1. Calculating shielding requirements in diagnostic X-ray
departments
M PETRANTONAKI, MSc, C KAPPAS, PhD, E P EFSTATHOPOULOS, MSc,
Y THEODORAKOS, BSc and G PANAYIOTAKIS, PhD
Department of Medical Physics, School of Medicine, University of Patras, 265 00 Patras, Greece
Abstract. Structural radiation protection for diagnostic X-ray facilities is most commonly per-
formed following the recommendations of the National Council on Radiation Protection and
Measurements Report No. 49. A number of analytical methods have already been developed to
improve the design of these facilities. Speci¢cally, these methods reassess shielding calculations in
X-ray areas with respect to the methodology of the calculation of the barrier thickness and the
number of sources considered in the area. Thus, they generate an overall solution for the cases
met at the medical radiation structural design. This paper presents an extension of an existing
method for calculating shielding requirements, for multiple X-ray tubes in a room operated at var-
ious beam qualities. The methodology computes the required shielding thickness such that the
exposure behind it stays below a desired value. The presented method eliminates the overestimation
of added shielding thickness which may occur using the other methods already mentioned. A user-
friendly windows-based program has also been developed to assist shielding computations.
Shielding requirements for diagnostic radiation
protective barriers are usually speci¢ed following
the calculation concept of the National Council
on Radiation Protection and Measurements
(NCRP) Report No. 49 [1]. The methodology pro-
posed by NCRP calculates the exposure levels of
primary, scatter and leakage radiation emitted
from an individual X-ray source, giving no speci¢c
guidance to account for the combination of all dif-
ferent radiation £uxes through the barrier, except
the general ``add one half value layer (HVL)''
approximation. This has been proved by Archer
et al [2] to be an arbitrarily conservative addition,
leading the weekly exposure of personnel to be
reduced more than required according to the
designed maximum permissible dose (MPD) lim-
its. The design and shielding barriers in a diagnos-
tic X-ray department generally follows the
ALARA principle. That means that, in practice,
the exposure levels are kept ``as low as reasonably
achievable'', taking into consideration economical
and technical factors. Additionally, the calculation
of barrier requirements include many uncertainties
(e.g. the workload, the actual kVp used etc.).
In an e¡ort to improve and extend the methodol-
ogy described in NCRP 49 [1], Archer et al [2] have
describeda¢rstapproachtodeterminethe``precise''
secondary barrier thickness required to meet the
designcriteria.Theyhavetriedtoeliminatetheresul-
tant overshielding barrier of NCRP 49 [1] and to
allow greater accuracy in the computation proce-
dure.Theirapproachhasbeenextendedandgeneral-
ized by McGuire [3], who illustrated methods for
performing shielding calculations for multiple
sources of radiation in a diagnostic room, operating
atthe same tube potential (kVp) values. McGuire [3]
further extended his general solution to enable addi-
tional shielding to be calculated and added to an
existing protective barrier, while Simpkin [4] pro-
posed a method to account for more than one X-ray
sourcebeinglocatedinaroom,operatingatdi¡erent
maximum tube potential (kVp) values.
This paper generalizes these techniques, propos-
ing a method to solve the problem of accurate calcu-
lation of the required thickness of shielding material
to be added in front of an existing protective barrier
which provides insu¤cient shielding in a diagnostic
X-ray room. Additionally, a user-friendlyWindows-
based program has been implemented, based on the
proposed method, to compute shielding require-
ments of a diagnostic X-ray room.
Methods and materials
Theoretical background
The required protective barrier thickness in a
diagnostic X-ray room can be calculated comple-
tely from a single equation proposed by McGuire
[3]. The method requires that the weekly exposure
radiation levels from primary, scatter and leakage
radiation emitted from each X-ray source in the
Received 13 November 1997 and in revised form 7 August
1998, accepted 24 August 1998.
Address correspondence to George Panayiotakis.
This work has been supported by the Greek Ministry of
Health (K.E.S.Y. contract E/133/95).
The British Journal of Radiology, 72 (1999), 179^185 E 1999 The British Institute of Radiology
179The British Journal of Radiology, February 1999

2. room should be determined. The recommendation
of NCRP 49 [1] that for the range of energies used
in diagnostic radiology, scatter radiation is essen-
tially of the same quality and penetrating ability
as primary beam, has been followed and the
required shielding is then predicted by working
out each weekly exposure contribution to the bar-
rier, taking into account the di¡erences in trans-
mission characteristics of leakage and primary/
scatter radiation. These have been generalized by
the equation:
P…x† ˆ
ˆn
iˆ1
PijTij…x† …1†
where P(x) is the total weekly exposure emitted
from n X-ray sources in the room at a point behind
a barrier of thickness x, which should be equal to
the design MPD for adequate protection and Pij is
the exposure from source i, radiation type (beam
quality) j. The i sources of radiation exposure
include primary, scatter and leakage radiation
from all the X-ray tubes in the room. The radiation
type j concerns the maximum operating potential
of the X-ray source and does not vary in the above
equation, providing the constraint that all the X-
ray tubes in the room operate at the same maxi-
mum tube potential (kVp) values. Tij(x) represents
the transmission characteristics of source i, radia-
tion type j, through the barrier material of thick-
ness x. It is determined, for primary and scatter
radiation, by the use of Archer's non-linear ¢tting
routine for the K curves of NCRP 49 by normal-
izing them with Ko, the radiation output (mSv
mA^1
min^1
at 1 m) of the primary X-ray beam in
free space. K characterizes attenuation of X-rays
for a certain material. The K curves for lead and
concrete and for potentials of 50 kV to 3 MV exist
in appendix D of NCRP 49 [1]. Transmission of
leakage radiation is expressed in terms of HVLs,
with a ¢rst order exponential equation of the form:
TLj…x† ˆ exp…{xln2aHVLj† …2†
TLj…x† represents the transmission characteristics
of leakage radiation of radiation type j. The above
method has the advantage of approaching the
problem of additional shielding calculation, when
structural shielding already exists, providing an
estimate for a material 1 of thickness x1 necessary
to be added in front of a barrier, constructed from
a material 2 of known thickness x2, so as to satisfy
the shielding requirements. The beam is considered
to be transmitted through the ¢rst material of
thickness x1 and, afterwards, it is assumed to be
hardened so much that the passage of all the three
types of radiation through the material 2 of thick-
ness x2 can be described in terms of number of
HVLs. Therefore, knowing the existing thickness
x2, x1 can be approximated by solving the equa-
tion:
The algorithm
Shielding requirements of a room with many X-
ray sources of di¡erent radiation types
Equation (1) accounts for more than one X-
ray source in a room, of the same radiation type j.
However, for a room with M X-ray sources oper-
ating at various maximum tube potential (kVp)
values and for the simplest case of no structural
shielding in place, Equation (1) must be extended
and rewritten as:
P
À
x
Á
~
ˆM
jˆ1
Â
PPjTPj…x
Á
zPSjTSj
À
x
Á
zPLjTLj
À
x
ÁÃ
(4)
or, analytically and using Equation (2),
P
À
x
Á
~
ˆM
jˆ1
n
PPj
Â
Kuxj
À
x
Á
aKoj
Ã
zPSj
Â
Kuxj
À
x
Á
aKoj
Ã
zPLjexp
À
{xln2aHVLj
Áo
(5)
where PPj, PSj and PLj are the unshielded expo-
sure levels from primary, scatter and leakage
radiation emitted from each tube of radiation
type j present in the room and de¢ned by
McGuire [3], including the ``use factor'' contribu-
tion. Kux are the values of K parameterized to ¢t
to Archer's model and are material dependent as
well as a function of material thickness x and kVp
values. The calculation problem is then to ¢nd the
necessary barrier thickness x which would satisfy
the above equation when P(x)5MPD.
Shielding requirements when existing protection is
in place
For the case of shielding already in place,
according to McGuire's methodology, the beam
is assumed to have been highly ¢ltered by passage
through the ¢rst material of thickness x1 and
being hardened, it is transmitted through the next
material of thickness x2 in order that the weekly
exposure can meet the protection criteria.
However, the appropriate material thickness for a
beam to be hardened cannot be exactly known
and the method leads to an overestimation
of added material, as will be shown in the
results section. The problem therefore deserves a
P…x1†~
Â
PPjTPj
À
x1
Á
zPSjTSj
À
x1
Á
zPLjTLj
À
x1
ÁÃ
exp
À
{x2ln2aHVL2j
Á
(3)
M Petrantonaki, C Kappas, E P Efstathopoulos et al
180 The British Journal of Radiology, February 1999

3. di¡erent approach, where the above assumption
would be ignored.
Consider a single radiation source emitting pri-
mary, scatter and leakage radiation. Since the
unshielded weekly exposures PP, PS and PL in the
area to be protected are known, one can calculate,
using Equation (5), the thickness of material x
needed to reduce the total weekly exposure to
MPD. Referring to Figure 1, for passage of
primary and scatter radiation through two adja-
cent slabs of identical material and with the thick-
ness x2 of existing shielding material to be known,
the thickness x1 of the same material to be added in
front of x2 can be estimated through a di¡erent
approach from that described by McGuire. The
transmission of primary or scatter radiation PP/S
through x1 can be expressed as:
P'PaS~TPaS
À
x1
Á
PPaS~
Â
Kux
À
x1
Á
aKo
Ã
PPaS …6†
where P9P/S is the radiation exposure behind x1
thickness. Leakage radiation exposure behind the
slab thickness x1 would be equal to:
P'L ˆ exp…{x1ln2aHVL1†PL …7†
After passing the ¢rst thickness x1, the primary
and scatter radiation has already been attenuated
from Ko to Kux(x1) and they will continue to be
transmitted through x2 up to Kux(x1+x2). The
exposure levels of primary, scatter and leakage
radiation behind the total barrier then equals to:
P''PaS~TPaS
À
x2
Á
P'PaS
~
Â
Kux
À
x1zx2
Á
aKux
À
x1
ÁÃ
P'PaS …8†
P''L~TL…x2†P'L~exp…{x2ln2aHVL2†P'L …9†
and the total exposure to the occupied area would
be:
PT ~P''PzP''SzP''L
~
À
Kux
À
x1zx2
Á
aKo
ÁÀ
PPzPS
Á
zexp
Â
{
À
x1zx2
Á
ln2aHVL
Ã
PL (10†
where HVL is the half value layer at high attenua-
tion, common for both slabs which is dependent on
both material and tube potential. Knowing x2, the
thickness x1 can be calculated so that PT is equal to
the design MPD.
To extend the above concept, consider the e¡ect
of putting a slab of material 1 in front of the exist-
ing barrier of di¡erent material 2. Referring to
Figure 2, suppose that x1 is the thickness of mate-
rial 1 required to be placed in front of an existing
Figure 1. Qualitative representation of the transmis-
sion of primary and scatter radiation through two adja-
cent slabs of the same material with thickness x1 and
x2. x is the total thickness shielding requirement. PP/S
is the primary or scatter radiation exposure to the bar-
rier. P9P/S is the transmitted radiation exposure of PP/S
through the wall slab of thickness x1 and P0P/S is the
transmitted radiation exposure of P9P/S through the
wall slab of thickness x2.
Figure 2. Qualitative representation of the primary
and scatter transmission curves through two di¡erent
materials. x1 is the thickness of material 1 that is
required to be placed in front of an existing barrier of
thickness x2 of material 2, so that the exposure at a
point behind the protective barrier is equal to the maxi-
mum permissible dose (MPD) limit. The same trans-
mission of the X-ray beam through thickness x1 can be
obtained by a thickness x3 of material 2.
Shielding in X-ray departments
181The British Journal of Radiology, February 1999

4. thickness x2 of material 2. The same transmission
of the X-ray beam through thickness x1 of material
1 corresponds to a thickness x3 of another material
2. The beam then can be considered to pass ¢rst
through width x3 of material 2 and to continue to
be transmitted through thickness x2 of the same
material. Each type of radiation exposure behind
the entire wall, according to Equations (6), (7),
(8) and (9), would then be:
P''PaS~
Â
Kux
À
x3zx2
Á
aKux
À
x3
ÁÃ
|
Â
Kux
À
x1
Á
aKo
Ã
PPaS …11†
P''L~exp…{x2ln2aHVL2†
|exp…{x1ln2aHVL1†PL …12†
where Kux(x1) equals Kux(x3) being the transmis-
sions of the primary or scatter beam through thick-
ness x1, material 1 and thickness x3, material 2,
respectively.
In summary, when M X-ray tubes emit radiation
of various beam qualities in a room with or without
existing protection, the exposure at a point behind
the protective wall can be expressed by combining
Equations (4), (10), (11) and (12) as:
PT ~
ˆM
jˆ1
ÈÂ
Kuxj
À
x1
Á
aKoj
Ã
T2j
À
PPzPS
Á
zexp
À
{x1ln2aHVL1j
Á
|exp
À
{x1ln2aHVL2j
Á
PL
É
…13†
where T2j is the transmission of primary or scatter
radiation of beam quality j through the second slab
of material and it is equal to 1 when no protective
barrier is present (i.e. x250). For the case of adding
a thickness x1 in front of an existing thickness x2
of the same material, transmission equals
Kux(x1+x2)/Kux(x1), while when a di¡erent mate-
rial is in place to that to be added, transmission
equals Kux(x3+x2)/Kux(x3). Using this equation,
the additional protective barrier thickness x1
required to set PT to MPD can be calculated.
Implementation
The described method has been developed in
Microsoft Visual Basic 4.0 for Microsoft
Windows 95 (Microsoft Corp., Redmond,
Washington, USA). It allows for input of room
type and it is concerned with various diagnostic
installations in the room (£uoroscopic, common
radiographic, angiographic, mammographic, CT
scanner etc.). The algorithm includes a simple
searching routine starting from x150 and search-
ing for the value of x1 that satis¢es the equation
to within some acceptable error (PT ^
MPD50.000001 mSv). The values of Kuxj(x) and
Koj for tube voltages of 50, 70, 100, 125 and 150
kVp and for lead, gypsum, steel and plate glass
constructed materials, have been calculated with
the use of Archer et al's mathematical model [2].
For this calculation the experimental determina-
tion of three parameters (alpha, beta and gamma)
is needed, which has been already reported by
Archer et al [5]. Transmission data, for voltages
of 30 and 35 kVp have been taken from Simpkin
[6, 7]. Published transmission data by Simpkin [6]
for concrete material have also been used. The high
attenuation HVLs have been taken from Archer et
al [5]. HVL values which are not provided in that
paper, were estimated by calculating the value of
(1n2)/a using the values of ``a'' provided by
Archer et al [5] and Simpkin [6]. Parameter a, as
stated by Archer et al [2, 5], is a ¢tted parameter
unique for each K curve and material.
Results
The shielding requirements for a barrier in a
general X-ray room are speci¢ed completely by
Equation (13). This equation takes the form of
Equation (14) of Simpkin [4] when multiple X-ray
tubes in a single room and operating at di¡erent
tube potential (kVp) values are considered and no
existing protection is present. The two formulae
are then in agreement, providing the same results.
The situation that is examined draws attention
to a method which allows more precise values of
additional required material to be given in case of
structural shielding in place. Note that the result
obtained by Equation (10), when the same material
thickness x1 needs to be added to the existing con-
structed barrier of thickness x2, is the same as if
only one slab of thickness x5x1+x2 had been con-
sidered, providing a true description of the trans-
mission through material 2 after passage through
material 1. Moreover, Equation (11) shows that
the transmission of primary or scatter radiation
(through thickness x1, material 1 and thickness x2,
material 2) is reduced to the one obtained when
two slabs of thickness x3 and x2 from material 2
have been used.
Results of the method proposed here are com-
pared with that of McGuire's, for the parameter
values shown in Table 1. These results are pre-
sented in Tables 2 and 3, when the same or a di¡er-
ent material is added to the existing one, for
concrete and lead. More results are presented in
Tables 4^7 for many combinations. The calcula-
tion methodology and the data sources have been
mentioned above. Lead and concrete materials are
examined for a barrier at 2 m distance exposed to
primary, scatter and leakage radiation, emitted
from a radiographic tube operating at 100 kVp.
The corresponding computer program screens,
M Petrantonaki, C Kappas, E P Efstathopoulos et al
182 The British Journal of Radiology, February 1999

5. for one sample case, are shown in Figures 3, 4
and 5.
Discussion
Transmission through a barrier is determined as
the ratio of exposure with to exposure without the
barrier. It does not, however, express the scattering
power or energy spectrum passed through it.
McGuire's method and the proposed method
in this paper obtain identical results, when no
structural shielding is in place. However, when
existing protection is present and additional
shielding of the same material is required,
McGuire's method leads to an overestimation
and disagreement with itself. For example, a con-
crete barrier of 156.1 mm is required when no exist-
ing protection is present while in the case that a
protective barrier of 78.1 mm being already in
place, the additional shielding is calculated to be
85.5 mm requiring a total concrete barrier of
163.6 mm thickness (Table 2). Generally, as the
existing barrier thickness increases, McGuire's
method necessitates greater thickness than the
appropriate one to be added to the existing wall,
resulting in a continuously increased overestima-
tion of the total required protection barrier. Even
in the case of an existing barrier with thickness
equal to that being calculated when no existing
protection is present, McGuire's method results
in additional shielding. The calculations result in
zero requirements at existing thicknesses higher
than that required previously. Similar remarks
arise from the calculated values presented in
Table 3. However, the results of both methods
depend on the speci¢c order of placement of two
di¡erent materials when constructing a barrier.
This is due to di¡erences in attenuation character-
istics of a beam as it passes through a lead^con-
crete barrier compared with a concrete^lead one
constructed of identical lead and concrete thick-
nesses. In the case of already existing shielding,
according to McGuire's methodology, the beam
is assumed to have been highly ¢ltered by passage
through the ¢rst material of thickness x1 and being
hardened, is transmitted through the second mate-
rial of thickness x2. Subsequently, x2 is calculated
in order that the weekly exposure meets the protec-
tion criteria. The required material thickness that
would result in beam hardening is not known,
and McGuire's method leads to an overestimation
of added material, as has been shown in the results
section (Tables 2^7). The problem therefore
Table 1. General parameter values used for the calcu-
lation of the results given in Tables 2 and 3
Parameter Value
Exposure limit (mSv) 0.1
Use factor 1/2
Field size (cm2
) 1000
Workload (mA min week^1
) 1000
Tube current (mA) 4
Table 2. Examples of additional same material thick-
ness required to be added (a) at an existing concrete
barrier and (b) at an existing lead barrier, as calculated
by McGuire's method and that proposed in this article
Existing protection McGuire [3] Proposed
(mm) method
(a) Concrete barrier
0.0 156.1 156.1
78.1 85.5 78.1
156.1 29.1 0.0
212.1 0.0 0.0
(b) Lead barrier
0.0 2.5 2.5
1.2 1.2 1.2
2.5 0.3 0.0
3.4 0.0 0.0
Table 3. Examples of additional di¡erent material
shielding requirements, as calculated by McGuire's
method and that proposed in this article
Existing protection McGuire [3] Proposed
(mm) method
(a) Additional lead (mm) to concrete barrier
37.5 1.9 1.8
78.1 1.3 1.1
156.1 0.3 0.0
212.1 0.0 0.0
(b) Additional concrete (mm) to lead barrier
1.2 83.7 83.2
2.0 45.1 37.5
2.5 26.7 0.0
3.4 0.0 0.0
Table 4. Examples of di¡erent material shielding
requirements, when no existing material is present. All
thicknesses are given in mm
Added material kVp McGuire Proposed
[3] method
Lead 70 1.0 1.0
100 2.5 2.5
125 2.9 2.9
Concrete 70 90.0 90.0
100 156.1 156.1
125 215.1 215.1
Gypsum wallboard 70 119.4 119.4
100 219.3 219.3
125 313.6 313.6
Steel 70 6.5 6.5
100 17.5 17.5
125 30.4 30.4
Plate glass 70 52.1 52.1
100 86.9 86.9
125 122.1 122.1
Shielding in X-ray departments
183The British Journal of Radiology, February 1999

6. deserves a di¡erent approach, where the above
assumption would be ignored.
The methodology described in this paper allows
more accurate shielding requirements to be
speci¢ed, when existing protection is present, fol-
lowing no assumption on beam hardening caused
by transmission through any material. While prac-
tical shielding of diagnostic X-radiation is most
often achieved with gross increments of sheets of
Figure 3. Main window of the program, where neces-
sary data inputs for the barrier(s) and the tube(s) of a
diagnostic X-ray room are entered, in order to be used
in a radiation protection study.
Figure 4. Window for introducing existing shielding
material and thickness. The example corresponds to
barrier 2.
Figure 5. Window presenting the calculated shielding
requirements for several materials. The example corre-
sponds to the additional shielding required for barrier
2.
Table 5. Examples of di¡erent material shielding
requirements, when 78.1 mm of concrete as existing
material is present. All thicknesses are given in mm
Added material kVp McGuire Proposed
[3] method
Lead 100 1.3 1.1
125 1.7 1.7
Concrete 100 85.4 78.0
125 137.8 137.0
Gypsum wallboard 100 122.0 113.6
125 196.6 195.6
Steel 100 8.9 8.0
125 17.8 17.6
Plate glass 100 49.8 46.3
125 78.5 78.0
Table 6. Examples of di¡erent material shielding
requirements, when 100 mm of Gypsum wallboard as
existing material is present. All thicknesses are given in
mm
Added material kVp McGuire Proposed
[3] method
Lead 100 1.9 1.1
125 2.3 1.8
Concrete 100 121.0 74.7
125 181.1 144.0
Gypsum wallboard 100 167.7 119.3
125 258.9 213.6
Steel 100 13.3 7.6
125 24.8 18.9
Plate glass 100 67.8 47.1
125 102.1 83.5
Table 7. Examples of di¡erent material shielding
requirements, when 50 mm of plate glass as existing
material is present. All thicknesses are given in mm
Added material kVp McGuire Proposed
[3] method
Lead 100 1.6 0.8
125 2.1 1.5
Concrete 100 105.5 56.4
125 163.1 123.0
Gypsum wallboard 100 147.3 92.3
125 232.1 182.8
Steel 100 11.4 5.4
125 21.9 15.5
Plate glass 100 59.9 36.9
125 92.1 72.1
M Petrantonaki, C Kappas, E P Efstathopoulos et al
184 The British Journal of Radiology, February 1999

7. lead, it is possible to replace this with a precise and
accurate technique which assumes little and allows
a variety of more cost e¡ective materials to be con-
sidered for protective barriers. The di¡erences in
the results between the two methods will be even
more pronounced when less attenuating materials
such as gypsum wallboard [8, 9] are used for a bar-
rier. This is shown in Tables 5, 6 and 7, which pro-
vide an extended presentation of the results arising
from the two methods, for several combinations of
¢ve materials.
Computer programs for shielding computations
are not widely available. In attempting to face this
de¢ciency, a Windows-based program has been
designed and implemented, based on the method
presented. It provides the accuracy of the method
presented, as well as assisting the physicist in
shielding computations in a user-friendly manner.
Conclusions
A method, which allows for accurate determina-
tion of the shielding material thickness required to
attenuate radiation beams to some prescribed
allowable dose limit, has been described. It takes
into account the case of multiple sources operating
at di¡erent maximum potentials in a diagnostic X-
ray room and it deals with the case of existing
shielding in place, e¡ectively removing all the
uncertainties inherent in previous work found in
the relevant literature and providing a useful
extension to the NCRP 49 [1] formalism. Based
onthismethod,acomputerprogramhasbeendevel-
oped. The program can be used for the studies of
diagnostic radiation protection enabling one to
calculateeasilythebarrierthicknessrequiredtopro-
tect areas around a source of X-ray radiation and to
estimate the e¡ectiveness of an existing barrier.
Acknowledgments
The authors wish to thank Dr Douglas J
Simpkin, for his invaluable comments and sugges-
tions, and Dr E Lynn McGuire for the helpful
information provided.
References
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Shielding in X-ray departments
185The British Journal of Radiology, February 1999