@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Science, Faculty of"@en, "Physics and Astronomy, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Astakhov, Vadim"@en ; dcterms:issued "2009-10-17T21:36:13Z"@en, "2003"@en ; vivo:relatedDegree "Master of Science - MSc"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description "Position Emission Tomography is a functional imaging modality where positron labeled radiotracers are used to investigate biological processes. The imaging process occurs via simultaneous detection of two 511keV gamma rays originating from positron annihilation. A PET camera is a γ detection apparatus. Reconstruction algorithms are used to reconstruct the original radioactivity source distribution in the camera field of view (FOV) from the simultaneous detection of y rays originating from the same annihilations. PET has been extensively used to investigate function in living organism, especially in human subjects. In order to make the detection process efficient and useful, PET camera designs strive for high detection sensitivity and high resolution. One of the factors influencing the resolution is the size of the detectors. Smaller detectors lead to a better spatial resolution. On the other hand sensitivity is affected by the detector crystal composition and by the solid angle subtended by the detection apparatus. An ideal tomograph design will therefore involve small, efficient detectors placed as close as possible to the object being scanned. The work described in this thesis examines various detector crystal configurations that would lead to an optimum tomograph performance. In order to make the results of this study immediately relevant to the PET community the overall tomograph geometry was constrained to that which is currently being built by a tomograph manufacturing company CTI. This design consists of an octagonal detector configuration where each detector head is built with two layers of detector material. Such a design allows for the identification of the y depth of interaction (DOI) in the detector assembly which in turn allows to minimize the effect of the parallax error and thus contributes to an increased resolution uniformity across the camera FOV. The studies presented here examine the effect of different crystal layer configuration on resolution and sensitivity. Octagonal HRRT geometry was also compared to circular detector geometry. As part of a system design optimization, several novel methods for crystal element identification were investigated: Genetic-algorithm, neural network algorithm and \"simple\" geometric algorithm were tested and showed relatively equal identification performance in identifying 64x64 crystal elements of each layer. A fuzzy-logic approach for estimation of depth-of-interaction (DOI) was investigated and compared with the decay time discrimination approach. The simulation results were used to generate a Look-Up-Table (LUT) that is accessed during simulated data acquisition for an effective and quick crystal identification. A correct crystal identification also facilitated an improvement of the capability for accurate energy discrimination, since the detector gain and appropriate energy thresholds were considered on an element-by-element basis by accessing energy LUT. The final result of the work presented in this thesis is the determination of the effect of DOI correction on resolution uniformity for different crystal configuration. DOI correction was found to improve the resolution uniformity up to 67%."@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/13973?expand=metadata"@en ; dcterms:extent "4268910 bytes"@en ; dc:format "application/pdf"@en ; skos:note "C R Y S T A L DESIGN SIMULATION FOR A HIGH RESOLUTION DEPTH ENCODING PET TOMOGRAPH by V A D I M A S T A K H O V B.Sc, Novosibirsk Russian State University, 1992 M . S c , Novosibirsk Russian State University, 1995 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE F A C U L T Y OF G R A D U A T E STUDIES (Department Physics and Astronomy) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH C O L U M B I A March 2003 @ Vadim Astakhov, 2003 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract Position Emission Tomography is a functional imaging modality where positron labeled radiotracers are used to investigate biological processes. The imaging process occurs via simultaneous detection of two 511keV gamma rays originating from positron annihilation. A PET camera is a y detection apparatus. Reconstruction algorithms are used to reconstruct the original radioactivity source distribution in the camera field of view (FOV) from the simultaneous detection of y rays originating from the same annihilations. PET has been extensively used to investigate function in living organism, especially in human subjects. In order to make the detection process efficient and useful, PET camera designs strive for high detection sensitivity and high resolution. One of the factors influencing the resolution is the size of the detectors. Smaller detectors lead to a better spatial resolution. On the other hand sensitivity is affected by the detector crystal composition and by the solid angle subtended by the detection apparatus. An ideal tomograph design will therefore involve small, efficient detectors placed as close as possible to the object being scanned. The work described in this thesis examines various detector crystal configurations that would lead to an optimum tomograph performance. In order to make the results of this study immediately relevant to the PET community the overall tomograph geometry was constrained to that which is currently being built by a tomograph manufacturing company CTI. This design consists of an octagonal detector configuration where each detector head is built with two layers of detector material. Such a design allows for the identification of the y depth of interaction (DOI) in the detector assembly which in turn allows to minimize the effect of the parallax error and thus contributes to an increased resolution uniformity across the camera FOV. The studies presented here examine the effect of different crystal layer configuration on resolution and sensitivity. Octagonal HRRT geometry was also compared to circular detector geometry. As part of a system design optimization, several novel methods for crystal element identification were investigated: Genetic-algorithm, neural network algorithm and \"simple\" geometric algorithm were tested and showed relatively equal identification performance in identifying 64x64 crystal elements of each layer. A fuzzy-logic approach for estimation of depth-of-interaction (DOI) was investigated and compared with the decay time discrimination approach. The simulation results were used to generate a Look-Up-Table (LUT) that is accessed during simulated data acquisition for an effective and quick crystal identification. ii A correct crystal identification also facilitated an improvement of the capability for accurate energy discrimination, since the detector gain and appropriate energy thresholds were considered on an element-by-element basis by accessing energy LUT. The final result of the work presented in this thesis is the determination of the effect of DOI correction on resolution uniformity for different crystal configuration. DOI correction was found to improve the resolution uniformity up to 67%. iii T A B L E OF C O N T E N T S Abstract ii Table of Contents iv List of Tables vii List of Figures ix Acknowledgements x 1. Introduction 1 1.1 Goal of this Thesis 1 1.2 Thesis outline 1 1.3 Motivation 1 1.4 Previous work 3 2. Principles of Positron Emission Tomography 4 2.1.1 Positron Emission Tomography 4 2.1.2 Positron-emitters and labeled compounds used in PET 4 2.1.3 Basics Principles of PET 6 2.1.4 Positron Decay X- 6 2.1.5 Loss of energy by the positron 7 2.1.6 Positron Annihilation 7 2.1.7 Interaction of the gamma rays 8 2.1.8 Scintillation 9 2.1.9 Coincidence detection 9 2.2 Sensitivity 10 2.3 Spatial resolution in PET 11 2.3.1 Physical limits of spatial resolution 11 2.4 Detector block and intrinsic detector resolution 12 2.5 Interaction between detector design resolution and sensitivity 18 3. Overview of the HRRT system 14 3.1 Detector Geometry 14 3.2 Simulated Scintillators 15 iv 4. Simulation study 17 4.1 GEANT overview 17 4.2 Summary of all simulated by GEANT physical processes 18 4.2.1 Simulated interactions of an 511 keV photon in scintillators material 19 4.2.2 Simulated continuing photon and recoil electron transport 19 4.2.3 Cut-off energies 19 4.2.4 Simulated creation of bremsstrahlung photons 20 4.2.5 Implemented Mechanism of scintillation 20 4.2.6 Photon Interactions NOT simulated 21 4.3 DETECT 22 4.3.1 Scintillation light propagation simulation 22 4.3.2 Scintillation of scintillation light detection by PMTs 23 4.4 Simulation of Photomultiplier tubes (PMTs) 23 4.5 Simulation of the surface of Crystals 25 4.6 Crystal position identification 25 4.6.1 Saw-cuts estimation 26 4.6.2 Transformed Anger Logic 28 4.6.3 Position Map Look-Up table 30 4.6.4 \"Simplest Algorithm\"(General steps) 30 4.6.5 Neural Net algorithm 31 4.6.6 \"Genetic algorithm\" (General steps) 32 4.6.7 Algorithm summary 34 4.7 Depth of Interaction information 35 4.7.1 Depth of Interaction Algorithm 35 4.7.2 Time discrimination Approach 35 4.7.3 Fuzzy Logic Approach 36 4.8 DOI estimation algorithms summary 43 5. Results 44 5.1 Energy Resolution 46 5.2 Detector efficiency 48 5.3 Miss position identification 48 5.4 Spatial Resolution 50 v 6. Validation of the simulations 56 7. Discussion 57 8. Conclusion 58 Bibliography 59 vi List of Tables 1. Table 1. Summary of some of the positron emitters and labeled compounds used in PET. 2. Table 2. Maximum energy imparted to the positron following the decay of its parent nucleus. 3. Table 3. Physical characteristics of simulated inorganic scintillators. 4. Table 4 Summary of algorithms. 5. TableS Data from CTI technical specification. 6. Table 6 LSO/GSO (7.5 mm-7.5 mm) Energy Resolution (%) 7. Table 7LSO/GSO (10.0 mm-10.0 mm) Energy Resolution (%) 8. Table 8 Energy resolution for different crystal configurations. 9. Table 9 Events stopped in crystals. 10. Table 10 Events correctly identified by Position Map. 11. Table 11 DOI miss position identification. 12. Table 12 HRRTgeometry LOR spatial resolution. 13. Table 13 Round geometry LOR spatial resolution. 14. Table 14 Spatial resolution for the most oblique LOR for three source positions. Data are shown in the format a/b, where a is the resolution obtained with DOI correction and b is the resolution obtained without DOI correction. All values are expressed in mm. 15. Table 15. Overall spatial resolution, for three source positions. Data are shown in the format a/b, where a is the resolution obtained with DOI correction and b is the resolution obtained without DOI correction. All values are expressed in mm. 16. Table 16. Spatial resolution for ECAT 953B. Vll List of Figures 1. Figure 1. What does a PET scan show? 2. Figure 2 Parallax errors. 3. Figure 3 Here the example of 18F-fluorodeoxyglucose molecule that mostly often used for glucose metabolism study. 4. Figure 4. Principles of the detection of coincident annihilation gamma rays. 5. Figure 5. Positron annihilation. 6. Figure 6 Compton scatter. 7. Figure 7 A schematic drawing of the detector block, top \"face\" view. And coordinate map setup for detector block surface. 8. Figure 8. HRRTgeometry 9. Figure 9. Detector block. 10. Figure 10. Simulated by GEANT propagation a 511kev photon through a media. 11. Figure 11. Algorithm diagram of simulation 511 keV gamma ray interaction in the detector block. 12. Figure 12 Interface between the Algorithm and the PET detector Simulator (GEANT/DETECT). 13. Figure 13 Distribution of events hitting a detector crystals. 14. Figure 14 Detected events distribution. 15. Figure 15 Position Maps. 16. Figure 16 Position Maps. 17. Figure 17 Real position map (CTI). 18. Figure 18. Signal distribution. 19. Figure 29. Chromosome in the Genetic algorithm. 20. Figure 20. Coincident-Event Correction. 21. Figure 21 Decay time distribution. 22. Figure 22 Decay time and energy distribution 23. Figure 23 Fuzzy Logic Model. 24. Figure 24 Degree of confidence. 25. Figure 25 Logical Space. 26. Figure 26 Defuzzification process. 2 7. Figure 2 7 DOI estimation dynamic generator for arbitrary number of layers. 28. Figure 28 Data flow chart for energy discrimination and spatial resolution. 29. Figure 29 Simulated LORs for the source located at center of the FOV, 5cm and 10cm off center for the octagonal geometry. 30. Figure 30LSO/LSO (15mm) 7.5mm-7.5 mm 31. Figure 31 Energy distribution for LSO/GSO(15mm) viii 32. Figure 32 Coincidence detection efficiency as a function of total crystal thickness (equal depth layers were used). Squares: LSO/GSO, triangles: LSO/LSO, x: LSO/GSO with an energy window of 350-650 keV and circles: LSO/LSO for the same energy window. 33. Figure 33. Represent source shifted Wsm left and LOR uniformly distributed over left top detector sector. 34. Figure 34. Source profiles without DOI correction. Squares: events stopped in the top layer, triangles: events stopped in the bottom layer, rombs: events, where one /-ray stopped in the top and the other one in the bottom layer and x: total profile 35. Figure 35. Source profiles after DOI correction. Squares: events stopped in the top layer, triangles: events stopped in the bottom GSO layer, rombs: events, where one y-ray stopped in the top and the other one in the bottom layer and x: total profile. ix Acknowledgements I would like acknowledging the contributions of my friends and colleagues at the Positron Emission Group at the Pacific Parkinson's Research Centre and at the TRIUMF National Laboratory for Particle and Nuclear Physics. I am very grateful to my supervisor, Dr. Vesna Sossi, for her encouragement, patience, and guidance over the course of this very exciting project. I am greatly indebted to Dr. Peter Gumplinger, his help in simulation set up was very important to start simulation study. Many thanks to Dr.Tom Ruth who involved me in this interesting project. x Chapter 1 1. Introduction 1.1 Goal of this Thesis This thesis will present a crystal design simulation for a High Resolution Research PET tomograph (HRRT) with depth of interaction encoding capability. The general goal of this research was to estimate an optimal crystal design for the HRRT in terms of detector efficiency, energy and space resolution. To reach this goal various parameters were simulated such as types of scintillation materials, geometric design and depth of interaction information. 1.2 Thesis Outline To understand the problems and the significance of the approaches applied to them, some background in PET is required. After an introduction in Chapter-1 a short summary of this will be presented in this Chapter-2, followed by a brief overview of the HRRT system in Chapter-3. Exposition of the general software parts will be described in Chapter-4. The simulation and validation of the results are present in Chapter-5 and Chapter-6. The discussion section Chapter-7 will examine the results and propose which of the detector block designs provides optimal data acquisition. The conclusion is in Chapter-8. 1.3 Motivation In order to improve the capability of PET to investigate human brain functions such as blood flow, metabolism and receptor characteristics, the spatial resolution and the y detection sensitivity has to be improved relative to what is available today. Figure 1. What does a PET scan show? Image produced by Positron Emission Group at the Pacific Parkinson's Research Centre. The brain function being studied during a PET scan determines which radiopharmaceutical is used. Oxygen-15 can be used to label oxygen gas for the study of oxygen metabolism, carbon monoxide for the study of blood volume, or water for the study of blood flow in the brain. Similarly, fluorine-18 is attached to a glucose molecule to produce FDG for use in the observation of the brain's sugar metabolism. Many more PET radiopharmaceuticals exist, and research is under way to develop still more to assist in the exploration of the working human brain. For example, dopa, a chemical active in brain cells, is labeled with positron-emitting fluorine or carbon and applied in research on the communication between certain brain cells which are diseased, as in dystonia, Parkinson's disease, or schizophrenia. 1 In order to meet this goal a new next generation high-resolution 3D-only brain PET scanner has been developed at CTI using a new scintillation material LSO (Lu(i_x) Ce 2 x (Si04)0). To improve the sensitivity in modern high-resolution brain PET system, it is necessary to reduce the detector radius to increase solid angle and place detectors as close as possible to the object being scanned. But for events coming from a source out of the detector center, a small detector radius leads to an increase of the number of events hitting the detector surface at a non-normal angle. These events have a high probability to be detected in a crystal that neighbors the one where they first hit the detector; this leads to a mis-identification of the crystal position. This is known as \"parallax error\" and leads to worse spatial resolution for off-center events. Figure 2 Parallax errors. Annihilations ofpositrons out off center of the detector will produce 51 lkev gamma photons that will hit the detector block at a non- normal That can leads to situations when angle a photon hitting a certain crystal will stop in a neighbor crystal. In that case, we will see the event shifted from its real position its real position. This possible shift will degrade spatial resolution for off-center regions. These mis-identifications of the position is called the parallax error. The depth of the y ray interaction (DOT) information is needed for correction of this spatial resolution degradation. This requirements is led to development of two-layer detector block designs like LSO/GSO (GSO - Gd2SiOs) where the two molecules have different scintillation decay times. The separation of the events occurring in LSO and the GSO layer by pulse shape discrimination allows discrete DOI information to be obtained. This type of tomograph is just currently being built by CPS (Knoxville, TN, USA) and it goes under the name of High resolution Research tomograph (HRRT). The HRRT is the first human size tomograph with DOI. At the time this thesis work was started the final design for HRRT was being finalized. It was therefore important to perform simulations to determine how much the DOI determination was going to improve the resolution uniformity. 2 1.4 Previous W o r k Over the past decade, new architectures and designs for high performance PET systems have been investigated. A design study of a depth encoding large aperture PET camera was performed at TRIUMF in 1995 [1]. This study showed the fundamental importance of the depth of interaction information (DOI) to correct the resolution. Simulation study for practical BGO ( Bi4(Ge04) )block detector with depth-encoding capability was performed in the works [2,3]. This study showed that up to 38% of image degradation resolution could be removed by DOI corrections. Also, DOI made the resolution nearly uniform across the useful field of view (FOV). In the last a few years new multiple layers design with new type of scintillator (LSO) was proposed. Preliminary studies were performed [4,5] where these designs have been simulated and first evaluation measurements were obtained. These results showed a significant improvement compare to old PET cameras designs. Different DOI estimation and corrections methods were investigated by various researchers around the world such as Critical On-line DOI Rebinning Method [13], Berkeley design [12] and application neuro-fuzzy approach [14] to DOI correction. None of these methods has been implemented in a human size scanner yet. 3 Chapter 2 Principles of Positron Emission Tomography 2.1.1 Positron Emission Tomography Positron Emission Tomography (PET) is an imaging modality that measures the spatial distribution of substances labeled with positron emitters. The potential for using positron emitters for imaging has been recognized since the 1950s when Brownell and Sweet localized brain tumors using the first practical positron camera. Since that time, PET has been used to visualize a host of physiological processes, including blood flow, substrate metabolism, and the binding of minute concentrations of various agents to receptor sites. PET has been used extensively in medical research, providing new insight into disorders including Parkinson's disease, epilepsy, schizophrenia, Alzheimer's disease, and depression. A better understanding of cardiac disorders and stroke has been obtained using PET. Application in neuropsychological studies are elucidating the response of the brain to various stimuli in terms of blood flow, blood volume or glucose metabolism. In addition, using animal subjects, new pharmaceuticals can be evaluated and screened in vivo. Finally, PET has been used successfully to monitor the metabolism and treatment of various cancers. PET, unlike some imaging technologies like MRI and X-rays, collects functional, rather than anatomical information which can be used to probe into the biochemical function of specific cells or to extract information about kinetic parameters of metabolic pathways. The physical basis for PET is fundamentally simple. The patient is injected with tracer amounts of a chemical compound, which have been labeled with a positron-emitting radioactive isotope. The tracer is either a close analogue of the endogenous species present in the body, and can be used to study a metabolic pathway, or has a high specificity for a particular binding site whose population is of interest. For example, glucose metabolism in the body is studied with 8F-deoxygluxose. The compound is 1 S similar to glucose except that one of the Hi has been replaced with the F isotope and 1 S one of the -OH groups is missing. The F allows the detection of the tracer in the body through the use of PET and the missing -OH traps the tracer in a specific metabolic step. Once the tracer has had time to diffuse to the organ of interest, the patient is placed in the detector and the tracer activity distribution is monitored with the scanner. 2.1.2 Positron-emitters and labeled compounds used in P E T The positron-emitters used in PET are isotopes of some of the most prevalent elements found in living systems (carbon, oxygen, and nitrogen). For this reason they can be used to synthesize various compounds that mimic the function of substances found physiologically. The most common radioisotopes used in PET, their half-lives (t 1/2), and some of the useful labeled compounds produced are listed in Table 1. These radioisotopes are typically produced in medical cyclotrons by bombarding stable isotopes with 4 positively charged particles (proton or deuterons). The nuclear reactions employed for each isotope are also listed in Table 1. Table 1. Summary of some of the positron emitters and labeled compounds used in PET. Isotope t >/2 (minutes) Nuclear Reactions used Labeled Compounds Application in PET imaging M C 20 10B(d,n)\"C 14N(p,a)nC \"CO u c-raclopride Cerebral blood volume Dopamine D 2 receptor 10 12C(d,n)1JN 160(p,a)!3N 1JN-amino acids 1 3 NH 3 Amino acid metabolism Cerebral blood flow 2 I4N(d,n)i:,0 15N(p,n)150 H 2 '-O, C 1 5 0 2 c 1 5 o 2 Cerebral blood flow Oxygen consumption Cerebral blood volume lop 110 180(p,n) lsF 20N(d,a)18F fluorodeoxy glucose f 8 F -fluorodopa mine Glucose metabolism Dopaminergic system The labeled compound is administered by injection or inhalation and enters the blood stream of the subject. The subsequent distribution of the substance throughout the body then closely imitates that of its naturally occurring analogue. Figure 3 Here is the example of 18F-fluorodeoxyglucose molecule that is mostly often used for glucose metabolism study. 2 fiuoro 2-deoxyD-gIucose \"FOG\" 5 2.1.3 Basic Principles of PET Conventional PET scanners consist of one or more rings of detectors surrounding the subject as shown in Figure 4. Each detector is composed of an arrangement of dense, high effective- atomic-number (Z) scintillation crystals optically coupled to photo-multipliers tubes (PMT). Figure 4. Principles of the detection of coincident annihilation gamma rays. Isotope distribution Channel 1 Channel 2 c o i n c i d e n c e e v e n t s After an amount of the administered positron-emitter has been distributed through the region of the body that is going to be imaged, a number of physical processes occur before the location of this activity is detected. Below, the underlying principles of PET are summarized by following these events in order, from the decay of the nucleus to the detection of coincident annihilation gamma rays. 2.1.4 Positron Decay The common feature shared between the radioisotopes listed in Table-1 is a surplus of nuclear positive charge, making the nuclei unstable. The nucleus decays to a lower energy state by emitting the net positive charge in the form of a positron. This process also results in the conversion of a proton to a neutron, and the emission of a neutrino: p+ -> n + e+ + v + energy (1) Both charge and lepton numbers are conserved in this process. The energy released is shared between the positron and the neutrino. The proportion of the total energy imparted to the positron as kinetic energy is a stochastic quantity, but it is described in terms of a maximal value, E m a x depends on the positron emitter used, as indicated in Table 2. The average value of kinetic energy received by the positron is approximately equal to 1/3 E m a x . 6 Table 2. Maximum energy imparted to the positron following the decay of its parent nucleus. Radioisotope Maximum Positron Energy (Emax) \"C 0.97 Mev 1.19 Mev lio 1.70 Mev 0.64 Mev 2.1.5 Loss of energy by the positron Positrons are emitted isotropically from the parent nucleus and travel several millimeters in the medium while continually losing energy through excitation and ionization interactions. A small amount of energy (-1%) is also lost in the form of bremsstrahlung radiation. The distance over which the positron travels is dependent upon the initial kinetic energy and the density of the medium into which it is emitted. 2.1.6 Positron annihilation The probability for in-flight annihilation of positron is very low. After duration of approximately 10\"9 s, the positron slows down to thermal energy and annihilates with an electron. In positron annihilation, the slow positron combines with a loosely bound electron located in one of the shells of an atom in the medium. The combined mass of the two particles (two times 511.1 Mev/c2) is entirely converted into energy, and two annihilation gamma rays are emitted. Figure 5.Positron Emission Tomography 7 The gamma rays emerge from the site of annihilation in approximately opposite directions. The line connecting two coincidently firing detectors is called \"line of response\"-LOR. This process must conserve both energy and momentum. It is unlikely, however, that the net momentum of the e+ e- system is zero just before the annihilation occurs, since the typical energy of the positron at this time is 10 eV, and the electron is orbiting in an atomic shell. In order to conserve momentum, the annihilation gamma rays are slightly non-collinear. The deviation of the angular separation of the gamma rays is described by a Gaussian distribution in water-equivalent materials, with a full-width-half-maximum (FWHM) of approximately 0.5° . 2.1.7 Interaction of the 511 kev gamma rays in tissue and in detector material. The 511 kev gamma rays interact with the matter through which they pass. The matter includes both the surrounding material of the subject (i.e. tissue, fat and bone) and the dense scintillation crystal in the PET detector. At the energy of 511 keV the probability for coherent (Rayleigh) scattering is negligible, and the energy is insufficient for pair or triplet production to occur. Hence, the dominant interactions of the annihilation gamma rays are Compton (incoherent) scattering and photoelectric absorption. Compton Scattering Compton scattering is an interaction that occurs between an incident photon of energy hv and an electron in the medium. Energy is transferred to the electron, and it recoils along an angle § from the initial trajectory of the photon with energy E'. The photon scatters through an angle of 0 and emerges with a reduced energy, hv' according to: hv hv' = (2) 1 + a(l-cosO) where hv a = m e c 2 Where c is the speed of light and me is electron mass. The Compton attenuation coefficient (a) is nearly independent of the atomic number of the medium in which the photon interacts (8), but increases with electron density. For photons in the energy range of interest in PET, this is the most predominant interaction in tissue. For a 511 keV photon in tissue, the relative probability for Compton scattering (given by o7p x 100%, where u. is the total attenuation coefficient) is approximately 99.7% (9). For a 511 keV photons in detection material-scintillator the relative probability for Compton is approximately 40-60 % and rapidly decreases to almost zero at an energy lower then 100-50 keV. 8 Photoelectric Absorption In photoelectric absorption, the entire energy of the incident photon is transferred to an electron ejected from the K, L, M or N shell of an atom and to either characteristic radiation photons or Auger electrons. The energy of the ejection photoelectron is hv - Ebind, where E bind is the binding energy of the shell in which it originated. The photoelectric cross section varies with photon energy according to, approximately, l/(hv) , and with atomic roughly according to Z 3 or Z 3 8 for low-Z materials (8). In the detection material-scintillatyor, the probability of photoelectric absorption is almost 100% at energy 50 keV and comes down to approximately 40-60 % at energy 511 keV. 2.1.8 Scintillation If a gamma ray escapes the volume of the patient and is incident upon a PET detector, it may deposit energy within the dense, high-Z scintillating crystal through the interactions outlined above. In LSO scintillator the relative probability of photoelectric absorption of 511 keV photon (x/u. X100%, where x is the photoelectric attenuation coefficient and where p is the total attenuation coefficient) is approximately 45%, while the relative probability for Compton scattering is approximately 55%o. The absorption of energy by the crystal is followed by scintillation, or the emission of light. This light is detected by the photomultiplier tube to which the crystal is coupled, and its detection is discussed in some details later in this chapter. 2.1.9 Coincidence detection As explained below in the discussion of PET detectors, the scintillation light produced is detected by the PMT, and converted into an electrical signal. Two gamma rays are considered to be temporally coincident if the detected signals arrive within a specified time interval, determined by the coincidence resolving time of the system (typically between 3-20 ns). Figure 6 Compton scatter. 9 The possibility of Compton scatter of the gamma rays was already discussed early. Scatter can occur both in tissue and in the detector. Because one or both gamma rays may have undergone scattering before coincidence detection, these events degrade the image quality and reduce the accuracy of quantitative measurements (10). In addition, accidental coincidences occur, corresponding to the coincident detection of two gamma rays originating from separate annihilations. Thus, the total count rate ' R ' is the sum of the true ( R t ) , scatter ( R s ) and accidental rate ( R « ) : R = R , + R s + R a (3) The true coincidence rate, R t , is equal to the product of the positron emission-rate of the nuclide (R p 0 si t rons)> the efficiencies of the detectors ( € A and G B ) , the geometric efficiency of a detector (g) and a factor accounting for attenuation of gamma rays through a thickness L of matter with an attenuation coefficient p.: Rt = Rpositrons G A G B g e (4) The detector efficiency (e) refers to the fraction of incident gamma rays that deposit a sufficient amount of energy so that they are detected. The geometric efficiency (g) is the ratio of the surface area of the detectors divided the area of a sphere of radius r equal to one-half of the detector separation. The accidental coincidence count rate for a given detector pair is determined by the coincidence resolving time of the detectors (x) and the singles count rates for the detectors ( R A s i n g and R e s m g ) : R a = 2T RAsing RBsing (5) The scatter count rate is the rate of detecting both gamma rays from the same annihilation in coincidence, where at least one gamma ray undergoes Compton scatter before detection. Unlike the accidental rate, the scatter count rate cannot be reduced by shortening the detector coincidence resolving time. The amount of scatter is highly dependent on the scanner used and on the size of the object being scanned. For a source located near the midpoint of two detectors, it is: R s = K Rpositrons G A G B g (6) The factor K is derived empirically and accounts for various geometrical and scanner design parameters. This is the factor that account for the size of the object. If the source is in the air that mean we don't have object then there is no that scatter factor. And we have just scatter in the detector material. The detection g scattered events is reduced by using energy discrimination, where the only events with energies located within specified range around the energy spectrum photopeak are accepted. 10 2.2 Sensitivity Sensitivity is defined by ratio between the number of detected events and the number of decays and it depends on several important criteria. The first is attenuation of the 511kev gamma photons in the detector and the second is the production of a detectable number of scintillation photons at a wavelength to which PMT is sensitive, following the deposition of energy by gamma rays. The time scale of this emission is also crucial, since it largely determines the count rate capabilities of the scanner, the coincidence resolving time, and in turn, the accidental coincidence rate defined in Equation 5 (Chapter 2.1). The scanner geometry also affects the sensitivity by introduction geometry factor for gamma rays paths in the detector materials. 2.3. Spatial resolution in P E T 2.3.1 Physical limits on spatial resolution Two factors, which occur in the course of positron decay and annihilation, introduce physical limits on the achievable spatial resolution of PET. The first is the finite range of the positron before annihilation. The coincidence detection of the annihilation gamma rays localizes the annihilation events, not the location of the parent nucleus, since the trajectory of the positron is undetermined. This introduces a blurring into the image, reducing the spatial resolution. On average, however, the error in estimating the location of the parent nucleus based on the annihilation location is less than the positron range, since some component of the positron trajectory likely will be along the line of response (LOR) between the two detectors (i.e. there is no error if the positron annihilates a point along the LOR). Dorenzo et al (11) have studied the point-spread function (PSF) due to positron range. This distribution is expressed by the sum of two exponentials, one accounting for small peak at a very short range where a small number of annihilation occur, and a second which introduces broad tails corresponding to the range of the majority of positrons. Because of the presence of these broad tails, the PSF is characterized by a full-width-tenth-maximum (FWTM) and by a full-width-half-maximum (FWHM). For F, which produces a comparatively low-energy positron, the resolution broadening due to positron range (12) is 0.22mm full-width-half-maximum (FWHM) and 1.09mm FWTM in water. The second limit on spatial resolution is introduced by the acollinearity of the annihilation gamma rays. Because the angular deviation of the gamma rays from 180° cannot be determined on an event-by-event basis, localizing the site of annihilation involves an assumption that the gamma rays were emitted in exactly opposite directions. The magnitude of the blurring introduced by this effect increases linearly with detector separation. In typical PET systems, the distance between opposite detectors, D, is typically -50 cm. For the arrangement of the high-resolution detectors described in this work the detector separation is D = 46.9 cm. The acollinearity of gamma rays originating 11 in the center of the ring results in a blurring of (±234.5 mm x tan (0.25°)), or ±1.0 mm, since the probability distribution of angular deviation is Gaussian with a FWHM of 0.5°. 2.4 Detector block and intrinsic detector resolution While the two effects described above impose theoretical physical limits on resolution, the intrinsic detector resolution is a factor that can be controlled to some extent in the design of the imaging system. Most modern PET system employs either individual scintillators or modular crystal detector blocks from which a number of discrete elements are cut. Scintillators produce, optical light when a high-energy particle like a 511 kev photon has interaction in the crystal. This optical light propagates through the block and is detected by photomultipliers (PMTs) The crystal matrix is coupled to PMTs through a light guide that is generally cut. These saw-cuts have different depth and they are used to selectively guide the optical photons from each crystal to the PMTs. The depth of the saw-cuts affects the light distribution for each crystal, which affects the number of scintillation photons detected by each PMT. A sub-optimal saw-cuts pattern will lead to a non-uniform distribution of signals for each crystal. That will cause poor crystal identification, since the peaks will not be easily separable. The identification of the crystal where the event occurred is based on the light distribution for each crystal. For an event that produced scintillation light detected by PMTs, we use the so called \"Anger Logic\" to estimate the coordinates where the event occurred (Xy Yy): Figure 7 A schematic drawing of the detector block, top \"face \" view and coordinate map setup for detector block surface. A xY I (A+C) - (B+D) where A, B, C and D are the amplitudes of the signal from the four PMTs corresponding to the detected event. Then all detected events are plotted on the plane (Xy Yy) that is divided on 1024x1024 bins. The number of events with discrete coordinates (Xy Yy) creates a histogram. Each peak of the histogram is associated to a specific crystal \"ID\". 12 The width and separation of the crystal elements determine the spatial frequency at which the radioactivity distribution is sampled. According to the Nyquist theorem, in order to detect a distribution of activity with spatial frequency of/\"at a particular location in the FOV of the scanner, the lines of response must pass though that location at a frequency of at least 2/in order to avoid aliasing artifacts in the image. Unfortunately, the crystal element dimensions are not the only intrinsic factor determining the frequency response. In addition, when modular detector blocks are used there is some uncertainty in determining in which element of the block the even occurred. This ambiguity may result from several factors, including limited scinitillation photon statistics or imprecision of the readout used to provide positioning signals. An empirical study by Moses and Derenzo [12] summarized the various factors affecting the spatial resolution discussed above. According to this work, the components add in quadrature, resulting in a spatial resolution defined by the expression T: r = 1.25* V {dl2f + (0.0022 D)z +sz + (8) Here, d is the crystal element width in mm, D is the detector separation in mm, s accounts for the positron range ~0.1-0.5 mm and b accounts for the uncertainty in the determination of the location of the event within a block detector with multiple crystal elements. If crystal elements are coupled to PMTs in 1:1 ratio, b equals zero. The factor 1.25 accounts for a degradation of resolution resulting from the image reconstruction process. 2.5 Interaction between detector design resolution and sensitivity Modular detector design where a detector is cut into 8x8 smaller crystal \"fingers\" has higher spatial resolution compared to a big single crystal because significant part of scintillation light will propagate through the crystal where an event occurred because of internal surface reflection. That lead to more precise event-to-crystal localization. A deep crystal increases the probability of 511kev photons to have photo interaction in the detector block, which increases the detector sensitivity but at the same time decreases the spatial resolution because of \"parallax error \" for events coming from a source out of the detector center. To minimize this problem, novel detectors employ a two-level detector block design to extract depth of interaction (DOI) information by various methods. Using this DOI information, we improve resolution for off-center events. 13 Chapter 3 3. Overview of the High Resolution Research Tomograph (HRRT). The octagonal design corresponds to the HRRT (CPS, Knoxville, TN) (Figure 8). Figure 8. HRRT geometry Eight panel detectors consisting of 117 (9x13) HRRT fast-LSO/slow-LSO or LSO/GSO phoswhich block detectors are arranged in the gantry with a 46.9 cm distance between two opposing heads. Each of the 936(8 panels x 117 detector blocks per panel) detector blocks has 128 single detector elements (1.9x1.9x10.0 mm3) in two layers. This leads to large number of electronic channels resolving the information of the 119,808 single crystals. Each head (14,976 crystals) in the system is in coincidence with the \"opposing\" 5 heads. That lead to 20 unique head to head pair coincidences that is equal to 4.486* 109 Line of Responses (LOR). 3.1 Detector geometry. In all cases the block is composed of a double layer 8x8 crystal matrix (single crystal x and y dimensions 2.1x2.1mm2). The simulated block design followed that of the HRRT [4]. In the simulated configuration the double crystal matrix was coupled to four PMTs via a light guide (figure 3). Each PMT was shared by four detectors [9]. Figure 9. Detector block. put mt The light-guide coupling the detector block with the PMTs contained saw-cuts of variable depths. This design allows the light originating from each crystal to be channeled in such a way as to produce a unique energy distribution between the four PMTs. The interaction position ( X , Y ) in the x and y plane (crystal surface plane) was thus identified from the energy output of the PMTs using a modified Anger logic approach yielding the following formula (see 9). Xy'=[exp(P*Xy)-l]/[exp(P)-l] (9) Yy'=[exp(P* Yy)-1 ]/[exp(P)-1 ] where X y and Y y are the standard combinations of the PMTs energy information [10] (see eq.7, Chapter 2 ) and P is an optimization parameter. The optimum saw cut pattern was identified by varying the saw cut depths until an optimum crystal separation was achieved. 3.2 Simulated Scintillators An analysis of the physical properties of various scintillators was performed. Various compound materials were simulated by GEANT. There are several important criteria to consider in selecting a scintillator to be used in a FfRRT detector. First, the detector must be able detect higher-energy 511kev gamma rays. Scintillators with very high effective atomic numbers and densities present large cross sections for Compton and photoelectric interactions, and therefore offer higher attenuation for 51 IkeV gamma rays. A second requirement is the production of a detectable number of scintillation photons, at a wavelength to which the PMT is sensitive, following the deposition of energy by gamma rays. The time scale of this emission is also crucial, since it largely determines the count rate capabilities of the scanner, the coincidence resolving time, and in turn, the accidental coincidence rate defined in Equation 5 (Chapter 2). Finally, several issues related to bulk properties of the scintillator are important, including whether the material is hygroscopic, and whether it can be easily grown and machined for the construction of PET detector blocks. Table 3.2 summarizes the physical properties of simulated scintillators. 15 Table 3. Physical characteristics of simulated inorganic scintillators. Property B G O L S O G S O Density (g/cm3) 7.13 7.4 6.71 Effective Z 74 66 59 Linear Attenuation Coefficient u(cm\"2) 0.903 0.870 0.6 Avg. number of photons per keV 6 24 9 Relative light yield (/100) 15 75 27 Scintillation decay time (ns) 300 40 60 Peak wavelength of emission (nm) 480 420 430 Refractive index 2.15 1.82 1.85 Hygroscopic No No No Chemical formula Lu(i-x) Ce2x (SiO4)0 Lu(i.x) Ce2x (SiO4)0 Gd 2Si0 5 BGO was simulated to evaluate the software and repeat previous results [3]. LSO and GSO were simulated for the detector block. Properties of this scintillator block and its dimensions were used as inputs to the detector simulation software. 16 Chapter 4 4. Simulation Study The simulation software was developed using the CERN simulation packet GEANT [5] and the program DETECT [7] developed at TRTUMF. GEANT was used to simulate the propagation of 511 kev photons through the detector block and the production of scintillation light. DETECT was used to simulate the propagation of scintillation photons through the detector block and to simulate the process of detection of these photons by photomultiplier tubes (PMTs). DETECT was modified to be applicable to this investigation. In additional to the HRRT geometry a circular scanner geometry was also simulated to investigate the effect of DOI correction on resolution as a function of scanner geometry. The same detector-to-detector distance (46.9cm) was used for both octagonal and circular design simulation. Four crystal configurations were simulated: two LSO layers 7.5 mm deep (LL_7.5), two LSO layers 10 mm deep (LL_10), a 7.5 mm deep LSO layer followed by a 7.5 mm GSO (LG7.5) layer and finally a 10 mm deep LSO layer followed by a 10 mm deep GSO layer (LG10). The LSO layer closely facing the object - top layer- was assigned a decay time centered on 33 nsec with standard deviation 5.2 nsec (fast LSO), the LSO closer to the photomultiplier tube (PMT) - bottom layer - a decay time centered on 40 nsec with standard deviation 6.4 nsec, while GSO was given a decay time centered on 60 nsec with standard deviation 12 nsec [8]. 4.1 G E A N T A GEANT based software was used to simulate a uniform beam of photons of energy 511 keV outgoing from a distant source. The source geometry could be set to be a point, a line or a flood. Each incident photon was then tracked in the volume of the detector block for photoelectric and Compton interactions. Cross sections for interactions in the scintillator material were derived using GEANT. The relative ratio of the cross-sections for the Compton and photoelectric processes was used to randomly choose which of these occurs at each interaction vertex. The distance traveled by the incident or Compton scattered photon between interactions was randomly generated according to an exponential distribution. The total cross-section at the energy of the interaction photon determined the interaction length of the photon. Values of the cross-sections were tabulated from 10-520 keV in bins of 5 keV. For Compton interactions, the angular distribution of the scattered photon follows the Klein-Nishima formula. Compton scattering of photons into the detector block from the surrounding supports like detector frame was not modeled. 17 Figure 10. Simulated by GEANT propagation a 511kev photon through a media. Scattered photon. Incident 511 kev photon \\ X-ray Compton recoil electron Scintillation photons Phptoelectron Compton recoil electron At each interaction vertex, the energy lost by the absorbed or scattered photon was assumed to be converted to scintillation light. The number of scintillation photons generated at each interaction was derived from the product of the energy lost at the interaction vertex and of the light yield of LSO from [9]. The scintillation response of LSO and GSO displays a significant dependence upon the energy of the incident photons. From the recent compilation available in Ref [6], the scintillation yield of this crystal effectively doubles as incident photon energies increase from 10 to 100 keV. Above 100 keV it reaches a nominal plateau of 23000 scintillation photons/MeV which extends at least up to 1 MeV. Implementing this effect in the model only requires a correction to the number of scintillation photons associated with each interaction vertex of an energetic photon tracked in the block. This effect was already implemented for LSO and we added a correction factor for GSO that was taken directly from the experimental scintillation response curve available in Ref[6]. For each interaction vertex, /, an event scintillation vector was written to an output Interaction List File. The first three words of the vector were the coordinates of the interaction point within the detector block volume (X„ Y„ Z,). The fourth word gave the number of scintillation photons released at that vertex, N,. This number was computed as the product of the energy lost at the vertex and the known light yield per unit of deposited energy for the scintillator material. The last word of the vector was a sequential index incremented for each interaction until the tracking was stopped. Tracking was stopped either by a photoelectric interaction, escape of the photon from the block volume, or by a Compton interaction leaving less than 10 keV to the outgoing photon. 4.2. Summary of all physical processes simulated bv GEANT A Monte-Carlo approach was used to simulate different physical processes involved in the propagation of 511kev photons through scintillation media. As mentioned before the distance traveled by the photon between interactions was randomly 18 generated according to an exponential distribution. The total cross-section of all processes at the energy of the interaction photon determines the interaction length in the of the exponent of the distribution. The probability of each type of interaction was calculated on the base of the cross-section of a particular reaction at a given energy. The type of a interaction was chosen for each point interaction by a Monte-Carlo generator implementing these probabilistic functions. 4.2.1 Simulated interactions of a incident 511 kev photon in scintillator material • Rayleigh scattering (negligible for hv> 100 keV) • Photoelectric effect dominant for hv < 50 keV and important for hv < 90 keV • Compton (incoherent) scattering important for hv > 50 keV and only interaction for 200 keV