A full-brain PET scanner based on the AX-PET concept: Monte Carlo performance study

Transcription

1 Universitat de València Master Thesis A full-brain PET scanner based on the AX-PET concept: Monte Carlo performance study Author: Gabriel Reynés-Llompart Principal Supervisor: Paola Solevi, PhD Co-Supervisor: Josep F. Oliver, PhD Màster Universitari en Física Mèdica September 214

2 Contents Contents Abstract Abbreviations Rationale i iii iv v 1 Introduction PET imaging Working principles of PET imaging Resolution limitations Types of coincidences Sensitivity PET radiopharmaceuticals Brain Imaging Methods AX-PET AX-PET proof of concept Monte Carlo simulation Reconstruction algorithm Materials Full Ring Brain Scanner Phantoms Cologne High Resolution Phantom NEMA HOT-COLD Simulation setup Image Analysis Results and discussion Cologne Phantom NEMA HOT-COLD Reconstructed image analysis Comparison of AX-PET geometries Inclusion of ICS events i

3 ii Conclusion and future outlook 35 A Supplementary Data 37 Bibliography 41

4 UNIVERSITAT DE VALÈNCIA Abstract Facultat de Física Grupo de Física en Imagen Médica Màster Universitari en Física Mèdica A full-brain PET scanner based on the AX-PET concept: Monte Carlo performance study by Gabriel Reynés-Llompart 1 AX-PET is a novel PET detector conceived in order to reduce the parallax error and simultaneously improve spatial resolution and sensitivity. Instead of the radial orientation of the scintillating crystals of conventional scanners, AX-PET design is based on long axially arranged crystals. The discrete geometry of AX-PET permits to detect and use the inter-crystal scattering (ICS) events to increase the system sensitivity. The aim of the present work is to test the capability of the AX-PET concept for brain imaging. Two full ring AX-PET geometries are compared, the standard, based on an AX-PET demonstrator setup, and a novel system with an optimized crystal arrangement; for both geometries, Monte Carlo simulations of different sources have been done: the Cologne phantom, for resolution studies, and a NEMA hot and cold phantom at different lesion-to-background ratios for image quality assessment. Both phantoms were reconstructed using only golden events or golden events plus ICS events, and several figures of merit were analysed. Novel geometry presents a slightly higher and more homogeneous sensitivity, thanks to its compact design. Both systems were capable to reconstruct and detect the 1 mm spheres; however, the novel system presents a better contrast. On the other hand, the standard geometry shows a better performance on all image quality figures of merit. The inclusion of ICS increase the contrast-to-noise ratio by 2% but also increases the spill-over ratio in 6%. Although the Novel geometry improves sensitivity and resolution, more efforts need to be done in terms of image quality. Furthermore, the incorporation of ICS data acquired simultaneously with golden coincidence measurements increases image quality and has potential to help identify lesions in images with a low LBR. AX-PET based brain scanner shows a potential in terms of spatial resolution, however more efforts shall be invested in the calculation of the system response matrix and sensitivity in order to achieve a better image quality when dealing with extended sources where the lack of an appropriate sensitivity correction can indeed compromise the reconstructed image. 1 greynesllompart@gmail.com

5 Abbreviations CT DOI FDG ICS LBR LOR MC MLEM MMPC NEMA PET ROI TSL SOPL WLS Computed Tomography Depth of Interaction 2-deoxy-2-Fluoro-d-Glucose Iinter-Crystal Scattering Lesion-to-Background Ratio Line of Response Monte Carlo Maximum-Likelihood Expectation-Maximization Multi Pixel Photon Counters National Electrical Manufacturers Association Positron Emission Tomography Region Of Interest Threshold Single Level Simulated One Pass List-mode WaveLength Shifter iv

6 Rationale The international AX-PET collaboration 2 is trying to improve the design of the current state positron emission tomography (PET) imaging by changing the typical alignment of the detectors. The collaboration showed the capabilities of the AX-PET demonstrator, based on two detector modules, in terms of both resolution and sensitivity. Results have been reported in different publications since 28. However, the AX-PET system was originally conceived for brain imaging, and the performance of an AX-PET based full-ring system for brain applications is for the first time studied in the present work. Inside the AX-PET collaboration, the Image Reconstruction Instrumentation and Simulation for medical imaging applications team (IRIS 3 ), part of the Institut de Física Corpuscular (IFIC), has developed simulation models for a full ring AX-PET prototype and novel reconstruction techniques adapted to the unique features of the system. The main objective of the present work is to test the capability of the AX-PET concept for brain imaging through the simulation, reconstruction and analysis of several phantoms. The standard scanner geometry based on the AX-PET demonstrator design is compared to a novel system with an optimized crystal arrangement; to achieve this goal, the understanding and employments of several tools, such as the Monte Carlo GATE and ML-EM reconstruction algorithms, were required. The original contributions to the assessment of the performance of the AX-PET brain scanner coming from this work are: the development and adaptation of phantoms to the AX-PET Monte Carlo simulations, the image reconstruction through different event selection (with and without Inter-Crystal Scatter events, with and without random and scatter events) and, most important, the posterior analysis of the different reconstructed images. The corresponding contributions are presented from chapter 3 -materials. 2 AX-PET website at CERN. 3 IRIS website. v

7 Chapter 1 Introduction 1.1 PET imaging Positron Emission Tomography (PET) is a technique used in medicine to provide a 3D image of metabolic body processes. This is why that PET images are called functional images, in contrast to other image techniques as computed tomography (CT) which provides anatomic images. PET has a role in the diagnosis of many different diseases, such as cancer, heart stroke or Parkinson s disease, conditions caused or accompanied by local changes in metabolism. The specific functional information that is sought in a PET scan depends on the injected tracer. In this sense, PET is an extremely flexible imaging modality whose applications are limited only by the research advances in the area of radioactive tracers and by the technological advances to improve the performance of PET scanners Working principles of PET imaging In PET imaging positron emitter radioisotopes are employed. The positron, emitted by spontaneous decay, travels a certain distance depending on its energy and the tissue density to finally interact with one electron of a surrounding atom, resulting in an annihilation of the positron and the electron. The annihilation process is done when the positron has lost almost all its kinetic energy. The general equation of positron decay is described in Eq

8 1. Introduction 2 A ZX A Z 1Y + 1 β + ν (1.1) where A and Z are the mass number and atomic number of the decaying nucleus, e + is a positron and ν is an antineutrino. Due to the energy and momentum conservation, two gamma rays are emitted, each having an energy equal to the rest mass of the electron (511 kev), which propagates in the opposite directions. The attenuation coefficients of the 511 kev gammas in water is.96 cm 2 /g, low enough to allow the two photons escaping the patient s body. Surrounding the patient there is a ring of detectors; if both emitted photons are detected, the process is called a coincidence event and a line of response (LOR) is created joining the points of the detection. The information recorded in every LOR is assembled and employed to produce an image of the activity uptake in the patient s body. Figure 1.1: Schema of the PET acquisition sequence: the back-to-back detection, the processing of the coincidences and the reconstruction procedures. Image belongs to Jens Maus, released to public domain. 1 The detection of coincidence events is performed by an electronic coincidence sorting unit through the application of a coincidence time window to detected photons. If two events are measured within the time window, it is interpreted as a coincidence event. The time window τ applied to score coincidences depends on the time resolution δt of the device. If data are stored in the list-mode each individual LOR is registered, preserving the 1

9 1. Introduction 3 spatial resolution of the detector. In this format, usually the time stamp of the LOR is not recorded. When dealing with analytic reconstruction and/or poor data statistics other formats such as the sinogram histogram format might be more convenient. LORs are binned thus the spatial resolution is decreased to the size of the bin. A schema of the PET acquisition sequence can be seen in Figure Resolution limitations In PET there are some intrinsic limitations to the best spatial resolution that can be achieved in the final image. Most of these limitations arise from detector itself or the physics associated to the positron annihilation [1, 2]. Detector resolution: The most important factor that degrades the spatial resolution is the scintillation detector intrinsic resolution of the PET scanner, which is due to solid angle coverage and the underdetermination of the exact position of the interaction inside the detector crystal. In particular, in order to achieve a higher sensitivity given the stopping efficiency of 511 kev photons in inorganic scintillators, longer radial detection units are employed. The larger radial thickness implies a larger uncertainty in the determination of the Depth Of Interaction (DOI) of the gamma photon within the crystal. The resolution loss due to DOI uncertainty increases by increasing the radial distance from the scanner centre. Thus the intrinsic resolution (R i ) primarily depends on the detector size. Positron range: The positron range is the distance from the point of emission to the point of annihilation; it depends on the kinetic energy with which the positron is emitted by the nuclide. Positron range limits the maximum resolution achievable by a PET scanner, it adds an intrinsic error R p in the determination of the position where annihilation occurred. With increasing scanner resolution, the trend is to incorporate the positron range into the imaging model. Table 1.1 presents the range of some commonly used radionuclides.

10 1. Introduction 4 Table 1.1: Half life, maximum positron energy, and average positron range in water of some nuclides commonly used in PET Isotope Half-life (min) Maximum Positron Energy (MeV) Average Positron Range (mm) 11 C N O F Rb A-collinearity: The positron and the electron are not completely at rest when annihilating. As a consequence, the angle between both gamma rays is not 18 degree and is instead better described as a distribution around this value. This angular distribution can be modeled as a gaussian function with a full width at half maximum (FWHM) of approximately.5 degree. The a-collinearity error (R a ) increases with the distance between the two detectors. Reconstruction technique: A factor on the total error (K r ) due to some reconstruction techniques is introduced by some filters in the filtered back-projection reconstruction method. Filters applied to suppress noise in the reconstructed image employ a cut-off frequency in the reconstruction resulting in a loss of spatial resolution. Detector localization: The use of block detectors instead of single detectors causes an error R l in the event localization which deteriorates the spatial resolution. Assuming that almost all the effects above add in quadrature, the total intrinsic reconstructed spatial resolution is described by Equation 1.2. R T = K r R 2 i + R2 p + R 2 a + R 2 l (1.2) Types of coincidences When both photons from the same annihilation are detected in coincidence without any kind of interaction prior to the detection, it is called a true coincidence.

11 1. Introduction 5 If at least one of the photons interacts within the patient s body by Compton scattering the original direction of the photon is changed, being then assigned a wrong LOR to the true event. This type of events are known as scattering events, and result in a noisy background to the true coincidence distribution, decreasing the image contrast and increases the estimation of the activity. Random coincidences occur when two photons from different annihilation events are detected within the coincidence time window of the system. When three or more photons are detected within the same time window then a multiple coincidence is scored. Depending on the coincidence policy of the scanner, multiple coincidences can be either included in the reconstruction or neglected. The fraction of random and multiple coincidence events increases with the activity in the imaged volume and may result in a loss of image contrast. Figure 1.2: Illustration of the main coincidence event types: a) true; b) multiple; c) single; d) random and e) scattered. (Adapted from Simon R. Cherry) Depending on the detectors employed in a PET scanner, a photon may undergo multiple interactions in different detectors (e.g. Compton + Compton, Compton+Photoelectric) As shown in Figure 1.3, these events, named Inter-Crytal Scatter events (ICS), can yield two possible LORs but only one will be true. Some PET scanners are not able to distinguish multiple hits, whereas modular detectors are usually capable of it, and the interaction sequence cannot be stated. Then, the position of the different interactions is stored in an arbitrary order. If this type of events are included in the image reconstruction they will produce an increase of the sensitivity, but in contrast, the spatial resolution of the image may be jeopardized.

12 1. Introduction 6 Figure 1.3: Inter-crystal scatter event of one photon produced in the annihilation pair. In this example, one photon suffers Compton scattering inside one crystal and photoelectric absorption in the next crystal. Two possible photon sequences resulting in two different LORs can be reconstructed: the wrong one represented in dashed blue, instead of the true one, represented in red, which is the one crossing the annihilation point Sensitivity PET sensitivity is determined by the intrinsic efficiency of the detectors employed and by the geometry of the PET scanner that determines the angular coverage of the imaged object. Some additionally parameters such as the energy thresholds applied at detector level and coincidence policy also affect the sensitivity of the system. The closer a detector is positioned to the source, the larger the solid angle it can cover. The intrinsic efficiency of a detector is the probability to detect a gamma photon once it enters a detection element, and it depends on the material composition and thickness of the detector. When the detector thickness increases, the intrinsic efficiency increases as well, but the depth of interaction (DOI) introduces an uncertainty on the origin of the gamma rays, known as parallax error, that decreases the spatial resolution. 1.2 PET radiopharmaceuticals The most common radiopharmaceutical used in PET is [ 18 F]FDG 2 for oncological imaging and several different pathologies. The success of PET imaging in clinical practice is associated to [ 18 F]FDG and its widespread availability, the relatively long half-life of the nuclide and the fact that many pathologies are associated with changes in the metabolic rate of glucose. For example, many tumors present a high uptake of glucose due to an 2 2-deoxy-2-( 18 F)fluoro-d-glucose

13 1. Introduction 7 accelerated metabolism required by tumoral cells to replicate faster. However, many PET compounds have been synthesized with other β+ emitters as 11 C, 13 N, 15 O. The short half-life of these radionuclides makes it necessary to produce them in a biomedical cyclotron in-situ for a fast transfer and synthesis of the radioisotopes. Figure 1.4: PET image of a normal brain using [ 18 F]FDG. 1.3 Brain Imaging The present work is focused on the performance estimation of a brain PET scanner. Brain imaging is covering an increasing importance in clinical practice for mostly two scenarios: oncological and neurological studies. Brain tumors are not very common, with less than.1% prevalence in western population. However, they are among the most fatal cancers [3], being gliomas the most frequent primary brain tumors, with an incidence of 7%. With respect to neurological studies, with the increase in life expectancy cognitive impairment has become a critical health issue. Projection of WHO expect more than 48 million people in 24 affected by dementia, with a dominant incidence of Alzheimer s disease (AD) [4]. There are two ways of extract the metabolic information of the central nervous system[5]. A first possibility is to extract information of brain functional activity and metabolism, such as blood flow, rates of glucose and oxygen metabolism. This first approach allows us to look for an specific abnormal function of the brain. An example of that is the use of [ 18 F]FDG for the diagnosis of several different pathologies as dementias, epilepsia, brain tumors, etc. A second approach is based on the measurement of neurotransmitter synthesis or enzyme activity. These are variables related to the function of the neuronal populations that compose the central nervous system. An example of this is the radiopharmaceutical [ 18 F]Fluoro-L-dopa used in the diagnosis and staging of the Parkinson disease. Table 1.2 presents a list of some common brain radiopharmaceuticals. From the technological point of view, brain imaging has different needs than whole-body

14 1. Introduction 8 Table 1.2: Positron Emission Tomography radiopharmaceuticals.[6] Compound Application 15 O 2 Oxygen metabolism and flow. 11 C methionine Amino acid metabolism. 11 C methylpiperone Dopamine receptor activity. 18 F FDG Glucose metabolism. 18 F fluoro-l-dopa Neurotransmitter. 18 F MISO Tumor hypoxia. imaging, then it is possible to create dedicated brain PET scanners with a small detector ring diameter, which provide higher sensitivity when compared with a multipurpose whole-body PET scanner. At the same time, the increased sensitivity achieved by such scanners comes with decreased of the a-collinearity degradation of the spatial resolution but usually increasing parallax and solid-angle errors. So the optimization of both sensitivity and spatial resolution is crucial in brain imaging given the variety of lesion and contrast magnitudes to be detected combined. In fact dealing with brain tumors requires the detection of small lesions with poor contrast activity given the high overall uptake of brain with [ 18 F]FDG as well as large necrotic regions. In degenerative dementia small hot and cold regions may be detected, with uptake and then contrast that may vary depending on the injected radio-tracer and on the stage of the dementia. Sensitivity is crucial in particular for early stage AD detection, when the neurodegeneration is less and treatment may still be administered.

15 Chapter 2 Methods 2.1 AX-PET Most PET systems are based on a radial arrangement of scintillating crystals [7]; such a geometry usually requires to optimize either the spatial resolution or the sensitivity, due to the lack of information about the DoI, which implies a parallax error. This problem can be partially solved with the use of smaller crystals, but then the sensitivity of the system is compromised. Therefore, a trade between both features is needed. AX-PET is a novel PET detector conceived in order to reduce the parallax error and simultaneously improve spatial resolution and sensitivity. Instead of the radial orientation of the scintillating crystals of conventional scanners, AX-PET design is based on long axially arranged crystals and orthogonal Wavelength shifter (WLS) strips, both individually read-out. This configuration allows obtaining the 3D coordinates of the gamma interaction point within the crystal. Similarly to common PET systems, the interaction of the photon with the crystal gives the 2D coordinates of the detections (X,Y) and the photon energy. However, to get the axial coordinate (Z), there are WLS plastic strips underneath each crystal layer, placed perpendicularly to the crystals, with a small gap between them. The process to detect each coordinate is described as follows: after the interaction of a photon within the detector the crystal emits light isotropically, which is partially absorbed by an MPPC 1 (Multi Pixel Photon Counters) to get the coordinates and the 1 Geiger Mode Avalanche Photodiode (G-APD) also known as SiPM and MPPC. 9

16 2. Methods 1 (a) (b) Figure 2.1: A) Drawing of a prototype of AX-PET module geometry. It is composed of six layers of eight crystals each interleaved with six layers of WLS. The MPPC are mounted in order to avoid dead areas. The crystals in adjacent layers are staggered by half a pitch size. B) Scheme of the method used for light propagation in the scintillation crystal and the WLS strips. Both pictures belong to the AX-PET collaboration, Beltrame et al. energy of the photon. A portion of the light escaping the LYSO 2 crystal will be absorbed by the WLS strips. These strips will absorb the blue light and re-emit it in the green band. Optical photons will travel inside the strips towards their own WLS MPPC. Moreover, not all light is absorbed by a given WLS 3, and more than one WLS can detect the light emitted by a given crystal (S i ), making possible to get the Z position with a higher resolution than the one obtained by a single WLS: z event = i S i z W LS,i S total (2.1) This design allows AX-PET to perform a 3D photon tracking and to identify the Compton interactions in the crystal matrix as ICS AX-PET proof of concept An AX-PET demonstrator has been built at CERN and tested with different phantoms and small animals at different radio-pharmaceutical facilities. The demonstrator consists of two identical modules, each AX-PET module is composed of six layers of eight crystals (LYSO), each one with an hodoscope of 26 WLS strips, hence a total of 48 scintillator crystals and 156 WLS strips. Crystals and strips are read-out by two different 2 Cerium-doped Lutetium Yttrium Orthosilicate. Composition: Lutetium (72%), Yttrium (4%), Silicon (6%), Oxygen (18%). Density: 7.1 g/cm 3, refractive index: The light is detected by about 3 different WLS.

17 2. Methods 11 types of MPPCs. From the two modules fully assembled and characterized, Table 2.1 presents some numbers of its performance. Is important to mind the substantial fraction of Compton scattered events which could be included in the reconstruction algorithm to enhance the sensitivity. Table 2.1: Some AX-PET demonstrator performance characteristics. Energy resolution measured at 511 kev. Data extracted from Bolle et al. Resolution FWHM x,y z Energy Compton events 2.3 mm 1.79 mm 11.7% 25% The potential of the AX-PET demonstrator to image small animals was successfully assessed; the measurements were performed at the ETH 4 radio-pharmaceuticals laboratory where a mouse and a rat were injected with [ 18 F]FDG and imaged by the two-modules AX-PET system. The image of a rat injected with the [ 18 F]FDG is shown in Fig 2.2. Figure 2.2: Maximum intensity projections of the rat imaged using [ 18 F]FDG, reconstructed with golden events and ICS events. Adapted from Gillam et al. 4

18 2. Methods Monte Carlo simulation The aim of the Monte Carlo (MC) method when used in radiation physics is to simulate the radiation transport in matter, by numerically sampling random variables associated to probability distributions of each kind of interaction that can occur. Thus, MC simulations are a common tool to address various issues related to PET imaging, from designing and optimizing imaging systems to developing and assessing correction methods or tomographic reconstruction algorithms for improved image quality. Within the context of the AX-PET system, the development of an accurate MC based model is an important tool for a better understanding of the device, and to exploit its specific system characteristics. GATE 5 is a Monte Carlo simulation tool based on Geant4 libraries, an object oriented multi-purpose Monte Carlo toolkit developed at CERN [11]. It offers easy tools to simulate SPECT and PET systems plus the description of source decay phenomena, modelling the signal processing or the inclusion of the time component like real acquisitions. AX-PET non-conventional design, which relies on the WLS strips signals to retrieve the interaction coordinate of the photon along the crystal, makes it necessary to develop a computational model for the propagation and some major modifications to the GATE source code. The adaptation of the AX-PET system to the MC simulation can be divided in three steps: Simulation of the optical phenomena: WLS strips behavior has to be included in the MC simulation to provide a realistic axial resolution and a good event selection. Since Monte Carlo simulations are time consuming, the optical photon transport in the crystal and in the WLS strips geometry is not simulated but computed through an analytical model. Light distribution on the WLS strips depends on the energy deposited in the LYSO E n, on the axial position of the interaction z n and on the depth of interaction in the crystal x n. This is modeled as a Gaussian distribution of the number of photoelectrons N pe, with N pe(i) photoelectrons on the ith strip: N pe(i) = N n=1 5 x i A(x n, E n )e (zn z i )2 2 σ 2 xn. (2.2)

19 2. Methods 13 In this expression indices i and n label the WLS strip and the interaction in the crystal, respectively. A represents the signal amplitude associated to the nth interaction and it varies with the deposited energy, E n, and the depth of the hit within the crystal, x n. (a) (b) Figure 2.3: (A) Experimental and simulated setup for the characterization of the WLS response. Two WLS strips were adjusted underneath a LYSO crystal excited by a collimated electron beam. Figure adapted from Solevi et al. (B) Monte Carlo simulation of the z resolution. Both figures adapted from P. Solevi at CHIPP meeting. GATE simulation adapted to the set up of AX-PET: The Monte Carlo model of the AX-PET uses a PET system available in GATE as a reference, which includes the staggering and layered structure of the device. GATE also processes the total energy deposited in the crystal which is used to model the electronics of the system. Given the photon interactions in the crystals -known as hits-, GATE is modified with the inclusion of the WLS model, described earlier, in order to produce the final output, named singles. The simulation uses a new digitizer module to operate on the generated WLS signals from each strip of the output Single data, determining the new axial coordinate through determination of the center of gravity. Moreover, the simulation output is adapted to the potential of the AX-PET with the processing of the ICS events. It includes information that can be used to reconstruct the true kinematics of the gamma-rays in the detector. The system stores the track ID describing the inter-crystal scatter and the number of photoelectric interactions occurring in the scintillation elements.

20 2. Methods 14 Electronics modeling via a dedicated sorter, performing an off-line processing of the GATE output: A threshold at single level (TSL) is applied to each single detected. For each single passing the threshold, the pile-up effect 6 is modeled as a 25 ns window, where all singles belonging to the same module and within this time window form an event. As described below, all the singles recorded in the LYSO crystals belonging to one module were then summed up and stored if the final energy is between the thresholds of 4 kev and 6 kev. If two such events are found in coincidence -that is, with a time difference below the 5 ns coincidence window applied- a coincidence is formed. Next, the coincidence is processed to introduce some dead-time. The dead time is parametrized as follows: τ dt = N wc τ wc + τ (µs). (2.3) Where N wc is total number of hit channels (world count), τ wc is the mean deadtime per readout channel, and τ is the intrinsic dead-time of the system. 2.3 Reconstruction algorithm AX-PET is a novel PET concept, and to exploit at best its potential, a huge effort in terms of dedicated reconstruction software development is required. In image reconstruction, there are two big families of algorithms: analytical and statistical iterative. The second group of algorithms can offer a higher image quality, but needs an accurate model of the system and the physics involved. An iterative reconstruction algorithm solves the problem defined by y = T x (2.4) where y is the measured data, x the voxelized image and T is the system matrix, see Figure 2.4. There is a large set of different approaches to solve this problem; all results from this document are obtained with the iterative Maximum-Likelihood Expectation-Maximization 6 Pile-up effect: dead time due to signal pulses arriving closer in time than the pulse resolution time of the system.

21 2. Methods 15 (MLEM) algorithm in the standard list-mode implementation. MLEM algorithm provides an estimation of the mean intensity from voxel j, λ j : λ k+1 j = λk j a ij s J j j= a ijλ k j i M where s j = I a ij (2.5) i= where n k j denotes the value of the voxel j at iteration k and a ij the probability that an emitted photon from the voxel j is detected in a measurement of i, and s j is the sensitivity matrix. For the list mode, M refers to the set of measurements. Computing a ij is one of the big challenges of the ML-EM algorithm. The matrix could be determined by calculations, simulations, or a combination of both; the more accurate way to calculate it is to position a point source at all locations within the imaged volume and record the counts in all elements of all possible projection profiles. Indeed, this is a very time consuming procedure and it is usually simplified using symmetry considerations. (a) (b) Figure 2.4: Reconstruction of an AX-PET image. A) The system matrix element a ij is defined as the probability to detect the activity in voxel j in LOR y i, adapted from P. Solevi at CHIPP meeting. B) Example of an inter-crystal event, from Gillam et al. As mentioned above, one of the main features of the AX-PET is the possibility to include the ICS events in the reconstruction procedure. Consider an ICS consisting of a triple event detection, figure 2.4. This means that there are two possible LOR but only one is correct, see figure 2.5. To include the ICS events into the MLEM algorithm one should maximize the probability to include the correct LOR. Given the i measurement of an ICS event there are usually two common approaches to include it in Equation 2.5,

22 2. Methods 16 Separation: each possible LOR is separated and added with an appropriate weight (η). a i j J j= a i jn k j η 1 a i1 j J j= a i 1 jn k j + η 2 a i2 j J j= a i 2 jn k j (2.6) Selection: only the most probable LOR is considered, or in case of ignorance the LOR will be selected randomly. a i j J j= a i jn k j η 1 a itj J j= a i tjn k j (2.7) The weights η t for t = 1, 2 are the probability that each LOR is the correct one. There are several ways to set these probabilities. The algorithm described by Gillam et al. uses the differential Klein-Nishina cross-section, computed using the geometrical scattering angle taken from the interaction location. If no extra information is given, a uniform η =.5 is assumed. Figure 2.5: Three different slices from reconstructed images of a NEMA phantom using either Golden or ICS events. Adapted from Gillam et al. For the AX-PET reconstruction, Gillam et al., propose an alternative approach to include the ICS events.

23 2. Methods 17 Inclusion or v-projection: it incorporates the full probability function associated to the measurement. a i j η 1 a i1 j + η 2 a i2 j (2.8) Using this method both LOR are kept, forming the v-shape, but with appropriate weights assigned. In this study, η =.5 is used, which is equivalent to a randomized selection. Fig 2.5 presents a comparison of the three different approaches to include ICS events on AX-PET. Data were reconstructed using simulated one pass list-mode (SOPL) [13]. SOPL is essentially a multi-ray algorithm; the method models the full detection response with less computational burden by spreading calculations over multiple iterations and with some approximations. The matrix elements are calculated on-the-fly (only during the reconstruction process) and events are handled in list-mode. The algorithm uses a bootstrap Monte-Carlo sampling to detect uncertainty functions and generate new rays at each iteration, the SOPL adds a blurring over the detector comparing to single one ray. For the present work, each measurement is modeled using five rays per LOR candidate. Each ray is simulated using different distributions (random flat in y, exponential in x and gaussian in z) with (dx, dy, dz) = [2.5, 2.5,.5] for the standard geometry, and (dx, dy, dz) = [2.5,,.5] for the novel geometry. The parameters used are optimized based on the cross-section of the LYSO crystals, 3 3 mm 2 and on the axial resolution. With this approach to image reconstruction, the treatment of ICS measurements interacts with the computational burden as both separation and inclusion incur a computational penalty. Figure 2.6: Schematic draw of a detector crystal and the SOPL algorithm. For each ray, five more rays are generated following a certain distribution; in the case of the z coordinate a gaussian distribution around the center of the crystal.

24 Chapter 3 Materials 3.1 Full Ring Brain Scanner AX-PET was initially conceived for brain imaging. After successful tests with small animals, we are now interested in studying and evaluating the performance of a brain scanner based on the AX-PET concept. Two scanner designs are proposed: a conservative one having a full ring of AX-PET modules, and an optimized design based on a slanted arrangement of the crystal layers. The latter has been designed at CERN in order to reduce the gaps between modules. In this configuration each 8 crystal layer is slanted 2 degree along the Z axis. Lower gaps will be translated in a better homogeneity of the field of view (FOV) which has the potential to improve the sensitivity performance of the system. The full ring AX-PET scanner based on the original demonstrator design contains 48 modules arranged over a ring with a diameter of 468 mm. In the novel slanted design the ring contains 3 layer blocks with a diameter of 476 mm. Since in the standard configuration one module consists of 48 crystals to which the trigger for coincidence scoring is applied, the same read-out logics is applied in the case of the novel geometry. In the latter, one module is defined as the sum of 6 consecutive layers, thus yielding a 5 module full-ring scanner. The slanted structure is based on the geometry of the high-energy physics detectors, where more weight is given to improve detection rather than the final product cost. Relevant parameters of both scanners for the coincidence scoring are: A 5 ns coincidence window is applied to select coincidences. 18

25 3. Materials 19 A threshold of [4,65] kev is applied at module level. Events with no associated WLS signal (e.g. interactions occurring at the edges of the crystals where no WLS strips are placed) are neglected. Additionally, each coincidence is stored together with a flag to identify the event type (true, random or phantom scatter). The LORs to be reconstructed are assigned to the center of the crystal in order to mimic the real acquisition conditions in PET scanners. (a) (b) Figure 3.1: Monte Carlo model of the conventional geometry (A) and the novel geometry (B). One can see the slanted configuration of the novel geometry which implies a better fit of the crystals and WLS. The effect of the slanted geometry can be noted in the sensitivity maps presented in Figure 3.2. For the standard geometry, the effect of the air gaps between the crystals can be observed as inhomogeneities on the sensitivity matrix. (a) (b) Figure 3.2: Comparison of sensitivity map for the conventional geometry (A), and the novel geometry (B). The homogeneity of the slanted geometry in comparison to the standard geometry can be appreciated.

26 3. Materials Phantoms In order to study the performance of the two full ring systems previously described, different phantoms have been simulated: a Cologne phantom for resolution studies and a NEMA phantom for image quality assessment Cologne High Resolution Phantom The idea behind the use of this phantom is to test the resolution of the system[14]. It consists of a container and two different inserts, which can be filled with radioactivity diluted in water. The hot insert of the Cologne High Resolution Phantom consists of a 28 mm thick lucite disk with a diameter of 219 mm. It is divided into areas with holes that have different diameters and center-to-center spacings, figure 3.3. The holes diameters are 2 mm with a spacing of 4 mm, 3 mm with a spacing of 6 mm, and 4 mm with spacing of 8 mm or 1 mm. (a) (b) Figure 3.3: Cologne High Resolution Phantom, A) schematic and B) real image. Hot inserts can be appreciated NEMA HOT-COLD The evaluation of the image quality using the National Electrical Manufacturers Association (NEMA) NU 2-27 [15] requires a test phantom only suitable for a scanner with a ring diameter of at least 35 mm. Then, the image quality test is designed to emulate

27 3. Materials 21 a whole-body imaging performance, and therefore is not appropriate for a brain-only tomograph. The same standard recommends the previous version, the NU [16], as a better choice for brain-only tomographs, although is not either designed for such equipments. The proposed phantom -usually refereed as Hot-Cold phantom- consists of a 2 cm diameter and 2 cm long cylinder filled with water and with two cylindrical inserts of 5 cm, usually one filled with activity (hot insert) and the other without (coldinsert). For the AX-PET performance analysis the phantom was slightly modified, 3.4a. The length of the phantom was reduced to 6 cm to adapt to the AX-PET FOV -which is not yet optimized for brain applications- and two more inserts of 4 mm diameter were added, one filled with activity and the other one not. This was performed in order to study the detection capability of small and big regions. (a) (b) Figure 3.4: A) Schematic draw of the NEMA modified phantom. B) Regions of interest analyzed. 3.3 Simulation setup The total activity in each phantom was set according to the computed noise equivalent count rate curve (NEC). NEC is a common metric used to describe the effective number of counts measured by a PET scanner as a function of the activity in the FOV. As commented in section 1, the main sources of statistical error in a PET system are random and scatter events, but only true events are what we want. The NEC is defined to show this effect as: NEC = T 2 T + S + R, (3.1)

28 3. Materials 22 where T, S and R are the true, scatter and random coincidences, respectively. For both AX-PET geometries, previous studies have shown that the NEC curve presents a maximum at about 6 MBq. phantom 2 cm long. The studies of the NEC were done with a uniform In case of the Cologne Phantom the total activity was set to the maximum of the NEC, this is 6 MBq. The activity of each sphere can be seen in Table 3.1. Table 3.1: Source setup for the Cologne phantom. The phantom is composed of 32 spheres of different radii and activity with a total activity of 6 MBq. Nº Radii (mm) Concentration (kbq/mm 3 ) In the case of the NEMA phantom the total activity was set at 24 MBq, lower than the NEC peak in order to work in a fiducial region. Each hot region of the phantom simulates possible brain lesions; in brain imaging sometimes lesions are difficult to distinguish from background activity, depending in the radiopharmaceutical employed, and tumor size at a certain stage. Afterwards, in order to simulate all possibilities in clinical practice, we used three different ratios between the hot inserts and the background, known as lesion-to-background ratio (LBR). The three LBR chosen were 2:1, 5:1 and 1.2:1. At the moment, the AX-PET reconstruction method does not use any attenuation correction. Then, in order to be confident with the results, in the presented study instead of water the phantom was filled with air. Similarly, in an initial attempt simulations were reconstructed only with true events, this is without any scatter or random events. Either for the Cologne Phantom and the NEMA Hot-Cold, the time of simulation was set to achieve at least one million golden events. 3.4 Image Analysis We are interested in quantifying the capability of the AX-PET system to perform brain imaging, considering different features of the AX-PET. Therefore, to estimate which

29 3. Materials 23 provides better image quality, we need to use the figures of merits (FOM) according to the tasks brain PET was designed for. A series of regions of interest (ROI) were extracted from the phantom data, figure 3.4b, and the following FOM for the NEMA Hot-Cold phantom were computed: Root-Mean-Square Error (RMSE): the discrepancy between the known emitted source and the MC simulation were computed using the RMSE. j (n j S j ) 2 RMSE = N (3.2) where n j and S j are the pixel values of the reconstructed image and the simulation respectively and N is the total number of voxels. Thus FOM is used also to study the global convergence of the image with iterations. It can be applied to all the reconstructed images or to a certain structure, as the hot insert. Signal-to-Noise Ratio: it compares the level of a desired signal to the level of background noise. It is defined as the ratio of signal to noise, SNR = µ U σ U, (3.3) where µ U and σ U refer to the mean and standard deviation of a uniform background region of the Hot-Cold phantom. Contrast: it refers to differences in intensity in parts of the image corresponding to different levels of radioactive uptake. Thus the contrast of the lesion is defined as C X = µ X µ U µ X + µ U, (3.4) where µ X can be any of the two hot regions of the Hot-Cold phantom which simulates a lesion. Contrast-to-Noise Ratio (CNR): even when the size of an object is substantially larger than the limiting spatial resolution of the image, noise can impair detectability, especially if the object has low contrast. A better definition of image contrast for noisy images is the CNR, CNR X = C X σ U (3.5)

30 3. Materials 24 where, as contrast, X can be any of the two hot regions that simulate a lesion. Spill-over ratio: the ratio of the mean in each cold region to the mean of the background uniform area was reported as spill-over ratio, SOR = µ C µ u, (3.6) where C can be any of the two cold regions of the Hot-Cold phantom. This parameter can give an idea about the inclusion of incorrect LORs in the reconstruction process due to scatter, random or ICS events. For an ideal image the value expected for a cold region is. Recovery coefficient (RC): this parameter indicates how similar is the activity concentration of a ROI to the expected value. RC X = For an ideal reconstructed image RC is equal to 1. µ X µ xexpected. (3.7) The RC value is affected by the resolution of the system and the consequent partial volume effect, by the sensitivity correction applied to the image, as well as by the cleanness of the data since random and scatter events can spread activity. Previous to the image analysis, in order to be able to compute some quantitative parameters, it is important to normalize the values of the image to some unit. In the present work we chose to normalize the image to the known background concentration, then each voxel has the value of Bq/ml (the voxel size chosen for the image reconstruction is mm 3 ).

31 Chapter 4 Results and discussion 4.1 Cologne Phantom The results for the Cologne phantom are presented in figures 4.1 and 4.2. Only golden events are selected, with a filter on scatter and random events. Images are reconstructed with golden and ICS counts for the standard geometry, and golden and ICS counts for the novel geometry. Both geometries present a good resolution performance. One can appreciate all sizes of spheres and different spacing, including the 1 mm spheres. From the plots of figures 4.2, an increase of the resolution in the central smallest spheres for the novel geometry can be observed, in comparison to the standard. Presented images correspond to iteration 1. x x (a) (b) Figure 4.1: Reconstruction of the Cologne phantom for the A) standard geometry, and B) novel geometry. 25

32 4. Results and discussion Standard Novel Counts (Arb. Units) (a) mm (b) Standard Novel Counts (Arb. Units) (c) mm (d) Figure 4.2: Plot profiles for the Cologne phantom for two different sets of spheres. 4.2 NEMA HOT-COLD Table 4.1 summarizes a list of all reconstructions performed and event selection. Most of the images have been reconstructed for both golden and golden with ICS events, to estimate the impact of ICS inclusion on the image. A more comprehensive study is performed for the 5:1 LBR, where images were reconstructed with and without scatter and random event rejection. Table 4.3 presents the scatter and golden events of all Table 4.1: List of all simulations and reconstructions performed for the NEMA phantom. It includes both geometries (standard and novel), if the reconstruction uses only golden events or golden and ICS, and if the simulations includes scatter and random events (s1) or not (s). Standard Novel Golden Golden & ICS Golden Golden & ICS s s1 s s1 s s1 s s1 1:1.2 x x x x 1:5 1:2 x x x x

33 4. Results and discussion 27 simulations. One can notice the higher sensitivity of the novel geometry, with more golden events and a higher ratio of golden events per ICS events. Table 4.2: Counts of golden events and ICS events depending on the lesion-tobackground ratio. LBR Standard Novel Ratio Golden Events ICS Ratio Golden Events ICS Ratio 1: E6 2.9E E6 2.38E :5 2.68E6 2.7E E6 2.37E :2 2.67E6 2.2E E6 2.35E Table 4.3: Counts of golden events, scatter in phantom and random events depending on the lesion-to-background ratio. LBR Standard Novel Ratio Scatter Random Scatter Random 1: : : For an LBR of 5:1, Figure 4.3 presents the central slice of the NEMA phantom. At first sight, both geometries present similar results, although it can be observed that in the slanted geometry appears a central artifact. In none of the two geometries the 4 mm lesion can be appreciated, requiring a higher LBR, see Appendix A. Moreover, in the reconstructions using golden and ICS events, Figure (4.3d and 4.3d) the image gains definition despite the cold region increases activity. Figure 4.4 presents a comparison between images obtained for both geometries with an LBR of 1.2:1 and 2:1. The small hot lesion can be clearly observed for the LBR of 2:1, in contrast to lower LBR; see also Figure 4.3. The novel geometry presents a slightly higher definition of the small lesion in agreement with the Cologne phantom, Figure Reconstructed image analysis Figure 4.5 presents the variation of the RMSE as a function of the iteration. Reconstructed data from Table 4.1 include scatter and randoms. For all different concentrations the minimum occurs between iterations 1 and 15, where minimum RMSE value is achieved by the standard geometry. The novel geometry presents a faster RMSE increase with iteration. In both geometries the inclusion of ICS events reduces the slope of

34 4. Results and discussion (a) (b) (c) (d) Figure 4.3: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesionto-background ratio 5:1. A) standard geometry using golden events, B) novel geometry using golden events, C) standard geometry using golden and ICS events, D) novel geometry using golden and ICS events. Random and scatter events are included. Images refer to iteration 1. the increase. In all simulated sets the standard geometry behaves better than the novel one, but once ICS events are included, the RMSE of the novel geometry gains over the standard with only golden events. The best RMSE is obtained for an LBR of 5:1, still comparable to the value achieved in the case of LBR 1.2:1. Larger RMSE values are computed for the highest 2:1 LBR, for both geometries. Figure 4.6 presents the RMSE of the hot 5 mm diameter insert as a function of the standard deviation of the uniform background ROI. The minimum value is between iterations 1 and 15 for both geometries. One can see a faster increases in the standard deviation and RMSE of the insert for the novel geometry, and for both geometries with the inclusion of ICS events. Nevertheless, for LBR of 1.2:1 and 5:1 all curves present the same tendency. An LBR of 2:1 novel geometry with the inclusion of ICS events shows a lower slope, Figure 4.6c. Figure 4.7 presents the value of RC for the 5 mm hot insert as a function of the number of iterations. The highest RC is obtained for the lowest LBR 1.2:1, although the convergence to the stability is lower for this ratio. Standard geometry achieves values closer to

35 4. Results and discussion (a) (b) (c) (d) Figure 4.4: Central slice of the NEMA Hot-Cold phantom reconstruction using only golden events for a lesion-to-background ratio of A) 1.2:1 and standard geometry, B) 1.2:1 and novel geometry, A) 2:1 and standard geometry, B) 2:1 and novel geometry. The reconstruction was stopped at 1th iteration. 1 x Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS.2.15 Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS.2 Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS RMSE 6 RMSE.1 RMSE Number of iterations Number of iterations Number of iterations (a) Figure 4.5: RMSE as a function of the number of iterations, for the novel and standard geometries and using only golden events or golden+ics events. LBR ratios of A) 1.2:1, B) 5:1, and C) 2:1. unity compared to the novel geometry. On the other hand, the inclusion of ICS events reduces the RC. For the 4 mm hot insert, the RC values as a function of the iterations are shown in Figure 4.7. The three figures present a slower convergence of the values compared to the previous figures. The RC stabilizes at iteration 4 in the case of 2:1 LBR, while no regular trend is seen for lower LBR 1.2:1.The size of the lesion can lead to partial volume

36 4. Results and discussion 3 5 mm insert RMSE Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS 5 mm insert RMSE Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS 5 mm insert RMSE Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Uniform ROI standard deviation (a) Uniform ROI standard deviation (b) Uniform ROI standard deviation (c) Figure 4.6: RMSE of the 5 mm diameter hot insert vs the standard deviation of a uniform background ROI, for the novel and standard geometry and using only golden events or golden+ics events. LBG ratios of A) 1.2:1, B) 5:1, and C) 2:1. Each point represents an increase of 5 iterations starting from Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (a) Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (b) Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (c) Figure 4.7: Recovery coefficient as a function of the number of iterations, for the novel and standard geometry and using only golden events or golden+ics events. LBG ratios of A) 1.2:1, B) 5:1, and C) 2: Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (a) Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (b) Recovery Coefficient Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Number of iterations (c) Figure 4.8: Recovery coefficient for the 4 mm lesion. Recovery coefficient as a function of the number of iterations, for the novel and standard geometry and using only golden events or golden+ics events. LBG ratios of A) 1.2:1, B) 5:1, and C) 2:1.

37 4. Results and discussion 31 effects, with consequent spreading of the activity to nearby voxels, probably more visible in the case of the lowest contrast scenario. According to previous results, all parameters for the analysis were computed at iteration 1 of the reconstruction. The difference with the expected contrast is presented in figure. Values are similar for both geometries, although the novel geometry presents slightly better results at low ratios. Contrast for both systems converges to a similar lower value at higher contrast. The difference with the expected contrast increases dramatically for low ratios and with the size of the lesion. Absolut difference with expected contrast (%) Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Ratios Absolut difference with expected contrast (%) Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Ratios (a) (b) Figure 4.9: Difference with the expected contrast vs the LBR, for A) 5 mm diameter hot insert, and B) 4 mm diameter hot insert. The SOR is represented in figure 4.1. As expected, the inclusion of ICS events slightly increases the reconstruction of false LOR, which is translated into activity in cold zones. The SOR increases as LBR increases or as lesion size decreases. At the same time, the standard geometry presents a better SOR curve. The SNR for the background ROI is presented in figure 4.11a; it decreases as the LBR increases, which is due to less activity in the background ROI and consequent noise increase. At the same time, it increases with the inclusion of ICS events, which could be related to an enhancement of data statistics, thus improving image noise. The novel geometry presents a better SNR, which can be related to a more uniform image background. As previously mentioned, for noisy images CNR can be a better figure of merit than pure contrast. Figure presents the CNR for both lesions, showing a comparable trend among

38 4. Results and discussion Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS 1.8 Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Spill Over Ratio.2 Spill Over Ratio Ratios Ratios (a) (b) Figure 4.1: Spill-over ratio vs LBR, for the A) 5 mm diameter hot insert, and B) 4 mm diameter hot insert Signal to Noise Ratio Standard Golden.2 Novel Golden Standard Golden+ICS Novel Golden+ICS Ratios (a) Figure 4.11: Signal-to-noise ratio vs LBR. the different systems. The standard geometry presents, for both Golden and Golden with ICS events, better values. At same time the inclusion of ICS events increases the CNR. That means that ICS inclusion on one side deteriorates the image contrast while improving the image noise by improving the statistics. The trend among the two figures usually results in better images when ICS events are reconstructed. As it can be seen, the detection of the small lesion can be only appreciated with higher LBR where CNR values are comparable with the largest hot lesion. 4.3 Comparison of AX-PET geometries From the results of the Cologne phantom, in terms of resolution both geometries present excellent results. At naked eye the smallest spheres of 1 mm radium can be appreciated, whose size is equal to the matrix resolution.

39 4. Results and discussion 33 Contrast to Noise Ratio Standard Golden Novel Golden Standard Golden+ICS Novel Golden+ICS Ratios (a) Contrast to Noise Ratio Standard Golden.5 Novel Golden Standard Golden+ICS Novel Golden+ICS Ratios (b) Figure 4.12: Contrast-to-noise ratio vs LBR for the A) 5 mm diameter hot insert, and B) 4 mm diameter hot insert. From image quality assessment, the novel geometry presents a promising higher uniformity in the FOV, which implies a more uniform sensitivity matrix, it does not present an enhancement in image quality but, on the contrary, the standard geometry seems to be superior to the slanted one. Appearance of an artifact at the centre of the image, specially for the novel geometry, suggests a problem with the employed sensitivity matrix. The method used to compute the sensitivity is less time consuming but compromises accuracy. At the same time, the uniformity of the sensitivity matrix implies an increase in detection sensitivity due to less gaps between detectors. Another point which could affect the image quality is the calculation of the system response elements using the SOPL algorithm. This method generates new rays for a given crystal associated to a LOR using different distributions, but the method was not optimized for a slanted geometry, what could implie that some rays are generated outside the crystal. From the point of view of the capability to perform a quantitative analysis of the activity, both geometries present comparable results, as the differences with the expected contrast are under 2% for normal LBR and for the big insert. For the small insert, errors on the contrast are above the 5%. In the case of the LBR of 1:1.2, the error associated to statistics makes it difficult to extract conclusions; a study with more counts needs to be performed.

40 4. Results and discussion Inclusion of ICS events As can be appreciated at naked eye, the inclusion of ICS events reduces noise in the images. This can be seen observing that there is a small decrease of the contrast but an increases of 2% on the CNR, in comparison to using only golden events. This effect is the same for both geometries. On the other hand, the only concern of using ICS events is the increase in the reconstruction of wrong LOR. This has a clear effect on the SOR parameter, which has maximum increase of 6%. There is also a decrease on the recovery coefficient for the LBR of 5:1 and 2:1, which could affect a quantitative analysis of activity. Nevertheless, an increase of the RC appears for the lower LBR, which shows the potential of ICS in cases where it is important to get more counts for an accurate image.

41 Conclusion and future outlook In this work we have studied the performance of a full ring scanner based on the AX- PET concept for brain imaging. AX-PET is a novel detector concept based on axially oriented crystals. The discrete geometry provides a 3D reconstruction of the gamma interaction point, and additionally yields a large fraction of ICS events that can be used to enhance the sensitivity of the system. The AX-PET detector was originally conceived for brain imaging, with the choice of 3 3 mm 2 crystal cross section. However, while the demonstrator was widely tested for small animals imaging, no previous study has been performed with respect to brain imaging. The presented work is the first attempt to investigate the potential of the AX-PET detector for brain imaging. In addition to the conventional AX-PET design, a second scanner geometry was also studied with tilted layers of crystals, expected to provide a more homogeneous response in the FOV. The Cologne high resolution phantom confirms the good spatial resolution of the system (in both geometrical configurations). Hot-Cold NEMA phantoms with different contrast ratios and lesion sizes have been simulated and reconstructed. With respect to extended sources, the conventional system provides better images in terms of noise and image contrast than the novel geometry. Such a result is against the expectations motivated by the more uniform sensitivity matrix of the novel geometry. However both scanners are unable to return with good contrast the smallest 4 mm lesion, only visible at highest contrast value (2:1). In order to understand the observed behavior several improvements are required. Among them we mention the need of a more accurate calculation of the sensitivity matrix. A dedicated Monte Carlo calculation to get a better sensitivity estimation may be required. Additionally, sensitivity changes when dealing with pure golden events and ICS events, thus possibly a dedicated calculation of the sensitivity matrix for both events selection may be of interest. The system matrix 35

42 Conclusion and future outlook 36 elements are computed on-the-fly. While the system response was widely tested for the standard scanner design, improvements may be required in the case of the novel configuration. Besides, the present study worked with a total number of counts lower than real studies statistics. The incorporation, during image reconstruction, of ICS data acquired simultaneously with golden measurements increases image quality and has potential to help identifying lesions in images with a low LBR. Since the last year the AX-PET collaboration started upgrading the detector, switching to digitalsipm, thus providing a better time resolution than conventional SiPM. The good time resolution promotes AX-PET to a potential Time-Of-Flight (TOF) system, with further chance to improve the image contrast. The benefits of TOF on brain images however are expected to be limited, even if higher resolution can help in random rejection whose fraction is not negligible for brain studies.

43 Appendix A Supplementary Data In this appendix we include a list of images of interest (a) (b) (c) (d) Figure A.1: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesionto-background ratio 2:1. A) standard geometry using golden events, B) novel geometry using golden events, C) standard geometry using golden and ICS events, D) novel geometry using golden and ICS events. The reconstruction was stopped at 1th iteration. 37

44 Appendix A. Supplementary Data (a) (b) (c) (d) Figure A.2: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesionto-background ratio 1.2:1. A) standard geometry using golden events, B) novel geometry using golden events, C) standard geometry using golden and ICS events, D) novel geometry using golden and ICS events. The reconstruction was stopped at 1th iteration.

45 Appendix A. Supplementary Data (a) (b) (c) (d) (e) (f) Figure A.3: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesionto-background ratio 1:5, only golden events, using a A) direct reconstruction of the true event localization (standard geometry), B) direct reconstruction of the true event localization (standard geometry), C) non inclusion of scatter or random events (standard geometry), D) non inclusion of scatter or random events (novel geometry), E) inclusion of scatter or random events, normal reconstruction, (standard geometry), F) inclusion of scatter or random events, normal reconstruction, (novel geometry). For the reconstructions of true events it was stooped at iteration, for the rest at iteration 1.

46 Appendix A. Supplementary Data (a) (b) (c) (d) (e) (f) Figure A.4: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesionto-background ratio 1:5, only golden events, stopped at A) 2 iterations (standard geometry), A) 2 iterations (novel geometry), A) 5 iterations (standard geometry), A) 5 iterations (novel geometry), A) 1 iterations (standard geometry), A) 1 iterations (novel geometry).