Università degli Studi di Torino Scuola di Scienze della Natura. Corso di Laurea in: Fisica Nucleare Subnucleare e Biomedica

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1 Università degli Studi di Torino Scuola di Scienze della Natura Corso di Laurea in: Fisica Nucleare Subnucleare e Biomedica Simulation of the TOFPET ASIC response function in reading SiPMs coupled to a continuous crystal. Simulazione della funzione di risposta dell ASIC TOFPET nella lettura di SiPM accoppiati a cristallo continuo Marco Boretto Relatrice: prof. Cristiana Peroni Co-relatore: dott. Francesco Pennazio Contro relatore: dott. Vincenzo Monaco

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3 Contents List of figures List of tables iii viii Abstract 1 1 POSITRON EMISSION TOMOGRAPHY Introduction to Positron Emission Tomography PET Radiotracers PET Physical Principles Beta Decay Positron Path in Matter Interaction of Photons in Matter Photons Attenuation in Annihilation Process PET Detectors The Scintillation Process in Inorganic Crystals Photo Multiplier Tubes in PET Silicon Photo Multiplier Coupling Scintillation Crystals to Photo Detectors Timing Resolution and Coincidence Detection Time Of Flight Sensitivity Energy Resolution Depth Of Interaction Multimodal Imaging i

4 PET-CT PET-MRI The 4DMPET PROJECT DMPET Block Design DMPET DOI Measurement Strategy DMPET TOF Measurement Strategy DMPET Readout Electronics Mixed-Mode Readout ASIC Time to Digital Converter ASIC Cluster Processor Digital Acquisition System Status of the 4DMPET Project TOFPET Readout Electronics TOFPET Front End Circuits TOFPET Time to Digital Converter and Signal Validation Data Buffer and Global Controller TOFPET Electronics Simulation DMPET Simulation Chain DMPET Block Detector Simulation Single Signal Generation Channel Signal Generator DMPET ASIC Simulation Cluster Processor and Measurement Merging Utilized Software TOFPET Model and Analysis The Simulink Blocks Simulink TOFPET Base Model Signal Processing Simulink TOFPET Model with Energy Integration TDCs Model Model Validation Choice of Simulink Parameters ii

5 3.3.2 Results Comparison TOT Characteristic and Linearization Simulation of All the Block Detector Channels Input Sequence DMPET TOFPET Remarks Experimental Preliminary Results Acquisition with Pixellated LSO Crystals Acquisition with Monolithic LYSO Crystal Conclusions and Future Works Results Achieved Future Works Acronym 111 Bibliography 115 iii

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7 List of Figures 1.1 Photo-electric effect Scattering Compton Pair production Total atomic cross-section Detectors A and B record attenuated count rates arising from a source Schematic diagram of a photomultiplier tube Basic structure of a SiPM with simplified electrical model Dynamic Range Dark count noise distribution in SiPM Dark count rate as a function of temperature and overvoltage Standard PET block detector scheme True coincidence, scatter coincidence, random coincidence, attenuation Graphical exemplification of non-tof and TOF spatial probabilities Transverse sections of two patients with different techniques The energy spectrum of a LSO-APD detector DOI uncertainty effects Comparison between PET/CT and PET/MRI Schematics of the 4DMPET block detector Cone of light see by the layer of SiPM Correlation between the DOI of primary photon and DOI m calculated from the cluster size asymmetry v

8 2.4 Trigger on dark count Time resolution with three different measurement techniques Block diagram of the mixed mode readout ASIC Distribution of the timestamps of signals in cluster Overview of the TOFPET channel architecture TOFPET FE amplifier circuits Dual threshold TOFPET scheme Internal logic of the TOFPET circuits Simulation results of the TOT curve DMPET simulation chain Equivalent circuit model of the SiPM coupled to the front-end electronics Front-end current output to single-cell avalanche input Typical output of a SiPM pixel, obtained from a simulation DMPET and TOFPET simulation chain Source and Sink Blocks Discriminator Block Delay Block AND and NOT Blocks D flip-flop Block Switch Block Transfer function and Amplifier Blocks From, Go to Blocks Terminator Block TOFPET Base Model TOFPET Logic in Simulink Rearmament of the circuit Signal with fast rise time Validation logic A signal with low rise time Logic diagram of a DOE signal cutted Signal with low rise time DOE without DOT signal vi

9 3.24 DOE without DOT logic An integrated signal with high rise time TOFPET model with energy channel integration Signal comparison between Simulink and Spice Time differences between Simulink and Spice Energy difference between Simulink and Spice Signal with highest energy discrepancies Input signal for TOT characteristics TOT characteristic as a function of the number of photo-electrons evaluated from the model TOT distribution obtained with the 4DMPET ASIC model Cluster size distribution obtained with the 4DMPET ASIC model Reconstructed energy spectrum obtained with the 4DMPET ASIC model X resolution with and without correction obtained with the 4DM- PET ASIC model Cluster size asymmetry as a function of the DOI obtained with the 4DMPET ASIC model DOI (z) resolution obtained with the 4DMPET ASIC model Linearized TOT distribution obtained with the TOFPET ASIC model Cluster distribution obtained with the TOFPET ASIC model Reconstructed raw energy spectrum obtained with the TOFPET ASIC model X resolution with and without correction obtained with the TOF- PET ASIC model Cluster size asymmetry as a function of the DOI obtained with the TOFPET ASIC model DOI (z) resolution obtained with the TOFPET ASIC model Experimental apparatus for segmented crystals Energy spectrum measured with segmented crystals Experimental apparatus for continuous crystal vii

10 Ge source cluster asymmetry anticorrelation and reconstructed event energy viii

11 List of Tables 1.1 Half-life, average β + energy and range for the main isotopes used in PET Parameters of the most commonly used PET scintillators A comparison between advantages and disadvantages of software and hardware-based image fusion TOFPET time constant for the RC filter on the energy TIA and Delay length of the DOT signal List of flags for the shaping constant Validation signal sequence: list of characteristics List of parameters used to generate the single signal List of parameters used for the block detector simulation Efficiency of the detector obtained with the 4DMPET ASIC Energy, x, y and DOI resolution results obtained with the 4DM- PET ASIC model Detector Efficiency with the TOFPET ASIC Energy, x, y and DOI resolution results obtained with the TOF- PET ASIC model ix

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14 Introduction Positron Emission Tomography (PET) is a Nuclear Medicine Technique that provides a functional image of the human body, through molecular interactions of biological processes in vivo. Clinical PET imaging is used in: Neurology, Cardiology and Oncology, where PET is widely used for tumor staging, follow-up, evaluation of treatment response and assessment of recurrence. The positronemitting isotope is injected into the blood stream and spreads inside the patients body, according to the metabolism. Emitted positrons annihilate with electrons (almost at rest) of the surrounding tissue; the photons pairs originated from the annihilation are approximately back-to-back, with an energy of 511 KeV. A ring of detectors around the patient detects the photon pairs, and the acquired data are used to reconstruct the functional image. Presently available clinical PET scanners are based on a compromise between spatial resolution and sensitivity. In order to improve the overall performance, it is necessary to introduce new features in block detector design. Namely, these features are: Time-of-flight (TOF) measurement of photon pairs, in order to minimize random coincidences contribution and to improve the reconstruction; Depth of interaction estimate, to correct the parallax error in the line-ofresponse (LOR) determination. In scientific research and clinical applications there is an interest in the development of simultaneous acquisition of morphological (CT or MR) and functional (PET) images. PET/MR simultaneous systems can integrate and in some case replace the PET/CT technique. The entire design of PET/MR systems has to be magnetic compatible, so PET modules feature silicon detectors like Silicon 1

15 Photomultipliers (SiPM) instead of Photo-Multipliers-Tubes. The 4DMPET (4- Dimensional Magnetic-compatible module for Positron Emission Tomography) project aims at building a PET block detector capable of working inside an MRI system. The module design is based on the combination of a monolithic large LYSO scintillator crystal coupled to SiPMs on both sides. This configuration allows to perform the measurement of the x and y coordinates, DOI and, with the proper ASIC (Application Specific Integrated Circuits), TOF. Currently some prototypes of the the 4DMPET ASIC have been built but it is not yet possible to assemble these elements on the detector. Another ASIC for TOF-PET imaging has been developed by the Endo-TOFPET US collaboration: TOFPET was designed for segmented crystals but, according to its specifications, the use with monolithic crystal is also possible. These characteristics make this ASIC suitable for the 4DMPET project, in order to provide an alternative solution while the prototypes with the custom ASICs are being assembled. In order to quantify the behavior and the expected performance of the TOFPET ASIC coupled to a continuous crystal, a model of the ASIC was implemented. Output signals from the model were studied in order to assess the strengths and weaknesses of the implemented model. The model validation was performed by comparing the results to a more detailed simulation of the same ASIC. An analysis of the entire block detector was then performed and the results compared to a 4DM- PET ASIC simulation. Finally, some preliminary experimental data obtained with a crystal read by TOFPET are reported and discussed. Simulation results show a lower efficiency of TOFPET compared to 4DMPET, limitations in the event energy reconstruction and the correlation between cluster size and DOI. 2

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18 Chapter 1 POSITRON EMISSION TOMOGRAPHY 1.1 Introduction to Positron Emission Tomography Positron Emission Tomography (PET) is a Nuclear Medicine Technique able to provide a functional image of the human body. It is a molecular imaging technique that makes use of radiolabeled molecules to image molecular interactions of biological processes in vivo. It is based on a positron-emitting isotope chemically bound to an organic molecule. This molecule is injected into the bloodstream and spreads inside the patient s body, according to her/his metabolism. The isotope achieved concentration is proportional to the uptake of each tissue. Positrons emitted from the decay processes annihilate with electrons of the surrounding tissue, the photons pairs originated from the annihilation are approximately back-to-back, with an energy of 511 KeV. A ring of detectors disposed around the patient, detects the photon pairs. If two events are detected in the same coincidence window, a Line Of Response (LOR) is reconstructed between the two detectors. From an entire set of detected LORs a backprojection algorithm reconstructs a three-dimensional image of the isotope concentration inside the patient s body. 5

19 Clinical PET imaging is used in three important clinical areas: Neurology and Psychiatry, Cardiology and Cardiac Surgey and Oncology where PET is widely used for tumor staging, follow-up, evaluation of treatment response and assessment of recurrence. PET shows changes in metabolic processes, that typically take place before morphological ones, so it is possible to have disease information when anatomical structures are still normal. That s a advantage from the clinical point of view. 1.2 PET Radiotracers A radiotracer must have some characteristics: -Mean life must be short enough to maximize the decay process during the data acquisition, to minimize the unnecessary dose contribution. On the other side its mean life must be long enough to let prepare and dispense it to the patient. -The decay scheme must minimize the not penetrating radiation (charged particles). Positrons produce two photons able to reach the detectors. The main isotopes used as PET radiotracers are 18 F, 11 C, 13 N, 15 O and 82 Rb (see tab. 1.1). All these positron emitters are produced in a cyclotron. For very short-lived nuclides such as 11 C, 13 N and 15 O, the cyclotron and the radiopharmaceutical production facility must be located near the scanner. Longer-lived nuclides like 18 F are also produced in specialized radiopharmacies and then delivered to clinical centers. 18 F (Half-life = 1.7 hours) It is the most common radiotracer because it has a relatively long lifetime and because it is used to produce the Fluorine- DesoxyGlucose (FDG), which is the most widely-employed radiotracer in oncology [1]. FDG was synthesized for the first time in 1976 in Brookhaven National Laboratory by A. Wolf and J. Fowler [2]. FDG is transported across the cell membranes, but then is not exactly metabolised as normal desoxyglucose: it is always transformed in 18 F desoxyglucose 6 P, which basically does not interact anymore with the cell nor can it penetrate the cell membrane, so the 18 F uptaken by the cell remains inside it for 6

20 a time longer than its lifetime. Since the living tumor cells have greater glycolitical activity they capture (uptake) an abnormal quantity of radiotracers (hot spots). 11 C Half-life = 20 min. It is produced with an on-site cyclotron and bound to methyonine (for bladder carcinoma), coline (for imaging bladder and prostate cancer) or butanol (for myocardial perfusion). 15 O Half-life = 2 min. It is produced with an on-site cyclotron and it is used as 15 O water, used for myocardial blood flow assessment. Intravenous 15 O-water or inhaled 15 O-carbon dioxide are used to image cerebral blood flow (CBF), 15 O 2 is also used for brain studies. An on-site distribution system from the cyclotron is required to synthesize the radiopharmaceutical and bring it to the patient who then inhales it. Isotope Half-life β+ Energy (MeV) average β+ range (mm) 11 C 20.4 m (99.8%) O 122 s (99.9%) F 110 m (100%) Rb 75 s (83.3%) (10.2%) 4.29 Table 1.1: Half-life, average β + energy and range for the main isotopes used in PET [1]. 1.3 PET Physical Principles Beta Decay Beta decay is a type of radioactive decay in which, an electron or a positron is emitted from an atomic nucleus. Electrons or positron emitted have a continuous spectrum of energies, ranging from zero to the maximum available en- 7

21 ergy. This is due to another particle emitted during the decay processes, the (anti)neutrino ( ν e, ν). This particle has a very low (if any) mass and no charge and it carries away the remaining energy. There are two kinds of beta decay: beta minus (β ) electron emitted and beta plus (β + ) positron emitted. The following shows the generic formula for beta minus beta plus decay A ZX A Z+1 Y + e + ν e (1.1) A ZX A Z 1 Y + e + + ν e (1.2) Positron Path in Matter After the emission from the nucleus, the positron loses kinetic energy by interacting with the surrounding matter. The loss of energy is caused of two components: ionization and Bremsstrahlung ( de dx ) e + (de dx ) ion + ( de dx ) bremm (1.3) The energy loss implies a finite path inside a medium with enough thickness to dissipate it all. The positron interacts with other nuclei and so deflects from its original path. Step by step the energy decreases until it is almost zero. The mean distance travelled by the particle is called range. The range (R) of a particle is defined by the integration of the loss of energy per unit length R = 0 1 de E 0 dx de (1.4) where E 0 is the initial energy. The range increases with the initial energy of the particle. In first approximation human body can be considered as water: particle ranges in water are reported in table 1.1. The positron eventually combines with an electron when both are essentially at rest. The distance that positrons travel after emission from the nucleus contributes to the uncertainty in the localisation of the decaying nucleus. When a positron and an electron annihilate two photons of 511 KeV, the rest mass equivalent of each particle, are produced. The two primary photons are typically emitted back to back. e + + e γ + γ (1.5) 8

22 Moreover, a fraction of photons pairs are not emitted exactly at 180 due to the non-zero momentum when the positron and the electron annihilate. This fraction is estimated to be as 65% in water, the average deviated angle is typically on the order of less than one degree [1]. This effect brings uncertainty to the localisation of the nuclear decay event and, together with the positron range, sets a fundamental lower limit to the spatial resolution than can be achieved in positron emission tomography Interaction of Photons in Matter High energy photons interact with matter in three mechanisms, depending of the energy on the electromagnetic radiation. These are: -Photoelectric effect (prevailing from 1 KeV to 100 KeV) -Compton effect (prevailing from 100 KeV to 1022 KeV ) -Pair production (prevailing at more than 1022 KeV) Photoelectric Effect γ + Atom ion + + e (1.6) The photoelectric effect (see figure 1.1) is an interaction of photons with an orbital electron of an atom. In this process, the photon is absorbed by the atom, and a single electron is ejected. Since the recoil kinetic of the atom is very small, the photon transfers all of its energy (hν 0 ) to the electron. Figure 1.1: Photo-electric effect scheme. 9

23 Part of the energy is used to overcome the binding energy of the electron, the remaining part is transfered to the electron in form of kinetic energy. The energy balance is therefore hν 0 = T e + B (1.7) where B is the magnitude of binding energy of the electron and depends on which shell the electron was in and T e is the kinetic energy of the electron. B ranges from 1 KeV to 100 KeV and depends on the atomic number Z. It can be seen than the reaction γ + e +e (1.8) is not possible, so the photoelectric effect can not occur on a free electron. Only with the atom recoil the correct energy balance can be written. The cross section of photoelectric process increases rapidly when the photon energy equals the binding energy of the electron in the shell. The photo electric cross section σ pe can be written as the sum of the contributeions for each shell σ pe = τ K + τ L + τ M +... (1.9) The energy dependence of σ pe is between E 2 and E 4. A very crude approximation, of σ pe, to the Z and E dependence is σ pe Z 4 E 3 (1.10) The photoelectric effect dominates in human tissue at energy approximately below 100 KeV. Above that threshold Compton scattering becomes more important. Compton Effect Compton scattering is a process involving a photon and an electron, either bound to a nucleus or isolated. The original photon scatter and an electron emerge (see fig. 1.2). Compton scattering is called coherent when a photon is scattered elastically from an atom, with none of the electrons leaving their energy levels. γ + atom γ + atom (1.11) 10

24 The primary mechanism for coherent scattering is the oscillation of the electron cloud in the atom in response to the electron field of the incident photon. In this process no energy is deposited in the medium or tissue [3]. When a photon of lower energy emerges the process is called incoherent Compton scattering (see figure 1.2) γ + e γ + e (1.12) Figure 1.2: Compton effect scheme. The conservation of energy gives hν 0 = hν + T e + B (1.13) where hν 0 and hν are the initial and the final energy of the photon, T e is the kinetic energy of the electron and B is the binding energy. The equation used to relate the energy and angle of the emerging photon and electron, is derived assuming that the electron is free and at rest (B = 0). Once measured θ v, the angle between the emerging photon and the incident photon, the other quantities are fixed. Even if the initial energy of the incident photon can be known, is not known a priori the amount of energy given to the electron during the scattering process. The equation for the energy of the scattered photon is where ɛ = hν = hν 1 + ɛ(1 cosθ v ) (1.14) hν m ec is the reduced energy of the incident photon. From consideration 2 of Compton equation it can be seen that the maximum energy loss occurs when 11

25 the scattering angle is 180 (cos(180 ) = 1), i.e., the photon is back-scattered. The energy of the recoil electron is T = hν 0 hν (1.15) The Compton scattering cross section also depends on scattering angles. The Quantum mechanical result, to determine the relative number of photons scattered at each angle, is know as the Klein-Nishina formula. For unpolarized photons, the cross section per solid angle unit for a photon to be scattered at an angle θ is dσ(θ) dω = r2 0 (1 + ɛ(1 cos θ)) 2 (1 + cos2 θ + ɛ2 (1 cosθ) ɛ(1 cos θ) ) (1.16) where r 0 = e 2 /mc 2 [4]. This equation can be integrated over all angles to obtain the total cross section of incoherent Compton scattering (σ incoh ). The density of tissue in human body is approximately the same as the water, so the mean free path of the 511 KeV photon is about 7 cm. Since the average thickness of a human body is greater than 7 cm, during the PET scan many of the photons originated inside the human body are Compton scattered. A number of Monte Carlo computer simulation studies, of the interaction of annihilation radiation with tissue-equivalent material in PET, have shown that the vast majority (> 80%) of detected scattered events have only undergone a single scattering interaction [5]. Pair Production The last mechanism for photons to interact in matter is pair production. This process consists in the creation of an electron-positron pair (see figure 1.3). γ + Atom Atom + e + e + (1.17) This is possible only if the photon energy is higher than 1022 KeV, the rest mass of electron and positron. Their rest energies must takes into account in the energy balance equation hν 0 = T + + T + 2m e c 2 (1.18) 12

26 Figure 1.3: Pair production scheme. Pair production always takes place in the Couloumb field of another particle (usually a nucleus) which recoils to conserve momentum. The higher is the energy of the photon, the larges is the probability of pair production (see fig. 1.4). The remaining energy after pair creation is shared between the particles as kinetic energy E k = E γ 2m e c 2 (1.19) If pair production occurs in the field of an electron, it is called triplet production, three particles appear: the original electron, the created electron and the created positron. The threshold for triplet production is 4m e c 2 = 2.04MeV. Those processes cannot take place during a PET acquisition, because the primary photon don t have enough energy to create a pair or triplet Photons Attenuation in Annihilation Process Photon interaction probabilities are given in terms of atomic cross section (σ). The total atomic cross section (σ T OT ) is given by the sum of the cross sections for all of the individual processes [6]. σ tot = σ pe + σ incoh + σ coh + σ pair + σ tripl + σ nph (1.20) with contributions from the photoelectric effect (pe), incoherent Compton scattering (inco), coherent Compton scattering (coh), pair production (pair), triplet production (tripl) and nuclear photoabsorption (nph) (see picture 1.4). 13

27 Figure 1.4: Total atomic cross-section as a function of photon energy for lead. The scattering cross-sections (σ) are given for coherent (COH), incoherent (IN- COH) or Compton scattering, photonuclear absorption (PH.N.), atomic photoelectric effect (τ), nuclear field pair production (k n ), electron field pair production (triplet) (K e ), and the overall total cross section [6]. The total cross section is related to the number of particles that have interacted in the scatterer. Let N be the number of particle passing through scattering material of thickness z. The number of interactions dn in dz is Integrating the equation one obtains N a ρ dn = σ tot Ndz (1.21) A N(z) = N 0 e µz (1.22) where µ is the total linear attenuation coefficent (m 1 ) µ = σ tot N a ρ A N (1.23) The attenuation coefficient is a measure of the probability than a photon will be attenuated in a unit length in the medium. Each layer of thickness dz provides 14

28 Figure 1.5: Detectors A and B record attenuated count rates arising from the source located a distance a from detector A and b from detector B. For each positron annihilation, the probability of detecting both photons is the product of the individual photons detection probabilities. Therefore, the observed combined count rate is independent on the source emitter position along the line of response. The total attenuation id determined by the total thickness D alone [5]. a separate chance for the beam to interact. The interaction probability in the layer is p = µdz. The quantity µ/ρ is call mass attenuation coefficient. It has been seen than the primary mechanism for photon interactions, at the energy of about 500 KeV, is Compton scattering (see section 1.3.3). This means that primary photons change direction and lose energy and the related LOR can then be far apart from the annihilation point. Positrons emission shows an important feature in terms of attenuation. Consider the count rate from a single-photon emitting point source of radioactivity at a depth, a, in an attenuated medium of total thickness, D. The count rate C observed by an external detector would depend on depth a: C a = C 0 e µa (1.24) Where C 0 represent the unattenuated count rate from the source, and µ is the attenuation coefficient of the medium, assumed to be constant here. If measurements of the source were made from the 180 opposed direction the count rate observed would be C b = C 0 e µ(d a) (1.25) Now consider the case for positron emitting source, where detectors A and B measure coincidence photons. The count rate is given by the product of the 15

29 probability of counting both photons and will be C = C 0 e µ(d a) C 0 e µa = C 0 e µd (1.26) which show that the observed count rate only depends on the total thickness of the object, D. In other words, the observed count rate is independent of the position of the source in the object. Therefore, to correct the attenuation of coincidence detection of annihilation radiation, only the total attenuation path length ( µd) is required. 1.4 PET Detectors Scintillation detectors are the most common and successful mode of detection of 511 KeV photons. Due to their high atomic numbers and therefore density, these detectors provide the highest stopping power for 511 KeV photons. The photon detectors consist in inorganic crystals (scintillator) which emit visible light photons (scintillation) within the detector. The number of scintillation photons is proportional to the energy deposited into the crystal by a charged particle The Scintillation Process in Inorganic Crystals The scintillation mechanism in inorganic materials depends on the energy state determined by the crystal lattice of the material. The lower band, called the valence band, contains electrons bound at lattice sites, and conductions band contains electron with enough energy to migrate into the crystal. Between the valence and conduction band there exists a band called forbidden band, in which electrons can never be found in pure crystal. Electrons in the valence band can absorb energy by the interaction of the photo-electron or the Compton scatter electron with an atom and get excited into the conduction band. In the pure crystal, the return of the electron to the valence band with the emission of a photons is an inefficient process. To enhance the probability of visible photon emission during the de-excitation process, small amounts of an impurity are commonly added to inorganic scintillators. Such impurityies are called activators, since they create special sites in the lattice at which the normal energy 16

30 band structure is modified from that of the pure crystal. There will be energy states created within the forbidden gaps. Now the transition can give rise to visible light. A charged particle passing through the detection medium will form a large number of electron-hole pairs created by the elevation of electrons from the valence to the conduction band. The electron are free to migrate through the crystal and will do so until they encounter such an ionized activator. Since the migration time for the electron is much shorter, all the excited impurity configurations are formed essentially at once and will subsequently deexcite with the half life characteristic of the excited state. Inorganic scintillators, in most cases, can be characterized by a simple exponential [7]. If τ represents the scintillation decay time, the intensity at time t following the excitation is I = I 0 e t τ (1.27) In most inorganic scintillators, τ is in the range of tens of nanoseconds (see table 1.2). More over, the scintillation photons produced are emitted isotropically. There are four main properties of a scintillator which are crucial for its application in PET detectors: 1. The stopping power characterized by the mean distance (attenuation length 1/µ see table 1.2) travelled by the photon before it deposits its energy within the crystal. To increase scanner sensitivity, it is desiderable to maximize the number of photons which interact and deposit energy in the detector. Thus a scintillator with a short attenuation length will provide the maximum efficiency in stopping 511 KeV photons. The attenuation length of a scintillator depends on its density (ρ) and the effective atomic number (Z eff see table 1.2). 2. The decay constant (τ see table 1.2) affects the timing characterisation of the scanner. A short decay time is desiderable to process each pulse individually at high counting rates, as well as to reduce the random coincidence number, occurring within the scanner geometry. 17

31 NaI(Tl) BGO LSO LYSO YSO GSO BaF 2 Density (g/cm ) Z eff Attenuation length (cm) Decay constant τ(ns) Light output (phot/kev) Peak Wavelength λ (nm) E/E(%) Refraction index µ (cm 1 ) µ/ρ (cm 2 /gm) Table 1.2: Parameters of the most commonly used PET scintillators [8, 9]. 3. The scintillation light yield affects a PET detector design in two ways: it helps achieving spatial resolution with high encoding ratio; and it affects the energy resolution needed to efficiently reject events which may have suffered Compton scatter in the patient before entering the detector. Furthermore it is also crucial for timing resolution. 4. The energy resolution ( E/E see table 1.2) achieved by PET detectors depends on the light output and on the intrinsic scintillator energy resolution, which is related to inhomogeneities in the crystal growth processes as well as non-uniform light output. 18

32 Figure 1.6: Schematic diagram of a photomultiplier tube Photo Multiplier Tubes in PET The photo detectors used in PET can be divided into two groups: Photo Multipliers Tube (PMTs) and semiconductor based photo diodes. Photo multiplier tubes represent the oldest and the most reliable technique to measure low levels of scintillation light. PMTs consist of a vacuum chamber with a thin photocatode layer at the entrance window (see fig. 1.6). An incoming scintillation photon deposits its energy at the photocatode and converts the light signal to an electric one (photoelectron) through the photoelectric effect (see section 1.1). Depending on its energy, the photo-electron can escape the surface potential of the photo-cathode. The presence of an applied electric field accelerates the photo-electron to a nearby dynode which is at a positive potential with respect to the photo-catode. Upon impact on the dynode, the electron, with its increased energy, will cause the emission of multiple secondary electrons. The process of acceleration and emission is then repeated through several dynode structures lying at increasing potentials, leading to a gain of more than 10 6 at the final dynode (anode). This high gain obtained leads to a very good Signal to Noise Ratio (SNR). This is the primary reason for the success and the applicability of photo-multiplier tubes coupled to scintillation detectors. A drawback of a photo-multiplier tube is the efficiency in emission and escape of a photo-electron from the cathode after the deposition of energy by a single scintillation photon. This property is called Quantum Efficiency (QE) and for the majority of photomultiplier tubes is about 25%. 19

33 Different complex arrangements of the dynode structures have been developed over the years in order to maximize the gain, reduce the travel time of the electrons from the catode to the anode, as well as reduce the variation of the travel time of individual electrons. In particular a fine grid dynode structure has been developed to restrict the spread of photo-electrons trajectories, thereby providing a position-sensitive energy measurement within a single photo-multiplier tube (Position Sensitive PMT PS-PMT) Silicon Photo Multiplier New generation PET scanners features silicon photodetectors (such as Silicon PhotoMultiplier (SiPMs)) instead of phototubes. A SiPM is a photodetector composed by a matrix of Avalanche PhotoDiodes (APD) connected in parallel, each working in single photon detection (not-proportional) Geiger mode [10]. The SiPM basic structure is shown in figure 1.7. APDs are based on reverse-biased p-n junctions, whose inner structure originates a low-field depletion region in which the photon is absorbed and creates an electron-hole couple. The electron generated by the photon in this kind of solid-state devices is usually called photo-electron. An inverse voltage is applied through the junction, so that the device is depleted and charges are collected and multiplied in proportional regime. When the bias provided to an APD is above the breakdown voltage, the carrier trigger a self sustained and energy independent avalanche; this working point is called Geiger mode. In this way a single photon absorption can produce a large current and can be detected: the carriers created in these regions drift towards the electrodes, creating the signal. A quenching mechanism is necessary in order to stop the avalanche process after the photon detection and return to the initial configuration. A resistive layer on top of the silicon wafer provides the negative feedback in the multiplication area: it decelerates the avalanche process and causes its termination. A single cell SiPM could not provide energy information because the Geiger avalanche time evolution does not depend on the trigger process: each cell of a SiPM works like a binary system activated by the passage of one or more photons. However thanks to parallel connection all the output of SiPM elementary cells are summed, so that the signal area is proportional to the number of firing 20

34 Figure 1.7: Basic structure of a SiPM (left) with its simplified electrical model (right): the SiPM can be seen as an array of elements (microcells) connected in parallel with common electrodes. Each cell is made by a photodiode operating in Geiger-mode and a quenching resistor in series; junctions are insulated from one another by means of polysilicon guard rings. cells, giving informations about the flux of photons. Avalanche multiplication of charge carriers is responsible for the internal gain in SiPMs, as large as The typical density is µ-cells mm 2. Photon Detection Efficiency The photon detection efficiency (PDE) of a SiPM is the statistical probability than an incident photon produces a Geiger pulse from one of the SiPM microcells. It depends on P DE(λ) = QE(λ) ɛ geom ɛ trigger (1.28) The Quantum Effiency (QE(λ)) of a silicon photon detector is the probability for a photon to generate a carrier that reaches the high field region. It depends on the photon wavelength and includes the transmission efficency, that is the probability for a photon not to be reflected by the external dielectric layer. The maximal value of QE 80-90% [11]. ɛ geom is the geometrical acceptance: only a fraction of the total surface is sensitive to the incoming photons because of the structures surrounding the microcells. The geometrical factor will be in range of 20-30% for PET detector 21

35 with SiPM coupled to a LSO crystal. LSO crystal for PET detection produces many photons and 1000 or more can be collected at the end face of the crystals. In order to avoid saturation effects the number of cells needs to be big and the cells small [11]. ɛ trigger is the avalanche initiation probability (the probability that the generated electron-hole couple will start an avalanche). This parameter is closely related to the ionization rate for carriers inside the active region, since the avalanche generation depends on how many carriers are generated [12]. Dynamic Range A signal linear response in current depends on the intensity of the incident radiation (see fig. 1.8). The discrete number of photodiodes in the SiPM can lead to devices saturation if the number of incident photons is not negligible compared to the number of microcells. The average number of triggering microcells N t as a function of the number of photons N ph can be derived from Poisson statistics as N t = P DE N cells (1 e N ph N cells ) (1.29) where P DE is the photon detection efficency and N cells is the number of SiPM microcells connected in parallel [13, 11]. For 1600 cells and average P DE about 20% the linearity is within 10% if N ph is less than 1/4 of the numbers of cells. Noise Sources in SiPM SiPM noise: There are several factors that contribute to the The Dark Count Rate (DCR) is the most important source of noise in SiPMs. It is given by pulses that are caused by thermal effects in the depletion region. Most dark pulses have an amplitude of 1 photo-electron. The probability of higher amplitude pulses arising from several simultaneously generated charge carriers. In figure 1.9 it can be seen than the count of multiple pulse decrease roughly an order of magnitude for each photo-electron [12]. Multiple spurious events have the same shape that those originated by the radiation, so they are indistinguishable. Tipical DCR values ranges from few khz/mm 2 to 1 MHz/mm 2 at 20 C [12]. 22

36 Figure 1.8: (a) Representation of a 400-cell SiPM at different light levels that results in (from left to right) 10, 100 and 300 cells firing. The grey scale indicates the number of photons interacting per cell, for a PDE of 25% (calculated from eq. 1.29). (b) Number of fired cells vs. number of incident photons: for a SiPM with 400 cells and different PDE values (5, 12, and 25% see eq. 1.29) [12]. After-pulses consist in secondary avalanches triggered by carriers trapped in the lattice structure and then released. Typical contributions for after pulse signals are between 0.01% and 0.1% of the counting rate [15]. Cross talk is a typical kind of background of all matrix devices: it emerges when two or more pixels interfere with each other. Optical cross talk happens when de-excitation photons are emitted from the avalanche. If one of them reaches the nearby pixel it can trigger another avalanche. Electronics cross talk emerges when carriers generated in a pixel spead in an adjacent pixel, causing more than one microcell to trigger 23

37 Figure 1.9: A SiPM pulse height spectrum generated by the dark rate is shown in figure. One can see an excellent single photo-electron (single pixel) resolution, which is a consequence of: good pixel to pixel gain uniformity,negligible contribution of electronics noise [14]. for the same signal photon. In order to limit those effects the distance between microcells (which causes a decrease of the geometrical efficency) is increased and/or a wall between microcells is built to create an optic-electro insulator. Figure 1.10: Dark count rate as a function of temperature and overvoltage for 1 1 mm 2 active area, 50µm cells in AdvanSiD SiPM ASD-SiPM1S-M-50 [16]. 24

38 (a) (b) Figure 1.11: Standard PET block detector scheme and photography [19] Coupling Scintillation Crystals to Photo Detectors There are several ways of coupling scintillation crystals to photo detectors. The first is the so called one-to-one coupling, where a single crystal is glued to an individual photo-detector. A close-packed array of small discrete detectors can then be used as a large detector. The spatial resolution of such detectors is limited by the crystal size. In order to achieve a spatial resolution better than 4 mm in one-to-one coupling, very small photo detectors are needed. Individual photo-multiplier tubes of this size are not currently manufactured. Another solution is coupling each individual channel of a PS-PMT to a small crystal. Due to the large package size of photo-multiplier tubes other techniques are needed to achieve a close-packed arrangement of the crystals in the scanner design. Despite the very good spatial resolution achieved by the one-to-one coupling design, the complexity related to the number of electronic channels needed and the cost of such PET detectors limits their use to research in small animal systems such as micropet scanner [17] [18]. Other designs are introduced to overcome this drawback, with the use of larger photo-multiplier tubes without intrinsic position-sensing capabilities. A typical block detector of a current commercial PET scanner is shown in figure 1.11, where a segmented crystal is read out by four PMTs. This block detector design used an 8x8 array of crystal glued to a slotted light guide [5]. The slots in the light guide are cut to varying depths with the deepest slots 25

39 cut at the detector s edge. The slotted light guide allows the scintillation light to be shared to varying degrees between the four photomultiplier tubes depending on crystal position in which the interaction takes place. This scheme of varying the depths of the cuts permits each of the four photomultiplier tubes to see a different amount of the light released after a photon has interacted within the block. The X and Y coordinates are given by: X = (B + D) (A + C) A + B + C + D (1.30) Y = (A + B) (C + D) A + B + C + D (1.31) where A, B, C, and D are the light read out by the four photomultipliers and X and Y are the uncalibrated reconstructed coordinates. A lookup table is used to determine the calibrated X c and Y c coordinates. This block detector has the benefit to reduce dead time, with respect to the one-to-one coupling, due to the restricted light spread. The major drawback for the block detector is count-rate performance, since the module can only process a single event from one individual detector in a particular block in a given time interval. 1.5 Timing Resolution and Coincidence Detection The basic of data acquisition in PET is the detection of photon pairs, emitted from the same annihilation event. Photons are detected by block detectors, the pairs are identified by coincidences of electronic signal. The timing resolution of a PET detector is important to identify correctly signals from the same primary point. When primaries photons arrive in the detectors, they generate a signal of amplitude proportional to the amount of energy release. Timing resolution represents the variability in the arrival time measurement for different events. To couple signals from the same annihilation event a coincidence technique is implemented with hardware or software. If the signal triggers a channel at time (t 1 ) a coincidence window of a predetermined width, 2τ is open. The second primary photon will eventually trigger at a later 26

40 time (t 2 ) it may overlap to the coincidence window. For detectors with poor timing resolution, a large value of 2τ must be provided to detect most of the valid coincidence events. The distance travelled by the primaries photons is different because they can be emitted from anywhere within the scanner Fiel-Of-View (FOV). For a typical whole-body scanner, this distance can be as large as 1 m. Corresponding to about 3-4 ns between the two signals. So the coincidence timing window can not be reduced to less than 3-4 ns. The line joining the two points where the primary photons interact in the detectors is called Line Of Flight (LOF), while Line Of Response (LOR) is the line joining the two interactions point as they are measured by the detectors. The set of LOR acquired is the base of the image reconstruction. The detected coincidence can be: True Coincidences (fig A) The primary photons, travelling in opposite directions without interaction within the body, are correctly detected by the PET block detectors. Figure 1.12: (A) True coincidence, (B) scatter coincidence, (C) random coincidence, (D) attenuation [20]. Scatter coincidences (fig B) One of the two primary photons is detected without any previous interaction, the other one suffers Compton scat- 27

41 tering and is then detected. In this case LOR is misleading because it does not include the annihilation point. In clinical scanners, to minimize the contributions from scatter coincidences an energy threshold is applied (usually 375 KeV) than discriminates the scattered photons because of their lower energy. In small animal applications this threshold is usually not applied because the small amount of tissue makes Compton scatter unlikely. Random coincidences (fig C) Random coincidences are a direct consequence of having a large timing window. They arise when two unrelated primaries photons are temporally close enough to be recorded within the coincidence timing window. For such events the system produces a false coincidence event. Due to the random nature of such events, they are labelled as random or accidental coincidences. Random coincidences decrease the image contrast if no correction is applied to the acquired data. The random coincidence rate in a PET scanner is proportional to 2τA 2, where A is the activity present in the scanner field of view. The true coincident rate, on the other hand, linearly increases with a given activity level in the scanner. Hence, at high activity levels, random coincidences will overwhelm true coincidences. The best way to improve the image contrast is to minimize the collection of random coincidences. Hence for PET imaging a fast scintillator with good timing resolution is desiderable, (little τ). Multiple coincidences Three or more photons are detected in coincidence. When three photons are detected by three different detectors they are rejected by PET coincidence system. To discriminates events in which more than one primary photon interacts inside the same detector, a high energy threshold is applied. Single event (fig D) When only one of the two primary photons is detected, the event is discarded. 28

42 1.6 Time Of Flight During data acquisition, if the coincidence system considers two photons belonging to same annihilation event, a line of response is given. The positron annihilation probability along the LOR is considered uniform by the reconstruction algorithm (fig a). (a) (b) Figure 1.13: Graphical exemplification of non-tof (a) and TOF (b) spatial probabilities. Good timing resolution of PET detector (less than 1 ns), besides helping in reducing the rate of random coincidences, can also be used to estimate the annihilation point along the LOR by recording the difference in the arrival times of the two photons. The event vertex is no longer described by a LOR with uniform probability but with a gaussian probability distribution (fig b) centered on the position corresponding to the measured time difference t and with FWHM x given by x = v t 2 (1.32) where v is the speed of light. The advantage in estimating is the improved signal-noise-ratio obtained in the acquired image; the relationship between SNR with and without TOF is given by: SNR T OF = D x SNR non T OF (1.33) This formula is the most used equation as a measure of the TOF gain [21]. The gain introduced by the TOF information could be used to improve the 29

43 Figure 1.14: Transverse sections of two patients with different acquisition techniques: low dose CT (left column), non-tof (middle column), and TOF (right column). Patient 1 (first row) with colon cancer shows a lesion in abdomen more clearly in TOF image than in non-tof image. Patient 2 (second row) with abdominal cancer shows a structures in the aorta much more clearly in TOF image than in non-tof image [23]. image SNR (see picture 1.14) or to achieve the same image quality, with less radiotracer delivered to the patients. The first commercial TOF-PET scanner, the Philips Gemini TF PET/CT was introduced in 2006 [22] and uses LYSO scintillation read out by PMT s. Presently the state of the art PET scanners from the main producers achieve a time resolution of about ps. 1.7 Sensitivity The sensitivity in PET scanners represents their ability to detect the coincident photons emitted from inside the scanner FOV. It is determined by two parameters of the scanner design: its geometry and the stopping efficiency of the detectors. The scanner geometry defines the fraction of the solid angle covered by it over the imaging field. Small diameter and large axial FOV typically leads to high sensitivity scanners. The stopping efficiency of the detector is related to the type of crystal used and to its thickness. Stopping power of the 30

44 Figure 1.15: Representative 511 kev energy spectrum acquired with LSO-APD detector in 7-T MRI scanner while applying spin-echo sequence. Energy resolution was 18.7% (511 kev, full width at half maximum) [24]. scintillation detector is dependent on the density and Z eff of the crystal used. A high sensitivity scanner collects more coincident events in a fixed amount of time and with a fixed amount of radioactivity present in the scanner FOV. This generally translates into improved SNR for the reconstructed image. 1.8 Energy Resolution The energy resolution of radiation detectors characterizes their ability to distinguish between radiation at different energies. In scintillation detectors the energy resolution is a function of the relative light output of the scintillator. Energy measurement is necessary for a PET detector in order to achieve good image contrast and reduce background in the image (mostly by rejecting the Compton scattering contribution). Since scattering involves loss of energy, in principle some of these scattered coincidences can be rejected using an energygating technique around the photopeak. Good energy resolution for the detector allows the application of a narrower energy gate, and thus a more extensive and accurate rejection of scatter coincidences can be performed. In figure 1.15 the energy resolution for LSO-APD detector in 7-T MRI scanner is approximately 20% at 511 KeV [24]. 31

45 1.9 Depth Of Interaction State of the art block detectors allow the measurement of the coordinates on the crystal surface of the primary photon trajectory with an uncertainty of about one millimeter or less in the case of radiation perpendicular to the detector. Typically, PET detectors do not measure the Depth Of Interaction (DOI) coordinate, usually indicated with z in the block detector reference system. For photons that enter the detector at oblique angles, DOI uncertainties can produce significant LOR deviation from the true interaction position (see fig 1.16), the introduced parallax error blurring the reconstructed image. Figure 1.16: DOI uncertainty effects: the spatial resolution blurs with the increase of the radial coordinate r, because of the parallax error introduced by the interaction depth variation for coincident photons entering obliquely into a couple of crystals [25]. A thin crystal helps reducing the distance travelled by the photon in the detector and so the parallax effects. However a thin crystal also reduces the scanner sensitivity. In general high stopping power is desiderable in order to limit the detector thickness. Another way to reduce parallax errors is to enlarge the diameter of the ring of detector, but, even in this case, the sensitivity is compromised. Thus, to separate this inter-dependence of sensitivity and parallax error, an accurate measurement of the photon depth-of-interaction is required. 32

46 Some PET applications would particularly gain in image quality if DOI measurement were implemented: -In small animal scanners, since the bore size is limited, the DOI measurement would allow smaller rings to be built with higher resolution and sensitivity. -In PET/MR applications such as brain scanners, since they are limited to a low diameter (around 40 cm) the DOI measurement would significantly reduce the parallax error. -Dedicated non-circular scanners, such as breast scanners, to obtain homogeneous spatial resolution Multimodal Imaging Anatomical and functional imaging techniques reflect different aspects of the disease process. CT and MRI are used primarily for imaging anatomical changes, instead PET captures functional or metabolic changes associated to a certain pathology. It is easy to understand than they are complementary. Historically, CT has been the anatomical imaging modality of choice for the diagnosis and staging of malignant diseases and monitoring the effect of the therapy. More recently whole body PET has begun assuming an increasingly important role in the detection and treatment assesstment of cancer [26]. Multi-modality imaging is an advantageous procedure because identification of changes in function without knowing accurately where they are localized, or equivalently, knowledge that there is an morphological change without understanding the nature of the underlying cause, compromises the clinical efficacy of both. The first attempt to use both CT and PET information was to read them in conjunction one next to the other. Images were often limited by the lack of anatomical references in the functional images, moreover they were acquired on a different scanner and usually on a different day. The first attempt to co-register and fuse together functional and anatomical images was made with software techniques. This approach is successful for the brain and rigid organs but for the other parts of the body it was found to be problematic. As a consequence, hardware techniques to combine functional and 33

47 morphological scanning in the same machine were developed. In table 1.3 some advantages of hardware co registration are listed. SOFTWARE FUSION image retrieval from different archives Repeated patient positioning Different scanner bed profiles Uncontrolled internal organ movement between scans Disease progression in time between exams Limited registration accuracy Less convenient for patient (two exams) Labour intesive registration algorthms HARDWARE FUSION images aviable from one device Single patient positioning One bed for both scans Consecutive scan with little internal organ movement in between Scan acquired close time Improved registration acuracy Single, integrated exam No further image aligment required Table 1.3: A comparison between advantages and disadvantages of software and hardware-based image fusion PET-CT The design of a combined PET/CT imaging, provides a clinical CT and clinical PET imaging capabilities within a single, integrated scanner. The short CT scan duration compared with a typical whole-body PET acquisition time essentially eliminates the requirements for simultaneous CT and PET acquisition. The PET and the CT components are mounted on the same support. Once acquired and reconstructed, the CT images are also used to provide the attenuation correction factors for the PET emission data [27]. After the PET reconstruction the two images are fused together and viewed at the computer console. The PET components are operative immediately after the acquisition of the 34

48 CT scan without requiring recovery time. PET and CT components cannot acquire data simultaneously because of the high flux of scattered CT photons incident on the PET detectors. Clinical Protocols and Evaluation Clinical PET/CT imaging begins with an injection of FDG, followed by an uptake period. The patient is then positioned in the scanner. The time required for a complete whole-body CT scan is less than 5 min. Instead the total PET scan duration length is about min (without the informations provided by attenuation correction). Clinical CT scans of the thorax are normally acquired with breath-hold at full inspiration. The PET image, on the other hand, represents an average over the scan duration of several minutes per bed position, during which the patient breathes normally. So exact alignment of the CT and PET images particularly in the lower lung is not possible. CT-Based Attenuation Coefficients (AC) In addition to acquiring co-registered anatomical and functional images, a further advantage of the combined PET/CT scanner is the use of CT images for the attenuation correction of PET emission data. The use of CT scan for attenuation correction not only reduces whole-body scan time by at least 30% [28], but also provides essentially noiseless attenuation correction factors compared to those from a standard PET scan. Integrated imaging with PET/CT is highly synergistic: the sum of PET and CT is more than its parts. The AC algorithm is based on the different value of µ/ρ between soft tissue and bone. The attenuation coefficient (see section 1.3.4) is higher in bone due to the increased photoelectric contribution from calcium [29] PET-MRI In scientific research and clinical applications there is an interest in the development of PET/MR integrated (simultaneous) systems. These dual modality scanners can integrate and in some case replace the possibilities provided by PET/CT technique. 35

49 The development of multimodality PET and MRI imaging has generally taken two distinct paths that can be distinguished by the temporal association between the two scans: Sequential Approach In the sequential approach, the two scans are carried out independently, with fusion of the resulting images after a spatial coregistration. In this case two completely independent PET and MRI systems are used. The principal drawback involves coregistration of PET and MR images. When the patients move from one bed to another, the position of internal organs can change substantially. Efforts have been done to keep the patient on the same bed for both scans. Sequential whole-body PET/MRI systems were developed for commercial sale [30, 31, 32]. Tecnologically, this is the most simple way, requiring little modification to the imaging hardware. General advantages include optimum image quality in each modality and lower investment in instrumentation development. Simultaneous Approach Simultaneous imaging with PET and MRI is technically much more challenging but offers some potentially significant advantage: optimal image coregistration, correction of the PET data for motion during the scan and improvement of spatial resolution owing to reduction of the positron range (see section 1.3.2) [33, 34]. MRI not only provides excellent anatomical detail but can also dynamically measure parameters such as blood oxygenation through functional MRI (fmri). MRI machines are made of massive magnets system and chiller, so the general approach to simultaneous imaging has been to develop new compact PET insert to be placed inside the MR. Usually, the PET scanner is located outside the radiofrequency (RF) coils so as not to interfere wiht RF transmission, but inside the gradient magnet system, which is not easily modificable. With this module inside, the space is reduced. Several techniques has been developed extract out the PET signal from the magnetic field of MRI, such as light guide, solid state photosensor and shielding methods. Presently many research groups, due to difficulties of scaling up fibers and PMT-based system, have turned to solid state photosensor such as APDs and SiPMs. These kind of photosensors are more compatible with a MRI environment [35]. Currently, only Siemens provides a commercially avaiable simultaneous PER/MRI 36

50 system, based on APDs [36]. Figure 1.17: PET/CT (top row) vs. PET/MR (bottom row) of a patient with an inflamed plaque. Higher soft tissue contrast of the MR image (bottom left) compared to the CT image (top left). [37]. Clinical PET/MR Applications Presently the clinical PET/MR applications are focused on the weak points of the well established PET/CT technique. ONCOLOGY Oncology is the main field of PET applications. The use of functional data in oncology is growing more and more, since mere anatomical imaging is often not sufficient to correctly assess the disease [37]. The use of PET/MR then adds more possibilities to perform multiparametric and multimodality imaging in clinical trials and pratice. 37

51 Head and neck cancers are one of the first PET/MR potential applications usually reported. In these tumors, surrounding soft tissue are important for local staging as well as surgical and radiotheraphy planning. MRI, due to its better contrast, is already the most significant morphological imaging modality for that kind of tissue, because of the poor CT contrast in soft tissue (see fig. 1.17). On the other hand this is also one of the cases where PET takes advantage from the CT data to correct for different depth absorption and allow a quantitative imaging. As a consequence the development of satisfactory correction techniques with MRI data will probably lead to good clinical reception [38]. The imaging of primary and metastatic liver lesion can profit from PET/MR data since CT contrast for soft tissues is poor and requires the use of contrast agents. Whole-body imaging for primary staging (for example lymphoma) will probably gain efficiency with PET/MR relating FDG uptake and MR diffusion imaging. For lung imaging, current pulse sequences provide poorer images than CT [38]. Neurology In neuroimaging, morphologic images are often a prerequisite for processing and analysis of functional data. Hence PET/MRI has a good potential to became powerful tool for quantitative imaging and objective decision making. The integration of PET and MR rather than PET/CT, allows for a dose reduction to the patient by omitting the CT scan. In PET imaging, the CT is in most cases only used for AC which in the future probably can also be done by MR. This is interesting especially for young patients. Multimodal PET/MRI has various interesting applications: -Neuro-Oncology. -Epilepsy. -Neurodegenerative Disease, for instance in the evaluation of disease progression in Alzheimer s disease, integrated morphologic and functional information from PET and MR is needed. PET/MR Challenges Interference in the Simultaneuos Approach High-quality MRI requires a high static magnetic field (up to 9 T especially for small-animal imaging). 38

52 Furthermore after the RF pulse transmisson, to manipulate the proton spins, a period of radiofrequecies incontamination is needed to detect the weak signal emitted from the subject. PET system inserted into the MRI bore can negatively affect these features, because the magnetic susceptibility of the material used in PET scanners can affect the field uniformity. PET electronics operates at high speed with timing, at least, at the nanosecond level, so circuit radiofrequencies can interfere the MR ones. In addition, MRI gradients can induce eddy currents in conductive PET components. The simplest approach to reduce interference is to increase the distance between PET and MRI imaging components. Even small increases in separation of PET and RF coil can reduce interference substantially [39]. Conductive RF shielding (Faraday cage) is typically used to minimize RF interference in both directions. The shielding thickness is typically dictated by the transmission power of the RF. To prevent eddy currents it is however necessary to open slits in the shielding [24]. Readout Electronics The use of non-magnetic electronic components is mandatory, but the entire design must be focused on with magnetic compatibility: for instance, large ground planes must be avoided, the number of cables crossing the MRI FOV must be minimized, loops must be avoided, cables should be substituted, when possible, with optical fibers, the clock distribution has to be carefully controlled to ensure that its frequency is not similar (MHz) to the MRI RF. Another challenge is in designing a front end electronics sufficiently compact and low power consuming. A typical approach is to minimize the amount of electronics located near the imaging field and move the remaining part to more distant locations. Optical fiber-based system represent an extreme choice, with the entire electronics located outside the main magnets. For other systems, this means putting only preamplifiers in the FOV. MRI-based Attenuation Coefficients (AC) MRI does not directly provide an attenuation map for ionizing radiation, so PET data cannot be subject to AC. MR data have to be transformed into quasi CT data and from there into the attenuation map. The major challenge in using MR data for AC of PET is related to the inability of conventional MR pulse sequence to unequivocally 39

53 show bones. Various approaches to overcome this problem are currently under investigation. 40

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56 Chapter 2 The 4DMPET PROJECT 2.1 4DMPET Block Design The 4DMPET (4-Dimensional Magnetic-compatible module for Positron Emission Tomography) project aims at building a PET block detector capable of working inside an MRI system. This work has been carried out in the context of the 4DMPET collaboration, which is a project funded by the Italian Institute of Nuclear Physics (INFN) and involves the sections of Pisa, Bari, Perugia and Torino. The module design is based on the combination of a single large LYSO scintillator crystal coupled to SiPMs on both sides. The continuous slab choice is motivated by the light spread on the different SiPM channels, allowing to perform DOI measurement; moreover the photodetector segmentation does not limit the event spatial resolution improving the precision in the determination of the x and y coordinates. Thanks to the choice of SiPMs, which are magnetic compatible to the electionics design and shielding, this detector is in principle able to simultaneously operate with an MR module, without mutual interference. The block detector, when equipped with a proper electronics, is also able to provide TOF measurement. With this configuration MR and PET images con be acquired simultaneously. The base structure of the detector represented in figure 2.1 uses a continuous 43

57 crystal slab with two layers of SiPM, one for each major surface. The adopted scintillator, LYSO, is the current state of the art for PET applications. Its dimensions are 57.6 mm x 57.6 mm x 10 mm (see fig. 2.1 a). The side faces are black painted to improve the spatial resolution. Figure 2.1: Schematics of the 4DMPET block detector: (a) Scintillator slab of 57.6 mm x 57.6 mm x 10 mm. (b) SiPM pixel detectors on the two large scintillator faces, 3 mm segmentation in 3.6 mm pitch. The nominal SiPM side is of 3.5 mm, an extra space of 100 µm is applied to take into account eventual fluctuations in the actual side. (c) Readout board on top of each SiPM layer, each electronic layer is independent of the other. (d) Application Specific Integrated Circuits (ASIC) in mixed mode analog/digital. (e) Cluster processor to analyse the output of the four ASIC s. (f) Optical interface to sent the cluster processor output to the DAQ board. Each layer of SiPM is composed of 4 matrices of 8x8 square pixels (see fig. 2.1 b). The pixel pitch is 3.6 mm, with a microcell size of 50 µm. The readout electronic is placed over each SiPM layer: the two sides work independently of each other and have identical electronic components (see fig. 44

58 2.1 c). The read out electronic coupled to a SiPM layer is composed of 4 Application Specific Integrated Circuits (ASIC), each one with 64 channels in analog/digital mixed modes (see fig. 2.1 d). The ASIC can perform time and Time Over Threshold (TOT) measurements: the latter quantity is related to the energy collected on each channel. The design choice is to process SiPM output to minimize the rate of data to bring out of the magnetic field. To achieve this goal a cluster processor analyze the ASIC outputs (see fig. 2.1 e), with the task of finding correlations between adjacent pixels. A region growing algorithm extracts the adjacent pixels above threshold to build the cluster, calculates the event energy and the x-y interaction coordinates. The cluster size asymmetry is used to determine the DOI (see sec ). At the end of the chain an optical interface brings out the event information to the digital acquisition system (DAQ) board by means of an optical fibre, a technology chosen in order to minimize the amount of cables inside the magnetic field (see fig. 2.1 f) DMPET DOI Measurement Strategy When a primary photon interacts inside the scintillator, secondary photons are emitted isotropically along the electron path. Since the electron range inside the scintillator is smaller than 1 mm, the photon emission can be considered isotropic from the interaction point. Since the LYSO reflective index is greater than the one of the typical optical grease the light spot on the SiPM matrices is limited to a circle that is the base of a cone (see fig. 2.2). The cone opening is limited by the refraction laws with the apex in the interaction point: α 2 = arcsin(n 2 n 1 ) (2.1) where n 1 and n 2 are the scintillator refraction indexes and the optical coupling medium respectively. In the case of LYSO (n= 1.81) and Saint-Gobain BC-630 optical grease (n = 1.465) [40] an angle α = 54 is obtained. The consequence of equation 2.1 is that there is a geometrical realtionship between the DOI and the cone base area: A = 2πDOIcos(α) (2.2) 45

59 Figure 2.2: Representation of the light see by the layer of SiPM. The area is related to the height of the cone. The cluster size is a measurement of the area subtended to the cone, so the DOI can be calculated by means of the cluster size asymmetry, since an interaction far from a SiPM surface implies a larger cluster size, while a close interaction implies a smaller one (see equation 2.2). The depth of interaction (DOI m ) is then calculated with DOI m = D 2 (1 + n up n down n up + n down ) (2.3) where, n up and n down are the cluster sizes (i.e the number of pixels in the cluster) on the two tiles and D is the total crystal depth [41]. Monte Carlo simulations have been evaluated in order to estimate the DOI resolution with the 4DMPET block detector. The expected resolution is found to be 1.4 mm FWHM [41]. In figure 2.3 is reported the simulated correlation between DOI and DOI reconstructed. One interesting feature of this DOI calculation method is that there is a relative insensitivity to edge effects. If an interaction is close to a crystal edge, some light is lost because it ends on the black painted side, leading to an incomplete cluster. This phenomenon happens on the two readout sides, so the cluster asymmetry is preserved and then the DOI measurement is not expected to change significantly DMPET TOF Measurement Strategy In order to reach the highest accuracy in time measurement, it is crucial to trigger the TOT signal rise when the signal is at the lowest possible level, i.e. 46

60 DOI (mm) 10 Entries DOI_m (mm) 0 Figure 2.3: Correlation between the DOI interaction of primary photon and DOI m calculated from the cluster size asymmetry. it is necessary to trigger on the first photo-electron. In order to measure the primary photon interaction time in the crystal, it is necessary to identify the first arrived photon that reaches any SiPM on one of the two layers. The main issue with this strategy is the SiPM background (dark counts, see par ) which leads to high false trigger rate. A threshold high enough to exclude it has to be set to at least 3 photo-electrons. A double threshold technique has then been implemented in order to filter dark counts despite the low threshold: a low threshold pins the event time stamp and a high one validates it. Monte Carlo simulations show that the result (Fig. 2.5) with a double threshold techniques a resolution of 0.17 ns is achievable, with a simple threshold the same parameter would be four times higher [42]. The double threshold technique does not guarantee that a signal is triggered on a background event and subsequently has validated on signal (see fig. 2.4), nor that a signal is formed only by background events DMPET Readout Electronics The double threshold technique can provide the time resolution needed to TOF PET. An ASIC would be split in two separate circuits: an analogue readout circuit to form the TOT signal and a time to digital converter (TDC). Once a valid event has been detected, the ASIC translates the relative timestamp into a digital word and evaluats the associated energy by exploiting a Time Over 47

61 Figure 2.4: The figure shows a signal preceded by dark counts. The low threshold (0.5 photo-electron) pins the event timestamp on the dark count instead of the signal. #counts normalized double thresh. time_resolution_dtp Entries Mean RMS double thresh. raw single threshold t (ns) Figure 2.5: Time resolution with three different measurement techniques, indicative result obtained with MC simulation. The uncertainty attribution to the TOF measurement due to 1-3 photo-electrons double-threshold technique is 0.20 ns RMS, while with a 3 photo-electrons single threshold one is 0,42 ns RMS. Best result are obtained merging the results of two of SiPM tiles an expected uncertainty of ns is achievable [42]. Threshold (TOT) technique. 48

62 2.2.1 Mixed-Mode Readout ASIC The SiPM signal is generated by the sum of several microcell signals: its shape is irregular and follows, at first approximation, the decay time of the crystal (see par ). The circuits exploits a current mode approach with low input impedance. The mixed-mode readout ASIC receives the signals by a SiPM pixel and produces digital pulses to be sent to the TDC. The circuit block diagram is shown in figure 2.6. Figure 2.6: Block diagram of the mixed mode readout ASIC [43]. The working mechanism is the following: the signal is compared with the low threshold (T h low ) by a Fast Comparator (FC) at the circuit input. The FC sets a flip-flop which triggers a counter labeled as Time Window A (TWA). Meanwhile an integrator starts integrating the input. When TWA expires, the Slow Comparator (SC) compares the integrated signal to T h high. If the logical output of this comparison is 0, the SiPM signal is labeled as background, the circuits reset and a digital pulse with fixed TWA duration is produced as output. T OT = T W A (2.4) If the SC output is 1, a second counter named Time Window B (TWB) is triggered and the shaper keeps integrating the SiPM output. When TWB expires 49

63 the integrator is discharged through a constant current. When the integrator output goes below T h high the circuits resets. In this case the output logical pulse T OT has a duration equal to T OT = T W A + T W B + T E (2.5) where Time Energy (T E), the time required by the constant current to discharge the integrated signal, is proportional to the energy associated to the event. The design choice in the 4DMPET ASIC is to divide the input signal in two differents paths in order to perform the time and energy measurements separately. For calibration issues the T W A and T W B counters will be programmable within 3-30 ns and ns, intervals respectively. With this implemented logic the noise pulses are shorter than signal ones: their length is fixed and is equal to TWA. On the other hand, the rising edge of the TOT output signal provides the timestamp associated to the event. The constant current discharge of the charge integrated during T W A and T W B eliminates any constraint in the stability and uniformity of the SiPM pulse and preserves a good linearity [43] Time to Digital Converter ASIC The TDC ASIC receives the logical pulses sent by the readout ASIC and converts the timestamp and energy information of valid data into digital words. Not all the pulses sent by the mixed-mode readout ASIC have to be converted by the TDC: the signals belong to two different classes: invalid and valid signals. Valid signals have a duration of at least TWB plus the discharge time; instead, signals of length TWA are generated by dark counts and have to be rejeced by the system. Once a valid input is identified, the TDC measures the time of its rise and fall edges: the format provides the event timestamp with a precision of 100 ps and, the falling edge provides the energy information with a precision of 400 ps [43]. The time resolution achieved by the TDC is finer than the one given by the clock. This is achieved by coupling the counter to a 4 stages Delayed Locked Loop (DLL) which has the effect of dividing the clock by 4, so that the time step is decreased down to 100 ps [43]. 50

64 2.2.3 Cluster Processor The cluster processor (CP) receives the digital output sent by the TDC and forwards the data to the digital acquisition system (DAQ). The first purpose of the CP is to perform data reduction and to contribute to the filtering of true signals from the background. The CP serves a full detector side: it has 256 input channels and one output, sent to the optical fibre interface. The CP logic recognizes the event by merging the information from all channels: signals caused by events are related in space and time; instead dark pulses are unrelated. The CP segments the portion of the pixels taking the relevant signal part, a process called cluster finding. This process is a second level filter to reject dark counts. After several Monte Carlo simulations of the CP evaluated the selected technique in cluster finding is the following: -The system starts when a certain threshold of firing pixels, within a 5 ns time interval, is exceeded. That signal is called multiplicity trigger and the threshold is set to 3 pixels. -When the multiplicity condition is met the cluster finding algorithm start to create the cluster. It groups all the signals in the 40 ns time window after the trigger. The cluster finding algorithm works as follow: if a channel is above the high threshold (ET high ), the event is valid and the corresponding pixel is used as cluster seed, otherwise the event is rejected because the signal is likely caused by background pulse pile up. If the event is valid, all the eight adjacent pixels are examinated. If they are above the low threshold (ET low ) they are added to the cluster; otherwise they are rejected. Recursively, each pixel surrounding one of the pixels added to the cluster (and not belonging yet to it) is compared with the low threshold and eventually added to the cluster. -The individuation of the spatial cluster does not guarantee that every TOT signal included in it comes from the signal. As shown in fig. 2.7 (a) there are timestamps likely caused by background events which are clearly distinguishable from the general distribution. The solution developed to discard those signals is based on the time correlation between the channels: the signal timestamps are ordered, then the difference between each of them and the following one is calculated, constructing the distribution of fig. 2.7 (b). Then each signal which is more than 400 ps far from the following one is discarded. 51

65 Tpixel - Tint (ns) leading edge distribution Tpixel - Tint (ns) 3 leading edge distribution Entries 27 5 time difference distribution Entries n. counts n. counts t i -t channel (ns) (a) t -t j+1 j (b) Figure 2.7: Distribution of the timestamps of signals in cluster (a) expressed as difference with the primary photon interaction time t i ; distribution of the time difference between each timestamp t j+1 t j (b). As visible in (a) there is a timestamp which anticipates the others by 9 ns, the time difference distribution in (b) allows to discriminate it from the others without the prior knowledge of the primary photon interaction time. The cluster processor will be initially implemented using standard FPGA system technology with the aim of transfering the design to a custom ASIC once sufficient pratical experience has been acquired with the front-end prototypes. Spatial Cluster Information can be extracted: From the spatial cluster, several informations -Spatial coordinates: at a first approximation the energy-weighted cluster centroid coordinates correspond to the primary photon x-y coordinates of the impact point. The simple centroid offers good performance if the cluster is far from the crystal edges. If some scintillation light hits the scintillator wall, it is absorbed and then the resulting cluster is incomplete. A simple calibration is sufficient to correct this effect (see [42] at section 4.4.3). -Cluster size: the number of pixels belonging to the cluster is the input of the DOI calculation (see eq. 2.3). -Event energy: the event energy is given by the sum of the TOT values of every pixel, on both sides. 52

66 2.2.4 Digital Acquisition System Once the information from each block are collected by the DAQ system, the data from the two sides must be merged to extract the x-y coordinates, the DOI, the event energy and time for each detected event. -Spatial coordinates can be everaged on the two sides, or alternatively the cleaner data set can be chosen for x-y reconstruction. -The DOI is calculated from the cluster size asymmetry on the two sides (see eq. 2.3). -The event energy is given by the sum of the cluster energy on the two sides: this improves the energy resolution, as it increases the number of measured photons. -Once the timestamps from each channel are filtered, the event time can be set by comparing the two times of the two sides. 2.3 Status of the 4DMPET Project Several simulations of the block detector and the relative electronics have been evaluated to perform the parameters of the ASIC [41]. They have shown the correlation between cluster size asymmetry as a function of DOI [43]. Currently some prototypes of the the FE and the TDC have been built, their behavior are under investigation, but yet is not possible assemble these elements. Furthermore the FE prototypes do not have enough channels to equip an entire block detector. Another ASIC for TOF-PET imaging has been developed by the EndoTOFPET- US collaboration [44]. It has 64-channel for the readout of 3 mm x 3 mm SiPM individually coupled to 3 mm x 3 mm x 15 mm LYSO crystals [45]. The circuit provides time and energy measurement of events. The timestamp provided by the TDCs has 50 ps LSB, which should allow to reach the 200 ps targeted time resolution for the whole EndoTOFPET system. The TOFPET ASIC has been designed for segmented crystal but, according to its specifications, the use with monolithic crystal is possible. TOFPET has been designed and simulated; some prototypes are available for test and measurement. This characteristics make this ASIC suitable for the 4DMPET 53

67 project, in order to provide an alternative solution while the custom ASIC are being developed. 2.4 TOFPET Readout Electronics In this section is reported an overview of the TOFPET ASIC electronics. The TOFPET readout chain (see fig. 2.8) is composed of an analogue front-end that amplifies the input signal and delivers the two logic signals (Timing Discrimination Output (DOT) and Energy Discrimination Output (DOE) to two mixed mode TDCs, whose output is a data set containing information on the time of the trigger and the TOT of the processed input signal. Other electronic stages are needed to extract and package time and energy measurements (Data Buffer and Global Controller). Figure 2.8: The two independent signal paths for independent timing energy measurements TOFPET Front End Circuits Front end circuits receive the signals from SiPMs and send two logical pulses to the TDCs. The channel front-end includes a current conveyor acting as preamplifier, two TransImpedence Amplifier (TIA) branches and two independent voltage discriminators (see fig. 2.9). The first stage is a ReGulated Cascode (RGC) [46, 47] that conveys the signal from a low input impedance to a high impedance output. The front-end input resistance can be adjusted between 10 and 60 Ω [45]. Two independent amplifiers branches generate V outt and V oute, sampled by two voltage comparators set by two Digital Analogue Converters (DAC). A selectable shaping function can be applied to the energy branch. Shaping V oute with an integrator can prevent re-triggering the TDC control. 54

68 Figure 2.9: The front-end amplifier (shown for the n-input circuits): a 6-bit DAC controls the DC input node voltage RGC current-conveyor, which output is mirrored AC coupled to a voltage amplifier stage with variable gain. A selectable shaping of τ = [ ] ns can be applied to the transfer function of the branch used for energy measurement. The threshold for the two voltage-mode discriminator is set by 6-bit DACs [45]. In table different shaping constant settable on the ASIC are shown. Time information is extracted by applying a single threshold to the leading edge of a fast signal replica (V outt ). This threshold (V tht ) is set as low as possible (0.5 photo-electrons charge equivalent, see sec ). When V tht is exceeded, the DOT logical pulse is generated. A second discrimination is set with higher threshold (V the ) on the V oute branches, so as to validate the events (i.e. dark count rejection) and provides the second time stamp used for TOT energy measurement. When V the is exceeded, the DOE logical pulse is generated TOFPET Time to Digital Converter and Signal Validation The mixed-mode Time to Digital Converter is built with two analogue TDCs, a channel logic control and a data registers. The input of this block are the DOT and DOE signals. Figure 2.10 illustrates the principle of operation. From the TDC two timestamps are derived corresponding to the t 0 and t 2 with 50 ps resolution. From this information the event time and the energy (with TOT technique) are measured. Data are serialized and the output is sent to an FPGA board. Valid signals must be discriminated from dark pulses. The TOFPET ASIC 55

69 Figure 2.10: Dual threshold scheme: a low threshold trigger tags t 0, providing the first time measurement for the TOT calculation. The falling edge of the higher threshold discrimination sets t 2, from which the TOT can be derived. This higher threshold (V the ) is also used for dark count rejection: the indicated hit validation flag is used by the channel logic control to discard low energy events [45]. embeds a logic system able to validate the event (see fig 2.11). DOT is delayed by a quantity equal to DOT delay. The delayed signal is set in logical AND with the output of a flip-flop (see fig. 2.11). Figure 2.11: The figure show the internal logic of the TOFPET ASIC. The flip-flop output becomes 1 if DOE commutes from 0 to 1 in a time 56

70 window equal to DOT delay. In this case the event is labeled as valid. In the other case the output remains 0 and the event is rejected. The flip-flop is reset when DOT goes down (it works in negative logic). The length of the delay can be choosen from the values shown in table 2.1, This feature allows to validate signals with different rise time. A drawback of this kind of logic is that it is possible to obtain a DOE signal without the DOT one: this is caused by the rearmament of the flip-flop on the delayed DOE signal. Shaping τ (ns) DOT delay (ns) Table 2.1: TOFPET the RC filter time constant of V oute (first row). R = 2500Ω C 1 = 1pF C 2 = 2pF Delay length settable for DOT signal (second row) Data Buffer and Global Controller This stage receives in input the timestamps from the TDCs. It performs the TOT calculation as T OT = t 2 t 0 (2.6) where t 0 corresponds to the rising edge of the DOT signal and t 2 corresponds to the falling edge of the DOE signal (see fig. 2.10). The typical signal falling edge is slower respect to the rise, DOE can trigger several times due to the multiple threshold cross. One front of DOT can be associated to more front of DOE. In this case the TOT (see eq. 2.6) is evaluated using the first DOE signal falling edge, other re-triggers are rejected. 57

71 The choice to perform the energy measurement (TOT length) in this way cause the TOT as a function of the number of photo-electrons not to be linear (see fig. 2.12). In this stage DOE signal without DOT one are considered invalid and rejected. Figure 2.12: Simulation results of the TOT curve (measured at the output of the discriminator) as a function of the deposited charge at the input. Bold lines are for the n-type input, dashed lines for p-type. Resulted are plotted for an input charge sweep using the calibration circuitry and an approximate signal model of the sensor [45]. 58

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74 Chapter 3 TOFPET Electronics Simulation A detailed model of the FE has been implemented in Spice by the TOFPET collaboration. This powerful instrument is well-suited to study and develop circuits but is not suitable to analyze a cluster of signals, because of the long time needed to perform the complete analysis (a 50 µs single-channel signal takes about a week to be evaluated by Spice). The Simulink environment [48] provides the instruments to model electronics circuits at high-level: processing signals with Simulink is less detailed, comparing it to Spice, but the time employed is drastically reduced. The realization of a TOFPET model in Simulink is a useful instruments in the context of the 4DM- PET project, because it allows to simulate and analyze the whole 512-channel signal of the block detector in less than a dozen of days. In this chapter, a model that simulates and evaluates the performance of the 4DMPET block detector with the TOFPET ASIC is presented. The model is implemented in Simulink and it is inserted into the 4DMPET simulation chain. The first part of this chapter explains the structure of the 4DMPET simulation scheme. In the second part, the TOFPET ASIC model is analyzed in detail and validated. Finally a simulation of an entire cluster of signals is performed and compared to a 4DMPET one. 61

75 3.1 4DMPET Simulation Chain Figure 3.1: 4DMPET simulation chain. In figure 3.1 the 4DMPET simulation chain is described. The simulation starts with the generation of the primary 511 KeV photons and their interaction inside the detector. The SiPMs signals are then generated and processed by the ASIC model. A final stage analyzes all the signals from both the SiPMs layers DMPET Block Detector Simulation The signal to be processed by the electronic model is calculated (see fig. 3.1 a) from the output of a Monte Carlo simulation. This simulation reproduces the 4DMPET block detector, with 16x16 9 mm 2 pixels coupled to a 1 cm thick LYSO slab on the top and the bottom sides Single Signal Generation The first step of the electronics simulation is the signal generation (see fig. 3.1 a). The output of a SiPM pixel is given by the sum of the output of each microcell. The strategy chosen to calculate the signal shape is based on the superposition of the single cell output waveform each time a photo-electron is detected. The procedure followed to calculate the single cell output is presented in [49]. In the equivalent circuit (see fig. 3.2) the firing cell is modelized as a current generator (I AV ) with the diode capacities (C d ) in parallel. This block is connected in series with R q and C q, posed in parallel, to model the avalanche 62

76 R q Cq R q /(N-1) (N-1)C q L C g R in A I I in C out R out C in I AV C d (N-1)C d I in SiPM Current-mode FE amplifier Figure 3.2: Equivalent circuit model of the SiPM (left) coupled to the front-end electronics (right) [49]. quenching. The firing block is connected in parallel with (N -1) other not firing microcells of the detector (i.e. to (N-1) other R q, C q and C d ). A further parasitic capacitance (C g ) and inductance (L) are connected in parallel to all the cells. The electronic front-end parameters must be taken into account, so that the entire SiPM model is connected in parallel to R in and C in. The transfer function from this model is then 1 + sτ q i SiP M (s) = Q tot a 4 s 4 + a 3 s 3 + a 2 s 2 (3.1) + a 1 s + 1 where the τ q time constant is given by τ q = R q C q. After defining the other time constants τ r = R q (C d + C q ) and τ in = R in C in, it is possible express the SiPM transfer function coefficients as follows: a1 = τ in + τ r + C g R in + NC d R in (3.2) a2 = τ in τ r + R in C g τ r + C g L + NC d R in τ q + NC d L (3.3) a3 = C g τ in L + C g τ r L + NC d τ q L + NC d τ in L (3.4) a4 = C g τ r τ in L + NC d τ q τ in L (3.5) The front-end amplifier is modelled with a gain (G) and a bandwidth (BW) with the transfer function 63

77 G i a = s(1/2πbw ) + 1 (3.6) The total transfer function considering the SiPM and FE is the given by the product of (3.1) and (3.6) i out (s) = i SiP M (s)i a (s) (3.7) This model calculates the output of the front-end current-mode amplifier when a photo-electron triggers an avalanche, the output is a current signal sampled with a 10ps clock (see fig. 3.3). Figure 3.3: Front-end current output to single-cell avalanche input Channel Signal Generator A signal is generated (see fig. 3.1 b), every time an avalanche occurs in the SiPM pixel (due to a photo-electron or a dark pulse) the single signal form (see section 3.1.2) is added to the signal of the corresponding channel, starting from the avalanche time. The signal is sampled every 10 ps. An example of signal output is shown in figure DMPET ASIC Simulation Once the signal from each channel is calculated, a detailed model of the ASIC is used to process it (see fig. 3.1 c). The model reproduces the analog FE ASIC described in section and

78 Figure 3.4: Typical output of a SiPM pixel, obtained from a simulation. The noise is caused by background pulses, while the signal is originated by the pileup caused by many single photon signals of the same shape. In principle, low signals (i.e. single photons) and background pulses are indistinguishable. The digital ASIC implements the Time-to-Digital Converter and measures the TOT rising edge of the valid signals and their duration Cluster Processor and Measurement Merging Once the pair of values (t,e) is obtained from each TDC channel, they must be analyzed by means of a cluster processor and finally processed by the DAQ (see fig. 3.1 d). This algorithm implements the steps to find the cluster explained as in section Utilized Software The steps of the chain are implemented with different software: -Block detector simulation (see section 3.1.1): The Monte Carlo toolkit used is GAMOS [50] (a Geant4-based Architecture for Medicine-Oriented Simulations), built on top of Geant4 9.5 [51], that provides a reliable environment to medical physics simulations. -Single signal generation (see section 3.1.2): This model is implemented in a MATLAB script [52], in order to calculate the output of the front-end currentmode amplifier. -Channel signal generator (see section 3.1.3): This step is performed by a C++ class. -4DMPET ASIC Simulation (see section 3.1.4): The ASIC model is implemented in Matlab and Simulink [48]. 65

79 -Cluster processor and measurement merging (see section 3.1.5): The last part of the chain is implemented in a C++ script. 3.2 TOFPET Model and Analysis Figure 3.5: 4DMPET and TOFPET simulation chain. In order to compare the expected performance of the 4DMPET ASIC and of the TOFPET ASIC coupled to the 4DMPET block detector, the TOFPET ASIC Simulink model was inserted in the 4DMPET simulation chain (see figure 3.5). The input of the model is the channel signal evaluated by the channel signal generation (see section 3.1.3). Its output is provided to the cluster processor (see section 3.1.5). In this configuration the same input can be processed by both models, and the results can be compared The Simulink Blocks The Simulink environment makes use of several blocks to perform disparate tasks. A list of the blocks used in the model is reported: Sink and Source The source block (see fig. 3.6) is the input of the Simulink environment and provides the data transfer from Matlab to Simulink. The sink block is the output of the Simulink environment and provides data the transfer from Simulink to Matlab. According to the TOFPET FE, in the model a source provides the analog signal from a SiPM and two sinks transfer the DOT and DOE digital signals to Matlab. In the source block the Sample Time (ST ) must 66

80 be specified: in this model it is equal to 10ps like the sampled signal (see section 3.1.3). Figure 3.6: Source and Sink blocks. Discriminator The discriminator block (see fig. 3.7) has two continuous input and one logic output. The first input is the signal to discriminate, while the second is the threshold to compare with. If the signal exceeds the threshold the logical output becomes 1, instead if the signal remains below the threshold, the logic output is 0. In the TOFPET model all the thresholds are set with a block than contains the constant value to compare to. Figure 3.7: Discriminator block. Delay The delay block (see fig. 3.8) has one input and one output. It delays the signal input of a quantity equal to delay length, measured in unit of sample time (see section 3.2.1). For example with delay length = 160 and ST = s signal is delayed of Signal delay = ST delay length = 1.6ns (3.8) A delay can be seen as a memory buffer : it stores the signal value and outputs it after a certain time. During the first phase of the simulation the output value of the delay can be undefined, an option of the block can set the output of the delay in this particular condition. In the delay blocks this value is set equal to 0. 67

81 Figure 3.8: Delay block. Logic Blocks These blocks implement boolean operations so inputs and outputs are boolean signals. Figure 3.9: AND and NOT blocks. D Flip-Flop This block has three logic inputs and two logic outputs (see fig. 3.10). If the input clear (!CLR) is equal to 1 the flip-flop is on. When the clock input (CLK) commutes from 0 to 1 the input value D is stored and sent to the output Q. The value at the output Q is updated each time the clock signal commutes again from 0 to 1. If the value of the clear input (!CLR) becomes 0 the stored value is canceled and the output Q goes to 0. Only when!clr is again high it is possible to store new information. The other output!q is simply the Q signal in negative logic. Figure 3.10: D flip-flop block. Switch The switch block (see fig. 3.11) has three inputs and one output. If the condition in the middle input is satisfied the upper path is chosen, instead 68

82 if the condition is not satisfied lower path is chosen. Figure 3.11: Switch block. Transfer Function The transfer function block models a linear system by a transfer function of the Laplace-domain variable s. Figure 3.12: Transfer function and amplifier blocks. Go To and From These two blocks work together: From is the continuation of Go To. It is like a junction between two parts of the circuits (see fig. 3.13). Figure 3.13: From, Go To blocks. Terminator flip-flop output (see fig. 3.14). This block is used to close an utilized pin of a block, useful for Simulink TOFPET Base Model In this section the TOFPET ASIC model, made of several Simulink blocks described in the previous section 3.2.1, is presented (see fig. 3.15). The signal 69

83 Figure 3.14: Terminator block. enters the model by means of the simin block, then it is amplified by mean the amplification block. After the amplification a switch coupled with a threshold clips the signal if it exceeds a certain threshold (it to implements the saturation of the transimpedance amplifier (see section 2.4.1)). Then the signal is branched in two paths (for time and energy measurement) and each of them is compared to a specific threshold (V tht and V the, see section 2.4.1). The discrimanted comparator outputs are the DOT and DOE signals, they must be validated before being sent to the TDCs, as explained in section and After the validation stage the DOT and DOE signal are sent to the TDCs by means of the DOT and DOE sink blocks. Implementation of TOFPET Validation Logic In figure 3.16 a detail of the entire circuit is reported, which implements the logic to validate the signal (see section 2.11). As explained in section 2.4.2, the DOE signal sets the flipflop so that it enables the logical AND with the delayed DOT signal. Since the output!q is not utilized, it is connected to the terminator block. Notice than the flip-flop!clr is controlled by the [Clear] block, behavior is explained in the next paragraph. Rearmament of the Flip-Flop When the system validates a signal the Q output of the flip-flop must be set to 0 in order to receive and eventually validate the subsequent one. As explained in section 2.11, the rearmament of the logic signal (figure 3.17) is made when the DOT signal becomes 0 (i.e the SiPM signal goes below the low threshold). First of all, to provide a rising edge when the DOT goes down, it is necessary to invert the signal logic, so a NOT block is placed between the delayed DOT and the input of the flip-flop clock. In an initial situation where the flip-flop output Q is 0 (i.e.!q is equal to 1), the flip- 70

84 Figure 3.15: TOFPET Base Model flop is ready to receive a trigger since the!clr control is 1 due to the feedback. When a trigger on CLK arrives, the Q output commutes to 1 (i.e.!q commutes 71

85 Figure 3.16: TOFPET validation logic in Simulink. Figure 3.17: Rearmament of the circuit. to 0) so the flip-flop is reset. The delay of a unit of sample time between!q and!clr is necessary to avoid Simulink to fall in a ambiguous state: removing the delay,!q would be directly connected to!clr. At the instant t 0 the!q output would switch from 1 to 0. Since!CLR has to reset the flip-flop, this means that Q would become 0 and!q 1, but!q is already 0 at time t 0. This ambiguous state brings Simulink to a stall. In order to overcome this situation a delay is inseted in the feedback chain. In this case, with the same initial condition, at the time t = t 0!Q commutes from 1 to 0 but!clr is always 1, since the delay of a unit of sample time 72

86 provides the value of!q at t = t 0 1. At t = t 0 + 1!CLR is 0, Q resets to 0 (i.e.!q to 1). In this interval the flip-flop is not able to receive trigger signals. At t = t the!q value is propagated through the delay so!clr is 1 and the flip-flop ability to receive new trigger signal is restored. With this further element the feedback chain works without stall, in other words the delay lets the!clr commute from 1 to 0 for a unit of sample time. The reset signal (!CLR) is caught by a Go To block ([Clear]) and provided where the reset signal on the DOT falling edge is needed Signal Processing A signal from a segmented crystal is evaluated by the model presented. Some interesting cases are reported in order to explain the strengths and weakness of the implemented model. Figure 3.18: Signal with fast rise time generated by a segmented crystal. DOT delay is set to 1.6 ns. Multiple re-triggers can be seen in the signal falling edge. Signal with High Rise Time In figure 3.18 the responses (DOT and DOE signals) generated by a signal with high rise time are shown. DOT and DOE rising edges correspond to instants in which the corresponding thresholds are exceded. 73

87 The high threshold is crossed several times during the falling edge of the signal, then multiple DOE re-triggers occur. This effect can be seen also in the TOFPET ASIC prototypes. In figure 3.19 the validation logical stages are shown as a function of the time, derived from the flowcharts shown in figure 2.11 or The first row shows the DOT and DOE signals; the second one represents the same signal delayed of a quantity equal to DOT delay. The third row shows the output (Q) of the flip-flop used to validate the signal and finally the output of the AND block between DOT and flip-flop output is shown. The instant t v corresponds to the signal validation, given by the DOE rising front. When this occurs the output of the flip-flop (Q) commutes from 0 to 1 and the t DOT is associated to the rising edge of the DOT delayed signal. Clearly when both DOT and Q are high even the AND output is. Finally t r is associated to the reset signal caused by the falling edge of the delayed DOT front. If t v, t DOT and t r occur in this order the signal is correctly validated and undistorted. In the next sections some possible alteration in the validation process, due to a different order of those stages, are discussed. Figure 3.19: Validation Logic. The figure shows the three stages for the signal evaluation. Two logical signals (DOT and DOE) are correctly validated and the DOT is reproduced at the output (OutputAND). Signal with Low Rise Time In figure 3.20 the responses (DOT and DOE signals) generated by a signal with low rise time are shown. Signals of this kind, (of the order of magnitude of tens of photo-electrons), are expected for a continuous crystal. The signal is recognized by the ASIC, and many DOE re-triggers can be seen. Furthermore the DOT signal rising edge does not correspond to 74

88 Figure 3.20: A SiPM signal generated by a segmented crystal DOT delay is set to 1.6 ns. Multiple DOE re-triggers can be seen. Furthemore the TOT rising edge does not coincide with the low threshold exceed. the low threshold overcoming. That effect is due to a delay window shorter than the time needed to validate the signal. In figure 3.21 it is represented what happens to the validation logic if the delay is too short with respect to the signal rising time. The validation instant (t v ) is after the rising edge of the delayed DOT front (t DOT ). This brings to a cut of the signal beginning, the DOT rising edge after the validation logic is triggered by the validation of the t v signal. This effect brings a non systematic error in the measure of TOF. To overcome this drawback a delay window with a longer DOT delay should be open. In figure 3.22 the same signal (see fig. 3.20) evaluated by the model with a longer DOT delay is correctly recognized. This effect can be seen by the Simulink model, it is not known if it is effectively reproduced also by the TOFPET ASIC. DOE without DOT In figure 3.23 a particular case of response (DOT and DOE signal) is reported. In the final part of the signal the presence of a DOE signal without the DOT one can be observed. This effect has been obtained by increasing the delay of the DOT signal. It occurs in particular condition, caused 75

89 Figure 3.21: DOT signal cutted. The order of the validation phases is not respected due to a short delay; the validation happens after the delayed front of the DOT. This effect causes the loss of the DOT signal beginning. Figure 3.22: A SiPM signal generated by a segmented crystal DOT delay is set to 5.6 ns. Multiple re-triggers of the DOE can be seen. The TOT rising edge coincides with the low threshold overcoming. by the reset triggered by the delayed DOT signal. Figure 3.24 explains in detail what happens in the validation logic. Two subsequent signals arrive to the ASIC: the t r of the first arrives after the validation one t v of the second, so the flip-flop does not commute and the DOT is locked. 76

90 Figure 3.23: A SiPM signal generated by a segmented crystal DOT delay is set to 5.6 ns. The rearmament on the delayed DOT can cause a DOE signal without a DOT one. Figure 3.24: DOE without DOT logic Simulink TOFPET Model with Energy Integration In order to reduce or avoid multiple DOE re-triggers signal the ASIC design includes the possibility to shape the energy branch before the discrimination (see section 2.4.1). This feature has been implemented in the Simulink model (see fig 3.26) with a switch and a transfer function on the energy branch. The time constants of the implemented circuit are chosen according to table 2.1. They can be set with 3 flags (see table 3.1). In figure 3.25 a signal, evaluated with the energy branch integration, is reported. The absence of DOE re-triggers can be seen when comparing it to figure

91 Figure 3.25: An integrated signal with high rise time: the signal is the same proposed in figure 3.18 with the integration constant τ set to 2.5 ns. Multiple DOE re-triggers do not occur. Flag F tau1 F tau2 F tau3 τ 2.5 ns 5 ns 7.5 ns Table 3.1: List of flags for the shaping constant time TDCs Model According to the circuits design, two TDCs have been implemented in the model, one for each FE ASIC logical output. TDCs have been implemented in Matlab, with the input being provided by the two sinks of the Simulink model. The Matlab script extracts the rise time and length of each DOT and DOE (t,e). The values are stored on disk. A subsequent step is performed to extract the final TOT length, by merging the information of the TDCs. In this stage multiple DOE re-triggers are ignored and signals without DOT are rejected. 78

92 Figure 3.26: TOFPET model with energy channel integration. 3.3 Model Validation Experimental measurements useful to validate the model are presently not available. The model has been preliminarily validated by comparising it with a de- 79

93 tailed FE simulation in SPICE. To this purpose, a sequence of signals for a segmented crystal has been generated and evaluated by the Spice simulation and the Simulink model. In this section the main steps of the comparison are reported and finally the results are shown. Spice simulation results are available thanks to the TOFPET collaboration and Dr. M. D. Rolo. Signal Characteristics The sequence has been generated for a segmented crystal with characteristics are reported in table 3.2. The single signal used to build the entire sequence has been generated using the model described in section with parameters as reported in table 3.3. Time Length Dark Count Rate Primary Intensity 50 µs 5MHz/channel Bq Table 3.2: Validation signal sequence: list of characteristics Choice of Simulink Parameters The Spice simulation takes several days to analyze the 50 µs sequence, to be compared to 10 minutes with Simulink. The output provided by Spice as a function of the time is: V outt, V oute, V tht, V the, DOT and DOE. The input sequence is known. The simulation does not provide directly the couples of time and energy values (t,e) evaluated by the model, so the DOT and DOE from the simulation have been analyzed by the Matlab TDCs (see section 3.2.5) in order to obtain (t,e) values needed for the comparison. Thresholds and Amplification The outputs from Spice have a baseline due to the working point of the electronics components. To find out the correct values for Simulink thresholds, the baseline has to be estimated and subtracted. Analyzing the V outt the baseline was found to be 0.43 V. The Spice thresholds are function of the time, since a little fluctuation (order V) occurs due to the electronics components. In the implemented model thresholds do not vary, neglecting the fluctuation and subtracting the baseline 80

94 Parameter Value Description Q tot Single-cell charge output (SiPM gain 10 6 ) C d 85 ff Photodiode capacitance C q 10 ff Quenching parasitic capacitance N 3600 Number of microcells in pixel (3 mm pixel, 50µm cells) R q ω Quenching resistance C g 27 pf Grid parasitic capacitance L 10 nh Parasitic inductance R in 20ω Input resistance C in 5 pf Input capacitance BW 500 MHz Amplifier bandwidth G 1 Amplifier gain Table 3.3: List of parameters used to generate the single signal. their values are estimated to be V tht = 0.01V (3.9) V the = 0.05V (3.10) To find out the amplification factor A, the dark counts height in the input sequence (DC i ) and in the V outt branches (DC o,t ), has been measured: DC o,t = A DC i (3.11) 81

95 Taking into account the baseline, the amplification is estimated to be A = 2066 (3.12) In figure 3.27a the same signal of the V outt branch from Simulink and Spice using the amplification factor reported in equation 3.12 are superposed. (a) (b) Figure 3.27: Signal comparison between Simulink and Spice. In figure 3.27a the overlay of the V outt branch evaluated by Spice (in blue) and by Simulink (in green). In figure 3.27b the overlay of the V oute branch evaluated by Spice (in blue) and by Simulink (in green). The energy branch signal is shaped with a RC circuit with a time constant τ set to 7.5 ns (see table 2.1). Shaping Constant The simulation has been performed with the shaping in the V oute branch (see paragraph 2.4.1). The best agreement between the signals shaped has been found setting the Simulink time constant (see section 2.1) equal to τ = 7.5ns (3.13) In figure 3.27b the result of the superposition of the V oute branch of Simulink and Spice is shown, the amplification factor is the same found previously. As can be seen from figure 3.27 the agreement to dark counts is satisfactory; instead examining big signals some discrepancies can be seen, although they are not considered a serious problem since our interest is addressed to the thresholds region where the agreement is better. 82

96 DOT Delay Several evaluations of the Simulink model have been performed in order to find the DOT delay that brings to the best results, which was found at DOT delay = 4.3ns (3.14) Results Comparison In this paragraph the comparison of results is presented with the Simulink configuration described in the previous section Efficency Both Simulink and Spice recognized the same 19 events out of 20. This is due to the presence of two events close in time (less than 150 ns), and so recognized as one. Figure 3.28: Time difference of the event timestamp evaluated by Spice and the Simulink (t Spice t Simulink ). Time Measurement In figure 3.28, the difference of the event timestamp evaluated by Spice (t Spice ) and Simulink (t Simulink ) is presented. Data are distributed around a peak; the uncertainty in time measurement between the Spice simulation and the Simulink model is 210ps RMS. 83

97 The result achieved in this measurement it due to the high agreement of the signal in the low threshold region, and to its shape. Figure 3.29: Difference of the energy reconstructed by Spice and the Simulink one. Energy Measurement In figure 3.29 the difference between the energy evaluated by Spice (t Spice ) and Simulink (t Simulink ), measured as described in section In the histogram a peak can be seen but not all the entries are distributed around it, since the energy measurement depends on the evaluation of two fronts of the signal. The timestamp provided by the DOE falling front is evaluated in a region where uncertainty, due to signal superposition, can bring to discrepancies (see fig. 3.30a and 3.30b). Furthermore in this region the shape of the signal is dominated by random arrivals of photo-electrons (see DOE re-triggers sec ). In the TOT measurement there is an offset of about twice the DOT delay between the Spice simulation and the Simulink model. This systematic discrepancy does not affect further studies and has yet to be in depth analyzed. The uncertainty attribution to the energy measurement between the Spice simulation and the Simulink model is 6.6 ns RMS. Since in the signal analyzed 84

98 by Spice the average TOT value is found to be 220 ns, the relative uncertainty obtained in the energy measurement is 3% RMS. (a) (b) Figure 3.30: The two signals with the highest discrepancy (between Simulink and Spice) in the energy measurements. The first one is a very small signal (a); the second one (b) has a lot of re-triggers on the falling front of the signal. 3.4 TOT Characteristic and Linearization As explained in section TOFPET has a TOT non linear characteristic as a function of the number of photo-electrons. In order to evaluate this curve with the Simulink model a sequence of signals, made of 200 signals, with a number of photo-electron from 1 to 200 (see fig. 3.31) has been generated. All the photoelectrons of the same event arrive at the same time in the SiPM so as to simulate the process of test charge pulses injection in the actual ASIC. The parameters employed in the model are the same obtained from the Spice validation. The reconstructed curve is shown in figure Knowing the curve characteristic is important because it allows to linearize the energy measurement and hence to properly calculate the cluster energy and the cluster energy centroid coordinates. A logarithmic fit has been used: T OT = A log(#photo electron) + B (3.15) where parameters (A,B) were found to be A = 23 ns and B = 8.4 ns. After the linearization the TOT can be measured in charge-equivalent photo-electrons. 85

99 Figure 3.31: The input signal to evaluate the characteristic TOT as a function of the number of photo-electrons (see fig. 3.32). Each signal is obtained from a certain number of photo-electrons arriving at the same time on the SiPM. In this way the signal height is proportional at the number of photo-electrons. 3.5 Simulation of All the Block Detector Channels The validation results show an adequate agreement in the reproduction of DOE and DOT ASIC outputs. The TOFPET model can then be used, keeping in mind the limits shown by the validation, to perform the analysis of all the 512 block detector channels. This evaluation, compared to the same one analyzed from the 4DMPET ASIC model, can quantify the different performance of the ASIC TOFPET in the readout of SiPM coupled to monolithic crystals. In principle the TOFPET inefficiency for low signals and its non-linearity could compromise measurements performed by the block detector such as the DOI reconstructed by the cluster asymmetry, or the spatial resolution. The results of the simulation will show the expected performance in the measurement of those quantities. 86

100 Figure 3.32: TOT characteristic as a function of the number of photo-electrons evaluated from the model implemented in Simulink Input Sequence The signal to be processed by the electronic models is calculated from the Monte Carlo simulation; it reproduces the 4DMPET block detector (see section 3.1.1), with 16 x 16 9 mm 2 pixels coupled to the top and bottom sides of a 1 cm thick LYSO slab. The source activity has been set to generate interactions inside the scintillator at a rate of 110 khz/cm 2 which is the typical operating condition of a preclinical PET detector. The background pulses have a rate of 55 MHz/cm 2 (see table 3.4). The signal single shape is the same used for the model validation. Time Length Dark Count Rate Signal Rate 1950 µs 55 MHz/cm KHz/cm 2 Table 3.4: List of parameters used for the block detector simulation. 87

101 DMPET In this section the analysis results performed by the 4DMPET ASIC model are reported. The parameters used in the cluster finding algorithm have been optimized for the response of this ASIC. The time window values are set to: TWA = 15 ns and TWB = 108 ns. The lower threshold is set to 0.5 photoelectrons. In table 3.5 the detector efficiencies are reported. The SiPM single layer readout by the 4DMPET ASIC reconstructs 82% of the events. Both layers reconstruct 65% of the events. Side 1 Side 2 Both Sides Table 3.5: Efficiency of the detector obtained with the 4DMPET ASIC. 88

102 TOT distribution ncounts 10 5 TOT distribution Entries Mean 3.63 RMS TOT (ns) Figure 3.33: TOT distribution obtained with the 4DMPET ASIC model. TOT and Cluster Size Distribution the TOT measured by the 512 channels is shown. In figure 3.33 the distribution of all cluster size ncounts clustersize Entries Mean RMS cluster size (number of pixel) Figure 3.34: Cluster distribution obtained with the 4DMPET ASIC model. In figure 3.34 the distribution of all the cluster reconstructed by the tiles of SiPMs is shown. 89

103 511 kev gamma Energy Spectrum(keV) 250 Energy Entries 3836 Constant Mean Sigma ncounts energy (kev) Figure 3.35: Reconstructed energy spectrum obtained with 4DMPET ASIC model. Energy Resolution In figure 3.35 the energy distribution of reconstructed events is shown. Data inserted in the histogram belong only to reconstructed events on both the SiPMs layers. As seen in the figure 3.35, the 511 KeV peak is visible and the energy resolution measured with a gaussian fit is found to be 14% (see table 3.6). 90

104 X resolution with edge correction (mm) ncounts Xint - Xrec_corr Entries 2865 Mean RMS X resolution with edge correction (mm) 200 X resolution (mm) Xint - Xrec (mm) Figure 3.36: X resolution with and without correction obtained with the 4DM- PET ASIC model. Spatial Resolution In figure 3.36 the X resolution with and without the edge correction is shown. The correction improves events far from the peak distribution; after the correction a higher peak is visible. The resolution achieved in the X coordinate is found to be 1.7 mm RMS; similar values are obtained for the Y coordinate (see table 3.6). RMS FWHM FWTM Energy resolution ( 511 kev) 14% σ - - X resolution 1.7 mm 1.12 mm 3.0 mm Y resolution 1.9 mm 1.12 mm 3.0 mm DOI resolution 1.7 mm 1.5 mm 3.7 mm Table 3.6: Energy, x, y and DOI resolution results obtained with the 4DMPET ASIC model. 91

105 (cl_size,down-cl_size,up) / (cl_size,down+cl_size,up) cluster asymmetry vs DoI DoI Entries 2865 Mean x Mean y RMS x RMS y Zint (mm) Figure 3.37: Cluster size asymmetry as a function of the DOI obtained with the 4DMPET ASIC model. DOI Resolution In figure 3.37 the correlation between cluster size and DOI is shown. The resolution in the DOI measurement (z coordinate) with the asymmetry of the cluster size is found to be 1.7 mm RMS (see fig 3.38 and table 3.6). DoI resolution (mm) ncounts 120 DoI resolution Entries 2865 Mean RMS Zint - Zrec (mm) Figure 3.38: DOI (z) resolution obtained with the 4DMPET ASIC model. 92

106 3.5.3 TOFPET In this section the analysis results obtained with the TOFPET ASIC model are discussed. The amplification factor in the model (A) was set to 2066 (the same value used in the validation with Spice see section 3.3); the maximum possible value of DOT delay was choosen: 5.6 ns in order to maximize the time available to validate the signal. Low threshold (V tht ) was set to 0.5 photo-electron and the high one (V the ) was set to 2.5 photo-electrons. On the energy branch the shaping time constant was set to 7.5 ns. The detector efficiencies are reported in table 3.7: the efficiency for a single layer or double is 48% or 25% of events respectively. Both layers reconstruct the 25% of events. Side 1 Side 2 Both Sides Table 3.7: Detector efficiency with the TOFPET ASIC. ncounts TOT distribution 3 10 TOT distribution Entries Mean RMS TOT (number of photo-electron charge equivalent) Figure 3.39: Linearized TOT distribution obtained with the TOFPET ASIC model. TOT and Cluster Size Distribution The TOT distribution recorded by the 512 ASIC of the block detector is shown in figure The TOT values 93

107 have been linearized inverting the relation found in 3.4. The distribution do not have entries smaller than 2 charge equivalent photo-electrons, due to the thresholds set in the model; that reject all the events that do not overcome the high threshold. The cluster size distribution is reported in figure 3.40: it has a bell shape centered at about 30 pixels. The contribution of small clusters is low because the threshold in the cluster finding algorithm has been set very low, so during the cluster growing several pixel contributions are added to it. cluster size ncounts 10 2 clustersize Entries 1421 Mean RMS cluster size (number of pixel) Figure 3.40: Cluster distribution obtained with the TOFPET ASIC model. 94

108 Linearized Cluster Energy ncounts ClEnergyRaw Entries 1421 Mean 9220 RMS TOT (number of photo-electron charge equivalent) 3 Figure 3.41: Reconstructed raw energy spectrum obtained with the TOFPET ASIC model. Energy Resolution The energy distribution of reconstructed events is shown in figure Data inserted in the histogram belong only to reconstructed events on both the SiPMs layers. As it can be seen in the figure, a clear peak can not be identified: this histogram shows the limits of the TOFPET ASIC coupled to a continuous crystal in the reconstruction of the event energy. This result is probably due to: -the way chosen to perform the energy measurement in the TOFPET ASIC (see section 2.4.3) that leads to a non linear characteristic. -the length of DOT delay, too short compared to the rising time of the signal. -multiple re-triggers that affects the energy measurement on the falling front of the signal (see section 3.20). 95

109 X resolution with edge correction (mm) ncounts Xint - Xrec_corr Entries 1229 Mean RMS 2.64 X resolution with edge correction (mm) X resolution (mm) Xint - Xrec (mm) Figure 3.42: X resolution with and without correction obtained with the TOF- PET ASIC model. Spatial Resolution The X resolution with and without the edge correction is shown in figure The correction does not substantially change the resolution, probably because the edge effect is neglecting compared to the uncertainty in the energy measurement (energy is used to weight the cluster see section 2.2.3). The resolution achieved in the X coordinate is found to be 2.6 mm RMS, similar values are obtained for the Y coordinate (other information are reported in table 3.8). 96

110 RMS FWHM FWTM Energy resolution ( 511 kev) X resolution 2.6 mm 1.8 mm 4.0 mm Y resolution 2.8 mm 1.2 mm 3.8 mm DOI resolution 1.5 mm 1.2 mm 3.3 mm Table 3.8: Energy, x, y and DOI resolution results obtained with the TOFPET ASIC model. cluster asymmetry vs DoI (cl_size,down-cl_size,up) / (cl_size,down+cl_size,up) DoI Entries 1227 Mean x Mean y RMS x RMS y Zint (mm) Figure 3.43: Cluster size asymmetry as a function of the DOI obtained with the TOFPET ASIC model. DOI Resolution In figure 3.43 the correlation between cluster size and DOI is shown. The resolution in the DOI measurement (z coordinate) with the asymmetry of the cluster size is found to be 1.5 mm RMS (see fig 3.44 and table 3.8). 97

111 DoI resolution (mm) ncounts 60 DoI resolution Entries 1227 Mean RMS Zint - Zrec (mm) Figure 3.44: DOI (z) resolution obtained with the TOFPET ASIC model Remarks The simulation of the entire block detector shows that the TOFPET ASIC model reconstructs less events with respect to 4DMPET one, the efficiency estimate for the TOFPET model is found to be 25%; instead the 4DMPET efficiency is found to be 65% (see table 3.7 and 3.5), but some further studies could be performed to optimize the cluster processor trigger condition. The limits encountered in the reconstruction of the event energy (see paragraph 3.5.3) are reflected in the determination of the cluster centroid, so the x-y spatial resolution achieved by the TOFPET model (2.6 mm RMS) is worse than the 4DMPET one (1.7 mm RMS). The event energy is not used in the DOI determination, which depends only on the cluster size, so the cluster asymmetry as a function of DOI shows a clear correlation even with the TOFPET model. The DOI resolution measured with the TOFPET model is found to be compatible with the 4DMPET one. 98

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114 Chapter 4 Experimental Preliminary Results The 8x8 channels 4DMPET module, equipped with the TOFPET ASIC was build and its characterisation is just started. Some very preliminary results are discussed in the following. 4.1 Acquisition with Pixellated LSO Crystals Figure 4.1: Experimental apparatus for segmented crystals. The first measurements have the goal to study TOFPET performances, vary- 101

115 ing: gain, threshold (with respect to the baseline of each channel) and shaping. The ASIC has been studied in its native environment: segmented crystals. The acquisition has been done with two pixellated 3 x 3 x 10 mm 3 LSO crystals (see fig. 4.1). A β + source ( 22 Na) was placed between the two crystals and only (a) (b) Figure 4.2: Energy spectrum measured with segmented crystals: the photopeak events are selected with a time-coincidence. The clearly visible photopeak is visually enhanced because of the logarithmic TOT-energy dependency (see figure 2.12). events in coincidence were recorded. Figures 4.2a and 4.2b show the energy peak of 511 KeV photons. Those are just a preliminary test, results do not represent the best achievable performances. 4.2 Acquisition with Monolithic LYSO Crystal A 32 x 32 x 10 mm 3 crystal was then coupled to two 8x8 pixels SiPM matrices with 3.5 mm pitch and it has been used for the 4DMPET characterization. As can be seen from figure 4.3 the crystal is a bit bigger than the surface covered by the SiPM matrix. The module has been irradiated using 22 Na and 68 Ge sources, preliminary results are shown in figures 4.4. The events have been selected with a minimum number of 4 total pixels fired on the two sides. Furthermore only an area of 20 mm x 20 mm has been considered, in order to avoid, at this time, edge effects. 102

116 Figure 4.3: Experimental apparatus for continuous crystal, the crystal is a bit bigger than the surface covered by the SiPM matrix. In figure 4.4a the anticorrelation between the two cluster reconstructed faces is reported. This result is important because it is the first step for the DOI measurement. In figure 4.4b the event energy reconstructed by means of cluster finding is reported: the spectrum is shifted towards lower values and shows a cut shortly after the photopeak, this suggest low efficiency for low energy events. (a) (b) Figure 4.4: 68 Ge cluster asymmetry anticorrelation and reconstructed event energy. 103