DIPLOMA THESIS - Amazon S3...DIPLOMA THESIS Calculation of solid-state track etched detectors response ... Pomocí této geometrie jsou vypoˇcteny a s nam ˇeˇrenými daty porovnány

CZECH TECHNICAL UNIVERSITY IN PRAGUE

FACULTY OF NUCLEAR SCIENCES AND PHYSICAL ENGINEERING

DEPARTMENT OF DOSIMETRY AND APPLICATION OF IONIZING RADIATION

DIPLOMA THESIS

Calculation of solid-state track etched detectors response

in 290 MeV/n and 400 MeV/n carbon ion beams

using Geant4

Author: Bc. Martin Šefl

Supervisor: Ing. Václav Štepán, Ph.D.

Prague, 2014

Název práce: Modelování spekter nabitých cástic ve stopových detektorech v pevné

fázi ozárených svazkem iontu uhlíku o energii 290 MeV/n a 400 MeV/n

Autor: Martin Šefl

Obor: Radiologická fyzika

Druh práce: Diplomová práce

Vedoucí práce: Ing. Václav Štepán, Ph.D., Ústav jaderné fyziky AV CR a

Université Bordeaux, CNRS/IN2P3, CENBG, Gradignan, Francie,

Konzultant: Ing. Marie Davídková, CSc., Ústav jaderné fyziky AV CR

Abstrakt: Experimenty Ústavu jaderné fyziky AV CR a NIRS (National Institute

of Radiological Sciences) na urychlovaci HIMAC (Heavy Ion Medical

Accelerator in Chiba, Japonsko) ukazují, že stopové detektory v pevné

fázi lze použít pro stanovení spektra lineárního prenosu energie (LET)

pro težké nabité cástice s LET od 5–10 keV/µm výše (Spurný et al.,

Rad. Prot. Dosim. 143, s. 519–522, 2011 and K. Pachnerová Brabcová

et al., Rad. Prot. Dosim. 143, s. 440–444, 2011). V této práci je pomocí

Monte Carlo kódu Geant4 reprodukována geometrie svazku urychlo-

vace HIMAC pro monoenergetické svazky 290 MeV/n a 400 MeV/n

a svazek 290 MeV/n spread out Bragg peak (SOBP) vcetne usporá-

dání detektoru v uvedených experimentech. Pomocí této geometrie jsou

vypocteny a s namerenými daty porovnány hloubkové dávkové krivky

ve vode, spektra lineárního prenosu energie pro ruzné tloušt’ky PMMA

stínení a urceny príspevky stopovými detektory detekovaných a nedete-

kovaných cástic k fluenci i dávce. Se zohlednením nejistot merení po-

mocí stopových detektoru je nalezena dobrá shoda mezi vypoctenými a

namerenými hodnotami.

Klícová slova: Geant4, Monte Carlo, detektory stop, lineární prenos energie, LET

1

Title: Calculation of solid-state track etched detectors response in 290 MeV/n

and 400 MeV/n carbon ion beams using Geant4

Author: Martin Šefl

Advisor: Ing. Václav Štepán, Ph.D.

Consultant: Ing. Marie Davídková, CSc.

Abstract: Experiments at the Heavy Ion Medical Accelerator in Chiba (HIMAC),

which were performed by researchers from the Department of Radia-

tion Dosimetry of the Nuclear Physics Institute, Academy of Sciences

of the Czech Republic and NIRS (Japanese National Institute of Radi-

ological Sciences) have revealed that solid state nuclear track etched

detectors can work as spectrometers of linear energy transfer (LET)

for particles with LET above 5–10 keV/µm (Spurný et al., Rad. Prot.

Dosim. 143, p. 519–522, 2011 and K. Pachnerová Brabcová et al.,

Rad. Prot. Dosim. 143, p. 440–444, 2011). In this thesis the HIMAC-

BIO beamline geometry was reproduced together with an experimen-

tal set-up for monoenergetic C12 ion beams of energies 290 MeV/n

and 400 MeV/n and spread out Bragg peak of the C12 beam with en-

ergy 290 MeV/n in Geant4. Geant4 is an open source Monte Carlo

simulation toolkit for simulations of transportation of particles through

matter. Using the described geometry, we calculated depth dose distri-

butions in water, the spectra of linear energy transfer for various thick-

nesses of PMMA shielding and the estimated contribution of detected

and undetected particles to the fluence and dose. When considering

the uncertainties of LET measurement with TEDs, we found a solid

agreement between the calculated and measured results.

Keywords: Geant4, Monte Carlo, track etched detectors, linear energy transfer,

LET

http://dx.doi.org/10.6084/m9.figshare.1050072

2

http://dx.doi.org/10.6084/m9.figshare.1050072

Contents

1 Introduction 7

1.1 Solid state nuclear track etched detectors . . . . . . . . . . . . . . . . . . . 9

1.2 Linear energy transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.1 LET definition ICRU (1968) . . . . . . . . . . . . . . . . . . . . . 10

1.2.2 TED as LET spectrometer . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Geant4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Methods 15

2.1 Simulation code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Geometry description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 Particle source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.2 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2.3 PMMA binary filters . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Spread out Bragg peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.3.1 Ridge filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.2 Ridge filter reconstruction procedure . . . . . . . . . . . . . . . . . 28

2.4 Linear energy transfer calculation . . . . . . . . . . . . . . . . . . . . . . 31

2.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3 Results 34

3.1 Depth dose distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.1.1 MONO 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.2 MONO 400 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1.3 SOBP 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 LET spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3

3.2.1 LET spectra of MONO 290 MeV/n in TD1 . . . . . . . . . . . . . 40

3.2.2 LET spectra of MONO 290 MeV/n in Page . . . . . . . . . . . . . 43

3.2.3 LET spectra of MONO 400 MeV/n in TD1 . . . . . . . . . . . . . 46

3.2.4 LET spectra SOBP 290 MeV/n in Page . . . . . . . . . . . . . . . 49

3.3 Comparison of LET spectra in water and plexiglass . . . . . . . . . . . . . 52

3.4 LET dependence on depth . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.5 Fraction of detected particles . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Discussion 59

4.1 Depth dose distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.1.1 MONO 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.1.2 MONO 400 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.1.3 SOBP 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2 LET spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.2.1 MONO 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4.2.2 MONO 400 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.2.3 SOBP 290 MeV/n . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.3 Fractions of detected particles . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Conclusion 70

5.1 Future perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Bibliography 71

Appendix 77

Example of a macro file for the Geant4 calculations . . . . . . . . . . . . . . . . 77

Table of PMMA/water equivalent thicknesses . . . . . . . . . . . . . . . . . . . 78

4

Declaration

Prohlašuji, že jsem tuto diplomovou práci vypracoval samostatne a uvedl jsem veškerou

použitou literaturu.

I declare that I wrote the thesis by myself and I used only the sources listed in the biblio-

graphy.

Martin Šefl

Prague, 4th of May 2014

5

Acknowledgements

I am especially grateful to Ondrej Ploc for the geometry of the HIMAC-BIO experiments and

related information and consultations, Iva Ambrožová and for consultations, Katerina Pach-

nerová Brabcová for photos, providing the experimental data and consultations and Marie

Davídková for support. The greatest thanks belongs to my supervisor Václav Štepán for

time spent helping me.

I would like to express my special gratitude to Sébastien Incerti for valuable advice and

comments and also to Mathieu Karamitros for helpful comments. The recommendations

from Vladimir Ivantchenko are also very appreciated. I thank to Lucas Burigo for sharing

his ridge filter design and Satoshi Kodaira for information about real ridge filter.

I am grateful to COST MP1002 for enabling the realization of a part of this project and

also to the Department of the Dosimetry and Application of Ionizing Radiation, FNSPE CTU

in Prague for essential support.

The access to computing and storage facilities owned by parties and projects contributing

to the National Grid Infrastructure MetaCentrum, provided under the programme “Projects

of Large Infrastructure for Research, Development, and Innovations” (LM2010005) is highly

appreciated.

I would like to thank to the Atlassian company for free hosting of a Git repository

at Bitbucket (https://bitbucket.org).

6

https://bitbucket.org

Chapter 1

Introduction

Track etched detectors (TED) can be used as spectrometers for linear energy transfer (LET)

of charged particles with LET within a certain range. There is a lower threshold, which is

approximately 10 keV/µm, below which particles are not detected. Particles are detected

above the upper threshold, but the LET spectrometry is no longer possible.

LET spectrometry measurements with track-etched detectors at HIMAC-BIO facility

(Heavy Ion Medical Accelerator in Chiba in Japan) were performed by researchers from

the Department of Dosimetry of Ionizing Radiation of the Nuclear Physics Institute of the Aca-

demy of Sciences of the Czech Republic and Japanese researchers from NIRS (National

Institute of Radiological Sciences). They used track-etched detectors from various produ-

cers to study the LET spectra of carbon ion beam; the monoenergetic (MONO) 290 MeV/n

and 400 MeV/n set-up and the spread out Bragg peak (SOBP) 290 MeV/n [1, 2]. All

the detectors were stored in a holder during irradiation (see Figure 1.1). The detectors were

shielded by PMMA (polymethylmetacrylate) filters of a varying thickness, to achieve mod-

ulation of the beam at the given depths in water. PMMA is water or tissue equivalent plastic

material, which is sometimes used instead of water for measurements at radiotherapy fa-

cilities. The data from the materials Page (Page Moulgings (Pershore) Ltd., UK) and TD1

(Japan Fukuvi Chemical Industry Co. Ltd.) was used and compared in this thesis.

The primary goals of this thesis involved calculations of the unrestricted linear energy

transfer using a Geant4 simulation tool-kit [3, 4] in the track etched detectors and an estima-

tion of the contribution of various particles to the fluence and absorbed dose. This required

reproducing the beamline geometry and experimental set-up of the Heavy Ion Medical Ac-

celerator in Chiba in Japan (HIMAC).

The geometry of the beamline was successfully reproduced and numerous simulations

7

were run on the Czech Computational Grid Metacentrum for both monoenergetic and SOPB

C 12 ion beams at 290 MeV/n and 400 MeV/n (MeV per nucleon). Using the Python 3.3

language [5, 6, 7] and the ROOT framework [8] the results were evaluated and compared

with the experimental data. These spectra were finally used to calculate the fractions of de-

tected and non detected particles and also their contribution to the total dose.

There is one issue, which needs to be discussed here. The energy of the beam is usually

described with unit MeV/u, where u is the atomic mass unit. In this thesis we use MeV/n

according to the article [1] which means MeV/nucleon. Since u is defined as 112 of mass

of C 12, in our case both MeV/u and MeV/n are the same and both are correct, since the only

beam we simulated was the C 12 beam.

Figure 1.1: Box with detectors [1, 9]. Photo courtesy of Katerina Pachnerová Brabcová.

8

1.1 Solid state nuclear track etched detectors

Heavily ionizing particles extensively ionize along their path in the medium and leave nar-

row trails of damage so-called a latent track. When irradiated material containing latent

ion tracks is exposed to a chemical agent (etchant), chemical reactions are more intensive

in the damaged region of the latent track. Etched tracks are visible under an optical micro-

scope. The etchants of plastic detectors are usually water solutions of sodium hydroxide

(NaOH) or potassium hydroxide (KOH) [10].

The detectors in the simulated experiment [1, 9] were made of polyallyldiglycolcarbonate

(PADC) and etched in a 5 M solution of sodium hydroxide at a temperature of 70 °C.

The chemical etching of the latent track is governed by two parameters – a track etch

rate Vt (the etching velocity of the particle track) and a bulk etch rate Vb (the etching velocity

of the undamaged material). Often the ratio V = VtVb

is used. The visible track is formed when

Vt >Vb [10]. The schema of the process is drawn in the Figure 1.2.

Figure 1.2: Track of the particle, which hits the detector surface under angle θ, is formed be-cause of different etching velocities (Vb: undamaged material etching velocity, Vt : damagedarea etching velocity). The layer of thickness B is removed by etching. Image reproducedfrom [11] with permission of Katerina Pachnerová Brabcová.

The track etch rates (or the ratio V ) depend on particle parameters (charge, energy, mass),

detector material (structure, purity), etching conditions, environmental conditions during ir-

radiation (presence of oxygen) etc. In general, the bulk etch rate is constant for given detector

and the track etch rate varies along particle trajectory [10].

Due to etching of the undamaged material a thin layer is removed from the detector.

The thickness of this layer depends on the etching protocol. For the case of protocols used

9

in the experiments [1] and [9] the layer is approximately 15 µm thick.

The determination of the V can be performed by an optical microscope. Researchers

at the Nuclear Physics Institute used HSP-1000 by SEIKO Precision (see the Figure 1.3).

The detectors were scanned and the Vt was calculated according to the size of the tracks.

It is also possible to determine the Vt using digital micrometer, atomic force microscope or

surface profilometer [10]. Details of the process are explained in references [10, 11, 12, 13].

1.2 Linear energy transfer

1.2.1 LET definition ICRU (1968)

The restricted linear energy transfer of charged particles in a medium is the quotient of dE

by dl, where dl is the distance traversed by the particle and dE is the mean energy loss on

the distance dl due to collisions with energy transfers less than some specified value ∆ [14]:

LET∆ =dEdl

. (1.1)

If the ∆ = ∞, it is an unrestricted LET. Since the track etched detectors were calibrated

to LET∞ in water, for further reading the LET means the unrestricted linear energy transfer

in water (which is equal to stopping power in this case).

1.2.2 TED as LET spectrometer

Track etched detectors are suitable for use as spectrometers for linear energy transfer. They

need to be calibrated for this usage. This entails finding the relationship between the response

of the detector (etch rate V ) and LET (LET∞). The procedure is described in detail in [11].

This was generally performed by irradiating the detector with particles with known LET,

and evaluating the V ratio for this beam. In this manner the following calibration equation

was obtained

LET = a − (a−b) · exp(−k(V −1))d , (1.2)

where a, b, k and d are calibration coefficients. Theirs values were fitted to the experimental

data.

In Table 1.1 are written the calibration coefficients from equation (1.2) for the materials,

the response of which was compared to the simulation results presented in this thesis. This

10

Figure 1.3: Microscope HSP-1000 by SEIKO Precision.

was the material from Page Moulgings (Pershore) Ltd (England) and TD1, which is a prod-

uct of Japan Fukuvi Chemical Industry Co. Ltd. The thickness of the Page is 0.5 mm while

the TD1 is 0.8 mm thick. The calibration curves for these two detectors together with the ex-

perimental points and 95% confidence intervals are plotted in the Figure 1.4. Those curves

were adopted from the PhD thesis [11].

Table 1.1: Parameters a, b, k, d of calibration equation 1.2, LET = f (V − 1) for Page andTD1 under etching conditions 5 M NaOH, 70°C, 18 hours [11].

a b k dPage 443.34 10.92 1.61 0.39TD1 334.75 9.27 1.58 0.44

The operational ranges of the various track etched detectors vary and strongly depend

on the etching protocol. They are limited by the detection threshold in the low LET region

and consequently do not detect any particles below this threshold. In the region of the high

LET values a saturation effect exists, thus only the counting of tracks is possible and the de-

tector can not work as a spectrometer for LET. The operational ranges are from 10 keV/µm

to approximately 440 keV/µm for the Page and from 9 keV/µm to approximately 340 keV/µm

for the detector TD1 and for this etching protocol [11].

11

Figure 1.4: Fitted calibration curves for detector TD1 and Page. The LET in water andits 95% confidence intervals are plotted as function of the shifted etch rate V − 1. Graphscourtesy of Katerina Pachnerová Brabcová [11].

12

1.3 Geant4

Geant4 [16] is a Monte Carlo tool-kit for simulating the transport of particles through mat-

ter [3, 4]. It is fully implemented in C++, open source and free. It can be run on multiple

computer platforms, including Microsoft Windows, GNU/Linux or Mac OS X. Geant4 is

designed and maintained by an international collaboration.

Geant4 is open source, the physics implementation is transparent and each component

can be inspected at the source code level. It exploits object oriented technology which en-

ables the development of parts of the code by different groups separately [3].

It is currently used in a variety of applications. It was utilized in numerous high energy

physics experiments such as ATLAS, GAUSS, ALICE and CMS at Large Hadron Collider

in CERN, in the field of Space & Radiation in projects of the European Space Agency SPEN-

VIS (Space Environment Information System), DESIRE (Dose estimation by Simulation

of the ISS Radiation Environment) and GLAST (Gamma Ray Large Area Space Telescope)

etc.

Geant4 is also applied in the medical field. The Geant4 North American Medical User

Organization (G4NAMU) and The Geant4 European Medical User Organization (G4EMU)

are organizations connecting up the Geant4 medical user community in North America and

Europe. A brief list of several projects which exploit or extend Geant4 simulation toolkit is

written below.

GATE

One such international project based on Geant4 is GATE, which was developed by the Open-

GATE collaboration. GATE is dedicated to simulations in medical imaging and radiotherapy.

It provides simulations of Positron Emission Tomography (PET), Single Photon Emission

Tomography (SPECT), Computed Tomography (CT) and also radiotherapy units. For fur-

ther information, the reader should visit the site [17].

GAMOS

GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) is a Geant4-based

framework which enables carrying out the Geant4-based simulation simply, without C++

knowledge. Additional information is available at the project homepage [18].

13

TOPAS

TOPAS (TOol for PArticle Simulation) is an innovative proton therapy simulation Monte

Carlo platform based on Geant4. It is dedicated to particle therapy. It can model passive scat-

tering or scanning beam treatment head, patient geometry based on CT and score dose [19].

Monte Carlo codes are usually difficult to learn and with the learning being time-consuming

for most clinical medical physicists. The developers tried to overcome this issue and devel-

oped TOPAS as a user-friendly tool.

Geant4-DNA

Geant4-DNA project is an extension of Geant4 for modelling of early damages induced

by ionizing radiation at the DNA scale. It extends physics models into the lower energy

range. The Geant4-DNA processes covers electrons (0.025 eV–1 MeV), protons (1 keV–

100 MeV), hydrogen (1 keV–100 MeV) and α-particles (10 keV–40 MeV) in liquid wa-

ter [20]. Interested reader should visit the Geant4-DNA homepage at [21].

14

Chapter 2

Methods

The first section of this chapter gives description of the simulation code 2.1. The beamline

geometry is described in 2.2. The next part is dedicated to process of creating the spread out

Bragg peak (SOBP) 2.3. The last section 2.4 describes the implementation of linear energy

transfer calculation in the simulation.

2.1 Simulation code

In Geant4, the user is supposed to build an application. Geant4 contains a lot of classes,

which can be used in the user’s application code. User chooses the classes which suit to given

purpose (geometry, physics lists etc.). There are numerous examples of working application

codes included in the distribution of Geant4.

The application, which was used to simulated the experiment, was derived from the basic

example B1. Using already working code simplified the development of the application.

I have not been experienced developer in C++, hence changing classes in a working code

was easier than writing a completely new code.

The application consisted of these classes: B1DetectorConstruction, B1PrimaryGene-

ratorAction, B1RunAction, B1EventAction and B1SteppingAction.

Geometry is handled in the class B1DetectorConstruction, which was adapted to the the-

sis purpose. The geometry is described in the subsequent section 2.2.

The particle source is controlled via the B1PrimaryGeneratorAction class. Changes

in this class are described in the subsection 2.2.1.

LET calculation was handled in the class B1SteppingAction. The process is described

in the section 2.4. Class B1SteppingAction controls the most elementary part of a track,

15

which is called a step. The step is a segment of the track defined by a pre-step and a post-

step point. The track of a particle usually consists of many steps. The hierarchy of tracking is

followed by B1EventAction. In our case one event meant one primary C 12 ion generation.

The class B1RunAction handles one whole run of the simulation.

We chose the FTF_BIC 2.0 physics list. It uses binary cascade models (BIC), which are

valid for hadrons up to 10 GeV [22]. A guide to choosing a physics list [22] recommends

to use physics list containing acronym "BIC", if the primary particle energy is below 5 GeV

(C 12 initial energy was 3.48 and 4.8 GeV).

Source files of the simulation application, Python scripts, ROOT scripts and LATEX source

files of this thesis were stored at https://bitbucket.org, which is a Git repository hosting

service. Git is a free and open source distributed version control system.

2.2 Geometry description

This section contains the description of the beamline geometry and HIMAC-BIO room.

The geometry of the HIMAC beamline at NIRS in Chiba was described in the reference [23]

and also in detail in [24]. The geometry, which was used also in [25] was improved. A sin-

gle PMMA block was replaced by a set of filters and also a ridge filter to create SOBP was

added. The geometry description was provided by Ondrej Ploc in SimpleGeo format [26].

SimpleGeo is an "interactive solid modeler" [27]. We used version 4.3.3 to read properties

of the solids.

SimpleGeo can export a geometry to following Monte Carlo tools: Fluka [28, 29],

MCNP(X) [30], PHITS [31] and also to a POV Ray [32] formats. Unfortunately, direct

export to Geant4 is not possible. The SimpleGEO also allows to export to additional file for-

mats (.3ds, .obj, .wrl, .stl, .dxf, .str, .ply, .pbrt), but attempt to obtain correct export of whole

geometry and utilize it in Geant4 failed. Therefore we decided to rewrite the whole geometry

into Geant4 manually using constructive solid geometry (CSG).

In the Figure 2.1 is the top view of the geometry without the walls. The description

of the beamline begins from the source.

16

https://bitbucket.org

Figure 2.1: Top overview of the beamline.

2.2.1 Particle source

The source was placed at z =−1172,5 cm at the beginning of the beamline. As the wobbling

systems was not reproduced, a planar source was chosen. The G4GeneralParticleSource

class was used instead of G4ParticleGun class, which was originally used in B1 example,

since the general particle source enables more variable setting of the source. The source set

up is handled by a macro file. Lines of the macro file responsible for the source are written

below.

/ gps / p a r t i c l e i o n

/ gps / i o n 6 12 6

/ gps / en e r gy 3480 MeV

/ gps / pos / t y p e P l a n e

/ gps / pos / shape Square

/ gps / pos / h a l f x 2 cm

/ gps / pos / h a l f y 2 cm

/ gps / pos / c e n t r e 0 . 0 . −1172.5 cm

/ gps / d i r e c t i o n 0 0 1

The first three lines choose the C 12 ion of energy 3480 MeV (12 × 290 MeV/n) or

4800 MeV (12×400 MeV/n). The other lines set the shape and size of the plane source and

its position. It should be emphasized that the sizes 2 cm are half lenghts, the size of the square

source is therefore 4×4 cm. The last line sets the initial particle direction.

17

2.2.2 Beamline

Generated particles passed in the beginning through two 10 µm thick aluminium windows

on both sides of Vacuum Tube 1. There were 11 of these 10 µm windows on the beamline

in total. The length of Vacuum Tube 1 is 205 cm and its radius was 3.25 cm. Vacuum Tubes

were all filled with G4_GALACTIC material.

In the next region were Scatter Filters. The Scatter Filters 1–4 were made of Tantalum

and the Scatter Filters 5–8 were made of Lead. The thicknesses of the Scatter Filters were

0.105, 0.215, 0.434, 0.805, 1.6, 3.2, 6.4 and 12.8 mm thick respectively, their sizes were 14×

14 cm. Their positions varied depending on the selected primary particle. Just the Scatter

Filter 3 was placed into the 290 MeV/n beam, and the Scatter Filters 1, 2, 3 were placed into

the 400 MeV/n beam. The detailed view of the Scatter Filters in the 290 MeV/n set up is

shown in the Figure 2.2.

A brass F Collimator was next, with 5 cm inner and 8 cm outer radius and length of 10 cm.

The centre of this collimator was placed at z =−893 cm.

Figure 2.2: Detailed view of Scatter Filters positions in the 290 MeV/n beam. The tantalumScatter Filters 1–4 are green, the lead Scatter Filters 5–8 are blue and the cylindric object isthe F Collimator made of brass.

18

Behind the F Collimator there was an Fe Tube with a Vacuum Tube 2 inside. Both were

282 cm long. The inner radius of Fe Tube was 11 cm and the outer radius was 18 cm.

The centre of the Fe Tube was placed at point z =−698.5 cm.

Ring Collimator, Main Monitor and SEM (secondary emission monitor) and also part

of the Fe Tube with one Aluminium Window are displayed in the Figure 2.3. The Ring

Collimator was a brass rectangular parallelepiped (94× 40× 20 cm) with a cylindric hole

in the middle. Its centre was placed at z = −529.5 cm. The cylindric holes were created

by boolean subtraction of two cylinders and the rectangular parallelepiped. The proximal

(to the source) hole had 10 cm radius, the distal 8 cm. The Ring Collimator was followed

by the Main Monitor (cylinder: inner rad = 10 cm, outer rad = 17 cm, length = 11 cm).

The last object in the Figure 2.3 is the SEM (inner rad = 10 cm, outer rad = 12 cm, length=

17 cm), inside which was a SEM Vacuum Tube. Both sides of SEM were covered by Alu-

minium Windows.

Figure 2.3: Fe Tube, Ring Collimator, Main Monitor and Secondary Emission Monitor(SEM).

19

The proximal cylinder in the Figure 2.4 is a Profile Monitor (inner rad = 11 cm,

outer rad = 18 cm, length = 16 cm). The Profile Monitor was placed at z = −336 cm.

It was also covered by Aluminium Windows. Behind it was placed a Four Leaf Collimator

(FLC Al). The FLC Al constituted of 4 aluminium blocks 14 × 36 × 20 cm. The posi-

tions of the centres of the blocks were (−18 cm,0,−314), (18,0,−314), (0,−18,−294),

(0,18,−294).

Figure 2.4: Profile Monitor, Four Leaf Collimator (FLC Al) and its cover (FLC Fe).

20

2.2.3 PMMA binary filters

Binary Filters were PMMA blocks of the following thicknesses: 256, 128, 64, 32, 16, 8, 4,

2, 1 and 0.5 mm. The xy-size was 32.5× 32.5 cm. Required total thickness of the PMMA

filter was reached as unique combination of the binary filters down to 0.5 mm precision.

For example:

170.5 mm = 0.5+2+8+32+128 mm.

User is supposed to define the required thickness when launching the program. For in-

stance, for 170.5 mm thickness one adds a parameter when calling the application

exampleB1 −pmma 170 .5

Figure 2.5: PMMA filters and brass Four Leaf Collimator (FLC Brass). Thicknessesof the inserted PMMA filters are 0.5, 2, 8, 32, 128 mm, the remaining binary filters 1, 4,16, 64 and 256 mm are retracted.

The detailed view of the Binary Filters positions is shown in the Figure 2.5. The Bi-

nary Filters were placed between z = −94.4 cm and z = −30.425 cm. The x-coordinate

of the centre of each block was 0 for block in or 31.25 out of the beam. The y-coordinates

were 0 for all Binary Filters. The G4_PLEXIGLASS was assigned to these filters.

Behind the Binary Filters there was another Four Leaf Collimator made of Brass blocks

of size 35× 15× 5. Blocks were placed (their centres) at points (0 cm,±18.5,−15.7) and

(±18.5,0,−20.7).

Fe Desk with a circle hole and Al Desk cover remain to be described. The Fe Desk is

21

2 mm thick, and has 95.1×95.1 cm in x and y, the radius of the hole was 13 cm. The desk

was placed at (0,1.95,−10.7 mm). Al Desk proportions were 37×36×1 cm. It was placed

above the hole at point (0,30.5,−10.1 cm).

2.2.4 Detectors

The detectors were fixed to a Board which was attached to a Table. Dimensions of the Table

and Board were 1.5 m× 1 cm× 30 cm and 20 cm× 20 cm× 1 cm. The Table material was

G4_POLYETHYLENE and the G4_PLEXIGLASS was assigned to the Board. The Table

was placed at (−60,−15.5,17 cm), the Board at (0,0,−0.55 cm). The view of the region

with detectors is shown in Figure 2.6. In this picture the Board hides the detectors, which

are placed before the Board.

Figure 2.6: View of the detector region.

The detectors were stored in a Box (see Figure 1.1) during the experiment. These boxes

were not simulated. Just a 12 × 12 × 0.1 cm lid was placed before detectors for the lid

of the Box. Also the real xy sizes of the detectors were not simulated, as wobbling magnets

were not included in the beam description. The whole plane 20×20 cm of thickness of given

detector was scored.

The simulations were performed only for Page and TD1, the first and the second layer

of the pile in the box. Positions of detectors in the box, together with their thicknesses, are

22

shown in Figure 2.7. As the particle tracks are visible only on the surface, we set the thick-

ness of the scoring layer to 100 µm for both the Page and TD1. The material of the detec-

tors was G4_PLEXIGLASS or G4_WATER. Hence the experimental results were calibrated

to LET in water, G4_WATER was used in a detector volume, where the LET was scored.

G4_PLEXIGLASS was used for those remaining detectors, where LET was not scored.

Figure 2.7: Positions of detectors.

Figure 2.8: View of the detector region with Water Tank.

Some simulations of depth dose distribution were calculated in a Water Tank (cylinder

radius = 10 cm, height = 26 cm), placed exactly at (0,0,0) (see Figure 2.8).

The beamline geometry ended with a concrete Dump. The beamline room was sur-

rounded by walls (see Figure 2.9). For walls and Dump the G4_CONCRETE material class

was used. The thickness of walls was 1 m. Dimensions of the walls are written in the Ta-

23

ble 2.1. There was a recess in the frontal wall of size 200×219×110 cm.

Table 2.1: Dimension of the Walls. Back Wall is the wall on the Dump side of the beamline.

Wall name x [cm] y [cm] z [cm]Wall 6 (Floor) 878 100 1577Wall 5 (Ceiling) 878 100 1220Wall 4 (Back Wall) 878 601 100Wall 2,3 (Lateral) 100 601 870Wall 1 (Front) 878 601 250

Figure 2.9: Beamline and the walls.

24

2.3 Spread out Bragg peak

The narrow monoenergetic Bragg peak is not suitable for cancer treatment. The elementary

peak needs to be spread in depth to obtain a uniform depth-dose distribution within the target

volume. There are several methods to spread the dose in depth which are currently used

at the ion therapy facilities; there are passive and active scanning methods.

Conventional passive techniques reach the uniform dose distribution in depth by modu-

lation of energy with certain layer of material. A range modulation wheel or ridge filter is

typically used. The lateral spread of the beam is reached by scattering or wobbling. Scat-

tering exploits one or more scatter foils, wobbling uses magnets to wiggle the beam and

to form the broad beam. These passive broadbeam techniques have disadvantage of produc-

ing a fixed energy spectrum [33]. For each width of spread out Bragg peak (SOBP) a special

ridge filter is needed and the sparing of healthy tissue is not optimal.

The active spot scanning and raster scanning techniques were invented to overcome this

drawback. The active scanning is applied at PSI (Paul Sherer Institute) for the protons and

for the carbon ions at GSI (Gesselshaft für Schwerionenforschung mbH) [33]. Also patients

at the Proton Therapy Center in Prague are successfully treated with active pencil beam

scanning. The pencil beam scans the tumour layer by layer. To skip from the one layer

to another, the energy modulation is needed. This is the best method to spare the healthy

tissue before the target volume. Because it takes time to scan whole volume, the elimination

of movements during irradiation is more important in comparison with passive methods,

in which the dose is delivered to the whole volume at the same time.

At NIRS in Japan the combination of both techniques was studied. This method is

called slice-scanning technique and it was described for instance in [33]. The lateral spread

of the beam is created by wobbling magnets, however the beam is spread in depth only

slightly by a ridge filter. It results in application of high dose slice. A combination of such

slices is then used to irradiate wider high dose region.

In this work we will focus on describing the passive ridge filter technique to obtain SOBP.

The simulated SOBP at NIRS in Chiba was created by the ridge filter. The utilization of range

modulator at NIRS was described in the reference [34]. The wobbling magnets are used

at this facility to spread the beam laterally.

Marginal but interesting are attempts to use laser accelerated protons or ions in radio-

therapy. It might get into clinical practice in the future. Laser accerelated beams are not mo-

25

noenergetic. In the article [35] authors exploited the Geant4 simulations to analyze SOBP

geometries in such beams. They found configurations which could produce SOBP within

one laser shot. For more details the reader is referred to [35].

2.3.1 Ridge filter

The ridge filter is collection of ridge bars. The cross-section shape of such ridge bar is shown

in the Figure 2.10

0.3 0.2 0.1 0.0 0.1 0.2 0.3Width [mm]

0

5

10

15

20

25

30

Alu

min

ium

thic

kness

[m

m]

Figure 2.10: Transverse cross-section of single ridge filter bar.

The formation of proton SOBP by superimposing several pristine Bragg curves was de-

scribed in [36]. It is a difficult task to obtain the weights of the elementary Bragg peaks

to create the resulting SOBP. An analytical approximation of SOBP curve as weighted

superposition of several elementary Bragg peaks was published in [37]. This results for

proton beam was extended in [38]. The authors David Jette and Welmin Chen exploited

the MCNPX Monte Carlo track-structure code and results from [37] and tested the parame-

ters of the model.

26

A ridge filter design method for proton beam at Hyogo Ion beam medical center is de-

scribed also in [39]. The main ideas used in this work came out from this article.

However there is a significant difference between the proton SOBP and the carbon ion

SOBP. For protons the constant relative biological effectiveness (RBE) assumption is suf-

ficient, because the protons RBE varies only slightly [39]. But the relative biological ef-

fectiveness varies greatly along the carbon ion track. With decreasing energy of the ion

(increasing depth) the RBE increases to the maximum in Bragg peak region. Thus the phys-

ical dose must decrease to ensure the biological dose is constant along the track in the SOBP

region 2.11. Direct comparison of RBE at proton and carbon spread out Bragg peaks can be

found in the article of Jan J. Wilkens and Uwe Oelfke [40].

Figure 2.11: Difference between biological dose and physical dose due to variable RBEin carbon beam [41].

Another difference between ions and protons is that the proton Bragg peak is wider than

the carbon ion peak. That leads to higher requirements on precision of ridge filter manufac-

ture. In [42] was described an improvement of SOBP flatness with combination of a simpli-

fied ridge filter and a ripple filter at NIRS. They replaced former ridge filter with 101 steps

with a ridge filter with only 31 steps. The ripple filter placed perpendicularly to the ridge

filter bars was used to smooth the depth dose distribution. The ripple filter slightly broad-

ens the single energy Bragg peak and the ridge filter spread out the beam to final SOBP.

Obviously it is easier to manufacture the ridge filter with 31 steps than the one with 101.

27

2.3.2 Ridge filter reconstruction procedure

The SOBP is formed as a weighted superposition of pristine Bragg peaks. Thus the physical

dose at a point in a SOBP region D(x,y,z) is given by superimposing dose contributions

from the elementary Bragg peaks with the appropriate weights as follows

D(x,y,z) = ∑i

wiBi(x,y,z), (2.1)

where Bi is the ith elementary Bragg peak, and wi is the ith weight of this curve. The weights

define the ridge filter shape [39].

source Al plate water phantom

PMMA filters

Figure 2.12: The view of geometry for the pristine Bragg peak simulation. The thicknessof Al plates varied from 0 to 31 mm. All PMMA filters were retracted and the beam did notpass through them.

Elementary Bragg curves calculations

In order to get elementary Bragg peaks, the geometry of the beamline was changed slightly.

In the detector region the cylindric water phantom was placed. This phantom diameter was

26 cm height and 20 cm in diameter and it was filled with G4_WATER material. It was

placed on the z-axis so the front side was at point 0 on the z-axis. The view of geometry

for this special situation is shown in the Figure 2.12. The 32 simulations were run with 105

primaries of C 12 with 0, 1, . . . , 31 mm thick aluminium slices, which were placed into

the beam at the expected position of the ridge filter z = −420 cm. The deposited energy

in water phantom was scored and written into a ROOT file for further analysis. The built-in

Geant4 function GetTotalEnergyDeposit() was used for this case.

A similar problem was solved by Sakama et al. in [41] in order to design a ridge fil-

28

ter at GHMC in Japan (Gunma Heavy Ion Medical Center of Gunma University). GHMC

is a compact ion therapy facility in a hospital environment. They utilized Geant4 simula-

tion tool-kit to calculate elementary Bragg curves with aluminium plates. They simulated

the beam with initial energy from 290 MeV/n to 400 MeV/n. The thickness of aluminium

plates which the beam passed through were from 0 to 60 mm with 5 mm step.

Using a ROOT [8] framework the deposits from the events within the central cylinder

of 2 cm diameter were evaluated and pristine depth-dose histograms were drawn and ex-

ported to text files. A selection of these curves is drawn in the Figure 2.13.

0 20 40 60 80 100 120 140 160Depth in water [mm]

0

50

100

150

200

250

300

Dose

[arb

itra

ry u

nit

s]

0 mm Al (147.1 mm)

2 mm Al (142.7 mm)

4 mm Al (138.4 mm)

6 mm Al (134.1 mm)

8 mm Al (129.9 mm)

10 mm Al (125.5 mm)

12 mm Al (121.2 mm)

14 mm Al (116.9 mm)

16 mm Al (112.7 mm)

18 mm Al (108.3 mm)

20 mm Al (104.1 mm)

22 mm Al (99.8 mm)

24 mm Al (95.5 mm)

26 mm Al (91.2 mm)

28 mm Al (86.9 mm)

Figure 2.13: Depth dose distributions in cylindric water phantom shielded by an aluminiumlayer of given thickness (0–31 mm). On x-axis is depth in water phantom in mm, the y-axisis dose in arbitrary units. In legend there is written which curve corresponds to a giventhickness of aluminium layer, the position of the maximum of the Bragg peak is writtenin brackets. Each curve was obtained by separate simulation with 105 primary particles.

Subsequent analysis was performed in Python. The calculation of the coefficients for

each pristine Bragg peak was done by the simplest conceivable algorithm. Firstly the exper-

imental SOBP was interpolated by linear interpolation, let denote this function as S(x). Let

B0 be the pristine Bragg peak with no Al plate, B1 curve obtained with 1 mm Al plate etc.

Thus the maximum of B0 lies deeper than the maximum of B1. Let i j be the index of the max-

29

imal bin of the Bragg curve B j. The coefficient α0 for B0 was obtained from the following

formula

α0 =S(i0)

B0(i0). (2.2)

Let f k be a residue in the kth step defined by

f k = S−α0 ·B0. (2.3)

Then the coefficient αk is defined in the kth step

αk =f (ik)

Bk(ik). (2.4)

Then αk denotes the fraction of given thickness of aluminium. Finally, the coefficients

were manually fine-tuned to get the best agreement with experimental distribution.

The method causes an overestimation of the dose with increasing depth due to a tail

behind a maximum of each pristine Bragg peak.

Better results can be given by the minimization of a cost function [39]

Q2 = ∑j(S( j)−∑

kαkBk( j))2. (2.5)

However, we failed to implement this method due to time. The main problem we faced

with the SciPy module was that the calculated coefficients were negative. Obviously

the weights of the pristine Bragg peaks must be non-negative, since delivering of negative

dose is impossible.

30

2.4 Linear energy transfer calculation

There are only few references dedicated to calculation of LET are available. First of all it is

the article by authors of Geant4 Hadrontherapy example [43]. Other Monte Carlo calcula-

tions of LET were studied also in a paper [44]. However, the authors exploited Monte Carlo

to get energy spectra and LET was calculated from the spectrum and a table of stopping

power. In both, the quantities "mean LET" or "dose averaged LET" were calculated in order

to obtain one number which describes the particle beam.

In this work we are interested in LET of every charged particle (except electrons, because

they are not detected by the TEDs) and in creating the LET spectrum. Therefore the follow-

ing method of LET calculation was implemented. The code, which solves this issue, was

written into the B1SteppingAction class.

When the particle entered the scoring volume the program started to count the step length

and energy loss at each step. Particles are transported over a few steps in the detector volume.

When the particle was leaving detector, LET was evaluated according to the formula

LET =total energy loss in the volume = the sum of energy losses at each step

total track length in the volume = the sum of step lengths(2.6)

This is written into the output file for each ion passing through scoring volume. This

quantity is the unrestricted linear energy transfer (stopping power).

Below there are listed all properties of incident particles in the scoring volume which

were written into the output file:

• LET [keV/µm].

• Energy loss in the scoring volume (the difference between the particle’s kinetic energy

when entering and leaving the scoring volume) [MeV].

• The name of the particle (proton, alpha, electron, C 12 ion etc.).

• The initial kinetic energy in the volume [MeV].

• The total length of the trajectory within the volume [mm].

• The total energy deposit of the particle in the volume (less or equal to the energy loss)

[MeV].

31

• The initial position of the particle or the position of particle birth in case it was created

inside volume [mm].

The G4Step class offers methods suitable to calculate LET, G4Step::GetTotalEnergy-

Deposit() and G4Step::GetStepLength(). One just need to divide these two values and

obtains LET. In our calculations the other method of LET calculation was chosen instead

of the total energy deposit.

The method G4Step::GetTotalEnergyDeposit() returns

1. the total energy deposit during the step is the sum of the energy deposited by the energy

loss process and

2. the energy lost by secondaries which have not been generated because each of their

energies was below the cut threshold [45].

However as mentioned before, detectors were calibrated to unrestricted linear energy

transfer in water. Therefore for this application is better to use the total energy loss of the par-

ticle instead of the deposit.

The energy loss of the particle in the scoring volume was calculated as the sum of differ-

ences of the kinetic energy of particle at the beginning and the end of each step. The code

lines handling this are listed below

G4Track * t r a c k = s t e p −>GetTrack ( ) ;

c o n s t G4StepPo in t * p o s t S t e p P o i n t = s t e p −>G e t P o s t S t e p P o i n t ( ) ;

c o n s t G4StepPo in t * p r e S t e p P o i n t = s t e p −>G e t P r e S t e p P o i n t ( ) ;

G4 in t t r a c k I D = t r a c k −>GetTrackID ( ) ;

fEne rgyLoss [ t r a c k I D ]+= p r e S t e p P o i n t −>G e t K i n e t i c E n e r g y ( )

−p o s t S t e p P o i n t −>G e t K i n e t i c E n e r g y ( ) ;

Each particle track is labeled by a trackID. The quantities were stored into C++ maps and

written into the output file for future analysis.

32

2.5 Data analysis

All histograms and graphs were plotted using ROOT framework [8] and Python 3.3 and

Python’s modules, especially matplotlib [5], NumPy and SciPy [6, 7]. Matplotlib module

enables drawing graphs and figures, NumPy handles matrices and vectors (like Matlab) and

SciPy contains libraries for numerous operations with data such as fitting, interpolating and

other mathematical tools.

Data processing can be time demanding. To make it automatic, we used Python to gene-

rate and run ROOT scripts for drawing all the histograms with the LET spectra. Depth

dose distributions were drawn using matplotlib and NumPy modules. We used Python also

to generate the tables.

33

Chapter 3

Results

Geant4 application describing the beamline and the experiment geometry was used to repro-

duce and complement experimental measurements as described in sections 2.1 and 2.2. We

calculated depth dose distributions in a water phantom and LET spectra in volumes corre-

sponding to detectors TD1 and Page.

All calculations were run with physics list FTF_BIC 2.0 (see section 2.1). Calculations

of depth-dose distributions in the water phantom were calculated with 105 primary C 12

ions, presented LET spectra with 2×105 C 12 primaries. LET spectra were scaled according

to the integral within the experimental detection range.

All experimental data, which are presented in this work, were kindly provided by Katerina

Pachnerová Brabcová.

3.1 Depth dose distributions

Depth dose distributions for monoenergetic beams 290 MeV/n and 400 MeV/n in the water

phantom are shown in Figures 3.1 and 3.2 respectively. The data are normalized to the value

at the 0 mm depth. Simulation of the depth dose distribution of MONO 290 MeV/n is

compared to the experimental response in the detector Page and TD1 is shown in Figure 3.1.

Depth dose distributions of the monoenergetic beam 400 MeV/n is compared to the response

of a reference dosimeter (ionization chamber), which was provided by the HIMAC staff,

since the depth dose curve data from TEDs are not available.

Depth dose distributions of the SOBP 290 MeV/n are shown in the section 3.1.3.

34

3.1.1 MONO 290 MeV/n

The maximum of experimental dose was at position 147.9 mm and the simulated curve had

its maximum at point 150.4 mm. This difference was 2.5 mm. However the experimental

points were sparsely distributed along the curve. To better estimate the shift, sums of square

differences χ2 for all experimental points and for shifts s with step 0.1 mm were calculated.

For each shift we obtained a value. Then the value s with minimum χ2 was the shift, when

the experimental data fitted the simulated curve. The χ2 values for several shifts are written

in the Table 3.1. It can be deducted that the closest match was found for 2.2 mm.

Table 3.1: Sum of the square differences of the experimental and the simulated pointson the Bragg curve 290 MeV/n χ2 for several values of the shift s.

s [mm] 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5χ2 9.3 6.3 4.3 2.9 2.3 2.9 3.5 3.5

0 20 40 60 80 100 120 140 160

Depth in water [mm]

0

1

2

3

4

5

6

Dose

[arb

itra

ry u

nit

s]

Depth dose distribution in water phantom, C12 290 MeV/n

Geant4-290_FTF_BIC 2.0

PageTD1

Figure 3.1: Depth dose distribution of MONO 290 MeV/n C 12 beam in the water phantomcalculated with the physics list FTF_BIC 2.0 and the comparison with the dose measure-ments with the detectors Page and TD1 (provided by K. Pachnerová Brabcová [9]).

35


Similarly as in the previous section, we tried to estimate the shift between the curves.

The calculated values of the quantity χ2 as defined in the section 3.1.1 are written in the Ta-

ble 3.2. The closest match was found for 0.77 mm.

Table 3.2: Sum of the square differences of the experimental and the simulated pointson the Bragg curve 400 MeV/n χ2 for several values of the shift s.

s [mm] 0.60 0.70 0.72 0.74 0.76 0.77 0.78 0.80 0.90χ2 2.80 1.14 0.98 0.87 0.83 0.81 0.83 0.89 1.75

Figure 3.2: Depth dose distribution of MONO 400 MeV/n C 12 beam in the water phan-tom calculated with the physics list FTF_BIC 2.0 and the experimental data measured bythe ionization chamber (provided by the HIMAC staff). The numbers in the graph are waterequivalent thicknesses of the PMMA filters in mm (real thicknesses of the PMMA filtersin mm are in brackets) for which the LET spectra were calculated and compared to the ex-periment.

36

3.1.3 SOBP 290 MeV/n

The final reconstructed shape of the ridge filter is presented in the Figure 3.3 and the resulting

depth-dose distribution in the water phantom with this ridge filter is shown in the Figure 3.4.

In the Figure 3.5 are also drawn depth dose distributions from the experimental response

of the Page and the simulated response in the scoring volume corresponding to the Page.

Figure 3.3: The final ridge filter shape as described in section 2.3.1. There are 31 bars with5 mm spacing. The width in x-axis is 15.5 cm and 15 cm is the y-axis.

Figure 3.4: Depth dose distributions of SOBP 290 MeV/n in the cylindric water phantom.Datasets are normalized to the 0 mm depth. Experimental data from a reference dosimeterwere kindly provided by K. Pachnerová Brabcová [9].

37

0 20 40 60 80 100 120 140 160Depth in water [mm]

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Dose

[arb

itra

ry u

nit

s]

Computed data

Reference dosimeter

Experiment Page

Figure 3.5: Depth dose distribution of 290 MeV/n SOBP carbon beam. The simulation pointsare the scored dose in the volume corresponding to the detector Page behind the given waterequivalent thickness of PMMA material. There are plotted the experimental results fromthe reference dosimeter and the results from the detector Page (provided by K. PachnerováBrabcová) [9].

38

3.2 LET spectra

Following subsections contain the simulated LET spectra of heavy charged fragments which

were compared to the Page and TD1 response as measured at HIMAC [1, 9]. Spectra

of MONO 290 MeV/n in TD1 and Page are shown in the subsections 3.2.1 and 3.2.2,

spectra of MONO 400 MeV/n in TD1 in subsection 3.2.3 and finally spectra of SOBP

290 MeV/n in Page are shown in section 3.2.4. The spectra are plotted in linear and log-

arithmic scales together with the experimental data [1, 9]. The experimental spectra were

provided with non-equidistant binning; we have reprocessed them into equidistant bins.

The values were randomly distributed within the bin and filled into the new histogram. All

the spectra were normalized to the integral of the experimental spectrum in the experimen-

tal range. The experimental spectra are plotted without the error bars, however the relative

errors of the values in the experimental bins are between 5% and 12% (from private commu-

nication with K. Pachnerová Brabcová). Calculated spectra are plotted with the error bars,

length of which are equal to the square root of the bin content.

The FTF_BIC 2.0 physics list was used for all the calculations and the production thresh-

old (cut off value) was set to 5 µm. This production cut corresponded to the following energy

cuts in water: 990 eV for photons, 4.36192 keV for electrons, 4.31172 keV for positrons,

500 eV for protons; and in plexiglass: 990 eV for photons, 5.80154 keV for electrons,

5.66266 keV for positrons, 500 eV for protons. These energy thresholds were not lim-

ited only by setting the production threshold to 5 µm, but also by ranges of applicability

of the employed models.

All the spectra were scored in a 100 µm surface layer of the detector TD1 (0.8 mm thick)

or the detector Page (0.5 mm thick) as described in the section 2.2.4.

39

3.2.1 LET spectra of MONO 290 MeV/n in TD1

LET [keV/micrometer]-110 1 10 210 310

Nu

mb

er o

f ev

ents

[-]

-210

-110

1

10

210

310

410Legend

TD1Geant4

C12

BBeHeH

LiC+N+O

LET of fragments C12 290 MeV/n, 0.0 mm PMMA

(a) Spectra of unrestricted LET in water in TD1–overview.

LET [keV/micrometer]0 10 20 30 40 50 60 70 80 90 100

Nu

mb

er o

f ev

ents

[-]

-210

-110

1

10

210

310

410Legend

TD1Geant4


(b) Spectra of unrestricted LET in water in TD1–detailed view.

Figure 3.6: Spectra of unrestricted LET in water of the monoenergetic unshielded C 12beam 290 MeV/n. The blue line represents the experimental results from the detector TD1.The black crosses with the error bars are the Geant4 results. The spectrum was calculatedusing 2×105 primaries and the physics list FTF_BIC 2.0.

40


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4

C12

BBe

HeH

Li

C+N+O




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4



Figure 3.7: Spectra of unrestricted LET in water of the monoenergetic C 12 beam 290 MeV/nshielded by 54.5 mm of PMMA. The blue line represents the experimental results fromthe detector TD1. The black crosses with the error bars are the Geant4 results. The spectrumwas calculated using 2×105 primaries and the physics list FTF_BIC 2.0.

41


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4

C12

BBe

HeHLi

C+N+O




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendTD1Geant4



Figure 3.8: Spectra of unrestricted LET in water of the monoenergetic C 12 beam 290 MeV/nshielded by 123 mm of PMMA (equivalent of 142.53 mm of water). The blue line is experi-mental data from detector TD1. The black crosses with the error bars are the Geant4 results.The spectrum was calculated using 2×105 primaries and the physics list FTF_BIC 2.0.

42

3.2.2 LET spectra of MONO 290 MeV/n in Page


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

LegendPageGeant4

C12

BBeHeH

LiC+N+O


(a) Spectra of unrestricted LET in water in Page–overview.


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

PageGeant4


(b) Spectra of unrestricted LET in water in Page–detailed view.

Figure 3.9: Spectra of unrestricted LET in water of the monoenergetic unshielded C 12beam 290 MeV/n. The blue line represents the experimental results from the detector Page.The black crosses with the error bars are the Geant4 results. The spectrum was calculatedusing 2×105 primaries and the physics list FTF_BIC 2.0.

43


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

PageGeant4

C12

BBe

HeH

Li

C+N+O




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

LegendPageGeant4



Figure 3.10: Spectra of unrestricted LET in water of the monoenergetic C 12 beam290 MeV/n shielded by 90.5 mm of PMMA (equivalent of 104.93 mm of water). The blueline represents the experimental results from the detector Page. The black crosses with the er-ror bars are the Geant4 results. The spectrum was calculated using 2× 105 primaries andthe physics list FTF_BIC 2.0.

44


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410Legend

PageGeant4

C12

BBe

HeHLi

C+N+O




Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510Legend

PageGeant4



Figure 3.11: Spectra of unrestricted LET in water of the monoenergetic C 12 beam290 MeV/n shielded by 123 mm of PMMA (equivalent of 142.93 mm of water). The blue linerepresents the experimental results from the detector Page. The black crosses with the er-ror bars are the Geant4 results. The spectrum was calculated using 2× 105 primaries andthe physics list FTF_BIC 2.0.

45

3.2.3 LET spectra of MONO 400 MeV/n in TD1


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4

C12

BBeHeH

LiC+N+O




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4



Figure 3.12: Spectra of unrestricted LET in water of the monoenergetic unshielded C 12beam 400 MeV/n. The blue continuous line is experimental data from detector TD1.The black crosses with the error bars are the Geant4 results. The spectrum was calculatedusing 2×105 primaries of C 12 and the physics list FTF_BIC 2.0.

46


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

TD1Geant4

C12

BBe

HeH

Li

C+N+O




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Figure 3.13: Spectra of unrestricted LET in water of the monoenergetic C 12 beam400 MeV/n shielded by 86 mm of PMMA. The blue continuous line is experimental datafrom detector TD1. The black crosses with the error bars are the Geant4 results. The spec-trum was calculated using 2×105 primaries of C 12 and the physics list FTF_BIC 2.0.

47


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410 LegendTD1Geant4

C12

BBe

HeH

Li

C+N+O



LET [keV/micrometer]0 50 100 150 200 250 300

Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendTD1Geant4



Figure 3.14: Spectra of unrestricted LET in water of the monoenergetic C 12 beam400 MeV/n shielded by 217.5 mm of PMMA. The blue continuous line is experimental datafrom detector TD1. The black crosses with the error bars are the Geant4 results. The spec-trum was calculated using 2×105 primaries of C 12 and the physics list FTF_BIC 2.0.

48

3.2.4 LET spectra SOBP 290 MeV/n in Page


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

LegendPageGeant4

C12

BBeHeH Li

C+N+O

LET of fragments C12 SOBP 290 MeV/n, 0.0 mm PMMA



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410Legend

PageGeant4



Figure 3.15: LET spectra of unshielded C 12 beam SOBP 290 MeV/n. The blue line rep-resents the experimental results from the detector Page. The spectrum was calculated using2×105 primaries and the physics list FTF_BIC 2.0.

49


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

LegendPageGeant4

C12

BBe

HeHLi C+N+O




Nu

mb

er o

f ev

ents

[-]

10

210

310

410

510 LegendPageGeant4



Figure 3.16: LET spectra of C 12 beam 290 MeV/n SOBP shielded by 117.5 mm of PMMA(equivalent of 136.34 mm of water). The blue line represents the experimental results fromthe detector Page. The spectrum was calculated using 2×105 primaries and the physics listFTF_BIC 2.0.

50


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410Legend

PageGeant4BBe

HeHLi

C




Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendPageGeant4



Figure 3.17: LET spectra of C 12 beam 290 MeV/n SOBP shielded by 127.5 mm of PMMA(equivalent of 147.92 mm of water). The blue line represents the experimental results fromthe detector Page. The spectrum was calculated using 2×105 primaries and the physics listFTF_BIC 2.0.

51

3.3 Comparison of LET spectra in water and plexiglass

The spectra of unrestricted LET presented in [25] were calculated in the G4_PLEXIGLASS.

However the TEDs were calibrated to the LET in water. Thus the spectra presented in this

thesis were calculated in the volumes filled with G4_WATER. Differences between the spec-

tra of the unrestricted LET in water and plexiglass are presented in this section. The spectra

of the fragments scored in the same solid filled with G4_WATER and G4_PLEXIGLASS

are drawn in the Figure 3.18. They were calculated behind 123 mm of PMMA (equivalent

of 142.53 mm of water). The difference is visible. The positions of the main peak were

52.5 keV/µm in water and 62.5 keV/µm in the plexiglass. The difference is 19%. Density

of the G4_WATER is 1000 kg/m3, density of G4_PLEXIGLASS is 1190 kg/m3. We tried

to multiply the LET of the particles in water by the factor 1.19 to test if the diffence can be

attributed to effect of density. The resulting comparison with the spectrum of the particles in

plexiglass is drawn in the Figure 3.19. A perfect agreement is visible.


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendWater Plexiglass

LET of fragments C12 290 MeV/n, 123 mm PMMA

Figure 3.18: Comparison of the LET spectra calculated in plexiglass and water. These calcu-lation were run for 2×105 primaries in the 100 µm thick layer, for the monoenergetic beam290 MeV/n shielded with 123 mm of PMMA. The spectra were calculated with 2× 105

primaries of C 12 and the physics list FTF_BIC 2.0.

52


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendWater Plexiglass

LET of fragments C12 290 MeV/n, 123 mm PMMA

Figure 3.19: Spectra of unrestricted LET multiplied by 1.19 calculated in water and compar-ison with the spectrum in plexiglass.

3.4 LET dependence on depth

In the Figure 3.20 there are plotted the calculated LET spectra with increasing thickness

of the PMMA shielding. It can be seen that the positions of the main peak shift to the higher

LET values with increasing depth (and decreasing energy of carbon ion). For 129 mm

of PMMA the carbon ion peak was not present anymore, because the carbon ions stopped

before they got into the scoring volume. These calculations were scored in the volume cor-

responding to the Page detector using 2×105 primary C 12 ions for each thickness.

The positions of the maximum of the carbon ion peak for several thicknesses of PMMA

filters are written in the Table 3.3.

Table 3.3: Positions of the maximum of the C 12 peak of 290 MeV/n beam behindgiven thickness of binary PMMA filters. Calculations were executed with physics listFTF_BIC 2.0, production threshold 5 µm and for 2×105 primaries.

PMMA thickness [mm] 0.0 54.5 90.5 112.0 119.0 123.0 127.0Water equivalent [mm] 0.0 63.26 104.93 129.81 138.02 142.53 147.29Peak maximum [keV/µm] 12.06 15.14 20.52 30.01 39.16 51.09 105.19

53

LET [keV/micrometer]1 10 210 310

Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

PMMA (water) [mm]

0 (0.0)

90.5 (104.93)

112 (129.81)

123 (142.53)

127 (147.29)

129 (150.15)

LET spectra behind several filters, FTF_BIC 2.0

Figure 3.20: Calculated LET spectra of 290 MeV/n beam behind several depthsof the PMMA filter. Depths and their water equivalent thicknesses are written in the legend.

3.5 Fraction of detected particles

Here we will present the estimates of fractions of the detected particles, the particles with LET

below and above the detection ranges. The detections ranges were calculated from the ex-

perimental spectra. The lower threshold of the detection range was set to the lower boundary

of the first non-zero bin and the upper threshold as the upper boundary of the last non-

zero bin. Then, all the particles were divided into three groups. The simulated particles

with the LET below the lower detection threshold were put to the first group, the second

group consisted of particles in the operational range of the detector, and the last group

contained particles with the LET above the biggest LET value in the experimental spec-

trum. The lower boundaries were 9.46 keV/µm for the detector TD1 and 11.02 keV/µm for

the detector Page. The upper boundaries depended on the highest LET bin in the experi-

mental spectrum. The upper boundaries of the last bin with the data for the monoenergetic

set-ups are written in the Table 3.4. The SOBP 290 MeV/n upper boundary was always

443.3 keV/µm.

Table 3.4: The highest LET bin in the experimental spectrum for the studied set-ups andPMMA shielding [mm]. Values are in keV/µm.

Detector andbeam energy

PMMA thickness0.0 54.5 86.0 90.5 112.0 119.0 123.0 217.5

Page 290 MeV/n 269.3 148.3 – 425.0 289.8 443.3 443.3 –TD1 290 MeV/n 25.4 292.2 – 307.8 344.8 344.8 344.8 –TD1 400 MeV/n 300.6 – 245.2 – – – – 344.7

54

The calculated fractions of the particles and energy deposits were written into the Tables

3.5, 3.6, 3.7, 3.8 for the monoenergetic beams 290 MeV/n in TD1 and Page, 400 MeV/n

in TD1 and SOBP 290 MeV/n in Page respectively. The columns Nb, Nw and Na contain

percentage fractions of the number of the particles, and the columns Db, Dw and Da contain

percentage fractions of the dose deposit of the particles from the given group. The frac-

tions of dose from the electrons are in the column De. The one letter indexes correspond

to the longer ones in Figures 3.21, 3.22, 3.23, 3.24. Db is the same as Dbelow, Dw as Dwithin,

Da as Dabove and De as Delectrons. The Figures 3.21, 3.22, 3.23, 3.24 show graphic represen-

tations of the data from the Tables 3.5, 3.6, 3.7, 3.8.

Table 3.5: Fractions of fluence and dose for the beam MONO 290 MeV/n and the detectorTD1 ±1σ. The columns Nb and Db contain the fractions of fluence and dose for the particlesbelow the lowest bin in experimental spectrum, Nw and Dw within and Na and Da correspondto particles above the highest experimental bin. See the graphic representation of the datain the Figure 3.21.

PMMA[mm]

Nb [%] Db [%] Nw [%] Dw [%] Na [%] Da [%] De [%]

0.0 5.8±0.1 0.9±0.1 94.0±0.3 72.1±0.2 0.2±0.1 0.9±0.1 26.2±0.254.5 42.5±0.2 4.7±0.1 57.5±0.2 69.5±0.2 0.1±0.1 0.3±0.1 25.4±0.190.5 53.8±0.2 6.0±0.1 46.2±0.2 69.2±0.2 0.1±0.1 0.4±0.1 24.4±0.1112.0 58.7±0.2 5.5±0.1 41.3±0.2 70.9±0.3 0.1±0.1 0.7±0.1 22.9±0.1119.0 60.5±0.2 4.9±0.1 39.4±0.2 72.5±0.3 0.1±0.1 0.9±0.1 21.8±0.1123.0 61.6±0.2 4.2±0.1 38.2±0.2 74.2±0.3 0.1±0.1 1.1±0.1 20.6±0.1

Table 3.6: Fractions of fluence and dose for the beam MONO 290 MeV/n and the detectorPage ±1σ. Columns Nb and Db contain the fractions of fluence and dose for the particlesbelow the lowest bin in the experimental spectrum, Nw and Dw within and Na and Da corre-spond to particles above the highest experimental bin. See the graphic representation of thesedata in the Figure 3.22.

PMMA[mm]

Nb [%] Db [%] Nw [%] Dw [%] Na [%] Da [%] De [%]

0.0 9.8±0.1 4.5±0.1 90.1±0.3 69.0±0.2 0.1±0.1 0.3±0.1 26.1±0.254.5 43.7±0.2 5.9±0.1 56.2±0.2 68.2±0.2 0.1±0.1 0.6±0.1 25.4±0.190.5 54.1±0.2 6.3±0.1 45.8±0.2 68.9±0.2 0.1±0.1 0.3±0.1 24.5±0.1112.0 58.8±0.2 5.7±0.1 41.1±0.2 70.7±0.3 0.1±0.1 0.5±0.1 23.0±0.1119.0 60.8±0.2 5.1±0.1 39.1±0.2 72.1±0.3 0.1±0.1 1.0±0.1 21.8±0.1123.0 62.0±0.2 4.5±0.1 37.9±0.2 73.9±0.3 0.1±0.1 0.7±0.1 20.8±0.1

55

Table 3.7: Fractions of fluence and dose for the beam MONO 400 MeV/n and the detectorTD1 ±1σ. Columns Nb and Db contain fractions of fluence and dose for the particles belowthe lowest bin in the experimental spectrum, Nw and Dw within and Na and Da correspondto the particles above the highest experimental bin. See the graphic representation of thesedata in the Figure 3.23).

PMMA[mm]

Nb [%] Db [%] Nw [%] Dw [%] Na [%] Da [%] De [%]

0.0 22.9±0.2 13.6±0.1 77.1±0.2 59.3±0.2 0.1±0.1 0.4±0.1 26.7±0.286.0 56.9±0.2 9.5±0.1 43.1±0.2 63.9±0.2 0.1±0.1 0.3±0.1 26.2±0.2

217.5 77.5±0.2 7.6±0.1 22.5±0.1 70.2±0.3 0.1±0.1 1.0±0.1 21.3±0.1

Table 3.8: Fractions of fluence and dose for the beam SOBP 290 MeV/n and the detectorPage ±1σ. Columns Nb and Db contain fractions of fluence and dose for the particles belowthe lowest bin in the experimental spectrum, Nw and Dw within and Na and Da correspondto particles above the highest experimental bin. See the graphic representation of these datain the Figure 3.24).

PMMA[mm]

Nb [%] Db [%] Nw [%] Dw [%] Na [%] Da [%] De [%]

0.0 6.3±0.1 0.9±0.1 93.7±0.3 72.9±0.2 0.1±0.1 0.2±0.1 26.0±0.2117.5 76.1±0.3 7.8±0.1 23.7±0.2 69.5±0.4 0.2±0.1 4.0±0.1 18.8±0.1127.5 92.8±0.3 31.1±0.3 7.1±0.1 43.4±0.5 0.1±0.1 6.9±0.1 18.7±0.2

0.0 54.5 90.5 112.0 119.0 123.0PMMA thickness [mm]

0

20

40

60

80

100

Num

ber

of

part

icle

s [%

] D

ose

[%

]

Beam C 12 290 MeV/n in volume TD1Nbelow

Nwithin

Nabove

Dbelow

Dwithin

Dabove

Delectrons

Figure 3.21: Fractions of fluence and dose from the particles with LET below (Nb, Db),within (Nw, Dw) and above (Na, Da) the detection range of the detector TD1 for severalthicknesses of the PMMA shielding and also fraction of dose from electrons (De). BeamC 12 MONO 290 MeV/n (see Table 3.5).

56

0.0 54.5 90.5 112.0 119.0 123.0PMMA thickness [mm]

0

20

40

60

80

100

Num

ber

of

part

icle

s [%

] D

ose

[%

]

Beam C 12 290 MeV/n in volume PageNbelow

Nwithin

Nabove

Dbelow

Dwithin

Dabove

Delectrons

Figure 3.22: Fractions of fluence and dose from the particles with LET below (Nb, Db),within (Nw, Dw) and above (Na, Da) the detection range of the detector Page for severalthicknesses of the PMMA shielding and also fraction of dose from electrons (De). BeamC 12 MONO 290 MeV/n (see Table 3.6).

0.0 86.0 217.5PMMA thickness [mm]

0

20

40

60

80

100

Num

ber

of

part

icle

s [%

] D

ose

[%

]

Beam C 12 400 MeV/n in volume TD1Nbelow

Nwithin

Nabove

Dbelow

Dwithin

Dabove

Delectrons

Figure 3.23: Fractions of fluence and dose from the particles with LET below (Nb, Db),within (Nw, Dw) and above (Na, Da) the detection range of the detector TD1 for severalthicknesses of the PMMA shielding and also fraction of dose from electrons (De). BeamC 12 MONO 400 MeV/n (see Table 3.7).

57

0.0 117.5 127.5PMMA thickness [mm]

0

20

40

60

80

100

Num

ber

of

part

icle

s [%

] D

ose

[%

]

Beam C 12 SOBP290 MeV/n in volume PageNbelow

Nwithin

Nabove

Dbelow

Dwithin

Dabove

Delectrons

Figure 3.24: Fractions of fluence and dose from the particles with LET below (Nb, Db),within (Nw, Dw) and above (Na, Da) the detection range of the detector TD1 for severalthicknesses of the PMMA shielding and also fraction of dose from electrons (De). BeamC 12 SOBP 290 MeV/n (see Table 3.8).

58

Chapter 4

Discussion

4.1 Depth dose distributions


The shift 2.2 mm between the depth dose distributions from the Page and the simulation,

as it was calculated in 3.1.1, could be solved by adding an additional shielding, equivalent

to 2.2 mm of water. This would point to a discrepancy between the description of the beam-

line as available and the real geometry. It is difficult to obtain the perfect and detailed descrip-

tion of the beamline. There were several objects on the beamline, for instance the aluminium

windows, the lid of the detector holder and the scatter filters through which the ions passed.

It is possible that the thicknesses of these objects were not set correctly. Also we can not

assure that the properties of the PMMA filters we used (density etc.), were exactly the same

as it was at the HIMAC. All these uncertainties together can cause the differences between

the simulated and experimental results. The effect of the shift of the Bragg peak on the LET

spectra results is described in further text.


There is a good visual agreement between the reference dosimeter data and the calculated

depth dose distribution in the Figure 3.2. The calculated shift between the data was 0.77 mm.

This means that additional equivalent of 0.77 mm of water would solve the shift of the posi-

tion of the Bragg peak. We just remark, that the shift 2.2 mm in the 290 MeV/n dose curve is

not comparable to the shift for 400 MeV. The experimental data were measured under various

conditions with various detectors, the scatter filters set-up was different etc.

59


Depth-dose distribution of the SOBP set-up was in a sufficient agreement with the experi-

ment for the purpose of our calculations. The SOBP curve was fitted to a depth dose distribu-

tion from reference dosimeter which consisted of 15 points. The first slight imprecision was

introduced using only the linear interpolation of these points to reconstruct the experimental

SOBP curve.

The other (and more serious) imprecision was that the real ridge filter bar consisted of 101

steps, but the simulated ridge filter consisted only from 32 steps (the thickness of ridge filter

was changing with a 0.1 mm step). It would have been better to use more steps to obtain

the smoother distribution. However in the Figure 3.5 are drawn the depth dose distributions

from simulated data, the points from the detector Page and also the points from the reference

dosimeter. There are differences between the reference dosimeter (ionization chamber) and

the Page results. In comparison to this dispersion, agreement in the depth dose distribution

was sufficient to the our calculations.

Better result could be obtained using better (an iterative) method to compose the SOBP

from the pristine Bragg peaks.

4.2 LET spectra

For all the spectra, there were disagreements in the region of the first bins of the experi-

mental spectra. These bins contain the content of the first experimental bin—the tracks with

the lowest detected LET. This content was spread during the rebinning of the experimental

histogram to the equidistant binning. The lowest LET particles (which are still detected)

leaves the smallest tracks. It is possible that some tracks with LET lower than the minimum

bin edge got visible during etching and then were added to this first bin. This bin can also

contain some dust or defects in the material, which were evaluated as particle tracks.

Regardless the first experimental bins, there was good agreement between the simulated

and experimental results. The uncertainties in the LET determination are difficult to estimate.

The statistical uncertainty of the experimental data are about 5–12% depending on the bin

content (from private communication with K. Pachnerová Brabcová).

An evaluation of all the uncertainties of the LET spectrometry with TEDs is described

in [13]. Even though the article discusses a different calibration, it can give an image of all

involved uncertainties. According to this article, the uncertainty due to the calibration can

60

reach 28% for the low LET particles.

Taking the uncertainty of the experimental data into consideration, the simulations are

in a good agreement to the experiment. However, there were issues, which need to be dis-

cussed in detail.


The positions of the main peak (corresponding to the C 12 ion) in the experiments and

the simulations (also for the spectra at the positions which were not shown in this work)

are written in the Table 4.1. The slight (3 keV/µm) difference between the experiment and

the simulation can be observed for the area before the Bragg peak. The reason of this dis-

agreement was not caused by the geometry, because LET of the primary particles varied

just a little at the plateau of the Bragg curve (see the Figure 4.1). Effect of the geometry

inaccuracy is getting more important in the region of the Bragg peak.

Table 4.1: Comparison of the positions of the maximum of the C 12 peak of 290 MeV/nbeam in experimental and calculated spectra for several thicknesses of binary PMMA filtersin detector TD1. Width of experimental bins were about 1–2 keV/µm, hence the error of thesevalues is approximately 2 keV/µm.

PMMA [mm] 0.0 54.5 90.5 112.0 119.0 123.0Experiment [keV/µm] 15.5 17.3 22.5 34.5 46.5 64.5Simulation [keV/µm] 12.5 15.8 19.5 31.5 40.5 52.5Difference [keV/µm] 3.0 2.5 3.0 3.0 6.0 8.0

The disagreement at the plateau (Figures 3.6, 3.7) can be explained by quite big 95% con-

fidence intervals in calibration of TEDs (Figure 1.4). These intervals are wider for the low

LET values. Hence the worse precision of TEDS in the low LET region could be expected.

Data in the columns with the positions of the maximum for the PMMA shielding (119 and

123 mm) differ more than the previous columns (6 keV/µm and 8 keV/µm). This difference

can be still explained by imprecision of the LET determination by the TEDs but also this

data were calculated close to the Bragg peak, thus the effect of the geometry imprecision

was stronger in comparison with the plateau of the dose curve.

This effect is also studied for 400 MeV/n beam in the subsection 4.2.2. The resulting

differences between the experiment and simulations were caused by combination of both.

We studied this effect. Comparison of the spectra for 123 mm PMMA shielding in the ex-

periment and simulations for 123.0, 123.5, 124.0, 124.5, 125.0 and 125.5 mm of PMMA are

61


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410 LegendTD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410 LegendTD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410 LegendTD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410 LegendTD1Geant4


Figure 4.1: Overview of the simulated LET spectra at different positions at the beginningof the Bragg curve of 290 MeV/n C 12 beam in TD1. The experimental spectrum is alwaysplotted for the unshielded beam. The thicknesses of PMMA shielding in the calculatedspectra were 0, 1, 2 and 4 mm.

shown in the Figure 4.2. Adding 1.5 mm of PMMA shielding shifted the peak in the spec-

trum to higher LET. For 124.5 mm there is a good visual agreement.

The calculated shift 2.2 mm of water as discussed in the section 4.1.1 does not exactly

correspond to 1.5 mm of PMMA. The difference between 123.0 and 124 mm of the PMMA

shielding is equivalent to approximately 1.9 mm of water. We did not calculate the spec-

tra between 124.5 and 125 mm, since the thinnest PMMA filter was 0.5 mm thick, hence

the difference is not exactly 0.3 mm. The difference was caused probably by imprecision

in thickness of the lid of the detector holder. The depth dose curve was calculated directly

in the water phantom with no lid in front of the water phantom.

Similar were the results calculated for the Page. Visually the experimental spectra were

shifted to higher LET according to the calculated spectra and the final result was worse

than in the detector TD1. To quantify the shift, the positions of the C 12 peak in the LET

spectrum and their differences are in the Table 4.2. Differences between the positions were

approximately 5–7 keV/µm. This was slightly worse in comparison with the TD1 results.

However it still matches within the margins of the experimental error, see the Figure 1.4.

62


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4



Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510Legend

TD1Geant4


Figure 4.2: Overview of the simulated LET spectra at different positions around Bragg peakof 290 MeV/n C 12 beam in TD1. The experimental spectrum is always for beam shielded by123 mm of PMMA. The thickness of PMMA shielding varies from 123.0 mm to 125.5 mmof PMMA with 0.5 mm step.

Table 4.2: Comparison of the positions of the maximum of the C 12 peak of 290 MeV/nbeam in experimental and calculated spectra for several thicknesses of binary PMMA filtersin detector Page. Width of all bins were about 1–2 keV/µm, so the error of these values isabout 2 keV/µm.

PMMA [mm] 0.0 54.5 90.5 112.0 119.0 123.0Experiment [keV/µm] 17.3 20.1 24.8 37.1 43.7 56.9Simulation [keV/µm] 12.2 15.2 20.6 29.9 38.6 50.9Difference [keV/µm] 5.1 4.8 4.2 7.2 5.1 6.0

63


According to the Figure 1.4, there is a big uncertainty in the calibration especially in the low

LET region (for given shifted etch rate V−1 = 0.5, the 95% confidence interval of LET is

almost from 0 to 50 keV/µm). Considering this, it can be seen a good agreement with the ex-

periment in the spectra for 400 MeV/n beam in the TD1 without shielding and for 86 mm

of the PMMA filter (99.79 mm of water) (see Figures 3.12 and 3.13). Table 4.3 contains

the positions of the peak corresponding to C 12 for the studied thicknesses of PMMA.

Table 4.3: Comparison of the positions of the maximum of the C 12 peak of 400 MeV/nbeam in experimental and calculated spectra for several thicknesses of binary PMMA filtersin detector TD1.

PMMA [mm] 0.0 86.0 217.5Experiment [kev/µm] 13.8 15.8 65.2Simulation [keV/µm] 9.8 11.8 47.3Difference [keV/µm] 4.0 4.0 17.9

However, the simulated spectrum for beam shielded with 217.5 mm of PMMA (equiv-

alent of 252.77 mm of water) in the Figure 3.14 is shifted more. This disagreement can be

explained by imprecision in geometry. Disagreement in the geometry for 290 MeV/n was

quantified in 3.1.1.

As we discussed before, the shift is important in the Bragg peak region, where LET was

considerably changing with depth in water.

LET spectra for 8 thicknesses in the region of the Bragg peak (from 217.5 mm

to 221.0 mm PMMA with 0.5 mm step) are plotted in the Figure 4.3. It can be seen that

the best agreement was for 220.5 mm PMMA (256.39 mm of water), but considering the ac-

curacy of track etched detectors, 220.0 mm PMMA (255.76 mm of water) would be accept-

able also.

The shift of 3 mm of PMMA does not correspond with 2.2 mm of additional water shield-

ing. We found out, that the LET spectra calculations of 400 MeV/n were run with the incor-

rect setting of the Scatter Filters. There should be additional 0.32 mm of tantalum (the Scatter

Filters 1 and 2 should be placed into the beam). Result for the corrected case for 217.5 mm

of PMMA are in the Figure 4.4. The agreement is better than before.

64

LET [keV/micrometer]0 20 40 60 80 100 120 140

Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 217.5 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 218.0 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 218.5 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 219.0 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 219.5 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 220.0 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 220.5 mm


Nu

mb

er o

f ev

ents

[-]

1

10

210

310

410

510

C12 400 MeV/u

TD1: 217.5 mm

G4: 221.0 mm

Figure 4.3: Overview of the simulated LET spectra at different positions around Braggpeak of 400 MeV/n C 12 beam. The experimental spectrum is always for beam shieldedby 217.5 PMMA. The thickness of PMMA shielding varies from 217.5 mm to 221.0 mmof PMMA with 0.5 mm step.

65


Nu

mb

er o

f ev

ents

[-]

-110

1

10

210

310

410

510 LegendTD1Geant4


Figure 4.4: Spectra of unrestricted LET in water of the monoenergetic C 12 beam 400 MeV/nshielded by 217.5 mm of PMMA, with corrected set-up of the Scatter Filters 1 and 2.The spectrum was calculated using 105 primaries of C 12 and the physics list FTF_BIC 2.0.

66


Spectra of unrestricted LET in water of the SOBP 290 MeV/n beam are drawn for 0, 117.5

and 127.5 mm of PMMA (Figures 3.15, 3.16 and 3.17). In comparison to the monoenergetic

beams the SOBP spectra of LET of C 12 are wider, because the energy of C 12 beam was

modulated by the ridge filter.

The beam shielded with 127.5 mm of PMMA generally contained no C 12. All C 12

stopped before this point. Therefore there is a good agreement in the Figure 3.17. We

remind that disagreement in the first experimental bins is caused by rebinning of the bin

with the lowest LET. Explanation is described in the introduction to this section 4.2.

Spectra for 117.5 mm of PMMA shielding 3.16 have good agreement in trend. The sim-

ulated spectrum contains 3 distinguishable peaks (with the positions at approximately 40,

55 and 70 keV/µm). The experimental spectrum is smoother in this region. It is probably

the effect of too rough ridge filter. The experimental ridge filter was more precise, thus

the experimental spectrum is more straight. The last experimental bin in the upper subfigure

3.16a contains all particles with LET above the given bin. TEDs can not work as spectrom-

eters for LET above certain threshold. They can only count tracks with LET higher than

the threshold (for Page this threshold is about 450 keV/µm).

The spectrum of the unshielded beam (Figure 3.15) differs even visually. The uncertainty

of TED calibration at low-LET values could explain the shift of the peak position. Disagree-

ment in the higher LET region can be explained by two reasons: there are more high-LET

values in the experiment than in simulation or there are less low-LET values in experiment,

and the difference in high-LET region were introduced due to scaling.

The reason of both probably lies in imprecise reproduction of the ridge filter. It would

be interesting to run calculations with true ridge filter design. We obtained a true design

of the ridge filter from Satoshi Kodaira, but we did not manage to implement it and to run

calculations with this ridge filter in time.

67

4.3 Fractions of detected particles

Monoenergetic beams (see Tables 3.5, 3.6, 3.7 or Figures 3.21, 3.22, 3.23) evince similar

trends with increasing depth in water. For all set-ups can be said:

Although the number of the particles above the upper LET detection threshold is neg-

ligible, these particles are responsible for a non-negligible fraction of dose (up to 7.2%

for the monoenergetic set-up and 17.5% for the SOBP set-up). On the contrary, the number

of the particles below the detection threshold is very significant (in some cases more than

50%), nevertheless dose caused by this particles is only around 10%. Both effects are ex-

pectable. High-LET particles deposit a lot of energy in a short track, so even small number

of them can cause high dose. And vice versa high number of the low-LET particles does

not have to cause high dose. The lower threshold is about 10 keV/µm and the upper is about

400 keV/µm. For instance 100 particles with LET of 5 keV/µm cause the same effect as one

single particle with LET of 500 keV/µm.

The fraction of particles below the detection threshold increases with the increasing

thickness of PMMA. Dose from the low-LET fragments increases at the beginning and then

decreases with the thicker PMMA shielding.

The number of secondary fragments (from 5% up to 60%) increases with the PMMA

thickness. However these particles cause less than 10% of the total dose (except SOBP and

400 MeV/n set-up). There is also one difference between TD1 and Page. Fractions below

the detection range are higher for Page than for TD1, because the lower detection thresholds

are 9.46 keV/µm for TD1 and 11.02 keV/µm for Page. Therefore the detector TD1 detects

more particles. This effect can be seen from the first column of the Tables 3.5, 3.6; most

significantly in the first row (0 mm PMMA). The fraction Nb is higher for the unshielded

MONO 400 MeV/n than MONO 290 MeV/n (Tables 3.5, 3.7), since the LET of C 12 is

lower for 400 MeV and some can be undetected. The MONO and SOBP results in the Page

differs due to the ridge filter for the unshielded beam (Tables 3.6, 3.8).

The particles with LET above the highest experimental value cause approximately 1%

of total dose. The fraction of dose of the high-LET fragments is up to 6.9% in the SOBP

set-up (Table 3.8), where the fragmentation is higher due to the ridge filter.

When the thickness of PMMA shielding increases and gets closer to the Bragg peak,

LET of ions rises, and these ions contribute to total dose more significantly. There is one

exception for the row with 123 mm in the Table 3.6. The highest LET in the experiment

68

for the Page for 123 mm is 442 keV/µm and for 119 mm PMMA and for 127 mm PMMA

it is 443.3 keV/µm. This small difference contributes to the fact that the dose contribution

decreases from 5.3% (at 119 row) to 5.0% (in the row 123 mm).

The dose fraction from the low-LET particles firstly increases (as the number of the frag-

ments rises) and then remains constant or slightly decreases (as LET of primary ions rapidly

rises).

The SOBP set-up (the Figure 3.24 and Table 3.8) gives similar results. The number

of fragments below the detection threshold rises with the increasing PMMA shielding. Since

the number of primary C 12 is decreasing with the rising PMMA thickness, the dose fractions

and number of particles within the detection range decreases. When one fraction decreases

the others must rise. Therefore there is no decrease in dose from low-LET, like in monoener-

getic set-up. Also for 127.5 mm PMMA (at the distal end of SOBP), there is no primary ion

present, and the effect of the dose increases, seen in monoenergetic set-up, is not observed

in this case.

The fractions of dose from electrons are usually about 20–26%. The fractions of dose

from electrons decrease with growing thickness of the PMMA shielding. As the ions slow

down and their LET increases, they contribute to dose more significantly. Therefore their

relative contribution to dose increases and the other fractions must decrease. However we

need to remind that the number of the simulated electrons (and also dose from the electrons)

is dependent on the production threshold. The lower the production threshold is, the higher

the number of the secondary electrons. Dose from the secondaries with the range below

the given production threshold is deposited locally, and those secondaries are not simulated.

69

Chapter 5

Conclusion

The geometry of the HIMAC-BIO beamline of the Heavy Ion Medical Accelerator in Chiba

at Japanese National Institute of Radiological Sciences was successfully implemented us-

ing Geant4. We calculated depth dose distributions in the water phantom for the following

beams: MONO 290 MeV/n, MONO 400 MeV/n and SOBP 290 MeV/n. The Bragg peak

for the beam MONO 290 MeV/n was shifted by about 2.2 mm according to the depth dose

measurements from the TEDs (see section 3.1.1). The depth of the dose maximum was

shifted by about 0.77 mm in case of MONO 400 MeV/n in comparison to the reference

data from ionization chamber, which were measured by the personnel of the HIMAC facility

(see section 3.1.2). The shifts differ from each other since the set-up of the scatter filters was

different and also the experimental data were obtained from the different measurements (ion-

ization chamber and TED). As it was shown in [25], also the physics list choice in Geant4

could affect the depth of the Bragg peak in both cases.

We developed a simplified model of the ridge filter for the calculations of the LET spectra

of SOBP 290 MeV/n. Depth dose distribution of the SOBP 290 MeV/n beam was in the suf-

ficient agreement with the measurements for the purpose of the LET spectra calculations

(see 3.1.3).

The simulations of the LET spectra of the carbon ion beam with track etched detectors

were successfully performed at the various positions of the Bragg curve for the monoener-

getic beams of energy 290 MeV/n (sections 3.2.1 and 3.2.2) and 400 MeV/n (section 3.2.3)

and for the SOBP configuration for 290 MeV/n (section 3.2.4). The calculated spectra of un-

restricted linear energy transfer in water were compared with the experimental measurements

with the solid state nuclear track etched detectors TD1 and Page. The calculated spectra

were in a good agreement with the experimental data regarding the uncertainties associated

70

with the calibration of the TEDs and the imprecisions in the geometry.

We estimated the fractions of fluence and dose deposits from the detected and undetected

particles for the simulated cases (see section 3.5). Fragments with LET below the detection

threshold of the studied detectors contributed significantly to fluence (up to 70% for the mo-

noenergetic and up to 90% for the SOBP set-ups), and yet the dose contributions were small

(depending on depth approximately 1–6% for MONO 290 MeV/n, 8–14% for 400 MeV/n

and 1–32% for SOBP 290 MeV/n). Dose contributions of the detected particles were ap-

proximately 60–70%, of electrons 20–26%. The particles with very high LET were not

numerous and their dose deposits varied around 1%, except in the tail of the SOBP where

their contributions to total dose was approximately 7%.

We verified that Geant4 is an applicable tool for the calculation of LET spectra and re-

production of the TED irradiation experiments. Thanks to this powerful toolkit we obtained

a reasonable agreement with the experiment and were able to complement the experiment

with the supplementary data. The detection range of the TEDs always covered the LET range

of the primary carbon ion according to the calculations.

5.1 Future perspectives

It is possible to work further on improvement in the accuracy of the geometry. This in-

cludes better ridge filter design and adding magnets, which were used for the lateral spread

of the beam. Recently, we got the true ridge filter description from Satoshi Kodaira. Their in-

clusion should result in better agreement between the calculations and measurements

for the SOBP configuration. Implementation of the magnets would enable the reproduction

of the beam profile.

Second direction of potential future work is to study the effect of the various settings

of the Geant4 calculations; physics list, production threshold and maximum step length.

The efficiency of the calculations can also be improved.

71

Bibliography

[1] F. Spurný, K. Pachnerová Brabcová, O. Ploc, I. Ambrožová, and Z. Mrázová, “Spec-

tra of linear energy transfer and other dosimetry characteristics as measured in

C290 MeV/n MONO and SOBP ion beams at HIMAC-BIO (NIRS, Japan) with dif-

ferent detectors.,” Radiation protection dosimetry, vol. 143, pp. 519–22, Feb. 2011.

[2] K. Brabcová, I. Jadrnícková, A. G. Molokanov, and F. Spurný, “Dosimetry in heavy

ion beams using various detectors,” Radiation Measurements, vol. 45, pp. 1384–1386,

Dec. 2010.

[3] S. Agostinelli, J. Allison, and K. Amako, “Geant4 – A Simulation Toolkit,” Nuclear

instruments and Methods in Physics Research, vol. A 506, pp. 250–303, 2003.

[4] J. Allison, K. Amako, J. Apostolakis, H. Araujo, and P. A. Dubois, “Geant4 Develop-

ments and Applications,” IEEE Transactions on Nuclear Science, vol. 53, pp. 270–278,

2006.

[5] J. D. Hunter, “Matplotlib: A 2D graphics environment,” Computing In Science & En-

gineering, vol. 9, no. 3, pp. 90–95, 2007.

[6] E. Jones, T. Oliphant, P. Peterson, et al., “SciPy: Open source scientific tools for

Python.” http://www.scipy.org/, 2001–. [Accessed: April 13, 2014].

[7] T. E. Oliphant, “Python for Scientific Computing,” Computing in Science & Engineer-

ing, vol. 9, no. 3, pp. 10–20, 2007.

[8] R. Brun and F. Rademakers, “ROOT – An Object Oriented Data Analysis Framework,

Proceedings AIHENP’96 Workshop, Lausanne, Sep. 1996,” Nuclear instruments and

Methods in Physics Research, vol. A 389, pp. 81–86, 1997.

72

http://www.scipy.org/

[9] K. Pachnerová Brabcová, I. Ambrožová, and F. Spurný, “Spectrometry of Linear En-

ergy Transfer with Track-Etched Detectors in Carbon Ion Beams, MONO and SOBP,”

Radiation Protection Dosimetry, vol. 143, no. 2–4, pp. 440–444, 2011.

[10] I. Jadrnícková, Spectrometry of Linear Energy Transfer and Its Use in Radiotherapy

and Radiation Protection in High-Energy Particle Fields. PhD thesis, Faculty of Nu-

clear Sciences and Physical Engineering, Czech Technical University in Prague, 2006.

[11] K. Pachnerová Brabcová, Study and development of track etch detectors for dosimetric

purposes. PhD thesis, Faculty of Nuclear Sciences and Physical Engineering, Czech

Technical University in Prague, 2010.

[12] K. Pachnerová Brabcová, I. Ambrožová, and Z. Kolísková, “Po stopách v detektorech

stop,” Bezpecnost jaderné energie, vol. 20(58), pp. 40–44, 2012.

[13] K. Pachnerová Brabcová, I. Ambrožová, Z. Kolísková, and A. Malušek, “Uncertainties

in Linear Energy Transfer Spectra Measured with Track-etched Detectors in Space,”

Nuclear Instruments and Methods in Physics Research A, vol. 713, pp. 5–10, 2013.

[14] International Commision on Radiation Units and Measurements, “Linear Energy trans-

fer,” ICRU Report, vol. 16, 1970.

[15] E. Benton, Radiation Dosimetry at Aviation Altitudes and in Low-Earth Orbit. PhD

thesis, The National University of Ireland, 2004.

[16] Geant4 Collaboration, “Geant4.” http://www.geant4.org/geant4, March 2014.

[Accessed: April 1, 2014].

[17] OpenGATE Collaboration, “GATE: Simulations of Preclinical and Clinical Scans in

Emission Tomography, Transmission Tomography and Radiation Therapy.” http://

www.opengatecollaboration.org, April 2014. [Accessed: April 1, 2014].

[18] “GAMOS: Geant4-based Architecture for Medicine-Oriented Simulations.” http://

fismed.ciemat.es/GAMOS, April 2014. [Accessed: April 1, 2014].

[19] J. Perl, J. Shin, J. Schumann, B. Faddegon, and H. Paganetti, “TOPAS: an innovative

proton Monte Carlo platform for research and clinical applications.,” Medical physics,

vol. 39, pp. 6818–37, Nov. 2012.

73

http://www.geant4.org/geant4

http://www.opengatecollaboration.org

http://www.opengatecollaboration.org

http://fismed.ciemat.es/GAMOS

http://fismed.ciemat.es/GAMOS

[20] Z. Francis, S. Incerti, R. Capra, B. Mascialino, G. Montarou, V. Stepan, and C. Villa-

grasa, “Molecular scale track structure simulations in liquid water using the Geant4-

DNA Monte-Carlo processes,” Applied Radiation and Isotopes, vol. 69, pp. 220–226,

2011.

[21] Geant4-DNA Collaboration, “The Geant4-DNA project.” http://geant4-dna.org,

April 2014. [Accessed: April 1, 2014].

[22] Dennis Wright, “A short guide to choosing a physics list.” http://geant4.slac.

stanford.edu/JLAB2012/PhysList.pdf, July 2012. [Accessed: April 25, 2014].

[23] S. Yonai, N. Matsufuji, and S. Kanai, “Monte Carlo study on secondary neutrons in

passive carbon-ion radiotherapy: Identification of the main source and reduction in the

secondary neutron dose,” Medical Physics, vol. 36, pp. 4830–4839, 2009.

[24] M. Torikoshi, S. Minohara, N. Kanematsu, M. Komori, M. Kanazawa, K. Noda,

N. Miyahara, H. Itoh, M. Endo, and T. Kanai, “Irradiation System for HIMAC.,” Jour-

nal of radiation research, vol. 48 Suppl A, pp. A15–25, Jan. 2007.

[25] M. Šefl, “Modelování spekter nabitých cástic ve stopových detektorech v pevné fázi

ozárených svazkem iontu uhlíku o energii 290 MeV/n a 400 MeV/n,” 2013. Výzkumný

úkol, FJFI CVUT v Praze.

[26] C. Theis, K. H. Buchegger, M. Brugger, D. Forkel-Wirth, S. Roesler, and H. Vincke,

“Interactive three dimensional visualization and creation of geometries for Monte Carlo

calculations,” Nuclear Instruments and Methods in Physics Research A, vol. 562,

pp. 827–829, 2006.

[27] C. Theis, “SimpleGeo.” http://theis.web.cern.ch/theis/simplegeo/, August

2012. [Accessed: January 15, 2014].

[28] G. Battistoni, S. Muraro, P. Sala, F. Cerutti, A. Ferrari, S. Roesler, A. Fasso, and

J. Ranft, “The FLUKA Code: Description and Benchmarking,” Proceedings of the

Hadronic Shower Simulation Workshop 2006, Fermilab 6–8 September 2006, M. Al-

brow, R. Raja eds., AIP Conference Proceeding, vol. 896, pp. 31–49, 2007.

[29] A. Ferrari, P. Sala, A. Fasso, and J. Ranft, “FLUKA: A Multi-Particle Transport Code,”

CERN-2005-10 (2005), INFN/TC_05/11, SLAC-R-773, 2005.

74

http://geant4-dna.org

http://geant4.slac.stanford.edu/JLAB2012/PhysList.pdf

http://geant4.slac.stanford.edu/JLAB2012/PhysList.pdf

http://theis.web.cern.ch/theis/simplegeo/

[30] Monte Carlo Code Group, “A General Monte Carlo N-Particle (MCNP) Transport

Code.” https://laws.lanl.gov/vhosts/mcnp.lanl.gov/index.shtml, April

2014. [Accessed: April 25, 2014].

[31] T. Sato, K. Niita, N. Matsuda, S. Hashimoto, Y. Iwamoto, S. Noda, T. Ogawa, H. Iwase,

H. Nakashima, T. Fukahori, K. Okumura, T. Kai, S. Chiba, T. Furuta, and L. Sihver,

“Particle and Heavy Ion Transport code System, PHITS, version 2.52,” Journal of Nu-

clear Science and Technology, vol. 50, pp. 913–923, Sept. 2013.

[32] E. Jones, T. Oliphant, P. Peterson, et al., “Persistence of Vision Raytracer (Version

3.6).” http://www.povray.org/download/, 2004. [Computer software],[Accessed:

April 22, 2014].

[33] B. Schaffner, T. Kanai, Y. Futami, M. Shimbo, and E. Urakabe, “Ridge filter design

and optimization for the broad-beam three-dimensional irradiation system for heavy-

ion radiotherapy,” Medical Physics, vol. 27, no. 4, p. 716, 2000.

[34] T. Kanai, Y. Furusawa, K. Fukutsu, H. Itsukaichi, K. Eguchi-kasai, and H. Ohara, “Ir-

radiation of Mixed Beam and Design of Spread-Out Bragg Peak for Heavy-Ion Radio-

therapy,” Radiation research, vol. 147, pp. 78–85, 1997.

[35] S. Schell and J. J. Wilkens, “Modifying proton fluence spectra to generate spread-out

Bragg peaks with laser accelerated proton beams.,” Physics in medicine and biology,

vol. 54, pp. N459–66, Oct. 2009.

[36] I. Park, “A new approach to produce spread-out Bragg peak using the MINUIT fit,”

Current Applied Physics, vol. 9, no. 4, pp. 852–855, 2009.

[37] T. Bortfeld and W. Schlegel, “An analytical approximation of depth-dose distributions

for therapeutic proton beams.,” Physics in medicine and biology, vol. 41, pp. 1331–9,

Aug. 1996.

[38] D. Jette and W. Chen, “Creating a spread-out Bragg peak in proton beams.,” Physics in

medicine and biology, vol. 56, pp. N131–8, June 2011.

[39] T. Akagi, A. Higashi, H. Tsugami, H. Sakamoto, Y. Masuda, and Y. Hishikawa,

“Ridge filter design for proton therapy at Hyogo Ion Beam Medical Center,” Physics in

medicine and biology, vol. 48, no. 22, pp. N301–N312, 2003.

75

https://laws.lanl.gov/vhosts/mcnp.lanl.gov/index.shtml

http://www.povray.org/download/

[40] J. J. Wilkens and U. Oelfke, “Direct Comparison of Biologically Optimized Spread-Out

Bragg Peaks for Protons and Carbon Ions,” International journal of radiation oncology,

biology, physics, vol. 70, no. 1, pp. 262–266, 2008.

[41] M. Sakama, T. Kanai, Y. Kase, K. Yusa, M. Tashiro, K. Torikai, H. Shimada, S. Ya-

mada, T. Ohno, and T. Nakano, “Design of ridge filters for spread-out Bragg peaks

with Monte Carlo simulation in carbon ion therapy.,” Physics in medicine and biology,

vol. 57, pp. 6615–33, Oct. 2012.

[42] Y. Hara, Y. Takada, K. Hotta, R. Tansho, T. Nihei, Y. Suzuki, K. Nagafuchi, R. Kawai,

M. Tanabe, S. Mizutani, T. Himukai, and N. Matsufuji, “Improvement of spread-out

Bragg peak flatness for a carbon-ion beam by the use of a ridge filter with a ripple

filter.,” Physics in medicine and biology, vol. 57, pp. 1717–31, Mar. 2012.

[43] G. A. P. Cirrone, G. Cuttone, S. E. Mazzaglia, F. Romano, D. Sardina, C. Agodi, A. At-

tili, A. A. Blancato, M. De Napoli, F. Di Rosa, P. Kaitaniemi, F. Marchetto, I. Petrovic,

A. Ristic-Fira, J. Shin, N. Tarnavsky, S. Tropea, and C. Zacharatou, “Hadrontherapy: a

Geant4-Based Tool for Proton/Ion-Therapy Studies,” Progress in NUCLEAR SCIENCE

and TECHNOLOGY, vol. 2, pp. 207–212, 2011.

[44] J. J. Wilkens and U. Oelfke, “Analytical linear energy transfer calculations for proton

therapy,” Medical Physics, vol. 30, no. 5, p. 806, 2003.

[45] Geant4 Collaboration, “Geant4 User’s Guide for Application Developers.”

http://geant4.web.cern.ch/geant4/UserDocumentation/UsersGuides/

ForApplicationDeveloper/BackupVersions/V9.6/fo/BookForAppliDev.pdf,

November 2012. [Accessed: October 10, 2013].

76

http://geant4.web.cern.ch/geant4/UserDocumentation/UsersGuides/ForApplicationDeveloper/BackupVersions/V9.6/fo/BookForAppliDev.pdf

http://geant4.web.cern.ch/geant4/UserDocumentation/UsersGuides/ForApplicationDeveloper/BackupVersions/V9.6/fo/BookForAppliDev.pdf

Appendix

Example of a macro file for the Geant4 calculations

Here is shown the macro file which was used in the calculations with 400 MeV/n beam.

The macro for the 290 MeV/n beam had different line with energy (3480 MeV instead

of 4800 MeV).

/ c o n t r o l / v e r b o s e 0

/ e v e n t / v e r b o s e 0

/ t r a c k i n g / v e r b o s e 0

# p a r t i c l e s o u r c e

/ gps / v e r b o s e 0

/ gps / p a r t i c l e i o n

/ gps / i o n 6 12 6

/ gps / en e r g y 4800 MeV

/ gps / pos / t y p e P l a n e

/ gps / pos / shape Square

/ gps / pos / h a l f x 2 cm

/ gps / pos / h a l f y 2 cm

/ gps / pos / c e n t r e 0 . 0 . −1172.5 cm

/ gps / d i r e c t i o n 0 0 1

# number o f p r i m a r i e s

/ run / beamOn 200000

77

PMMA/water equivalent thickness: part 1PMMA water PMMA water PMMA water PMMA water PMMA water[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm]0.0 0.00 20.0 23.23 40.0 46.36 60.0 69.59 80.0 92.720.5 0.63 20.5 23.86 40.5 46.99 60.5 70.22 80.5 93.351.0 1.14 21.0 24.37 41.0 47.50 61.0 70.73 81.0 93.861.5 1.77 21.5 25.00 41.5 48.13 61.5 71.36 81.5 94.492.0 2.31 22.0 25.54 42.0 48.67 62.0 71.90 82.0 95.032.5 2.94 22.5 26.17 42.5 49.30 62.5 72.53 82.5 95.663.0 3.45 23.0 26.68 43.0 49.81 63.0 73.04 83.0 96.173.5 4.08 23.5 27.31 43.5 50.44 63.5 73.67 83.5 96.804.0 4.76 24.0 27.74 44.0 51.12 64.0 74.25 84.0 97.484.5 5.39 24.5 28.37 44.5 51.75 64.5 74.88 84.5 98.115.0 5.90 25.0 28.88 45.0 52.26 65.0 75.39 85.0 98.625.5 6.53 25.5 29.51 45.5 52.89 65.5 76.02 85.5 99.256.0 7.07 26.0 30.05 46.0 53.43 66.0 76.56 86.0 99.796.5 7.70 26.5 30.68 46.5 54.06 66.5 77.19 86.5 100.427.0 8.21 27.0 31.19 47.0 54.57 67.0 77.70 87.0 100.937.5 8.84 27.5 31.82 47.5 55.20 67.5 78.33 87.5 101.568.0 9.27 28.0 32.50 48.0 55.56 68.0 79.01 88.0 101.998.5 9.90 28.5 33.13 48.5 56.19 68.5 79.64 88.5 102.629.0 10.41 29.0 33.64 49.0 56.70 69.0 80.15 89.0 103.139.5 11.04 29.5 34.27 49.5 57.33 69.5 80.78 89.5 103.7610.0 11.58 30.0 34.81 50.0 57.87 70.0 81.32 90.0 104.3010.5 12.21 30.5 35.44 50.5 58.50 70.5 81.95 90.5 104.9311.0 12.72 31.0 35.95 51.0 59.01 71.0 82.46 91.0 105.4411.5 13.35 31.5 36.58 51.5 59.64 71.5 83.09 91.5 106.0712.0 14.03 32.0 37.09 52.0 60.32 72.0 83.52 92.0 106.7512.5 14.66 32.5 37.72 52.5 60.95 72.5 84.15 92.5 107.3813.0 15.17 33.0 38.23 53.0 61.46 73.0 84.66 93.0 107.8913.5 15.80 33.5 38.86 53.5 62.09 73.5 85.29 93.5 108.5214.0 16.34 34.0 39.40 54.0 62.63 74.0 85.83 94.0 109.0614.5 16.97 34.5 40.03 54.5 63.26 74.5 86.46 94.5 109.6915.0 17.48 35.0 40.54 55.0 63.77 75.0 86.97 95.0 110.2015.5 18.11 35.5 41.17 55.5 64.40 75.5 87.60 95.5 110.8316.0 18.47 36.0 41.85 56.0 64.83 76.0 88.28 96.0 111.3416.5 19.10 36.5 42.48 56.5 65.46 76.5 88.91 96.5 111.9717.0 19.61 37.0 42.99 57.0 65.97 77.0 89.42 97.0 112.4817.5 20.24 37.5 43.62 57.5 66.60 77.5 90.05 97.5 113.1118.0 20.78 38.0 44.16 58.0 67.14 78.0 90.59 98.0 113.6518.5 21.41 38.5 44.79 58.5 67.77 78.5 91.22 98.5 114.2819.0 21.92 39.0 45.30 59.0 68.28 79.0 91.73 99.0 114.7919.5 22.55 39.5 45.93 59.5 68.91 79.5 92.36 99.5 115.42

78

PMMA/water equivalent thickness: part 2PMMA water PMMA water PMMA water PMMA water PMMA water[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm]100.0 116.10 120.0 139.08 140.0 163.04 160.0 186.10 180.0 209.33100.5 116.73 120.5 139.71 140.5 163.67 160.5 186.73 180.5 209.96101.0 117.24 121.0 140.22 141.0 164.18 161.0 187.24 181.0 210.47101.5 117.87 121.5 140.85 141.5 164.81 161.5 187.87 181.5 211.1102.0 118.41 122.0 141.39 142.0 165.35 162.0 188.41 182.0 211.64102.5 119.04 122.5 142.02 142.5 165.98 162.5 189.04 182.5 212.27103.0 119.55 123.0 142.53 143.0 166.49 163.0 189.55 183.0 212.78103.5 120.18 123.5 143.16 143.5 167.12 163.5 190.18 183.5 213.41104.0 120.61 124.0 143.84 144.0 167.48 164.0 190.86 184.0 213.84104.5 121.24 124.5 144.47 144.5 168.11 164.5 191.49 184.5 214.47105.0 121.75 125.0 144.98 145.0 168.62 165.0 192.00 185.0 214.98105.5 122.38 125.5 145.61 145.5 169.25 165.5 192.63 185.5 215.61106.0 122.92 126.0 146.15 146.0 169.79 166.0 193.17 186.0 216.15106.5 123.55 126.5 146.78 146.5 170.42 166.5 193.80 186.5 216.78107.0 124.06 127.0 147.29 147.0 170.93 167.0 194.31 187.0 217.29107.5 124.69 127.5 147.92 147.5 171.56 167.5 194.94 187.5 217.92108.0 125.37 128.0 149.01 148.0 172.24 168.0 195.37 188.0 218.6108.5 126.00 128.5 149.64 148.5 172.87 168.5 196.00 188.5 219.23109.0 126.51 129.0 150.15 149.0 173.38 169.0 196.51 189.0 219.74109.5 127.14 129.5 150.78 149.5 174.01 169.5 197.14 189.5 220.37110.0 127.68 130.0 151.32 150.0 174.55 170.0 197.68 190.0 220.91110.5 128.31 130.5 151.95 150.5 175.18 170.5 198.31 190.5 221.54111.0 128.82 131.0 152.46 151.0 175.69 171.0 198.82 191.0 222.05111.5 129.45 131.5 153.09 151.5 176.32 171.5 199.45 191.5 222.68112.0 129.81 132.0 153.77 152.0 176.75 172.0 200.13 192.0 223.26112.5 130.44 132.5 154.40 152.5 177.38 172.5 200.76 192.5 223.89113.0 130.95 133.0 154.91 153.0 177.89 173.0 201.27 193.0 224.4113.5 131.58 133.5 155.54 153.5 178.52 173.5 201.90 193.5 225.03114.0 132.12 134.0 156.08 154.0 179.06 174.0 202.44 194.0 225.57114.5 132.75 134.5 156.71 154.5 179.69 174.5 203.07 194.5 226.2115.0 133.26 135.0 157.22 155.0 180.20 175.0 203.58 195.0 226.71115.5 133.89 135.5 157.85 155.5 180.83 175.5 204.21 195.5 227.34116.0 134.57 136.0 158.28 156.0 181.51 176.0 204.57 196.0 228.02116.5 135.20 136.5 158.91 156.5 182.14 176.5 205.20 196.5 228.65117.0 135.71 137.0 159.42 157.0 182.65 177.0 205.71 197.0 229.16117.5 136.34 137.5 160.05 157.5 183.28 177.5 206.34 197.5 229.79118.0 136.88 138.0 160.59 158.0 183.82 178.0 206.88 198.0 230.33118.5 137.51 138.5 161.22 158.5 184.45 178.5 207.51 198.5 230.96119.0 138.02 139.0 161.73 159.0 184.96 179.0 208.02 199.0 231.47119.5 138.65 139.5 162.36 159.5 185.59 179.5 208.65 199.5 232.1

79

PMMA/water equivalent thickness: part 3PMMA water PMMA water PMMA water PMMA water PMMA water[mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm] [mm]200.0 232.53 211.5 245.81 223.0 259.21 234.5 272.56 246.0 285.89200.5 233.16 212.0 246.49 223.5 259.84 235.0 273.07 246.5 286.52201.0 233.67 212.5 247.12 224.0 260.35 235.5 273.70 247.0 287.03201.5 234.30 213.0 247.63 224.5 260.98 236.0 274.38 247.5 287.66202.0 234.84 213.5 248.26 225.0 261.49 236.5 275.01 248.0 288.09202.5 235.47 214.0 248.80 225.5 262.12 237.0 275.52 248.5 288.72203.0 235.98 214.5 249.43 226.0 262.66 237.5 276.15 249.0 289.23203.5 236.61 215.0 249.94 226.5 263.29 238.0 276.69 249.5 289.86204.0 237.29 215.5 250.57 227.0 263.80 238.5 277.32 250.0 290.40204.5 237.92 216.0 251.00 227.5 264.43 239.0 277.83 250.5 291.03205.0 238.43 216.5 251.63 228.0 265.11 239.5 278.46 251.0 291.54205.5 239.06 217.0 252.14 228.5 265.74 240.0 278.82 251.5 292.17206.0 239.60 217.5 252.77 229.0 266.25 240.5 279.45 252.0 292.85206.5 240.23 218.0 253.31 229.5 266.88 241.0 279.96 252.5 293.48207.0 240.74 218.5 253.94 230.0 267.42 241.5 280.59 253.0 293.99207.5 241.37 219.0 254.45 230.5 268.05 242.0 281.13 253.5 294.62208.0 241.73 219.5 255.08 231.0 268.56 242.5 281.76 254.0 295.16208.5 242.36 220.0 255.76 231.5 269.19 243.0 282.27 254.5 295.79209.0 242.87 220.5 256.39 232.0 269.62 243.5 282.90 255.0 296.30209.5 243.50 221.0 256.90 232.5 270.25 244.0 283.58 255.5 296.93210.0 244.04 221.5 257.53 233.0 270.76 244.5 284.21210.5 244.67 222.0 258.07 233.5 271.39 245.0 284.72211.0 245.18 222.5 258.70 234.0 271.93 245.5 285.35

80

Documents

DIPLOMA THESIS - Amazon S3...DIPLOMA THESIS Calculation of solid-state track etched detectors response ... Pomocí této geometrie jsou vypoˇcteny a s nam ˇeˇrenými daty porovnány