RADIOPHARMACEUTICAL 11 C ACTIVITY MEASUREMENTS BY MEANS OF THE TDCR-CERENKOV METHOD BASED ON A GEANT4 STOCHASTIC MODELING

C:\Documents and Settings\Mark McClure\Desktop\LSC2010\P-21- Thiam.fm printed: 27 July 2011 PAGE PROOF MM AUTHOR S PROOF Please check carefully and return any corrections via email as soon as possible RADIOPHARMACEUTICAL 11 C ACTIVITY MEASUREMENTS BY MEANS OF THE TDCR-CERENKOV METHOD BASED ON A GEANT4 STOCHASTIC MODELING C Thiam C Bobin 1 J Bouchard CEA, List, Laboratoire National Henri Becquerel (LNE-LNHB), F-91191 Gif-sur-Yvette Cedex, France. ABSTRACT. In radionuclide metrology, the TDCR (triple-to-double coincidence ratio) method is a widely implemented method when liquid scintillation detectors are used (3-photomultiplier counting system). In practice, the activity is determined using a statistical model that incorporates a free parameter to establish a relationship between the detection efficiency of the counter (double coincidences) and the experimental TDCR ratio. As an alternative to this standard model, the capabilities of modeling based on the simulation code Geant4 are investigated at LNE-LNHB. In order to implement a stochastic calculation of coincidences between photomultipliers, the propagation of optical photons is simulated from their creation in the optical chamber to the production of photoelectrons in the photomultipliers. The first application of this stochastic approach confirmed the hypothesis that coincidences are counted due to Cerenkov photons emitted from the photomultiplier window as a consequence of Compton scattering. Recently, this Geant4 modeling was extended to radionuclide measurements by means of the TDCR-Cerenkov technique. This stochastic approach has been validated in the case of 90 Y standardization. Using the same method, this article presents the activity measurement of the short half-life radiopharmaceutical 11 C (T 1/2 = 20.370 (20) min) in order to test the Geant4 model in the case of a low detection efficiency close to 20% (E +,max 960 kev). Moreover, since Cerenkov measurements can be directly carried out with aqueous samples, this technique makes source preparation easier and is not affected by chemical and ionization quenching processes encountered in liquid scintillation. Cerenkov-TDCR measurements could thus be an interesting alternative to conventional liquid scintillation for short half-life radionuclide standardization. INTRODUCTION Developed for radionuclide standardization using liquid scintillation detectors, the TDCR (triple-todouble coincidence ratio) method is based on a specifically designed 3-photomultiplier system (Broda et al. 2007). Knowing the radionuclide decay scheme, the activity is determined using a freeparameter statistical model, enabling us to establish a mathematical relationship between the detection efficiency (double coincidences) and the experimental TDCR ratio given by coincidences between photomultipliers. Using the same detection setup, the TDCR method can be extended to Cerenkov measurements when an additional free parameter is included to the statistical model in order to take into account the anisotropy of Cerenkov light emission (Kossert 2010). An alternative to this standard practice is to create a stochastic model, enabling us to simulate the different optical processes that exist in the TDCR counter from the creation of photons in the sample vial to the detection of photoelectrons in photomultipliers. Based on the Monte Carlo code Geant4 (Agostinelli et al. 2003), this stochastic approach to calculate double and triple coincidences was recently validated when standardizing 90 Y by Cerenkov counting (Bobin et al. 2010). As Cerenkov radiation is the result of an electromagnetic perturbation in a transparent medium, this application provides a useful test of the optical modeling without the need to simulate physicochemical processes related to liquid scintillation counting (LSC). This stochastic modeling was also applied to confirm the hypothesis that Cerenkov photons are emitted from photomultiplier windows due to electrons produced by Compton scattering (Thiam et al. 2010). Cerenkov measurements are not frequently used in radionuclide standardization because higher detection efficiencies are obtained with liquid scintillation counting. Cerenkov light emission is characterized by a threshold effect that limits the production of photons when an electron is emitted. However, this property can be advantageously used to discriminate the radionuclide to be standard- 1 Corresponding author. Email: christophe.bobin@cea.fr. 2011 by the Arizona Board of Regents on behalf of the University of Arizona Proceedings of the LSC 2010 International Conference edited by Philippe Cassette, p 1 8 1

2 C Thiam et al. ized from potential impurities that emit electrons having energies lower than the Cerenkov threshold. LSC can be sensitive to chemical reactions that occur after the mixing of the sample solution with the scintillation cocktail. For instance, photons due to chemiluminescence can interfere with those created by ionizing radiation (L Annunziata 2003). Such chemical reactions could be the cause of the stability problems observed in preliminary 11 C measurements. Since Cerenkov counting has the advantage to be carried out with aqueous solutions without the addition of a fluorescent cocktail, the TDCR-Cerenkov technique can also be an interesting alternative to LSC. With a half-life of 20.370 (20) min (Bé et al. 2004), 11 C disintegrates mainly by an allowed + transition through a 99.750 (13) % branch corresponding to a maximum energy of about 960.5 (9) kev (brain imaging is one of the applications of this radiopharmaceutical). For the standardization of 11 C using the TDCR-Cerenkov technique, the same procedure adopted for 90 Y activity measurements has been applied using the stochastic calculation of coincidences between photomultipliers (Bobin et al. 2010). In order to refine the optical modeling, the simulation of a meniscus that is at the surface of the aqueous sample was added. The intensity profile of light emitted outside the sample vial was computed for comparison with experimental data available in the literature. As for the 90 Y standardization, the activity calculations were realized according to different TDCR experimental values obtained by defocusing the photomultipliers. THE TDCR DETECTION SYSTEM AND EXPERIMENTAL RESULTS The description of the Cerenkov effect is well documented in the literature (L Annunziata 2003). Cerenkov counting (Cerenkov 1937) is possible for radionuclides emitting electrons having energies greater than a threshold that decreases when the refractive index of the transparent medium increases (in aqueous samples, for a refractive index of ~1.34 at 400 nm, the energy threshold is 257 kev). The Cerenkov light emission is directional: photons are emitted according to a cone with respect to the charged particle path and with an angle that depends on the velocity of that particle and the refractive index. The continuous spectral distribution of Cerenkov photons is predominant in the ultraviolet region and decreases in the visible wavelengths region. All these properties that are characteristic of the Cerenkov effect have to be considered in order to obtain a realistic optical modeling of the TDCR counter. The 3-photomultiplier system originally designed for LSC is also used for Cerenkov measurements without any modifications. Based on XP2020Q photomultipliers equipped with a fused silica window, the detection system is sensitive in the ultraviolet region (bandwidth range: 160 650 nm), which makes it well adapted to Cerenkov counting. The Teflon optical cavity where the counting vial is positioned has a spherical shape. Variation of the detection efficiency is applied by defocusing the photomultipliers. The focus voltages are controlled by computer; different settings can be applied between photomultipliers in order to reduce the efficiency asymmetry. The electronic chain dedicated to coincidence counting is based on the MAC3 module (Bouchard and Cassette 2000). Specially designed for liquid scintillation measurements, this module processes counting losses according to the live-time technique using extendable deadtimes. This system provides robust protection against counting excess due to afterpulses. 11 C radioactive samples were prepared in standard low-potassium borosilicate vials filled with 15 ml of inactive solution (10 g/g of C in Na 2 CO 3 diluted in H 2 O). Polyethylene vials are more advantageous for Cerenkov counting due to the lower absorption in the ultraviolet region and scattering effects of the plastic (L Annunziata 2003). Nevertheless, standard borosilicate vials were used for modeling purposes. Four sources were measured. The defocusing technique applied to photomultipliers gave experimental TDCR values ranging from about 0.25 to 0.3.

11 C Activity Measurements by TDCR-Cerenkov Method 3 Optical Modeling of the TDCR Detection System with Geant4 The Geant4 simulation toolkit (Agostinelli et al. 2003) provides all the packages needed for the construction of the optical modeling of the TDCR counter that includes the geometry presented in Figure 1 and the associated material properties as well as the transport of all particles generated in the case of 11 C Cerenkov measurements (positrons, gamma photons, Cerenkov photons). As already described for the 90 Y standardization (Bobin et al. 2010), the geometry of the optical cavity was implemented to simulate the creation and the propagation of Cerenkov photons in any transparent material. Based on the UNIFIED model (Levin and Moisan 1996), optical properties were defined according to the photon wavelengths to simulate reflection and refraction processes depending on refractive indexes of medium boundaries. Assuming that the number of Cerenkov photons lost by absorption is negligible, no length attenuations in transparent materials were considered. However, optical transmittances that limit the continuous spectral bandwidth are taken into account in the Geant4 modeling: in the low-wavelength region, the cut-off is defined by the borosilicate vial transmittance ( 290 nm); and for the other part, the limit comes from the sensitivity of the bialkali photocathode ( 650 nm). Figure 1 Geant4 modeling of the TDCR counter geometry including the counting vial. The optical parameters defined for the different elements constituting the optical cavity of the TDCR counter are listed hereafter: The sample solution is considered as liquid water using a dispersive refractive index. The liquid-air and liquid-vial interfaces are modeled using dielectric-dielectric boundaries (Levin and Moisan 1996). The meniscus between the liquid surface and the inner vial wall is also defined. The vial geometry (1-mm wall thickness) is drawn from a description given in Cassette et al. (2006). A dispersive refractive index is also defined for the borosilicate vial ( 1.52 at 400 nm) and the vial-air interface is modeled with a dielectric-dielectric boundary. The inner and outer surfaces are defined as polished. The sample vial is hung inside a Teflon spherical chamber in which the photomultiplier windows emerge; the surface of the optical cavity is modeled as a dielectric-metal boundary using a lambertian-type reflectivity of 95%. The optical properties of the XP2020Q photomultiplier window, including the bialkali photocathode, are also implemented. The geometry of the fused silica window is defined as a 52-mmdiameter cylinder with a spherical inner surface (1.5 mm thickness at the center and 7 mm at the periphery). The metallic ring (46 mm inner diameter) deposited around the bialkali coating for

4 C Thiam et al. its voltage polarization, is modeled as dielectric-metal boundary with a 95% reflectivity. A dispersive refractive index is defined for the fused silica material (1.47 at 400 nm); the surface of the photomultiplier window is modeled as polished. The bialkali photocathode is simulated through its optical properties at the fused silica-bialkali boundary in order to calculate the number of refracted Cerenkov photons. The refractive indexes depending on photon wavelengths are drawn from experimental data available in the literature (Motta and Schönert 2005; Harmer et al. 2006). In the Geant4 simulation, Cerenkov photons are emitted on the surface of a cone with an angle that opens up as a charged particle slows down in transparent materials constituting the optical cavity. Depending on the step length, the number of Cerenkov photons in a given spectral region is calculated from a Poisson distribution with a mean value determined from the Frank and Tamm theory (Jelley 1958). The number of photons depends on the properties of the charged particle at the beginning of the step; any changes that occurred along the track in terms of energy loss or material boundary crossing are used to determine the step length (the maximum step allowed in tracking charged particles was set to 100 nm). In the case of 11 C standardization, Cerenkov photons are mainly produced by positrons in the sample vial and the borosilicate wall; the light emission following Compton scattering of 511-keV annihilation photons is also simulated. Primary positrons are randomly generated in the 15-mL aqueous solution with an energy distribution calculated using a code based on Grau Malonda (1999) and Wilkinson (1970). The low-energy package based on Livermore data (Apostolakis et al. 1999) is used for the simulation of positrons and photons. Figure 2 displays the intensity profile of Cerenkov emission emerging along the vial height given by the Geant4 simulation. This result is similar to the experimental profiles given in the literature for borosilicate vials (Ramiro and García-Toraño 2005). In Figure 2, the simulated profile can be separated according to 3 main regions: liquid, meniscus, and air. In particular, an increase of light emission is observed above 30 mm of liquid (15 ml), corresponding to the meniscus. The intensity decreases in the air region of the vial (above the meniscus) is also well described by the simulation. Light intensity profile 0 10 20 30 40 Height / mm Figure 2 Intensity profile of Cerenkov emission emerging along the vial height

11 C Activity Measurements by TDCR-Cerenkov Method 5 RESULTS For each positron randomly generated in the liquid volume (15 ml), the simulation gives the number of photoelectrons produced at the photocathode of each photomultiplier; these results are obtained from a binomial trial applied to the Cerenkov photons refracted at the fused silica-bialkali boundary using the dispersive quantum efficiency given by Araújo et al. (1998) (~24% in the 300 400 nm region). The defocusing technique is carried out to alter the detection efficiency by reducing the number of photoelectrons detected at the first dynode. For each photoelectron given by the Geant4 modeling, the defocusing technique is simulated by a second binomial trial with a focusing parameter leading to a count in a photomultiplier when at least one success is obtained. For the same primary positron generated in the sample vial, additional successes in a photomultiplier are not considered. Consequently, at least 2 binomial successes in 2 different photomultipliers lead to a double coincidence; the same procedure is applied for the calculation of triple coincidences. As already described for the 90 Y standardization, a conservative method was adopted to calculate the uncertainty related to the Geant4 modeling. For that purpose, 2 parameters, which have a significant influence on the number of photoelectrons created at the bialkali photocathode, have been used to estimate the variability of the stochastic calculations: the distance of the photomultiplier window to the center of the optical cavity (16 17 mm) and the dispersive refractive index of the photocathode drawn from experimental data available in the literature (Motta and Schönert 2005; Harmer et al. 2006). From these parameters, 4 different configurations of the optical modeling were constructed: i.e. the configuration Ha16 corresponds to the bialkali refractive index given by Harmer et al. (2006) and a distance to the center of 16 mm; the Mo17 configuration is based on the refractive index published by Motta and Schönert (2005) and a position to the center of 17 mm. For each experimental TDCR value, the detection efficiency to double coincidences between photomultipliers is calculated by adjusting the focusing parameter. The activity concentrations calculated for the 11 C standardization are displayed in Figure 3 according to different optical modeling configurations (the results related to the Mo16 configuration are not displayed because they are close to the Ha17 values). No systematic trends of the activity calculations with TDCR are observed within the counting uncertainties. The maximum detection efficiency to double coincidences (~23.5%) is obtained for a TDCR value of 0.305. The focusing parameter corresponding to the maximum detection efficiency is about 0.97; this value is coherent with the maximum focusing parameter obtained in the case of 90 Y. This result represents an interesting indicator of the Geant4 modeling robustness over a large detection efficiency range ( 70% in the case of 90 Y). It has to be noted that the second binomial trial with the focusing parameter is based on the assumption that photoelectrons are uniformly produced by the photocathode. Therefore, the adjustment procedure applied to determine the detection efficiency is also used to compensate the variability of the photocathode surface response. The 11 C activity concentration is estimated to be 410.0 (35) MBq/g at the reference date (the uncertainty budget is displayed in Table 1). This result is deduced from the mean value calculated using the Ha16 and Mo17 configurations corresponding to the lowest and highest results; the Geant4 modeling uncertainty is obtained from the maximum deviation from the mean. The uncertainty component related to the decay correction is not included when comparing these results with those given by the - coincidence method. The maximum influence of the photomultiplier asymmetry is represented by the related uncertainty estimated by using 3 different focusing parameters for each photomultiplier. Concerning the comparison with the - coincidence method (Campion 1959), a conventional detection system was used: a proportional counter in the channel (CH 4 gas, atmospheric pressure)

6 C Thiam et al. Activity concentration / kbq.g -1 4.20e+5 4.15e+5 4.10e+5 4.05e+5 Ha17 Ha16 Mo17 4.00e+5 0.25 0.26 0.27 0.28 0.29 0.30 0.31 TDCR Figure 3 11 C activity concentrations calculated according to different experimental TDCR values and optical modeling configurations. The results related to the Mo16 configuration are not displayed because they are close to the Ha17 values. Table 1 Uncertainty budget associated with the 11 C activity concentration obtained using the TDCR-Cerenkov technique (1 relative standard deviation). Statistics Uniform distribution applied to 4 sources 0.15% Background 0.05% Live time Counting losses treated using the MAC3 module 0.1% Weighing Gravimetric measurements using the pycnometer method 0.05% TDCR modeling Conservative estimation obtained by variation of modeling 0.8% parameters influencing the production of photoelectrons PMT asymmetry Estimation obtained from the Geant4 modeling 0.2% Decay scheme 0.1% Relative combined standard uncertainty 0.85% and a NaI(Tl) detector in the channel. The counting processing was implemented using a livetimed anticoincidence system based on extendable deadtimes designed at LNE-LNHB (Bobin et al. 2007). Sources were prepared on gold-coated VYNS foils mounted on a stainless-steel ring (de Sanoit et al. 2004); the drying process was performed using the source dryer developed at the Institute for Reference Materials and Measurements (IRMM, Belgium) based on nitrogen jets operating at elevated temperature (Denecke et al. 2000). The detection efficiency in the channel estimated from the coincidence counting is greater than 98%. An activity concentration equal to 411 (2) kbq/ g was obtained; this value is coherent with the result given by the TDCR-Cerenkov technique. DISCUSSION AND PERSPECTIVES Based on modeling implemented using the Geant4 code, the TDCR-Cerenkov technique has been carried out for the radiopharmaceutical 11 C standardization. The stochastic approach is experimented in order to have a TDCR model based on a complete description of the detection system as

11 C Activity Measurements by TDCR-Cerenkov Method 7 well as a realistic simulation of the Cerenkov emission (continuous spectral bandwidth, directional emission according to a cone, threshold effect). Already applied to 90 Y activity measurements (Bobin et al. 2010), this new result shows that reliable radionuclide activities can be obtained with the Geant4 model over a large range of detection efficiencies (20 70%). These Cerenkov measurements represent also a good test for the optical modeling of the TDCR counter before its extension to liquid scintillation with additional processes such as ionization quenching. Since Cerenkov measurements are directly carried out using aqueous solutions, this technique represents an interesting alternative to LSC when it is affected by chemical instabilities. Despite the low detection efficiency (maximum 23%), the 11 C activity concentration agrees with the result obtained by - coincidence counting. Based on a conservative estimation, the relative uncertainty component related to the stochastic modeling is <1%. Further radionuclide measurements such as 32 P (maximum detection efficiency 57%) and 18 F (max detection efficiency 4%) are underway in order to gather more experience on the optical modeling and to refine the calculation of its associated uncertainty. The simulated intensity profile of Cerenkov light emerging from the vial was presented for comparison with the experimental results available in the literature. Similar results were obtained in the meniscus region, indicating that the simulation correctly takes into account refraction and reflection processes between the liquid and vial surfaces. Another study is underway in order to optimize the sample volume; first results show that the detection efficiency can be slightly increased by reducing the liquid volume to ~10 ml. The detection efficiency can also be improved by using polyethylene vials. In that case, additional properties need to be included in the modeling: an optical transmission more sensitive in the ultraviolet region, photon scattering effects in the vial wall, and the possibility to have a Teflon coating in the vial inner surface. REFERENCES Agostinelli S, Allison J, Amako K, et al. 2003. Geant4 a simulation toolkit. Nuclear Instruments and Methods in Physics Research A 506(3):250 303. Apostolakis J, Giani S, Maire M, Nieminen P, Pia MG, Urban L. 1999. Geant4 low energy electromagnetic models for electrons and photons. CERN-OPEN-99-034, Geneva. Araújo HM, Chepel VY, Lopes MI, Van der Marel J, Ferreira Marques R, Policarpo AJPL. 1998. Study of bialkali photocathodes below room temperature in UV/ VUV region. IEEE Transactions on Nuclear Science 45(3):542 9. Bé MM, Chisté V, Dulieu C, Browne E, Chechev V, Kuzmenko N, Helmer R, Nichols A, Schönfeld E, Dersch R. 2004. Table of Radionuclides, Monographie 5. ISBN 92-822-2204-7. Gif-sur-Yvette: CEA. Bobin C, Bouchard J, Hamon C, Iroulart MG, Plagnard J. 2007. Standardization of 67 Ga using a 4 (LS) - anticoincidence system. Applied Radiation and Isotopes 65(7):757 63. Bobin C, Thiam C, Bouchard J, Jaubert F. 2010. Application of a stochastic TDCR model based on Geant4 for Cherenkov primary measurements. Applied Radiation and Isotopes 68(12):2366 71. Bouchard J, Cassette P. 2000. MAC3: an electronic module for the processing of pulses delivered by a three photomultiplier liquid scintillation counting system. Applied Radiation and Isotopes 52(3):669 72. Broda R, Cassette P, Kossert K. 2007. Radionuclide metrology using liquid scintillation counting. Metrologia 44:S36 S52. Campion PJ. 1959. The standardization of radioisotopes by the beta-gamma coincidence method using high efficiency detectors. International Journal of Applied Radiation and Isotopes 4(3 4):232 48. Cassette P, Ahn GH, Alzitzoglou T, Aubineau-Lanièce I, Bochud F, García-Toraño E, Grau Carles A, Grau Malonda A, Kossert K, Lee KB, Laedermann JP, Simpson BRS, van Wyngaardt WM, Zimmerman BE. 2006. Comparison of calculated spectra for the interaction of photons in a liquid scintillator. Example of 54 Mn 835 kev emission. Applied Radiation and Isotopes 64(10 11):1471 80. Cerenkov PA. 1937. Visible radiation produced by electrons moving in a medium with velocities exceeding that of light. Physical Review 52:378 9. Denecke B, Sibbens G, Szabo T, Hult M, Persson L. 2000. Improvements in quantitative source preparation. Applied Radiation and Isotopes 52(3):352 5. de Sanoit J, Leprince B, Bobin C, Bouchard J. 2004. Freeze-drying applied to radioactive source preparation. Applied Radiation and Isotopes 61(6):1391 5.

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