International Journal of Radiation Biology, November 2014; 90(11): 953–958 © 2014 Informa UK, Ltd. ISSN 0955-3002 print / ISSN 1362-3095 online DOI: 10.3109/09553002.2014.955144
Cellular dosimetry calculations for Strontium-90 using Monte Carlo code PENELOPE Nora Hocine1, Delphine Farlay2,3, Georges Boivin2,3, Didier Franck1 & Michelle Agarande1
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1Institut de Radioprotection et de Sûreté Nucléaire, 2INSERM UMR 1033, Lyon, and 3Université de Lyon, Lyon, France
Abstract Purpose: To improve risk assessments associated with chronic exposure to Strontium-90 (Sr-90), for both the environment and human health, it is necessary to know the energy distribution in specific cells or tissue. Monte Carlo (MC) simulation codes are extremely useful tools for calculating deposition energy. The present work was focused on the validation of the MC code PENetration and Energy LOss of Positrons and Electrons (PENELOPE) and the assessment of dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part. Materials and methods: S-values (absorbed dose per unit cumulated activity) calculations using Monte Carlo simulations were performed by using PENELOPE and Monte Carlo N-Particle eXtended (MCNPX). Cytoplasm, nucleus, cell surface, mouse femur bone and Sr-90 radiation source were simulated. Cells are assumed to be spherical with the radii of the cell and cell nucleus ranging from 2–10 mm. The Sr-90 source is assumed to be uniformly distributed in cell nucleus, cytoplasm and cell surface. Results: The comparison of S-values calculated with PENELOPE to MCNPX results and the Medical Internal Radiation Dose (MIRD) values agreed very well since the relative deviations were less than 4.5%. The dose distribution to mouse bone marrow cells showed that the cells localized near the cortical part received the maximum dose. Conclusion: The MC code PENELOPE may prove useful for cellular dosimetry involving radiation transport through materials other than water, or for complex distributions of radionuclides and geometries.
(Sr-90), it is necessary to have an appropriate knowledge of the distribution of this radionuclide at tissular and cellular levels, then to know the energy deposited in specific cells for a given activity. Sr-90 is readily taken into the body because of its similarity to calcium (Armbrecht et al. 1998). It can incorporate into bone and irradiate the bone tissue and bone marrow (BM) cells (Agency for Toxic Substances and Disease Registry [ATSDR] 2001). Hence, immune and erythropoietic systems located in the BM are susceptible to injury as well. Thus, it is of interest to know the dose distribution to BM cells. The Strontium distribution can be obtained through the use of X-ray microanalysis. This technique was used in our previous study (Hocine et al. 2014) to localize numerous chemical elements such as calcium, phosphorus and strontium present in embedded bone samples. X-ray microanalysis allows identification and localization of elemental constituents on samples (Boivin et al. 2010, Doublier et al. 2011). The distribution of the non-radioactive Srontium was assessed in bone samples from postmenopausal women treated with 2 g/d of Strontium ranelate for 60 months. This element was mainly associated with bone newly formed during treatment (Doublier et al. 2011). To calculate the distribution of a deposited energy at the tissue, cellular and sub-cellular scale of Sr-90, Monte Carlo (MC) code event-by-event simulations can be particularly suitable. The MC simulation code PENetration and Energy LOss of Positrons and Electrons (PENELOPE) is used here to perform cellular dosimetry of Sr-90 and to map the beta particle dose in medullary cavity, in order to test the applicability of PENELOPE MC code for cellular dosimetry applications. The S-values (absorbed dose per unit cumulated activity) calculations were provided for source distributed uniformly in cell nucleus, cytoplasm and cell surface. The mouse femur was used as a theoretical model to assess the dose distribution to BM cells from the punctual Sr-90 source localized within the cortical bone part.
Keywords: PENELOPE, MCNPX, MIRD, Sr-90, validation, cellular dosimetry
Introduction To better understand the nature and importance of biological effects caused by chronic exposure through the ingestion of drinking water containing low doses of Strontium-90
Correspondence: Dr Nora Hocine, Internal Dosimetry Department, Institute for Radiological and Nuclear Safety (IRSN), 31 avenue de la Division Leclerc, 92260 Fontenay-aux-Roses, France. Tel: 33 (0) 15835 7731. E-mail: [email protected] (Received 20 December 2013; revised 28 April 2014; accepted 7 July 2014)
953
954 N. Hocine et al. The present study was conducted in two phases: (1) Comparison between calculated MC results and the Medical Internal Radiation Dose (MIRD) values, and (2) assessment of the dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part.
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Materials and methods The MIRD provides some of the tools necessary to estimate the absorbed dose at the cellular level. These tools take the form of cellular S-values (absorbed dose per unit cumulated activity). S-values are used to calculate the radiation dose received by a target region t when the radioactivity is distributed in a source region s. The relation between the mean absorbed dose D to the target region and the S-value is: D (t ←s ) = A s .S t ←s (
where:
)
D (t ←s ) is the mean absorbed dose in Gray (Gy) in the target t from radiation coming from the source s, A s is the cumulated activity in Becquerel second (Bq.s) in the source region s, and S(t ←s ) is the mean absorbed dose in Gray per Becquerel second (Gy/Bq.s) in the target t per cumulated activity in the source s, often referred to as the S-factor. S-values calculations are performed with the 2011 version of PENELOPE, a Monte Carlo algorithm and computer code for the simulation of coupled electron-photon transport. The basic principles of the Monte Carlo code PENELOPE have been described elsewhere (Salvat et al. 1996, Sempau et al. 1997). PENELOPE is an acronym for PENetration and Energy LOss of Positrons and Electrons. The simulation algorithm is based on a scattering model combining numerical databases with analytical cross-section models for the different interaction mechanisms and is applicable to energies from a few hundred eV to 1 GeV. The physics model and cross sections implemented in the PENELOPE code system have been described in detail by the authors (Salvat and Fernandez-Varea 2009). The crucial component of the PENELOPE code system is a set of Fortran 77 routines that can be used to perform electron-photon simulations. Geometry operations are performed by the subroutine package PENGEOM, which automatically tracks particles through the different bodies and materials. PENELOPE reads the required physical information about each material from an input material data file. The material data file is created by means of the auxiliary program material, which extracts atomic interaction data from the database. Information about the considered material is supplied from the program: Chemical composition (i.e., elements present and stoichiometric index, or weight fraction, of each element), mass density, mean excitation energy and oscillator strength of plasmon excitations. Two-dimensional viewer (GVIEW2D) and threedimensional viewer (GVIEW3D), a pair of programs, are used
Figure 1. 3D view for the cellular model. This Figure is reproduced in color in the online version of International Journal of Radiation Biology.
to display the geometry. GVIEW3D generates three-dimensional pictures of the geometry by using a simple raytracing algorithm. Bodies are displayed with the same color code used by GVIEW2D (in the material display mode). Two geometries have been studied. The first model uses a spherical geometry with the radii of the cell and cell nucleus ranging from 2–10 mm (Figure 1). The spheres are filled with liquid water (mass density r 1 g/cm3). The radiation source is assumed to be uniformly distributed in one of the following regions: Cell nucleus, cytoplasm and cell surface. S-values were calculated with PENELOPE MC CODE for source-to-target (t←s) combinations, namely nucleus to nucleus (N←N), cytoplasm to nucleus (N←Cy) and together with MCNPX (version 2.5f ) for cell surface to nucleus (N←CS). The basic principles of MC code MCNPX were
Figure 2. 3D-Femur modelized geometry displayed with GVIEW3D. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
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Cellular dosimetry calculations for Strontium-90 955
Figure 3. 3D-modelized femur midshaft cross section displayed with GVIEW2D. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
described in detail by Pelowitz (2005) and the calculation method was presented in previous work carried out by Hocine et al. (2014). The Sr-90 source emits beta-particles with energies in a continuum up to 0.5 MeV. Knowledge of beta-ray spectrum is important as it is used for the input file. The complete radiation spectrum for Sr-90 is taken from Weber et al. (1989). The second model uses mouse femur with cortical bone and medullary cavity (see Figure 2). In this theoretical model, several BM cells corresponding to different cellular regions (cytoplasm or nucleus) found inside medullary cavity, cortical bone part and Sr-90 source are considered. The punctual Sr-90 source was
assumed to be localized in the cortical bone part (see Figures 2 and 3). The mouse BM cells correspond to a spherical region composed of material which is active marrow with a thickness of 0.5 mm surrounded by cortical bone.
Results PENELOPE MC code validation Calculated S-values for the radii of the cell and cell nucleus ranging from 2–10 mm and for three source-to-target combinations (t←s) namely N←N, N←Cy and N←CS are presented in Tables I, II and III.
Table I. S-values for Intracellular Sr-90 for the N←N configuration: Comparison with Hocine et al. (2014) and Goddu et al. (1997). S (N←N)(Gy/Bq.s) S (N←N)(Gy/Bq.s) MIRD e1 = RC RN Goddu et al. (micrometers) (micrometers) (1997) PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
3.20E-03 1.39E-03 3.20E-03 7.68E-04 1.39E-03 3.20E-03 4.85E-04 7.68E-04 1.39E-03 3.33E-04 4.85E-04 7.68E-04 1.39E-03 2.42E-04 3.33E-04 4.85E-04 7.68E-04 1.84E-04 2.42E-04 3.33E-04 4,85E-04 1.44E-04 1.84E-04 2.42E-04 3.33E-04 4.85E-04
3.20E-03 1.39E-03 3.20E-03 7.71E-04 1.39E-03 3.20E-03 4.88E-04 7.72E-04 1.39E-03 3.35E-04 4.88E-04 7.72E-04 1.39E-03 2.45E-04 3.37E-04 4.89E-04 7.73E-04 1.86E-04 2.45E-04 3.37E-04 4.89E-04 1.46E-04 1.87E-04 2.46E-04 3.37E-04 4.89E-04
R PENELOPE − R MIRD R MIRD 0.15% 0.05% 0.11% 0.40% 0.17% 0.13% 0.71% 0.51% 0.20% 0.59% 0.65% 0.57% 0.26% 1.23% 1.07% 0.86% 0.60% 1.22% 1.39% 1.15% 0.92% 1.12% 1.37% 1.48% 1.15% 0.93%
MCNPX Hocine et al. (2014) 3.13E-03 1.37E-03 3.14E-03 7.64E-04 1.36E-03 3.13E-03 4.85E-04 7.64E-04 1.37E-03 3.33E-04 4.85E-04 7.63E-04 1.37E-03 2.43E-04 3.33E-04 4.84E-04 7.64E-04 1.85E-04 2.43E-04 3.33E-04 4.85E-04 1.45E-04 1.85E-04 2.43E-04 3.33E-04 4.84E-04
e2 =
R PENELOPE − R MCNPX R MCNPX 2.25% 1.82% 2.17% 0.98% 2.06% 2.26% 0.72% 1.08% 1.92% 0.52% 0.71% 1.21% 1.99% 0.81% 0.93% 0.99% 1.18% 0.73% 0.88% 1.06% 0.99% 0.19% 0.89% 1.16% 1.12% 1.05%
e1: the relative difference of PENELOPE results (RPENELOPE) with MIRD values (RMIRD); e2: the relative difference of PENELOPE with MCNPX results (RMCNPX).
956 N. Hocine et al. Table II. S-values for Intracellular Sr-90 for the N←Cy configuration: Comparison with the Goddu et al. (1997) and Hocine et al. (2014) results. S (N←Cy) (Gy/Bq.s) S (N←Cy)(Gy/Bq.s)
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MIRD e1 = RN Goddu et al. RC (micrometers) (micrometers) (1997) PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
1.04E-03 5.41E-04 6.55E-04 3.31E-04 3.80E-04 4.50E-04 2.23E-04 2.48E-04 2.83E-04 1.60E-04 1.74E-04 1.94E-04 2.18E-04 1.20E-04 1.29E-04 1.41E-04 1.56E-04 9.37E-05 9.90E-05 1.07E-04 1.16E-04 7.49E-05 7.85E-05 8.37E-05 9.02E-05 9.79E-05
1.02E-03 5.38E-04 6.49E-04 3.31E-04 3.81E-04 4.51E-04 2.21E-04 2.48E-04 2.84E-04 1.59E-04 1.75E-04 1.96E-04 2.21E-04 1.20E-04 1.30E-04 1.43E-04 1.58E-04 9.32E-05 9.99E-05 1.08E-04 1.19E-04 7.46E-05 7.92E-05 8.50E-05 9.20E-05 1.00E-04
R PENELOPE − R MIRD R MIRD
MCNPX Hocine et al. (2014)
e2 =
1.04E-03 5.54E-04 6.72E-04 3.41E-04 3.87E-04 4.60E-04 2.28E-04 2.54E-04 2.87E-04 1.63E-04 1.79E-04 1.95E-04 2.25E-04 1.23E-04 1.32E-04 1.45E-04 1.58E-04 9.68E-05 1.02E-04 1.09E-04 1.20E-04 7.77E-05 8.10E-05 8.65E-05 9.21E-05 1.01E-04
2.40% 0.55% 0.98% 0.01% 0.31% 0.23% 0.88% 0.10% 0.48% 0.78% 0.51% 0.85% 1.46% 0.00% 0.57% 1.08% 1.46% 0.51% 0.92% 1.29% 2.23% 0.37% 0.95% 1.57% 2.01% 2.33%
R PENELOPE − R MCNPX R MCNPX 2.86% 2.86% 3.52% 2.78% 1.49% 1.88% 2.99% 2.32% 0.88% 2.70% 2.29% 0.40% 1.65% 3.01% 1.42% 1.58% 0.00% 3.68% 1.91% 0.83% 0.98% 3.90% 2.12% 1.68% 0.12% 0.48%
Table III. S-values for Intracellular Sr-90 for the N←CS configuration: Comparison of PENELOPE with MCNPX results. S (N←CS)(Gy/Bq.s) R PENELOPE − R MCNPX e= R MCNPX RC (micrometers) RN (micrometers) MCNPX PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
4.62E-04 2.87E-04 2.61E-04 2.22E-04 2.17E-04 1.93E-04 1.58E-04 1.45E-04 1.41E-04 1.19E-04 1.11E-04 1.03E-04 9.91E-05 8.58E-05 8.64E-05 8.17E-05 7.89E-05 6.88E-05 6.42E-05 6.57E-05 6.43E-05 5.71E-05 5.36E-05 4.82E-05 4.86E-05 4.65E-05
4.56E-04 2.83E-04 2.64E-04 2.15E-04 2.07E-04 1.90E-04 1.53E-04 1.42E-04 1.36E-04 1.15E-04 1.07E-04 1.02E-04 9.90E-05 8.93E-05 8.32E-05 7.94E-05 7.68E-05 6.68E-05 6.27E-05 6.36E-05 6.15E-05 5.49E-05 5.16E-05 5.00E-05 4.78E-05 4.65E-05
e: the relative difference of PENELOPE results (RPENELOPE) with MCNPX results (RMCNPX).
1.24% 1.43% 0.98% 3.14% 4.45% 1.58% 2.61% 1.73% 3.33% 3.09% 3.44% 0.95% 0.07% 4.14% 3.68% 2.85% 2.62% 2.87% 2.26% 3.30% 4.45% 3.73% 3.81% 3.73% 1.72% 0.01%
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Cellular dosimetry calculations for Strontium-90 957
Figure 4. 2D dose map visualized with GNUPLOT. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
The relative deviation e is defined as: R − RREF e = PENELOPE RREF i.e., the relative difference of our results with respect to the data taken as reference. RPENELOPE are the results calculated with PENELOPE MC code and RREF are the reference data (MIRD values or MCNPX results). The calculations results showed that the relative deviations are less than 2.5% (2.26%) for N←N, less than
4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations.
Dose distribution to bone marrow cells The dose distribution to mouse bone marrow cells is shown in Figures 4 and 5. Assumption was applied in localizing of Sr-90 source in the cortical bone area, in the adjacent marrow cavity. Figures 4 and 5 show that the dose is close to zero after 150 mm.
Figure 5. Dose distribution to bone marrow cells. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
958 N. Hocine et al.
Discussion
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Comparison between PENELOPE, MCNPX calculations and MIRD values The PENELOPE calculations were compared to MCNPX results obtained by Hocine et al. (2014) and to values tabulated by the MIRD Committee (Goddu et al. 1997). The comparison of PENELOPE results (RPENELOPE) in the case of uniform volume distribution of Sr-90 source with MCNPX and those tabulated by the MIRD Committee (Goddu et al. 1997) showed that the maximum relative deviations are less than 4.5% (4.45%). A very good agreement was found between the S-values calculated with PENELOPE and the MIRD values since the maximum relative deviation e between these two data sets is less than 2.5%; the relative deviations are less than 1.5% (1.48%) for N←N and less than 2.5% (2.4%) for N←Cy configurations. The comparison between PENELOPE and MCNPX calculations results agreed very well since the relative deviations are less than 2.5% (2.26%) for N←N, less than 4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations. The PENELOPE calculated values are above those tabulated by the MIRD Committee, especially for the N←N configuration (when the 90Sr source is localized in the nucleus). It was observed that S-values decrease with increasing target sphere size. We generally find the largest relative deviations with MIRD where the target is at some distance from the source. This can be caused by the electron penetration capability which decreases with increasing sphere size. The overall uncertainty of the MC calculations is difficult to estimate since it includes uncertainties in cross section. The standard statistical uncertainty in the calculations is less than 2%. However, for the MIRD values the standard deviation associated with the cellular S-value was not evaluated. Assuming that the punctual Sr-90 source is localized within the cortical bone part, the dose distribution to bone marrow cells was assessed and shown in Figures 4 and 5. The present study shows that the dose strongly decreases by increasing the distance from the Sr-90 source and the BM cells localized near the cortical bone which received the maximum dose. Boivin (2010) showed that the Strontium was localized mainly in bone tissue recently formed in both cancellous and cortical bone. The dose distribution to mouse BM cells is an approach which can be of considerable interest for providing reliable radiation dose calculations with PENELOPE, involving radiation transport through materials other than water, or for complex distributions of radionuclides and geometries. It can therefore probably be used in therapy procedures with internal emitters to aid in optimizing individual patient therapy.
Conclusions The comparison of PENELOPE calculations results with those tabulated by the MIRD Committee showed that the
relative deviations are less than 1.5% (1.48%) for N←N and less than 2.5% (2.4%) for N←Cy configurations. A good agreement was found between the S-values calculated with PENELOPE and MCNPX since the relative deviations are less than 2.5% (2.26%) for N←N, less than 4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations. The assessment of dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part showed that the dose strongly decreases by increasing the distance from the source; in addition the BM cells localized near the cortical bone received the maximum dose, whereas this dose is close to zero after 150 mm. This study revealed that PENELOPE MC code is a useful tool to assess cellular dosimetry involving radiation transport through materials other than water or to simulate more complex and realistic geometries.
Declaration of interest The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
References Armbrecht HJ, Boltz MA, Christakos S, Bruns MEH. 1998. Capacity of 1,25-dihydroxyvitamin D to stimulate expression of calbindin D changes with age in the rat. Arch Biochem Biophys 352:159–164. Agency for Toxic Substances and Disease Registry (ATSDR). 2001. Toxicological profile for Strontium. U.S Department of Health and Human Services. Atlanta. Available from: http://www.apa.gov/ radiation/radionuclide/strontium.html Boivin G, Farlay D, Khebbab MT, Jaurand X, Delmas, PD, Meunier PJ. 2010. In osteoporotic women treated with strontium ranelate, strontium is located in bone formed during treatment with a maintained degree of mineralization. Osteoporosis Int 21:667–677. Boivin G. 2010. Bone quality and strontium ranelate. Int Bone Mineral Soc Bonekey 7:103–107. Doublier A, Farlay D, Khebbab MT, Jaurand X, Meunier PJ, Boivin G. 2011. Distribution of strontium and mineralization in iliac bone biopsies from osteoporotic women treated long-term with strontium ranelate. Eur J Endocrinol 165:469–476. Goddu SM, Howell RG, Bouchet LG, Bolch WE, Rao DV. 1997. MIRD cellular S values. Reston, VA: Society of Nuclear Medicine. Hocine N, Farlay D, Bertho JM, Boivin G, Desbrée A, Franck D, Agarande M. 2014. Cellular dosimetry of Strontium-90 using Monte Carlo code MCNPX-detection and X-ray microanalysis. Radioprotection 49: 101–105. Pelowitz DB, editor. 2005. MCNPX user’s manual, Version 2.5.0. Los Alamos National Laboratory report LA-CP 05-0369. Salvat F, Fernandez-Varea JM, Baro J, Sempau J. 1996. PENELOPE, an algorithm and computer code for Monte Carlo simulation of electron-photon showers Informes Tecnicos CIEMAT, report no. 799 (Madrid: CIEMAT). Salvat F, Fernandez-Varea JM. 2009. Overview of physical interaction models for photon and electron transport used in Monte Carlo codes. Metrologia, 46: S112–S138. Available at http://stacks.iop.org/ Met/46/S112. Sempau J, Acosta E, Baro J, Fernandez-Varea JM, Salvat F. 1997. An algorithm for Monte Carlo simulation of coupled electron-photon transport. Nucl Instrum Meth Phys Res Sect B 132:377–390. Weber DA, Eckerman KF, Dillman T, Ryman JC. 1989. MIRD: Radionuclide data and decay schemes. New York: Society of Nuclear Medicine.
Cellular dosimetry calculations for Strontium-90 using Monte Carlo code PENELOPE Nora Hocine1, Delphine Farlay2,3, Georges Boivin2,3, Didier Franck1 & Michelle Agarande1
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1Institut de Radioprotection et de Sûreté Nucléaire, 2INSERM UMR 1033, Lyon, and 3Université de Lyon, Lyon, France
Abstract Purpose: To improve risk assessments associated with chronic exposure to Strontium-90 (Sr-90), for both the environment and human health, it is necessary to know the energy distribution in specific cells or tissue. Monte Carlo (MC) simulation codes are extremely useful tools for calculating deposition energy. The present work was focused on the validation of the MC code PENetration and Energy LOss of Positrons and Electrons (PENELOPE) and the assessment of dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part. Materials and methods: S-values (absorbed dose per unit cumulated activity) calculations using Monte Carlo simulations were performed by using PENELOPE and Monte Carlo N-Particle eXtended (MCNPX). Cytoplasm, nucleus, cell surface, mouse femur bone and Sr-90 radiation source were simulated. Cells are assumed to be spherical with the radii of the cell and cell nucleus ranging from 2–10 mm. The Sr-90 source is assumed to be uniformly distributed in cell nucleus, cytoplasm and cell surface. Results: The comparison of S-values calculated with PENELOPE to MCNPX results and the Medical Internal Radiation Dose (MIRD) values agreed very well since the relative deviations were less than 4.5%. The dose distribution to mouse bone marrow cells showed that the cells localized near the cortical part received the maximum dose. Conclusion: The MC code PENELOPE may prove useful for cellular dosimetry involving radiation transport through materials other than water, or for complex distributions of radionuclides and geometries.
(Sr-90), it is necessary to have an appropriate knowledge of the distribution of this radionuclide at tissular and cellular levels, then to know the energy deposited in specific cells for a given activity. Sr-90 is readily taken into the body because of its similarity to calcium (Armbrecht et al. 1998). It can incorporate into bone and irradiate the bone tissue and bone marrow (BM) cells (Agency for Toxic Substances and Disease Registry [ATSDR] 2001). Hence, immune and erythropoietic systems located in the BM are susceptible to injury as well. Thus, it is of interest to know the dose distribution to BM cells. The Strontium distribution can be obtained through the use of X-ray microanalysis. This technique was used in our previous study (Hocine et al. 2014) to localize numerous chemical elements such as calcium, phosphorus and strontium present in embedded bone samples. X-ray microanalysis allows identification and localization of elemental constituents on samples (Boivin et al. 2010, Doublier et al. 2011). The distribution of the non-radioactive Srontium was assessed in bone samples from postmenopausal women treated with 2 g/d of Strontium ranelate for 60 months. This element was mainly associated with bone newly formed during treatment (Doublier et al. 2011). To calculate the distribution of a deposited energy at the tissue, cellular and sub-cellular scale of Sr-90, Monte Carlo (MC) code event-by-event simulations can be particularly suitable. The MC simulation code PENetration and Energy LOss of Positrons and Electrons (PENELOPE) is used here to perform cellular dosimetry of Sr-90 and to map the beta particle dose in medullary cavity, in order to test the applicability of PENELOPE MC code for cellular dosimetry applications. The S-values (absorbed dose per unit cumulated activity) calculations were provided for source distributed uniformly in cell nucleus, cytoplasm and cell surface. The mouse femur was used as a theoretical model to assess the dose distribution to BM cells from the punctual Sr-90 source localized within the cortical bone part.
Keywords: PENELOPE, MCNPX, MIRD, Sr-90, validation, cellular dosimetry
Introduction To better understand the nature and importance of biological effects caused by chronic exposure through the ingestion of drinking water containing low doses of Strontium-90
Correspondence: Dr Nora Hocine, Internal Dosimetry Department, Institute for Radiological and Nuclear Safety (IRSN), 31 avenue de la Division Leclerc, 92260 Fontenay-aux-Roses, France. Tel: 33 (0) 15835 7731. E-mail: [email protected] (Received 20 December 2013; revised 28 April 2014; accepted 7 July 2014)
953
954 N. Hocine et al. The present study was conducted in two phases: (1) Comparison between calculated MC results and the Medical Internal Radiation Dose (MIRD) values, and (2) assessment of the dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part.
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Materials and methods The MIRD provides some of the tools necessary to estimate the absorbed dose at the cellular level. These tools take the form of cellular S-values (absorbed dose per unit cumulated activity). S-values are used to calculate the radiation dose received by a target region t when the radioactivity is distributed in a source region s. The relation between the mean absorbed dose D to the target region and the S-value is: D (t ←s ) = A s .S t ←s (
where:
)
D (t ←s ) is the mean absorbed dose in Gray (Gy) in the target t from radiation coming from the source s, A s is the cumulated activity in Becquerel second (Bq.s) in the source region s, and S(t ←s ) is the mean absorbed dose in Gray per Becquerel second (Gy/Bq.s) in the target t per cumulated activity in the source s, often referred to as the S-factor. S-values calculations are performed with the 2011 version of PENELOPE, a Monte Carlo algorithm and computer code for the simulation of coupled electron-photon transport. The basic principles of the Monte Carlo code PENELOPE have been described elsewhere (Salvat et al. 1996, Sempau et al. 1997). PENELOPE is an acronym for PENetration and Energy LOss of Positrons and Electrons. The simulation algorithm is based on a scattering model combining numerical databases with analytical cross-section models for the different interaction mechanisms and is applicable to energies from a few hundred eV to 1 GeV. The physics model and cross sections implemented in the PENELOPE code system have been described in detail by the authors (Salvat and Fernandez-Varea 2009). The crucial component of the PENELOPE code system is a set of Fortran 77 routines that can be used to perform electron-photon simulations. Geometry operations are performed by the subroutine package PENGEOM, which automatically tracks particles through the different bodies and materials. PENELOPE reads the required physical information about each material from an input material data file. The material data file is created by means of the auxiliary program material, which extracts atomic interaction data from the database. Information about the considered material is supplied from the program: Chemical composition (i.e., elements present and stoichiometric index, or weight fraction, of each element), mass density, mean excitation energy and oscillator strength of plasmon excitations. Two-dimensional viewer (GVIEW2D) and threedimensional viewer (GVIEW3D), a pair of programs, are used
Figure 1. 3D view for the cellular model. This Figure is reproduced in color in the online version of International Journal of Radiation Biology.
to display the geometry. GVIEW3D generates three-dimensional pictures of the geometry by using a simple raytracing algorithm. Bodies are displayed with the same color code used by GVIEW2D (in the material display mode). Two geometries have been studied. The first model uses a spherical geometry with the radii of the cell and cell nucleus ranging from 2–10 mm (Figure 1). The spheres are filled with liquid water (mass density r 1 g/cm3). The radiation source is assumed to be uniformly distributed in one of the following regions: Cell nucleus, cytoplasm and cell surface. S-values were calculated with PENELOPE MC CODE for source-to-target (t←s) combinations, namely nucleus to nucleus (N←N), cytoplasm to nucleus (N←Cy) and together with MCNPX (version 2.5f ) for cell surface to nucleus (N←CS). The basic principles of MC code MCNPX were
Figure 2. 3D-Femur modelized geometry displayed with GVIEW3D. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
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Cellular dosimetry calculations for Strontium-90 955
Figure 3. 3D-modelized femur midshaft cross section displayed with GVIEW2D. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
described in detail by Pelowitz (2005) and the calculation method was presented in previous work carried out by Hocine et al. (2014). The Sr-90 source emits beta-particles with energies in a continuum up to 0.5 MeV. Knowledge of beta-ray spectrum is important as it is used for the input file. The complete radiation spectrum for Sr-90 is taken from Weber et al. (1989). The second model uses mouse femur with cortical bone and medullary cavity (see Figure 2). In this theoretical model, several BM cells corresponding to different cellular regions (cytoplasm or nucleus) found inside medullary cavity, cortical bone part and Sr-90 source are considered. The punctual Sr-90 source was
assumed to be localized in the cortical bone part (see Figures 2 and 3). The mouse BM cells correspond to a spherical region composed of material which is active marrow with a thickness of 0.5 mm surrounded by cortical bone.
Results PENELOPE MC code validation Calculated S-values for the radii of the cell and cell nucleus ranging from 2–10 mm and for three source-to-target combinations (t←s) namely N←N, N←Cy and N←CS are presented in Tables I, II and III.
Table I. S-values for Intracellular Sr-90 for the N←N configuration: Comparison with Hocine et al. (2014) and Goddu et al. (1997). S (N←N)(Gy/Bq.s) S (N←N)(Gy/Bq.s) MIRD e1 = RC RN Goddu et al. (micrometers) (micrometers) (1997) PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
3.20E-03 1.39E-03 3.20E-03 7.68E-04 1.39E-03 3.20E-03 4.85E-04 7.68E-04 1.39E-03 3.33E-04 4.85E-04 7.68E-04 1.39E-03 2.42E-04 3.33E-04 4.85E-04 7.68E-04 1.84E-04 2.42E-04 3.33E-04 4,85E-04 1.44E-04 1.84E-04 2.42E-04 3.33E-04 4.85E-04
3.20E-03 1.39E-03 3.20E-03 7.71E-04 1.39E-03 3.20E-03 4.88E-04 7.72E-04 1.39E-03 3.35E-04 4.88E-04 7.72E-04 1.39E-03 2.45E-04 3.37E-04 4.89E-04 7.73E-04 1.86E-04 2.45E-04 3.37E-04 4.89E-04 1.46E-04 1.87E-04 2.46E-04 3.37E-04 4.89E-04
R PENELOPE − R MIRD R MIRD 0.15% 0.05% 0.11% 0.40% 0.17% 0.13% 0.71% 0.51% 0.20% 0.59% 0.65% 0.57% 0.26% 1.23% 1.07% 0.86% 0.60% 1.22% 1.39% 1.15% 0.92% 1.12% 1.37% 1.48% 1.15% 0.93%
MCNPX Hocine et al. (2014) 3.13E-03 1.37E-03 3.14E-03 7.64E-04 1.36E-03 3.13E-03 4.85E-04 7.64E-04 1.37E-03 3.33E-04 4.85E-04 7.63E-04 1.37E-03 2.43E-04 3.33E-04 4.84E-04 7.64E-04 1.85E-04 2.43E-04 3.33E-04 4.85E-04 1.45E-04 1.85E-04 2.43E-04 3.33E-04 4.84E-04
e2 =
R PENELOPE − R MCNPX R MCNPX 2.25% 1.82% 2.17% 0.98% 2.06% 2.26% 0.72% 1.08% 1.92% 0.52% 0.71% 1.21% 1.99% 0.81% 0.93% 0.99% 1.18% 0.73% 0.88% 1.06% 0.99% 0.19% 0.89% 1.16% 1.12% 1.05%
e1: the relative difference of PENELOPE results (RPENELOPE) with MIRD values (RMIRD); e2: the relative difference of PENELOPE with MCNPX results (RMCNPX).
956 N. Hocine et al. Table II. S-values for Intracellular Sr-90 for the N←Cy configuration: Comparison with the Goddu et al. (1997) and Hocine et al. (2014) results. S (N←Cy) (Gy/Bq.s) S (N←Cy)(Gy/Bq.s)
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MIRD e1 = RN Goddu et al. RC (micrometers) (micrometers) (1997) PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
1.04E-03 5.41E-04 6.55E-04 3.31E-04 3.80E-04 4.50E-04 2.23E-04 2.48E-04 2.83E-04 1.60E-04 1.74E-04 1.94E-04 2.18E-04 1.20E-04 1.29E-04 1.41E-04 1.56E-04 9.37E-05 9.90E-05 1.07E-04 1.16E-04 7.49E-05 7.85E-05 8.37E-05 9.02E-05 9.79E-05
1.02E-03 5.38E-04 6.49E-04 3.31E-04 3.81E-04 4.51E-04 2.21E-04 2.48E-04 2.84E-04 1.59E-04 1.75E-04 1.96E-04 2.21E-04 1.20E-04 1.30E-04 1.43E-04 1.58E-04 9.32E-05 9.99E-05 1.08E-04 1.19E-04 7.46E-05 7.92E-05 8.50E-05 9.20E-05 1.00E-04
R PENELOPE − R MIRD R MIRD
MCNPX Hocine et al. (2014)
e2 =
1.04E-03 5.54E-04 6.72E-04 3.41E-04 3.87E-04 4.60E-04 2.28E-04 2.54E-04 2.87E-04 1.63E-04 1.79E-04 1.95E-04 2.25E-04 1.23E-04 1.32E-04 1.45E-04 1.58E-04 9.68E-05 1.02E-04 1.09E-04 1.20E-04 7.77E-05 8.10E-05 8.65E-05 9.21E-05 1.01E-04
2.40% 0.55% 0.98% 0.01% 0.31% 0.23% 0.88% 0.10% 0.48% 0.78% 0.51% 0.85% 1.46% 0.00% 0.57% 1.08% 1.46% 0.51% 0.92% 1.29% 2.23% 0.37% 0.95% 1.57% 2.01% 2.33%
R PENELOPE − R MCNPX R MCNPX 2.86% 2.86% 3.52% 2.78% 1.49% 1.88% 2.99% 2.32% 0.88% 2.70% 2.29% 0.40% 1.65% 3.01% 1.42% 1.58% 0.00% 3.68% 1.91% 0.83% 0.98% 3.90% 2.12% 1.68% 0.12% 0.48%
Table III. S-values for Intracellular Sr-90 for the N←CS configuration: Comparison of PENELOPE with MCNPX results. S (N←CS)(Gy/Bq.s) R PENELOPE − R MCNPX e= R MCNPX RC (micrometers) RN (micrometers) MCNPX PENELOPE 3 4 4 5 5 5 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10
2 3 2 4 3 2 5 4 3 6 5 4 3 7 6 5 4 8 7 6 5 9 8 7 6 5
4.62E-04 2.87E-04 2.61E-04 2.22E-04 2.17E-04 1.93E-04 1.58E-04 1.45E-04 1.41E-04 1.19E-04 1.11E-04 1.03E-04 9.91E-05 8.58E-05 8.64E-05 8.17E-05 7.89E-05 6.88E-05 6.42E-05 6.57E-05 6.43E-05 5.71E-05 5.36E-05 4.82E-05 4.86E-05 4.65E-05
4.56E-04 2.83E-04 2.64E-04 2.15E-04 2.07E-04 1.90E-04 1.53E-04 1.42E-04 1.36E-04 1.15E-04 1.07E-04 1.02E-04 9.90E-05 8.93E-05 8.32E-05 7.94E-05 7.68E-05 6.68E-05 6.27E-05 6.36E-05 6.15E-05 5.49E-05 5.16E-05 5.00E-05 4.78E-05 4.65E-05
e: the relative difference of PENELOPE results (RPENELOPE) with MCNPX results (RMCNPX).
1.24% 1.43% 0.98% 3.14% 4.45% 1.58% 2.61% 1.73% 3.33% 3.09% 3.44% 0.95% 0.07% 4.14% 3.68% 2.85% 2.62% 2.87% 2.26% 3.30% 4.45% 3.73% 3.81% 3.73% 1.72% 0.01%
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Cellular dosimetry calculations for Strontium-90 957
Figure 4. 2D dose map visualized with GNUPLOT. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
The relative deviation e is defined as: R − RREF e = PENELOPE RREF i.e., the relative difference of our results with respect to the data taken as reference. RPENELOPE are the results calculated with PENELOPE MC code and RREF are the reference data (MIRD values or MCNPX results). The calculations results showed that the relative deviations are less than 2.5% (2.26%) for N←N, less than
4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations.
Dose distribution to bone marrow cells The dose distribution to mouse bone marrow cells is shown in Figures 4 and 5. Assumption was applied in localizing of Sr-90 source in the cortical bone area, in the adjacent marrow cavity. Figures 4 and 5 show that the dose is close to zero after 150 mm.
Figure 5. Dose distribution to bone marrow cells. This Figure is reproduced in color in the online version of International Journal of Radiation Biology
958 N. Hocine et al.
Discussion
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Comparison between PENELOPE, MCNPX calculations and MIRD values The PENELOPE calculations were compared to MCNPX results obtained by Hocine et al. (2014) and to values tabulated by the MIRD Committee (Goddu et al. 1997). The comparison of PENELOPE results (RPENELOPE) in the case of uniform volume distribution of Sr-90 source with MCNPX and those tabulated by the MIRD Committee (Goddu et al. 1997) showed that the maximum relative deviations are less than 4.5% (4.45%). A very good agreement was found between the S-values calculated with PENELOPE and the MIRD values since the maximum relative deviation e between these two data sets is less than 2.5%; the relative deviations are less than 1.5% (1.48%) for N←N and less than 2.5% (2.4%) for N←Cy configurations. The comparison between PENELOPE and MCNPX calculations results agreed very well since the relative deviations are less than 2.5% (2.26%) for N←N, less than 4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations. The PENELOPE calculated values are above those tabulated by the MIRD Committee, especially for the N←N configuration (when the 90Sr source is localized in the nucleus). It was observed that S-values decrease with increasing target sphere size. We generally find the largest relative deviations with MIRD where the target is at some distance from the source. This can be caused by the electron penetration capability which decreases with increasing sphere size. The overall uncertainty of the MC calculations is difficult to estimate since it includes uncertainties in cross section. The standard statistical uncertainty in the calculations is less than 2%. However, for the MIRD values the standard deviation associated with the cellular S-value was not evaluated. Assuming that the punctual Sr-90 source is localized within the cortical bone part, the dose distribution to bone marrow cells was assessed and shown in Figures 4 and 5. The present study shows that the dose strongly decreases by increasing the distance from the Sr-90 source and the BM cells localized near the cortical bone which received the maximum dose. Boivin (2010) showed that the Strontium was localized mainly in bone tissue recently formed in both cancellous and cortical bone. The dose distribution to mouse BM cells is an approach which can be of considerable interest for providing reliable radiation dose calculations with PENELOPE, involving radiation transport through materials other than water, or for complex distributions of radionuclides and geometries. It can therefore probably be used in therapy procedures with internal emitters to aid in optimizing individual patient therapy.
Conclusions The comparison of PENELOPE calculations results with those tabulated by the MIRD Committee showed that the
relative deviations are less than 1.5% (1.48%) for N←N and less than 2.5% (2.4%) for N←Cy configurations. A good agreement was found between the S-values calculated with PENELOPE and MCNPX since the relative deviations are less than 2.5% (2.26%) for N←N, less than 4% (3.9%) for N←Cy and less than 4.5% (4.45) for N←CS configurations. The assessment of dose distribution to bone marrow cells from punctual Sr-90 source localized within the cortical bone part showed that the dose strongly decreases by increasing the distance from the source; in addition the BM cells localized near the cortical bone received the maximum dose, whereas this dose is close to zero after 150 mm. This study revealed that PENELOPE MC code is a useful tool to assess cellular dosimetry involving radiation transport through materials other than water or to simulate more complex and realistic geometries.
Declaration of interest The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.
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