IN DEGREE PROJECT TECHNOLOGY,FIRST CYCLE, 15 CREDITS

, STOCKHOLM SWEDEN 2020

Monte Carlo-simulation of whole-body absorbed dose

MIKAEL WESTLUND

MATTIAS JENSEN

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ENGINEERING SCIENCES

Nuclear Physics

Monte Carlo-simulation of whole-body absorbed dose

Mattias Jensen, Mikael Westlundmatjen@kth.se, miwestlu@kth.se

SA114X Degree Project in Engineering Physics, First LevelDepartment of Nuclear Physics

Royal Institute of Technology (KTH)Supervisors: Torbjörn Bäck and Linda Eliasson

May 28, 2020

Abstract

Radiation protection is important when working in lab environments where radioactivesources are frequently used. Simplified geometrical models are sometimes used in litera-ture or in education to analytically estimate the absorbed dose a human receives. Thisstudy investigates the accuracy of these models by comparing them to more advancedmodels and how the results differ if the dose is simulated in Geant4. Three cuboids withdifferent shapes, and two more human-like models were used as the bodies that wouldreceive the absorbed dose. It turned out, for such simplified cases, that the result seemedto be a factor of 1.6 - 3 times larger than the results achieved in the Geant4 simulation.This result is a consequence of the Compton scattering that occurs when the photonsenter the bodies, a process which the analytical method does not account for. It alsoturned out that besides using a more human-like model, the closest result was givenwhen the cuboids surface area was reduced to get a more human-like weight instead ofits thickness.

Strålskydd är viktigt inom jobbmiljöer där radioaktiva preparat förekommer ofta. Enklageometriska modeller används ofta inom litteratur för att analytiskt uppskatta hur stordos en person upptar. Den här rapporten diskuterar hur dessa modeller förhåller sig tillmer avancerade modeller och hur annorlunda resultatet blir om dosen simuleras iGeant4. Tre rätblock med olika dimensioner och två mer människoliknande modellerhar använts för att uppskatta den absorberande dosen. Det visade sig att resultatet varmellan 1.6 och 3 gånger större än resultatet som fås i Geant4simulationen. Detta är enkonsekvens av Comptonspridningen som händer när en foton kommer in i kroppen ochsom inte tas hänsyn till i analytiska metoden. Det visade också sig att förutom de mermänniskoliknande modellerna så ges det bästa resultatet av att minska på rätblocketsarea istället för tjocklek för att rätblocket ska väga lika mycket som en människa.

Contents

1 Introduction 2

2 Background Material 32.1 Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Absorbed dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Geant4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.4 Interactions between photons and matter . . . . . . . . . . . . . . . . . . 4

3 Investigation 73.1 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.2.1 Model 1, 2 and 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2.2 Model 4 and 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.3 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3.1 Calculation of absorbed dose . . . . . . . . . . . . . . . . . . . . . 103.3.2 Calculation of models . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.3 Calculation of absorption coefficient . . . . . . . . . . . . . . . . . 11

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Conclusions 17

5 Appendix 185.1 Energy and MAC values for isotopes . . . . . . . . . . . . . . . . . . . . 185.2 Geant4 scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.2.1 run.mac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.2.2 B1PrimaryGeneratorAction.cc . . . . . . . . . . . . . . . . . . . . 195.2.3 B1DetectorConstruction.cc . . . . . . . . . . . . . . . . . . . . . . 21

Bibliography 29

1

Chapter 1

Introduction

Radiation is everywhere around us and every day we are exposed to it. In a lab envi-ronment, where radioactive sources are frequently used, it is very important to manageand store these sources properly in order to not absorb a too high dose. In literature andeducation, very simple models are created in order for students to calculate the absorbeddose a person receives. This project investigated how accurate these simplified modelswere by comparing them to more advanced models simulated in the program Geant4.

The ICRP (International Commission on Radiological Protection) have a human modelwith more realistic proportions [1]. Unlike in this project where the whole body isapproximated as soft tissue this "phantom" also takes bone, blood, organs, etc. intoaccount. Not only is this important when calculating the absorbed dose but when thedamage of ionizing radiation is calculated other factors must be accounted for, such asthe fact that different organs are differently susceptible to radiation. The health effectsof ionizing radiation is measured in sievert (Sv) and is called the "effective dose" [2].The effective dose is calculated by multiplying the absorbed dose with a constant. Thevalue of this constant depends on the type of radiation as is shown in table 1.1.

Radiation type Radiation weighting factorPhotons 1

Electrons and muons 1Protons and charged pions 2

Alpha particles, fission fragments, heavy ions 20

Table 1.1: Recommended radiation weighting factors. Data collected from ICRP [3].

Note that since this report only analyses photon radiation, effective dose is equivalentto absorbed dose as a result of the weighting factor for photons being equal to 1.

2

Chapter 2

Background Material

2.1 Radioactive DecayAn unstable particle will eventually decay radioactively. The particle may decay in afew different ways. Beta- and alpha-decay are some examples. Depending on the type ofdecay the "mother particle" will emit different kinds of particles such as alpha particles,neutrons and photons. In this report, only the photons (also called electromagnetic ra-diation) will be taken into account. This electromagnetic radiation will be ionizing anda too high dose will be harmful to living cells.

2.2 Absorbed doseThe absorbed dose [4] [5] D measures the energy deposited in a person by ionizingradiation and can be written as:

D =E

m, (2.1)

where m is the mass of the person and E is the radiation energy absorbed by theperson. The absorbed dose is measured in the unit Gy, where 1 Gy = 1 J/Kg.The absorbed energy can be calculated by determining: how many decays there are,how many of the photons hit the target and how many of the photons are absorbed bythe target given the energy of the gamma-particle. In equation form:

E = Ω ·N · Eγ · fγ, (2.2)

where Ω is the solid angle for an isotropic source, N is the amount of decays, Eγ is theenergy for the photon and fγ is the proportion of photons absorbed by the target.The total absorption shows an exponential decrease in intensity as the model depthdecreases. Using this, the absorption coefficient (that is the fraction of photons that willbe absorbed by the target and thus contributing to the absorbed energy) is given by:

fγ = 1− e−µγρ·ρ·T , (2.3)

where µγ/ρ is the photon mass attenuation coefficient (MAC) in cm2/g, ρ is the densityin g/cm3 , and T is the depth in cm. See Table 5.1 in Chapter 5.

3

2.3 Geant4Geant4 is a Monte Carlo toolkit distributed by CERN for realistic simulations of particlesinteracting with matter. It is based on the object orientated programming language C++and has a large variety of applications. Geant4 allows the user to set up a geometry toact as the the object receiving the radiation. A particle source radiating set particlescan then be created in this geometry. These particles will then interact with materialscreated in the geometry and thus interact according to the set physics in that geometry.Information such as energy deposited in the material can be stored and presented to theuser. Geant4 comes with a lot of pre-made examples that a lot of times only need to bemodified to fit the problem or model the user wants to solve or simulate respectively.

2.4 Interactions between photons and matterWhen a photon meets an object, considering the photon energies studied, theinteraction can go five different ways. The photon can go straight through the objectnot interacting at all as can be seen in Figure 2.1.

Figure 2.1: The green line is the photon and the white rectangle is the object. Here it canbe observed that the photon does not interact with the body.

The photon can interact by Compton or Rayleigh scattering: The photon transfers apart of its energy to an electron (in the case of Rayleigh scattering this energy isminimal). Both the electron and photon are scattered in a way that conserves the totallinear momentum. This can be seen in Figure 2.2.

4

Figure 2.2: The photon is Compton or Rayleigh scattered, not all of the photon’s energyis absorbed by the body.

The photon can interact by photoelectric effect: All the energy of the photon isabsorbed by an electron in a way that conserves total linear momentum. This can beseen in Figure 2.4.

Figure 2.3: The photon is scattered until all energy is absorbed by an atomic electronthrough the photoelectric effect. The electron is freed from its atom but quickly interactswith the other atoms in the body.

Finally, the photon can interact by pair production. In the pair production, a photoninteracts with an atomic nucleus in the material. This interaction creates one electronand one positron. This happens only at very high energies since the energy of thephoton must be larger than the mass energy of the created particles.

What is the most likely interaction? The answer can be found by studying theattenuation of the photon intensity for different interactions at different photon

5

energies. In figure 2.4 soft tissue is approximated with water and shows attenuationversus photon energy.

Figure 2.4: Attenuation in water vs photon energy. The points represent the approximateinterval of photon energy that is being studied. Compton scattering is the dominantinteraction for all studied energies. Data collected from XCOM [6].

6

Chapter 3

Investigation

3.1 ProblemThe problem setup originates from an exam question in the course "Radiation, Protec-tion, Dosimetry and Detectors (SH2603)" taught at KTH, and is roughly stated as thefollowing: A person is at a distance r from a spherical spreading, high energy photonradiating, non-open (the object will receive no beta radiation), point source. See Figure3.1 for a visualization of the setup. Given the activity A, the time t, the area of theperson facing the source Area and the mass m, calculate the absorbed dose that theperson receives. In this study, the distance, activity and time were fixed for all modelsto r = 3.5 m, A = 1 mCi and t = 1 h respectively, and the dimensions of the person (willbe referred to as model for the rest of the report) varied. 1 Ci is equivalent to 3.7 · 1010

decays per second. The absorbed dose was calculated for each model with four differentradioactive isotopes; Na-22, Co-60, Cs-137 and Am-241. See Table 5.1 in Chapter 5 forphoton energies used.

7

Figure 3.1: Geant4 simulation with 100 high energy photons. The point source in themiddle and the model to the right. The green rays are photons. The red wires are photonscolliding with the air.

3.2 ModelsFive different models, constructed to represent a person, were used. All the models wereof the material "Tissue, soft (ICRU four-component)" [7] , which has a density of 1 g/cm3.

3.2.1 Model 1, 2 and 3

The first three models were cuboids with different dimensions and mass as can be seenin Table 3.1. These three models were used to calculate the absorbed dose using boththe analytical method as well as the Geant4 simulation. Cuboid1 was supposed torepresent a human of average height, width, and depth, and calculating the mass fromthose dimensions. The mass was fixed to be the average mass in Cuboid2 and Cuboid3and instead the width and depth respectively were calculated to give the desired mass.The height was constant in all cuboids because the absorbed dose is only dependant onthe surface area and the depth, so changing the height or width would give the sameresult.

Height Width Depth MassCuboid1 173 cm 37.5 cm 20.0 cm 129.75 kgCuboid2 173 cm 22.0 cm 20.0 cm 76 kgCuboid3 173 cm 37.5 cm 11.7 cm 76 kg

Table 3.1: Dimensions and mass of the cuboids

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3.2.2 Model 4 and 5

Instead of representing the two final models with cuboids, more advanced andhuman-like models were used (See Figure 3.2 and Figure 3.3). The fourth model wascreated in Python by drawing a body with average dimensions using vectors and thenintegrating over the vectors to find the surface area of the body. The depth of themodel was then calculated by using the same average mass used in Cuboid2 andCuboid3. The fourth model was used exclusively in the analytical method. Similarly,the fifth model was supposed to represent a more human-like model. By combiningsmaller geometries in Geant4, a model that looked similar to a human and had thesame mass as Cuboid2 and Cuboid3 was created by combining multiple geometricfigures. The depth of this model varied with body parts, since legs and upper bodyhave a different average depth. The fifth model was only used in the Geant4 simulation.

Figure 3.2: The surface of the fourth model

Figure 3.3: The fifth model. Viewed from the front

The original problem setup as well as the models were generated in Geant4 bymodifying the enclosed example B1 (an example that was included in the installation ofGeant4).

9

3.3 Calculations

3.3.1 Calculation of absorbed dose

The analytical method

The absorbed dose was calculated by combining equation 2.1 and equation 2.2. Since theradioactive source was assumed to be isotropic, Ω is the solid angle and thus:

Ω =Area

4 · π · r2, (3.1)

where Area is the model’s surface area facing the source, r is the distance between themodel and the radioactive source. N is the amount of decays:

N = A · t, (3.2)

where A is the radioactive activity in Bq, n is the number of photons and t is time inseconds. Eγ is the photon energy in Joule (taken from table 5.1 in Chapter 5) and fγ iscalculated using 2.3.

Plugging these into equation 2.1 with m being the mass of the model in kilograms weget the following equation:

D =Area4·π·r2 · A · t ·

∑ni=1Eγi · fγi

m, (3.3)

where D is the absorbed dose in Gy. The sum covers if there are photons of differentenergy emitted in the decay. By plugging in the different values stated in the problemsection and from Table 3.1 the dose could be calculated.

Note that with this method a photon will either be fully absorbed by the body or notinteract at all.

The Geant4 simulation

A spherical spreading, photon-emitting point source was placed at 3.5 m from the model.The amount of decays is given by:

N = A · t, (3.4)

where A and t is given in Bq and s respectively. Since the activity A and time t in theoriginal problem were assumed to be 1 mCi and 1 h respectively, this givesN = 1.332·1011

decays. Depending on the isotope, there might be more than one photon emitted in thedecay (that is the case for Na-22 and Co-60). It turned out the best way was to simulateeach photon separately and then sum the absorbed doses from those particles. In order tofind the absorbed dose, the absorbed energy was calculated in Geant4 and then dividedby the mass of the model. However, since simulating N decays would take a very longtime, 107 decays were simulated instead and the dose was assumed to linearly dependon the number of decays after that. 107 was a reasonably large number and the error(presented in Geant4) was less than 1%. The dose absorbed by the model from the first107 decays was then multiplied by 1.332·104 in order to get the desired number of decays.

10

The root mean square errors [8] for the different particles were added in the followingway:

xRMStot =

√√√√ N∑i=1

x2RMSi (3.5)

(For Am-241 and Cs-137, no sum was needed for the error nor the absorbed dose sincethere is only one photon emitted in their decays).

3.3.2 Calculation of models

The first cuboid was supposed to represent a rough estimate of human dimensions. Theaverage height and mass [9]. The average person was used (average of male and female).of a Swedish person was 173 cm and 76 kg, the average width [10] was 37.5 cm and thedepth was approximated using our own bodies to be 20 cm. It is important to note thatthe calculated mass of Cuboid1 was not used in Equation 3.1 . Its mass would have,based on its dimensions, been calculated to 129.75 kg. However, when Equation 3.3 wasapplied to Cuboid1, m has been set to the average mass of 76 kg.

The second cuboid has the same height and depth as Cuboid1 but the width was scaledto achieve the correct mass of the average human.

width =mass

depth · height · density(3.6)

The third cuboid has the same height and width as Cuboid1 but the depth was scaledto achieve the correct mass of the average human.

depth =mass

width · height · density(3.7)

The fourth model uses an area calculated with Python. The depth was scaled toachieve the correct mass of the average human.

depth =mass

area · density(3.8)

The fifth and final model combine multiple geometric figures to create a union withhuman-like dimensions. The average depth is also calculated in order to position it at3.5 meters away from the point source.

depth =

∑mbodypart · depthbodypart

mtotal

(3.9)

3.3.3 Calculation of absorption coefficient

Another calculation that was done was to estimate the absorption coefficient in Geant4 byreviewing 500 photons with Eγ = 1332 keV (one of the photons resulting from the Co-60decay) being shot towards Cuboid1 and counting how many that went straight throughthe model. If a photon interacted with the model (Compton/Rayleigh scattering and/or

11

photoelectric effect) then it was counted as absorbed. Photons that collided with airwere ignored. The absorption coefficient was calculated using the following formula:

fγ = 1− S

P − α(3.10)

Where S is the number of photons going straight through, P is the total number ofphotons and α is the number of photons colliding with air. This estimate was done toroughly compare the absorption coefficients for the analytical calculation and Geant4simulation.

3.4 Results

Na-22 Co-60 Cs-137 Am-241Cuboid1 2.11 ·10−6 2.12 ·10−6 6.50 ·10−7 6.92 ·10−8

Cuboid2 1.24 ·10−6 1.24 ·10−6 3.81 ·10−7 4.05 ·10−8

Cuboid3 1.60 ·10−6 1.54 ·10−6 5.06 ·10−7 6.39 ·10−8

Model4 1.21 ·10−6 1.22 ·10−6 3.73 ·10−7 3.93 ·10−8

Table 3.2: Results from analytical calculations. Measured in Gy.

Na-22 Co-60 Cs-137 Am-241Cuboid1 0.733(3) ·10−6 0.767(4) ·10−6 2.22(1) ·10−7 2.33(2) ·10−8

Cuboid2 0.707(3) ·10−6 0.742(4) ·10−6 2.11(2) ·10−7 2.15(2) ·10−8

Cuboid3 0.846(4) ·10−6 0.875(5) ·10−6 2.58(1) ·10−7 3.06(2) ·10−8

Model5 0.731(4) ·10−6 0.751(4) ·10−6 2.22(2) ·10−7 2.39(2) ·10−8

Table 3.3: Results from Geant4. Measured in Gy. (x) is the xRMStot and implies thevalue is ±x to the last significant figure. See Equation 3.5.

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Figure 3.4: Absorbed doses for all cuboids and models versus radioactive isotopes.

As seen in Table 3.2, Table 3.3 and Figure 3.4, the absorbed dose appears to be lower inthe Geant4 simulation than in the analytical case. Figure 3.5 illustrates how theanalytical doses1 varies from a factor 1.6 to 3.0 larger than the Geant4 simulated dosedepending on the isotopes and the model used. The x-axis covers the models and they-axis shows the fraction between the analytical dose and the Geant4 simulated dose foreach model and each isotope. The analytical dose for the fourth model is divided by thethe Geant4 dose calculated for the fifth model.

1The doses from the analytical calculations.

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Figure 3.5: The ratio between analytical dose and Geant4 dose vs model number. Model1, 2, 3 and 4 are Cuboid1, Cuboid2, Cuboid3, and Model4/Model5. The error bars arevery small due to the small xRMStot.

If the dose calculated for Model5 is assumed to give the most realistic approximation ofthe actual absorbed dose a person receives, then it is interesting to compare and seewhich model comes the closest to the fifth model for the analytical calculations. InFigure 3.6, the fraction between analytical doses for all models and the Geant4 dose forModel5 has been plotted. This has been done for all isotopes.

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Figure 3.6: The ratio between analytical dose and the dose calculated in Geant4 for Model5vs isotopes.

Finally, the absorption coefficient in the Geant4 simulation was calculated and out ofthe 500 photons with Eγ = 1332 keV being shot towards Cuboid1, 11 collided with airand 155 went straight through. The absorption coefficients with were calculated to be0.683 and 0.714 using equation 3.10 (with α = 11, and S=155) and equation 2.3respectively.

3.5 DiscussionAnalysis of Figure 3.5 shows that the factor is the largest for Cuboid1, which makes sensesince the dose D is inverse proportional to the mass of the model. And in the analyticalcalculation for Cuboid1, the energy is divided by a smaller mass than the mass of themodel calculated in Geant4. This results in a larger dose from the analytical calculationand thus the factor is larger.

The fact that the Geant4 method gives a lower dose than the analytical method couldbe a result of energy being Compton or Rayleigh scattered out of the body or becauseGeant4 has a different absorption coefficient (see Equation 2.3). However, by estimatingthe absorption coefficient in Geant4 and calculating it by using Equation 2.3, we seethat 0.714

0.683≈ 1. The result is close to 1 and therefore the difference in doses should be

mainly a result of the aforementioned Compton/Rayleigh scattering.

15

Another thing to note is that in the Geant4 simulation, the dose increased as the depthof the model (comparing Cuboid1 and Cuboid3) decreased. This means that the energyabsorbed decreases more slowly than the mass of the model when the depth decreases.This is not the case in the analytical calculation since the m in Equation 3.3 is 76 kgfor both Cuboid1 and Cuboid3, and thus only the energy decreases =⇒ the dosedecreases.

From Figure 3.5 it is also possible to compare how different isotopes impact thefraction. Am-241 seems to have the largest factor and this is because it has the lowestEγ. Lower Eγ means that the photons are less penetrative. The analytical methodassumes vacuum between the source and model. In Geant4 however, air is simulatedbetween the source and model. But the air will have less of an effect on the absorbeddose (and the difference between analytical solution and Geant4 and thus the fraction)for higher energy photons.Also, Figure 3.6 shows that the best approximation is given by Cuboid2 and Model4. Itis no surprise that Model4 is a better model to use than the other three models since ithas more human-like dimensions. Cuboid2 gives a surprisingly good answer. This is aresult of the area and depth of Cuboid2 being approximately the same as Model4.

Another thing that is important to discuss is error sources. For the Geant4 simulation,a number of 107 decays were simulated and then the calculated dose was multiplied by1.332 · 104 in order to get the desired number N of decays. This multiplication assumesthat the dose is linearly dependent on the amount of decays which is true as long as thedose from the first 107 decays is accurate. The error from the first 107 decays was lessthan 1% and thus the error from the N was also less than 1%.For the analytical calculation MAC values were gathered from NIST. Since there is nota MAC value for every single energy the photon energy had to be rounded to thenearest energy with a measured MAC value.Another source of error is the number of photons used in estimation of the absorptioncoefficient in Geant4. Using more number of photons would give a more accurateanswer.

16

Chapter 4

Conclusions

The original analytical approximation of radioactive dose can be improved. The dif-ferences in doses is an effect of Compton/Rayleigh scattering, which is not taken intoaccount for the analytical calculations. If the Human-like simulation in Geant4 is to beconsidered the most realistic the Human-like model constructed with Python will givethe best result. If one does not have access to a software like or similar to Python thenCuboid2 is simpler for analytical calculations while still giving a fairly accurate result.That means a good model to use in analytical calculations should have the average massand depth, and calculate the surface area from those. It is important to note that in theanalytical method scattering cannot occur. Therefore, Geant4 simulation must be usedin order to obtain an accurate calculation.

Future improvements to the method can be made by creating a more detailedHuman-like model in Geant4. If not only photons are to be studied it might be moreeffective to simulate a radioactive source directly in Geant4 instead of the individualparticles by themselves. Another future improvement would be to calculate the correctabsorption coefficient in Geant4. This would make the absorption coefficientcomparison more accurate. Absorbed dose as a result of radioactive isotopes within abody can also be studied.

17

Chapter 5

Appendix

5.1 Energy and MAC values for isotopes

Gamma particle energy in keV MAC in cm2/gNa-22 511, 511, 1275 0.09593, 0.09593, 0.06262Co-60 1173, 1332 0.06262, 0.06262Cs-137 661.7 0.08870Am-241 59.54 0.2025

Table 5.1: Gamma particle energy [11] [12] [13] [14] and MAC [7] of the studied isotopesin "Tissue, Soft (ICRU Four-Component)". When there are multiple energies and MACvalues the first energy corresponds to the first MAC value and so forth.

5.2 Geant4 scripts

5.2.1 run.mac

Used to run the simulation.

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗#run .mac Created by Mikael Westlund and Mattias Jensen KTH.#miwestlu@kth . se matjen@kth . se#Monte Carlo−s imu la t i on o f whole−body absorbed dose .

# I n i t i a l i z e k e rne l/ run/ i n i t i a l i z e#/ v i s / scene /endOfEventAction accumulate 500/ con t r o l / verbose 0/run/ verbose 0/ event / verbose 0/ t rack ing / verbose 0#

18

##po s i t i o n o f the source . T i s the average th i c kne s s o f the model .#(c a l c u l a t ed ana l y t i c a l l y , v a r i e s depending on the model . )/gps/ po s i t i o n 0 0 T/2 cm

#I s o t r o p i c source/gps/ang/ type i s o

#Energy va lue s . Gamma−p a r t i c l e i s s e t by d e f au l t .

#na22#/gps/ energy 0 .511 MeV#/gps/ energy 1 .275 MeV

#co60#/gps/ energy 1 .173 MeV#/gps/ energy 1 .332 MeV

#cs137#/gps/ energy 0 .6617 MeV

#am241#/gps/ energy 0.05954 MeV

#Star t the s imu la t i on with 10000000 gamma p a r t i c l e s#spread ing from the po int source .#gps/run/beamOn 1000000

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

5.2.2 B1PrimaryGeneratorAction.cc

B1PrimaryGeneratorAction.cc was used for all models and was modified in order to usea general particle source instead of a particle gun since it fit our project better.

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗/////// \ f i l e B1PrimaryGeneratorAction . cc/// \ b r i e f Implementation o f the B1PrimaryGeneratorAction c l a s s

#inc lude "B1PrimaryGeneratorAction . hh"

#inc lude "G4LogicalVolumeStore . hh"

19

#inc lude "G4LogicalVolume . hh"#inc lude "G4Box . hh"#inc lude "G4RunManager . hh"#inc lude "G4Genera lPart ic l eSource . hh"#inc lude "G4Part ic leTable . hh"#inc lude "G4Par t i c l eDe f i n i t i on . hh"#inc lude "G4SystemOfUnits . hh"#inc lude "Randomize . hh"

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . . . .

B1PrimaryGeneratorAction : : B1PrimaryGeneratorAction ( ): G4VUserPrimaryGeneratorAction ( ) ,

fGene ra lPa r t i c l eSou r c e ( 0 ) ,fEnvelopeBox (0 )

G4int n_part i c l e = 1 ;fGene ra lPa r t i c l eSou r c e = new G4Genera lPart ic l eSource ( ) ;

// d e f au l t p a r t i c l e k inemat icG4Part ic leTable ∗ pa r t i c l eTab l e = G4Part ic leTable : : GetPart i c l eTable ( ) ;G4String part ic leName ;G4Par t i c l eDe f i n i t i on ∗ p a r t i c l e= par t i c l eTab l e−>FindPar t i c l e ( part ic leName="gamma" ) ;

fGene ra lPar t i c l eSource−>Se tPa r t i c l eD e f i n i t i o n ( p a r t i c l e ) ;

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . .

B1PrimaryGeneratorAction : : ~ B1PrimaryGeneratorAction ( )

d e l e t e fGene ra lPa r t i c l eSou r c e ;

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . .

void B1PrimaryGeneratorAction : : GeneratePr imar ies (G4Event∗ anEvent )

// t h i s func t i on i s c a l l e d at the beg in ing o f ecah event//

// In order to avoid dependence o f PrimaryGeneratorAction// on DetectorConstruct ion c l a s s we get Envelope volume// from G4LogicalVolumeStore .

G4double envSizeXY = 0 ;G4double envSizeZ = 0 ;

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i f ( ! fEnvelopeBox )

G4LogicalVolume∗ envLV= G4LogicalVolumeStore : : GetInstance()−>GetVolume (" Envelope " ) ;

i f ( envLV ) fEnvelopeBox = dynamic_cast<G4Box∗>(envLV−>GetSol id ( ) ) ;

i f ( fEnvelopeBox ) envSizeXY = fEnvelopeBox−>GetXHalfLength ( ) ∗ 2 . ;envSizeZ = fEnvelopeBox−>GetZHalfLength ( ) ∗ 2 . ;

e l s e

G4Except ionDescr ipt ion msg ;msg << "Envelope volume o f box shape not found . \ n " ;msg << "Perhaps you have changed geometry . \ n " ;msg << "The gun w i l l be p lace at the cent e r . " ;G4Exception (" B1PrimaryGeneratorAction : : GeneratePr imar ies ( ) " ,"MyCode0002" , JustWarning ,msg ) ;

G4double s i z e = 0 . 8 ;G4double x0 = s i z e ∗ envSizeXY ∗ (G4UniformRand () −0 .5 ) ;G4double y0 = s i z e ∗ envSizeXY ∗ (G4UniformRand () −0 .5 ) ;G4double z0 = −0.5 ∗ envSizeZ ;

fGene ra lPar t i c l eSource−>Se tPa r t i c l ePo s i t i o n (G4ThreeVector ( x0 , y0 , z0 ) ) ;

fGene ra lPar t i c l eSource−>GeneratePrimaryVertex ( anEvent ) ;

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗

5.2.3 B1DetectorConstruction.cc

Cuboids

This modified file was used as B1DetectorConstruction.cc for the three first models(this is the file that creates the models).

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗#inc lude "B1DetectorConstruct ion . hh"

#inc lude "G4RunManager . hh"#inc lude "G4NistManager . hh"#inc lude "G4Box . hh"#inc lude "G4Cons . hh"

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#inc lude "G4Orb . hh"#inc lude "G4Sphere . hh"#inc lude "G4Trd . hh"#inc lude "G4LogicalVolume . hh"#inc lude "G4PVPlacement . hh"#inc lude "G4SystemOfUnits . hh"

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . . .

B1DetectorConstruct ion : : B1DetectorConstruct ion ( ): G4VUserDetectorConstruction ( ) ,

fScoringVolume (0)

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . .

B1DetectorConstruct ion : : ~ B1DetectorConstruct ion ( )

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . . .

G4VPhysicalVolume∗ B1DetectorConstruct ion : : Construct ( )

// Get n i s t mate r i a l managerG4NistManager∗ n i s t = G4NistManager : : In s tance ( ) ;

// Envelope parameters//G4double env_sizeXY = 1000∗cm, env_sizeZ = 1000∗cm;G4Material∗ env_mat = ni s t−>FindOrBuildMater ial ("G4_AIR" ) ;

// Option to switch on/ o f f check ing o f volumes ove r l ap s//G4bool checkOverlaps = true ;

//// World//G4double world_sizeXY = 1.2∗ env_sizeXY ;G4double world_sizeZ = 1.2∗ env_sizeZ ;G4Material∗ world_mat = ni s t−>FindOrBuildMater ial ("G4_AIR" ) ;

G4Box∗ so l idWorld =new G4Box("World " , // i t s name

0 .5∗world_sizeXY , 0 .5∗world_sizeXY , 0 .5∗ world_sizeZ ) ;// i t s s i z e

22

G4LogicalVolume∗ log icWorld =new G4LogicalVolume ( sol idWorld , // i t s s o l i d

world_mat , // i t s mate r i a l"World " ) ; // i t s name

G4VPhysicalVolume∗ physWorld =new G4PVPlacement (0 , //no r o t a t i on

G4ThreeVector ( ) , // at ( 0 , 0 , 0 )logicWorld , // i t s l o g i c a l volume"World " , // i t s name0 , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

//// Envelope//G4Box∗ so l idEnv =

new G4Box(" Envelope " , // i t s name0 .5∗ env_sizeXY , 0 .5∗ env_sizeXY , 0 .5∗ env_sizeZ ) ; // i t s s i z e

G4LogicalVolume∗ log icEnv =new G4LogicalVolume ( sol idEnv , // i t s s o l i d

env_mat , // i t s mate r i a l"Envelope " ) ; // i t s name

new G4PVPlacement (0 , //no r o t a t i onG4ThreeVector ( ) , // at ( 0 , 0 , 0 )logicEnv , // i t s l o g i c a l volume"Envelope " , // i t s namelogicWorld , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

//mate r i a l and s t a r t p o s i t i o n f o r the cuboid .G4Material∗ shape2_mat = ni s t−>FindOrBuildMater ial ("G4_TISSUE_SOFT_ICRU−4");G4ThreeVector pos2 = G4ThreeVector (0 , 0∗cm, 350∗cm) ;

// Shape o f the cuboid . x −> width , y−> height , z−> depth .//Vary these parameters f o r the d i f f e r e n t cuboids .G4double shape2_dxa = 37.5∗cm, shape2_dxb = 37.5∗cm;G4double shape2_dya = 173∗cm, shape2_dyb = 173∗cm;G4double shape2_dz = 20∗cm;

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G4Trd∗ so l idShape2 =new G4Trd(" Shape2 " , // i t s name

0 .5∗ shape2_dxa , 0 .5∗ shape2_dxb ,0 .5∗ shape2_dya , 0 .5∗ shape2_dyb , 0 .5∗ shape2_dz ) ; // i t s s i z e

G4LogicalVolume∗ l og i cShape2 =new G4LogicalVolume ( so l idShape2 , // i t s s o l i d

shape2_mat , // i t s mate r i a l"Shape2 " ) ; // i t s name

new G4PVPlacement (0 , //no r o t a t i onpos2 , // at p o s i t i o nlog icShape2 , // i t s l o g i c a l volume"Shape2 " , // i t s namelogicEnv , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

// Set Shape2 as s c o r i ng volume//fScoringVolume = log icShape2 ;

//// always re turn the phy s i c a l World//return physWorld ;∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ ’

Model5

Finally this modified file was used for B1DetectorConstruction.cc for the last Model5.

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗#inc lude "B1DetectorConstruct ion . hh"

#inc lude "G4RunManager . hh"#inc lude "G4NistManager . hh"#inc lude "G4Box . hh"#inc lude "G4Cons . hh"#inc lude "G4Orb . hh"#inc lude "G4Sphere . hh"#inc lude "G4Trd . hh"#inc lude "G4LogicalVolume . hh"#inc lude "G4PVPlacement . hh"

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#inc lude "G4SystemOfUnits . hh"#inc lude "G4UnionSolid . hh"#inc lude "G4El l ip so id . hh"#inc lude "G4Tubs . hh"#inc lude "G4Subtract ionSol id . hh"#inc lude "G4RotationMatrix . hh"/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . . . .

B1DetectorConstruct ion : : B1DetectorConstruct ion ( ): G4VUserDetectorConstruction ( ) ,

fScoringVolume (0)

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . .

B1DetectorConstruct ion : : ~ B1DetectorConstruct ion ( )

/ / . . . . oooOO0OOooo . . . . . . . . oooOO0OOooo . . . . . . . .

G4VPhysicalVolume∗ B1DetectorConstruct ion : : Construct ( )

// Get n i s t mate r i a l managerG4NistManager∗ n i s t = G4NistManager : : In s tance ( ) ;

// Envelope parameters//G4double env_sizeXY = 1000∗cm, env_sizeZ = 1000∗cm;G4Material∗ env_mat = ni s t−>FindOrBuildMater ial ("G4_AIR" ) ;

// Option to switch on/ o f f check ing o f volumes ove r l ap s//G4bool checkOverlaps = true ;

//// World//G4double world_sizeXY = 1.2∗ env_sizeXY ;G4double world_sizeZ = 1.2∗ env_sizeZ ;G4Material∗ world_mat = ni s t−>FindOrBuildMater ial ("G4_AIR" ) ;

G4Box∗ so l idWorld =new G4Box("World " , // i t s name

0 .5∗world_sizeXY , 0 .5∗world_sizeXY , 0 .5∗ world_sizeZ ) ;// i t s s i z e

G4LogicalVolume∗ log icWorld =

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new G4LogicalVolume ( sol idWorld , // i t s s o l i dworld_mat , // i t s mate r i a l"World " ) ; // i t s name

G4VPhysicalVolume∗ physWorld =new G4PVPlacement (0 , //no r o t a t i on

G4ThreeVector ( ) , // at ( 0 , 0 , 0 )logicWorld , // i t s l o g i c a l volume"World " , // i t s name0 , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

//// Envelope//G4Box∗ so l idEnv =

new G4Box(" Envelope " , // i t s name0 .5∗ env_sizeXY , 0 .5∗ env_sizeXY , 0 .5∗ env_sizeZ ) ; // i t s s i z e

G4LogicalVolume∗ log icEnv =new G4LogicalVolume ( sol idEnv , // i t s s o l i d

env_mat , // i t s mate r i a l"Envelope " ) ; // i t s name

new G4PVPlacement (0 , //no r o t a t i onG4ThreeVector ( ) , // at ( 0 , 0 , 0 )logicEnv , // i t s l o g i c a l volume"Envelope " , // i t s namelogicWorld , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

//mate r i a l o f the shape .G4Material∗ shape2_mat = ni s t−>FindOrBuildMater ial("G4_TISSUE_SOFT_ICRU−4");

// the head .G4Material∗ head_mat = ni s t−>FindOrBuildMater ial ("G4_TISSUE_SOFT_ICRU−4");G4ThreeVector headpos = G4ThreeVector (0 , 0 , 0 ) ;G4double huvudradie = 11.5∗cm;G4Orb∗ so l i dhead = new G4Orb("Head" , huvudradie ) ;

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// the upper bodyG4double bodyx = 37∗cm;G4double bodyz = 18∗cm;G4double bodyy = 70∗cm;G4Box∗ so l idbody = new G4Box(" body " , 0 .5∗ bodyx , 0 .5∗ bodyy , 0 .5∗ bodyz ) ;

//merge head and body .G4VSolid∗ bodyheadunion = new G4UnionSolid (" bodyhead " , so l idbody ,so l idhead , 0 , G4ThreeVector ( 0 , 0 . 5∗ bodyy + huvudradie , 0 ) ) ;

// the arms// r o t a t e s so they are not h o r i s o n t a l nor v e r t i c a l .

G4RotationMatrix∗ rm = new G4RotationMatrix ( ) ;rm−>rotateZ (−75.∗deg ) ;G4double armlength = 68∗cm;G4double armr = 7∗cm;G4Box∗ so l idarm = new G4Box("arm" , 0 .5∗ armlength , 0 .5∗ armr , 0 .5∗ armr ) ;

//merge arm with upper body and head .G4VSolid∗ armbodyunion = new G4UnionSolid (" armbody" , bodyheadunion ,sol idarm , rm , G4ThreeVector (−0.5∗bodyx − 0 .5∗ armlength+0.32∗ armlength ,0 .5∗ bodyy−0.5∗armr −0.45∗ armlength , 0 ) ) ;

// r o t a t e s in the other d i r e c t i o n .rm−>rotateZ (75 .∗ deg ) ;rm−>rotateZ (75 .∗ deg ) ;

//merges the other arm .G4VSolid∗ armbodyunion2 = new G4UnionSolid (" armbody" , armbodyunion ,sol idarm , rm , G4ThreeVector ( 0 . 5∗ bodyx + 0.5∗ armlength − 0 .32∗ armlength ,0 .5∗ bodyy−0.5∗armr−0.45∗ armlength , 0 ) ) ;

// l e g sG4double l e g l e ng th = 80∗cm;G4double l e g r = 10.15∗cm;

//merges l e g s with r e s t o f bodyG4Box∗ s o l i d l e g = new G4Box(" l e g " , 0 .5∗ l e g r , 0 .5∗ l e g l eng th , 0 .5∗ l e g r ) ;G4VSolid∗ legbodyunion = new G4UnionSolid (" legbody " , armbodyunion2 ,s o l i d l e g , 0 ,G4ThreeVector ( 0 . 5∗ bodyx − 0 .5∗ l e g r , −0.5∗bodyy − 0 .5∗ l e g l eng th , 0 ) ) ;G4VSolid∗ legbodyunion2 = new G4UnionSolid (" legbody2 " , legbodyunion ,s o l i d l e g , 0 ,G4ThreeVector (−0.5∗bodyx + 0.5∗ l e g r , −0.5∗bodyy−0.5∗ l e g l eng th , 0 ) ) ;

// s t a r t p o s i t i o n o f the body .

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G4ThreeVector pos2 = G4ThreeVector (0 , 0 .5∗ bodyy + leg l eng th , 350∗cm) ;

G4LogicalVolume∗ l og i cShape2 =new G4LogicalVolume ( legbodyunion2 , // i t s s o l i d

shape2_mat , // i t s mate r i a l"headunion " ) ; // i t s name

new G4PVPlacement (0 , //no r o t a t i onpos2 , // at p o s i t i o nlog icShape2 , // i t s l o g i c a l volume"Shape2 " , // i t s namelogicEnv , // i t s mother volumef a l s e , //no boolean opera t i on0 , // copy numbercheckOverlaps ) ; // ove r l ap s check ing

// Set log i cShape2 as s c o r i ng volume//fScoringVolume = log icShape2 ;

//// always re turn the phy s i c a l World//return physWorld ;

∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗ ’

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