Annals of Nuclear Energy 57 (2013) 246–255

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Annals of Nuclear Energy

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An inverse calculation technique for optimization of gamma rayshielding designs

0306-4549/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.anucene.2013.01.053

⇑ Corresponding author.E-mail addresses: kvs2552@gmail.com (K.V. Subbaiah), thilagam@igcar.gov.in (L.

Thilagam).

K.V. Subbaiah a, L. Thilagam b,⇑, R. Sarangapani c, D.K. Mohapatra b

a Manipal Centre for Natural Sciences, Manipal University, Manipal 576 104, Indiab AERB-Safety Research Institute, Kalpakkam 603 102, Indiac Radiological Safety Division, IGCAR, Kalpakkam 603 102, India

a r t i c l e i n f o

Article history:Received 4 September 2012Received in revised form 28 January 2013

Keywords:Gamma ray shieldingSHIELD DESIGN codeInverse calculation techniqueIterative procedures

a b s t r a c t

A new computer code named as SHIELD DESIGN has been developed in Visual Basic Version 6.0 for pre-cise estimation of shielding thickness in gamma ray shielding designs. In the conventional forward cal-culations using point kernel method, the sources and geometry are specified along with the shieldthickness to obtain dose rates at desired locations. But in this code, a new computational technique basedon inverse calculation and iterative procedures have been employed to estimate the shield thicknessusing the dose rate criteria as input information. This new technique enables quicker and easier wayof shield design optimization by computing shield thickness required in a single run whereas in the for-ward shield design optimization method, dose rate computations need to be carried out for various shieldthicknesses. The shielding thickness arrived with this code provides a first hand information to thedesigner to carry out forward calculations for accurate optimization. Also, the code is very useful to reg-ulators for quicker verification of shield calculations submitted by the designers for approval. Further,various options available in this code extend its flexibility and user friendliness. This paper briefly pre-sents the development and validation of the code, SHIELD DESIGN. The validation has been carried outby performing analyses of the gamma shielding design for some standard problems. The results werecompared with those of renowned forward calculations, experimental measurements, NCRP-51 bench-marks and other gamma radiation shielding utilities like RAD-PRO and satisfactory agreement wasobserved. These validation tests demonstrate the precise estimation of shield thickness.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Radiation shielding computer codes need to be developed withthe newer algorithms for the quicker optimization of shield designwith the choice for materials of efficient shield characteristics. Thisstudy introduces a new computer code, SHIELD DESIGN based oninverse calculation technique for precise estimation of shieldingthickness in gamma ray shielding designs.

In the usual forward shielding calculations (Penner et al., 1994;QADCGGP, 1980; Subbaiah and Sarangapani, 2006, 2008), generallythe source specifications for geometry, strength, energies andemission probabilities, source to detector distance, shielding mate-rial and thickness are given. By using the above information in thestandard point kernel method, the dose rates are estimated. How-ever, often the shield designer is not provided with the type ofshielding material and the thickness required. Instead, only the

dose rate criteria and source strength are provided to arrive atthe suitable material and the thickness required. Shield thicknessis arrived at by computing the dose rates for various shield thick-nesses. This kind of shield design optimization in practice usuallyinvolves many trial runs and is time consuming. Hence, a needwas felt to develop a new code with an innovative computationaltechnique for quicker and easier way of optimization of shieldingthickness.

Towards this objective, a new algorithm based on inverse calcu-lation technique has been made and implemented in the code,SHIELD DESIGN. Though the radiation utility tool like RAD-PRO(RAD PRO, 2009) employs similar approach, it is with several lim-itations viz. It can handle only a point source, slab shield geometryand standard sources with built-in energy information whereasvolume sources with multiple energies are frequently encounteredin practice. On the other hand, SHIELD DESIGN code can handlemultiple sources of different shapes and sizes, various shieldgeometries and user defined energy information of sources in addi-tion to built-in energy information of standard sources. Also, thecode has several user friendly input options regarding source

K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255 247

description, source to detector distance, target dose rates, selectionof shield materials and their properties and choice of shield calcu-lations say either shield design optimization for the prescribeddose criteria or dose rate calculations for the given shield thick-ness, etc. These options extend the flexibility and usefulness ofthe code in various radiation shield design applications.

The following sections explain in sequel about the mathemati-cal formulations employed in SHIELD DESIGN, various OPTIONSavailable in it, its validation and conclusions.

2. Mathematical formulations

SHIELD DESIGN code has been developed based on inverse cal-culation technique, i.e., the shield thickness required is calculatedfor the prescribed dose from the target dose rate at the desiredlocation. In shield design computations, three types of sourcesare generally expected. They are (1) a point source emitting singlegamma energy, (2) a point source emitting multiple gammaenergies, (3) Multiple point sources emitting single/multiple gam-ma energies and (4) Multiple volume sources emitting single/mul-tiple gamma energies. Simplified flow diagram of SHIELD DESIGNcode is given in Fig. 1. The mathematical formulations for theabove source descriptions are given below.

2.1. A point source emitting single gamma energy

The dose rate D(E, d) at any point at a distance ‘d’ from thesource after transmitting through shield slab of thickness ‘x’ cmis given by

DðE;dÞ ¼ DoðE; dÞBðE;lxÞe�lx ð1Þ

where D(E, d) is the dose rate at distance ‘d’ due to gamma ray ofenergy ‘E’, Do(E, d) is the dose rate at distance ‘d’ due to gammaray of energy ‘E’ by considering only the geometric attenuation,B(E, lx) is the buildup factor of the medium (ANSI/ANS-6.4.3,1991) based on energy ‘E’ and mean free path ‘lx’, l is the linearattenuation coefficient of the shield material at the energy ‘E’MeV (cm�1), x is the thickness of the shield material (cm).

Do(E, d), which is valid in the energy range of 0.1–3.0 MeV, is gi-ven by

DoðE; dÞ ¼0:54CE

d2

Rh

� �

,where C is in ‘Curies (Ci)’, E is in ‘MeV’ and d is in ‘m’ (Cember andJohnson, 2009).

DoðE; dÞ ¼0:54CEx10�6

d2

Svh

� �; ð2Þ

where d is in ‘cm’. More precisely, Do(E, d) can also be obtained bymultiplying photon flux at that point with the flux-to-dose rate con-version factors for entire gamma energy range of 10 keV–30 MeVANSI/ANS-6.4.3, 1991). In the forward calculations, generally thesource strength, energies, emission probabilities, shielding materialand thickness are given. By substituting the given information inEqs. (1) and (2) the dose rate can be estimated. However, oftenthe designer is not provided with the type of shielding materialand the thickness required. Instead, only the dose rate criteriaD(E, d) and source strength are provided. The shield designer is ex-pected to arrive at suitable material and thickness required. Theshield thickness can be obtained straight away by rearranging theEq. (1).

Rearranging Eq. (1) as

elx ¼ DoðE;dÞ � BðE;lxÞDðE; dÞ ð3Þ

where DoD

� �is obtained based on the calculated dose rate Do and the

dose rate criterion D. In Eq. (3), l can be calculated knowing shieldmaterial and density and taken it to be known in subsequent in dis-cussions. The other parameters ‘x’ and ‘B’ are unknown and more-over ‘x’ is an implicit function of ‘B’. To solve for two variables, weneed two equations. To circumvent this difficulty, we assume B(E,lx) = 1, which gives minimum thickness, thus eliminating one var-iable. Initial minimum thickness lx0 is computed as given in step 0below, where all other quantities are known. The algorithm adoptedin the computation is explained in steps below.

Step 0: Initial thickness is obtained from lx0 = Ln{Do/D}.Step 1: Compute the ratio Do

D

� �based on dose rate in air (Do) and

dose rate criterion (D). ‘DO’ can be estimated through Eq. (2)once source strength is known.Step 2: Compute B(E, lx) using the following equation

BðE;lxÞ ¼ 1þ ðb� 1ÞðKx � 1ÞðK � 1Þ for K– 1

BðE;lxÞ ¼ 1þ ðb� 1Þ � x for K ¼ 1

where

KðE; xÞ ¼ c � xa þ dtan hðx=Xk � 2Þ � tan hð�2Þ

1� tan hð�2Þ

where E is the incident photon energy, x is the penetration depth inmean free path, a, b, c, d and Xk are the G–P fitting parameters and bis the value of buildup factor at 1 mfp. The parameter K(E, x) is thephoton dose multiplication factor and change in the shape of thespectrum.

Step 3: Compute lx0 ¼ ln DoðE;dÞ�BðE;lxÞDðE;dÞ

h iStep 4: Check for convergence lx0

lx � 1��� ��� 6 0:001

If it is satisfied, exit.Else, Goto Step 2 and repeat the other steps.These iterations will go on till final convergence has been

achieved. As the function ‘B’ is a smooth and monotonically in-creases with thickness ‘x’ and hence convergence is very fast andit is observed that within four iterations the expected convergenceof 0.1% in ‘x’ is obtained.

On Exit: Compute

x ¼ lxl

Then, STOP. Thus by few iterations, the algorithm given con-verges and gives out precise estimate of thickness required.

2.2. A point source emitting multiple gamma energies

In the case of problems involving source with the multipleenergies, the algorithm is complex. If the gamma source is ofmultiple energies of ‘N’ components, then the dose rate in airdue to each energy component is computed with the followingexpression

DoðE;dÞ ¼0:54C � 10�6

d2 EiPiSvh

� �ð4Þ

where Pi is the probability of emission of ith component Ei.The shield thicknesses [x1, x2, x3, . . . , xi] required to reduce

the above dose rate in air to target dose rate is calculated firstfor each energy component by using the technique as explained

Fig. 1. Flow diagram of SHIELD DESIGN code.

248 K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255

in previous Section 2.1. Then, the maximum of thicknessx = max[x1, x2, x3, . . . , xi] is selected. The total dose rate at thedesired point (due to shield thickness ‘x’ cm) due to all energycomponents is computed. It is obvious that the sum due to all

energy components lies between targeted dose rate D and i�D,since ‘x’ is the maximum thickness chosen as initial value. There-fore, further calculations are carried out to reduce the total doserate due to all energy components to the target dose rate by

K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255 249

adding extra layer of shield thickness based on tenth value layerinformation. These calculations are carried out in iterations untilfinal optimized thickness is arrived.

2.3. Multiple point sources emitting single/multiple gamma energies

If more than one source (N sources) is involved say as in thecase of array of sources with each with multiple emission lines(M energies), the shield thickness required for each of energy com-ponent is arrived with the procedure described in Sections 2.1 and2.2. This procedure results in N �M values of thicknesses andx = max[x11, x12, . . . , x1M, x21, x22, . . . , x2M, . . . , xN1, xN2, . . . , xNM]is selected as the initial thickness required. Iterations are carriedout to arrive at the final optimized thickness as discussed inSection 2.2.

2.4. Multiple volume sources emitting single/multiple gamma energies

So far Do(E, d) is estimated by using the formula which is validin the range of gamma ray energies between 0.3 and 3 MeV andfor point source. This can be overcome by estimating photon fluxat the desired point in shield due to any type source geometricalshape using Point kernel codes such as QAD-CGGP. Subsequentlythe dose rate can be obtained by multiplying photon flux at thatpoint with the flux-to-dose rate conversion factors (ANSI/ANS-6.4.3, 1991). Once D and Do are known, the iterative procedure de-scribed in Section 2.2 can be employed to arrive at the preciseshield thickness. Simplified flow diagram of SHIELD DESIGN codeis given in Fig. 1.

Fig. 2. Layout of SHIE

3. Options in shield design

SHIELD DESIGN code has separate blocks to provide each of theinput information like source specification, source to detector dis-tance, shield materials and their properties, target dose rates andchoice of shield calculations, etc. in user friendly way. Layout ofSHIELD DESIGN code depicting these input blocks and output win-dow is shown in Fig. 2 with the explanations in detail in the follow-ing subsections.

3.1. Source specification

As shown in Fig. 2., source description block has input options:(i) to select source geometrical shape, (ii) to specify source materialattenuation and density, (iii) to select standard gamma sources,(iv) to specify number of sources in an array and their surface tosurface separation (pitch) and (v) to provide source gamma energy(MeV) and their intensities in terms of curies (1 curie(Ci) = 3.7 � 1010 Bq = 3.7 � 1010 disintegrations/s) multiplied byrespective probability of emissions for sources other than standardgamma sources.

Standard gamma sources included are the most common radio-isotopes at nuclear reactors and at other nuclear industries. Forstandard gamma sources, information like their emission energiesand probabilities are built-in inside the code. Source strength canbe either in terms of total activity (Ci) or in terms of specific activ-ity (Ci/g) for volumetric sources.

Source geometrical shape option includes point, line, cylinder,sphere and box sources. While selecting particular source geome-try, the relevant source dimensions need to be provided. For exam-

LD DESIGN code.

250 K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255

ple, radius and height information are required for cylindricalsource.

For source material attenuation, five standard material attenu-ation types are available with the built-in density information.They are for air, water, concrete, medium-Z (Iron) and high-Z (lead)materials. The density information can be user defined also.

3.2. Source to detector distance and dose rate in air

The dose rate at any distance in air (without shield) is calcu-lated by providing source to detector distance in cm and clickingon the command button ‘‘Compute Dose Rate in Air (lSv/h)’’. Thedose rates due to each source in air are calculated with the infor-mation on contributions from each energy component and theywill form the basis for the shield design optimization calculations.

3.3. Shield materials and their properties

Shield material can be any one of the five standard materials sayair, water, concrete, medium-Z (Iron) and high-Z (lead) with thebuilt-in density information, which can be changed if it is desired.

3.4. Choice of shield design calculations

Shield design calculations are carried out in two ways: (i) Opti-mization of shield thickness for target dose rate and (ii) Dose rate forgiven shield thickness. Shield thickness optimization for target doserate is based on the present new inverse calculation techniquewhereas dose rate for given shield thickness is based on point ker-nel based forward calculations. The latter is provided to crosscheck the results obtained with the inverse calculation technique.

3.5. Output window

SHIELD DESIGN output window for a sample problem of opti-mizing Lead shield thickness to achieve a target dose rate of1 lSv/h at 1 m from an array of three Co-60 point sources (eachof 1 Ci) is given in Appendix A.

The very first information available in the output window is in-put details about the source and shield, detector distance and tar-get dose rate for optimizing shield thickness followed by results ofdose rate computations in air (without shield). Then, dose rate re-sults in air are available for each of the source in an array and thattoo with the dose rate contribution from each energy component.This is followed by the maximum shield thickness required withthe energy component contributing that maximum, half and tenthvalue layers for that energy component and number of tenth valuelayers required. Then, the results of further iterative calculationsare displayed with the information on additional shield thicknessrequired to carry out subsequent dose rate calculation to reduce

Table 1Dose rate at 1 m due to various gamma sources: SHIELD DESIGN vs. RAD PRO.

Source Dose rate at 1 m (lSv/h)

RAD PRO (RP) (len/q) SHIELD DESIGN (SD) (len/q)

Ar-41 5.7809E+03 5.726E+03Co-57 4.2704E+02 4.860E+02Co-60 1.1347E+04 1.125E+04Cs-137 2.8189E+03 2.781E+03I-131 1.7867E+03 1.865E+03Ir-192 4.1857E+03 4.197E+03K-40 6.8260E+02 6.786E+02La-140 1.0082E+04 1.038E+04Mn-54 4.0694E+03 4.054E+03Na-24 1.6044E+04 1.620E+04

the sum due to all sources to be equal to target dose rate. Resultsof all these iterative calculations are displayed until the shieldthickness is optimized for target dose rate. At the end the finaloptimized shield thickness is displayed.

4. Validation of shield design

Validation of the calculational technique employed in SHIELDDESIGN was carried out against other gamma radiation shieldingutilities like RAD-PRO (RAD PRO, 2009), forward calculations (Sub-baiah and Sarangapani, 2008), experimental measurements (Thak-are et al., 2010) and NCRP-51 benchmarks (NCRP-51, 1977) byanalyzing gamma shield design for some standard problems.

4.1. Validation against RAD PRO code (RAD PRO, 2009)

4.1.1. Dose rate at 1m due to various standard gamma ray sourcesComparison of dose rates at 1 m calculated using SHIELD DE-

SIGN and RAD PRO (applicable for Point Source only) is given in Ta-ble 1 for various gamma sources. RAD PRO values are obtainedwith len/q (Hubbell et al., 2004) values as dose conversion factors.Dose rate at 1 m are obtained using SHIELD DESIGN code by using(i) len/q values and (ii) ICRP flux to dose conversion factors forphotons (ICRP-21, 1971). RAD PRO values are in good agreementwith the dose rates computed with len/q values. The percentagedeviations of dose rates using len/q from RAD PRO results arefound to be within 5% for most of the gamma sources except forCo-57, where the deviation is found to be 14%. The emission ener-gies and their probabilities are unknown information to the user inRAD PRO calculations. If there is any difference in emission ener-gies and emission probabilities considered, then that may yieldappreciable percentage deviation. The dose rates using ICRP fluxto dose conversion factors are found to be more up to 25%. CPUtime taken is just a fraction of second for these calculations andhence not compared.

4.1.2. Source strength to produce dose rate of 1 lSv/h at 1mSHIELD DESIGN simulated source strengths (in Ci/lSv/h & Bq/

lSv/h) required to produce dose rate of 1 lSv/h at 1 m are com-pared with the results of RAD PRO in Table 2 for various standardgamma sources. The comparison generally shows very good agree-ment (i.e.) the deviation within ±4% with respect to RAD PRO re-sults for most of the gamma sources. For Co-57 source, themaximum deviation of �12% is observed.

4.1.3. Tenth Value Layer (TVL) of different shield materialsTVLs calculated for different shield materials like lead, concrete

(ANSI/A138.1-1972 and A138.1a-1974), water and iron were com-pared with RAD PRO results in Table 3. The Comparison in generaldemonstrates the good agreement for most of the shield materials

CSDðlen =qÞCRP

CSDðICRPÞCRP

SHIELD DESIGN (SD) (ICRP)

6.365E+03 0.99 1.105.359E+02 1.14 1.251.252E+04 0.99 1.103.097E+03 0.99 1.102.106E+03 1.04 1.184.738E+03 1.00 1.137.533E+02 0.99 1.101.156E+04 1.03 1.154.492E+03 1.00 1.101.820E+04 1.01 1.13

Table 2Source strength for dose rate of 1 lSv/h at 1 m for various standard gamma ray sources: SHIELD DESIGN vs. RAD PRO.

Source RAD PRO (RP) SHIELD DESIGN (SD) CSDCRP

SHIELD DESIGN (SD) CSDCRP

Ci/lSv/h Bq/lSv/h Ci/lSv/h Bq/lSv/h

Ar-41 1.7298E�04 6.4068E+06 1.746E�04 1.01 6.462E+06 1.01Co-57 2.3417E�03 8.6729E+07 2.058E�03 0.88 7.613E+07 0.88Co-60 8.8129E�05 3.2640E+06 8.886E�05 1.01 3.288E+06 1.01Cs-137 3.5474E�04 1.3139E+07 3.596E�04 1.01 1.330E+07 1.01I-131 5.5970E�04 2.0730E+07 5.363E�04 0.96 1.984E+07 0.96Ir-192 2.3891E�04 8.8484E+06 2.382E�04 1.00 8.815E+06 1.00K-40 1.4650E�03 5.4259E+07 1.474E�03 1.01 5.452E+07 1.00La-140 9.9187E�05 3.6736E+06 9.631E�05 0.97 3.564E+06 0.97Mn-54 2.4573E�04 9.1012E+06 2.467E�04 1.00 9.127E+06 1.00Na-24 6.2328E�05 2.3084E+06 6.173E�05 0.99 2.284E+06 0.99

Table 3Tenth Value Layer (TVL) of different shield materials for standard gamma sources: SHIELD DESIGN vs. RAD PRO.

Source Tenth Value Layer (TVL) in cm

Lead Concrete Water Iron

RPa SDb SD/RP RP SD SD/RP RP SD SD/RP RP SD SD/RP

Co-60 4.5 4.5 1.00 28.1 30.5 1.09 64.7 67.4 1.04 8.8 9.8 1.11Ar-41 4.6 4.6 1.00 28.6 30.9 1.08 63.7 68.0 1.07 8.9 9.9 1.11Cs-137 2.2 2.3 1.05 23.9 25.0 1.05 54.3 57.6 1.06 6.6 7.1 1.08I-131 1.0 1.1 1.10 20.3 21.7 1.07 52.1 53.0 1.02 5.5 4.7 0.85Ir-192 1.1 1.1 1.00 21.2 21.5 1.01 49.9 52.8 1.06 5.4 4.7 0.87Na-24 5.8 5.8 1.00 37.4 37.1 0.99 85.1 81.0 0.95 11.5 11.4 0.99Co-57 0.1 0.1 1.00 13.8 12.8 1.08 46.0 42.9 1.07 1.6 1.4 1.14K-40 5.1 5.1 1.00 32.7 31.2 1.05 70.5 76.2 0.93 9.9 9.7 1.02La-140 4.8 4.6 1.04 31.1 28.9 1.08 68.6 65.0 1.06 9.4 9.0 1.04Mn-54 3.1 3.0 1.03 26.8 22.6 1.19 60.5 50.2 1.21 7.9 7.1 1.11

a RAD PRO calculated values.b SHIELD DESIGN calculated values.

Table 4Comparison against forward calculations for various source geometries.

Source description Detectordistance (d incm)

Dose rate inair (lSv/h)

Target doserate (lSv/h)

Lead thickness required toachieve target dose rate (cm)

Forwardcalculations

Reversecalculations(%DEV)

Point source: E = 0.5 and 1.5 MeV and A = 2 � 10 Ci 10 9.861E+06 7.986E+05 5.0 5.0 (0)100 9.861E+04 7.986E+03 5.0 5.0 (0)

Line source: E = 0.5 and 1.5 MeV and A = 2 � 10 Ci, L = 10 cm 10 9.149E+06 6.780E+05 5.0 5.2 (4)100 9.853E+04 7.971E+03 5.0 5.0 (0)

Cylindrical source: E = 0.5 and 1.5 MeV and A = 2 � 125.663 Ci, R = 2 cm, h = 10 cm,Mat: IRON

10 8.716E+07 5.213E+06 5.0 5.7 (14)100 9.202E+05 6.122E+04 5.0 5.5 (10)

Spherical source: E = 0.5 and 1.5 MeV, A = 2 � 33.51 Ci, R = 2 cm, Mat: IRON 10 2.563E+07 1.718E+06 5.0 5.4 (8)100 2.542E+05 1.740E+04 5.0 5.4 (8)

Array of 5 Cyl. Sources: Y array E = 0.5 and 1.5 MeV, and A = 2 � 125.663 Ci, R = 2 cm,h = 10 cm, Mat: IRON Pitch (Source Sur. Separation): 1 cm

10 3.180E+08 1.357E+07 5.0 6.3 (26)50 1.804E+07 1.170E+06 5.0 5.5 (10)

100 4.578E+06 3.055E+05 5.0 5.4 (8)

K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255 251

except for iron. The percentage deviations range from �15% to 14%for iron, �5% to 21% for water and �1% to 19% for concrete whereasfor lead they are observed to be less ranging from 3% to 10%.

4.2. Validation against forward calculations

SHIELD DESIGN code has been validated against forward calcu-lations of IGSHIELD (Subbaiah and Sarangapani, 2008) by carryingout shield thickness optimization for some standard problems withthe different source geometries like point, line, cylinder, sphereand cylindrical array. To understand the effect of material and geo-metrical attenuation, two detector distances say 10 cm and 100 cm

are considered. Gamma energies and activities used in the respec-tive source simulations are given in Table 4.

Initially, forward calculations were carried out using IGSHIELDto calculate dose rates with and without lead shield of thickness5.0 cm for the different source geometries considered with theirenergy and activity prescriptions as given in Table 4. Then, by pre-scribing the dose rate with lead shield from forward calculations astarget dose rate inverse calculations have been carried out usingSHIELD DESIGN code. Results of SHIELD DESIGN calculations arecompared with those of forward calculation in Table 4 for varioussource geometries. It is clearly observed from the comparisons thatthe lead thickness optimized using the newly developed tool is

252 K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255

found to be in very good agreement within ±5% deviation with theforward calculations for point source configuration.

For other source geometries, most of the cases are in goodagreement with ±10% deviation and there are some deviations upto 15% for single sources and that too up to 26% for array ofsources. These larger deviations observed may be attributed tothe fact that these are the cases where usually source materialattenuation, geometrical attenuation and buildup come into pic-ture and they contribute to the more deviation with respect tothe present point source approximation. It is important to mentionhere that the present algorithm considers source material and geo-metrical information to take care of attenuation and build up insource only at the time of calculating dose rate in air. While opti-mizing shield thickness this source geometrical information isnot taken into account. This fact contributes to the more deviationin the case of array of sources and sources geometries other thanpoint and that too more significant for detectors at shorter dis-tance. This can be understood from the results given for array ofcylindrical sources at three different detector distances.

Another important cause for the deviation is the present algo-rithm uses source material buildup for dose rate calculation inair and shield material buildup for optimizing shield thicknesswhereas the forward calculations employed in IGSHIELD usesbuildup medium (ANSI/ANS-6.4.3, 1991) based on computed meanfree path (mfp) for various regions between source and detector forentire dose rate calculations with shield.

4.3. Validation against measurements

Dose rate measurements (Thakare et al., 2010) carried out out-side the lead pot containing 131I of various source strengths havebeen used for validating the code against the experiments. Mea-surements were carried out with 3.0 cm thick lead pot employing

Table 5Comparison against experimental measurements.

S. No I131 source activity mCi Measured dose rates (lSv/h) with 3 cm lead shield

Contact At 15 cm At 20 cm

1 6.5 24.8 (22.3–28) 5.1 (4.8–5.6) 3.3(3.03–3.72 46.0 145.9 (112–185) 23.8 (21–28) 14.0 (13–153 68.7 231.5 (179–279) 37.2 (32.9–35.7) 22.6 (21.6–24 136.7 419.3 (290–514) 69.2 (59.7–80) 42.7 (38.5–4

a Measured dose rates are taken to be target dose rates at that location for optimizin

Fig. 3. Schematic of ex

three types of radiation survey meters for four different activitiesof 131I solution contained in vials. Activities of source and detectordistances considered in experimental study (Thakare et al., 2010)are given in Table 5. Schematic of experimental setup depictingsource, lead pot with dimensions and detector locations is givenin Fig. 3. Dose rates measured at different detector distances wereconsidered to be respective target dose rates for estimating leadshield thickness. SHIELD DESIGN optimized lead thicknesses arealso given in Table 5. These values are generally in good agreementwith the experiments within the deviations of ±10% for most of thecases. The maximum deviation �17% is observed when the magni-tude of the measured dose rate is small. For smaller dose rates,background dose rate is comparable to the measurement and itmay impose more uncertainties.

4.4. Validation for electron accelerator shielding design

SHIELD DESIGN code validity was discussed above for gammaray lines emitted by radioactive isotopes. We have attempted tocheck the applicability of this code for spectrum of gamma raysproduced by electron LINACs. In radiotherapy installations usinglinear electron accelerators it is very important to consider theX-rays which are produced as secondary radiations to provide anaccurate estimation of the shielding requirements. Even thoughthe primary electrons in an external beam can be completely ab-sorbed in shielding materials, additional shield thickness is re-quired in the barrier to attenuate these X-rays produced due toelectron interactions. The X-rays produced are more penetratingthan their parent electrons. Two standards, NCRP-51 (NCRP-51,1977) and DIN-6847 (DIN-6847, 1977) are generally used to esti-mate shielding requirements in those installations. These stan-dards recommend transmission curves of broad-beam X-raysproduced by electrons through different shield materials to arrive

thicknessa SHIELD DESIGN optimized lead shield thickness (cm)

At 25 cm Contact 15 cm 20 cm 25 cm

3) 2.8 (2.6–2.74) 3.1 2.9 2.8 2.5.2) 9.9 (9.5–10.5) 3.3 3.3 3.2 3.14.4) 15.5 (14.6–16.9) 3.2 3.2 3.1 3.07.8) 29.0 (26.6–32.0) 3.3 3.3 3.2 3.2

g shield thickness.

perimental setup.

Fig. 4. Transmission of X-rays produced by 6 MeV electron through lead.

Fig. 5. Transmission of X-rays produced by 6 MeV electron through concrete.

Fig. 6. Transmission of X-rays produced by 6 MeV electron through steel.

K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255 253

at the required shielding thickness. Shielding thickness required isdirectly proportional to the tenth value thickness, which can be ob-tained from the transmission curves recommended. In this analy-sis, SHIELD DESIGN code has been validated against NCRP-51recommendations by generating broad-beam transmission curvesof X-rays produced in 6MV electron beam. The X-ray spectrumproduced in 6MV Varian Linac (Sheikh-Bagheri and Rogers, 2002)is grouped in six energy bins (1–6 MeV) with 1 MeV interval andused in SHIELD DESIGN simulations.

The transmission factors as a function of shield thickness wereobtained for lead, concrete, and steel shield materials and com-pared with the NCRP-51 recommended curves in Figs. 4–6. Theplots clearly demonstrate that SHIELD DESIGN simulated valuesare in good agreement with the NCRP-51 recommended valuesfor all the three materials. The percentage deviations from NCRP-51 values are found to be more for smaller shield thickness andthey decrease with the increase in shield thickness. They are with-in ±5% for larger shield thickness.

For smaller thickness, better agreement is observed in lead withthe lesser deviations of 6% whereas the deviations observed in steeland concrete are more up to 14%. Considering more energy bins ofX-ray spectrum i.e., fine energy bins may yield better comparisonfor steel and concrete.

5. Conclusions

A new computer code, SHIELD DESIGN based on inverse calcu-lation technique was developed and validated for precise estima-tion of shielding thickness in gamma ray shielding designs.Validation was carried out by performing the analysis of gammaray shield design for some standard problems and compared withthose of the conventional forward calculations, experimental mea-surements, NCRP-51 recommendations and other gamma radiationshielding utilities like RAD-PRO, etc. The following are the broadobservations:

� Comparison of SHIELD DESIGN results with those of RAD PROfor some basic calculations like dose rate at 1 m, source strengthrequired to produce dose rate of 1 lSv/h at 1 m and tenth valuelayer of different materials for various standard gamma sourcesdemonstrate that the results of SHIELD DESIGN are in goodagreement with RAD PRO for all the analyses performed.� For Dose rate at 1 m due to various gamma sources, results of

SHIELD DESIGN using len/q are found to be in close comparisonto RAD PRO values whereas the deviations observed for the doserates using ICRP flux to dose conversion factors are found to bemore up to 25%. The percentage deviations of dose rates at 1 musing len/q from RAD PRO results are found to be within 5% formost of the gamma sources except for Co-57 where the devia-tion is found to be 14%.� The emission energies and their probabilities are unknown

information to the user in RAD PRO calculations. If there isany difference in emission energies and emission probabilitiesconsidered, then that may yield appreciable percentagedeviation.� Comparison of source required to produce dose rate of 1 lSv/h

at 1 m generally shows very good agreement with RAD PRO, i.e.,the deviation within ±4% for most of the gamma sources. ForCo-57 source, the maximum deviation of �12% is observed.� For tenth value layer of different materials for various standard

gamma sources, the percentage deviations from RAD PRO rangefrom�15% to 14% for iron, �5% to 21% for water and�1% to 19%for concrete whereas for lead they are observed to be less rang-ing from 3% to 10%.

254 K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255

� Comparison with the results of forward calculations showsgood agreement within ±5% deviation for point source configu-ration and within ±10% deviation for most of the cases of othersource geometries. For other source geometries, there are somedeviations up to 15% for single sources and that too up to 26%for array of sources.

These larger deviations observed may be attributed to the factthat these are the cases where usually source material attenuation,geometrical attenuation and buildup come into picture and theycontribute to the more deviation with respect to the present pointsource approximation.

� Comparison against the experimental measurements demon-strate that SHIELD DESIGN calculated values are generally ingood agreement with the experiments within the deviationsof ±10% for most of the cases. The maximum deviation �17%is observed when the magnitude of the measured dose rate issmall.

For smaller dose rates, background radiation is comparable tothe measurement and it may impose more uncertainties.

� Plots of transmission factors of X-rays produced by 6 MV LINACas a function of shield thickness clearly demonstrate thatSHIELD DESIGN simulated values are in good agreement withthe NCRP-51 recommended values for all the three materialslead, concrete and steel. The percentage deviations fromNCRP-51 values are found to be more for smaller shield thick-ness and they decrease with the increase in shield thickness.They are within ±5% for larger shield thickness. For smaller

��� Display of Dose-Rate (lSv/h) results with-out Shield Follows ����

S. No E (MeV)/Int.(Ci) In vacum (lSv/

1. 1.173/0.999 5.945E+032xSource-2 1.177E+04Sum 1.772E+04

2. 1.333/1.000 6.562E+032x Source-2 1.299E+04Sum 1.956E+04Sum due to all sources 3.727E+04

After Target Dose Rate & Shield Material SpecificationsMax. Shield Thic

Whose T1/10 & T1/2 layers (cm) = 3.653E+00 &1.100E+00Shield-Material = LEADShield density(g/cm3) = 1.134E+01No. of Tenth value layers Required is = 4.4 cm

��� IterationNO = 1 & Total Thickness Required(cm) = 1.608e+01��� Dose

S. No E(MeV)/Int.(Ci) In air (lSv/h)

1. 1.173/0.999 5.945E+032xSource-2 1.177E+04Sum 1.772E+04

2. 1.333/1.000 6.562E+032xSource-2 1.299E+04Sum 1.956E+04Sum due to all sources 3.727E+04

thickness, better agreement is observed in lead with the lesserdeviations of 6% whereas the deviations observed in steel andconcrete are more up to 14%.

Considering more energy bins of X-ray spectrum i.e., fine energybins may yield better comparison for steel and concrete.

In summary, it is noted that the validation studies prove theaccuracy and the suitability of the code for the quicker and preciseestimation of shielding thickness by converging after a few itera-tions in all analyses performed. Overall, the code is found to bevery useful by providing first hand information on shield thicknessto the designers and to the regulators for the quick verification ofthe results submitted by the designers.

Appendix A

SHIELD DESIGN output window for a sample problem of opti-mizing Lead shield thickness to achieve a target dose rate of1 lSv/h at 1 m from an array of three Co-60 point sources (eachof 1 Ci) is demonstrated below.

Output window

���� INPUT-DATA SOURCE and SHIELD DETAILS ����

1. Source Shape = Dimensions (cm)2. No. of Sources in Linear Array = 23. Surface-to-Surface Distance (cm) = 10.04. Source Activity distribution Type=5. Source Material=6. Source Material Density (g/cm3) = 0.0012

h) Source-attenu (lSv/h) Source-med BD

5.945E+03 1.000E+001.177E+04 1.000E+001.772E+046.562E+03 1.000E+001.299E+04 1.000E+001.956E+043.727E+04

kness is due to Gamma of Energy (MeV) = 1.333

-Rates are (lSv/h)

With shield (lSv/h) No. of mfps Buildup factor

3.428E�01 1.112E+01 3.889E+003.253E�01 1.117E+01 3.901E+006.681E�011.007E+00 1.014E+01 3.885E+009.601E�01 1.019E+01 3.897E+001.967E+002.635E+00

��� IterationNO = 2 & Optimum Thickness Required (cm) = 1.767e+01 ��� to Reduce Dose-Rate Around �1.00 l-Sv/h)���

S. No E(MeV)/Int.(Ci) In air (lSv/h) With shield (lSv/h) No. of mfps Buildup Factor

1. 1.173/0.999 5.945E+03 1.212E�01 1.222E+01 4.127E+002xSource-2 1.177E+04 1.144E�01 1.228E+01 4.140E+00Sum 1.772E+04 2.356E�01

2. 1.333/1.000 6.562E+03 3.927E�01 1.114E+01 4.129E+002xSource-2 1.299E+04 3.727E�01 1.120E+01 4.142E+00Sum 1.956E+04 7.655E�01Sum due to all sources 3.727E+04 1.001E+00

Optimized Shield Thickness (cm) = 1.767e+01.

K.V. Subbaiah et al. / Annals of Nuclear Energy 57 (2013) 246–255 255

7. Source-to-Receiver Distance (X-cm) = 100.0 & Z = 0.08. SHIELD Material=9. SHIELD Material Density (g/cm3) = 11.34

10. Allowable Dose Rate (l-Sv/h) = 1

References

ANSI/A138.1-1972 and A138.1a-1974, 1972. Specifications for Structural Concretefor Buildings (ACI 301-72), ACI Committee 301, American Concrete Institute,Detroit, 36p.

ANSI/ANS-6.4.3, 1991, American National Standard for gamma-ray AttenuationCoefficients and Buildup Factors for Engineering Materials, American NuclearSociety.

Cember, Herman, Johnson, Thomas E., 2009. Introduction to Health Physics, fourthed. Copyright � 2009 by the McGraw-Hill Companies.

DIN-6847, 1977. Medical Electron accelerators, Part2: Radiation Protection rules forinstallation, DIN – Deutsches Institut fur Normung.

Hubbell, J.H., Seltzer, S.M., 2004. Tables of X-Ray Mass Attenuation Coefficients andMass Energy-Absorption Coefficients (version 1.4), NIST, Gaithersburg, MD.<http://physics.nist.gov/xaamdi>.

ICRP-21, 1971. International Commission on Radiological Protection, Data forProtection against Ionizing Radiation from External Sources, Supplement toICRP Publication 15. Springer, Graz. April-1971, pp. 319–320.

NCRP-51, 1977. Recommendations of the National Council on Radiation Protectionand Measurements, Radiation Protection Guidelines for 0.1-100 MeV Particleaccelerator Facilities, Bethesda, MD: NCRP; NCRP Report No. 51, 1977.

Penner, G.R., Litwin, K.A., 1994. ‘‘Point Kernel Code System for Neutron and GammaRays Shielding Calculations Using the GP Buildup factor (Appendix-A)’’,Contributed by AECL Research, RSICC CCC-645.

QADCGGP, 1980. A combinatorial geometry version of QAD-P5A – a Point KernelCode System for Neutron and Gamma Ray Shielding Calculations Using the GPBuildup Factor’’, RSICC-CCC-493.

RAD PRO, 2009, Version 3.26, Ray McGinnis, RAD PRO Software development, MIT.<http://www.radprocalculator.com/RadProDownloads.aspx>.

Sheikh-Bagheri, Daryoush, Rogers, D.W.O., 2002. Monte Carlo calculation of ninemegavoltage photon beam spectra using the BEAM code. Med. Phys. 29 (3),391–402.

Subbaiah, K.V., Sarangapani, R., 2006. GUI2QAD-3D: a graphical user interfaceprogram for QAD-CGPIC program. Ann. Nucl. Energy 33 (2006), 22–29.

Subbaiah, K.V., Sarangapani, R., 2008. IGSHIELD: a new interactive point kernelgamma ray shielding code. Ann. Nucl. Energy 35 (2008), 2234–2242.

Thakare, S.V., Jagadeesan, K.C., Sarangapani, R., Vimalnath, K.V., Rath, D.P.,Joshi, P.V., 2010. Comparative study of theoretical and experimental doserate profile outside lead shield for 131I activity, NIC-2010, December13–15, pp. 59–62.