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Calibration of the HML’s portable whole body counter as a function of BOMAB phantom size and energy modelled by MCNP Gary H. Kramer and Kevin Capello Human Monitoring Laboratory, Radiation Protection Bureau, 775 Brookfield Road, Ottawa, Ontario K1A 1C1, Canada (gary_h_kramer@hc-sc.gc.ca, www.hc-sc.gc.ca/ ca/hecs-sesc/hml/) Abstract. The Human Monitoring Laboratory’s portable whole body counter has been calibrated using Monte Carlo simulations. The validity of the calibrations was checked by measuring a 95-percentile man phantom distributed by the International Atomic Energy Agency as part of an international In Vivo intercomparison exercise. The agreement between the predicted activity of 137Cs and 60Co and the amounts that were measured in the Human Monitoring Laboratory’s fixed whole body counter was ±4%. A function was also found that related counting efficiency to photon energy and size of the phantom (or person) being measured. The accuracy of this function was in the range of 8% to -9%. Finally, some retrospective design was performed using a combination of Monte Carlo simulations and measured background data to show that the optimum configuration for the portable whole body counter would have been two detectors that were 9.2 cm in diameter and 12.7 cm thick instead of the current configuration: upper detector, 7.6 cm in diameter and 7.6 cm thick; lower detector, 9.2 cm in diameter and 12.7 cm thick. The modified portable whole body counter would have a minimum detectable activity that was lower than the original design by 13% - 23%, in the range 126 keV to 2,754 keV, for the Reference Male phantom. 1. Introduction The Human Monitoring Laboratory’s portable whole body counter, PWBC, [1,2] has undergone a number of changes including software updates necessitating the instruments re-calibration. In the aforementioned studies the PWBC was only calibrated for 137Cs and size dependency was based on height alone. Since the events of 11th September 2001 it became necessary to keep the PWBC in a state of readiness should it need to be deployed into the field. The previous success of accurately modeling a whole body counter [3] using Monte Carlo simulation led to the decision to basis the primary calibration of the PWBC on these calculations. The simulations have used BOMAB phantoms modeled on the BRMD BOMAB phantom family [4]. The use of Monte Carlo simulations to establish calibration data has several advantages as the purchase of a BOMAB phantom family can be both expensive and its use time consuming. The establishment of all the calibration curves for the PWBC would require the HML to: purchase radioactive standards that cover the required energy range (100 - 2,000 keV), fill each phantom with a single radionuclide at a sufficiently high level to be easily measured in the open, unshielded environments or empty on of the counting chambers to perform the calibration within (the latter choice would shut down either the HML’s lung counter or scanning detector WBC for the length of the PWBC’s calibration), develop the calibration sets, and establish a correction factor methodology for persons of intermediate height and weight. 2. Methods and Materials 2.1. Modelling of the BOMAB phantoms: The HML uses BOMAB phantoms that simulate: a Reference four year old child, a Reference ten year old child, a five-percentile male, a Reference Female, a Reference Male, a 95-percentile male. The Reference phantoms were developed from data contained in Reference Man [5]. The other phantoms were designed using selected anthropometry data [6]. The phantoms were measured to determine

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the height, semi-major, and semi minor axis of each phantom. The thickness to the high density polyethylene wall was 0.25 cm except at the filling cap end where it was 1.5 cm. This data, shown elsewhere [3], was used to construct a series of virtual BOMAB phantoms. 2.2. The Portable Whole Body Counter: The PWBC is shown in Fig. 1. It consists of a modified X-ray stand that is mobile. Attached to the horizontal arm are two detectors (see below) that can move in the vertical and horizontal planes. The subject, or phantom, is counted in a seated geometry with the lower detector close to the abdomen and just above the thighs, and the upper detector is placed opposite the sternum. The signals from the two detectors are summed using a sum-invert amplifier before being passed to an EG&G Ortec DART. The resulting spectrum is analysed on a laptop computer using EG&G’s ScintiVision V1.03 software. None of the support mechanism was modelled.

Fig 1: The PWBC measuring a Reference Man BOMAB phantom seated in a chair.

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2.3. The Detectors The PWBC is equipped with two NaI(Tl) detectors: one upper and one lower. Both detectors are cylindrical NaI(Tl) crystals. The upper detector is 7.6 cm in diameter and 7.6 cm thick. The lower detector is 9.2 cm in diameter and 12.7 cm thick. The crystals are optically coupled to a low background photomultiplier tube. The outer casing of the detector is stainless steel 304 (Fe, 70%; Cr, 19%; Ni,11%; specific gravity, 8.02) which is 0.635 mm thick. Only the detectors were modeled. One set of simulations had the two detectors as described above. The second set of simulations used two detectors corresponding in size to the lower detector described above. 2.4. The Simulations: The following energies were simulated: 126, 280, 364, 468, 662, 834 , 1173, 1332, 1460, 1836 and 2754 keV. Many photon energies were chosen to represent radionuclides frequently used in calibrations: 57Co, 131I, 137Cs, 60Co, 54Mn, 40K, 88Y, 24Na. The remaining energies are interpolations to fill in areas so that efficiency versus energy curves can be constructed. Each photon energy was run independently and were mono-energetic for each of the twenty counting positions. The photons that interacted with the NaI and deposited their full energy were tallied so that a detector efficiency was obtained for each configuration. The Monte Carlo code used for the simulations has been described in detail elsewhere [3]. The authors of MCNP consider that a relative error value of 0.1 - 0.2 suggests that the tally result is questionable [7]. Tally results for which the relative error is above 0.2 are not likely to be meaningful, but are generally reliable for a relative error less than 0.1. The number of photons used in the simulations was 107 so that the relative error varied from 0.0026 to 0.0069 for the lower detector and 0.0045 to 0.0171 or 0.008 to 0.0029 for the upper detector (small and large diameter detectors, respectively). 2.5. Geometry Compensation: To account for the simplifications in the modeling a point source was both modeled and simulated and the results compared with experimental observations. A 137Cs point sources was used (~7 kBq) fixed to each detector using a Perspex rod to attach it to the centre of the detectors end cap. 2.6. Minimum Detectable Activity: Real background data was obtained by counting a BOMAB phantom containing 140 g of potassium overnight in the HML. Background spectra were collected for each detector separately. The two files were combined to obtain a realistic estimate of the background counts in a given region of interest for the two-detector array. The regions of interest that were evaluated are shown in Table 1 and the background spectra are shown in Fig. 2. Table 1: Background regions and their counts from a 36,000 second measurement.

Energy (keV) start (keV) stop (keV) Upper Det Lower Det Array 126 115 137 985186 2341569 3326755 280 255 305 884774 2368828 3253602 364 331 397 613175 1670724 2283899 468 426 510 377080 1070321 1447401 662 602 722 366189 1083689 1449878 834 759 909 295848 892084 1187932 1173 1067 1279 246218 744318 990536 1332 1212 1452 256810 969832 1226642 1460 1329 1591 280149 968039 1248188 1836 1671 2001 67279 215334 282613 2754 2507 3001 32662 110632 143294

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The following formula for MDA is based on the work of Currie [8], with Brodsky’s modification [9], although in practice the second term is often neglected as it adds little to the magnitude of the result when N is large:

(1)

where N background counts in the region of interest, E counting efficiency (cps Bq-1 or cps mg-1), and T counting time (sec). The background for the two-large detector PWBC was simulated simply by doubling the background of the lower detector shown in Fig 2.

2.7. Surface Fitting: TableCurve3D (SPSS Incorporated, Chicago, IL 60606-6307) was used to fit the surface to the data obtained from the simulations described above. Microsoft Excel was used for data manipulations and simple curve fitting. 2.8. Benchmark: During the course of the International Atomic Energy Agency’s (IAEA) Direct Measurements intercomparison an opportunity arose to count a phantom using the

MDA. N

ET ET= +

4 65 3

Energy (keV)0 500 1000 1500 2000 2500 3000

0

20000

40000

60000

80000

100000

120000

140000

1600003x3 detector5x4 detectorarray

Fig 2: Background spectra for each detector component of the PWBC.

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HML’s PWBC. The phantom supplied by the IAEA was a BOMAB bottle phantom simulating the stature of a 95th percentile adult male. The filling of the BOMAB phantom was a solid plastic tissue substitute with the radionuclides distributed uniformly through the volumes of the component phantom cylinders. This phantom was counted in front of the PWBC, similar to the phantom shown in Fig. 1, for 36,000 seconds. The spectrum was exported to Excel for subsequent analysis. 3.0. Results and Discussion 3.1. Geometry Compensation: The results of the simulated and measured counting efficiencies for the upper and lower detector are shown in Table 2. The relative error was 0.0107 for the upper detector and 0.0059 for the lower detector. The efficiency of the lower detector was experimentally observed to be a factor of 1.37 lower than that predicated by MCNP and similarly for the upper detector, a factor of 1.45. The efficiencies predicted by MCNP have, therefore, been adjusted by these factors. Table 2: Measured and simulated counting efficiencies of a 137Cs point source.

Detector Net Counts Activity, Bq (decay corr.)

Count Time (secs)

Branching Ratio Efficiency (cnt/photon)

Upper (3x3) 63767 6918.24 1800 0.851 6.017 x 10-3 Lower (5x4) 216128 6918.24 1800 0.851 2.039 x 10-2

MCNP Upper - - - - 8.699 x 10-3 MCNP Lower - - - - 2.786 x 10-2

3.2. Counting Efficiency: The counting efficiencies of the virtual BOMAB phantoms as a function of photon energy are shown in Tables 3 - 5. Table 3 shows that the counting efficiency as a function of phantom size and photon energy for the lower detector, Table 4 shows similar data for the upper detector and Table 5 is simply the sum of Tables 3 and 4 and represents the counting efficiency of the two-detector array as a function of phantom size and photon energy. The maximum counting efficiency for all detectors is about 280 keV for all detector arrangements after which it falls off almost exponentially as the energy increases. Comparing Table 3 with Table 4 one sees that the upper detector is correspondingly less efficient as the energy rises due to the lower stopping power of the smaller NaI crystal. The ratio of the counting efficiencies of the lower to upper detector varies from about 2.6 at low energies to about 5 at the highest photon energy. Table 6 is the efficiency of the upper detector when it is changed to be the same size as the lower detector. Table 7 is the array combination of the two large detectors (upper and lower). The values in Table 7 are not the sum of Tables 6 and Table 3 as the new simulation produced slightly different values for the lower detector when the upper detector was enlarged. For example, the P4 efficiency at 126 keV become about 2% lower than the value in Table 3. Similarly at 2,754 keV it was about 0.9 % lower. As the phantom increased in size these small differences became smaller.

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Table 3: Counting efficiency (count/photon) of the HML’s PWBC using different sized virtual BOMAB phantoms as a function of photon energy for the lower detector. P4 = four year old phantom, P10 = 10 year old phantom, PM5 = five percentile phantom, PF = female phantom, PM = male phantom, PM95 = ninety fifth percentile phantom. Energy (keV) P4 P10 PF PM5 PM PM95

126 1.01 x 10-2 7.63 x 10-3 5.60 x 10-3 5.54 x 10-3 3.94 x 10-3 2.59 x 10-3

280 1.07 x 10-2 8.23 x 10-3 6.12 x 10-3 6.02 x 10-3 4.37 x 10-3 2.91 x 10-3

364 1.01 x 10-2 7.89 x 10-3 5.90 x 10-3 5.80 x 10-3 4.25 x 10-3 2.85 x 10-3

468 9.40 x 10-3 7.38 x 10-3 5.57 x 10-3 5.45 x 10-3 4.03 x 10-3 2.71 x 10-3

662 8.27 x 10-3 6.57 x 10-3 4.98 x 10-3 4.88 x 10-3 3.65 x 10-3 2.49 x 10-3

834 7.56 x 10-3 6.04 x 10-3 4.60 x 10-3 4.52 x 10-3 3.40 x 10-3 2.33 x 10-3

1173 6.57 x 10-3 5.31 x 10-3 4.08 x 10-3 3.99 x 10-3 3.05 x 10-3 2.12 x 10-3

1332 6.22 x 10-3 5.05 x 10-3 3.90 x 10-3 3.81 x 10-3 2.91 x 10-3 2.03 x 10-3

1460 5.96 x 10-3 4.86 x 10-3 3.76 x 10-3 3.67 x 10-3 2.81 x 10-3 1.97 x 10-3

1836 5.31 x 10-3 4.33 x 10-3 3.41 x 10-3 3.30 x 10-3 2.54 x 10-3 1.81 x 10-3

2754 4.25 x 10-3 3.55 x 10-3 2.82 x 10-3 2.73 x 10-3 2.11 x 10-3 1.52 x 10-3

Table 4: Counting efficiency (count/photon) of the HML’s PWBC using different sized virtual BOMAB phantoms as a function of photon energy for the upper detector. P4 = four year old phantom, P10 = 10 year old phantom, PM5 = five percentile phantom, PF = female phantom, PM = male phantom, PM95 = ninety fifth percentile phantom. Energy (keV) P4 P10 PF PM5 PM PM95

126 3.35 x 10-3 2.07 x 10-3 1.62 x 10-3 1.67 x 10-3 1.16 x 10-3 7.86 x 10-4

280 3.27 x 10-3 2.05 x 10-3 1.63 x 10-3 1.68 x 10-3 1.17 x 10-3 8.12 x 10-4

364 2.94 x 10-3 1.85 x 10-3 1.48 x 10-3 1.53 x 10-3 1.06 x 10-3 7.37 x 10-4

468 2.56 x 10-3 1.62 x 10-3 1.29 x 10-3 1.34 x 10-3 9.33 x 10-4 6.56 x 10-4

662 2.05 x 10-3 1.31 x 10-3 1.05 x 10-3 1.10 x 10-3 7.68 x 10-4 5.40 x 10-4

834 1.78 x 10-3 1.13 x 10-3 9.21 x 10-4 9.67 x 10-4 6.77 x 10-4 4.77 x 10-4

1173 1.44 x 10-3 9.23 x 10-4 7.55 x 10-4 7.97 x 10-4 5.59 x 10-4 4.00 x 10-4

1332 1.33 x 10-3 8.54 x 10-4 6.97 x 10-4 7.34 x 10-4 5.20 x 10-4 3.75 x 10-4

1460 1.26 x 10-3 8.05 x 10-4 6.60 x 10-4 6.94 x 10-4 4.91 x 10-4 3.60 x 10-4

1836 1.05 x 10-3 6.90 x 10-4 5.69 x 10-4 6.03 x 10-4 4.21 x 10-4 3.10 x 10-4

2754 7.92 x 10-4 5.19 x 10-4 4.32 x 10-4 4.65 x 10-4 3.28 x 10-4 2.37 x 10-4

Table 5: Counting efficiency (count/photon) of the HML’s PWBC using different sized virtual BOMAB phantoms as a function of photon energy for the two-detector array detector. P4 = four year old phantom, P10 = 10 year old phantom, PM5 = five percentile phantom, PF = female phantom, PM = male phantom, PM95 = ninety fifth percentile phantom. Energy (keV) P4 P10 PF PM5 PM PM95

126 1.35 x 10-2 9.70 x 10-3 7.22 x 10-3 7.21 x 10-3 5.10 x 10-3 3.37 x 10-3

280 1.39 x 10-2 1.03 x 10-2 7.75 x 10-3 7.70 x 10-3 5.55 x 10-3 3.72 x 10-3

364 1.31 x 10-2 9.74 x 10-3 7.37 x 10-3 7.33 x 10-3 5.31 x 10-3 3.59 x 10-3

468 1.20 x 10-2 9.00 x 10-3 6.86 x 10-3 6.79 x 10-3 4.97 x 10-3 3.37 x 10-3

662 1.03 x 10-2 7.88 x 10-3 6.03 x 10-3 5.98 x 10-3 4.42 x 10-3 3.03 x 10-3

834 9.34 x 10-3 7.17 x 10-3 5.52 x 10-3 5.49 x 10-3 4.08 x 10-3 2.81 x 10-3

1173 8.01 x 10-3 6.23 x 10-3 4.84 x 10-3 4.79 x 10-3 3.61 x 10-3 2.52 x 10-3

1332 7.55 x 10-3 5.90 x 10-3 4.59 x 10-3 4.54 x 10-3 3.43 x 10-3 2.41 x 10-3

1460 7.22 x 10-3 5.67 x 10-3 4.42 x 10-3 4.37 x 10-3 3.30 x 10-3 2.33 x 10-3

1836 6.36 x 10-3 5.02 x 10-3 3.98 x 10-3 3.91 x 10-3 2.96 x 10-3 2.12 x 10-3

2754 5.05 x 10-3 4.07 x 10-3 3.25 x 10-3 3.20 x 10-3 2.44 x 10-3 1.76 x 10-3

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Table 6: Counting efficiency (count/photon) of the HML’s PWBC using different sized virtual BOMAB phantoms as a function of photon energy for the upper detector when it is changed to be the same size as the lower detector. P4 = four year old phantom, P10 = 10 year old phantom, PM5 = five percentile phantom, PF = female phantom, PM = male phantom, PM95 = ninety fifth percentile phantom. Energy (keV) P4 P10 PF PM5 PM PM95

126 8.38 x 10-3 5.25 x 10-3 4.04 x 10-3 4.23 x 10-3 2.89 x 10-3 2.05 x 10-3

280 8.88 x 10-3 5.64 x 10-3 4.38 x 10-3 4.61 x 10-3 3.18 x 10-3 2.28 x 10-3

364 8.47 x 10-3 5.40 x 10-3 4.23 x 10-3 4.44 x 10-3 3.08 x 10-3 2.21 x 10-3

468 7.90 x 10-3 5.02 x 10-3 3.97 x 10-3 4.17 x 10-3 2.89 x 10-3 2.09 x 10-3

662 6.97 x 10-3 4.47 x 10-3 3.55 x 10-3 3.76 x 10-3 2.62 x 10-3 1.91 x 10-3

834 6.38 x 10-3 4.11 x 10-3 3.31 x 10-3 3.46 x 10-3 2.44 x 10-3 1.79 x 10-3

1173 5.55 x 10-3 3.62 x 10-3 2.92 x 10-3 3.08 x 10-3 2.19 x 10-3 1.62 x 10-3

1332 5.26 x 10-3 3.44 x 10-3 2.78 x 10-3 2.92 x 10-3 2.08 x 10-3 1.55 x 10-3

1460 5.04 x 10-3 3.31 x 10-3 2.69 x 10-3 2.82 x 10-3 2.01 x 10-3 1.50 x 10-3

1836 4.50 x 10-3 2.97 x 10-3 2.42 x 10-3 2.54 x 10-3 1.83 x 10-3 1.36 x 10-3

2754 3.68 x 10-3 2.43 x 10-3 2.00 x 10-3 2.10 x 10-3 1.52 x 10-3 1.15 x 10-3

Comparing Tables 5 and 7 one sees that the two large detector array is between a factor of 1.3 to 1.6 times more efficient, depending upon phantom size and photon energy. The factor only increases sightly with phantom size (1.32 for P10 and 1.39 for PM95 at 126 keV) but more with increasing energy (1.32 at 126 keV and 1.47 at 2,754 keV for P10). Table 7: Counting efficiency (count/photon) of the HML’s PWBC using different sized virtual BOMAB phantoms as a function of photon energy for the two-large-detectors array detector. P4 = four year old phantom, P10 = 10 year old phantom, PM5 = five percentile phantom, PF = female phantom, PM = male phantom, PM95 = ninety fifth percentile phantom. Energy (keV) P4 P10 PF PM5 PM PM95

126 1.83 x 10-2 1.28 x 10-2 9.60 x 10-3 9.72 x 10-3 6.83 x 10-3 4.67 x 10-3

280 1.94 x 10-2 1.38 x 10-2 1.05 x 10-2 1.06 x 10-2 7.55 x 10-3 5.21 x 10-3

364 1.84 x 10-2 1.33 x 10-2 1.01 x 10-2 1.02 x 10-2 7.33 x 10-3 5.08 x 10-3

468 1.72 x 10-2 1.24 x 10-2 9.52 x 10-3 9.59 x 10-3 6.92 x 10-3 4.83 x 10-3

662 1.51 x 10-2 1.10 x 10-2 8.52 x 10-3 8.61 x 10-3 6.27 x 10-3 4.42 x 10-3

834 1.38 x 10-2 1.01 x 10-2 7.89 x 10-3 7.96 x 10-3 5.84 x 10-3 4.15 x 10-3

1173 1.20 x 10-2 8.92 x 10-3 6.99 x 10-3 7.05 x 10-3 5.23 x 10-3 3.75 x 10-3

1332 1.14 x 10-2 8.47 x 10-3 6.67 x 10-3 6.71 x 10-3 4.99 x 10-3 3.61 x 10-3

1460 1.09 x 10-2 8.15 x 10-3 6.43 x 10-3 6.47 x 10-3 4.82 x 10-3 3.50 x 10-3

1836 9.75 x 10-3 7.29 x 10-3 5.82 x 10-3 5.83 x 10-3 4.37 x 10-3 3.18 x 10-3

2754 7.89 x 10-3 5.97 x 10-3 4.82 x 10-3 4.82 x 10-3 3.63 x 10-3 2.68 x 10-3

3.3. Size Dependency: If all phantoms had the same efficiency at a given photon energy, the ratio of the counting efficiency of a phantom to the male-sized phantom would be unity. Table 8 for the existing PWBC only) shows this not to be the case for either of the simulated PWBCs.

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Table 8: Ratio of the counting efficiency of a given virtual phantom to the male-sized phantom as a function of photon energy for the simulation of the existing PWBC and the PWBC with two large detectors. Energy (keV) P4 P10 PF PM5 PM PM95

existing PWBC

126 2.64 1.90 1.42 1.41 1.00 0.66 280 2.51 1.85 1.40 1.39 1.00 0.67 364 2.46 1.83 1.39 1.38 1.00 0.68 468 2.41 1.81 1.38 1.37 1.00 0.68 662 2.34 1.78 1.36 1.35 1.00 0.68 834 2.29 1.76 1.35 1.34 1.00 0.69

1173 2.22 1.73 1.34 1.33 1.00 0.70 1332 2.20 1.72 1.34 1.33 1.00 0.70 1460 2.19 1.72 1.34 1.32 1.00 0.71 1836 2.15 1.70 1.35 1.32 1.00 0.72 2754 2.07 1.67 1.33 1.31 1.00 0.72

Two large detectors PWBC

126 2.68 1.88 1.41 1.42 1.00 0.68 280 2.57 1.83 1.39 1.40 1.00 0.69 364 2.52 1.81 1.38 1.39 1.00 0.69 468 2.48 1.79 1.38 1.39 1.00 0.70 662 2.41 1.76 1.36 1.37 1.00 0.70 834 2.37 1.74 1.35 1.36 1.00 0.71

1173 2.30 1.71 1.34 1.35 1.00 0.72 1332 2.29 1.70 1.34 1.35 1.00 0.72 1460 2.27 1.69 1.34 1.34 1.00 0.73 1836 2.23 1.67 1.33 1.33 1.00 0.73 2754 2.18 1.65 1.33 1.33 1.00 0.74

As expected, the size dependency varies with photon energy with the largest deviations occurring at low energies. This data shows that if the default counting efficiency (based on the male BOMAB phantom) would be applied to counting data from persons either much smaller or much larger than the male-sized phantom, a large error would be introduced into the activity estimate. For example, the data from the four-year-old phantom shows that the error would be about a factor of about 2.5 at any energy. This result is only important for emergency monitoring as the P4 phantom is not representative of persons in the workforce. Other phantoms, representative of people in the workforce differ from the PM phantom by approximately 35%. The data obtained from the PM95 phantom show that large persons emit fewer photons, presumably to self-attenuation. If such a person were measured using the default calibration factors (male-sized) then the activity estimate would be a factor of about 1.4 (at any energy) lower than the true value. Similarly, smaller persons than what is represented by the male-sized phantom (PM) will have the activity estimate inflated by a factor of approximately 1.4; however, as the PWBC is meant to be used in the field, for emergency response, these uncertainties are acceptable.

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3.4. Size Dependent Function: The mathematical function that was best found to fit the counting efficiency data is given by the following equation:

(2)

where z the counting efficiency, x the photon energy, y is (weight/height)½, a - j curve fit parameters. The results of the fit are shown in Table 9 and the curve fit parameters are shown in Table 10. Table 9 shows that there some systematic trends in the residuals indicating that the model is perhaps not the best fit; however, a function that performs better that Eqn 1 is not known at this time. Table 9: Results of the curve fit of Equation 2 to the counting efficiency data expressed as a bias of counting efficiency compared to predicted efficiency (i.e., [pred - obs]/obs). Data for simulation of the existing PWBC.

(weight/height)½ Energy (keV)

3.91 (4 yr old)

4.56 (10 yr old)

5.02 (5% male)

5.33 (female)

5.78 (male)

6.92 (95% male)

126 -0.01 0.00 0.08 -0.07 0.05 -0.09280 0.00 0.00 0.08 -0.07 0.06 -0.07364 -0.01 -0.01 0.07 -0.08 0.05 -0.07468 -0.01 -0.01 0.07 -0.07 0.05 -0.06662 0.00 0.00 0.08 -0.06 0.06 -0.05834 0.00 0.00 0.08 -0.06 0.06 -0.04

1173 -0.01 -0.01 0.07 -0.06 0.05 -0.051332 -0.01 -0.02 0.06 -0.07 0.05 -0.051460 -0.01 -0.02 0.06 -0.07 0.05 -0.051836 0.00 -0.01 0.07 -0.07 0.06 -0.042754 0.01 -0.01 0.07 -0.06 0.06 -0.02

Table 10: Curve fit parameters for simulation of existing PWBC.

Parameter Value a -26.1275 b -0.72287 c 412.2089 d 18.03111 e -2946.74 f -222.875 g 10498.62 h 1018.716 I -15504.3 j -1624.78

Correlation coefficient 0.9954 Standard error 0.00029

F-Value 674.9

{ } { } { }Z ea by c dy

Ln xe fy

Ln xg hyLn x

i jyLn x=

+ ++

++

++

++⎡

⎣⎢⎢

⎤

⎦⎥⎥

( )( )

( )( )

( )( )

( )( )2 3 4

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Table 9 shows that the equation predicts efficiency values that agree with the observed values in the range of 8% to -9% with an average bias of 0.00 ± 0.05. These predicted values are well within the North American performance criteria of 50% to -25% [10, 11] and show that this technique has merit. Furthermore, in an emergency situation a measurement bias of about 8% can be considered negligible. 3.5. MDA: In previous field deployments [1,2] the counting time has been short, usually about 5 minutes. Similarly, in an accident scenario throughput will be important necessitating short counting times, perhaps as short as one minute. MDA’s have, therefore, been calculated for short counting times. Previously the MDA of the PWBC was reported as lying in the range of 100 to 300 Bq [1]; however, this value was based on the ambient background and without an uncontaminated person (who contains 40K) sitting in front of the detectors. A more realistic MDA value would be obtained if an uncontaminated person was being measured as the 40K will raise the background continuum. These simulations have been coupled with a real spectrum obtained from a BOMAB phantom, containing 140g K to simulate the amount of radio-potassium found in Reference Man, to obtain more realistic MDA values. The use of this spectrum to estimate the MDA for other sizes will, however, bias the smaller phantoms slightly high and the larger phantom slightly low; nevertheless, it is a useful indicator of the expected field performance of the PWBC. Table 11 shows the expected MDA values for a 5-minute count using the data from Table 1 and the efficiency values in Tables 3 - 5. The data show that: the upper detector has a higher MDA than the lower detector (factor 2 - 3), MDA decreases with phantom size (based on efficiency only), MDA drops with increasing photon energy for all arrangements, the array has a lower MDA than either the upper detector (factor 2 - 4) or lower detector (2% - 9%). The simulations described above also included a change to the counting system where the upper and lower detector were made the same size. Table 12 shows the expected MDA values for the modified PWBC using a 5-minute count using the data from Table 1 (both upper and lower detector were assumed to have the same background as the lower detector - the array was simply double that of the lower detector) and the efficiency values in Tables 6 - 8. The data show that: the upper detector has a slightly higher MDA than the lower detector (27% - 33%), MDA decreases with phantom size (based on efficiency only), MDA drops with increasing photon energy for all arrangements, the array has a lower MDA than either the upper detector (60% - 65%) or lower detector (23% - 26%), the modified PWBC has a lower MDA than the original design (13% - 23%) for the PM phantom, at all energies.

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Table 11: MDA, expressed in photons, of the simulated existing PWBC for a five-minute count. The MDA values must be adjusted by the gamma yield to convert the values in Table 11 into Bq.

Energy (keV)

P4 P10 PF PM5 PM PM95

3x3 Detector (upper) 126 419 677 870 839 1215 1788 280 407 648 819 790 1137 1640 364 376 598 751 725 1044 1503 468 340 537 673 647 931 1325 662 417 656 817 777 1114 1585 834 433 680 836 796 1137 1615 1173 487 761 930 881 1255 1756 1332 540 840 1028 977 1380 1912 1460 596 930 1135 1079 1527 2081 1836 349 532 644 608 871 1184 2754 323 492 592 550 779 1078

5x4 Detector (lower) 126 214 284 386 391 549 837 280 204 265 356 362 498 749 364 181 232 310 315 430 641 468 156 198 263 269 363 540 662 178 224 296 302 404 593 834 177 221 290 296 393 573 1173 186 230 299 306 400 576 1332 224 276 358 366 479 685 1460 233 286 371 379 496 706 1836 124 152 193 199 259 364 2754 111 132 167 172 223 310

Detector Array 126 191 266 358 358 506 765 280 183 248 329 331 460 686 364 164 220 290 292 402 596 468 142 189 248 251 343 505 662 165 216 283 285 386 563 834 165 215 279 281 378 549 1173 176 226 291 294 390 559 1332 208 266 341 345 457 650 1460 219 279 358 362 479 678 1836 118 150 189 193 254 356 2754 106 132 165 168 220 305

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Table 12: MDA, expressed in photons, of the simulated two-large-detector PWBC for a five-minute count. The MDA values must be adjusted by the gamma yield to convert the values in Table 12 into Bq.

Energy (keV)

P4 P10 PF PM5 PM PM95

Upper Detector 126 258 412 536 512 749 1054 280 245 386 498 473 685 955 364 216 339 432 412 594 828 468 185 291 369 351 506 700 662 211 330 414 392 562 772 834 210 325 404 386 548 747 1173 220 337 418 397 559 755 1332 265 405 501 477 669 899 1460 276 421 518 494 693 929 1836 146 221 271 259 358 482 2754 128 194 235 224 310 410

Lower Detector 126 218 285 389 394 550 827 280 208 266 357 365 499 744 364 183 233 312 317 431 638 468 158 199 264 270 364 535 662 181 225 297 303 404 587 834 179 222 291 297 393 566 1173 188 230 300 307 401 571 1332 227 277 359 368 480 678 1460 236 287 372 381 496 696 1836 125 152 193 200 259 362 2754 112 133 167 173 223 307

Detector Array 126 167 238 319 315 449 655 280 159 223 294 291 408 591 364 140 195 256 253 353 509 468 121 167 218 216 299 429 662 138 189 245 242 332 472 834 137 187 239 238 324 456 1173 143 193 247 245 330 460 1332 173 233 296 294 395 547 1460 180 241 306 304 409 563 1836 95 127 159 159 213 292 2754 84 111 138 138 183 248

3.6. Benchmark: The spectrum obtained from the IAEA’s BOMAB phantom using the HML’s PWBC is shown in Fig. 3. The identified nuclides in the phantom were 133Ba, 137Cs, and 60Co. At the time of writing, the known activities of these three radionuclides was not available; however, the phantom was counted in the HML’s shielded whole body counter and the activities reported to the IAEA were: 245.0 kBq, 202.5 kBq, and 235.5 kBq respectively. The spectrum was analysed by fitting Gaussian peaks to the photopeaks from 137Cs and 60Co to obtain net peak areas. These were converted to activities by applying the appropriate

13

counting efficiency obtained from the Monte Carlo simulations, the counting time, and the appropriate branching ratio. The 133Ba was not analysed due to the excessively high background shoulder. The activities in the phantom were predicted to be 210.3 kBq and 225.9 kBq, respectively. As can be seen, the agreement between predicted and measured is ± 4%.

4.0. CONCLUSIONS This paper has shown how Monte Carlo can be used to perform a primary calibration that would otherwise be both expensive and difficult. The effect of phantom, or a person’s, size on the activity estimate can be mitigated by the use of a size dependent calibration equation based on a function of height and weight. The design change in the simulation suggests that the HML’s PWBC could be improved by replacing the upper detector with one that is similar in size to the existing lower detector. Comparing the predicted activity with the measured activity of a phantom used for an international intercomparison exercise has shown that this approach has a high degree of accuracy, and validates the use of Monte Carlo simulations for this purpose.

Energy (keV)0 200 400 600 800 1000 1200 1400 1600

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

Fig 3: Spectrum of the IAEA phantom collected by the PWBC.

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