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A model for calculating shielding requirements in diagnostic X-ray facilities

¹ Medical Physics Unit, "Konstantopoulio-Agia Olga" Hospital, 3–5 Agias Olgas, Nea Ionia, 142 33, Athens, ² Medical Physics Department, Medical School, University of Athens, 75 Mikras Asias, 115 27, Athens and ³ Radiology Department, Areteion Hospital, 76 Vasilissis Sophias, 115 28, Athens, Greece

	Abstract

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In this study a new model for calculating shielding requirements in diagnostic X-ray facilities is presented. It is based on the combination and modification of models and concepts originally proposed by other authors in order to calculate barrier requirements in diagnostic X-ray facilities accurately and realistically without unjustified exaggerations. With this model, multiple sources of radiation operating at different potentials, leakage radiation reduction when operating at potentials less than the maximum rated value, secondary radiation use factors reduction for primary barriers, attenuation by image receptor hardware and existing building materials are all taken into account. Examples of shielding calculations for typical cases are given illustrating the differences between the various models and concepts proposed, as well as the potential reduction in shielding requirements without compromising the radiation protection of public and staff.

	Introduction

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The basic principles for calculating shielding requirements for diagnostic X-ray facilities have been described in report no. 49 of the National Council on Radiation Protection and Measurements (henceforth referred to as NCRP49) [1]. Although NCRP49 remained for many years the basic shielding handbook, many authors have since proposed other shielding calculation models, which, apart from being well suited for computerized applications, are also more accurate and dispense with the over-conservatism inherent in NCRP49.

In this study, models and concepts introduced by various authors are combined in order to build a calculation model appropriate for computerized applications. The bases are the model introduced by Simpkin [2] for calculation of shielding requirements of multiple sources of radiation and the model proposed by Petrantonaki et al [3] that reviewed the aforementioned model and additionally accounted for the attenuation offered by existing building materials.

Furthermore, in this study the formulation of Petrantonaki et al [3] is used to account not only for building materials, but also for the primary attenuation in the image receptor hardware (cassette, grid, cassette holder and X-ray table structures) reported by Dixon [4] and Simpkin et al [5]. To account for the reduced leakage radiation observed when the tube operates at potentials less than the maximum rated value, as has been reported by Kelley et al [6] and Simpkin et al [7], a new approach is proposed.

The reduction of secondary radiation use factors for primary barriers reported by Simpkin et al [7] is also incorporated into the new model. Finally, the concept of workload distribution at various potentials [8] is utilized as well as the equations proposed to predict scattered fraction for a range of tube potentials [9].

Since a detailed explanation of the way the referenced models and formulations were deduced would require too many pages, the equations used to build our model are presented briefly and comments on the differences between models and concepts are kept as short as possible. Examples of shielding calculations are given to show the marked reduction in barrier requirements obtained with this model, at no cost to the radiation protection of public and staff.

	Methods

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The existing models
The following equation, originating from the models proposed by Simpkin [2] and Petrantonaki et al [3], can be used to calculate shielding requirements:

where B_p(x), B_s(x) and B_L(x) in Equation (1) are the relative transmission of primary, scatter and leakage radiation, respectively, by thickness x of shielding material and x is the shielding thickness required to reduce the total exposure to P, the weekly dose limit for the area to be shielded. D_p, D_s and D_L are the doses at the point of interest from primary, scatter and leakage radiation, respectively (without shielding), given by the following equations:

In the above equations, K_o is the relative radiation output in mSv (mA·min)^-1 at 1 m from the X-ray focus for the tube potential assumed, W is the workload in mA·min, U_p is the use factor for the primary radiation, T is the occupancy factor, d_pri=d_L, d_sca, d_sec are the distances in metres of the X-ray source focus to point of interest for primary and leakage radiation, focus to scatterer, and scatterer to point of interest, respectively. F is the field size in cm² at the entrance surface of the scatterer, _s the scattered fraction, L is the leakage radiation dose expressed in mSv h^-1 and I the maximum continuous fluoroscopic current. U_s and U_L are the use factors for scatter and leakage radiation, respectively, normally omitted as both are considered equal to unity for all barriers. Since F is proportional to , F and can be equivalently defined at the focus to image receptor distance instead of the focus to entrance surface distance [7].

It should be noted that the dose limits in general refer to the effective dose to the person who may be irradiated and are given in Sv. However, since exposure is given in R and air kerma in Gy, the relation between exposure, air kerma and the dose to a person should be clarified. In this study, exposure and air kerma values have been converted to equivalent dose by assuming that an exposure of 1 R corresponds to an air kerma of 8.73 mGy, a dose to tissues of 10 mGy and an equivalent dose of 10 mSv, [Archer et al 10]. In shielding work Gy and Sv are interchangeable when tissues are irradiated by photons. K_o, L, D_p, D_s and D_L described above are all expressed in terms of equivalent dose so that the units agree with P.

Archer et al [11] first proposed the following non-linear equation to describe the relative transmission of X-rays through thickness x of a shielding material:

The three parameters ,, are strongly dependent on the tube potential and the shielding material and therefore B(x) is indirectly dependent on both the tube potential and the shielding material. ,, can be influenced by a number of factors including generator waveform and X-ray beam filtration as reported by Rossi et al [12]. In the following, to avoid the use of too many parameters inside parentheses, a subscript will be used to denote different operating potentials while different shielding materials will be noted by different letters, e.g. x,y,t.

Assuming that primary and scattered radiation are more or less of the same quality, the same parameters ,, can be used in Equation (5) to describe both B_p(x) and B_s(x). However, it has also been suggested that different parameters should be used for primary and scattered radiation [9] as will be discussed later.

The thickness x required to obtain a relative transmission B is given by the following equation:

The half value layer (HVL) can be determined as a function of penetrated material thickness, using the following equation:

This expression, will tend to (ln2)/ at large values of x, and provides an estimate of the HVLs at high attenuation, as is required when shielding of leakage radiation is considered [12]. Leakage radiation is assumed to behave like a monoenergetic beam since the primary beam has been greatly hardened by the tube housing shielding and the following equation can be used to describe B_L(x):

When more than one unit is used in the same room, or when the same unit is operated at different tube potentials Equation (1) can be written as:

where the subscript i denotes the different units or operating conditions.

Primary, scatter and leakage shielding requirements can be also calculated separately as in the methodology of NCRP 49 [1], by using Equations (1) or (9) and accounting separately for each term (by setting the other use factors equal to zero).

If a shielding material of thickness y₁ is already in place, e.g. wall building materials, then according to the model of Petrantonaki et al [3] the thickness x₁ required to be placed in front of y₁ in order to fulfil the shielding requirements can be found by the following equation:

where, as can be seen in Figure 1, y₂ is the thickness of existing material that would cause the same attenuation as x₁, that is:

It should be noted that in the study of Petrantonaki et al [3] the above condition is not given in terms of relative transmission but in terms of transmitted exposure, that is K_ux(x₁)=K_ux(y₁). However, when the attenuation data are for the same X-ray unit and thus the same K_o, K_ux(x₁)=K_oB(x₁) and K_ux(y₁)=K_oB(y₁). Therefore the aforementioned conditions are also valid.

View larger version (19K): [in this window] [in a new window]   Figure 1. A schematic diagram explaining the principle of the model introduced by Petrantonaki et al [3]. If a material Y, e.g. a concrete wall, of thickness y1 is already present, then the thickness x1 of another shielding material X, e.g. lead, that should be placed in front of y1 to bring the exposure down to the limit, is that attenuating the X-ray beam by as much as thickness y2 of material Y, where B(y2+y1) is the required relative attenuation to comply with the dose limit.

where

Thus the model of Petrantonaki et al [3] takes into account not only the attenuation introduced by the presence of a material but also the beam hardening caused by the first material met by the X-ray beam. The underlying assumption is that the beam hardening by different materials is the same when the relative transmissions B (or transmitted exposures K_ux) are the same.

By analogy with Equation (1), Equations (10) and (12) can be applied to the case where more than one unit is used in the same room or when the same unit is operated at different tube potentials or conditions.

A new model based on the modification and combination of existing models and concepts
The models of Simpkin [2] and Petrantonaki et al [3] will now be modified to incorporate the adjustments proposed for primary, secondary and leakage radiation mentioned in the introduction.

Leakage radiation
A diagnostic-type protective tube housing is defined in the report No.34 of the National Council on Radiation Protection and Measurements [13], as one "so constructed that the leakage radiation measured at a distance of 1 m from the source cannot exceed 100 mR in 1 h when the tube is operated at its maximum continuous rated current for the maximum rated tube potential". However, as has been noted by Kelley et al [6] and Simpkin et al [7], when the tube is operated at a lower tube potential, leakage radiation is greatly reduced. This reduction can be very significant for lower kVp where leakage radiation virtually determines the secondary shielding requirements.

Since 100 mR corresponds to an equivalent dose of 1 mSv, the tube housing thickness t_H required to comply with the limit for leakage radiation, can be calculated using Equation (6) and setting B equal to that given by the following equation:

where I_max is the maximum rated fluoroscopic current (in mA) for the maximum rated tube potential (V_max).

Thus, thickness t_H represents the shielding required to reduce the dose rate from the primary beam down to 1 mSv h^-1, when the tube is operated at maximum rated settings. It should be also noted that tubes are usually over-shielded and the maximum leakage can be much lower [6, 7].

When the tube is operated at a tube potential lower than the maximum value where maximum continuous current is I the leakage radiation L will be equal to:

Substituting L in Equation (4) by Equation (15) we can write:

The above equation introduced for D_L is simpler and more straightforward than the corresponding equation proposed by Simpkin et al [7].

Primary attenuation by image receptor hardware structures
In traditional calculations for primary barriers, the primary beam attenuation by the patient, X-ray table, grid, cassette and cassette holder structures is ignored. However, as has been reported by Dixon [4] and Dixon et al [5], even if the attenuation offered by the patient is not considered (as one might argue that not all the primary beam area passes through the patient), the attenuation offered by the image receptor hardware is quite important and should not be ignored. This attenuation B_T was found by Dixon [4] to depend on operating potential (kVp) and is satisfactorily described for various types of image receptor hardware by the following equation:

Dixon et al [5] proposed that the thickness x_T of the shielding material that gives attenuation equal to B_T could be found by using Equation (6) and should be subtracted from the total primary barrier thickness. However, this approach cannot be used when shielding requirements are calculated against all sources of radiation and the primary barrier accepts secondary radiation as well.

The alternative approach is to consider that the image receptor hardware acts like a shielding material already in place for primary radiation. Therefore, using the formulation of Petrantonaki et al [3] we can substitute the first term of Equation (1) with:

where x_T is the thickness of the shielding material to be used that provides equivalent attenuation with the image receptor hardware (B(x_T)=B_T (kVp)).

Secondary use factor reduction for primary barriers
Use factors for secondary and leakage radiation are traditionally considered equal to one for all barriers. However, as proposed by Simpkin et al [7] for a primary barrier the secondary radiation use factors should be taken both equal to 1-U_p. Indeed, for primary barriers any leakage radiation from the tube front face is already included when measuring the tube output while the scattered radiation by the patient is generated as a consequence of primary attenuation by the patient that is ignored. Thus, in Equations (3) and (4) U_s and U_L will be taken equal to 1-U_p.

Shielding for a workload distributed at various tube potentials
According to the NCRP49 methodology, shielding calculations were made for a single value of operating potential (usually 100 kVp for fluoroscopic or radiographic installations), as if all radiographs and fluoroscopy were carried out with the same tube potential. However, in practice the workload is distributed across various tube potentials and assuming a single conservatively high value for the tube potential can lead to significant overestimation of the barrier thickness requirements [8].

Therefore, given the marked dependence of the relative transmission on tube potential, the type of examinations carried out and the exposure conditions used can dramatically alter the shielding requirements. It should be noted, however, that when the operating potential is increased the mAs required to produce the desired optical density on the film and therefore the workload is reduced.

Scatter radiation dependence on cassette size and scatter angle
In addition various film sizes are used depending on the examined area. Usually it is assumed that all projections are carried out using the largest cassette size that is 35 x 43 cm² and therefore F=1505 cm² at d_sca equal to focus to film distance. However, according to our data on film consumption for the last year in a general radiology department, the film sizes used for radiography were: 35 x 43 cm² (48.1%), 35 x 35 cm² (30.2%), 30 x 40 cm² (8.5%), 24 x 30 cm² (10.4%) and 18 x 24 cm² (2.8%). Thus, considering all films to be 35 x 43 cm² leads to 17% overestimation of the scattered radiation. This overestimation of the field size can be much bigger in mammography shielding calculations, where all films are often considered to be 24 x 30 cm² instead of 18 x 24 cm² that is usually used (67% increase in F and therefore in D_s).

Nevertheless, in view of all the uncertainties involved in the assumptions used for shielding calculations and particularly in the scattered fraction _s where different values have been proposed as discussed below, the use of the largest available cassette size for F could be thought as preserving some of the traditional NCRP49 conservatism, erring on the side of safety.

As far as the scatter fraction _s is concerned, various values and formulations have been proposed [6, 7, 9, 14]. However, as concluded by Sutton et al [9] the combined effect of inverse square law and scattered beam HVL variation with angle, means that for practical purposes the greatest transmission occurs at 90° even if the greatest scatter air kerma occurs at approximately 120°. In this study the scatter ratios _s were derived using the equation given in Sutton et al [9] to describe scatter factors S (the ratio of scatter dose in µGy per dose area product in Gy cm²) at angle for tube potentials 50 to 125 kVp:

Incorporating the aforementioned adjustments to the existing model of Petrantonaki et al [3] and making allowance for the possible presence of a material of thickness y already in place, the required shielding thickness x of a material to be added in front of that existing, is that satisfying the following equation:

where D_p, D_s and D_L are given by Equations (2), (3) and (16), respectively, with U_s=U_L=1-U_p, B_T(kVp) is given by Equation (17), B_p(x_T)=B_T(kVp), B_p(x+x_T)= B_p(y₁) and B_s(x)=B_s(y₂).

By analogy with Equation (9), Equation (21) can be written as:

When no material is present (that is y=0) the last factor in each term of Equation (22) is equal to unity and can be ignored.

	Shielding calculation examples and discussion

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In Figure 2 a schematic diagram of a typical X-ray facility with chest bucky is given. In Table 1 the shielding requirements for the chest bucky wall (AB), a side wall (BC) and the floor (FL) are given, assuming that all areas behind these barriers are non-controlled and T=1. The chest bucky wall and the floor receive mainly secondary radiation except the area behind the chest bucky (A'B') and under the X-ray table that are met by the primary beam, whereas the side wall receives only secondary radiation.

View larger version (22K): [in this window] [in a new window]   Figure 2. A schematic diagram of an X-ray facility for general radiography with chest bucky.

View this table: [in this window] [in a new window]   Table 1. Shielding requirements for a non-controlled area for the X-ray facility of Figure 1 for different assumptions and calculation modelsa. Shielding requirements for chest bucky wall and side wall are in mm Pb, for the floor in cm concrete. Numbers in parentheses in column 6 are the secondary barriers according to Sutton et al [9]

In columns 1–3 the shielding requirements have been calculated according to the NCRP49 [1] methodology, taking into account the reduction of P for non-controlled areas because of the corresponding reduction of annual dose limit (from 5 mSv year^-1 to 1 mSv year^-1) and the introduction of dose constraints (0.3 mSv year^-1). It can be seen that these changes increase the barrier requirements significantly, even to more than double the values required before.

In column 4 the shielding requirements have been calculated using the model proposed by Simpkin [2]. It can be seen that shielding requirements for primary barriers are slightly increased compared with column 3 values because of the inclusion of secondary radiation, whereas for secondary barriers are lower because the NCRP49 "add one HVL" rule has been abolished.

In column 5 the barrier requirements have been calculated with the model proposed by Simpkin [2] where the X-ray unit is assumed to be two different units: Unit 1 when the beam is directed to the chest bucky and Unit 2 when the beam is directed to the X-ray table. The reduced shielding requirements for the primary for chest bucky wall and all secondary barriers is due to the greater d_sca=1.9 assumed for Unit 1 compared with d_sca=1.1 assumed for Unit 2 and for column 4 calculations.

In column 6 the reduction in secondary barrier requirements due to allowance for leakage reduction when the tube is operating at lower tube potential than its maximum rating is shown. Numbers in parentheses have been calculated assuming no leakage radiation and using the parameters ,, suggested for secondary radiation by Sutton et al [9]. It can be seen that differences between shielding requirements are small. However to apply the methodology of Sutton et al [9] different sets of parameters are required for the secondary radiation transmission curves and these are not available for all materials and tube potentials.

In columns 7 and 8 the effect on primary barriers of allowance for the attenuation introduced by image receptor hardware given by Equation (17) and secondary use factors reduction (U_s=U_L=1-U_p) respectively, are shown. The values of column 8 are lower than the corresponding figures in column 3 and comparable with those of column 2, while for primary barriers they can even be lower than the figures in column 1.

Finally, in the last column shielding requirements are determined using Equation (22) (assuming no existing material i.e. y=0) and the distribution of a total workload of 270 mA ^·min at various tube potentials given by Simpkin [8] (table III, Radiography room). It can be seen that values in column 9 are significantly lower than the corresponding figures in column 8 and comparable with those in column 1. This suggests that X-ray facilities shielded in the past according to NCRP49 guidelines could still comply with the new dose limits and dose constraints, provided that realistic assumptions are now used for the re-evaluation of the adequacy of the existing shielding.

In Table 2 an example of shielding of a panoramic X-ray unit is given. It can be seen that when the attenuation of the primary beam by the patient and cassette holder structures is not being taken into account, primary barrier requirements (numbers in brackets) are quite high whereas in practice there is no primary radiation when the patient and cassette holder structures are present [9]. It also worth mentioning that if the tube housing shield has been determined assuming that V_max is 70 kVp (or even 85 kVp) the leakage contribution prevails over scatter contribution and virtually determines shielding requirements. Therefore in such cases ignoring leakage radiation as proposed by Sutton et al [9] may lead to underestimation of barrier thickness, if the manufacturers of panoramic X-ray tubes do not incorporate more shielding than the minimum required by the current limit for leakage. As far as we know, data on the actual leakage from panoramic and dental units are not available in the literature, so, as a precautionary measure the maximum allowed value should normally be assumed.

Finally in Table 3 the model presented is used for shielding calculations for secondary barriers in mammography, exhibiting marked reduction when the operation potential is realistically assumed to be 30 kVp instead of 50 kVp that has often been used in the past. It can be seen that a gypsum wallboard sheet is sufficient to provide the required protection for side walls, whereas 1 cm plate glass is enough to protect the operator even when the control panel is considered as a non-controlled area.

Received for publication April 5, 2002. Revision received May 26, 2003. Accepted for publication June 11, 2003.

	References

Top Abstract Introduction Methods Shielding calculation examples... References

 

1. National Council on Radiation Protection and Measurements. Structural shielding design and evaluation for medical use of x rays and gamma rays of energies up to 10 MeV. NCRP Report 49. Bethesda MD: NCRP, 1976.
2. Simpkin DJ. A general solution to the shielding of medical x and rays by the NCRP report no. 49 methods. Health Phys 1987;52:431–6.[Medline]
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6. Kelley JP, Trout ED, Larson VL. Leakage radiation from a diagnostic tube housing when operated at less than the maximum rated kilovoltage. Health Phys 1976;31:27–31.[Medline]
7. Simpkin DJ, Dixon RL. Secondary shielding barriers for diagnostic X-ray facilities: scatter and leakage revisited. Health Phys 1998;74:350–65.[Medline]
8. Simpkin DJ. Evaluation of NCRP report No. 49 assumptions on workloads and use factors in diagnostic radiology. Med Phys 1996;23:577–84.[CrossRef][Medline]
9. Sutton DG, Williams JR, editors. Radiation shielding for diagnostic X-rays. Report of a joint BIR/IPEM working party. London: The British Institute of Radiology, 2000.
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11. Archer BR, Thornby JI, Bushong SC. Diagnostic X-ray shielding design based on an empirical model of photon attenuation. Health Phys 1983;44:507–17.[Medline]
12. Rossi RP, Ritenour R, Christodoulou E. Broad beam transmission properties of some common shielding materials for use in diagnostic radiology. Health Phys 1991;61:601–8.[Medline]
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16. Simpkin DJ. Shielding requirements for mammography. Health Phys 1987;53:267–79.[Medline]

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This Article Abstract Figures Only Full Text (PDF) Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via Google Scholar Google Scholar Articles by Tsalafoutas, I A Articles by Sandilos, P Search for Related Content PubMed PubMed Citation Articles by Tsalafoutas, I A Articles by Sandilos, P