Characterization of BGO crystals for Time of Flight Positron Emission Tomography

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UNIVERSITÀ DI PISA

SCUOLA DI INGEGNERIA

Corso di Laurea Magistrale in Ingegneria Nucleare

Tesi di Laurea Magistrale

Effects of reflecting material and

surface finish on the timing

properties of BGO

Relatori:

Prof. Francesco d’Errico, Dott. Ing. Riccardo Ciolini, Ing. Marialisa Staglianò

Candidato:

Mohita Gupta

Reactor Institute Technical University of Delft

Dott. Dennis Schaart and Dott. Stefan Brunner

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he remarked to Leopold Infeld that until he was almost 30 he had never seen a real theoretical physicist. To which Infeld replied ‘except in the mirror!”

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Abstract

With new developments in the field of medical imaging, the time-of-flight method has gained increasing popularity in positron emission tomography (TOF-PET) [1]. Clinical TOF-PET systems using L(Y)SO:Ce have proven the benefits of the TOF-method which is now a widely accepted method [2]. The Cherenkov effect is an optical phenomenon which provides an almost instantaneous response to the photoelectric absorption of 511 keV annihilation photons. The Cherenkov yield is mostly in the blue and UV-region of the light spectrum (300-500 nm) and is extremely low (around 20 photons per photoelectric absorption of a 511 kev annihilation photon) [2]. This complicates energy discrimination and is unfavorable for clinical PET.

BGO crystals have been state-of-the-art in PET systems until about a decade ago. In addition to lower price, BGO offers superior physical properties required for detection of annihilation photons. After the introduction of L(Y)SO:Ce, BGO was replaced due to its inferior scintillation properties. However, the optical properties of BGO crys-tals, especially its high refractive index and transparency to blue-UV light make it a good Cherenkov radiator. Previous studies have proven the feasibility of applying BGO crystals as hybrid scintillator/Cherenkov radiator in TOF-PET in lab-scale coincidence experiments [2]. In this work we try to translate these results to prototype detector modules. Therefore, BGO arrays with various optical reflector materials have been ex-amined and are being compared in terms of coincidence resolving time (CRT), photon detection yield and energy resolution.

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List of Figures v Acknowledgements 1 1 Introduction 4 2 Background 6 2.1 Nuclear Imaging . . . 6 2.2 PET Imaging . . . 7

2.2.1 True Coincidence Events. . . 8

2.2.2 Scattered Coincidence Events . . . 8

2.2.3 Random Coincidence Events . . . 9

2.3 Image Quality . . . 9

2.3.1 Spatial Resolution . . . 10

2.3.2 Scanner Sensitivity . . . 11

2.4 Time-of-flight PET . . . 11

3 Materials and Electronics 14 3.1 Photon interaction in matter . . . 14

3.2 Scintillation . . . 14

3.3 Scintillators . . . 15

3.4 Cherenkov Effect . . . 18

3.5 Philips Digital Photon Counter . . . 19

4 Study of NECR for BGO crystals using GATE 22 4.1 Introduction. . . 22

4.2 Detector Geometry . . . 23

4.3 The Monte Carlo simulation model . . . 23

4.3.1 Signal Processing . . . 24 4.3.2 Dead Time . . . 24 4.4 Phantom . . . 25 4.5 Source . . . 26 4.6 Calculations . . . 27 5 Data Analysis 30 5.1 Past Work . . . 30 5.1.1 Simulations . . . 30 iii

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Contents iv

5.1.2 Experimental Studies . . . 31

5.2 Experimental Setup . . . 33

5.2.1 Dark Count Map . . . 35

5.3 Coincidence Sorting . . . 36

5.4 Calculations . . . 39

6 Characterization Studies - I 43 6.1 Primary Characterization : Reflecting Material Comparison Studies . . . 43

6.2 Crystal A : Polished with ESR . . . 44

6.3 Crystal B : Unpolished with ESR . . . 50

6.4 Crystal C : Polished with BaSO4 . . . 55

6.5 Crystal D : Unpolished with BaSO4 . . . 58

6.6 Crystal Comparisons . . . 62

7 Characterization Studies - II 63 7.1 Justification . . . 63

7.2 Secondary Comparison Studies : Polished vs Unpolished . . . 63

7.3 Crystal A : Polished with ESR . . . 64

7.4 Crystal B : Unpolished with ESR . . . 69

7.5 Crystal Comparison . . . 74

8 Conclusions and Future Work 75

A Appendix: Coincidence Sorting Code 77

B Appedix: Data Analysis Code 79

C Appendix: Gate Simulation Code 82

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2.1 PET imaging in neurology [3].. . . 7

2.2 A) The radiotracer emits a positron which interacts with an electron to produce two 511 keV gamma-photons traveling in opposite directions. B) The coincident detection of two 511 keV photons by the circular ring of detectors is used for to know the spatial distribution of the radiotracer [4]. 8

2.3 True coincidences vs scatter and random coincidences[5]. . . 9

2.4 Figure showing PET data acquisition with incorporation of time-of-flight (TOF) reconstruction: (A) Without TOF information (B) With TOF information [6]. . . 12

2.5 Comparison of slices from reconstructive images with and without TOF algorithms [7]. . . 12

3.1 The band structure of an organic scintillator [8]. . . 15

3.2 The photoelectric effect in which incident photons deposit all of their energy to an electron in the crystal lattice which are then free to move within the crystal lattice [9].. . . 16

3.3 Blue-UV shock-wave emitted in a dielectric medium when a charged par-ticle travels faster than the speed of light in it [10]. . . 19

3.4 Philips Digital Photon Counter Tile. It consists of an array of 8 ∗ 8 pixels each with 3200 SPADs [11]. . . 20

3.5 Event accusation sequence in the Philips DPC [11]. . . 21

4.1 Description of the geometry of the PET system modeled in GATE. . . 24

4.2 NEMA IEC body phantom consists of a body phantom, a lung insert and an insert with six spheres with various sizes[12] . . . 26

4.3 NECR for a phantom of volume 9700 ml water at the measured activity concentrations. . . 29

4.4 Rate of true events for a phantom of volume 9700 ml water at the mea-sured activity concentrations. . . 29

5.1 The basic for coincidence measurement used for Geant4 simulation studies [1]. . . 30

5.2 Energy Resolution (top) and mean number of photons detected (bottom) of BGO crystal samples for an incoming 511 keV annhilation photon as a function of the crystal length [2]. . . 32

5.3 Normalized timing histogram comparison between a crystal of length 3 mm and 20 mm [2].. . . 32

5.4 An image showing four BGO arrays that were used with two Philips DPC tile sensors on each side. . . 33

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Contents vi

5.5 Figure (Scale 2:1) showing the source, O, placed right in front of the reference crystal, ABC, and at a distance of at least 80 mm from the

BGO array, DEF. . . 34

5.6 A dark count map showing the microcells in red with the highest dark count rates [11].. . . 36

5.7 Figure showing that all pixels activated in the test tile (top) and only one pixel activated on the reference till. The numbers on the pixels represent the number of microcells fired in the absence of any light and a source. . . 37

5.8 A screen shot of the raw data file obtained form the Philips DPC. . . 38

5.9 Photon count saturation effect [11]. . . 40

6.1 Histogram of the light yield of the Die 1 pixel 1. . . 45

6.2 Histogram of the CRT of Die 1 pixel 1.. . . 45

6.3 Histogram of the light yield of the die 2 pixel 3. . . 46

6.4 Histogram of the CRT of die 2 pixel 3. . . 46

6.5 Histogram of the light yield of the die 5 pixel 3. . . 47

6.6 Histogram of the CRT of die 5 pixel 3. . . 47

6.7 Histogram of the light yield of the Die 10 pixel 1. . . 48

6.8 Histogram of the CRT of Die 10 pixel 1. . . 48

6.9 Figure of the DPC-Tile showing the arrangement of the Dies and pixels. . 49

6.10 Values of the Energy Resolution (%) and CRT (ps) for the individual crystals. . . 49

6.11 Histogram of the Average Light yield of the Pixel. . . 51

6.12 Histogram of the CRT of the Pixel. . . 51

6.18 Histogram of the Average Light yield of the pixel. . . 56

6.19 Histogram of the CRT of the pixel. . . 56

6.22 Values of the Energy Resolution (%) and CRT (ps) for the individual crystals . . . 58

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7.7 Figure of the DPC-Tile showing the arrangement of the Dies and pix-els. Their ER and CRT values have been written at their corresponding locations in the table below. . . 68

7.11 Histogram of the Average Light yield of the pixel . . . 71

7.12 Histogram of the CRT of the pixel . . . 71

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Acknowledgements

I would like to extend my heart felt gratitude to the many people who so generously contributed to the work presented in this thesis.

Special mention goes to my supervisors, Dr. Stefan Brunner and Dr. Dennis Schaart. My masters thesis has been an amazing experience and I thank Stefan and Dennis wholeheartedly, for their tremendous academic support and excellent input. I would also like to extend a big thank you to Dr. Eelco Lens and Dr. Jeremy Brown for helping me with the presentation and writing. None of this would have been possible without the help of the ever smiling tennis enthusiast Stefan van der Sar.

I am also hugely appreciative to the staff at University of Pisa. Prof. d’Errico for always taking care of everything. Dr. Ciolini and Marialisa for their never ending support, encouragement for going far beyond the call of duty.

Special mention goes to Ellen, Coen, Aishani, Esha and Asshish for always being there and believing in me.

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Chapter 1

Introduction

Positron-emission tomography (PET) is a nuclear medicine functional imaging technique that is used to observe metabolic processes in the body [5]. The system detects pairs of gamma photons emitted indirectly by a positron-emitting radionuclide (tracer), which is introduced in the body on a biologically active molecule. The time-of-flight (TOF) method involves calculating the difference in arrival time of the two photons to have more information about the location of the annihilation event [6]. This method has gained increasing popularity and commercial interest as it has a large potential for improvement in image quality and accurate quantification of data [13].

The image quality of a PET system depends on how accurately the tracer distribution is reconstructed. The accuracy depends on the number of annihilation photons detected by the PET system and localization of each gamma photon in space and time [7]. The basic component of a PET detector is a block of crystal arrays which detect annihilation photons. There are various crystals that are used commercially available for the current PET systems. One of the most common detector crystals is Lutetium Orthosilicate (L(Y)SO:Ce). It has shown promising results in terms of both energy resolution and coincidence resolving time(CRT) [14]. However, L(Y)SO:Ce crystals are expensive and radioactive. Bismuth Germanate (BGO), another type of detector crystal, was very common until a few decades ago, but were replaced after the introduction of LSOs. This was because even though BGOs was more economic, offered better physical properties required for detection of annihilation photons than L(Y)SO:Ce, it had lower scintillation yield response [15].

The Cherenkov effect is an optical phenomenon exhibited by certain material, BGOs being one of them. BGOs emit Cherenkov light after a photoelectric interaction of the annihilation photons in them. This effect happens almost instantaneously and thus provides a fast response to the 511 keV annihilation photons. The Cherenkov yield is

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mostly in the blue and UV- region of the light spectrum (300-500 nm) and is extremely low (about 20 photons per photoelectric absorption of a 511 kev annihilation photon). This complicates energy discrimination and is therefore unfavourable for clinical PET [2]. However, the optical properties of BGO crystals, especially its high refractive index and transparency to blue-UV light make it a good Cherenkov radiator [1]. Previous studies have proven the feasibility of applying BGO crystals as hybrid scintillator/Cherenkov radiator in TOF-PET in lab-scale coincidence experiments [2].

The main aim of this thesis is to study the influence of surface finishes and reflec-tor materials on detecreflec-tor crystal in order to optimize the CRTs of BGO based hybrid scintillator/Cherenkov TOF-PET detectors. Simulations were performed to study the performance of a detector crystal in PET ring. Experimental studies were also per-formed to compare the timing performance of the crystal with different surface finishes and reflector materials.

In the first chapter a general background about the matter is presented. It includes a detailed description of positron emission tomography, the factors that contribute to image quality and the time of flight method.

Chapter two gives a detailed description about the physical properties required of a detector crystal, the scintillation and Cherenkov effect. It also includes a description of the electronic devices that were used to perform the studies.

Chapter three presents a simulation study using a Monte Carlo code. The geometry of a commercially available PET system is simulated using a Geant4 based software with BGO crystals and its findings are discussed.

Chapter 4 describes the experimental setup and data analysis methods that were used.

Finally, chapters 5 and 6 present the results obtained from two phases of of experiments. It discusses all the data and the graphics obtained with the method described in the previous chapter.

The thesis ends with a conclusion and a part called “future work”, with visions about the next generation of the detector unit.

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Chapter 2

Background

2.1 Nuclear Imaging

Molecular imaging techniques allows the visualization of biological processes in living organisms. This is done by using certain synthetic biomolecules called ‘radiotracers’ that target a specific area where the biological process of interest is occurring, with minimum interference. If the property which allows the visualization of these processes is radioactivity, then the technique is called nuclear imaging.

Positron emission tomography (PET) is one of the many available nuclear imaging tech-niques used today. This method uses positron emitting radiotracers for image recon-struction. The radiotracer is injected into the subject so that it accumulates in the area of interest. The radiations emitted are then collected and interpreted to form an image.

PET is commonly used in oncology to identify tumor cells and is usually the first step towards treatment planning [16]. The patients are injected with 18F-labelled glucose analogue, 2-deoxy-2-fluoro-D-glucose (FDG) as the radiotracer. PET helps to provide the necessary information on tumors such as its growth, location and internal structure which is later used for treatment planning [16]. PET can also be used in cardiology for detection of coronary artery disease by measuring blood flow to the heart. In neurology PET is used for detection and diagnosis of various diseases such as Alzheimer’s disease (figure 2.1), Parkinson’s disease and epilepsy [16] [3].

PET also plays a very important role in the field of molecular biology. This type of research involves the study of disease formation and drug development by conducting experiments on laboratory animals. An advantage of PET in this field of research is that the distribution of a radiotracer can be followed as a function of time in a single

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Figure 2.1: PET imaging in neurology [3].

living animal, allowing an in vivo study of biomolecular kinetics. The same animal can also be used at a later stage to follow disease formation and propagation [16].

2.2 PET Imaging

Tumor cells have a very rapid mitosis rate and need large amounts of glucose for sus-tenance. Typically a PET examination starts with an injection of FDG in the patient. The radiotracer then spreads within the subject and accumulates in the region where the tumour lies. The radionuclides decay and emit positrons with a certain kinetic en-ergy. The positrons slow down by several interactions in the biological tissue. Their energy loss continues till the positron reaches thermal equilibrium with its surrounding medium. Eventually the positrons annihilate with electrons in the surrounding medium to form two back-to-back gamma photons of 511 keV energy each, following Einstein’s mass-energy-equivalence equation. This process is illustrated in Fig 2.2. These pho-tons are then detected by a ring of detectors surrounding the patient. The coincident detection of two photons is the basic principle in establishing that they came from the same annihilation event. The responding detectors are then virtually connected by a straight line. This line is called as the line of response (LOR) and it is assumed that the annihilation event occurred somewhere along this line. A collection of many of such LORs is used to create an image of the spacial distribution of the radiotracer [5].

State-of-the-art PET scanners consist of a 2-dimensional array of detector crystals cou-pled to photo sensors. When incident 511 keV photons from the annihilation event hit these crystals, they interact by depositing all of their energy via the photoelectric effect, that produces a light flash due to the characters of the scintillator. The optical photons are then detected by the coupled photo sensors.

Coincidence events in PET are broadly classified into three categories: true, scattered, random. These are illustrated in figure 2.3.

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Figure 2.2: A) The radiotracer emits a positron which interacts with an electron to produce two 511 keV gamma-photons traveling in opposite directions. B) The coinci-dent detection of two 511 keV photons by the circular ring of detectors is used for to

know the spatial distribution of the radiotracer [4].

2.2.1 True Coincidence Events

True coincidences occur when both photons from an annihilation event are detected by detectors in coincidence, neither photon undergoes any form of interaction prior to detection, and no other event is detected within the coincidence time-window [8].

2.2.2 Scattered Coincidence Events

Scattered coincidence events occur when annilation photons interact via the Compton effect. A photon with an incident energy, E0, transfers a part of its energy to the atomic

electrons along its path and is in turn deflected from its original path by an angle θ. The final energy is given by Es The equation relating θ, E0 and Es is given by the law

of conservation of momentum and energy and is as follows [8],

Es = E0 1+E0(1−cosθ)

m0c2

(2.1)

where m0c2 is rest energy of the the electron ejected from the atom. In principle, the

angle θ can vary from 0 to π. Detected annihilation photon pairs for which one or both photons had a previous Compton interaction loose most of the information regarding the position and energy of the annihilation event [5]. They contribute to image noise and background along with the random coincidence events.

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2.2.3 Random Coincidence Events

Since the width of the coincidence time window is non-zero, there can be more than two single events that are detected within the same time window. This implies that pho-tons from different annihilation events are falsely classified as annihilation pairs. Such incorrectly classified pairs are called random coincidence events The rate of occurrences of random events for a PET detector ring is given by the equation [5]

rrandom = 2τ r1r2 (2.2)

where τ is the coincidence resolving time, r1 and r2 are the rate of counting of single

events for the two detecting crystals where the two photons interacted. Further, the count rate of single events is inversely proportional to the diameter of the scanner ring. Therefore, equation 2.2 can be rewritten as[14]

rrandom∝

1

R2 (2.3)

where R is the ring diameter. Increasing ring diameter will reduce rrandom but will

increase the value of τ . Therefore, it is important to keep the value of τ low but choose an appropriate ring diameter to minimize the random events [16].

Figure 2.3: True coincidences vs scatter and random coincidences[5].

2.3 Image Quality

The image quality obtained form a PET detector can be described in terms of its spatial resolution and signal-to-noise ratio.

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2.3.1 Spatial Resolution

Spatial resolution is essentially the smallest describable detail in an image. It represents the size of the spatial features that can be distinguished and depends on several factors such as type of crystals used, scanner design and geometry, and the image reconstruction algorithm used. The geometry of the detector crystals used also play a role in the spatial resolution of a PET image [1].

Another factor that is consequential to spatial resolution is the physics of positron decay and annihilation. Before the emitted positron comes to rest and annihilates with an electron, it travels a certain distance in the human body. The length of the distance traveled, or the range of the positron, depends on the initial energy of the positron which in turn depends on the type of emitting isotope. The maximum energy of positrons of some common isotopes used in PET are given in table 2.1 [17],

Isotope Energy(MeV)

18_F _0.635 11_C _0.970

13_N _1.9

15_O _1.72

Table 2.1: Energy of positrons of some common isotopes used in PET

When a positron annihilates with an electron to form two 511 keV photons, their com-bined center of mass may have a residual momentum with respect to the laboratory frame of reference. Since the momentum is conserved, the angle between the 2 photons is 180◦ in theory, but in practice, it is slightly less than that. The angular uncertainty in the direction of the paths of the two photons is in the order of a few milliradians. This photon non-collinearity has a blurring effect on the final image that increases with increasing in scanner diameter [15].

In addition, poor spatial resolution in a PET scan can also be caused due to an effect called as the parallax error. When a 511 kev photon deposits its energy on a detector crystal, the system registers a single point of interaction, for example, a point on the front surface of the crystal. However, for obliquely incident photons, this may result in mis-positioning the LOR further, leading to a blurred reconstructed image. This happens because the crystal elements in the current PET systems are usually longer in the axial and transversal directions than their diameter in the axial and transversal directions. The area of response for each annihilation interaction has a great dependency from which angle it is viewed or calculated. However, this error can be reduced by providing information about the depth-of-interaction inside the crystals [1]. This information constrains the volume of response in the radial direction and mends the parallax error.

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The photoelectric absorption of one or both of the photons within the patient is also another plausible cause. If this error is not corrected during image reconstruction then it results in a sort of ‘darkening’ of the inner part of the body, and reduces imaging quality [5].

2.3.2 Scanner Sensitivity

Scanner sensitivity can be defined as the ratio of the number of coincident counts reg-istered per second in a particular volume, to the total number of radioactive decays per second in the same volume [16].

Scanner sensitivity can be improved by increasing the geometric efficiency, GE, which is given by the following equation [5]

GE = n0

n (2.4)

where n is the number of photons that are detected and n0 is the total number of photons

emitted by the source.

Geometric efficiency improves by increasing the solid angle between the detector and the source and can be practically achieved by decreasing scanner diameter and increasing its axial extent. However, a reduction in scanner diameter increases parallax errors, requiring a trade off between scanner sensitivity and image resolution [18].

2.4 Time-of-flight PET

In the time-of-flight method, the time difference of when the two 511 keV photons are detected is calculated. The information of time difference helps to indicate the region of where the annihilation took place. The TOF-PET method entails calculating the distance, d, between the point of annihilation event and the center of the line of response. In ideal conditions, this can be correlated with the difference in arrival time, ∆t, of the two photons at their respective detectors and c is the speed of light [16].

d = c∆t

2 (2.5)

Figure 2.4 compares PET data acquisition with and without the incorporation of time-of-flight (TOF) reconstruction. Without TOF information, the probability of annihilation

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is equal along the LOR of length 40 cm. With TOF information Figure 2.4 (B), annihi-lation point can be localized to limited range on the LOR for example, a time difference of 500-ps corresponds to 7.5-cm [6]

Figure 2.4: Figure showing PET data acquisition with incorporation of time-of-flight (TOF) reconstruction: (A) Without TOF information (B) With TOF information [6].

Figure 2.5: Comparison of slices from reconstructive images with and without TOF algorithms [7].

A histogram of the time difference is plotted and its full width at half maximum is known as the coincidence resolving time (CRT) [5]. A small CRT is important to reduce the number of random coincidences [16]. Additional benefits can be achieved if the system can achieve a CRT less than 1 ns by making use of the time of flight (TOF) information

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In conventional PET the probability that the annihilation event took place is the same on any point along the LOR, as shown in fig 2.4 (case A). The TOF method allows one to use a probability distribution function dependant on the CRT and allows to determine in which region the annihilation event took place. The accuracy is this correlated with a term, ∆, and is given by [14]

∆ = c

2CRT (2.6)

As the CRT improves, the spatial resolution along the LOR also improves [16]. Equation 2.5 and 2.6 are used in image reconstruction to determine the most probable location of the electron-positron annihilation event.

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Chapter 3

Materials and Electronics

3.1 Photon interaction in matter

Photons with energies 511 keV travel an average distance of 10.4 cm in human tissue [15]. Before reaching the detector they may have interactions along its path in the human tissue particularly via the photoelectric and Compton effect. If the photon has a photoelectric interaction, it loses all of its energy and gets absorbed in the process. On the other hand, if it has a Compton interaction, it loses a part of its energy and gets deflected from its original path. Absorption reduces photon counting statistics and Compton events lead to misinformation about the line of response (LOR). 85% of the signal is lost due to absorption or Compton interactions [15]. These are some of the most important physical limitations in PET which degrade the energy resolution. Thus in order to overcome these, it becomes very important to have detector crystals with high energy resolution and detecting efficiency [15].

3.2 Scintillation

The basic component of a PET detector is a block of crystal arrays. They convert the energy deposited on them by the 511 keV gamma photons to optical photons, which is then detected and amplified by the electronics coupled to the system. Detector ma-terials can be liquid, organic or inorganic [8]. For all current PET scanners, inorganic scintillators are used [15].

In inorganic scintillators the emission of light is a property that depends on the structure of the crystal lattice. In pure inorganic crystals lattices, electrons are only allowed to occupy selected lower energy bands called the valance band. The absorption of energy

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can elevate electrons from the valence band to a higher energy conduction band leaving a gap in the valence band. The valance band and conduction band are usually separated by a 4-6 eV forbidden energy band gap [8]. As shown in figure 3.1, when an ionizing radiation, such as a 511 keV gamma photon interacts with the crystal, it causes an electron to jump from the valance band to the conduction band. While the electron is still bound to the crystal, it is no longer bound to any atom and can move freely through the crystal lattice. It releases its excess energy in form of light. The optical phenomenon is called scintillation [8].

Figure 3.1: The band structure of an organic scintillator [8].

.

3.3 Scintillators

Upon arrival, the annihilation photons interact with the detector crystals by means of mostly photoelectric absorption and Compton scattering. If the photon deposits all its energy and gets absorbed after the first interaction, then it is called as the photoelectric effect. If the photon deposits only a part of its energy, then this is called Compton effect. Often there are several successive Compton interactions at several locations in the material. Both these processes result in electrons being excited from the valance band to the conduction band and releasing photons. The number of scintillation photons released in the process depends on the how much of the energy of the incident photon was transferred to the electron. Therefore a photoelectric absorption is desired over Compton scatter. The higher is the number of scintillation photons released, higher is probability of detection by the coupled electronics. Good energy resolution properties of the crystal contribute towards rejecting a large fraction of energy deposition events below a certain energy threshold allowing for mostly photoelectric interaction and some Compton interactions with a small scatter angle [5].

Compton scattering and photoelectric absorption both depend on the crystal as a func-tion of its density ρ and effective atomic number, Zef f [8]. The probability of

photo-electric effect is proportional to Z3

ef f. The probability of Compton effect is proportional

to ρZef f

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Figure 3.2: The photoelectric effect in which incident photons deposit all of their energy to an electron in the crystal lattice which are then free to move within the

crystal lattice [9].

.

chances of interaction of photons within the crystal and a high Zef f increases the

prob-ability of a photoelectric interaction. The excited electron returns to its ground state by releasing the excess energy in the form of light. A higher light yield guarantees a more linear response to the electronics coupling and therefore gives a better energy resolution. Thus, a crystal with a high Zef f is required [8].

De-excitation of these electrons eventually stops and it comes back to its ground state in the valance band. This transition is called quenching and is a radiation-less process. Quenching can last very long and result in a long photon tail. The time required by an excited electron to come back to its ground state is called decay time. A long decay time is detrimental to PET imaging as it would need a longer coincidence window which would increase the rate of random coincidences. Moreover, the emitted light should also have a desired wavelength matching the light response characteristics of the connected electronic systems [8].

To summarize, the following are the ideal properties for a PET detector crystal

• high density and Zef f

• high detection efficiency

• high probability of photoelectric effect • short decay time

• good energy resolution

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Some of the most common scintillator materials used for PET are Bi4Ge3O12 (BGO),

NaI:Tl, Lu2SiO5 : Ce (LSO), Gd2SiO5 : Ce (GSO), Lu1.8O2SiO3 : Ce (LGSO),

LuAlO3 : Ce (LuAP), Y AlO3 : Ce (YAP), Lu2Si2O7 : Ce (LPS), Lu3Al5O12 : Ce

(LuAG) and CsI:Tl. Selection of a specific detector material depends on the specifica-tions and requirements of the scanner and availability in the market and costs involved. Some of the properties of these crystals are described in the table 3.1 [15].

Material Density (g/cm3) Zef f Attenuation length for 511keV gamma pho-tons (mm) Prob. of PE (%) Light output (ph/MeV) Decay Time (ns) Scintillation photon wavelength (nm) BGO 7.1 75 10.4 40 9,000 300 480 LSO 7.4 66 11.4 32 30,000 40 420 NaI:Tl 3.67 51 29.1 17 41,000 230 410 CsI:Tl 4.51 52 22.9 21 66,000 900 550 GSO 6.7 59 14.1 25 8,000 60 440 LGSO 23,000 40 420 LuAP 8.3 64.9 10.5 30 12,000 18 365 YAP 5.5 33.5 21.3 4.2 17,000 30 350 LPS 6.2 63.8 14.1 29 30,000 30 380 LuAG 6.7 62.9 13.4 27 5,606 510

Table 3.1: some physical properties of detector crystals

Leutetium Oxyorthosilicate Lu2SiO5 : Ce (LSO) is one of the most widely PET

scin-tillator materials. It has high sensitivity to the incoming gamma photons owning to its high density and Zef f. LSO has a high probability of photoelectric effect and a high

light yield. It also has a short decay time and good energy resolution and coincidence resolving time. These properties and its commercial availability make it a very popular crystal for TOF-PET. In fact, CRT less than 100 picoseconds has been achieved using LSOs [19]. However, there are certain disadvantages with LSO. For instance, its energy resolution depends on the amount of Cs added as dopant [20]. Moreover, the presence of 176_{Lu isotope in the crystal makes it radioactive. It has been estimated that 2.6% of}

the Lu present in the crystal is176Lu. Its decay chain gives two prompt gamma rays of 201 and 306 keV each which add to the background noise[15].

The crystal studied in this masters thesis is Bismuth Germanate(Bi4Ge3O12 ) or BGO.

It was very commonly used in PET detectors until about a few decades ago, before the introduction of LSO [2]. It is a low cost, relatively hard, rugged material. Its higher density and Zef f than LSO, gives a high probability for photoelectric effect, almost 60%

higher [15]. Much of the luminescence comes from within the crystal which reduces the need for a dopant. Another advantage of BGO is its low decay time and almost no ’afterglow’, making it highly suitable for TOF-PET and an excellent choice for good

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spatial and energy resolution [15]. However, the scintillation light yield of BGO is much lower than that of LSO. Moreover, it has a dependency on temperature. The light intensity increases by 1% for every 1◦C decrease in temperature [2]. Thus, it requires a more stringent temperature control for BGO based PET scanners in comparison with other materials.

3.4 Cherenkov Effect

Cherenkov radiation is an electromagnetic radiation emitted when a charged particle, such as an electron, passes through a dielectric medium, such as a BGO crystal, at a speed greater than the phase velocity of light in that medium. As the charged particle travels through the crystals, it electrically polarizes the medium by disrupting local electromagnetic field in it. If the particle is traveling fast enough, the energy contained in this disturbance radiates as a coherent shock-wave which is in the UV-blue spectrum (300 − 500 nm) [8] [10] as shown in the figure 3.3. In recent years, the Cherenkov effect for electrons with energy around 511 keV has gained increasing interest and popularity in the field of Time-of-Flight PET as it promises an immediate response, better timing resolution and almost no afterglow [21] [1].

The number of Cherenkov photons emitted by an electron in a dielectric medium can be estimated using the Frank-Tamm equation [10],

dN2 dxdλ = 2πα λ2 (1 − 1 β2_n2) (3.1) where,

• α: fine structure constant

• n : refractive index of the medium, which is assumed to be constant for all wave-lengths

• λ : wavelength (nm)

• β : ratio of velocity of electron and light in that medium

When 511keV annihilation photons transfer their energy (partially or completely) to electrons in the crystal lattice, these electrons reach an excited state. This is followed by a cascade of radiative and non-radiative energy relaxation processes, one of which is scintillation. All of them introduce an additional time spread to the de-excitation

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Figure 3.3: Blue-UV shock-wave emitted in a dielectric medium when a charged particle travels faster than the speed of light in it [10].

process [22]. In the case of Cherenkov emissions, all of these processes are bypassed since it happens during the phase of electron scattering. It happens almost instantaneously with respect to scintillation photons [21].

Cherenkov for TOF-PET:

Due to its almost instantaneous response, the Cherenkov effect has gained increasing popularity and interest in the last decade. BGO crystals exploiting the Cherenov effect coupled to digital silicon photo-multipliers have achieved a coincident resolving time (CRT) of less than 200 ps FWHM [1].

Typically, for a TOF-PET system based on Cherenkov radiations, the ideal properties of the crystal should be high transparency to its own radiations (so that the Cherenkov photons are not absorbed within the crystal) and a high refractive index. Both of these conditions are satisfied by BGO crystals [1]. Its high probability of photoelectric effect, low cost and no intrinsic background radiation makes BGO a good option for a hybrid scintillator/Cherenkov detector [2].

3.5 Philips Digital Photon Counter

Albeit faster, Cherenkov photon yield, in comparison to scintillation photon yield, is much lower [1]. For BGO crystals, it is only about 10 - 30 photons for every 511 keV photon. This makes Cherenkov emission very hard to exploit in PET because of lower statistics and less energy discrimination. Moreover, the timing resolution becomes hugely dependant on the single photon time resolution (SPTR) of the photosensor. S.Brunner et

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al 2017 proposed the development of BGO as a hybrid scintillator/Cherenkov radiator for cost-effective time-of-fight PET using extremely accurate single photon counting photosensors [2].

Sensor Layout:

The Philips Digital Photon Counter (PDPC) is essentially an array of thousands of avalanche photo diodes called microcells. An avalanche photodiode (APD) is an ex-tremely sensitive Silicon based semiconductor device in reverse bias which converts light energy to an electronic signal. This creates a mobile electron which leaves behind a vacancy, or a hole. In the presence of an electric field in the semiconductor diode, the electron will move towards the positive voltage. If the electric field is strong enough, the mobile electron may be accelerated to high enough speeds to knock other bound electrons free, creating more free-electron-hole pairs. This process increases the current in the diode and leads to further ”knocking out” and creating what is known as an avalanche breakdown [11].

Figure 3.4: Philips Digital Photon Counter Tile. It consists of an array of 8 ∗ 8 pixels each with 3200 SPADs [11].

The voltage at which the avalanche occurs is called the breakdown voltage.The Single Photon Avalanche Diode operates at a voltage above the breakdown voltage. This makes the diode slightly unstable such that even a single photon can set off an avalanche and

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produce millions of electrons per second which can later be converted to a readable output signal.

The PDPC essentially consists of an array of thousands of single photon avalanche diodes (SPAD). The smallest measurable unit is a pixel which is made up of 3200 SPADs.The number of avalanche breakdowns is summed up at the pixel level to produce photon count value. A array of 2x2 pixels make a die and an array of 4x4 dies make a PDPC tile. Each pixel is also equipped with a pair of time-to-digital converter which generate a timestamp for every pixel. Thus, there are four photon count values, one from each pixel, per die. The data acquisition sequence is depicted in the figure 3.5

Figure 3.5: Event accusation sequence in the Philips DPC [11].

The acquisition starts with a trigger signal which is set to 1, implying that the first detected photon would start the validation sequence. In the case of BGO as detector crystal, a photon from Cherenkov emission is considered, thereby making the response faster. The validation sequence is used to filter out unwanted trigger events caused by thermal electrons. This is done by adjusting a photon counting threshold of 8 in a configurable time range of 10 ns meaning, that if the system detects 8 photon within 10 ns, then the event is validated. Next comes the integration process where the sensor waits for the arrival of the scintillation photons to further the photon count. The duration of the integration process is specific for each crystal and can be configured according to the type of crystal coupled to the PDPC tile. The integration process is followed by the readout process, which lasts 680 ns and it sums up the number of microcells per pixel which experienced an avalanche breakdown and sends the value to a readout buffer. Thus, the result of this whole process is four photon count values (one per pixel) each with a timestamp. After this is the recharge phase, which lasts 5 to 80 ns at the end of which, the die is ready for a new acquisition cycle [11].

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Chapter 4

Study of NECR for BGO crystals

using GATE

4.1 Introduction

Positron annihilation results in the emission of two photons in a direction opposite to one another. As explained in section 2.2 there is also scattering of gamma rays which give rise to false coincidence events. Thus, it becomes necessary to measure count losses and the rate of random events to draw conclusions about the sensitivity and efficiency of a positron emission tomograph. In the last few decades, Monte Carlo simulations have played an important role in the field of emission tomography. Geant4 Application for Tomographic Emission(GATE) is a Monte Carlo simulation platform based on Geant4 libraries specially for Positron emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) application [23].

The advantage of this software is that it allows the user to simulate time dependent phe-nomena like source decay kinetics, process management etc with a simple and straight-forward scripting interface for image modeling [24] [25]. Further, GATE provides a set of modules to model the signal processing which allows the user to simulate data flow as well [26]. The Gate toolkit is gaining increasing popularity in the last few years and many simulation studies of GATE models for clinical PET systems have been carried out. One of the biggest reasons for this is that GATE allows its users to define a detailed model for a real PET system and it can be used to simulate data acqisition which are more difficult to measure in a realistic experiment [27].

Noise Equivalent Count Rate NECR is one of the most important characteristics of a PET system. It is used to measure the image quality. A high NECR value indicates a

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better the PET image quality. NECR is a global measure of PET performance and is used to understand a wide range of imaging situations[25]. In this study, the NECR of a PET-system using Bismuth Germante (BGO) crystals was simulated on GATE and its output was studied. All the simulation studies were performed based on the specifi-cations of The Association of Electrical Equipment and Medical Imaging Manufacturers (NEMA NU-2) [12].

4.2 Detector Geometry

The first step to model a PET system is to define its geometry in detail. A cylinder is defined to model the PET scanner ring. The PET detector geometry is based on the Vereos digital PET/CT system by Philips [28]. It is is a digital photon-counting PET scanner combined with a 64- or 128- channel Computed Tomography system. The system has an inner radius of 382 mm and an outer radius of 402 mm. The basic unit of the scanner is a tile, which consists of an 8 ∗ 8 BGO crystal array. Each crystal has a dimension of 3.95 ∗ 3.95 ∗ 20 mm3. 20 tiles are grouped together, 4 axially and 5 tangentially to form a module.Modules are further are arranged in 18 rings.

All the parameters used in the program are summarized in the table 4.1 : Description

Ring outer radius 402 mm Ring inner radius 394 mm

Ring diameter 2 ∗ 394 = 764 mm Crystal dimen-sions 3.95 ∗ 3.95 ∗ 20 mm3 Crystal array 8 ∗ 8 Tile array 4 ∗ 5 Number of rings 18 Total number of crystals 18 ∗ (4 ∗ 5) ∗ (8 ∗ 8) = 23, 040.

Field of view 8∗4 = 32 mm repeated 5 times with 1 mm gap between them = 164 mm

Table 4.1: Physical parameters defined for the PET system

4.3 The Monte Carlo simulation model

Gate version 7.2 is used to model the Monte Carlo simulation of PET systems. GATE incorporates GEANT4 libraries and combines the GEANT4’s capabilities of accurate

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Figure 4.1: Description of the geometry of the PET system modeled in GATE.

geometric modeling tools, validated physics’ process models and efficient visualizations [28]. Further, GATE allows its users to model the various components of a PET system such as geometry, physics, source selection, signal processing chain and enable time dependant components to share the coherent time synchronization [27].

4.3.1 Signal Processing

GATE is capable of converting photon interactions into counts and reproduce the be-havior of the signal processing chain in an analogous manner like in a real scanner. This process is accomplished by the digitizer feature in the software [29]. The digitizer incorporates a sequence of steps to simulate the complete signal processing chain [30]. Hit is the basic output of GATE. It incorporates all the particle information with all its physical parameters, such as time, energy, type etc. Adder is the first step of the digitizer chain that regroups the different Hits in a single crystals into a pulse. The next step is Readout which is applied to collect total pulses at 8 ∗ 8 crystal array level. To model the energy resolution of the system a function called blurrer is defined and applied on output pulses. This simulation is modeled as a Gaussian energy blur with 15% full width at half max at 511 keV for BGOs.

4.3.2 Dead Time

Two pluses may overlap and form one distorted pulse if the second one happens before the first one ends. This is called dead time losses. To avoid this we apply a ”non-paralysable dead time”. After each event, a certain dead time is introduced, during

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which events will not be recorded. Thus, if a photon hits the photosensor occurring during the period of its dead time, it will not be counted. The counting would resume after the period of dead time is finished. Net dead time loss depends on the electronics of system and the crystal. The dead time calculation sequence the same similar to the acquisition sequence as shown in figure 3.5.

The acquisition starts with a trigger signal which is set to 5, implying that after 5 photons are detected, the system would proceed to the validation sequence. The validation sequence is used to filter out unwanted trigger events caused by thermal electrons. This is done by adjusting a photon counting threshold of 10 in a configurable time range of 10 ns meaning, that if the system detects 8 photons within 10 ns, then the event is validated. Next comes the integration process where the sensor waits for the arrival of more optical photons to further the photon count. The duration of the integration process is specific for each crystal and can be configured according to the type of crystal used and for BGOs it is configured as 2565 ns. The integration process is followed by the readout process, which lasts 680 ns and it sums up the number of microcells per pixel which experienced an avalanche breakdown and sends the value to a readout buffer. After this is the recharge phase, which lasts 80 ns at the end of which, the photosensor is ready for a new acquisition cycle [11].

Therefore the dead time, DT, is,

DT = T rigger + V alidation + Integration + Readout + Recharge (4.1)

which then for BGO is,

DTBGO = 5 + 10 + 2565 + 680 + 80 = 3340ns (4.2)

An energy window of 350-650 keV is then applied. To simulate coincidences, the coin-cidence window is set at 10 ns [16].

After these processing steps the coincidence events were taken and stored and analyzed in a ROOT file [12].

4.4 Phantom

The phantom is designed according to the recommendations by the International Electro-technical Commissions (IEC) and The Association of Electrical Equipment and Medical Imagining (NEMA)[12]. The phantom set is a lung insert with six spheres of different sizes filled with water. The phantom is particularly useful for simulating whole body

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imaging using PET and camera-based coincidence imaging and evaluating reconstructed image quality of the same. The phantom has an interior length of 180mm. The inner diameters of 6 spheres are 10 mm, 13 mm, 17 mm, 22 mm, 28 mm, and 37 mm. The net volume of the empty cylinder is 9.7 liters. The parameters are described as follows,

∗ Interior length of phantom: 180 mm

∗ 6 fill-able spheres of inner diameter: 10 mm, 13 mm, 17 mm, 22 mm, 28 mm, 37 mm. ∗ Distance from sphere plane to inside wall: 70 mm

∗ Volume of empty cylinder: 9.7 liters

∗ Cylindrical insert dimension: Outside diameter: 51 mm ∗ Cylindrical insert dimension: Length 180 mm

Figure 4.2: NEMA IEC body phantom consists of a body phantom, a lung insert and an insert with six spheres with various sizes[12]

4.5 Source

The source is also defined as per the standards given in the NEMA NU 2-2012 guide [12]. It is a line source filled with radioactive18_{F. Thus, a cylinder is defined with length}

700mm and radius 0.5mm. The line source is centered inside the test phantom. The half life of the radionuclide is defined as 6585 s. While running the program, it must be kept in mind that each data acquisition contains a minimum of 500,00 prompt counts and for a duration not more than half the radionuclide half-life [12].

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4.6 Calculations

The beginning and the end of the acquisition are defined as in a real life experiment. In addition, Gate needs a time slice parameter which defines time period during which the simulated system is assumed to be static. In this simulation a regular time slice approach was used which mean, slice has the same duration of 1 s.

The measurement of noise equivalent count rates (NECR) is based on work described in Strother, S.C.Casey, M.E. and Hoffman, E.J., Measuring PET Scanner Sensitivity: Relating Count-Rates to Image Signal-to-Noise Ratios Using Noise Equivalent Counts, IEEE Trans Nucl Sci, NS-37(2):783-788, 1990.The adaptation of these methods to scan-ners with intrinsic background counts is discussed in Watson, C.C., et al., NEMA NU 2 Performance Tests for Scanners with Intrinsic Radioactivity, J Nucl Med, 45(5):822-826, 2004 [12].

If,

∗ C_total : total interactions

∗ C_singles : total random and scatter events ∗ Ctrue : total true coincidences

∗ Tacq : acquisition time

Then, for each acquisition j,

Rate of total events (counts/sec), for each slice i Rtotal,i,j =

Ctotal,i,j

Tacq,j

Rate of true events, for each slice i, Rtrue,i,j = C_Ttrue,i,j_acq,j

Rate of random events, for each slice i Rrandom,i,j =

Crandom,i,j

Tacq,j

Noise equivalent count rate, for each slice i RN ECR,i,j =

R2 true,i,j

Rtrue,j+Rrandom,j+Rscatter,j

And so for all slices, Rtotal,i=

P

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28 Rtrue,i=P_jRtrue,i,j Rrandoms,i =PjRrandoms,i,j Rscatter,i =P_jRscatter,i,j RN ECR,i= P jRN ECR,i,j

Figure 4.3 shows the results obtained from the simulation studies. The simulations were run to study the linear dependency of the NECR as a function of activity. Specific activity is the activity per quantity of a radioactive mass and can be defined as the ratio between the activity and the volume of the phantom, which in our case is 9700 ml. The figure shows, the rate of true random and scatter events as a function of the activity for different acquisition times. The simulation was run for an acquisition time, so that at least 500,000 prompt events were obtained [12]. It was seen that NECR value increases linearly with an increase in activity. It reaches a maximum value and then reduces. It is at this peak value when the rate of detected true events is highest. Thus, it gives us an idea about optimum dose limits for the phantom for a particular PET system. It also provides information about the maximum value of the rate of true events which in turn is linked to the quality of a PET detecting system.

Figure 4.3 represent the NECR values as a function of specific activity for all measured activity concentrations for a 9700 ml phantom. It can be seen from figure 4.3 that the NECR value increases linearly as a function of the specific activity and then reduces. This PET system attains its peak NECR value at a specific activity of around 30 kBq/ml.

Activity (kBq) Specific Activity (kBq/ml) Time (s) Total events (counts) True events (counts) Random + Scat-ter events (counts) NECR (counts/sec) 50 0.0051 1000 532.061 531.353 0.708 530.64 100 0.010 500 1064.122 1062.706 1.416 1061.29 500 0.052 200 2660.305 2656.765 3.54 2653.23 1000 0.103 100 5320.61 5313.53 7.08 5306.46 3000 0.31 50 35896.92 33085.6 2811.36 30494.45 5000 0.515 50 62400 54600 14.16 47775 10000 1.031 20 137800 107300 3051.35 83550.72 50000 5.15 2 1105882 457067.5 645000 188908.67 75000 7.73 2 3889031 1241740 2647290 198239.38 100000 10.31 2 2885000 848694.5 2100000 249664.6 200000 20.62 1 20884421 3123440 17760981 467136.6 300000 30.93 1 21117796 21117796 33314450 520204.8 400000 41.24 2 25792000 2214450 1.68E+06 190128.28

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Figure 4.3: NECR for a phantom of volume 9700 ml water at the measured activity concentrations.

Figure 4.4: Rate of true events for a phantom of volume 9700 ml water at the measured activity concentrations.

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Chapter 5

Data Analysis

5.1 Past Work

5.1.1 Simulations

According to works done based on [21] and [1], Geant4 based simulations were performed to study the yield of Cherenkov photon emission post photoelectric interaction with 511 keV annihilation photons. Simulation was done for both LSO and BGO and their results were compared. The test crystals were polished cubic crystals of dimension 3 ∗ 3 ∗ 3 mm3. A description of the simulation coincident setup is shown in the figure 5.1.

Figure 5.1: The basic for coincidence measurement used for Geant4 simulation studies [1].

The number of Cherenkov photons emitted by an electron varies as a function of equation 3.1 (section 3.4). The first column in the table below gives the calculated Cherenkov yield per photoelectric interaction within the crystal [1]. The second column gives the percentage of events detected per events created. The values are summarized in the table 5.1 [1].

The low detection percentage is due to the high loss of Cherenkov photons while they propagate within the crystal. According to the Cherenkov equation 2.1, the light yield

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Material Number of Cherenkov photons

Created to detected ra-tio (%)

LSO:Ce 18 7.97 LuAg:Ce 27 29.62 BGO 28 14.024

Table 5.1: Cherenkov photon yield per photoelectric interaction of a 511 keV Photon

is inversely proportional to the wavelength [10]. For electrons with energy close to 511 keV, the maximum yield is in the blue and UV light spectrum. The Cerium doped in LSO have a high absorption coefficient for light in this spectrum. One could, in the theory, reduce the amount of doping in the previously mentioned two crystals to reduce internal absorption within the crystals, but then this would reduce their scintillation photon yield [1].

A fast detector response important an important factor for TOF-PET. It influences the CRT directly [16]. As stated in section 3.4, Cherenkov photons are created much before the scintillation photons. Tabled 5.2 presents a comparison between the ratio of the number of Cherenkov to scintillation photons detected in the first 25 ps and 100 ps [1]. It can be seen the number of photons created in the first 25ps is higher for BGO than for LSO. The opposite is true if we consider the photons created in the first 100 ps. This implies that the Cherenkov yield is higher for BGO. LSO on the other hand is more dominant with respect to scintillation light yield, but it happens slightly later [1].

Material <25ps <100ps LSO:Ce 1.78 0.16

BGO 364 28

Table 5.2: Comparison between the ratio of the number of Cherenkov to scintillation photons detected in the first 25 ps and 100 ps

5.1.2 Experimental Studies

Experiment studies were performed [2] on optically polished BGO crystals of different lengths. They had a 3 x 3 mm3 cross-sections and their lengths were 3 mm, 5 mm, 8 mm, 12 mm, 20 mm [2].

Three different parameters were studied : Transmittance to UV, energy resolution and CRT. Cherenkov emissions for 511 keV in BGO crystals are primarily in the Blue-UV spectrum (300-700 nm). It was seen experimentally that BGO crystals are acceptably transparent to their own emissions through the length of the crystal [2]. In another experiment the number of detected photons were noted and their energy resolution was

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calculated for the crystals of different length at different temperatures [2]. The results of this experiment are summarized in the figures 5.2 and 5.3 below.

Figure 5.2: Energy Resolution (top) and mean number of photons detected (bottom) of BGO crystal samples for an incoming 511 keV annhilation photon as a function of

the crystal length [2].

Figure 5.3: Normalized timing histogram comparison between a crystal of length 3 mm and 20 mm [2].

It can be seen that number of detected photons, CRT and energy resolution improve as both temperature and crystal length reduces. This can be attributed to the fact that for shorter crystals the Cherenkov photons have to travel a shorter distance within the crystal lattice before being detected. The decrease in length decreases the probability of further interactions or absorption within the crystal lattice [2]. As for the temperature, the dark count rate of the photon counter used reduces by about 50 for every 7◦C reduction in temperature, thereby improving its detecting capability [2].

Thus, BGO can qualify as potential candidate for a hybrid scintillator/ Cherenkov-radiator. Its low cost, easy accessibility and promising energy and CRT makes it a good option for a cost effective TOF-PET detector [2].

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5.2 Experimental Setup

In the previous experiments, the properties of individual BGO crystals were studied. This thesis is about studying the properties of BGO crystal arrays. The effects of surface finish and reflector material are the two properties of interest that were investigated in this research project.

Comparisons were made between four types of 8∗8 crystal arrays with dimensions 3∗3∗5 mm each and their properties were are as follows,

• Crystal A : Polished surface with Enhanced Specular Reflector (ESR) as reflector material.

• Crystal B : Unpolished surface with Enhanced Specular Reflector (ESR) as reflec-tor material.

• Crystal C : Polished with Barium Sulphate as reflector material. • Crystal D : Unpolished with Barium Sulphate as reflector material.

Figure 5.4: An image showing four BGO arrays that were used with two Philips DPC tile sensors on each side.

A BGO array is coupled to the photo-sensor, the Philips DPC Tile, using BC630, an optical grease from Saint Gobain exhibiting good transparency especially in the blue-UV region. Primary experiments were conducted by using LSO:Ce of dimension 3 ∗ 3 ∗ 5 mm, with one side polished, as reference crystal. The reference crystal was coupled to the second Philips DPC Tile using the same optical grease. The two tiles were mounted

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opposite each other. A positron emitting source, 22Na is placed immediately in front of the reference crystal. The tile with the BGO array is placed at a certain constant distance from the source.

Positioning the BGO array

Figure 5.5: Figure (Scale 2:1) showing the source, O, placed right in front of the reference crystal, ABC, and at a distance of at least 80 mm from the BGO array, DEF.

The side view of the experimental setup is shown in the figure 5.5. If AB is the reference crystal (3 ∗ 3 ∗ 5 mm3) and it is placed in front of a source O. The distance between the source and the reference crystal (taking into account the source casing as well) is measured. FED represents the BGO array (40 ∗ 40 ∗ 5 mm3). The minimum distance required between the source and BGO array, x, is 80 mm and it is depicted in the calculations below. AB = 1.5 mm (Crystal dimension) OB = 7.5 mm (measured value) ∠AOB = tan−1 1.5_7.5 = 11.30◦ Thus, ∠AOC =2*11.30= 22.60

∠DOF = ∠AOC = 22.60◦ (lighttravelsinastraightline) ∠DOE = 11.30 = tan−1 16_x

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x = _tan11.316

x = 80mm = 8cm

5.2.1 Dark Count Map

The Philips DPC is a very sensitive photo sensor. It is essentially an array of thousands of single-photon avalanche diodes (SPADs). These diodes are reverse biased p-n junction semiconductors which function at a voltage slightly above their breakdown voltage and are slightly unstable[11]. It is this instability which allows them to have an avalanche breakdown even by a single photon. However, they are so sensitive that even electrons or background radiations can cause an avalanche breakdown, which would result in a false signal. Thus, we perform a study called as dark count mapping which measures the output pulses of SPADs in the absence of any light or radioactive source. Philips DPC gives you the option of addressing individual cells. Thus, the user is able to manually turn off those cells which give the highest dark count rate. The majority of the contribution to the overall dark count rate of the sensor tile is made only by a small percent of the cells. 5 -10 of the cells contribute to 70 - 80 of the the overall dark count rate of a tile [11]. Therefore, by disabling these cells the user can significantly reduce the amount of dark counts.

The two tiles (without attaching the crystals) are first placed in complete darkness at a temperature of 10◦C, to minimize thermal electrons. The dark count rates are measured for both the tiles and 5 % of the microcells generating the highest dark count rates were turned off. Figure 5.6 is the dark count map of a Philips DPC tile. It shows that most of the tile is blue, implying negligible dark count rate. The microcells that gave a high dark count rate are the ones in red, were turned off.

Out of the two Philips-DPC tiles used, one is coupled to the referenced crystal and is referred to as the ’reference tile’. The other coupled to the BGO array is referred to as the ’test tile’. In the test tile all the pixels are activated and in the reference tile only one is activated. This sole activated pixel in the reference tile is located at Die 6, pixel 3.

At the end of this procedure, the LSO crystal and BGO array are attached to their corresponding DPC tiles using BC630.

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Figure 5.6: A dark count map showing the microcells in red with the highest dark count rates [11].

5.3 Coincidence Sorting

Once the set up is ready, the Sodium-22 source was introduced in front of the LSO crystal. Primary measurements were performed at 20◦C. From the annihilation event, one 511 keV photon hits the reference crystal and the other hits the BGO array. Scin-tillation photons are released in the LSO crystal and both Cherenkov and scinScin-tillation are released in the BGO array crystal lattice.

In theory, one microcell is discharged per optical photon. In this way, the DPC is ca-pable of counting the total number of optical photons emitted by counting the number of microcells that experienced an avalanche breakdown. The DPC reference tile (with the LSO crystal attached) registers the timestamp and counts the scintillation photons released. The DPC test tile (with the BGO array attached) on the other hand, registers the timestamp of the Cherenkov photon and then counts the scintillation photons to pro-duce a corresponding signal. A Matlab code was developed to only keep the information of those coincident gamma photon pairs both of which had photoelectric interactions in their respective crystals.

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Figure 5.7: Figure showing that all pixels activated in the test tile (top) and only one pixel activated on the reference till. The numbers on the pixels represent the number

of microcells fired in the absence of any light and a source.

The data file obtained initially is a raw data file that stores all of the events that resulted in an avalanche breakdown in both the tiles. The raw data file is the output generated by the Philips DPC system. A screenshot of the raw data file is presented in figure 5.8. The columns of interest are

• tile : gives information in which tile the avalanche breakdown happened. Tile 3 is the DPC tile where the reference crystal is attached and tile 4 is where the BGO array is mounter.

• die : gives information where the annihilation photon interacted

• frame nr : The default clock in the Philips DPC runs at 200 MHz with a cor-responding clock cycle of 5 ns. A frame is formed by a 16 bit clock cycle, ie 216∗ 5ns = 327.68µs after which the clock resets to zero [11].

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Figure 5.8: A screen shot of the raw data file obtained form the Philips DPC.

• timestamp : the coincidence window is set to 20ns, thus for a 16 bit channel, each time bin corresponds to a value 20∗10₂1₆3ps = 19.53125 ps [11]

• p1 : the number of microcells fired in pixel 1 of the die • p2 : the number of microcells fired in pixel 2 of the die • p3 : the number of microcells fired in pixel 3 of the die • p4 : the number of microcells fired in pixel 4 of the die

Events are characterized by their Timestamp, Frame Number and Event ID.

Events are identified by Frame Numbers and Event ID s for a total of 327.68µs and then the clock restarts. Two events that happened on two different tiles with the same Frame Number and a difference in time stamps of less than 1024 bins (corresponding to the coincidence window of 20 ns) are classified as coincidence events. The complete Matlab file is presented in the appendix of this thesis.

It can be seen for tile 3, p1, p2 and p4 values are zero and the event always happens at die 6. This is is because tile 3 is the reference tile and is active only at one location, ie die 6 pixel 3. On the contrary, tile 1 shows a response at all the dies from 0 to 15 on all pixels (p1 to p4) because this is the tile where the BGO array is placed and has all its pixels activated.

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A pixel is the smallest measurable unit of the Philips tile. Each crystal in the BGO array, is of around the same dimension as a pixel in the Philips tile. Therefore, every crystal can be individually studied by having the information of its corresponding pixel. The number of microcells fired per pixel is recorded. In the raw data file obtained post an experiment, the number of microcells fired in all four pixels of a die per annihilation photon is presented. As seen in figure 5.8 For a single event, most microcells fired per die, were seen in one pixel. The remaining come from secondary events that the incident annihilation photon causes in the neighbouring three pixels of the same die. Light yield from the secondary events was not considered.

5.4 Calculations

For the primary analysis, reference crystal used was an LSO crystal of dimension 3 ∗ 3 ∗ 5 mm3. It was coupled to the Philips DPC using BC630. One of the more practical features of this Philips device is that it allows one to address each pixel individually. The reference crystal was placed at Die 6, pixel 3. This was the only pixel that was activated in the whole tile, which can also be seen in figure 3.7.

Sodium-22, a positron emitting source was placed immediately in front of it. Another Philips DPC tile was placed diametrically opposite to this setup. This tile was coupled to a BGO array using the same glue and it had all of its pixels activated. After performing the coincidence sorting, the data was sorting into 64 files, each one belonging to a pixel on the Philips DPC test tile.

The following calculations were performed individually per pixel

• Photon Count Saturation Correction : As described earlier, each pixel in a Philips DPC tile consists of 3200 SPADs or microcells out of which only 3040 of these cells are active, since 5% are turned off to reduce dark count losses. For high photon count values, there is a high probability that multiple photons hit the same microcell simultaneously. Since the DPC is capable of counting only one microcell per event acquisition, any later photon that hits the same microcell will not be counted. It can be corrected by the equation 5.1 [11]

p = N ln[1 − (k/N )] (5.1)

where,

– N : number of available cells per pixel = 3040

(47)

40

– p : the corrected number of photons corrected for pixels photon detection efficiency.

Figure 5.9: Photon count saturation effect [11].

• Light Yield :

The number of microcells fired per pixel corresponds to the number of photons that caused it. The number is noted, and saturation correction is performed on it. • Energy Resolution :

A histogram is plotted for the light yield per pixel. It typically has a bell-shaped curve. A Gaussian fit is performed on this curve which is given by the following equation, F (x) = ae− (x−b)2 2σ2 (5.2) where – F is the fit

– a is the height of the curve’s peak,

– b is the position of the center of the peak and – σ is the standard deviation and controls

Energy resolution is calculated using the full width at half max (FWHM) of the curve. FWHM is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude. A Gaussian fit is made on the bell-shaped. Energy resolution is given by the ratio of the FWHM and the mean value of the Gaussian peak [8].