Small scale dosimetry for 211 At distribution in thyroid and liver models using AlfaMC Monte Carlo simulations

Transcription

1 Small scale dosimetry for 211 At distribution in thyroid and liver models using AlfaMC Monte Carlo simulations M.Sc. Thesis Author: Arman Romiani Supervisors: Eva Forssell-Aronsson and Roumiana Chakarova Department of Radiation Physics University of Gothenburg Gothenburg, Sweden

2 Table of contents Abstract... 2 Acknowledgements Introduction Microdosimetry Monte Carlo technique Aims... 8 Part I. Thyroid-gland follicle model...8 Part II. Liver model...8 Part I. Thyroid-gland follicle model 3. Methods Geometries Sources Monte Carlo technique Calculations Results Discussion Part II. Liver model 6. Methods Geometry Sources Monte Carlo technique Calculations Results Discussion Conclusions: Part I and II References

3 Abstract Radionuclide therapy is increasing for therapy of cancer, and 211 At is a radionuclide of interest for future applications. It is known that 211 At can accumulate in the thyroid gland as well as in other risk organs such as liver. The work was divided in two parts. The aims of part one was to determine microdosimetric quantities for homogeneous and heterogeneous 211 At distributions within different thyroid models using Monte Carlo code AlfaMC and compare the results with previously published results from similar studies using Monte Carlo code MCNPX. The second part of the work consisted of the development of a new liver model and of performing dosimetric calculations for 211 At distributed in various source regions in the model. The Monte Carlo program AlfaMC was used in these simulations. Both a single and multiple thyroid follicle model was designed for man, rat and mouse based on previously published studies. The simulation and dose-calculation was done for different locations and distributions of the source. The mean specific energy and single-hit mean specific energy was calculated for follicle cell nuclei in models for each species. The overall agreement between AlfaMC results and MCNPX was found to be within 6% which can be considered as very good. The new human liver model was developed based on data from histology books and published articles with description of dimensions of the structures in the liver. The simulations were done with different source locations: 211 At distributed inside the central vein, in the two portal artery/venule regions, the distributing venule, the hepatocytes and the sinusoids (including Kupffer cells). Hepatocytes and Kupffer cells were targets for all simulations. The dose contribution for each source location together with the summation of all source locations was illustrated with heat-maps for respective target. 2

4 Acknowledgements I want to express my gratitude to my supervisors, Eva Forssell-Aronsson and Roumiana Chakarova, for your help and fruitful ideas that made this thesis possible. Many thanks to Anders Josefsson, whose work has been the basis for the validation of my results. Luis Peralta is acknowledged for making AlfaMC-code available and his startup support. Many thanks to my family for their endless support, love and food supply. And finally thanks to my beloved Sofia for your support and encouraging mood. 3

5 1. Introduction Radionuclide therapy, using radionuclides either in free form (usually as ions) or attached to tumor targeting carriers, is an increasing method well suited for therapy of metastatic tumor diseases. The requirement of such therapy is that the absorbed dose in tumor tissue is high enough compared with that in normal tissues. Free radionuclides can be used if the distribution is with high accumulation in the tumor tissue. This is the case for radioiodine and thyroid cancer, where 131 I is used for therapy. Certain types of tumors have an overexpression of antigens or receptors on their cell surface, which motivates creating carriers for these types. Such carriers labeled with suitable radionuclides are used for therapy. Some examples are 131 I-MIBG and 177 Lu-octreotate, which are used for treatment of certain neuroendocrine tumor types, such as pheocromocytomas, paraganliomas, carcinoids and endocrine pancreatic cancer. Depending on the decay scheme of the radionuclide different types of radiation can be emitted. The physical properties of the radionuclide necessary for treatment are a suitable half-life (it is not desirable that the majority of the radionuclide has decayed before being absorbed in the region of interest and a half-life too long would lead to a low dose rate) and high energy deposition locally (high amount of particle emission in relation to photon emission). 211 At is an alpha emitter with suitable attributes for radionuclide therapy, and the two main energies for the emitted alpha particle are MeV and MeV. Because of the short range of alpha particles (48-70 µm in water) and high linear energy transfer (~100 kev/µm) [1], the frequency of DNA double strand breaks is higher than that caused by electrons or photons. Due to the more complex DNA damage cell death will probably occur more frequently. These mentioned attributes make 211 At interesting in the choice of radionuclide and in the treatment process to eradicate small tumors. 211 At is proposed to be administered to patients both as a free radionuclide and attached to carriers. Regardless of the therapy method it is necessary to estimate the biodistribution of free 211 At. The bond between 211 At and the carrier molecule can break after administration. Also personnel (handling) 211 At are exposed to a risk of internal contamination. Hence the knowledge of 211 At biodistribution is required for estimating the absorbed dose to normal tissue and potential risk organs. Astatine is a halogen and has therefore chemical resemblances with iodine. Studies on mice and rats have shown that 211 At is accumulated in the thyroid gland [2-3]. The thyroid gland is therefore considered to be one of the vital risk organs in case of internal contamination of free 211 At. The studies also showed increased uptake in other organs such as liver, lungs, stomach and spleen. 4

6 211 At has a half-life of 7.2 h and emits alpha particles through two possible decay pathways to stable 207 Pb (Figure 1). X-rays with energies up to 92 kev are also emitted during the decay process (Table 1), allowing external quantification of the radionuclide distribution. Figure 1. The decay chain for 211 At. The half-life is presented below respectively nuclide. The main energy of respectively alpha particle is presented for the possible alpha decays. Table 1. Nuclear decay data consisting of the energies (E) and respective yield (Y) for alpha particle (α), gamma- (γ) and X-rays (X) from 211 At and 211 Po [4]. Radionuclide E α (kev) Y α (%) E γ (kev) Y γ (%) E X (kev) Y X (%) 211 At Po

7 1.1 Microdosimetry The short range of alpha particles in combination with its high LET results in a large statistical variation of the energy deposition in different cells. Therefore, it may be inappropriate to use the mean absorbed dose to the tumor or organs at risk to estimate the biological effects. Taking into account that alpha particles have a higher biological effectiveness than electrons or photons, due to high LET [5], the need to use a more accurate dosimetric method increases further. Microdosimetry takes the stochastic nature of the energy deposit into account and is therefore appropriate to apply to alpha particle irradiation. In this work several microdosimetric quantities will be used as presented below. A more detailed description of the quantities can be found in the ICRU report 36 [6]. Energy deposit, ε i, is the elementary quantity and is needed in order to express the other quantities. ε i can be described as the energy deposited in a single interaction, i: ε i = T in T out + Q Δm, where T in is the energy of the incident ionizing particle, T out is the sum of all particles energy leaving the interaction and Q Δm is the changes of the rest mass of the atom and all particles involved in the interaction [6]. The energy imparted, ε, is defined as the summation of all ε i in a certain volume. ε = ε i The unit of ε i and ε is joule [J], but they may also be expressed in the unit electron volt [ev]. The specific energy, z, is expressed as ε divided by the mass of the volume, m. The unit of z is [J/kg] or [Gy] i z = ε m. Compared with the three mentioned stochastic quantities above the mean specific energy, < z >, and the single-hit mean specific energy per event, < z 1 >, are non-stochastic quantities. < z > is defined as z = zf(z) dz, 0 where f(z), is the probability density and expresses the probability for a specific energy deposition to occur. f(z) also includes the probability of z = 0 (i.e. the probability of no energy deposition in the volume). < z 1 > is defined similar to z but has a probability density, f(z 1 ), that does not include z = 0, i.e. includes only particles that deposit energy in the target. 6

8 1.2 Monte Carlo technique There are different methods for calculating dosimetrical quantities. One of these methods uses scaled point kernels, to describe the isotropic energy deposition from a point source. It randomizes the location of the point source, within the source region, and the direction of the vector, which describes the energy deposition [12]. In this way scaled point kernels can be used to calculate dosimetrical quantities, but the method is better suited for calculations at more macroscopic levels. It is possible to develop a simplified Monte Carlo (MC) application by making certain assumptions about the alpha particle transportation. By neglecting both energy- and angular straggling and therefore considering the pathway of the alpha particle to be a straight line it is possible to determine the energy deposition by range-energy tables [7]. The energy difference of the alpha particle, before and after traversing e.g. a cell, corresponds to the deposited energy in that cell. Such calculations can be made on a spreadsheet and do not require a certain MC program [7]. MC technique is a useful statistical method for dosimetric calculations. By generating random numbers to simulate the stochastic process and using probability density functions to describe the possibility of each interaction process the MC method is well suited to master the stochastic nature of the radiation transport. Hence the MC method can be applied for all types of ionizing radiation. Today there are a number of different MC codes that can be used for various dosimetric calculations. MCNPX (Monte Carlo N-Particle extended) was developed at the Los Alamos National Laboratory and can simulate the transport of 34 different types of particles [8].The National Research Council in Ottawa has developed the MC code EGSnrc (Electron Gamma Shower), which simulates the transport of photons and electrons for energies between a few kev to TeV [9].The Conseil Européen pour la Recherche Nucléaire (CERN) developed their MC code GEANT4 (GEometry ANd Tracking), which is a platform that describes the radiation transport of charged particles and photons through matter [10]. Of these MC codes MCNPX and GEANT4 can be used to simulate the radiation transport of alpha particles. AlfaMC is a relatively new MC code that was introduced in 2012 by Luis Peralta and Alina Louro at the Science faculty of the University of Lisbon [11].AlfaMC has a powerful geometrical software package based on combinatorial geometry that allows the user to create complex models. Comparison with other MC codes has shown good agreement for alpha particles with energies between 1 MeV and 12 MeV [11]. Previous small scale dosimetric studies of 211 At in thyroid follicle models Thyroid models for mouse, rat and man have been developed previously and applied for dosimetric analysis of 211 At [13]. These studies examined how different factors such as the distribution of 211 At and the geometrical dimensions of respective model affect microdosimetric quantities, using MCNPX. 7

9 2. AIMS The aims of this work were to: determine microdosimetric quantities for homogeneous and heterogeneous 211 Atdistributions within different thyroid gland and follicle models by using AlfaMC,- compare the results from AlfaMC with previously published results from MCNPX for the same modelds, develop a detailed liver model, and determine microdosimetric quantities for homogenous and heterogeneous 211 Atdistributions within the model using AlfaMC. This work is divided into two parts: the thyroid study (part I) and the liver study (part II). 8

10 3. Methods - Part I. Thyroid gland-follicle models 3.1 Geometries A previously published single thyroid follicle model, for man, rat and mouse were used [13]. The model represents a single sphere-shaped thyroid follicle and consists of a spherical follicle lumen, a layer of follicle cells (shaped as a shell around the follicle lumen) and six spherical follicle cell nuclei distributed symmetrically at equal distances from the center of the follicle lumen (Figure 2). Each component has the density as liquid water (1.0 g/cm 3 ). The diameter of the follicle lumen, thickness of the follicle cell layer and the diameter of the follicle cell nucleus were 150, 10, 8 µm; 70, 8, 6 µm; 50, 6, 4 µm for man, rat and mouse, respectively. Figure 2. Schematic figure over the single thyroid follicle model [13]. The follicle cells, the follicle lumen and the follicle cell nucleus are shown in green, blue and red, respectively. A multiple thyroid follicle model for respective species, was also used, based on the previously published work [13]. The model represents a simplification of the case where the thyroid follicle was surrounded by neighboring follicles (Figure 3a). The follicle cells from the neighboring cells formed both a spherical shell around the follicle cells in the center follicle and around their merged lumens (Figure 3b). Figure 3. Schematic figure over seven adjacent thyroid follicles (a) and the simplified multiple thyroid follicle model [13] (b). The follicle cells, the follicle lumen and the follicle cell nuclei are green, blue and red respectively. The light green and blue color represents the neighboring follicles. The model was applied by combining basic volumes available in the geometric package of AlfaMC. The organization of the volumes uses a mother-daughter system, which allows the user to create volumes inside each other. For example, the follicle cell nuclei were daughters of the follicle cells in 9

11 figure 2. To ensure that the geometry of the model was correct a tool component, SHOWTRACK, was used. The source distribution was also examined using SHOWTRACK. Figure 4. SHOWTRACK displaying a 2D image over the single thyroid follicle model. The blue lines represent the pathway of 50 alpha particles, and in this case their pathways were not simulated outside the model. The projected plane is XZ at y=0, hence the lengths of the blue lines differ. 3.2 Sources Only the two main energies for the emitted alpha particle, MeV and MeV with a yield of 41.8% respectively 58.2% (total yield per 211 At disintegration), were considered to contribute to the deposited energy in the present work. Isotropic emission of the alpha particles was assumed. Four different 211 At distributions were used for simulations: 1) 211 At homogeneously distributed within the follicle lumen, 2) 211 At homogeneously distributed within the follicle cells, 3) 211 At homogeneously distributed within the follicle cell nuclei and 4) 211 At uniformly distributed on the surface of concentric spheres, with their center located at the center of the follicle lumen. The radius of the spheres varied from 0 µm to 150 µm with 5 µm intervals, hence spheres were both within the follicle lumen and in some cases outside the layer of follicle cells. This simulation represented the heterogeneous distribution of 211 At. In all simulations the targets were the six follicle cell nuclei. 3.3 Monte Carlo technique The Monte Carlo code used for all simulations was AlfaMC [11] on Ubuntu LTS, with processor Intel Core i and 3.40GHz 8, OS type 64-bit. The code is based on the Continuous Slowing Down Approximation (CSDA) in consideration of energy- and angular straggling and uses the stopping-power values from NIST/ASTAR database. The code is customized for calculating microdosimetric quantities and is focused on reducing the calculation time. The energy straggling function selected for each simulation was based on a Gaussian/Vavilov/Landau model that was available in AlfaMC. For each simulation 10 7 alpha particles were simulated and their cut-off energy was set to 1 kev. Part I Thyroid models 10

12 3.4 Calculations The code in AlfaMC was programmed so that the energy imparted, expressed in MeV, in each follicle cell nucleus was multiplied by the conversion factor and divided by the mass, expressed in kg, of the nucleus yielding the specific energy, ε m = z, [Gy], where is the conversion factor with the units J/MeV. The sum of the specific energy in each target was either divided by the total number of simulated alpha particles (N) in order to calculate the mean specific energy, N z = 1 N z i i=1, [Gy], or divided by the number of alpha particles that have hit the target (M) to calculate the single-hit mean specific energy, M z 1 = 1 M z i i=1, [Gy]. One simulation returned six output values, due to the chosen six follicle cell nuclei targets, of z and z 1 directly expressed in Gy. Each simulation, except the case where 211 At was uniformly distributed on the surface of concentric spheres, was made twice with different random seeds to retain twelve output values hence increasing the statistical accuracy. The output values were used to calculate a mean standard deviation for respective parameter. The frequency histograms in AlfaMC were used for describing the single-hit mean specific energy distribution. Data of the distribution was obtained by scoring the number of events per bin, the bin size was 20 mgy for all histograms. Part I Thyroid models 11

13 4. Results - Part I. Thyroid models Single thyroid follicle models Tables 2-4 show the mean values of the mean specific energy, z, and the single-hit mean specific energy, z 1, simulated with AlfaMC and MCNPX [13] for the single thyroid model for mouse, rat and human depending on the location of the source. When the source and target was identical z and z 1 was identical (Table 2). In Table 4 there is also data presented from a simulation made with GEANT4 [23]. The results of each code were compared with one another and were presented as the percentage difference between them. Table 2. The mean specific energy, z, and the single-hit mean specific energy, z 1, for single thyroid follicle models of mouse, rat and man with the six nuclei both as sources and targets determined by AlfaMC and MCNPX [13]. Data is given as mean (SD). The percentage difference between the results from AlfaMC and MCNPX is also given. Note that z and z 1 were equal since the source and target was identical. Nucleus Nucleus AlfaMC MCNPX [13] AlfaMC-MCNPX z and z 1 [Gy] z and z 1 [Gy] z and z 1 [%] Mouse 5.20E E (2.75E-4) (1.13E-4) Rat 2.32E E (1.02E-4) (5.07E-5) Man 1.30E E (1.06E-4) (2.86E-5) Table 3. The mean specific energy, z, and the single-hit mean specific energy, z 1, for single thyroid follicle models of mouse, rat and man with the follicle cells as the source location and the six nuclei as targets determined by AlfaMC and MCNPX [13]. Data is given as mean (SD). The percentage difference between the results from AlfaMC and MCNPX is also given. Nucleus Follicle cells AlfaMC MCNPX [13] AlfaMC-MCNPX z [Gy] z 1 [Gy] z [Gy] z 1 [Gy] z [%] z 1 [%] Mouse 2.63E E E E (4.73E-6) (2.87E-3) (1.91E-5) (3.48E-3) Rat 1.36E E E E (8.14E-6) (1.87E-3) (9.38E-6) (1.61E-3) Man 3.07E E E E (6.04E-6) (1.31E-3) (3.36E-6) (1.42E-3) Part I Thyroid models 12

14 Probability density f(z 1 ) [1/Gy] Table 4. The mean specific energy, z, and the single-hit mean specific energy, z 1, for single thyroid follicle models of mouse, rat and man with the follicle lumen as the source location and the six nuclei as targets determined by AlfaMC, MCNPX [13] and GEANT4 [23]. Data is given as mean (SD). The percentage difference between the results from AlfaMC, MCNPX and GEANT4 is given below. Nucleus Lumen AlfaMC MCNPX [13] GEANT4 [23] z [Gy] z 1 [Gy]] z [Gy] z 1 [Gy] z [Gy] z 1 [Gy] Mouse 1.95E E0 2.03E E0 1.94E E0 (3.34E-6) (4.93E-3) (1.76E-5) (4.67E-3) (9.78E-6) (2.16E-3) Rat 1.04E E E E E E-1 (5.28E-6) (2.27E-3) (9.12E-6) (2.33E-3) (5.10E-6) (9.16E-4) Man 1.68E E E E E E-1 (3.79E-6) (2.97E-3) (2.83E-6) (2.79E-3) (2.78E-6) (7.94E-4) AlfaMC-MCNPX AlfaMC-GEANT4 GEANT4-MCNPX z [%] z 1 [%] z [%] z 1 [%] z [%] z 1 [%] Mouse Rat Man Figures 5-7 show the distribution of the single-hit specific energy for the three source locations and respective species model simulated with AlfaMC and MCNPX [13]. The curves simulated with AlfaMC were normalized, so that the area under each curve is equal to 1. The bin size was 20 mgy for all simulations. 5,0 4,5 4,0 3,5 3,0 2,5 2,0 1,5 1,0 0,5 AlfaMC MCNPX 0,0 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 2,0 Specific energy, z 1 [Gy] Figure 5. Single-hit mean specific energy distribution, f(z 1), in single thyroid follicle models of mouse, rat and man with the nuclei as the source locations simulated with AlfaMC and MCNPX [13]. 211 At was homogenously distributed within the nuclei. Both the single-hit mean specific energy- and the mean specific energy distribution can be observed hence they are equal when the sources and targets are the same. The bin size was 20 mgy for both graphs. The curves simulated with AlfaMC were normalized so that the area under each curve is equal to 1. Due to different normalizations the scales on y-axes differ. Part I Thyroid models 13

15 Probability density f(z 1 ) [1/Gy] Probability density f(z 1 ) [1/Gy] 3,0 2,5 AlfaMC MCNPX 2,0 1,5 1,0 0,5 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 Specific energy, z 1 [Gy] Figure 6. Single-hit mean specific energy distribution, f(z 1), in single thyroid follicle models of mouse, rat and man with the follicle cells as the source location simulated with AlfaMC and MCNPX [13]. 211 At was homogenously distributed within the follicle cells. Targets were the six follicle cell nuclei. The bin size was 20 mgy for both graphs. The curves simulated with AlfaMC were normalized so that the area under each curve is equal to 1. Due to different normalizations the scales on y-axes differ. 3,0 2,5 AlfaMC MCNPX 2,0 1,5 1,0 0,5 0,0 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 Spcecific energy, z 1 [Gy] Figure 7. Single-hit mean specific energy distribution, f(z 1), in single thyroid follicle models of mouse, rat and man with the follicle lumen as the source location simulated with AlfaMC and MCNPX [13]. 211 At was homogenously distributed within the follicle lumen. Targets were the six follicle cell nuclei. The bin size was 20 mgy for both graphs. The curves simulated with AlfaMC were normalized so that the area under each curve is equal to 1. Due to different normalizations the scales on y-axes differ. Part I Thyroid models 14

16 Single-hit mean specific energy per decay [mgy] Single-hit mean specific energy per decay [mgy] The results from the heterogeneous distribution of 211 At, where 211 At was uniformly distributed on the surface of concentric spheres fixed at the center of the follicle lumen, simulated with AlfaMC are presented in figure 8a. The six follicle cell nuclei were the targets. The single-hit mean specific energy per decay is plotted as the function of the radius of the spheres, which increased with 5 µm intervals until the layer of follicle cells were reached for respective species. Figure 8b shows corresponding results from simulations performed by MCNPX [13]. a) b) At distributed on the surface of concentric spheres simulated with AlfaMC Surface source radius, r, [μm] Mouse model Rat model Human model 211 At distributed on the surface of concentric spheres simulated with MCNPX Mouse model Rat model Human model Surface source radius,r, [μm] Figure 8. Single-hit mean specific energy per decay simulated with a) AlfaMC and b) MCNPX [13] for 211 At uniformly distributed on the surface of concentric spheres and the six nuclei as the targets. The radius of the spheres varied from 0 µm with 5 µm intervals until the layer of follicle cells was reached for respectively species. The standard deviation is calculated for each measurement and presented as error bars, but due to their low values they are visible. Part I Thyroid models 15

17 Single-hit mean specific energy [Gy] z 1 (AlfaMC)/z 1 (MCNPX) Figure 9 shows the comparison between the results from AlfaMC and MCNPX, figure 6, for 211 At distributed on the surface of concentric spheres. 2,5 2 1,5 1 0,5 0 Comparing data from AlfaMC and MCNPX Surface source radius, r, (μm) Mouse model Rat model Human model Figure 9. The ratio between single-hit mean specific energy from simulations made with AlfaMC and MCNPX [13] for 211 At uniformly distributed on the surface of concentric spheres with the six nuclei as the targets. The radius of the spheres varied from 0 µm with 5 µm intervals until the layer of follicle cells was reached for respective species. Multiple thyroid follicle models Figures show single-hit mean specific energy and the mean specific energy for 211 At located in the lumens of the multiple thyroid follicle models. The radius of the spheres varied from 0 µm to 150 µm with 5 µm intervals, hence spheres were both within the follicle lumen and in some cases outside the layer of follicle cells. In all simulations the targets were the six follicle cell nuclei in the central follicle. Each figure shows data from simulations with AlfaMC and MCNPX [13] presented with blue and white dots, respectively. 0,6 211 At - Human model 0,5 0,4 0,3 0,2 0,1 0, Surface source radius [µm] Figure 10. The single-hit mean specific energy as function of the surface source radius for the human model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the basal layer of follicle cells was reached at 75 µm and continued from the apical layer at 95 µm to 150 µm, these layers are represented by the dotted lines. The standard deviation for each measurement is presented as error bars, but due to their low values they are not visible for all measurements. Thedotted lines represent the apical and basal follicle cell surfaces Part I Thyroid models 16

18 Single-hit mean specific energy [Gy] Mean specific energy [Gy] 4E At - Human model 3E-4 2E-4 1E-4 0E Surface source radius [um] Figure 11. The mean specific energy as function of the surface source radius for the human model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the basal layer of follicle cells was reached at 75 µm and continued from the apical layer at 95 µm to 150 µm, these layers are represented by the dotted lines. The standard deviation is calculated for each measurement and is presented as error bars, due to their low value are they not visible for all data points. 1,0 211 At - Rat model 0,5 0, Surface source radius [µm] Figure 12. The single-hit mean specific energy as function of the surface source radius for the rat model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the basal layer of follicle cells was reached at 35 µm and continued from the apical layer at 55 µm to 110 µm, these layers are represented by the dotted lines. The standard deviation is calculated for each measurement and is presented as error bars, due to their low value are they not visible for all data points. Part I Thyroid models 17

19 Single-hit mean specific energy [Gy] Mean specific energy [Gy] 2E At - Rat model 1E-3 0E Surface source radius [µm] Figure 13. The mean specific energy as function of the surface source radius for the rat model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the first layer of follicle cells was reached at 35 µm and continued from the second layer of follicle cells at 55 µm to 110 µm, these layers are represented by the dotted lines. The standard deviation is calculated for each measurement and is presented as error bars, due to their low value are they not visible for all data points. 2,5 211 At - Mouse model 2,0 1,5 1,0 0,5 0, Surface source radius [µm] Figure 14. The single-hit mean specific energy as function of the surface source radius for the mouse model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the first layer of follicle cells was reached at 25 µm and continued from the second layer of follicle cells at 40 µm to 85 µm, these layers are represented by the dotted lines. The standard deviation is calculated for each measurement and is presented as error bars, due to their low value are they not visible for all data points. Part I Thyroid models 18

20 Mean specific energy [Gy] 3E At - Mouse model 2E-3 1E-3 0E Surface source radius [µm] Figure 15. The mean specific energy as function of the surface source radius for the mouse model, simulated with AlfaMC and MCNPX [13]. Data from AlfaMC is presented in the left graph and data from MCNPX in the right graph. 211 At was uniformly distributed on the surface of the concentric spheres and the six nuclei were the targets. The radius of the spheres increased with 5 µm until the first layer of follicle cells was reached at 25 µm and continued from the second layer of follicle cells at 40 µm to 85 µm, these layers are represented by the dotted lines. The standard deviation is calculated for each measurement and is presented as error bars, due to their low value are they not visible for all data points. Part I Thyroid models 19

21 5. Discussion Part I. Thyroid models The mean specific energy, z, and the single-hit mean specific energy, z 1, were determined for homogenous and heterogeneous 211 At-distributions within the thyroid model for mouse, rat and human using AlfaMC. For the homogenous distribution of 211 At a good agreement was observed between results simulated with AlfaMC and previously published results from similar studies using MCNPX [13]. AlfaMC returned a lower value of z and z 1 in comparison with MCNPX in each case for respectively species (tables 2-4). The difference between the results from AlfaMC and MCNPX for mouse, rat and human varied from 1.7 to 4.6 %. The results from AlfaMC showed better agreement with results from GEANT4 (presented in Table 4) and the percentage difference for respective species varied from 0 to 1.7 %. Also in this comparison a trend could be seen that AlfaMC returned lower z and z 1 values, but not for all cases. The single-hit mean specific energy distribution, f(z 1), for respective species and source location, simulated with AlfaMC showed resemblances with f(z 1) simulated with MCNPX (figures 5-7). The maximum and the minimum of the probability density functions occurred at approximately the same specific energy for respective species and source location in both graphs. The ratio between z 1 simulated with AlfaMC and MCNPX for respective species, in the cases where 211 At was uniformly distributed on concentric spheres (to represent a heterogeneous distribution in the follicle lumens), varied from 0.93 to 1.0 for the majority of the data points (Figure 9). Also in this case AlfaMC underestimated the z 1 compared with MCNPX. However, for the human model two data points with values of 2.2 and 1.2 differed in comparison with the rest. The reason for this difference between the codes is due to the uncertainties at the Bragg-peak-tail for each code. The distance between the source location and the center of the targets were 70 and 65 µm for respectively measuring point, which is approximately the maximum range of the emitted 7.45 MeV alpha particles. The other results from the heterogeneous distribution shows good resemblances with MCNPX [13] for both z and z 1. Similarities in the shape of the curves were observed for respective species (Figures 10-15). The differences between the results from AlfaMC, MCNPX and GEANT4 are partly due to their different ways of describing the transport and the energy deposition of the alpha particles. One factor is the difference in stopping-power values in different databases. The ASTAR database, on which AlfaMC is based, is part of NIST Standard Reference Database including stopping-power and range tables for various particles calculated according to methods described in ICRU Reports 37 and 49 [14]. ASTAR has stated the uncertainties in collision stopping power for high energies (>2 MeV) of the alpha particle to be 1-4 %. For energies below 100 kev, which is in the energy region of the Bragg-peak tail, the uncertainties exceed 10%. Hence small difference in the Bragg-peak tail leads to fluctuations in the energy deposition. Approximations in the evaluation of cross sections for elastic scattering cause uncertainties also in the nuclear stopping power data. MCNPX and GEANT4 include several physics models (e.g. intra nuclear cascade physics, multiple Coulomb scattering, etc.) using tabulated or modeled cross sections. GEANT4 results presented here were obtained by using the Low energy electromagnetic Part I Thyroid models 20

22 physics package, where excitation and charge increase/decrease processes are not taken into account. In general, none of the models is free from uncertainties and assumptions to be considered as the most correct one. Another factor that could influence the result is the voxel size of the phantom, which has been shown to affect the microdosimetric results of MCNPX and GEANT4 [13]. This shows that even if the physics models and processes are the same, the way of application of the codes may give deviating results. Altogether, the dosimetric results from the AlfaMC and MCNPX codes agreed within 6%, which validates the accuracy of the AlfaMC code for microdosimetric calculations performed on the level of this study. The overall agreement between AlfaMC and MCNPX results was considered as very good. Part I Thyroid models 21

23 6. Methods - Part II. Liver model 6.1 Geometry The human liver consists of hexagon-shaped hepatic lobules arranged tightly next to each other like the structure of a honeycomb. Each hepatic lobule has a hepatic triad located at each corner of the lobule and consists of the portal artery, portal venule and the branch of bile duct (figure 16). Both the venous and the arterial blood run through the sinusoids to the central vein. There is also distributing venules (demonstrated with the minor blue lines in Figure 16) that lead the venous blood between each portal venule. Figure 16. Schematic figures that demonstrates the microstructure of the human liver [14]. Based on this description, a new liver model was developed. Its small scaled dimensions were based on data from a number of histology books and various published articles involving the dimensions of the structures in the liver [17-22]. The proposed dimensions for the hepatic lobule and its various components are presented in table 5, the first column from the right contains the selected dimensions for the liver model. Table 5. Various proposed dimensions, all presented as the maximum diameter in µm, for the different liver components in human. The dimensions applied for our liver model is presented in first column from the right. a) Basic Histology 9th ed. [15]. b) A small scale-scale anatomical dosimetry model of the liver. Stenvall.A.2014 [18]. c) Hepatic Structural Dosimetry in 90-Y Microspheres Treatment. Gulec. Seza A.2010 [19] d) A multi-scale modeling framework for individualized. Juan G.2013 [20]. e) Simulating Microdosimetry in a Virtual Hepatic Lobule. Wambaugh.J.2010 [21]. f) MacSween's Pathology of the Liver [22]. Liver components Diameter [µm] Our liver model [µm] Hepatic lobule 700 a 1000 b 1200 c 1000 d 3000 e 700 Portal artery/ venule 10/30 b 30/36 c 10/30 Sinusoid 7 b 10 d 25 e 4-15 f 10 Hepatocytes a 66 b 23 d 100 e f 30 Kupffer cells a 16 b 30 Central vein 70 b 56 c 70 Part II Liver model 22

24 One layer of the hepatic lobule was simulated with a thickness of 30 µm corresponding to the diameter of the hepatocytes and the Kupffer cells. The layer consisted of one part of the hepatic lobule that had been rotated 60, 300 and also flipped 180 degrees (see figure 19), to simulate the dose contribution from all possible directions in the hepatic lobule. The shape of the Hepatocytes and the Kupffer cells were boxes with dimensions 30x30x30 µm 3 and 10x30x30 µm 3 respectively. The Kupffer cells were simulated inside each sinusoid of the model (light blue colored in figure 17). The central vein (C.V in figure 17) was simulated as a cylinder with a radius and height of 35 µm and 30 µm respectively. The portal artery and the portal venule in respectively corner of the hepatic lobule were merged together and a cylinder with a radius and height of 18 µm and 30 µm respectively was simulated to replace them both (P in figure 17). Between the two cylinders the distributing venule (dark blue colored in figure 17) was simulated as a cylinder, rotated in relation to the other cylinders, with the radius and height of 5 µm and 350 µm, respectively. Figure 17. A 2D schematic figure illustrating the simulated liver model. The central vein (C.V) was simulated as a cylinders with a radius and height of 35 µm and 30 µm, respectively. The portal artery and portal venule, in each corner of the hepatic lobule, were merged together and replaced by a cylinder (P). The cylinders had the radius and height of 18 µm and 30 µm, respectively. The distributing venule, colored dark blue, was simulated as a rotated cylinder with the radius and height of 5 µm and 350 µm, respectively. The light blue colored areas represent the sinusoids and has the same dimensions as the Kupffer cells, hence they are placed inside the sinusoids, 10x30x30 µm 3. The hepatocytes (H) are simulated as boxes with dimensions 30x30x30 µm 3. To ensure that the geometry of the model was correct SHOWTRACK was used (see methods part I). 6.2 Sources Five distributions of 211 At was chosen for simulations. 211 At was homogenously distributed inside the 1) central vein, 2) the two portal arteries/venules (P in Figure 17), 3) the distributing venule, and 4) the hepatocytes in the non-rotated part of the hepatic lobule. For the fifth simulation the 211 At was distributed inside the sinusoids (therefore also in the Kupffer cells) in the non-rotated part of the hepatic lobule, the two minor sinusoids had an activity two times the rest. The targets were the hepatocytes and the Kupffer cells. The geometries used are illustrated in Figure 18. Part II Liver model 23

25 a) b) c) Figure 18. Schematic illustration of the sources (in blue) and targets (in red) that were used for the Monte Carlo simulations. When 211 At was homogenously distributed in the central vein and the portal arteries/venules only the hepatocytes in the non-rotated part of the hepatic lobule were targets (a). When 211 At was homogenously distributed in the distributing venule all hepatocytes except those in the 180 degrees flipped part of the hepatic lobule were targets (b). When 211 At was homogenously distributed in the hepatocytes in the non-rotated hepatic lobule and the distributing sinusoids all hepatocytes were targets (c). Same conditions were applied for the Kupffer celss. 6.3 Monte Carlo technique See Monte Carlo technique in methods part I. 6.4 Calculations For calculating z and z 1 in the hepatocytes and the Kupffer cells the energy imparted was multiplied by the conversion factor and divided by the mass of respectively target (more detailed explanation is found in the Calculations in methods part I). Each simulation returned z and z 1 for all hepatocytes and Kupffer cells in the model. The values of z and z 1 were summed separately for each target and its corresponding position in the rotated parts of the model (illustrated in figure 19) for respective simulation. a) b) Figure 19. Schematic figure of all the targets in the simulations, both the hepatocytes a) and the Kupffer cells b). One randomly selected hepatocyte and Kupffer cell and their corresponding cells in the rotated parts of the model are colored red in both figures. 7. Results - Part II. Liver model The contribution of z and z 1 from each source location to the hepatocytes is presented in separate heat-maps (Figures 20-24). The values of z and z 1 were summed separately for each Part II Liver model 24

26 hepatocyte and its corresponding position in the rotated parts of the model (illustrated in Figure 19) for respective source location. Central vein Hepatocytes z, [mgy] z 1, [mgy] Figure 20. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte as 211 At was homogeneously distributed in the central vein. The central vein was simulated as a cylinder, colored blue in the figure, with the radius and height of 35 µm and 30 µm, respectively, and the hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Portal arteries/venules Hepatocytes z, [mgy] z 1, [mgy] Figure 21. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte when 211 At was homogeneously distributed in the portal arteries/venules. The portal artery/venule was simulated as a cylinder, colored blue in the figure, with the radius and length of 18 µm and 30 µm, respectively, and the hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Part II Liver model 25

27 Distributing venule Hepatocytes z, [mgy] z 1, [mgy] Figure 22. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte when 211 At was homogeneously distributed in the distributing venule. The distributing venule was simulated as a cylinder, colored blue in the figure, with the radius and length of 5 µm and 350 µm, respectively, and the hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Sinusoids (Kupffer cells) Hepatocytes z, [mgy] z 1, [mgy] Figure 23. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte when 211 At was distributed in the sinusoids (Kupffer cells). The sinusoids (Kupffer cells), colored blue in the figure, were simulated with the width and thickness of 10 µm and 30 µm, respectively, and the hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. The two minor sinusoids had an activity two times the rest. Part II Liver model 26

28 Hepatocytes Hepatocytes z, [mgy] z 1, [mgy] Figure 24. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte when 211 At was homogeneously distributed in all hepatocytes. In this case the hepatocytes were both the targets and the sources. The hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. The summation of the contribution from each source location to the hepatocytes is presented in figure 25. Summation of each source location Hepatocytes z, [mgy] z 1, [mgy] Figure 25. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each hepatocyte when 211 At was homogeneously distributed in the central vein, the portal arteries/venules, distributing venule and all hepatocytes. 211 At were also distributed in the sinusoids. The two minor sinusoids had two times higher activity then the rest, when the sinusoids were the sources. The hepatocytes had the dimensions 30x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. The contribution of z and z 1 from each source location to the Kupffer cells is presented in separate heat-maps (Figures 26-30). The values of z and z 1 were summed separately for each Kupffer cell and its corresponding position in the rotated parts of the model (illustrated in Figure 19) for respective source location. Part II Liver model 27

29 Central vein Kupffer cells z, [mgy] z 1, [mgy] Figure 26. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 211 At was homogeneously distributed in the central vein. The central vein was simulated as a cylinder, colored blue in the figure, with the radius and height of 35 µm and 30 µm, respectively, and the Kupffer cells had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Portal artery/venule Kupffer cells z, [mgy] z 1, [mgy] Figure 27. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 11 At was homogeneously distributed in the portal arteries/venules. The portal artery/venule was simulated as a cylinder, colored blue in the figure, with the radius and height of 18 µm and 30 µm, respectively, and the Kupffer cells had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Part II Liver model 28

30 Distributing venule Kupffer cells z, [mgy] z 1, [mgy] Figure 28. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 211 At was homogeneously distributed in the distributing venule. The distributing venule was simulated as a cylinder, colored blue in the figure, with the radius and height of 5 µm and 350 µm, respectively, and the Kupffer cells had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Sinusoids (Kupffer cells) Kupffer cells z, [mgy] z 1, [mgy] Figure 29. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 211 At was distributed in the sinusoids (Kupffer cells). In this case the Kupffer cells were both the targets and the sources. The Kupffer had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. The two minor sinusoids had an activity two times the rest. Part II Liver model 29

31 Hepatocytes Kupffer cells z, [mgy] z 1, [mgy] Figure 30. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 211 At was homogeneously distributed in the hepatocytes. The Kupffer cell had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. The summation of the contribution from each source location to the Kupffer cells is presented in figure 31. Summation of each source location Kupffer cells z, [mgy] z 1, [mgy] Figure 31. The mean specific energy, z, and the single-hit mean specific energy, z 1, calculated for each Kupffer cell when 211 At was homogeneously distributed in the central vein, the portal arteries/venules, distributing venule and all hepatocytes. 211 At were also distributed in the sinusoids. The two minor sinusoids had two times higher activity then the rest, when the sinusoids were the sources. The Kupffer cell had the dimensions 10x30x30 µm 3. The values of z and z 1 are presented as mgy per decay. Part II Liver model 30

32 8. Discussion Part II. Liver model The new liver model was based on the structures and dimensions from different histology books and articles. As seen in table 5, the dimensions of each component in the liver lobule varied in the different references. The choices of the dimensions have a significant impact on the results due to the short-range of alpha particles. Targets were simulated outside the non-rotated -part of the hepatic lobule to take into account the dose distribution from the rotated-parts of the hepatic lobule. Although the results apply for onesixth of the hepatic lobule it can be applied for layers of hepatic lobules and so on, due to the symmetry of the liver lobules (see Figure 16). The difference between the mean specific energy, z, and the single-hit mean specific energy, z 1, is that the sum of the energy deposited in the cell is divides the by the total number of particles simulated in order to calculate z while z 1 is calculated by dividing the sum by the number of particles that have hit the cell. This can clearly be observed in figures 22 and 28 where the total energy deposition is higher in the first row but the particles that have hit the cells in the second row will deposit higher energy per hit, which is shown in respective heat-map. The distribution of 211 At was assumed to be homogeneous in almost all cases, however, it is possible to weight the results for different distributions in the hepatic lobule. Depending on the chemical properties of the carriers, it may occur that 211 At is accumulated in certain parts of the hepatic lobule. Part II Liver model 31