Mathematical Calibration of a Whole-Body Counter Martin Schläger*

Forschungszentrum Jülich GmbH Division of Safety and Radiation Protection D-52425 Jülich, Germany.

Abstract. This paper describes the mathematical efficiency calibration of the whole-body counter at Forschungs-zentrum Jülich using Monte Carlo codes and mathematical anthropomorphic phantoms. As a prerequisite for the Monte Carlo simulations a precise model of the 4 high-purity germanium (HPGe) detectors had to be developed. Because the technical data provided by the manufacturer were not sufficient for this purpose, more reliable infor-mation about the constructional features was obtained by scanning measurements with collimated radiation at the front window and the sides of each detector. Efficiency calibrations were performed for many different combina-tions of body height, weight and photon energy. The required efficiency values for the whole energy range of in-terest (50 keV − 2 MeV) were simulated with the Monte Carlo codes MCNP 4C2 and MCNP 5 using a detailed geometrical model of the detectors and various Medical Internal Radiation Dose (MIRD) phantoms representing adults and children. The dependence of the efficiency on height and weight of the measured person is discussed. The calculated efficiency curves based on mathematical MIRD phantoms were compared with conventional cali-bration results from measurements of bottle phantoms and brick phantoms. Generally, good agreement was found between the simulated and experimental results. In a sensitivity analysis simulations with MIRD phantoms were used to analyse the influence of possible sources of error (such as an incorrect position of the measured person or the detectors) on the accuracy of whole-body counting results. KEYWORDS: Monte Carlo simulation; MCNP; HPGe detectors; whole-body counter; mathematical calibration; anthropomorphic phantoms. 1. Introduction Whole-body counters (WBCs) are gamma-ray spectrometers used for the detection and quantitative measurement of radioactivity within the human body; they are usually equipped with one or more semiconductor or scintillation detectors. This in vivo measuring technique is applicable to radionu-clides emitting penetrating radiation, such as gamma rays, X-rays or bremsstrahlung produced by high-energy beta emitters. Generally efficiency calibrations for whole-body counters are performed by means of anthropomor-phic phantoms containing known quantities of various gamma-emitting radionuclides. In this conven-tional calibration method, gamma-ray spectra from phantom measurements are used to determine the full-energy peak efficiencies for all gamma energies of the radionuclide mixture. Finally, a calibration curve (full-energy peak efficiency versus photon energy) covering the whole energy range of interest is constructed by interpolation between the measured data points. In a mathematical calibration, the required efficiency values are simulated using Monte Carlo codes and mathematical phantoms instead of deriving them from real measurements [1–4]. For these simu-lations, input files with a detailed model of all relevant components of the measuring system (detec-tors, phantoms and surrounding area) are needed; in order to obtain correct results, the model should describe the geometry and elemental composition of the measuring system as precisely as possible. A mathematical calibration has many advantages and some disadvantages compared with the conven-tional calibration procedure. First of all, a mathematical calibration does not require the expensive and time-consuming manufacture of radioactive phantoms and hence the handling of unsealed radioactive material and the disposal of radioactive waste can also be avoided. Only relatively few radionuclides suitable for the efficiency calibration of gamma-ray spectrometers are commercially available. For this reason the traditional calibration curves are mostly based on a small number of data points and the

* Presenting author, E-mail: m.schlaeger@fz-juelich.de

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calculation of the required efficiency values by interpolation between these points can result in a con-siderable uncertainty in some energy ranges. By contrast, in a mathematical calibration the efficiency for any desired photon energy can be simulated, regardless of the availability of appropriate radio-nuclides. An obvious disadvantage of a calibration procedure based on Monte Carlo simulations is the great expenditure for the creation of a precise geometrical detector model and its verification; a con-ventional calibration using radioactive reference materials can be performed without any information about the constructional features of the detector system. 2. Materials and methods The whole-body counter at Forschungszentrum Jülich (Research Centre Jülich, FZJ) is equipped with four closed-end coaxial HPGe (high-purity germanium) detectors with carbon-epoxy windows. One is of the reverse-electrode (REGe) type (Canberra Model Number GR5522), and the others are extended range (XtRa) detectors with a thin contact on the front surface (Canberra GX6020). The detectors are installed in a fixed geometry within a shielded chamber with walls, ceiling and floor made of 15 cm low-activity steel and 3 mm lead as an inner lining to reduce the background radiation [5]. During the measurement, a person lies on a Plexiglas stretcher covered with a soft mattress. Two detectors are placed above and below the stretcher, respectively. With an adult test person, detector 1 (REGe) is approximately situated above the chest, detector 2 above the hip region, detector 3 below the back and detector 4 below the buttocks. For efficiency measurements during the detector modelling, three radioactive point sources (Am-241, Cs-137, Co-60) were used which are enclosed in small plastic slabs with the dimensions 23 x 11 x 2 mm. The activities were in the range of 100 to 400 kBq. An overall uncertainty of 4 % (coverage factor k = 3) is quoted by the manufacturer (Amersham Buchler). Two brick-shaped collimators made, respectively, of lead (150 x 120 x 50 mm; 10.3 kg) and tungsten alloy (95 % W, 5 % Ni and Fe; 150 x 100 x 42 mm; 11.5 kg) were used for scanning measurements. Both contain a hollow rectangu-lar channel (150 x 11 x 2 mm), into which the above-mentioned reference sources can be inserted.

For Monte Carlo simulations versions 4C2 and 5 of the MCNP code (Monte Carlo N-Particle Trans-port Code) [6] were used. Because only negligible differences were found between the results of these two versions, no distinction between them is made in the following text. The software was run on a personal computer (Pentium 4 processor, 3.0 GHz, 1 GB RAM) under Windows XP. Efficiency values were calculated using the pulse height tally of MCNP. To keep the uncertainty of the calculation results lower than 1 % the histories of up to 30 million particles had to be simulated in each case, depending on the gamma energy and the phantom size. The corresponding runtimes were between 1 and 2 hours for each efficiency value.

Various Medical Internal Radiation Dose (MIRD) phantoms [7] representing adults and children were used to calculate efficiency values by means of Monte Carlo simulation; MCNP input code for these mathematical phantoms was generated with the BodyBuilder software (White Rock Science [8]) and integrated into the mathematical model of the whole-body counter after some manual adaptation. 3. Modelling of the detectors In order to obtain detailed information about the constructional features of each detector, scanning measurements with collimated radiation were performed at the front window and the sides of the housing [9]. The collimated beam was aligned perpendicular to the window and housing, respectively, with the collimator touching the surface of the detector (Fig.1). For the front scans the beam was moved in 1 to 5 mm steps along the diameter of the front window; at each step a spectrum was taken and the full-energy peak efficiency was determined. The side scans were performed either by posi-tioning the collimator at different angles around the detector housing keeping the z-coordinate con-stant or by moving the collimator along the axis of the detector (z-axis) at a constant angle.

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Figure 1: Schematic drawing of the experimental setup [9] (parts of the detector and the collimator have been removed )

Three photon energies were used for the scanning measurements: 59.5 keV (Am-241), 661.6 keV (Cs-137) and 1332.5 keV (Co-60). The weakly penetrating low-energy radiation of Am-241 is well suited for analysing the outer dimensions of the cylindrical crystal, the thickness of the endcap and holder and the dead layers, whereas the penetrating radiation of Cs-137 or Co-60 reveals more details of the inner parts of the crystal. Fig. 2 shows the results from two scans with Am-241, perpendicular to each other, at the front window of the REGe detector. The sensitivity to the low-energy radiation is very uniform across the detector front. By contrast, the response to the more penetrating Cs-137 radi-ation drops clearly in the middle of the window due to the influence of the central well. As an approximation, coaxial germanium detectors are often regarded as rotation-symmetric. Never-theless, the lateral scans in Figs. 3 and 4 show that there are considerable deviations from this simpli-fication. If the REGe detector were really rotation-symmetric, the three curves in Fig. 3 should be congruent and each of the four curves in Fig. 4 would have to be a straight horizontal line. The ob-served asymmetries are caused by attenuating objects located between the germanium crystal and the housing.

Figure 2: Experimental and calculated results for scanning measurements at the front window of the REGe detector [9]

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Figure 4: Experimental and calculated results for scanning measurements [9] with collimated Am-241 radiation at the side of the REGe detector (beam movement around the detector at different heights)

Figure 3: Experimental and calculated results for scanning measurements with collimated Am-241 radiation at the side of the REGe detector (beam movement parallel to the z-axis at different angles)

When several hundred experimental data points from scanning measurements were available for each of the four detectors, a precise mathematical model of the detectors was created. Starting with an initial detector model, based on the manufacturer’s drawings, efficiency values for the experimental setup (Fig. 1) were calculated by means of Monte Carlo simulations. These simulation results were compared with the corresponding measured efficiencies and whenever a discrepancy occurred the model was corrected by the trial-and-error method. Many changes were made concerning the dead layer thickness and some objects (e.g. steel screws) not mentioned in the manufacturer’s specifications were introduced into the model. After each correction the simulations were repeated with the adjusted detector model and again calculated and experimental data were compared. This iterative process was continued until a good agreement between simulation and experiment was achieved. The final simula-tion results for the REGe detector after making all adjustments are shown in Figs. 2 - 4. Modelling of the three XtRa detectors was more complicated than in the case of the REGe detector, because the dead layer thickness at the cylindrical surfaces is obviously not constant. Fig. 5 shows some of the experimental results from scanning measurements. Due to a decrease of the dead layer the measured efficiency of detectors 3 and 4 generally rises from the closed end (z ≈ 0.5 cm) to the open end (z ≈ 7 cm) of the crystal. By contrast, the efficiency of detector 2 shows an overall decrease from the closed end to the open end, which most likely results from an increase of the dead layer. According to the manufacturer’s specifications, the aluminium holder of each detector should have three swell-ings (see Fig. 1). Actually, the additional attenuation effect of these thicker regions in the holder can be seen in Fig. 5 in the curves for detectors 2 and 4 at z ≈ 0.8 cm, z ≈ 2.5 – 3.5 cm and z ≈ 5.0 – 6.0 cm. The experimental data for detector 3 do not agree with the specifications; only two swellings are

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indicated by the measured efficiency curve and one of them (z ≈ 1.1 – 2.0 cm) is dislocated by approx. 1.5 cm relative to its theoretical position. These examples show that, although the three detectors are of the same type (Canberra GX6020), the differences between them are remarkable and the model designed for a specific detector cannot be used for a different one.

Figure 5: Experimental and calculated results for scanning measurements with collimated Am-241 radiation at the sides of 3 XtRa detectors (collimator movement parallel to the z-axis) Finally, after completion of the modelling, the quality of the detector models was verified by measure-ments with uncollimated point sources (Am-241, Cs-137, Co-60), which were placed in 77 different positions on a 10 x 10 cm grid on the stretcher of the whole-body counter. The stretcher-detector distance was 50 cm. For all photon energies and all source positions the deviation between measured and simulated efficiencies was found to be less than 3 % with detectors 1, 3 and 4 and less than 2 % with detector 2. The results for detector 2 are shown in Fig. 6. The intersection point of the detector axis and the stretcher surface is at x = 0/y = 0. Positive deviations of the simulated efficiency values relative to the measured values are displayed in shades of blue, negative deviations in yellow to orange shades.

Figure 6: Relative deviation between simulated and measured efficiencies (in percent) for measure-ments of point sources with detector 2 (XtRa)

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4. Mathematical anthropomorphic phantoms After a precise model of the detector system had been designed and verified, a mathematical represen-tation of the human body was needed for the simulation of whole-body counter measurements. In prin-ciple, many different types of mathematical anthropomorphic phantoms are suitable for this purpose. The simplest practical solution would be to create models of phantoms which are used in conventional calibrations, such as the Bottle Mannequin Absorption (BOMAB) phantom or the St. Petersburg Brick Phantom [10]. Such primitive phantoms permit only a rough approximation of the human body be-cause all internal details (organs, skeleton) are missing. On the other hand, there are very complex mathematical voxel phantoms [11] which often comprise several million cells; their acquisition and handling is difficult. For the calibration of the WBC in Jülich a decision was made in favour of MIRD phantoms, which are simplified but still rather detailed representations of human bodies in various weight classes. Each phantom consists of four sections (Fig. 7): an elliptical cylinder capped by half an ellipsoid representing the head; a circular cylinder as neck; an elliptical cylinder repre-senting the trunk and arms; two truncated circular cones repre-senting the legs and feet. The surfaces of the skeleton and the internal organs are described by linear and quadratic inequa-tions. Three tissue types are distinguished in the phantoms: skeletal, lung, and all other tissues with densities of 1.4, 0.296 and 1.04 g/cm3, respectively. Most of the required MIRD phan-toms were created with the BodyBuilder software; only the ver-sions taller than 180 cm had to be constructed manually by modifying the input file for the tallest BodyBuilder phantom (179 cm). Because the phantoms were intended for the simu-lation of a nearly homogeneous activity distribution, only the skeleton and the lungs were explicitly specified inside the phantom; the space occupied by all other organs and tissues of the body was defined as soft tissue with a density of 1.04 g/cm3, which is a good approximation of muscle, fat and organ tissue. The radiation source was defined as a homogeneous activity dis-tribution within the whole phantom except for the skeleton; this is a more or less realistic scenario for many radionuclides (e.g. Cs-137, K-40) which are not concentrated in a specific organ after intake.

Figure 7: Surface (left) and inner structure (skeleton and lungs) of a MIRD phantom.

5. Efficiency calculations by Monte Carlo simulation To perform a mathematical efficiency calibration of the whole-body counter for a wide range of phan-tom weights and photon energies, an input file was created for each required combination of phantom size and photon energy, and an MCNP run was started to simulate the gamma-ray spectrum for the corresponding whole-body counter measurement. The essential result of each run was the calculated full-energy peak efficiency for this measurement. Regardless of their size, all phantoms were position-ed on the stretcher with the skullcap in a fixed position 10 cm from the wall. Fig. 8 shows the calculated efficiency curves in the energy range 60 keV to 2000 keV for 8 different phantoms representing adults and children of ‘normal build’ (14.7 kg/95 cm, 20.2 kg/111 cm, 30.0 kg/ 134 cm, 41.1 kg/150 cm, 49.7 kg/161 cm, 61.2 kg/171 cm, 74.7 kg/179 cm, 87.7 kg/190 cm). In prin-ciple, all the curves have the same shape: an efficiency maximum close to 140 keV, a sharp decrease of the efficiency on the low-energy side of the maximum and a decrease on the high-energy side which becomes flatter with increasing energy. Due to the decreasing self-attenuation within the phan-toms the efficiency generally rises when the phantom weight is reduced. Because of the fixed head position of the phantoms this is no longer true for phantom weights less than 20 kg, where a very small

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mean solid angle between the phantom and the four detectors outweighs the effect of reduced self-attenuation.

Figure 8: Simulated peak efficiency of the WBC as a function of phantom weight and photon energy

The calibration curves used for routine WBC measurements at Forschungszentrum Jülich are based on phantoms of normal build, but these efficiency calibrations are also applied to persons whose pro-portions show moderate deviations from perfection. This is acceptable because for a given weight a variation of the body height does not have a great influence on efficiency. In Fig. 9 calculated peak efficiencies for two MIRD phantoms with (nearly) the same weight and different heights are com-pared. Although the heights differ by 11 %, the relative deviation between the efficiency values is only between 9 % and 7 % in the low-energy region below 200 keV, between 7 % and 5 % in the range

Figure 9: Comparison of the calculated peak efficiencies for two phantoms with the same weight and different heights

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from 200 keV to 1000 keV, and less than 5 % for high photon energies above 1000 keV. This example shows that most people can be measured with the standard calibration for the applicable weight class without any problems. Only for very corpulent or extremely slim persons is a special ad hoc cali-bration necessary, which can be best performed by means of an appropriate mathematical phantom and Monte Carlo software. 6. Comparison of simulated and conventional calibration results In order to assess the compatibility of simulated and experimental efficiency calibrations, calculated efficiency values from an MIRD phantom and measured values from a bottle phantom and a brick phantom are compared in Fig. 10; all three phantoms represent a person with a weight of 70 kg and a height of 170 cm. Bottle phantoms in the weight range from 10 kg to 100 kg are used for routine cali-brations of the whole-body counter at the FZJ; they consist of 1- and 2-litre plastic bottles, which are filled with a radionuclide solution. In intercomparison exercises organised by the German Federal Office for Radiation Protection, brick phantoms containing Ba-133, Cs-137, Co-60 and K-40 are used. The maximum relative deviation between the simulated and the measured efficiencies is 13 % for en-ergies below 200 keV, 8 % in the energy range 200 – 1000 keV, and 5 % for photon energies greater than 1000 keV. In the whole energy range of interest, the simulated efficiency values are lower than the measured values from the bottle and brick phantoms. Probably this difference can be explained by a stronger self-absorption in the mathematical phantom due to the skeleton, which is not present in the physical phantoms. In addition to this effect there are large hollow spaces between the bottles in the bottle phantom which also reduce the self-absorption and thus increase the efficiency.

Figure 10: Comparison of simulated and measured efficiency values

7. Sensitivity analysis By means of Monte Carlo simulations a sensitivity analysis was performed for several parameters which can have an effect on the peak efficiency of a whole-body counter measurement. Most impor-tant in this regard is the positioning of the measured person or phantom and the detectors. Fig. 11 shows the simulated relative deviation of the full-energy peak efficiency resulting from the displacement of a 61 kg MIRD phantom parallel to the x-, y- or z-axis. Results are shown for low-energy (60 keV, Am-241) and high-energy (1461 keV, K-40) photon radiation. In principle, the speci-fied position of the person during a measurement is clearly defined but in routine operation there are certainly deviations from this ideal position. Most likely in practice is a displacement of the person along the y-axis, which runs from the foot to the head of the stretcher. A variation of the phantom’s

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y-coordinate between –15 cm and +9 cm relative to its specified position results in deviations of the peak efficiency between –4 % and +1 %, which is negligible. The z-axis is perpendicular to the stretcher plane with positive (negative) coordinate values above (below) the stretcher. Because the phantom position is fixed by the stretcher, a considerable displacement along the z-axis is hardly possible; only a maximum shift by ±3 cm is estimated to occur in practice due to a variable com-pression of the mattress and bending of the Plexiglas stretcher resulting from different phantom weights and shapes. The corresponding relative deviations of the peak efficiency range from –1 % to +4 %. A variation of the phantom’s x-coordinate from –12 cm to +12 cm corresponds to a shift of the phantom from the right edge to the left edge of the stretcher. The resulting maximum relative devia-tion of the peak efficiency is –6 % for high-energy photons and –12 % for low-energy photons. When the phantom is moved from its specified position towards one of the edges of the stretcher, not only the solid angle between the radiation source and the detectors is reduced but also the self-absorption of the photons within the phantom is increased in the direction towards the detectors. The latter effect is more pronounced for low-energy radiation; therefore in Fig. 11 the efficiency decrease caused by a displacement along the x-axis is much stronger for the 60 keV photons than for the 1461 keV photons.

Figure 11: Variation of the WBC peak efficiency resulting from incorrect positions of a 61 kg phantom on the stretcher (see text)

Figure 12: Variation of the WBC peak efficiency for 662 keV photons resulting from incorrect positioning of detector 1 (see text)

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Incorrect positioning of the detectors during a measurement is not very likely. An exception may be detector 1, which is used in two different configurations for whole-body and also thyroid measure-ments. For these two configurations the y- and z-coordinates of the detector have to be changed, which can be a source of error if the settings are not checked thoroughly. In Fig. 12 the effect of incorrect detector positioning on the peak efficiency of the whole-body counter is shown. A displacement of detector 1 from its specified position towards the negative y- or z-axis increases the efficiency because the mean solid angle between the phantom and the detector is increased. A displacement towards the positive y- or z-axis or in any direction along the x-axis reduces the solid angle and thus the efficiency. 7. Conclusions The results from this work show that the mathematical efficiency calibration of a whole-body counter by means of Monte Carlo simulations can be a useful alternative to conventional calibrations with phantoms containing radioactive reference sources. Both methods have various advantages and dis-advantages and numerous sources of error; nevertheless the quality of a mathematical calibration is comparable to that of a conventional calibration provided that a precise model of the measuring sys-tem and an appropriate mathematical phantom are used. There are some calibration problems which cannot be solved easily by means of commercially avail-able physical phantoms; examples are partial-body calibrations for radionuclides which are concen-trated in a specific organ after intake or whole-body calibrations for persons who are very overweight or extremely slim. In such cases a mathematical efficiency calibration is particularly valuable. Acknowledgements The author is indebted to Dr P. Hill and Dr R. Lennartz for their support of this work and Mrs J. Carter-Sigglow for proofreading. REFERENCES [1] GENICOT, J. L., KOUKOULIOU, V., CARINOU, E., Monte Carlo calculations applied to the

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