size of the room in terms of the area of ceiling contributing to the scatter, and the extent of the operator cubicle beyond the barrier will all influence the result. In order to simplify the problem a standard arrangement with the x-ray tube and patient at a distance of 3 m in front of the barrier was chosen. Measurements by McVey and Weatherburn (2004) and calculations by Fog and Cormack (2010) had indicated that the dose at the height of the head from scatter was greatest at distances between 0.8 and 1.7 m behind the barrier, while that at hip level was greatest at distances between 1.4 and 2.5 m. Preliminary work using the MATALB model, with a ceiling height of 4 m and a barrier height (h b ) of 2.2 m was in broad agreement with their findings (figure 4) and a barrier to operator distance (d op ) of 1.5 m was chosen on the grounds that it should correspond to the region in which higher doses are received by the whole of the trunk. The image intensifier in an interventional room only provides protection in the direction of the primary beam, so that the entire ceiling will be irradiated by secondary scatter from the patient with the resulting tertiary scatter from the ceiling slab contributing to the dose to an operator behind a barrier. A tube potential of 85 kv has been adopted as representative of factors

380 C J Martin et al Figure 4. Variation in relative scatter air kerma at the level of the eye and trunk with distance of the operator behind a barrier for a barrier height 2.2 m and ceiling height of 4 m. The distance from barrier to the back wall was 7 m. towards the upper end of the normal range employed in interventional radiology. The x-ray beam will generally be incident on the patient from either beneath or to the side of the patient in an interventional room. The secondary scatter air kerma from a patient varies with angle and that in a particular direction can be estimated from the KAP workload (Sutton et al 2012). A conversion factor equal to the average value for all tube orientations was considered appropriate for interventional radiology calculations. The value obtained by integrating results over angles of scatter from 0 to 180 was 4.7 µgy (Gy cm 2 ) 1. For CT installations where the scatter level is more substantial results are presented for 100, 120 and 140 kv to provide additional information to allow future changes in practice to be taken into account. Scatter levels were derived from the DLP workload using a conversion factor of 0.36 µgy (mgy cm) 1 (Wallace et al 2012). The extent of the scatter from a patient in a CT room is limited by the gantry, so that only x-rays at angles greater than 30 to the vertical need be considered. Simulations have been carried out for these arrangements to determine how the scatter factor varies for ceiling slabs at heights in the range 3 5 m and for barriers of 1.8 m up to the height of the ceiling. A simplified method for deriving an estimate of scatter air kerma taking account of ceiling and barrier heights has been developed. In order to predict tertiary scatter levels that might be observed in a clinical environment, data on UK hospital workloads in terms of patient dose descriptors have been collated. Information on 38 CT scanners in terms of dose-length product (DLP) have been recorded and for ten Cardiac Catheterisation Laboratories in terms of KAP. 2.5. Simulation and assessment of tertiary scatter from walls In CT, interventional and other x-ray rooms, there can also be a potential problem from scatter coming from an adjacent wall. CT control cubicles would normally incorporate a protected door, but this is not necessarily the case for other equipment. Therefore an additional simulation has been performed to assess scatter levels through a 1 m gap at the side of a barrier adjacent to a wall (figure 5). This has been modelled for scatter from an area of wall extending for 3 m above and 1 m below the isocentre. The distance of the patient/x-ray unit isocentre from the wall is the most important geometrical factor influencing the scatter level, so the scatter air kerma has been determined as a function of this distance. The air kerma values incident

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 381 Figure 5. Arrangement used for calculation of tertiary scatter air kerma from the wall adjacent to the entry point to a control cubicle. on a person at distances up to 3 m behind the barrier and at 0.0, 0.2, 0.4 and 0.6 m from the edge have been calculated. The walls, unlike the ceiling, are generally not constructed from concrete and are more likely to be leaded plasterboard or brick. Scatter factors in RSAC (1971) for the 45 scatter configuration (figure 1(a)) have been used to derive scatter factors for a wall protected by lead. A separate simulation taking account of the limitation on scatter angle by a CT gantry was not performed, since this will in many cases be determined by the orientation of the CT scanner. The same simulation for an x-ray unit operating at 120 kv was used to provide an indication of the scatter level for a CT room. In order to investigate how well these simulations portrayed tertiary scatter from walls, air kerma levels have been measured in the control area for a CT scanner room with a similar configuration to that illustrated in figure 5. The scanning room had a protected door that opened into the room, and this was left open during the experiment. Measurements were made at a height of 1 m at about 0.2 m from the edge of the barrier, as a function of distance behind the barrier. Results were compared with simulations using the MATLAB model based on the specific room geometry. Scatter was calculated for 2 m high sections of wall, since the area above the door was shielded. 3. Results 3.1. Scatter measurements The scatter factors derived from measurements for different tube potentials are shown in figure 6. They increased linearly with tube potential between 60 and 120 kv. The data from each experiment were consistent, but measurements on different walls varied by ±17%. No data were available on concrete or brick densities for the walls used. A mean of three data sets from different walls was taken for application in the scatter calculations. Since there will only be 10% transmission of a 120 kv x-ray beam through 30 mm of concrete density 2350 kg m 3 or 40 mm of lightweight concrete kg m 3 (Sutton et al 2012), it will be the superficial layers that are the prime determinant of the scatter level. Placement of a double thickness of plasterboard (25 mm thick) in front of one concrete wall, while keeping all other factors identical, was found to reduce the scattered air kerma by 16%, demonstrating the significance of the superficial layers. Relationships from an earlier report (RSAC 1971), which are included in figure 6 for comparison, are similar in magnitude to the highest scatter level measured from concrete, and show a dependence on tube potential within the experimental error of the patient results. The

382 C J Martin et al Figure 6. Variation in scatter factor f (kv) with tube potential for different concrete walls. The results represent the three independent sets of data from different walls and the error bars relate to the standard deviation of the data from the different sets. Curves are also included showing the relationship reported in RSAC (1971) for concrete and brick. data from the present study fitted the linear equation given below. S(kV) = 0.000 178kV 0.0025 mgy (mgy m 2 ) 1 (8) with R 2 = 0.999, p < 0.001, and this was used to derive scatter factors for substitution into the simulation. The present study covered the range 60 120 kv, but RSAC (1971) data indicate that a similar relationship applied up to at least 140 kv. The results from the RSAC report for brick are also included in figure 6, but these values are substantially greater than measurements of scatter from brick walls covered by a layer of plaster in this study, which were between 30% and 50% lower than scatter from concrete. The decline in scatter with lateral position x/h from the plane in which the x-rays were incident on the wall is shown in figure 7. Error bars are based on the precision with which the x-ray tube and ionisation chamber could be positioned and the accuracy of the reading. Although the magnitude of the scatter changed with tube potential, the form of the relationship between scatter factor and lateral displacement was similar for results recorded at different tube potentials within the accuracy of the experiments. A fit to an exponential law for data at 100 kvp was applied to derive a factor to describe the fall-off in scatter to the side in terms of x/h. The factor f (x/h) derived from the measurements was: f (x/h) = e 0.2x/h (9) where x is the lateral displacement of the scattering element expressed and h is the distance from the wall. Measurements made of the variation in scatter with the angle of scatter emergence ϕ in the plane of the incident radiation were more variable, partly because of the difficulty in positioning the chamber while keeping it away from the main x-ray beam and shielding it against tube leakage. Results showed that the variation in the scatter factor with angle of scatter between 90 and 0 was small, but started to decline when the radiation was scattered back in the direction of the source. Two studies RSAC (1971) and McVey and Weatherburn (2004) have measured scatter air kerma emerging from concrete blocks with an x-ray beam incident perpendicularly on a wall. Values reported in RSAC (1971) were in the range 0.04 0.06 mgy mgy 1 m 2, but a single value is given for a broad range of tube

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 383 Figure 7. Variation in scatter f (x/h) with lateral displacement from the plane containing the x-ray source and detector for 100 kv x-rays incident on different concrete wall surfaces (figure 1(b)) corrected for the inverse square law decline. Curves representing the exponential relationships used in the simulation are shown. potentials from 100 to 300 kvp. The results of McVey and Weatherburn for 120 kvp were similar in magnitude to the present 45 scatter data. Both sets of results described above show a decline in the scatter fraction away from the perpendicular. The derived scatter factors for 120 kvp x-rays incident perpendicularly on a concrete surface gave values for scatter factors of 0.025 mgy mgy 1 m 2 for scatter at 30, 0.020 mgy mgy 1 m 2 at 45 and 0.014 mgy mgy 1 m 2 at 60. Scatter angles contributing to the air kerma incident on the operator from areas of ceiling above the x-ray unit and patient where this geometry would apply are virtually all greater than 45, so use of a scatter factor of 0.019 mgy mgy 1 m 2 for all angles ϕ should not underestimate the scatter air kerma from areas of ceiling within the body of the room. Therefore f (ϕ) is assumed to be equal to 1.0 for the simulation. Neglecting the variation with angle ϕ represents a conservative approach and contributions will be smaller because of the inverse square law, as these areas lie either beyond the operator or behind the x-ray source in the other direction. No attempt was made to study scatter for x-ray beams incident on walls at different angles. The measurements undertaken have been based on scatter from a vertical wall, but are applied to represent scatter from walls or ceilings. Inserting these results into equation (7) gives the air kerma for an x-ray beam at tube potential kv scattered from the ceiling as: K s = S(kV)A y=fl x=+w e 0.2x/h y=nl x= W D 2 pat D2 op. (10) 3.2. Simulation of x-ray room tertiary scatter Equation (10) has been used in simulations to determine scatter factors for an interventional radiology or interventional cardiology suite and a CT room. Figure 8 shows tertiary scatter air kerma for a scenario with fixed tube potential of 85 kv relative to the secondary scatter at 1 m from the x-ray unit isocentre (centre of the patient). A room 20 m long by 6 m wide was used with a distance of 7 m from the protective barrier to the wall behind the operator and scatter from the entire ceiling area of 78 m 2 on the patient side of the barrier was included. The scatter

384 C J Martin et al Figure 8. Variation in relative tertiary scatter from a concrete ceiling slab incident on an operator at 1.5 m behind a barrier as a function of ceiling height for 85 kv x-rays, expressed as a fraction of the air kerma at 1 from the centre of the x-ray beam at the patient. Figure 9. Relative magnitudes of tertiary scatter over a barrier from a ceiling slab as a function of barrier height for an interventional room with a 4 m high ceiling. Results show the effect of limiting the area of ceiling contributing to the scatter at various distances to the rear of the patient (NL negative) and in front of the patient approaching the barrier (NL positive). A near limit (NL) of zero relates to the ceiling directly above the patient and curves for NL 0 are superimposed. levels increase as the ceiling height is reduced with smaller barriers. Barriers progressively reduce the level of scatter as their height increases. The extent of the ceiling contributing to the scatter is limited by the barrier, but also depends on the height of the ceiling. A plot showing how scatter varies with barrier height for a 4 m ceiling when the near limit of the ceiling contributing to the scatter (figure 2) is set at the position of the patient (NL zero), beyond the patient (NL negative) or closer to the barrier (NL positive) is shown in figure 9. Thus for a barrier 2 m or more in height, little scatter comes from the ceiling beyond the patient. When the limit is moved closer to the operator, excluding scatter from directly above the patient, this reduces the scatter level incident on a person behind barriers of 1.8 2.5 m high.

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 385 Figure 10. Variation of relative scatter air kerma from a ceiling slab with the width of the x-ray room for an interventional room with a 4 m ceiling height. A similar analysis shows that there is very little scatter generated beyond a far limit (FL) of 10 m from the patient (7 m from the barrier). The dependence of the scatter on the width of the ceiling slab is illustrated by figure 10. As the width of the room is increased from 4 to 5 to 6 m, the scatter increases by 7% and then by a further 3%, but further increases for wider rooms are small. A 6 m wide room was chosen as a realistic conservative assumption, but a wider room would not increase the scatter level significantly. No account has been taken of scatter from the side walls, however 75% of the scatter air kerma comes from a 3 m wide strip of ceiling between the patient and the operator (figure 10). Figure 11 shows two scenarios representing an interventional cardiology or interventional radiology suite, and a CT scanning room derived to represent scatter from concrete ceiling slabs 6 m wide extending from the patient. The protective barrier is 3 m from the patient and the operator is 1.5 m behind the barrier. In these plots the scatter has been linked to the patient KAP workload for interventional procedures and the DLP workload for CT. For the interventional suite a tube potential of 85 kv has been assumed, as being towards the upper end of the range normally used. For a given ceiling height the scatter level falls steadily until the barrier reaches the ceiling slab. For the CT room, a tube potential of 120 kv was used and the area of the ceiling slab contributing to the scatter was reduced to take account of shielding by the scanner gantry (Wallace et al 2012). Namely, only x-rays at angles of greater than 30 to the vertical were included. The curves for the CT room begin to level off at lower barrier heights. The arrangement that has been modelled is for a patient at a distance of 3 m from the protective barrier. This distance may be substantially larger in some facilities, such as modern interventional rooms. If the patient is further from the barrier, the radiation fluence incident on the ceiling above the barrier will decline approximately as an inverse square law, but the area of ceiling irradiated will increase. Simulations were carried out of the decline in air kerma behind the barrier as the patient to barrier distance was increased. These showed that a realistic estimate of the scatter air kerma level behind a barrier at distances over 3 m can be obtained by multiplying the result for the 3 m simulation by the ratio (3/d pat ) where d pat is the patient to barrier distance in metres. This approximation will give a result within ±20% for barriers between 1.8 and 3.0 m in height, for ceilings between 3 and 5 m high.

386 C J Martin et al Figure 11. Variation in scatter from ceiling slabs incident on an operator at 1.5 m behind a barrier, arising from a patient 3.0 m in front of the barrier, as a function of barrier height. Results are shown for rooms with different ceiling heights used for (a) interventional cardiology or radiology with a tube potential of 85 kv as a function of KAP and (b) a CT scanning room with a tube potential of 120 kv as a function of DLP. 3.3. Method for estimation of scatter air kerma from ceiling slabs The purpose of this study is to develop a methodology for predicting scatter levels in x-ray rooms. When scatter factors are plotted against barrier height for ceiling slabs at different heights (figures 8 and 11) it is apparent that the decline in scatter level with barrier height is almost linear. By fitting the data sets for each ceiling height, it is possible to derive sets of simple linear equations for the tertiary scatter (K ceiling ) based on the ceiling height of the form: K ceiling = (C mh b ) K pat (11) where h b is the height of the proposed barrier in m, K pat is the scattered air kerma at 1 m from the patient, and m and C are constants that depend on the tube potential and ceiling height. Since the influence of room size and contributions to scatter from the ceiling beyond the patient and behind the operator are comparatively small, scatter levels in any x-ray room can be predicted from a simple equation of this form. Coefficients C and m have been determined for different ceiling heights relating to the scatter air kerma at 1 m from the patient for an interventional

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 387 kv Table 1. Values for the gradient coefficient m (m 1 ) that can be substituted into equation (11) to predict approximate levels of tertiary scatter air kerma from concrete ceiling slabs at different heights above an x-ray room. The scatter is that incident on a person behind a protective barrier and is calculated from the secondary scatter air kerma at 1 m from the isocentre of the x-ray unit. Ceiling height (m) 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 60 0.00139 0.00112 0.00090 0.00073 0.00060 0.00049 0.00041 0.00034 0.00028 0.00024 0.00020 70 0.00169 0.00136 0.00110 0.00089 0.00073 0.00060 0.00050 0.00041 0.00034 0.00029 0.00024 80 0.00200 0.00161 0.00130 0.00105 0.00087 0.00070 0.00058 0.00048 0.00040 0.00034 0.00029 85 0.00215 0.00173 0.00140 0.00113 0.00093 0.00076 0.00063 0.00052 0.00043 0.00036 0.00031 90 0.00230 0.00185 0.00150 0.00121 0.00100 0.00081 0.00067 0.00056 0.00047 0.00039 0.00033 100 0.00260 0.00210 0.00169 0.00137 0.00113 0.00092 0.00076 0.00063 0.00053 0.00044 0.00037 110 0.00291 0.00234 0.00189 0.00153 0.00126 0.00102 0.00085 0.00070 0.00059 0.00049 0.00042 120 0.00321 0.00258 0.00209 0.00169 0.00139 0.00113 0.00094 0.00078 0.00065 0.00054 0.00046 CT 100 0.00247 0.00188 0.00143 0.00110 0.00086 0.00067 0.00053 0.00041 0.00032 0.00026 0.00021 CT 120 0.00304 0.00232 0.00177 0.00136 0.00106 0.00082 0.00063 0.00050 0.00040 0.00032 0.00026 CT 140 0.00362 0.00276 0.00210 0.00162 0.00126 0.00098 0.0077 0.00059 0.00047 0.00038 0.00031 kv Table 2. Values for the coefficient C that can be substituted into equation (11) to predict approximate levels of tertiary scatter air kerma from concrete ceiling slabs at different heights above an x-ray room. The scatter is that incident on a person behind a protective barrier and is calculated from the secondary scatter air kerma at 1 m from the isocentre of the x-ray unit. Ceiling height (m) 3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5 60 0.00409 0.00350 0.00299 0.00256 0.00221 0.00188 0.00164 0.00142 0.00124 0.00108 0.00095 70 0.00498 0.00426 0.00364 0.00311 0.00269 0.00229 0.00199 0.00173 0.00151 0.00131 0.00115 80 0.00587 0.00502 0.00429 0.00367 0.00317 0.00270 0.00235 0.00203 0.00178 0.00155 0.00136 85 0.00631 0.00540 0.00461 0.00395 0.00341 0.00291 0.00253 0.00219 0.00191 0.00166 0.00146 90 0.00676 0.00578 0.00494 0.00423 0.00365 0.00311 0.00271 0.00234 0.00204 0.00178 0.00156 100 0.00765 0.00654 0.00559 0.00478 0.00413 0.00352 0.00306 0.00265 0.00231 0.00201 0.00177 110 0.00854 0.00733 0.00624 0.00534 0.00461 0.00393 0.00342 0.00296 0.00258 0.00225 0.00198 120 0.00943 0.00806 0.00689 0.00590 0.00509 0.00434 0.00377 0.00327 0.00285 0.00248 0.00218 CT 100 0.00729 0.00595 0.00482 0.00394 0.00325 0.00267 0.00223 0.00181 0.00151 0.00127 0.00108 CT 120 0.00899 0.00733 0.00595 0.00486 0.00401 0.00329 0.00274 0.00223 0.00186 0.00156 0.00133 CT 140 0.01069 0.00871 0.00707 0.00578 0.00477 0.00391 0.00326 0.00265 0.00221 0.00186 0.00158 suite or other conventional x-ray room operating at different tube potentials based on curves of the form shown in figure 8 (tables 1 and 2). Coefficients have been derived for a CT room based on curves similar to those depicted in figure 11(b). Factors have also been determined that will allow tertiary scatter levels to be predicted directly from patient dose workload data in terms of the KAP for interventional procedures for an average tube potential of 85 kv (Williams 1996, Sutton et al 2012) and the DLP for CT scans (Wallace et al 2012) (figure 11) and these are given in table 3. For interventional cardiology and radiology the equation will be: K ceiling = (C KAP m KAP h b )KAP. (12) For CT scanning the DLP workload used should be half the DLP for the head added to that of the body, so that the equation for the scatter will be: K ceiling = (C DLP m DLP h b )(DLP body + DLP head /2). (13)

388 C J Martin et al Table 3. Values for the coefficients that can be substituted into equations (12) and (13) to predict levels of tertiary scatter air kerma incident on a person behind a protective barrier in rooms with different ceiling heights from the patient dose workload. Ceiling height (m) Coefficient 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 Fluoroscopy/radiography 85 kv mkap (µgy (Gy cm 2 ) 1 m 1 ) 0.0101 0.0081 0.0066 0.0053 0.0044 0.0036 0.003 0.0024 0.00204 0.00171 0.00145 CKAP (µgy (Gy cm 2 ) 1 ) 0.0297 0.0254 0.0217 0.0186 0.0160 0.0137 0.0119 0.0103 0.00898 0.00782 0.00687 CT 100 kv mdlp (µgy (Gy cm) 1 m 1 ) 0.889 0.679 0.516 0.397 0.310 0.240 0.190 0.146 0.1156 0.0926 0.0756 CDLP (µgy (Gy cm) 1 ) 2.62 2.14 1.74 1.42 1.17 0.962 0.802 0.650 0.543 0.456 0.387 CT 120 kv mdlp (µgy (Gy cm) 1 m 1 ) 1.10 0.836 0.636 0.490 0.382 0.296 0.234 0.180 0.143 0.114 0.0932 CDLP (µgy (Gy cm) 1 ) 3.24 2.64 2.14 1.75 1.44 1.19 0.988 0.801 0.669 0.562 0.478 CT 140 kv mdlp (µgy (Gy cm) 1 m 1 ) 1.30 0.994 0.756 0.582 0.454 0.351 0.278 0.214 0.169 0.136 0.111 CDLP (µgy (Gy cm) 1 ) 3.85 3.14 2.54 2.08 1.71 1.41 1.175 0.952 0.795 0.668 0.568

Derivation of factors for estimating the scatter of diagnostic x-rays from walls and ceiling slabs 389 Figure 12. Variation in tertiary scatter air kerma from walls protected by lead and concrete adjacent to a control cubicle entrance with the distance of the patient from the wall. Results are shown for a person 1.5 m behind the edge of the barrier as a function of KAP for a range of tube potentials. The uncertainties in the scatter factors (±20%), the approximations in the summation (±15%), and the simplification in terms of the linear equations (±15%) combine to give an uncertainty of ±30% in the scatter levels derived. As discussed above, if the patient to barrier distance d pat is substantially greater than 3 m, equations (11), (12) or (13) can be modified by multiplying by the ratio 3/d pat as shown below. K ceiling = (C mh b ) 3/d pat K pat. (14) 3.4. Scatter air kerma from walls The control cubicle for an interventional suite will often, but not always, include a protected door. The scatter air kerma through the gap between the wall and the protective barrier has been modelled to allow more information on the potential scatter level to be derived. Since the x-ray room walls are frequently protected by leaded plasterboard, simulations have been carried out for lead as well as concrete, and coefficients derived to allow calculations of scatter for both surfaces. Figure 12 shows tertiary scatter air kerma per unit KAP as a function of the distance of the patient from the side wall for a range of tube potentials. The scatter factor for lead varies less with photon energy in the diagnostic energy range (RSAC 1971). The decline in scatter with distance from the wall approximates to an exponential form and results have been fitted to derive an equation that can be used to predict the tertiary scatter at the edge of a protective barrier (K wall ) from the distance of the patient to the wall x and the secondary scatter air kerma at 1 m from the patient (K pat ) using an equation of the form: K wall = K pat a kv e 0.56x (15) where a kv is a constant depending on the tube potential. Values for the constant a kv to allow the prediction of scatter from a wall when there is no door on the control cubicle are given in table 4. This equation describes the scatter for a patient 3 m from the barrier. Simulations of the air kerma level with larger patient to barrier distances showed that multiplication of the results by the ratio 3/d pat will give results within ±20% for distances up to 5 m, where the patient is

390 C J Martin et al Figure 13. Measurements of tertiary scatter air kerma from a wall protected by lead plasterboard adjacent to a control cubicle entrance as a function of the distance behind the protective barrier. Results were derived for a body phantom irradiated with 120 kv x-rays and are portrayed per unit secondary scatter at 1 m from the phantom. In the room, the x-ray tube and phantom were 2.7 m from the side wall and 4.7 m from the barrier, and the entrance gap was 0.86 m. Simulations are shown for a similar configuration for measurement points at different distances from the edge of the barrier. between 1.4 and 3 m from the side wall, so that equation (15) transforms to: K wall = K pat a kv 3/d pat e 0.56x. (16) Coefficients a KAP and a DLP have been derived to enable K wall to be predicted from the patient dose workload in terms of the KAP or DLP respectively. If a department did not wish to include a door, calculations could be performed using equation (16) to determine scatter levels behind the barrier incident on a person near the edge of the barrier. Measurements of the variation in air kerma with distance behind a control barrier for 120 kv x-rays are compared with results from simulations in figure 13 in order to assess how well the model describes scatter levels in practice. The solid curve gives air kerma from simulations at 0.2 m from the edge of the barrier, which was the position of the centre of the chamber. Scatter measurements were 15% lower, but followed a similar relationship to position. Other curves representing scatter at different distances from the barrier edge are included for information. Workload data in terms of annual total patient dose parameters are given in table 5 for interventional cardiology and table 6 for CT from the data collected. The corresponding levels of tertiary scatter air kerma incident on the operator have been calculated. 4. Discussion 4.1. Experimental measurements of scatter Results show that the scatter factors for x-ray beams incident on concrete walls at 45 increase linearly with tube potentials between 60 and 120 kv with a dependence described by equation (8) (figure 6). Variations of ±20% in results for different walls are considered to depend on composition, particularly that of the superficial layers. Scatter levels from brick walls were 30% 50% lower than for concrete, and less than results in RSAC (1971). Differences are thought to reflect primarily the large variations in the composition of