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Universitat de Valencia
Master Thesis
A full-brain PET scanner based on theAX-PET concept: Monte Carlo
performance study
Author:
Gabriel Reynes-Llompart
Principal Supervisor:
Paola Solevi, PhD
Co-Supervisor:
Josep F. Oliver, PhD
Master Universitari en Fısica Medica
September 2014
Contents
Contents i
Abstract iii
Abbreviations iv
Rationale v
1 Introduction 1
1.1 PET imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Working principles of PET imaging . . . . . . . . . . . . . . . . . . 1
1.1.2 Resolution limitations . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Types of coincidences . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.4 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 PET radiopharmaceuticals . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Brain Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Methods 9
2.1 AX-PET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 AX-PET proof of concept . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Reconstruction algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Materials 18
3.1 Full Ring Brain Scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Phantoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.1 Cologne High Resolution Phantom . . . . . . . . . . . . . . . . . . 20
3.2.2 NEMA HOT-COLD . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Simulation setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Image Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4 Results and discussion 25
4.1 Cologne Phantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 NEMA HOT-COLD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.1 Reconstructed image analysis . . . . . . . . . . . . . . . . . . . . . 27
4.3 Comparison of AX-PET geometries . . . . . . . . . . . . . . . . . . . . . . 32
4.4 Inclusion of ICS events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
i
ii
Conclusion and future outlook 35
A Supplementary Data 37
Bibliography 41
UNIVERSITAT DE VALENCIA
Abstract
Facultat de Fısica
Grupo de Fısica en Imagen Medica
Master Universitari en Fısica Medica
A full-brain PET scanner based on the AX-PET concept: Monte Carlo
performance study
by Gabriel Reynes-Llompart1
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 20% 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.
Abbreviations
CT Computed Tomography
DOI Depth of Interaction
FDG 2-deoxy-2-Fluoro-d-Glucose
ICS Iinter-Crystal Scattering
LBR Lesion-to-Background Ratio
LOR Line of Response
MC Monte Carlo
MLEM Maximum-Likelihood Expectation-Maximization
MMPC Multi Pixel Photon Counters
NEMA National Electrical Manufacturers Association
PET Positron Emission Tomography
ROI Region Of Interest
TSL Threshold Single Level
SOPL Simulated One Pass List-mode
WLS WaveLength Shifter
iv
Rationale
The international AX-PET collaboration2 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 2008. 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 (IRIS3), part of the Institut de Fısica
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 phan-
toms. 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.
2AX-PET website at CERN.3IRIS website.
v
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.
1.1.1 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. 1.1.
1
1. Introduction 2
AZX −→ A
Z−1Y +01 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
0.096 cm2/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, theprocessing 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
1http://jens-maus.de/home
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 1.1.
1.1.2 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 scintilla-
tion detector intrinsic resolution of the PET scanner, which is due to solid angle
coverage and the underdetermination of the exact position of the interaction in-
side 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
(Ri ) 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 Rp 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.
1. Introduction 4
Table 1.1: Half life, maximum positron energy, and average positron range in waterof some nuclides commonly used in PET
Isotope Half-life (min)Maximum PositronEnergy (MeV)
Average PositronRange (mm)
11C 20.3 0.96 1.5213N 9.97 1.19 2.0515O 2.03 1.7 3.2818F 109.8 0.64 0.8382Rb 1.26 3.15 7.02
• 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 180 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 0.5 degree. The a-collinearity error (Ra) increases with the distance
between the two detectors.
• Reconstruction technique:
A factor on the total error (Kr) due to some reconstruction techniques is intro-
duced 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 Rl in the
event localization which deteriorates the spatial resolution.
Assuming that almost all the effects above add in quadrature, the total intrinsic recon-
structed spatial resolution is described by Equation 1.2.
RT = Kr
√R2i +R2
p +R2a +R2
l (1.2)
1.1.3 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.
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.
1. Introduction 6
Figure 1.3: Inter-crystal scatter event of one photon produced in the annihilationpair. In this example, one photon suffers Compton scattering inside one crystal andphotoelectric absorption in the next crystal. Two possible photon sequences resultingin 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.
1.1.4 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 [18F]FDG2 for oncological imag-
ing and several different pathologies. The success of PET imaging in clinical practice is
associated to [18F]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
22-deoxy-2-(18F)fluoro-d-glucose
1. Introduction 7
accelerated metabolism required by tumoral cells to replicate faster.
However, many PET compounds have been synthesized with other β+ emitters as 11C,
13N, 15O. 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 [18F]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 0.1% prevalence in western population. However, they are among the most
fatal cancers [3], being gliomas the most frequent primary brain tumors, with an inci-
dence of 70%. 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 2040 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 [18F]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 radio-
pharmaceutical [18F]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
1. Introduction 8
Table 1.2: Positron Emission Tomography radiopharmaceuticals.[6]
Compound Application
15O2 Oxygen metabolism and flow.11C methionine Amino acid metabolism.11C methylpiperone Dopamine receptor activity.18F FDG Glucose metabolism.18F fluoro-L-dopa Neurotransmitter.18F MISO Tumor hypoxia.
imaging, then it is possible to create dedicated brain PET scanners with a small detec-
tor 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 sen-
sitivity 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 [18F]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.
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 orienta-
tion 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 MPPC1 (Multi Pixel Photon Counters) to get the coordinates and the
1Geiger Mode Avalanche Photodiode (G-APD) also known as SiPM and MPPC.
9
2. Methods 10
(a) (b)
Figure 2.1: A) Drawing of a prototype of AX-PET module geometry. It is composedof six layers of eight crystals each interleaved with six layers of WLS. The MPPC aremounted in order to avoid dead areas. The crystals in adjacent layers are staggered byhalf a pitch size. B) Scheme of the method used for light propagation in the scintilla-tion 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 WLS3, and more than one WLS can detect
the light emitted by a given crystal (Si), making possible to get the Z position with a
higher resolution than the one obtained by a single WLS:
zevent =
∑∀i Si · zWLS,i
Stotal(2.1)
This design allows AX-PET to perform a 3D photon tracking and to identify the Comp-
ton interactions in the crystal matrix as ICS.
2.1.1 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 con-
sists 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 scin-
tillator crystals and 156 WLS strips. Crystals and strips are read-out by two different
2Cerium-doped Lutetium Yttrium Orthosilicate. Composition: Lutetium (72%), Yttrium (4%), Sili-con (6%), Oxygen (18%). Density: 7.1 g/cm3, refractive index: ∼ 1.8.
3The light is detected by about 3 different WLS.
2. Methods 11
types of MPPCs.
From the two modules fully assembled and characterized, Table 2.1 presents some num-
bers 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 resolu-tion measured at 511 keV. Data extracted from Bolle et al.
Resolution FWHM Compton eventsx,y z Energy
2.03 mm 1.79 mm 11.7% 25%
The potential of the AX-PET demonstrator to image small animals was successfully as-
sessed; the measurements were performed at the ETH4 radio-pharmaceuticals laboratory
where a mouse and a rat were injected with [18F]FDG and imaged by the two-modules
AX-PET system. The image of a rat injected with the [18F]FDG is shown in Fig 2.2.
Figure 2.2: Maximum intensity projections of the rat imaged using [18F]FDG, recon-structed with golden events and ICS events. Adapted from Gillam et al.
4http://www.radiochem.pharma.ethz.ch/
2. Methods 12
2.2 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 associ-
ated 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 meth-
ods 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.
GATE5 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 acquisi-
tions.
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 de-
velop 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
En, on the axial position of the interaction zn and on the depth of interaction in
the crystal xn. This is modeled as a Gaussian distribution of the number of
photoelectrons Npe, with Npe(i) photoelectrons on the ith strip:
Npe(i) =
N∑n=1
xiA(xn, En)e(zn−zi)
2
2σ2xn . (2.2)
5http://www.opengatecollaboration.org/
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, En, and the depth of the hit
within the crystal, xn.
(a) (b)
Figure 2.3: (A) Experimental and simulated setup for the characterization of theWLS response. Two WLS strips were adjusted underneath a LYSO crystal excitedby a collimated electron beam. Figure adapted from Solevi et al. (B) Monte Carlosimulation 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, deter-
mining 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 recon-
struct 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.
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 250 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 400 keV and 600 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:
τdt = Nwc · τwc + τ0(µs). (2.3)
Where Nwc is total number of hit channels (world count), τwc is the mean dead-
time per readout channel, and τ0 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 sta-
tistical 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 doc-
ument are obtained with the iterative Maximum-Likelihood Expectation-Maximization
6Pile-up effect: dead time due to signal pulses arriving closer in time than the pulse resolution timeof the system.
2. Methods 15
(MLEM) algorithm in the standard list-mode implementation. MLEM algorithm pro-
vides an estimation of the mean intensity from voxel j, λj :
λk+1j =
λkjsj
∑i∈M
aij∑Jj=0 aijλ
kj
where sj =
I∑i=0
aij (2.5)
where nkj denotes the value of the voxel j at iteration k and aij the probability that
an emitted photon from the voxel j is detected in a measurement of i, and sj is the
sensitivity matrix. For the list mode, M refers to the set of measurements.
Computing aij 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 aijis defined as the probability to detect the activity in voxel j in LOR yi, adapted fromP. 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,
2. Methods 16
• Separation: each possible LOR is separated and added with an appropriate weight
(η).ai′j∑J
j=0 ai′jnkj
≡ η1ai1j∑Jj=0 ai1jn
kj
+η2ai2j∑Jj=0 ai2jn
kj
(2.6)
• Selection: only the most probable LOR is considered, or in case of ignorance the
LOR will be selected randomly.
ai′j∑Jj=0 ai′jn
kj
≡ η1aitj∑Jj=0 aitjn
kj
(2.7)
The weights ηt 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 = 0.5 is assumed.
Figure 2.5: Three different slices from reconstructed images of a NEMA phantomusing either Golden or ICS events. Adapted from Gillam et al.
For the AX-PET reconstruction, Gillam et al., propose an alternative approach to in-
clude the ICS events.
2. Methods 17
• Inclusion or v-projection: it incorporates the full probability function associated
to the measurement.
ai′j ≡ η1ai1j + η2ai2j (2.8)
Using this method both LOR are kept, forming the v-shape, but with appropriate weights
assigned. In this study, η = 0.5 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 es-
sentially 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 sam-
pling 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, 0.5] for the standard geometry, and (dx, dy, dz) = [2.5, 0, 0.5] for
the novel geometry. The parameters used are optimized based on the cross-section of
the LYSO crystals, 3×3 mm2 and on the axial resolution.
With this approach to image reconstruction, the treatment of ICS measurements inter-
acts with the computational burden as both separation and inclusion incur a computa-
tional penalty.
Figure 2.6: Schematic draw of a detector crystal and the SOPL algorithm. For eachray, 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.
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 20 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 300
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 50 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
3. Materials 19
• A threshold of [400,650] 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 novelgeometry (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), andthe novel geometry (B). The homogeneity of the slanted geometry in comparison to the
standard geometry can be appreciated.
3. Materials 20
3.2 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.
3.2.1 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 10 mm.
(a) (b)
Figure 3.3: Cologne High Resolution Phantom, A) schematic and B) real image. Hotinserts can be appreciated.
3.2.2 NEMA HOT-COLD
The evaluation of the image quality using the National Electrical Manufacturers Associ-
ation (NEMA) NU 2-2007 [15] requires a test phantom only suitable for a scanner with
a ring diameter of at least 350 mm. Then, the image quality test is designed to emulate
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 2-1994 [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 20 cm diameter and 20 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 (cold-
insert).
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 ofinterest 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)
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 60 MBq. The studies of the NEC were done with a uniform
phantom 20 cm long.
In case of the Cologne Phantom the total activity was set to the maximum of the NEC,
this is 60 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 320spheres of different radii and activity with a total activity of 60 MBq.
NºRadii(mm)
Concentration(kBq/mm3)
120 1 69.6100 1.5 105.050 2 139.150 2 217.4
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 dis-
tinguish 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 20:1, 5:1 and
1.2:1.
At the moment, the AX-PET reconstruction method does not use any attenuation cor-
rection. 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
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.
RMSE =
√∑j(nj − Sj)2
N(3.2)
where nj and Sj 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 =µUσU
, (3.3)
where µU and σU 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
CX =|µX − µU |µX + µU
, (3.4)
where µX 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 detectabil-
ity, especially if the object has low contrast. A better definition of image contrast
for noisy images is the CNR,
CNRX =CXσU
(3.5)
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 =µCµu, (3.6)
where C can be any of the two cold regions of the Hot-Cold phantom. This param-
eter 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 ex-
pected for a cold region is 0.
• Recovery coefficient (RC): this parameter indicates how similar is the activity
concentration of a ROI to the expected value.
RCX =µX
µxexpected. (3.7)
For an ideal reconstructed image RC is equal to 1. 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 param-
eters, 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
1×1×1 mm3).
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 10·105 golden and 8·105 ICS counts for the standard geometry, and 11·105 golden
and 8·105 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 10.
0
2
4
6
8
10x 10
8
(a)
0
2
4
6
8
10x 10
8
(b)
Figure 4.1: Reconstruction of the Cologne phantom for the A) standard geometry,and B) novel geometry.
25
4. Results and discussion 26
(a)
50 100 150 200
0
0.2
0.4
0.6
0.8
1
1.2
mm
Co
un
ts (
Arb
. U
nits)
Standard
Novel
(b)
(c)
50 100 150 200
0
0.2
0.4
0.6
0.8
1
1.2
mm
Co
un
ts (
Arb
. U
nits)
Standard
Novel
(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 phan-tom. It includes both geometries (standard and novel), if the reconstruction uses onlygolden events or golden and ICS, and if the simulations includes scatter and random
events (s1) or not (s0).
Standard NovelGolden Golden
& ICSGolden Golden
& ICSs0 s1 s0 s1 s0 s1 s0 s1
1:1.2 x√
x√
x√
x√
1:5√ √ √ √ √ √ √ √
1:20 x√
x√
x√
x√
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-to-background ratio.
LBR Standard Novel
Ratio Golden Events ICS Ratio Golden Events ICS Ratio
1:1.2 2.69E6 2.09E6 1.28 2.72E6 2.38E6 1.141:5 2.68E6 2.07E6 1.30 2.74E6 2.37E6 1.151:20 2.67E6 2.02E6 1.32 2.76E6 2.35E6 1.32
Table 4.3: Counts of golden events, scatter in phantom and random events dependingon the lesion-to-background ratio.
LBR Standard Novel
Ratio Scatter Random Scatter Random
1:1.2 78 136584 72 1325211:5 73 134837 68 1307791:20 71 130719 68 126906
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 20:1. The small hot lesion can be clearly observed for the LBR of 20:1,
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 4.1
4.2.1 Reconstructed image analysis
Figure 4.5 presents the variation of the RMSE as a function of the iteration. Recon-
structed data from Table 4.1 include scatter and randoms. For all different concentra-
tions the minimum occurs between iterations 10 and 15, where minimum RMSE value
is achieved by the standard geometry. The novel geometry presents a faster RMSE in-
crease with iteration. In both geometries the inclusion of ICS events reduces the slope of
4. Results and discussion 28
0
10
20
30
40
50
60
70
80
90
100
(a)
0
10
20
30
40
50
60
70
80
90
100
(b)
0
10
20
30
40
50
60
70
80
90
100
(c)
0
10
20
30
40
50
60
70
80
90
100
(d)
Figure 4.3: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesion-to-background ratio 5:1. A) standard geometry using golden events, B) novel geometryusing golden events, C) standard geometry using golden and ICS events, D) novelgeometry using golden and ICS events. Random and scatter events are included. Images
refer to iteration 10.
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 20:1 LBR, for both geometries.
Figure 4.6 presents the RMSE of the hot 50 mm diameter insert as a function of the
standard deviation of the uniform background ROI. The minimum value is between
iterations 10 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 20:1 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 conver-
gence to the stability is lower for this ratio. Standard geometry achieves values closer to
4. Results and discussion 29
0
10
20
30
40
50
60
(a)
0
10
20
30
40
50
60
(b)
0
50
100
150
(c)
0
50
100
150
(d)
Figure 4.4: Central slice of the NEMA Hot-Cold phantom reconstruction using onlygolden events for a lesion-to-background ratio of A) 1.2:1 and standard geometry, B)1.2:1 and novel geometry, A) 20:1 and standard geometry, B) 20:1 and novel geometry.
The reconstruction was stopped at 10th iteration.
0 20 40 60 80 1002
4
6
8
10x 10
−3
Number of iterations
RM
SE
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
0 20 40 60 80 1000
0.005
0.01
0.015
0.02
Number of iterations
RM
SE
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
0 20 40 60 80 1000
0.005
0.01
0.015
0.02
Number of iterations
RM
SE
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
Figure 4.5: RMSE as a function of the number of iterations, for the novel and standardgeometries and using only golden events or golden+ICS events. LBR ratios of A) 1.2:1,
B) 5:1, and C) 20:1.
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 40 in the case of 20:1 LBR, while no
regular trend is seen for lower LBR 1.2:1.The size of the lesion can lead to partial volume
4. Results and discussion 30
0 5 10 15 20 25 30 350
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
50 m
m in
se
rt R
MSE
Uniform ROI standard deviation
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
0 5 10 15 20 250
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
50 m
m in
se
rt R
MSE
Uniform ROI standard deviation
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
0 5 10 15 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
50 m
m in
se
rt R
MSE
Uniform ROI standard deviation
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(c)
Figure 4.6: RMSE of the 50 mm diameter hot insert vs the standard deviation of auniform background ROI, for the novel and standard geometry and using only goldenevents or golden+ICS events. LBG ratios of A) 1.2:1, B) 5:1, and C) 20:1. Each point
represents an increase of 5 iterations starting from 0.
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(c)
Figure 4.7: Recovery coefficient as a function of the number of iterations, for thenovel and standard geometry and using only golden events or golden+ICS events. LBG
ratios of A) 1.2:1, B) 5:1, and C) 20:1.
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
Number of iterations
Re
co
ve
ry C
oe
ffic
ien
t
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(c)
Figure 4.8: Recovery coefficient for the 4 mm lesion. Recovery coefficient as a functionof 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) 20:1.
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
10 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.
0 5 10 15 200
20
40
60
Ab
solu
t d
iffe
ren
ce
with
exp
ec
ted
co
ntr
ast
(%
)
Ratios
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
0 5 10 15 200
50
100
150
200
250
300
350
400
450
Ab
solu
t d
iffe
ren
ce
with
exp
ec
ted
co
ntr
ast
(%
)
Ratios
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
Figure 4.9: Difference with the expected contrast vs the LBR, for A) 50 mm diameterhot insert, and B) 4 mm diameter hot insert.
The SOR is represented in figure 4.10. 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 back-
ground.
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
4. Results and discussion 32
0 5 10 15 200
0.1
0.2
0.3
0.4
Sp
ill−
Ove
r R
atio
Ratios
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(a)
0 5 10 15 200
0.2
0.4
0.6
0.8
1
Sp
ill−
Ove
r R
atio
Ratios
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
Figure 4.10: Spill-over ratio vs LBR, for the A) 50 mm diameter hot insert, and B)4 mm diameter hot insert.
0 5 10 15 200
0.2
0.4
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na
l−to
−N
ois
e R
atio
Ratios
Standard Golden
Novel Golden
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Novel Golden+ICS
(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.
4. Results and discussion 33
0 5 10 15 200
0.05
0.1
0.15
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0.25
Co
ntr
ast−
to−
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ise
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tio
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(a)
0 5 10 15 20−0.1
−0.05
0
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ntr
ast−
to−
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ise
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tio
Ratios
Standard Golden
Novel Golden
Standard Golden+ICS
Novel Golden+ICS
(b)
Figure 4.12: Contrast-to-noise ratio vs LBR for the A) 50 mm diameter hot insert,and B) 4 mm diameter hot insert.
From image quality assessment, the novel geometry presents a promising higher unifor-
mity 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 20% for normal LBR and for the big insert. For the small insert, errors on
the contrast are above the 50%. 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.
4. Results and discussion 34
4.4 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 20% 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 reconstruc-
tion 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 20:1, 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.
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
mm2 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 (20:1). 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
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.
Appendix A
Supplementary Data
In this appendix we include a list of images of interest.
0
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150
(a)
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(b)
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Figure A.1: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesion-to-background ratio 20:1. A) standard geometry using golden events, B) novel geometryusing golden events, C) standard geometry using golden and ICS events, D) novel ge-ometry using golden and ICS events. The reconstruction was stopped at 10th iteration.
37
Appendix A. Supplementary Data 38
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Figure A.2: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesion-to-background ratio 1.2:1. A) standard geometry using golden events, B) novel geom-etry using golden events, C) standard geometry using golden and ICS events, D) novelgeometry using golden and ICS events. The reconstruction was stopped at 10th itera-
tion.
Appendix A. Supplementary Data 39
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(e)
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Figure A.3: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesion-to-background ratio 1:5, only golden events, using a A) direct reconstruction of the trueevent localization (standard geometry), B) direct reconstruction of the true event lo-calization (standard geometry), C) non inclusion of scatter or random events (standardgeometry), D) non inclusion of scatter or random events (novel geometry), E) inclusionof scatter or random events, normal reconstruction, (standard geometry), F) inclusionof scatter or random events, normal reconstruction, (novel geometry). For the recon-
structions of true events it was stooped at iteration 0, for the rest at iteration 10.
Appendix A. Supplementary Data 40
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Figure A.4: Central slice of the NEMA Hot-Cold phantom reconstruction for a lesion-to-background ratio 1:5, only golden events, stopped at A) 20 iterations (standardgeometry), A) 20 iterations (novel geometry), A) 50 iterations (standard geometry), A)50 iterations (novel geometry), A) 100 iterations (standard geometry), A) 100 iterations
(novel geometry).
Bibliography
[1] W. W. Moses, Nuclear Instruments and Methods in Physics Research Section A: Ac-
celerators, Spectrometers, Detectors and Associated Equipment 648, S236 (2011).
[2] M. E. P. Simon R. Cherry, James A. Sorenson, Physics in nuclear medicine, 4th
edition (Elsevier Sounders, 2012).
[3] S. Bauer, R. Wiest, L.-P. Nolte, and M. Reyes, Physics in medicine and biology 58,
R97 (2013).
[4] J. Jimenez Bonilla and J. Carril Carril, Revista Espanola de Medicina Nuclear e
Imagen Molecular (English Edition) 32, 301 (2013).
[5] C. Schiepers and M. Allen-Auerbach, Diagnostic nuclear medicine (Springer, 2006).
[6] H. A. Ziessman, J. P. O’Malley, and J. H. Thrall, Nuclear medicine: the requisites
(Elsevier Health Sciences, 2013).
[7] P. Beltrame, E. Bolle, a. Braem, C. Casella, E. Chesi, N. Clinthorne, R. De Leo,
G. Dissertori, L. Djambazov, V. Fanti, et al., Nuclear Instruments and Methods in
Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment 654, 546 (2011), ISSN 01689002.
[8] P. Beltrame, E. Bolle, A. Braem, C. Casella, E. Chesi, N. Clinthorne, R. D. Leo,
G. Dissertori, L. Djambazov, C. Joram, et al. (????).
[9] E. Bolle, A. Braem, C. Casella, E. Chesi, N. Clinthorne, E. Cochran, R. De Leo,
G. Dissertori, G. Djambazov, V. Fanti, et al., Nuclear Instruments and Methods in
Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated
Equipment 617, 214 (2010).
41
Bibliography 42
[10] J. E. Gillam, P. Solevi, J. F. Oliver, C. Casella, M. Heller, C. Joram, and M. Rafecas,
Physics in medicine and biology 59, 4065 (2014).
[11] S. Jan, G. Santin, D. Strul, S. Staelens, K. Assie, D. Autret, S. Avner, R. Barbier,
M. Bardies, P. Bloomfield, et al., Physics in medicine and biology 49, 4543 (2004).
[12] P. Solevi, J. F. Oliver, J. E. Gillam, E. Bolle, C. Casella, E. Chesi, R. De Leo,
G. Dissertori, V. Fanti, M. Heller, et al., Physics in medicine and biology 58, 5495
(2013), ISSN 1361-6560.
[13] M. G. Bickell, L. Zhou, and J. Nuyts (????).
[14] M. Schmand, K. Wienhard, M. Casey, L. Eriksson, W. Jones, J. Reed, J. Treffert,
M. Lenox, P. Luk, J. Bao, et al., Nuclear Science Symposium, 1999. Conference
Record. 1999 IEEE 2, 1067 (1999).
[15] N. E. M. Association, NEMA Standards Publication NU 4-2008: Performance Mea-
surements of Positron Emission Tomographs (2008).
[16] N. E. M. Association, NEMA Standards Publication NU 4-2008: Performance Mea-
surements of Positron Emission Tomographs (1994).