Monte Carlo Simulation of a Curved-Detector Gamma Camera


Master's Thesis, 2020

49 Pages, Grade: with Honours Degree


Free online reading

Table of Contents

ABSTRACT

EPIGRAPH

LIST OF TABLES

LIST OF FIGURES

LIST OF ABBREVIATIONS

CHAPTER 1. INTRODUCTIO
1.1 Gamma Camera
1.1.1 PET
1.1.2 SPECT
1.3 Purpose of this study
1.4 Organisation of this thesis

CHAPTER 2. LITERATURE REVIE
2.1 SPECT Acquisition
2.1.1 Collimator
2.1.1.1 Parallel-Hole Collimator
2.1.1.2 Converging and Diverging Collimators
2.1.1.3 Pinhole Collimator
2.1.2 Solid-State Semiconductor
2.2 Scatter in SPECT
2.3 Advances in SPECT
2.3.1 D-SPECT
2.3.2 CardiArc

CHAPTER 3. METHODOLOGY: MONTE CARL
3.1 Methodology
3.2 Methods
3.2.1 First Step: The World Volume
3.2.2 Second Step: Scanner Geometry
3.2.3 Third Step: The Phantom
3.2.4 Fourth Step: The Source
3.2.5 Fifth Step: Sensitive Detectors
3.2.6 Sixth Step: Physics Processes
3.2.7 Seventh Step: Digitiser
3.2.8 Eighth Step: Data Output
3.2.9 Ninth Step: Data Acquisition
3.3 Data Analysis Methods
3.3.1 ROOT
3.3.2 Jupyter Notebook

CHAPTER 4. RESUL
4.1 Point Source
4.2 30-mm-Diameter Water Phantom
4.3 10-mm-Diameter Water Phantom
4.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number
4.5 Experimental Setup Results
4.5.1 Detector Head and Phantom Position
4.5.2 Source Position Validation
4.5.3 Energy Spectra

CHAPTER 5. DISCUSSIO
5.1 Point Source Discussion
5.2 30-mm-Diameter Water Phantom Discussion
5.3 10-mm-Diameter Water Phantom Discussion
5.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number Discussion
5.5 Experimental Setup Discussion
5.5.1 Detector Head and Phantom Position
5.5.2 Source Position Validation
5.5.3 Energy Spectra
5.6 Advantages and Disadvantages

CHAPTER 6. CONCLUSION
6.1 Future Work

BIBLIOGRAPHY

Abstract

This study aims to develop a fully curved gamma camera using a Monte Carlo simulation in GATE to investigate whether there are any advantages to this configuration in terms of sensitivity or resolution. Both flat and curved detectors were simulated using the same materials and collimator hole diminutions to ensure valid comparable results. There were four sets of simulations conducted with different phantom sizes and different parameters to get comprehensive results. Then, ROOT and Jupyter Notebook were used to analyse the data to give the necessary visual and quantitative data to compare the two detectors. As a result, the curved detector proved to be better in terms of sensitivity in all simulation sets and yielded a better result with less noisy images when imaging small phantoms; nevertheless, it was more susceptible to high-energy photons, which penetrated the collimator and effected the image negatively. However, the flat detector was shown to be better in terms of resolution when imaging a large phantom and more immune to the high-energy collimator-penetrating photons. in addition, the flat detector images when imaging a larger phantom had less scattered photons and less noise. To conclude, further studies could be done to develop the proposed configuration and reach its maximum potential.

‘Scatter is the enemy.’

- Edward J. Hoffman

List of Tables

Table 4.1 Quantitative data resulting from the detectors imaging a point source

Table 4.2 Quantitative data resulting from the detectors imaging the 30-mm-diameter water phantom

Table 4.3 Quantitative data resulting from the detectors imaging the 10-mm-diameter water phantom

Table4.4 Quantitative data resulting from the detectors imaging the 10-mm-diameter water phantom with no fixed primaries

Table 5.1 Advantages and disadvantages of the curved and flat detectors

List of Figures

Figure 1.1 A schematic diagram of a gamma camera. The collimator, scintillator, PMTs and the computer are displayed

Figure 1.2 PET camera detecting two gamma photons after an annihilation event

Figure 1.3 SPECT imaging process. The SPECT camera rotates around the patient; then, the projections are reconstructed to create the image

Figure 2.1 Different types of SPECT collimators. Parallel-hole, diverging-hole, converging-hole and pinhole collimators

Figure 2.2 Difference in the energy peaks between a Nal scintillation detector and a CZT detector imaging a technetium-99m source

Figure 2.3 A schematic illustration of the different types of scattered photons

Figure 2.4 A schematic diagram of the D-SPECT gantry, with the position of the nine detectors

Figure 2.5 A schematic design of a CardiArc camera, showing the three curved Nal crystals, PMTs arranged in three rows and the aperture arc (six slots)

Figure 3.1 An empty World Volume box

Figure 3.2 The Cartesian coordinate system in the x, y and z directions, which can go either upward or downward

Figure 3.3 A - Flat SPECT head. B - Curved SPECT head. The layers mentioned above are coloured and presented in the figure: shielding (red), back compartment (grey), crystal (yellow) and collimator (white)

Figure 3.4 A 30-mm-diameter water phantom

Figure 4.4 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Flat detector's hits subtracted by curved detector's hits

Figure 4.5 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Flat detector's hits subtracted by curved detector's hits

Figure 4.6 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Curved detector's hits subtracted by flat detector's hits

Figure 4.7 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Curved detector's hits subtracted by flat detector's hits

Figure 4.5 Several views from different angles of the curved detector, with the phantom in the middle of the detector

Figure 4.6 Several views from different angles of the flat detector, with the phantom in the middle of the detector

Figure 4.7 Source position according to X, Y and Z axes, which were the same in all simulations

Figure 4.8 Energy spectra of TC-99m (140 keV), which were similar in all simulations. Note: All figures referenced in the captions.

List of Abbreviations

2D Two-dimensional

ASCII American Standard Code for Information Interchange

CERN Conseil Européen pour la Recherche Nucléaire

CT Computed tomography

CZT Cadmium zinc telluride

FOV Field of view

MRI Magnetic resonance imaging

Nal Sodium iodide doped with thallium

PET Positron emission tomography

PMT Photomultiplier tubes

SD Sensitive detector

SPECT Single-photon emission computed tomography

vGate Virtual Gate

Introduction

Contents

CHAPTER 1. INTRODUCTION
1.1 Gamma Camera
1.1.1 PET
1.1.2 SPECT
1.3 Purpose of this study
1.4 Organisation of this thesis

Chapter 1. Introduction

Nuclear medicine imaging has become increasingly popular in recent years due to its prominent role in molecular imaging. The main difference between nuclear medicine and other radiological modalities is that nuclear imaging is able to characterise and visualise tissues at the cellular and molecular levels in living organisms.1 A radioactively tagged drug (radiopharmaceutical) is administered to the patient, aiming to be taken up by a particular tissue or organ of interest. Consequently, after a certain duration, the radiopharmaceutical will accumulate in the targeted tissue or organ.2 The patient will then be imaged using a modality such as positron emission tomography (PET) or single-photon emission computed tomography (SPECT) to map the concentration of the radiopharmaceutical uptake. This contributes to a better understanding of the pathological and physiological processes and provides a more sophisticated diagnostic imaging technique.3 Currently, most studies are interested in the design of novel geometries with different types of scintillation materials, and that is what this study is offering: to investigate a new type of fully curved detector with a more advanced scintillator material, which will be discussed below.

This chapter contains an introduction to the gamma camera, which is the focus of this research, followed by the overall organisation of this thesis.

1.1 Gamma Camera

A gamma camera detects the distribution of the radioisotope uptake in the tissue or organ of interest by recording the gamma photons emitted as they undergo radioactive decay.2 Th king principle of a gamma camera can be explained as follows: the radiopharmaceutical is absorbed by the organ, which emits gamma photons. The photons collide with the collimator, which ideally will allow only the perpendicular photons to hit the scintillator. The scintillator material (crystal) generates visible light photons, which are fed into the photomultiplier tubes (PMTs) via a light guide. The computer (including readout electronics) then finally displays the image.4 Figure 1.1 shows a basic schematic diagram of a gamma camera. There is similarity in the basic principles of gamma cameras in SPECT and PET as well as some differences, which are discussed below.

1.1.1 PET

Overall, PET utilises approximately the same principles of a gamma camera but uses two gamma rays, which are detected in opposite directions after an annihilation event of the radiotracer inside the patient.5 After an annihilation event happens, the two gamma rays, while travelling in opposite directions, create a line of response known as 'coincidence detection'. This method uses a ring of detectors 360° around the patient to detect the two gamma photons at approximately the same time. A physical collimator is not used in PET. Instead, it uses an electronic collimator to define direction.6 Figure 1.2 shows a basic schematic of detecting the two gamma photons.

1.1.2 SPECT

As the name suggests, sPECT, unlike PET, utilises the basic components of gamma cameras by using single gamma photons emitted from a radiopharmaceutical alongside a tomographic imaging technique to create a functional image. Tomography is the technique of combining two-dimensional projection images acquired at various angles to create three-dimensional information using a reconstruction algorithm.3 Moreover, SPECT uses two flat detectors with physical collimators to define the direction and reduce the scattered photons that attenuate almost 99% of the emitted radiation.7 Thus, PET has higher sensitivity, which leads to better

1.3 Purpose of this study

This study aims to model a curved gamma camera in a Monte Carlo simulation and to investigate whether there are any advantages to this configuration in terms of sensitivity or resolution in comparison to a regular flat gamma camera. As the radioactive material from a point source decays, gamma photons are emitted in a spherical manner.8 A regular gamma camera has a parallel square head, detecting only the gamma photons emitted perpendicularly to the detector, while the remaining photons in the sphere are considered scattered because they do not pass through the perpendicular physical collimator.9

1.4 Organisation of this thesis

This thesis is organised into six major chapters. Chapter 1 includes an introduction to nuclear medicine and brief background information about gamma cameras, including information about the SPECT and PET imaging modalities. Chapter 2 is a literature review of the relevant published research on SPECT. Chapter 3 presents the methodology used in the study, the method and design of the simulation and the data analysis methods. Chapter 4 provides the results obtained from simulations of both flat and curved detectors. Chapter 5 discusses the results and compares the flat and curved detectors. Chapter 6 presents the conclusion of the thesis and possible future work.

Literature Review

Contents

CHAPTER 2. LITERATURE REVIEW
2.1 SPECT Acquisition
2.1.1 Collimator
2.1.1.1 Parallel-Hole Collimator
2.1.1.2 Converging and Diverging Collimators
2.1.1.3 Pinhole Collimator
2.1.2 Solid-State Semiconductor
2.2 Scatter in SPECT
2.3 Advances in SPECT
2.3.1 D-SPECT
2.3.2 CardiArc

Chapter 2. Literature Review

This chapter covers some of the relevant studies related to SPECT and provides a brief background on the published literature. The chapter is structured as follows: 2.1 SPECT Acquisition, 2.2 Scatter in SPECT and 2.3 Advances in SPECT.

2.1 SPECT Acquisition

Usually, SPECT is combined with another anatomical imaging modality to fuse the functional/physiological information in order to improve the diagnostic detail. Such anatomical imaging modalities include computed tomography (CT) and magnetic resonance imaging (MRi). The field of SPECT is rapidly developing, with new changes in both imaging processing algorithms and hardware technology arising in recent years along with enhancements in scintillator detectors and significant improvements at the semiconductor level.6 Nevertheless, SPECT has not been able to contribute more in terms of temporal and spatial resolution and sensitivity like PET. However, the accessibility of SPECT radiopharmaceuticals has encouraged innovation and development in SPECT studies.10 Most of the recent research regarding SPECT instrumentation has been on collimator and solid­state semiconductor detection, which is discussed below.

2.1.1 Collimator

The collimator has an important role in defining a system's extrinsic imaging characteristics, since it is the first layer of the gamma camera to collide with the photons from the radiotracer, which allows them to be counted. Some of the photons are rejected because they are not within a specific angular range.11 There are different designs of collimators, such as parallel­hole, diverging-hole, converging-hole and pinhole collimators.9 Figure 2.1 shows the different types of SPECT collimators used.

2.1.1.1 Parallel-Hole Collimator

Anger first presented a parallel hole collimator in 1964,12 and it is still commonly used as the standard collimator in clinical practice. This collimator is a mechanical selector of gamma photons wherein all holes are parallel to each other. In this type of collimator design, ideally only photons travelling perpendicularly to the detector head interact with the crystals, and the other photons are absorbed by the septa.13 A significant limitation of the parallel-hole collimator is its sensitivity, since the sensitivity and the number of photons have a positive relationship (higher count = better sensitivity). Therefore, the sensitivity is determined by the collimator's septal thickness and its material and hole diameter.14

2.1.1.2 Converging and Diverging Collimators

The difference between converging and diverging collimators is the viewing angles from the detector to the collimator hole. In a converging collimator, the holes are not parallel; it has a focused field of view (FOV) that will fit the whole organ in the centre. When this type of collimator design is used, the image is magnified (small FOV), which helps to detect small objects. Therefore, it can yield finer-resolution and higher-sensitivity images when compared to parallel-hole collimators. A diverging collimator is similar to a converging collimator, but when it is flipped over, the focal point is behind the collimator. The FOV is enlarged, and the image is minified, which helps when imaging an object larger than the detector. Therefore, it yields a decrease in both sensitivity and resolution.15 Both converging and diverging collimators cause a distortion in the image size because the size of the image depends upon the distance between the surface of the collimator and the source of the gamma photons.16

2.1.1.3 Pinhole Collimator

A pinhole collimator is a cone-shaped collimator that allows the gamma photons to travel in a straight line through a lead aperture. When this type of collimator design is used, the image is magnified (small FOV), so it is usually used for small organs like the thyroid or joints. The spatial resolution of a pinhole collimator is affected by the aperture material.16 Pinhole collimators also cause a distortion in the image, but an added benefit of a pinhole collimator is that it can image with high energies without any major septa penetration. Meanwhile, in parallel hole collimators, a larger septa must be used to avoid septal penetration with high energies.17

There are other types of collimators, which recent research works compare. Some of the recent collimators and hybrid collimators include multi-pinhole collimators, rotating-slat collimators, multi-segment slant-hole collimators and multi-focal cone-beam collimators. However, they are not further discussed here.9

2.1.2 Solid-State Semiconductor

Solid-state semiconductor detection provides the ability to convert the absorbed gamma photons directly into an electrical signal. As there is no transitional stage between gamma photons and electrical signals, the precision of the signal is improved in comparison to scintillation detectors. Consequently, solid-state semiconductor detectors have better energy resolution.3 There is a considerable amount of research on the use of solid-state semiconductor detection materials in nuclear medicine imaging, and the most prominent and promising material is cadmium zinc telluride (CZT).18 It has been used in several medical imaging modalities, such as PET, SPECT and CT. The use of CZT material in detectors improves the energy, contrast resolution, spatial resolution and stopping power of the imaging systems.19 The major disadvantages of solid-state semiconductor detectors are their intrinsic efficiency, especially with high-energy gamma photons, and manufacturing costs. However, in the past decade, the technology has been enhanced, and the costs of production have dropped.19,2 Figure 2.2 shows the difference in the energy peaks between the most used scintillator material, a sodium iodide doped with a thallium (Nal) detector, and a CZT detector when imaging a technetium-99m source(TC-99m); it indicates a narrower energy peak for CZT, resulting in a higher energy resolution.20 Therefore, CZT material could be an optimal choice for the purpose of the study.

Abbildung in dieser Leseprobe nicht enthalten

Figure 2.2 Difference in the energy peaks between a Nal scintillation detector and a CZT detector when imaging a technetium-99m source. From Khoshakhlagh, M., Islamian, J. P., Abedi, S. M., & Mahmoudian, B. (2015). Development of scintillators in nuclear medicine. World Journal of Nuclear Medicine, 14(3), 156.

2.2 Scatter in SPECT

When photons are emitted from radioactive material, they can undergo photoelectric absorption or be scattered, either by the Rayleigh effect or the Compton effect. Photoelectric absorption is when gamma photons interact with the atoms of the absorbing material. Then, all photons disappear, and their energy is transferred to the orbital electrons of the atoms, which are then ejected. The overall process is the complete exchange of the photons' energy into fast electrons carrying the energy. Subsequently, the fast electrons are then detectable through further interactions; this can serve as an indication of the presence of the gamma photons, which is useful in SPECT imaging.21 Rayleigh scatter is a change in the direction of the photons without any reduction in the energy, and there is a quite low probability of a Rayleigh event happening in soft tissues at the SPECT energy level. However, Compton scatter is the most probable interaction to happen in soft tissue or water between the energies of 40 keV and 10 MeV.22 Compton scatter is when gamma photons change their direction and energy due to an interaction between the gamma photons and free electrons or loosely bound valence-shell electrons.23 Approximately 30%-40% of the photons detected in the sPEcT head in clinical use are scattered photons, which cause a reduction in the spatial resolution and a blurring effect in the image.24 Scatter produces a false contribution of counts that must be corrected.25 There are different approaches for the correction of scatter, some of which are simple while others are complex. Scatter correction requires an estimation of the scatter component of the projection data combined with a compensation method.26 Figure 2.3 shows a schematic illustration of the different types of scattered photons that

2.3 Advances in SPECT

Nuclear medicine has advanced from a clinical subspecialty used in basic tests to the best method to image organ physiology. It has truly become a molecular imaging technique. Hybrid techniques like SPECT/CT, which combine anatomical and functional imaging, have allowed for the characterisation of processes even on the subcellular levels for better assessment of the functions. At the same time, this progress in imaging modalities requires an increase in training time and improvement in practice. Moreover, research continues on the design of various geometries and different detector technologies for SPECT cameras, and this is the most common direction in academic research and the nuclear medicine industry. This is what this study is about, and some of the related research work will be discussed below. However, radiopharmaceuticals have also played an important part in the improvement of the nuclear medicine practice. There are different types of radiopharmaceutical research approaches, such as multi-mode imaging, the theragnostic approach, radioactive nanoparticles and quantification of SPECT radiopharmaceuticals.27 It is exciting to see which technology or approach will be the most popular in the future.

2.3.1 D-SPECT

The D-SPECT (Spectrum Dynamics) is a unique detector technology and a novel acquisition geometry, providing potential advantages in nuclear cardiology compared to the standard flat gamma camera. Which has some principles that match the purposed curved detector in this study. It is equipped with tungsten collimators and has nine arrays of CZT detectors, each one of which rotates around its central axis with angular rotation that can be programmed. This allows the detectors to move in a way that is not feasible with a flat detector with Nal crystals. This configuration has advantages over the flat SPECT camera, including a higher count rate, faster acquisition time and energy resolution. However, this configuration has poor geometric resolution compared to conventional SPECT because the tungsten collimators have a larger aperture area with a shorter length.28 Figure 2.4 shows a schematic diagram of the D-SPECT gantry, with the position of the nine detectors.

2.3.2 CardiArc

CardiArc is a SPECT system dedicated to cardiac imaging, with a circular gantry that uses a 180° arc about the patient while they sit in an upright chair. The system detector utilises three curved Nal crystals with 60 PMTs arranged in three rows, and horizontal collimation is accomplished in each slice by using a curved thin lead sheet with six narrow vertical slots. While vertical collimation is accomplished using a series of vertically stacked stationary lead vanes that are between the Nai crystals and the aperture arc to collect a 1-mm-thick slice, which can acquire high-definition and high-spatial-resolution images in a short scan time.29 Figure 2.5 shows the schematic design of a CardiArc camera.

To sum up, these two types of unique detectors were discussed here briefly to show that innovative detector geometrics have been shown to have a high potential and that the research work is interested in improving the SPECT geometry along with other areas.

Methodology

Contents

CHAPTER 3. METHODOLOGY: MONTE CARLO
3.1 Methodology
3.2 Methods
3.2.1 First Step: The World Volume
3.2.2 Second Step: Scanner Geometry
3.2.3 Third Step: The Phantom
3.2.4 Fourth Step: The Source
3.2.5 Fifth Step: Sensitive Detectors
3.2.6 Sixth Step: Physics Processes
3.2.7 Seventh Step: Digitiser
3.2.8 Eighth Step: Data Output
3.2.9 Ninth Step: Data Acquisition
3.3 Data Analysis Methods
3.3.1 ROOT
3.3.2 Jupyter Notebook

Chapter 3. Methodology: Monte Carlo

This chapter presents the methodology used in the study, the methods that were used and the simulation design and its setups. This chapter is structured as follows: 3.1 Methodology;

3.2 Methods (including simulation designs); and 3.3 Data Analysis Methods.

3.1 Methodology

In this thesis, a Monte Carlo method was used to build and simulate two SPECT scanners, i.e. a standard flat detector and a curved detector, to investigate whether there are any advantages to this configuration in terms of sensitivity or resolution. Monte Carlo methods are widely used in several modalities in nuclear medicine because they have been proven to be a very useful tool to design new types of medical imaging technologies, new techniques for scatter correction and new algorithms for reconstruction.30 Additionally, these methods have helped in studying imaging characteristics and have provided measurements of parameters that could not be obtained experimentally.31 Nuclear medicine simulations have utilised Monte Carlo methods for over 50 years.32 A Monte Carlo simulation is a computational technique that uses algorithms to creates random variables to compute or model physical quantities.32 Thus, when building a model in the Monte Carlo method, the simulation goes through a range of substituting the probability distribution, and the results are repeatedly calculated, with different values being randomly set each time. Due to the use of probability distribution in the input variable, the outcome generates different paths. As a result, a Monte Carlo simulation can be time-consuming when modelling a SPECT camera, for instance, because every particle and each physics interaction has to model for millions of particles.32 Moreover, a Monte Carlo simulation requires an accurate model of the underlying processes to be examined. In nuclear medicine, this involves well-defined models of all interactions related to the radiation emitted by radiopharmaceuticals and radioactive materials, such as alpha particles, beta particles, gamma rays, x-rays and electrons, to get a more accurate simulation and, eventually, a valid result.33 One of the most popular simulation software packages is GATE, which was developed at an open GATE collaboration between a number of research groups from 21 laboratories around the world that are dedicated to the development and validation of the software. It is very suitable to perform simulations for conventional and novel detection systems.33

3.2 Methods

Herein, the curved and flat detector models were developed using virtual Gate (vGate). This is a virtual machine that can run GATE simulations using the free software Virtual Box, which enables vGate to run on any host machine, including Windows, MacOS and Linux.34 After installing Virtual Box and running vGate, the simulation could be launched in a few steps. The vGate machine operates using macro scripting language instead of the complex C++ coding, which is required when using Geant4 (on which GATE is built) directly. The macros are American Standard Code for Information Interchange (ASCII) files, and each line in those files contains a comment or a command; comments start with the character (#).35 Furthermore, a macro or set of macros should include all the commands of the simulation components in the right order. Typically, there is a master macro, which will call on another macro that is more specific. Additionally, there are several simulation benchmarks, some of which are included in vGate and some of which are online. The benchmarks are used to check the integrity of the installation and provide some examples of the main features and how to use them in GATE simulations of SPECT or PET experiments. All benchmarks contain macro files that run the simulation, create figures and analyse the simulation output.

There are necessary steps to complete before performing a full imaging application simulation using vGate. These steps and how to design the conducted simulations are listed below.

3.2.1 First Step: The World Volume

The world volume is the first step in establishing a vGate model. It is specified as a large box made up of air centred at the origin. Figure 3.1 shows the world volume. The location of all material databases defined in one file must be specified at the beginning. The size of the world volume should be large enough to include the scanner and all simulation parts. It can be any size so long as it is not too large in order to avoid an excessive duration of simulation time because the software will simulate the photons travelling from the source away from the scanner until exiting the world volume, which will be of no relevance to the simulation's final results. The location inside the world volume is stated according to a Cartesian coordinate system using x, y and z directions. Figure 3.2 shows an example of a Cartesian coordinate system.

3.2.2 Second Step: Scanner Geometry

The world volume includes one or more sub-volumes called daughter volumes, each of which has a specific name and meaning. The first daughter volume of the world volume is known as the system, which will work as a general template for the scanner that encompasses all the geometry. The scanner system named in these simulations was 'SPECThead' and contained several layers, each layer having a smaller volume and a certain function. The layers in both simulations were the same regarding their function and material for the sake of the validity of the simulation but had different geometries. The scanner head 'SPECThead' contained the following layers: shielding, back compartment, crystal and collimator. Parameters such as the collimator holes were the same (septal length= 20mm, hole size=2mm, septal thickness= 0.1mm) but the dimensions of the layers were different between the flat and curved detectors to establish an optimal arrangement of layers. Furthermore, a rectangular collimator hole used in the simulations would have been more realistic if a hexagonal hole were used instead, but due to technical deficiencies in the software, it was not feasible to arrange a curved collimator with hexagonal holes. According to Weng et al. (2013), the second-best choice is a rectangular hole when comparing hexagonal, rectangular and circular holes in tungsten-based collimators.18 Moreover, CZT was utilised in the crystal due to the fact that CZT has a better energy resolution than NaI crystal along with the other advantages mentioned in Chapter 2, Section 2.1.2. Figure 3.3 shows the scanner heads' geometry shapes used in the simulations.

3.2.3 Third Step: The Phantom

The second daughter volume of the world volume is called the phantom and uses the same principles to position and place the phantom in the FOV. When conducting a simulation with gamma source emitters, the phantom is necessary to provide a medium for the emission. Usually, SPECT studies in GATE simulations use a human-like phantom, but some use a water phantom, which is easier to use and can work as a tissue or muscle equivalent. In this study, a water phantom was used to be filled with a gamma source. In addition, there were two phantom sizes (10-mm, 30-mm diameter) used in the simulations to see how the sensitivity might change between the two detectors. Figure 3.4 shows the 30-mm diameter phantom.

3.2.4 Fourth Step: The Source

The GATE software provides its users with different types of sources, either gamma rays, ions or positrons. The users can also select the characteristics and geometries of the source. Additionally, the users can define the distribution of the energy and emission direction. A point gamma source with a radius of 2 mm was used in this study, namely technetium-99m at 140 keV, as this is the most commonly used radioactive material in SPECT. The gamma photons require the phantom around the source to simulate the acquisition accurately, or else they will escape the world volume, resulting in errors in the simulation.35

3.2.5 Fifth Step: Sensitive Detectors

When the basic volumes like the scanner and phantom have been defined, the sensitive detectors must be specified in the simulation to record all interactions between particles. These interactions are identified as 'hits'. All information and energy deposition of every interaction are stored in the hits. In addition to other parameters, the position, time of the interaction and type of particle are recoded. The GATE software provides two sensitive detectors with different vital functions to ensure accurate results. First, the crystal sensitive detector (SD) is attached to a sensitive volume (scintillation crystal) to obtain the hit data from only the CZT layer. Second, the phantom SD is attached to the phantom, which allows the program to differentiate whether the photon is unscattered or scattered within the phantom or from somewhere else. Moreover, the phantom SD is attached to all volumes that might have an interaction with the photons to be recorded.35

3.2.6 Sixth Step: Physics Processes

Once the volumes and SDs are specified, the interaction processes in the simulation must be described, which allows the simulation to create physical processes as in an actual environment. Monte Carlo simulations provide an estimated solution. More accurate parameters allow for more reliability in the simulation. The user can set cuts or thresholds to customise the simulation.

3.2.7 Seventh Step: Digitiser

The digitiser uses a complex algorithm to model readout schemes and track the energy response, threshold (80keV to 180keV) and dead time of the detector to build physical observables from the hits. For example, one of the digitiser modules is to insert an adder to gather the hits produced per elementary volume into a pulse. If one photon enters the detector and creates multiple hits inside two crystal volumes before being stopped, that will involve two pulses. Every pulse is added as follows: the total energy in every volume plus the position of the hits.35

3.2.8 Eighth Step: Data Output

By default, GATE provides two types of data output formats for almost all user systems, namely ASCII and ROOT. The ROOT output is very important when carefully studying the scanner performance and when considering the system's graphical validation. The ASCII output allows for more flexibility, and it is very intensive since it records a large number of emission parameters in text formats that can be further processed. The outputs are further discussed below in the data analysis section.

3.2.9 Ninth Step: Data Acquisition

Data acquisition is the final step to be defined, as the start and the end of the simulation are defined in real-life experiments. Even the time-slice parameter should be defined to set the time duration that the system assumes to be static. Additionally, the total number of events can be fixed by the user, so the number of particles is divided between the slices of the whole simulation.

3.3 Data Analysis Methods

The data analysis methods were ROOT and Jupyter Notebook, which were used to evaluate the detectors' performance and provide useful information that could lead to a better understanding of the simulation.

3.3.1 ROOT

Developed by Conseil Européen pour la Recherche Nucléaire (CERN), ROOT is a framework for processing data; ROOT applications can be used to analyse data or to execute simulations. its files save data in a compressed binary form and have containers for the data called trees; leaves in a tree have substructure branches called leaves. A tree is useful for fast and easy access to a large amount of data. Thus, ROOT provides a powerful statistical and mathematical tool to manage data. it can show the results in scatter plots, histograms and fitting functions, and it can easily create graphics in real time.36

3.3.2 Jupyter Notebook

Jupyter Notebook is a web-based interactive software developed by the iPython Project in 2014. Jupyter is used to create and share documents that contain narrative text, equations and live code. A Jupyter Notebook document includes an ordered list of input/output cells, which usually contain plots, code, mathematics and rich media; the document usually ends with an '.ipynb' extension. Several applications utilise Jupyter, such as for statistical modelling, data cleaning and transformation and machine learning.37

Contents

CHAPTER 4. RESULTS
4.1 Point Source
4.2 30-mm-Diameter Water Phantom
4.3 10-mm-Diameter Water Phantom
4.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number
4.5 Experimental Setup Results
4.5.1 Detector Head and Phantom Position
4.5.2 Source Position Validation
4.5.3 Energy Spectra

Chapter 4. Results

This chapter provides the results obtained from the simulations of both flat and curved detectors. Four sets of simulations were conducted in this study to give a clear evaluation and comparison between the flat and curved detectors. This chapter is structured as follows: 4.1 Point Source; 4.2 30-mm-Diameter Water Phantom; 4.3 10-mm-Diameter Water Phantom; 4.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number; and 4.5 Experimental Setup Results.

4.1 Point Source

Abbildung in dieser Leseprobe nicht enthalten

Figure 4.1 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Flat detector's hits subtracted by curved detector's hits.

Quantity type/Detector Curved Flat

Abbildung in dieser Leseprobe nicht enthalten

Table 4.1 Quantitative data resulting from the detectors imaging a point source.

4.2 30-mm-Diameter Water Phantom

A cylindrical water phantom with a 30-mm diameter with a fixed number of primaries total of 160,000 recoded in 16 slices. A point source with a radius of 2 mm was placed in the middle of the phantom. Figure 4.2 shows the positions of the hits in the camera in 2D produced by Jupyter Notebook. Table 4.2 shows the quantitative results produced by ROOT from the

Quantity type/Detector Curved Flat

Abbildung in dieser Leseprobe nicht enthalten

Table 4.2 Quantitative data resulting from the detectors imaging the 30-mm-diameter water phantom.

4.3 10-mm-Diameter Water Phantom

A cylindrical water phantom with a 10-mm diameter with a fixed number of primaries total of 160,000 recoded in 16 slices. A point source with a radius of 2 mm was placed in the middle of the phantom, and the distance between to the detector head and phantom was increased. Figure 4.3 shows the positions of the hits in the camera in 2D produced by Jupyter Notebook. Table 4.3 shows the quantitative results produced by ROOT from the simulations.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4.3 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Curved detector's hits subtracted by flat detector's hits.

Quantity type/Detector Curved Flat

Abbildung in dieser Leseprobe nicht enthalten

Table 4.3 Quantitative data resulting from the detectors imaging the 10-mm-diameter water phantom.

The cylindrical water phantom with a 10-mm diameter with no fixed number of primaries eight slices only were acquired. A point source with a radius of 2 mm was placed in the middle of the phantom. Figure 4.4 shows the positions of the hits in the camera in 2D produced by Jupyter Notebook. Table 4.4 shows the quantitative results produced by ROOT from the simulations.

Abbildung in dieser Leseprobe nicht enthalten

Figure 4.4 A - Hits' positions in the curved detector. B - Hits' positions in the flat detector. C - Curved detector's hits subtracted by flat detector's hits.

Quantity type/Detector Curved Flat

Abbildung in dieser Leseprobe nicht enthalten

Table4.4 Quantitative data resulting from the detectors imaging the 10-mm-diameter water phantom with no fixed primaries.

4.5 Experimental Setup Results

This section provides the graphical validity evidence and the energy spectra of the simulation models.

4.5.1 Detector Head and Phantom Position

Figure 4.5 shows several views from different angles of the curved detector. Figure 4.6 shows several views from different angles of the flat detector.

4.5.2 Source Position Validation

The source was positioned in the middle of the detector, and Figure 4.7 shows the match as

4.5.3 Energy Spectra

As technetium-99m (140 keV) was used in all simulations, energies from 80 keV to 180 keV only were allowed, as presented in Figure 4.8, which was produced by ROOT.

Discussion

Contents

CHAPTER 5. DISCUSSION.
5.1 Point Source Discussion
5.2 30-mm-Diameter Water Phantom Discussion
5.3 10-mm-Diameter Water Phantom Discussion
5.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number Discussion
5.5 Experimental Setup Discussion
5.5.1 Detector Head and Phantom Position
5.5.2 Source Position Validation
5.5.3 Energy Spectra
5.6 Advantages and Disadvantages

Chapter 5. Discussion

This chapter discusses the results obtained from the four simulation sets for the curved and flat detectors and whether there are any advantages of the new configuration. This chapter is structured as follows: 5.1 Point Source Discussion; 5.2 30-mm-Diameter Water Phantom Discussion; 5.3 10-mm-Diameter Water Phantom Discussion; 5.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number Discussion; 5.5 Experimental Setup Discussion; and 5.6 Advantages and Disadvantages.

5.1 Point Source Discussion

As presented earlier in the results, a point gamma source with a radius of 2 mm was used to conduct the simulations. This was technetium-99m (140 keV), as it is the most gamma­emitting material used in SPECT. The source was placed in air and imaged with a fixed number of primaries for a total of 80,000 hits recoded in 16 seconds at 1 second for each slice for a total of 16 slices. As a result, Figure 4.1 shows the 2D positions of the hits in the camera and seems to be similar for both detectors, with a slight difference in the main volume. However, the flat detector's main volume of hits looked more defined with less scattered photons around the main volume, as is illustrated in the image of the flat detector's hits subtracted by the curved detector's hits. This was the visual assessment. However, in Table 4.1, the effect of the scattered photons was also reflected quantitatively because the curved detector had a higher Compton interactions number. Meanwhile, in terms of sensitivity, the curved detector recorded a higher hits number, with higher photoelectric interactions and less Rayleigh scattering. Although Rayleigh scattering is usually negligible in SPECT, for more accurate quantitative calculations, it was included here. Moreover, the curved detector had a collimator that worked similarly to a converging collimator and should have worked better with small objects. However, as the distance between the point source in the air and the collimator was short, there might have been more collimator penetration of gamma photons. Theoretically, if a water phantom is used or the distance between the source and detector head is increased, this might change because the photons will be attenuated either inside the phantom or by the distance. Consequently, the collimator penetration will be decreased.

5.2 30-mm-Diameter Water Phantom Discussion

As obtained earlier in the results, a cylindrical water phantom with a 30-mm diameter was imaged with a fixed number of primaries for a total of 160,000 hits recoded in 16 slices at 1 second per slice. The same point gamma source of Tc-99m was centred inside the water phantom. Thus, Figure 4.2 provides 2D images of the positions of the hits in the camera, and it appears that the flat detector has a better image, with less scattered photons around the edges. Therefore, in Table 4.2, the flat detector has less Compton interactions and less Rayleigh scattering, although this is a small difference. The scatter is more focused in the edges as the flat detector's hits were subtracted by the curved detector's hits, as the image shows. Nevertheless, the curved detector seemed to be consistent in having a higher sensitivity, as Table 4.2 shows a higher number of hits and higher number of photoelectric interactions. However, imaging large objects in curved detector has shown as a limitation which badly reflected in the visual results and in the total number of scattered photons. usually, a converging collimator as it is similar to the curved detector is used when the detector surface area is relatively large. However, as an advantage of the curved detector, more hits were detected, and this allowed for one of the following effects in case imaging a smaller phantom: a decrease in the image noise, a faster acquisition time or a reduction of the effective dose needed to achieve a full SPECT exam.

5.3 10-mm-Diameter Water Phantom Discussion

As discussed previously in Section 5.1, using a curved detector with a point gamma source in the air increased the collimator penetration and negatively affected the image. It was thought theoretically that if a water phantom were used or the distance between the source and detector were increased, this might give better results. Additionally, in Section 5.2, a water phantom was used, but it did not yield better results due to the use of a large water phantom, which caused a higher scattering number that also negatively affected the image. For this reason, the same point source and same experiment time were used but with a 10-mm- diameter water phantom and an increase in the distance between the source inside the phantom and the detector head. As a result, Figure 4.3 displays the positions of the hits in the camera in 2D, and it looks like the curved detector clearly had the upper hand in imaging small objects or organs. Its image is more defined with less scatter around the main volume, as the image of the curved detector's hits subtracted by the flat detector's hits shows. This advantage is also reflected quantitatively, as the curved detector had a higher photelectric interactions number, less Rayleigh scattering and approximately the same Compton interactions number. Additionally, in sensitivity, the curved detector kept the same consistency to have a higher hits number.

5.4 10-mm-Diameter Water Phantom with No Fixed Primaries Number Discussion

This last simulation set was conducted using the same source, phantom and detector head distance as in Section 5.3 but with no fixed primaries number to investigate whether the curved detector would continue the same pattern of having a higher hits number and whether that would affect the image. Additionally, the experiment timing was reduced to half, i.e. eight slices at one second per slice, due to the lack of computing power to process the full simulation. However, Figure 4.4 shows the hits in the camera in 2D, and it appears that the curved detector continued to have the same advantage in imaging small objects. The results might have been too noisy to be differentiated, but the image of the curved detector's hits subtracted by the flat detector's hits was helpful to be in the visual assessment. Similarly, in the quantitative data, the results seemed to be a kind of trade-off between resolution and sensitivity, as Table 4.4 represents that the curved detector had a higher photoelectric interaction number but more Compton interactions and Rayleigh scattering. Although the flat detector had less scattered photons, the main volume in the middle was very noisy as can be seen. Meanwhile, in terms of sensitivity, the curved detector continued in the same pattern to have a higher hits number in every simulation.

5.5 Experimental Setup Discussion

This section, as represented in the results, is to provide a discussion on the graphical validity and the energy spectra of the simulation models. It should be noted that an actual SPECT camera is different than the simulated scanners. The simulated scanners were different from the real scanners in their geometry and the method of processing the pulses or generating the photons. Of the several graphical validation data, only a few were added to the results to avoid an intensive representation.

5.5.1 Detector Head and Phantom Position

Figure 4.5 and Figure 4.6 are a visual representation of the curved and flat detectors' heads and show the phantom centred in the middle of the detectors. In addition, it was confirmed that there was no overlap in the layers of the detectors, that they were all arranged together optimally and that the collimator blocked the line-up at the edges.

5.5.2 Source Position Validation

It is important to check the source position among the detector heads' positions and phantom positions, as the source position is an essential part to be validated. The source position was positioned in the centre of the detector, and Figure 4.7 shows the position according to the X, Y and Z axes, as it was the same in all conducted simulations.

5.5.3 Energy Spectra

One of the main focuses of Monte Carlo simulations using GATE is to produce realistic circumstances so that the results are comparable with real-life experimental outcomes within satisfactory margins. This incorporates a realistic model of all possible physical interactions, including attenuation and scattering effects throughout the simulation. As shown in Figure 4.8, the validation of energies ranging from 80 keV to 180 keV was only allowed because Tc- 99m with an energy of 140keV was used in all simulations which were similar, but with minor variations.

5.6 Advantages and Disadvantages

In this section, Table 5.1 shows a brief general summary of the advantages and disadvantages of the curved and flat detectors, which were discussed above earlier or noted during the simulation.

Abbildung in dieser Leseprobe nicht enthalten

Table 5.1 Advantages and disadvantages of the curved and flat detectors

Conclusion

Contents

CHAPTER 6. CONCLUSION
6.1 Future Work

Chapter 6. Conclusion

Nuclear medicine imaging has become increasingly popular in recent years due to its prominent role in molecular imaging. Specifically, due to the availability of SPECT radiopharmaceuticals, innovation and development was encouraged. SPECT uses two flat detectors with parallel-hole collimators to reduce the scattered photons. Most relevant research means to design and test the various geometries and different detector technologies of SPECT cameras. The aim of this study was to model a curved gamma camera using GATE simulations to test this configuration and determine whether there are any benefits in terms of sensitivity or resolution. There was a geometrical limitation during the arrangement of the curved detector layers: a collimator with hexagonal holes arranged in a curved manner was not possible due to technical limitations in GATE. Thus, instead, rectangular holes were used in a tungsten-based collimator, which was considered the second-best choice. Both detectors had the same collimator hole dimensions, same layer arrangements and same materials and functions for the validity of the simulations.

A brief background on the published literature about SPECT and about some of the research related to the study was presented, such as on the types of collimators used. One of the types is a converging collimator, which is similar to the curved collimator but with the main difference in the scintillator part. It is also curved along the whole geometry in the simulated detector but is flat in the converging collimator. Additionally, a more sophisticated scintillator material, known as CZT, was used in this study; it has more advantages than the most used material, Nal. The results were analysed using the ROOT and Jupyter Notebook methods, which were explained earlier. There were four sets of simulations conducted in the study with different imaging objects and parameters: point source, 30-mm-diameter water phantom, 10-mm-diameter water phantom and 10-mm-diameter water phantom with no fixed primaries number. To sum up the outcomes, the first simulation set was to image a point source of Technetium-99m (140 keV), and the flat detector yielded a better result because the curved detector had a high number of high-energy photons penetrating the collimator, which affected the results adversely. The second simulation set was to image the same point source with a 30-mm water phantom to reduce the number of photons penetrating the collimator with a fixed number of primaries, but the flat detector also produced a better result due to the curved detector's limitation in imaging large objects, which increased the scattered photon number. The third simulation set was to image with the same objects used in the second simulation but with one-third of the phantom size and an increase in the distance between the source and detector head. A 10-mm water phantom was utilised to reduce the number of scattered photons, and the curved detector yielded a better result, as expected. In all previous simulations, the curved detector had better sensitivity (higher hits), so the fourth simulation set was to image the same objects with the same parameters used in the third simulation but with no fixed primaries number and half the experiment time due to a limitation in the computing power to process a full simulation. To investigate whether the curved detector would continue to have a higher hits number and the advantage of imaging small objects. The results shows that the curved detector proved to have the upper hand in imaging small objects and a better sensitivity. Finally, several experimental setups were represented to provide validation evidence for the conducted simulations.

6.1 Future Work

As illuminated in Chapter 3, the proposed approach to design and develop a curved detector was a GATE Monte Carlo simulation to produce realistic SPECT simulation data. This was the first attempt to develop a fully curved detector with CZT material in a Monte Carlo simulation, and several potential future studies can be done to develop it. There are several potential directions to investigate further, such as:

1 The GATE software can provide very accurate results. However, for a newly proposed model such as the curved SPECT detector, it would be exciting to have more investigations to gain a comparative analysis with other available Monte Carlo simulation tools.
2 Building a low-cost design for the curved detector and conducting further integration for this configuration could be a major future direction for this study.
3 There were some limitations in the computing power; a further examination with a more powerful computer could yield more data to analyse.
4 The curved detector in this study was shown to have a better sensitivity than the standard flat detector. This configuration is not like the gamma cameras available commercially, so more studies are needed to develop this configuration commercially.

Bibliography

1 Kharfi, F. (2013). Principles and applications of nuclear medical imaging: A survey on recent developments. Imaging and Radioanalytical Techniques in Interdisciplinary Research—Fundamentals and Cutting Edge Applications.

2 Vallabhajosula, S. (2009). Molecular imaging: Radiopharmaceuticals for PET and SPECT. Springer Science & Business Media.

3 Madsen, M. T. (2007). Recent advances in SPECT imaging. Journal of Nuclear Medicine, 48(4), 661-673.

4 Prasad, G. L. (2009). Biomedical applications of nanoparticles. In Safety of Nanoparticles (pp. 89­109). Springer.

5 Decristoforo, C., Haberkorn, U., Haubner, R., Mier, W., & Ziegler, S. I. (2017). PET and SPECT. In Small Animal Imaging (pp. 361-402). Springer.

6 Rahmim, A., & Zaidi, H. (2008). PET versus SPECT: Strengths, limitations and challenges. Nuclear Medicine Communications, 29(3), 193-207.

7 Bushberg, J. T., & Boone, J. M. (2011). The essential physics of medical imaging. Lippincott Williams & Wilkins.

8 L'Annunziata, M. F. (Ed.). (2012). Handbook of radioactivity analysis. Academic Press.

9 Van Audenhaege, K., Van Holen, R., Vandenberghe, S., Vanhove, C., Metzler, S. D., & Moore, S. C. (2015). Review of SPECT collimator selection, optimization, and fabrication for clinical and preclinical imaging. Medical Physics, 42(8), 4796-4813.

10 Schillaci, O. (2005). Hybrid SPECT/CT: a new era for SPECT imaging? European Journal of Nuclear Medicine and Molecular Imaging, 32 (5), 521-524. https://doi.org/10.1007/s00259-005-1760-9

11 Song, X., Segars, W. P., Du, Y., Tsui, B. M. W., & Frey, E. C. (2005). Fast modelling of the collimator-detector response in Monte Carlo simulation of SPECT imaging using the angular response function. Physics in Medicine & Biology, 50 (8), 1791.

12 Anger H. O. (1964). Scintillation camera with multichannel collimators. Journal of Nuclear Medicine, 5, 515-531.

13 Sorenson, J. A., & Phelps, M. E. (1987). Physics in nuclear medicine. Grune & Stratton.

14 Clinthorne, N. H., Ng, C. Y., Hua, C. H., Gormley, J. E., Leblanc, J. W., Wilderman, S. J., & Rogers, W. L. (1996). Theoretical performance comparison of a Compton-scatter aperture and parallel-hole collimator. 1996 IEEE Nuclear Science Symposium Conference Record (Vol. 2), 788-792.

15 Wernick, M. N., & Aarsvold, J. N. (2004). Emission tomography: The fundamentals of PET and SPECT. Elsevier.

16 Wilson, R. J. (1988). Collimator technology and advancements. Journal of Nuclear Medicine Technology, 16 (4), 198-203.

17 Islamian, J. P., Azazrm, A., Mahmoudian, B., & Gharapapagh, E. (2015). Advances in pinhole and multi-pinhole collimators for single photon emission computed tomography imaging. World Journal of Nuclear Medicine, 14 (1), 3.

18 Weng, F., Bagchi, S., Huang, Q., & Seo, Y. (2013). Design studies of a CZT-based detector combined with a pixel-geometry-matching collimator for SPECT imaging. 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference ( 2013 NSS/MIC ), 1-4.

19 Bhattacharya, P., Fornari, R., & Kamimura, H. (2011). Comprehensive semiconductor science and technology: Online version. Newnes.

20 Khoshakhlagh, M., Islamian, J. P., Abedi, S. M., & Mahmoudian, B. (2015). Development of scintillators in nuclear medicine. World Journal of Nuclear Medicine, 14(3), 156.

21 Nelson, G., & Reilly, D. (1991). Gamma-ray interactions with matter. Passive nondestructive analysis of nuclear materials, 27-42.

22 Dahlbom, M. (Ed.). (2017). Physics of PET and SPECT imaging. CRC Press.

23 Hoppe, R., Phillips, T. L., & Roach, M. (2010). Leibel and Phillips textbook of radiation oncology-e­book: Expert consult. Elsevier Health Sciences.

24 Jaszczak, R. J., Floyd, C. E., & Coleman, R. E. (1985). Scatter compensation techniques for SPECT. IEEE Transactions on Nuclear Science, 32 (1), 786-793.

25 Ljungberg, M., & Gleisner, K. S. (2015). Hybrid imaging for patient-specific dosimetry in radionuclide therapy. Diagnostics, 5 (3), 296-317.

26 Hutton, B. F., Buvat, I., & Beekman, F. J. (2011). Review and current status of SPECT scatter correction. Physics in Medicine & Biology, 56 (14), R85.

27 Ilem-Ozdemir, D., Gundogdu, E. A., Ekinci, M., Ozgenc, E., & Asikoglu, M. (2019). Nuclear medicine and radiopharmaceuticals for molecular diagnosis. In Biomedical Applications of Nanoparticles (pp. 457-490). William Andrew Publishing.

28 Erlandsson, K., Kacperski, K., Van Gramberg, D., & Hutton, B. F. (2009). Performance evaluation of D-SPECT: a novel SPECT system for nuclear cardiology. Physics in Medicine & Biology, 54(9), 2635.

29 Slomka, P. J., Patton, J. A., Berman, D. S., & Germano, G. (2009). Advances in technical aspects of myocardial perfusion SPECT imaging. Journal of Nuclear Cardiology, 16(2), 255-276.

30 Assie, K., Breton, V., Buvat, I., Comtat, C., Jan, S., Krieguer, M., ... & Simon, L. (2004). Monte Carlo simulation in PET and SPECT instrumentation using GATE. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 527 (1-2), 180-189.

31 Garcia, M. P., Bert, J., Benoit, D., Bardiès, M., & Visvikis, D. (2016). Accelerated GPU-based SPECT Monte Carlo simulations. Physics in Medicine & Biology, 67 (11), 4001.

32 Fahey, F. H., Grogg, K., & El Fakhri, G. (2018). Use of Monte Carlo techniques in nuclear medicine. Journal of the American College of Radiology, 15(3), 446-448.

33 Jan, S., Santin, G., Strul, D., Staelens, S., Assie, K., Autret, D., ... & Brasse, D. (2004). GATE: a simulation toolkit for PET and SPECT. Physics in Medicine & Biology, 49 (19), 4543.

34 Open Gate. (2020). VGate (virtual Gate). https://opengate.readthedocs.io/en/latest/vgate.html

35 Open Gate. (2020). Getting started. https://opengate.readthedocs.io/en/latest/getting_started.html?highlight=macros

36 Brun, R., & Rademakers, F. (1997). ROOT—an object oriented data analysis framework. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 389 (1-2), 81-86.

37 The Jupyter Notebook. (2015). Jupyter Notebook 7.0.0.dev0 documentation. https://jupyter- notebook.readthedocs.io/en/latest/notebook.html

[...]

49 of 49 pages

Details

Title
Monte Carlo Simulation of a Curved-Detector Gamma Camera
College
University of Aberdeen
Course
Medical Physics
Grade
with Honours Degree
Author
Year
2020
Pages
49
Catalog Number
V950694
ISBN (Book)
9783346293114
Language
English
Tags
monte, carlo, simulation, curved-detector, gamma, camera
Quote paper
Khalid Alhamad (Author), 2020, Monte Carlo Simulation of a Curved-Detector Gamma Camera, Munich, GRIN Verlag, https://www.grin.com/document/950694

Comments

  • No comments yet.
Read the ebook
Title: Monte Carlo Simulation of a Curved-Detector Gamma Camera



Upload papers

Your term paper / thesis:

- Publication as eBook and book
- High royalties for the sales
- Completely free - with ISBN
- It only takes five minutes
- Every paper finds readers

Publish now - it's free