Contents
1 Introduction 4
2 Combined PET/MRI systems 6
2.1 Medical Imaging techniques . . . 6
2.2 Multimodal imaging techniques . . . 11
2.3 Sequential PET/MRI devices . . . 14
2.4 Integrated PET/MR devices . . . 14
3 The PET insert approach to the PET/MRI combination 19 3.1 Technical challenges . . . 19
3.2 Technical developments in PET/MRI inserts . . . 21
4 The PET insert prototype MADPET4 30 4.1 The MADPET4 prototype . . . 30
4.2 The 7 Tesla GE/Agilent Discovery MR 901 scanner for small animals . . . 33
5 Simulation with the MADPET4 components in the MRI elds 36 5.1 The 3D models of the main MADPET4 components . . . 38
5.2 Uniformity of the static magnetic eld . . . 42
5.3 Uniformity of the RF magnetic eld . . . 44
5.4 Heating induced by RF magnetic eld . . . 46
6 Results and discussion 49 6.1 Uniformity of the static B0 magnetic eld . . . 49
6.2 Heating of the components . . . 58
6.3 Uniformity of the RF B1 magnetic eld . . . 64
6.4 MRI images analysis . . . 69
A The nite element method 76
A.1 De nition of the problem . . . 76
A.2 Approximation of u(x) . . . 77
A.3 The Galerkin method . . . 79
List of abbreviations
APD: Avalanche PhotoDiode CT: Computed Tomography EEG: ElectroEncephaloGram FDG: FluoroDeoxyGlucose FGRE: Fast GRadient Echo FOV: Field Of View
GRE: Gradient Echo LOR: Line Of Response
LVDS: Low Voltage Dierential Signalling MRI: Magnetic Resonance Imaging PCB: Printed Circuit Board
PET: Positron Emission Tomography PMT: PhotoMultipler Tube
ppm: Part Per Million
PSAPD: Position Sensitive Avalance PhotoDiode RF: RadioFrequency
ROI: Region Of Interest SDM: Single Detector Module SE: Spin Echo
SiPM: Silicon PhotoMultiplier SNR: Signal to Noise Ratio SPU: Single Processing Unit TR: Repetition Time
Chapter 1
Introduction
In the last two decades, the eld of medical imaging has seen an increasing interest and development of multimodal techniques. Aim of such techniques is to merge images from dierent diagnostic imaging devices to provide com-plementary information on a particular disease or a particular physiological process. Among the existing multimodal techniques, during the last 10 years the combination of Positron Emission Tomography (PET) and Magnetic Resonance Imaging (MRI) is being subject of intensive research. The PET technique is able to trace tiny amounts of radioactive tracers, allowing in vivo imaging of several functional processes, as blood perfusion of the heart and brain or the tumour cells metabolism, but it lacks the ability to resolve detailed anatomical structures. On the contrary, this is the main character-istic of a MRI scanner: it excels in providing anatomical images with an high spatial resolution. Furthermore it oers a variety of functional and biochemi-cal methods, such as spectroscopy, diusion and perfusion. Compared to the already existing PET/CT (Computed Tomography), PET/MRI devices are designed to perform simultaneous data acquisitions; moreover, MRI shows a better soft-tissue contrast and higher spatial resolution than the CT, and does not require ionizing radiation.
The design of a combined PET/MRI is not an easy challenge, because the two systems suer of mutual interferences: the PET components, specially electronics, are in uenced by RadioFrequency (RF) pulses and switching eld gradients used in the MRI sequences, while the presence of the PET in the MRI modify the intensity and uniformity of the magnetic elds, with a consequent introduction of artefacts in the MRI images. Since the perfor-mance of the two systems must not decrease in a combined con guration, special care has to be taken in the design of the combined PET/MRI system. Among the several ways to combine PET and MRI, the most aordable one is to build a PET detector that can be placed inside an already existing MRI scanner: this is called the PET insert approach. This solution allows to combine PET and MRI without modify the MRI scanner, that is the most
expensive device, and the PET insert can be easily installed and removed from the bore of the MRI.
Since the PET insert is placed inside the MRI, a careful design of ge-ometry, components, materials and electronics must be followed to minimize the mutual interferences between the two systems. Components made of magnetic compatible material have to be chosen for the PET system, to minimize alterations of the magnetic elds that would produce artefacts in the MRI images; moreover, PET components must be insensitive to the magnetic elds, to avoid PET performance degradation; nally special care have to be taken for the PET preampli cation and readout electronics, be-cause of the interferences with the RF magnetic eld and the gradients of the MRI. Such technical challenges have brought the PET insert to become, in the last decade, a subject of increasing studies by several research groups. Some PET inserts have been successfully built, while other are currently studied, with dierent choices in terms of geometry, components, materials and electronics.
Aim of this thesis is to study the impact of a PET insert in a MRI scanner. This PET insert under study is called MADPET4 and it has been designed to work in an MRI scanner for small animals. The MADPET4 hardware prototype is under construction at the Klinikum rechts der Isar of the Technische Universität Müenchen, Munich, Germany. The core of the thesis is the simulation of speci c MADPET4 components (detectors and Printed Circuit Boards) that has been carried out through the 3D simu-lation software COMSOL Multiphysics, focusing on the in uence of these components on the homogeneity of the static 7 Tesla magnetic eld and the RF magnetic eld of the MRI, and on the heating of the components caused by the electrical currents induced by the RF magnetic eld.
This thesis is organised as follows: in Chapter 2 Positron Emission To-mography, Magnetic Resonance and dierent methods to combine PET and MRI are described; in Chapter 3 PET insert approach to the combination of PET and MRI is presented; technical challenges will be discussed and exist-ing PET insert solutions will be reviewed; Chapter 4 presents the MADPET4 prototype and the MRI scanner in which the MADPET4 will be inserted; in Chapter 5 a detailed description of the simulation software COMSOL Multiphysics and the planning of simulations in terms of geometry, PET components models and physical settings is reported; in Chapter 6 results obtained by the simulations are shown and nally, in Chapter 7, conclu-sions and outlook of future works are presented. Finally, in Appendix A, a mathematical explanation of the nite element method is reported.
Chapter 2
Combined PET/MRI systems
2.1 Medical Imaging techniques
The medical imaging techniques are based on the formation of an image of the human body according to a particular physical process, that can use magnetic elds, X-rays, γ-rays, ultrasounds, etc. Each technique has been developed and optimised during these years to be an helpful tool in the daily hospital healthcare.
In this work, I will focus on two particular techniques: the PET and the MRI.
2.1.1 Positron Emission Tomography
The Positron Emission Tomography [20, 1, 33] is a diagnostic imaging to-mographic technique based on the detection of the γ photons obtained from the annihilation between the electron and its antiparticle, the positron. The annihilation of the electron and the positron yields two γ photons of 511 keV, that are emitted on a straight line but in opposite directions (back to back). These two photons are detected by speci c detection modules (usually composed of scintillation crystals coupled to photodetectors), that converts the light signal in an electrical signal, which can be read by an appropriate electronics (Figure 2.1(a)). The detection modules of a PET are arranged in a ring shape, that select the slice of the tomography from which the signal is detected, and the inner volume of the ring is normally called Field Of View (FOV). The line of light of the two back to back photons is called LOR. The PET image i reconstructed through the intersection of several LORs providing the annihilation position in the patient body. (Figure 2.1(b)).
In a PET exam, a pharmaceutics labelled with a positron emitting isotope (radiotracer) is injected in the body of the patient. The patient is then placed on a sliding bed that pass through the detector ring, and several slices of a certain section of the body or the whole body are acquired: thus, tomographic images are obtained.
(a)
(b)
Figure 2.1: The Positron Emission Tomograpy. Top: the annihilation process (on the left) yields two γ photons of 511 keV that are detected in the ring by the detection modules (on the right). Bottom: the formation of the PET image, based on the detection of several LORs, whose intersection point is the annihilation point in the patient body.
Then, a PET image shows the annihilation points spatial distribution due to the presence of the positrons emitter: the higher is its concentration in a certain point, the higher the signal from that point will be and the brighter the image in that point will be. The positrons emitters are linked to a biological molecule: this particular molecule is called radiotracer. The PET is able to localize the radiotracer, and its localization in the patient body depends on the body physiology, so the PET provides functional images. A typical example of radiotracer is the FluoroDeoxyGlucose ([18F]FDG),
where the 18F , a positron emitter isotope of the Fluor, is linked to the
glucose molecule in place of an -OH group. The FDG is mainly used in the tumour cells localization, due to their large glucose consumption: the
Figure 2.2: Examples of PET images of a human brain in the transaxial plane based on FDG [46]. In the left image a red point is localized, where the FDG accumulates due to the presence of a tumour. On the right, the tumour area is delimited. As can be seen, little anatomical informations are given by the images.
FDG is collected by the tumour cells more than in other body regions, and a PET image shows a bright point in correspondence of the tumour cells (Figure 2.2) [31].
2.1.2 Magnetic Resonance Imaging
Physical principles
The Magnetic Resonance Imaging [64, 58, 21] is a diagnostic imaging tomo-graphic technique based on magnetic elds and their eects on the magnetic dipoles of the atoms [5, 47]. In a classical model, atoms as hydrogen (with an odd number of protons and electrons) have an associated magnetic dipole moment mp equal to
mp= γI (2.1)
where γ is the gyromagnetic ratio and I is the angular momentum. The magnetic dipole moment arises to contrast the magnetic eld generated by the electron that circulates around the nucleus. An external B0 magnetic
eld applied exerts a couple C on the magnetic dipole moment: C = mp× B0 =
dI
dt =⇒
dmp
dt = γmp× B0 (2.2)
This is the Larmor equation, that describes the precession of mp around B0
with an angular velocity:
and the associated frequency ν0 = γB02π is called Larmor frequency
(Fig-ure 2.3). In a 1 Tesla B0 eld the Larmor frequency of a proton is 42.57
MHz, thus the gyromagnetic ratio for a proton is γ = 42.57MHz/T .
Figure 2.3: Larmor precession of a proton around a B0 eld.
In a sample comprising many nuclei (as the human body) the total netic moment vector M (called magnetization) is the sum of all the mag-netic moments and, at equilibrium, in a magmag-netic eld B0 along the z-axis,
is aligned with B0 and is then equal to Mz. The transiaxial components of
M is zero because the transaxial components of the single nuclei are out-of-phase and cancelled each other. In a MRI scanner the B0 eld along the
z-axis is generated by the main coil (that is usually a superconductive coil). However, the MRI signal is obtained from the xy components of M: thus, in order to measure M, it must be tilted with respect to the z direction. This is obtained applying a magnetic ux density B1 oriented in the xy plane
and rotating at the Larmor frequency (this is why the technique is called Magnetic Resonance): M will experience a second torque which will rotate it into the xy plane. The resulting angle α between the z-axis and the M vector depends upon the magnitude and duration of B1. In MRI measurements,
the frequency B1 is in the RF range, and is generated by an RF coil. A
particular RF pulse is one that ips M in the xy plane: it is called 90°RF pulse and, through a suitable coil along the x o y direction, a signal can be measured through the variation of the magnetic ux induced in the coil by the rotation of the xy component of M.
A classical description of the behaviour of the magnetization after an RF stimulus has been given by F. Bloch [5]. After an RF pulse the magnetization recovers the equilibrium through the following equations:
dMz dt = − Mz−M0 T1 dMx dt = − Mx T2 dMy dt = − My T2 (2.4)
Figure 2.4: Top: eect of an applied RF B1 eld: the magnetization is ipped of a
certain angle (90°in this example), with a consequent presence of Mx and
My components in the transaxial plane. Bottom: eect of the RF B1 eld
on the magnetization as a function of the time: a longer B1 pulse leads to
an higher ip angle.
where M0 is the equilibrium value of the magnetization, while T1 and T2 are
called respectively longitudinal and transverse relaxation time. After an RF pulse, the z component is recovered following an exponential process (due to the energy transfer from the nuclei to the environment) with a time constant T1, while the transaxial components disappear following an exponential
pro-cess (given by the loss of phase coherence among the spins of the nuclei) with a time constant T2. Thus, most of the MRI signals are sinusoids that decay
exponentially with a time constant T2.
The MRI scanner
A typical MRI scanner is usually composed of the main coil that generates the B0 eld and inside which the patient is placed, an RF coil, that generates the
RF B1 eld in the transaxial plane. In order to obtain a magnetic resonance
image, another three coils, called gradient coils, are needed. These are coils able to generate a linear variation of the magnetic eld along the x, y and z directions. The gradient along the z direction is used to select the slice for the tomographic image, because the variation of B0 along the z-axis induces
a dierent Larmor frequency in every transaxial plane: when an RF pulse is sent, only the plane with the same Larmor frequency is excited by the resonance. The gradients along the x and y directions are used to encode the spatial informations in the transaxial plane. The acquisition of an MRI
tomography involves all the coils and is obtained through repetitions of the so-called sequences: while the patient is exposed to the B0 eld, the RF and
gradient coils are turned on and o in a well de ned sequence, that allows to de ne the slice of the tomography and to acquire the spatial data. The signal is received by a speci c coil or by the RF coil, that can work in transmitting and receiving mode.
Summarising, the MRI acquisition is based on the ip of the M vector through an RF signal with the same Larmor frequency of the particular nucleus. In an MRI exam of a human body, the Larmor frequency of the hydrogen atom is chosen due to the large presence of the hydrogen in the human body in the water molecules: thus an MRI exam acquires the signal of the hydrogen nuclei distributed in the body. The MRI shows the spatial distribution of the hydrogen in the transaxial plane, so the image obtained is an anatomical image.
Figure 2.5: Example of an MRI image of the human brain in the transaxial plane. The image show an high de nition of anatomical details of the brain structure.
2.2 Multimodal imaging techniques
The fusion of two images from dierent techniques can be very useful to the medical diagnosis [54], since the information given by two images can be complementary. A typical example is given by the images provided by the PET, that show physiological informations related the radiotracer con-centrations in the body, and the CT images, where the human anatomy is represented with high spatial resolution: the fusion of these two images
would be useful to localize the radiotracers in an anatomical environment. From this purpose the combination of the PET and CT called PET/CT has been developed [3, 56]. This imaging system allows to merge the anatomi-cal information, given by the CT, and the in-vivo physiologianatomi-cal information, given by the radiolabelled biomolecule distribution given by the PET, in an unique image. The PET/CT system developed by Townsend [56, 55, 3] had a moving bed, that passed rst through the CT scanner and then through the PET scanner: thus the images were acquired sequentially, rather than simultaneously. The success of this multimodal imaging technique has been demonstrated by several works of dierent research groups [55, 56, 37, 14, 2, 4, 15, 57]. However, compared to the Magnetic Resonance Imaging (MRI), the CT encounters some limitations: the CT adds a signi cant radiation dose to the patient, in addition to the dose due to the PET radiotracers [7], while the MRI does not require ionizing radiation; the CT shows a soft-tissue low contrast, while on the contrary the high soft-soft-tissue contrast is a peculiarity of the MRI; in the oncology eld, MRI shows an higher speci- city than the CT in recognizing melanoma and tumour cells in some parts of the human body, especially those where an high soft-tissue contrast is required (liver, subcutaneous tissues, spleen, bone marrow, muscles, brain) [34, 32]. Thus, the advantages of the MRI performance in the acquisition of anatomical images and the variety of functional and biochemical methods, such as spectroscopy and diusion, that an MRI oers, have led the research in multimodal imaging of the last 10 years to combine PET and MRI in an unique device, calling it PET/MRI.
One of the rst attempts to combine MRI and PET was made in 1994, when Christensen et al. [11] acquired the spectrum of68Ge in a 5T magnetic
eld, with NaI crystals (magnetic compatible) for the detection of the two 511 keV γ-rays, placed inside the MR and connected to PhotoMultiplier Tubes (PMT) via 5 m length lightguides. The use of lightguides was needed to bring the PMTs far enough from the high magnetic eld, due to the high sensitivity of the PMTs to the magnetic eld. In another experiment, Shao et al. [53], in 1997, obtained simultaneous PET and MR images, using a phantom lled with 18F in a 0.2T magnetic eld. The PET signal was
acquired with LSO crystals (magnetic compatible too) within the bore of the MR system and coupled to PMTs by 4 m length optical bres, in a way that the magnetic eld of the MR system could not aect the PMTs. These experiments showed the feasibility of a simultaneous PET/MR acquisition, but some problems still aected this approach: the PMTs, the standard detectors of a PET system, are highly sensitive to the magnetic eld and too bulky to be integrated inside an MR. Thus, they have to be far away from the high magnetic eld and, to connect them to the scintillator crystals, long lightguides are needed, with a consequent loss of PET signal due to the coupling with the crystals and the PMTs, through the lightguides length.
de-tectors, small, compact and insensitive to the magnetic eld, were needed to make possible the integration of the PET inside the MR bore. A solution was found in the Avalance PhotoDiode (APD) [38], a solid state photo-detector based on doped silicon and, later, on the Silicon PhotoMultipliers (SiPM) [8, 36]: arrays of hundred (or thousand) of APDs working in Geiger-mode on a common silicon substrate. These detectors show a signal amplitude comparable to that of the PMTs, they are insensitive to the magnetic eld, compact and tillable.
Up to today, several con gurations have been studied to acquire multi-modal PET/MR images (an exhaustive discussion of which can be found in [12] and [65]). The main issue for combining PET and MR systems in a single device is to avoid degradation of the performance of either scanners. Such con gurations can be divided in sequential PET/MR and combined PET/MRI device, that can be further achieved through a PET insert placed in the MR or fully-integrated PET/MR system (Figure 2.6). Here, a brief presentation of them is reported.
(a) (b)
(c)
Figure 2.6: Dierent approaches in combining PET and MRI. Top left: Sequential PET/MRI. Top right: PET insert placed inside the MRI scanner. Bottom: fully integrated PET/MRI system [12].
2.3 Sequential PET/MRI devices
This type of con guration, also called tandem con guration, is very similar to the PET/CT: the patient, on a moving bed, slides through the MR and the PET FOV(Figure 2.6(a)). The tandem con guration is advantageous be-cause minimizes the modi cations of the individual system. A technological improvement required is the electromagnetic shielding of the PET compo-nents, due to the presence of the MR magnetic eld. An example of such architecture is given by the Philips Ingenuity TF PET/MR [66], an hybrid imaging system with Philips time-of- ight GEMINI TF PET and Achieva 3T X-series MRI system (Figure 2.7).
Figure 2.7: The sequential Philips time-of- ight GEMINI TF PET and Achieva 3T X-series MRI system. The moving bed facilitates patient motion between the MRI system on the left and the PET system on the right [66].
This solution, despite advantages as reduced cost (marginally above the cost of the two single scanners), exhibits limitations related to the non-simultaneity of the images acquisition and to the size of the room where the system should be installed: such architecture needs larger room than standard PET/CT or integrated PET/MRI systems.
2.4 Integrated PET/MR devices
The necessity to perform MRI and PET examinations simultaneously in space and time have brought to the concept of insert: a PET scanner directly placed inside the MRI (Figure 2.6(b)). Later on, a "fully integrated" concept raised, where a dedicated whole-body PET scanner is built in a dedicated MRI scan (Figure 2.6(c)).
2.4.1 Split- eld magnet
The rst attempt to implement a simultaneous PET/MR acquisition with PMTs was made by Shao's [53] and Christensen's [11] groups, as discussed before. The main disadvantages of this approach is the high magnetic sensi-bility of the PMTs. The use of long optical bres and the reduced FOV of the PET in this con guration lead to a loss of the PET signal and a degradation of the PET images.
Currently, a magnetic compatible PET scanner based on PMTs is be-ing pursued by Lucas et al. [30], in which a split-magnet low- eld MRI system (1 T) is employed (Figure 2.8). The adopted magnet is an actively shielded superconducting magnet, with a split region in the center where a microPET© focus 120 system (Siemens Moleculare Imanging Preclinical
So-lutions, Knoxville) can be accommodated (Figure 2.8(a)). This PET system is composed of a scintillating crystals placed inside the central split, a 120 cm length optical bres that outcome radially from the split magnet, and a PTM at the end of each optical bre, to detect the scintillation light. The PMTs are located in a 10 gauss eld region, that produces minimal eects on image quality (Figure 2.8(b)). Although the degradation of the signal due to the presence of the optical bres and the fact that is possible to use only low eld magnets, the PET system is able to maintain the same spatial res-olution and no interference between the system due to the RF and gradient elds is observed.
(a) (b)
Figure 2.8: The PET insert developed by Lucas and his group. Left: cut-away view of the PET/MRI system, where crystal scintillation ring (dark blue), optical bres (light blue), PMTs (dark blue outside the magnet) and split gradient coil (brown) are shown in their nal con guration. Right: transaxial view of the PET/MRI system. The four grey circles are four posts, that counter the attractive force between the two part of the split magnet [30].
2.4.2 PET insert
The dierence between this approach and the PET/MR scanner discussed in sec. 2.4.1 is that the PET insert ts completely inside the bore of the MR system. To allow such a combination, the PMT must be replaced by a photodetector insensitive to the magnetic eld. These type of PET inserts make use of the APDs (and recently, of the SiPMs): solid state detectors that are magnetic compatible and can be installed inside a MRI device. Several research groups have studied the feasibility of this con guration [42, 18, 41, 9, 48, 60, 23, 62, 63, 22, 39, 59, 51], and prototypes for small animal imaging human brain have been built in the last years, capable to acquire simultaneous PET/MRI images.
A typical architecture of a PET insert can be summarized using as ex-ample the PET insert developed at the University of Tübingen, Germany [41] (this PET insert will be described deeply in the next chapter). The single detector module consists of 12 × 12 LSO scintillator array (1.6 × 1.6 × 4.5 mm3) each coupled via light guides to a 3 × 3 APD array and
custom preampli er electronics. The detector module is enclosed within a thin copper shielded housing, in order to prevent electromagnetic interac-tions between the two systems. The entire insert comprises 10 LSO-APD detector modules, arranged in a ring con guration around the PET and MR FOV (Figure 2.9). Some dierent PET inserts use an optical gel or short optical bres [9] between the crystals and the solid state detectors. New PET inserts based on SiPM take advantage on the Geyger-mode operation of the detector: the SiPMs signal is higher than the APDs siganl, and it do not need a preampli cation, but only a read-out electronics, that could be placed outside the MRI. This solution can reduce the interferences between the PET electronics and the RF eld.
This approach has shown to work, and simultaneous PET/MR images of small animals and human brain have been acquired [9, 48, 25, 26, 13, 35], but some problems still remains to be solved. Nevertheless, the insert solution suers of degradation of the PET and MRI performance due to the interference between the PET electronics and the RF and gradient elds of the MRI scanner, and the space reduction for the patient inside the bore of the MR due to the PET insert.
2.4.3 Fully integrated PET/MRI system
This solution is the latest one that have been proposed for combined PET/MRI systems eld. This approach proposes a fully integrated system, where a PET scanner and an MRI scanner are combined in a single device. This solution is the most challenging, due to the high interactions that exist be-tween the PET electronics and the gradient and RF coils in a current MR system. The PET electronics might impact the signal-to-noise of the MR
Figure 2.9: PET insert developed in the University of Tübingen. a: the PET insert in its position within the bore of the MR scanner, between the gradient coil and the RF coil. b: photograph of the PET insert, composed of ten modules. c: single detection module showing LSO scintillator crystals, APD light detectors array and preampli er coated by a copper layer for electromagnetic shielding [26].
system; to prevent this eect, a copper screen is usually introduced, but lead to a degradation of the MR pulses with an SNR reduction of about 30% [41]. Thus, the new instrumentation for the next generation PET module com-patible with the MR environment are very challenging: the PET module will have to provide highly accurate position and timing information, while hav-ing an high intrinsic e ciency. This will probably lead to a new types of scintillator crystals coupled with fast, novel photodetectors.
The fully integrated PET/MRI systems developed so fare are based on eld-cycled MR or on the insertion of a PET ring behind the RF coil of the MRI. The rst approach makes use of two separate and dynamically controlled magnets, one for polarization and the other for readout. This allows to obtain some temporal windows in the acquisition of the MR images that are free of magnetic eld and that can be used to acquire PET images [17]. In the second approach scintillator crystals and photodetectors for PET are locate behind the RF coil of the MR scanner. This solution can be set up either by reducing the radius of the RF coil, in order to obtain space for the PET system, or by using a split gradient coil. This solution has been already developed by Siemens (Biograph mMR [13], Figure 2.10), while another whole body PET/MRI scanner is being developed by Philips (under the EU SUBLIMA project, http://www.sublima-pet-mr.eu/).
integrates a PET detector ring in a 3 Tesla MRI scanner. The PET system has a detector block consisting of 8 × 8 LSO scintillation crystals coupled to a matrix 3 × 3 APDs, with integrated cooling channels to avoid APDs heat-ing. The detector matrix is directly connected to a 9 channel preampli er ASIC board (Figure 2.10, bottom). The PET detector is placed between the gradient coil and the RF coil of the MRI (Figure 2.10, top right). The MRI has a transaxial FOV of 50 cm and an axial FOV of 45 cm; on the other hand, the PET detector, consisting of 8 ring of 56 detector blocks, has an axial FOV of 25.8 cm and a ring diameter of 65.6 cm. The bore of the system has a diameter of 60 cm and the length of the whole system is 199 cm
Figure 2.10: View of the whole-body Biograph mMR PET/MRI scanner developed by Siemens. Top: frontal view of the scanner, with a scheme (in the zoom) of the main components and their position within the structure. As can be seen, the PET scanner is placed between the gradient and the RF coils. Bottom: schematic view of the PET detector module, consisting of 8 × 8 LSO crystal array, 3 × 3 APD array and preampli er board. Courtesy of Siemens Healthcare.
Chapter 3
The PET insert approach to
the PET/MRI combination
3.1 Technical challenges
The combination of PET and MRI scanners is not a simple problem, because several di culties are encountered integrating the PET detector in the MRI scanner [61]. As discussed in the previous chapetr, among the solutions proposed so far, the PET insert is one of the most aordable approaches: the PET detector is the only device that has to be designed from scratch and adapted to an already-built MRI scanner (the most expensive of the two devices), in order to t inside it. The purpose of the PET insert is to obtain a combined device in which the two scanners work as they were alone, without interfere each other. To achievethis objective the technical challenge is complex due to the following problems:
geometrical constraints given by the bore of the MRI scanner; interferences given by the MRI to the PET system;
modi cation of the uniformity of the MRI magnetic elds due to the presence of the PET detector in the MRI bore.
Geometrical constraints The geometrical constraints are given by the diameter of the MRI bore, that are ∼70-80 cm for clinical MRI and ∼15-30 cm for small animal MRI. Adding a PET insert inside the bore means to reduce further the available space in the MRI bore. In this sense, as already discussed in the previous chapter, the PMTs, the current detectors of light of the PET systems, are too bulky to be inserted within a MRI bore. Since an increase of the MRI coil involves a large rise of costs of the MR scanner, the possible solutions are to continue to use the PMTs outside the MRI as the research group of Shao [53] did, or to nd a new small and compact
detectors of light, as APD and SiPM, in order to build a PET insert that can t within the MRI bore, but, at the same time, leaves enough space in the bore for the patient. This second approach is studied in this thesis work. Interferences given by the MRI to the PET system When placed inside the magnetic resonance, the PET insert suers from interferences with the strong magnetic elds that are used for the generation of the MRI image. The PMTs detect the photons emitted by the scintillator crystals, converting them in electrons. These electrons are accelerated by a strong electric eld between the dinodes of the PMT: this lead to a cascade of electrons that reach the last dinode, giving the nal signal of the PMT. The strong magnetic eld of the MRI de ects the electrons through the Lorentz's force, resulting in a corruption of the PET data. For this reason, in addition to their bulky dimensions, the PMTs cannot be inserted in an MRI scanner. On the other hand, APD and SiPM have already proven to be insensitive to the magnetic elds generated by the MRI: this property, together with their compact dimensions, currently makes them the best choice as photodetector of a PET insert.
Another interference of the MRI scanner is caused by the magnetic elds and time variation of gradients, that disturb the PET readout electronics and corrupt the PET data. A solution applied so far is to screen the PET com-ponents and electronics that are placed inside the MRI with a diamagnetic material that could keep away the magnetic elds (usually copper is used). Moreover, another eect of the fast switching magnetic eld is the induction of electrical Eddy currents in conductive materials, with a consequently ef-fect of heating such components. This could be a problem, in particular for photodetectors as APD and SiPM, whose operational characteristics depend on the temperature.
Interference given by the PET to the magnetic elds In combining PET and MRI, it is a mandatory to preserve the quality of MR images. The imaging performance of an MRI system is strongly dependent on the high homogeneity (about a few ppm) of the static magnetic eld (B0) and the
RF magnetic eld (B1), so the PET detectors and electronics inserted in the
MRI have to preserve the homogeneity of such magnetic elds.
In the design of the PET insert, any ferromagnetic materials (such iron, nickel, cobalt) should be avoided: such materials distort the B0 eld. Loss of
signal and spatial displacement of voxels in the MR image results in a general degradation of the MRI image quality, and for these reasons such materials are called magnetic-incompatible. The choice of the PET materials has to be conveyed to those materials with a magnetic permeability very close to that of the water and human tissues and they are called magnetic-compatible (copper, silicon).
Another interference is due to the eddy currents that could arise in the conductive components of the PET, due to the gradient time variation and the B1 elds, as explained in the previous paragraph. Such eddy currents
generate magnetic elds that can, in return, aect the MRI elds leading to a spatial distortion in the MR images.
3.2 Technical developments in PET/MRI inserts
Due to the intrinsic limits of the PMTs described in the previous section, several groups in the last 15 years have chosen solid state detectors for PET inserts, after the rst work realized by the group of B. Pichler [38]. This group carried out an experiment in which the signal of a 22Na positronsource was acquired by a detection module, composed of an LSO (Lutetium oxyorthosilicate) crystal coupled to an APD, in a 9.4 Tesla MR scanner: the results obtained showed that the APD performance did not degrade in a magnetic eld. In a couple of years rst PET detectors based on APDs instead of PMTs were built [28, 43, 40, 19]. Once demonstrated the mag-netic compatibility of the APDs and their application in a PET system, the rst PET APD-based inserts were limited to preclinical small animal MRI scanners. After few years, the rst PET insert prototype for human brain (called BrainPET [49, 24, 23, 35]) was available and simultaneous PET/MRI images of a human brain could be acquired [48]. Approximately during the same years, SiPM had been developed and tested as new generation of PET inserts photodetectors.
In this section, two APD-based PET inserts for small animals and a PET insert based on SiPM are illustrated. A discussion of the choices made by the dierent research groups to overcome the technical challenges described before is also reported.
3.2.1 APD-based PET insert: the prototype developed in Tübingen
An APD-based PET insert was developed at the University of Tübingen: Pichler and Judenhofer's group designed a rst prototype [41] which, with further developments [25, 26, 27, 59], has been able to acquire simultane-ous PET/MRI images of a msimultane-ouse. This PET insert was built to t inside two small animal MRI scanners (7 Tesla BioSpec 70/30 USR and 7 Tesla ClinScan, Bruker BioSpin MR, Germany) and the nal prototype consists of 10 block detectors arranged in a ring of 60 mm inner and 120 mm outer diameter: in this way a transaxial FOV of approximately 45 mm is obtained (Figure 3.1(a)).
The single detector module (SDM) of the PET scanner is composed of 19 × 19mm2 crystal block comprising 12 × 12 individual 1.5 × 1.5 × 4.5 mm3 LSO crystals separated with a highly re ective foil, and it allows to obtain
(a) (b)
Figure 3.1: Schematic view of the PET insert developed in Tübingen within the MR scanner. Left: axial view of the PET insert, made of 10 detector modules in a ring shape, inside the MR scanner; in the zoom, the single PET detector module is enhanced. Right: section view of the PET insert in the MRI system, between the gradient coil and the RF coil [25].
an axial FOV of 19 mm, enough for imaging the brain, heart or abdominal regions of a mouse. The crystal block is coupled via 3 mm thick light guide to a monolithic 3×3 APD array (Hamamatsu, Japan). Each APD has an active surface of 5 × 5 mm2 and operates with a negative bias voltage. Through a
exible connection, the APD signal feeds the preampli er, whose components and connectors are non-magnetic and are mounted on a custom 6-layers PCB (Printed Circuit Board). Finally, the preampli er signal is connected, via 6 m fully shielded non magnetic coaxial cables, to the readout electronics installed outside the 5 Gauss line, that is the limit of the safety area for MRI operators. Crystals, APD and preampli er are coated by a 10 µm copper for electromagnetic shielding (Figure 3.2). The prototype can be tted within the two MR scanners in the bore of the gradient coil, then the RF coil of the MR scanner can be placed inside the PET insert, leaving a bore of 36 mm diameter for the mouse (Figure 3.1(b)).
The detector module of this prototype is designed with the APD facing directly the LSO crystals, via short lightguides: this con guration avoids the use of optical bres and the loss of light caused by them, but keeps the APDs close to the MRI FOV (de ned by the RF coil), with the consequent risk of distortion of the magnetic elds and loss of MR image quality. Since the APDs work in the proportional region, with the bias voltage few Volts below the breakdown voltage (in this prototype -405 V), their gain is only about 100 times the input signal. This is why they need a preampli cation electronics immediately after the collection of the signal. In this prototype the preampli er is placed inside the MR bore, but is connected to the APDs through the exible cables, in order to keep it as far as possible from the FOV and minimize the magnetic eld distortions induced by the electronics
Figure 3.2: Single detection module of the PET insert prototype developed in Tübin-gen. Top: crystal block coupled to lightguide (a) and APD array (b) cou-pled through exible connection (c) to the PCB containing the preampli er (d), buers (e) and connectors (f). Center: PCB, APD array and crystals mounted, in their nal con guration, within the detector housing. Bottom: The nal PET detector module [25].
in the image region. Finally, to protect the PET electronics from distortions induced by MR sequences, a shield of copper coating the detector module and the PCB is enclosed in a shielding of copper of only 10 µm thick to minimize Eddy currents.
The PET module shows an energy resolution of 25.8% FWHM at 511 keV that becomes 25.1% FWHM during the PET/MR acquisition, and a timing resolution on average 8.0 ns outside and 8.2 ns inside the MR. Measurements of MRI SNR (Signal to Noise Ratio), B0 and B1 homogeneity and image
quality showed only minor eects caused by the presence of the PET insert. This PET insert has been used for several applications, reviewed in the references at the beginning of this section, and it is an example of a well functioning PET insert.
3.2.2 APD-based PET insert: the prototype developed in California
Another PET prototype for small animals has been built at the University of California by the research group of Ciprian Catana [9], approximately the same years the Tübingen prototype has been developed. In this prototype the single detector module is composed of a 8 × 8 matrix of LSO scintillator crystals, each measuring 1.43 × 1.43 × 6 mm3 arranged with a pitch of 1.55
mm to allow space for 66 µm thick dielectric re ector lm (Figure 3.3). A custom-made optical bres bundle is coupled, through optical grease, to the scintillator crystals and it consists of an array of 6 × 6 optical bres, each measuring 1.95 × 1.95 mm2. This bundle bends sharply at 90°as it exits the
16 mm and the length of the straight portion of the ber is 10 cm. These are doubleclad plastic optical bres, the outside of each one is coated with a 25 µm layer of white extramural absorber that acts like a re ector and reduces crosstalk between adjacent bres. The other end of the bundle is coupled to the an 14×14 mm2PSAPDs [52] (Position Sensitive Avalanche Photodiode).
The PSAPD is directly connected to the preampli cation electronics made of nonmagnetic components and installed on a custom-made PCB. The com-plete prototype consists of 16 detector modules described before. Finally, 2 concentric cylinders of copper conductive laminate (inner diameter 65 mm and outer diameter 118 mm) are applied at both ends of the prototype, in correspondence of the PET electronics, for electromagnetic shielding, and copper conductive tape was also applied to the end caps and to the ring through which the bre-optic bundles pass, to further reduce interference. The entire structure is mounted on a carbon bre tube for support (lenght 55 cm, inner diameter 60 mm, outer diameter 62.8 mm) and can be seen in Figure 3.3. The nal system has an inner diameter of 60 mm and an outer diameter of 118 mm, with an axial FOV of 12 mm and a transaxial FOV of 35 mm. To bring the preampli er signal to a dedicated readout electron-ics, located at a safe distance, 50 Ω subminiature coaxial cables are used. Since the PSAPDs improve their performance with a moderate cooling, the PSAPDs are kept at approximately -5°C by a network of tubes where cold nitrogen gas ows. This insert is designed to t inside a Bruker 7 Tesla Biospec animal MRI system (Figure 3.4(b)), between the gradient coil and the RF coil: the mouse is located inside the bore of the RF coil, of 35 mm diameter (Figure 3.4(a)).
The main dierence between this prototype and the Tübingen prototype described before, is the design of the detector module. The Californian group designed the 16 optical bre bundles to place the PSAPDs outside the MRI FOV, in order to minimize any distortion of the magnetic elds due to the PSAPDs presence and consequent artefacts in the MR images; however, the signal of the PET is inevitably aected by the light losses in the optical bres. On the other hand, similar choices concern the location of the PET electronics, that is placed outside the MRI FOV as in the previous prototype, and the laminate copper shielding of the PET electronic components, to minimize the distortion of the PET signal by the MR sequences. Moreover, the laminate copper is useful to keep under control the Eddy currents induced in the material.
This prototype showed in several experiments [10, 63] an energy reso-lution of 23.2% FWHM outside the MRI and 23.6% FWHM, that becomes 24.3% FWHM and 24% FWHM in presence of Spin Echo and Gradient Echo respectively, within the MRI, and a spatial resolution of 1.51 mm in the cen-ter of the FOV. Moreover, weak eects on the MRI performances by the presence of the PET insert were observed.
exam-Figure 3.3: The PET insert developed in California. Top: single detector module, com-posed of the scintillator crystals array, the optical ber bundle bent through 90°, the PSAPD coupled to the other end face of the bundle and the pream-pli er on the PCB. Bottom: the mounted PET insert, with the 16 modules displaced axially and facing each other. The crystal ring (in the center) is completely covered by the 16 crystal arrays. On the right the copper shield-ing cylinder is visible, on the left it is removed and both the end cap and the ring with the copper tape for electromagnetic isolation are clearly visible. The carbon bre tube is visible under the optical bres bundles [9].
ple of working PET insert, where dierent choices, compared to the proto-type developed in Tübingen, to overcome the interferences between the two devices, have brought anyway to a current functioning PET insert.
3.2.3 SiPM-based PET insert: the prototype developed in Aachen
Recent studies on SiPM have brought to the buildings of PET inserts based on this new photodetectors: one of these is the prototype designed in Aachen, by the research group of Volkmar Schulz [51], with further modi cations and improvements [62]. The nal design of this insert makes use of 10 detector modules arranged in a ring shape, and each module could interface 3 × 2 (transverse × axial) detector stacks in order to obtain three detector rings; currently only one ring have been built. The single stack contains six lay-ers: scintillation crystal array, light guide, sensor board, digitization board, interface board and control board. The scintillation crystal chosen is the cerium-doped lutetium yttrium oxyorthosilicate (LYSO) arranged in an
ar-(a) (b)
Figure 3.4: The position of the PET insert within the bore of the MR scanner. Left: Axial view of the PET insert, between the gradient coil and the RF coil. Right: tridimensional view of the PET insert inside the MRI system [9].
ray of 22×22 (22×24 for the inner stack) crystals that measure 30.1×30.1×10 mm3 (30.1 × 32.9 × 10 mm3 for the inner stack) optically isolated by 67 µm
thick re ective lms. A light guide (glass plate) 1.5 mm thick couples the crystals to the light detectors and spreads the light over the sensor array: this allows to calculate the crystal position from the sensor signal. The sensor board has 16 monolithic 2×2 SiPM arrays [44, 45, 29] mounted and bonded. The digitisation board contains two dedicated application-speci c integrated circuits (ASIC) for ampli cation and digitisation. The ASICs digital signal is sent, through the interface board, to a Field-Programmable Gate Array (FPGA) placed on the control board (Figure 3.5(a)). The control board, also called singles processing unit (SPU) houses the FPGAs for signal pre-processing, temperature sensor, heat sinks and the connectors to supply bias voltage SiPMs (-39 V), ASICs (3 V), FPGAs (1.7 V) and some circuits (4.5 V), and is able to supply and control up to 3 × 2 stacks. The SPU collects and processes the data from the detector stacks and sends then, through op-tical bres, to the data acquisition and processing server located outside the clinical exam room. All electronic components are chosen to be low or non-magnetic. The single detector module is cooled via combined water (15°C) and gas (18°C, 29% relative humidity) chilling system. ASICs, FPGAs and bias supplier are cooled through two independent system to achieve equal temperature over the whole stack (Figure 3.5(b)). The module housing is manufactured out of a resin with ceramic particles and, after being prepared with a silver-based conductive lacquer, a 18 µm thick copper layer has been electrogalvanised.
The PET system built so far has a tansaxial FOV of 160 mm and an axial FOV of 30 mm (95.6 mm for the full equipped system) and can t inside a 3 Tesla Achieva small animal MRI system, between the gradient coil and the
(a)
(b)
Figure 3.5: Top: single detection module open (on the left) and detector stack layers (zoom on the right). In the module are represented two out of the total six stacks that can be installed. Also, single processing unit, cooling tubes and cables connections can be seen. Bottom: exploded view of the single processing unit structure and its components, and the liquid cooling system of the SDM (only one of the two cooling pipes and one digitisation board and interface board are shown) [62].
RF coil. The bore in which the mouse is located has a diameter of 145 mm. As said before, SiPMs do not need preampli cation electronics: since they work in Geiger-mode (few volts above the breakdown voltage) their gain is very high (∼ 106) and their signal can be directly read by a readout
electronics (ASIC and FPGA circuits). The research group decided to put the readout electronics directly in contact with the SiPMs inside the PET FOV, so each single detector module is electromagnetic shielded by 18 µm thick electrogalvanised copper layer; special care was taken by the group also for power supply, synchronisation clock and cooling tubes insertions in the module using RF gaskets around the plates of the cables and tubes connec-tions (Figure 3.7), in a way that the electromagnetic insulation of the module is always as e cient as possible. Also the synchronization module (needed
Figure 3.6: The PET insert mounted on the patient bed of the 3 Tesla MRI system. The RF coil placed inside the PET detector and the PET itself enters in the MRI bore, while all the devices on the right are kept outside [62].
to control the PET readout electronics), that stays outside the MR scanner, but close enough to disturb the measurements, is completely shielded by a copper coat. Some expedients were applied in the single detector module de-sign to minimize the interferences between the components and the magnetic elds:
the connections between SiPMs and ASICs make use of dierential pair lines to be less prone to electromagnetic interferences, and the two boards are composed of two completely separate parts to keep conductive area small and avoid Eddy currents over the connectors; fast digital circuits on the ASICs are realised in constant current logic,
to reduce RF emission from internal switching and power supply lines; the interface board allows the communication between ASICs and SPU in shielded Low Voltage Dierential Signalling (LVDS), to reduce elec-tromagnetic emission and to be resistant against elecelec-tromagnetic in-duction from outside;
the glass bres used to bring the signal outside the detection module ensure no interferences with MRI;
the copper pipes of the cooling system are electrically insulated and a non conductive plastic feeds the water through the module, in order to not penetrate the RF shield;
the heat sink that couples power regulators and FPGA to the water is splitted in two parts to reduce electrically conductive area.
Figure 3.7: Power supply and synchronisation cables inlets in the SDM, all enclosed in RF gaskets [62].
This PET prototype allows to reach a very high uniformity of the B0
magnetic eld: distortions are <2 ppm in a region of interest (ROI) of 90 mm diameter, while in the entire FOV (96mm × 130mm diameter) the dis-tortion is below 5 ppm. MRI SNR decreases of 14% with the PET insert and the image uniformity changes from 93.6% to 92.9%, but spurious sig-nals from PET electronics are not directly visible in the MRI images. PET performances are 29.7% FWHM energy resolution, 2.5 ns timing resolution and spatial resolution of 1.2 × 1.3 mm2 transaxial and 1.15 mm axial, and
seem to be unaected by the MR sequences.
This PET insert has shown to work in the experiments carried out by the group: measurements of static magnetic eld uniformity acquired with and without the PET insert have shown an high magnetic compatibility, with variations of the magnetic eld intensity less than 2 ppm with the PET in the MRI. Moreover, simultaneous PET/MRI images of a phantom and of a rat brain have been successfully acquired [62].
Chapter 4
The PET insert prototype
MADPET4
In order to study the magnetic compatibility of a PET insert, a real PET prototype has been studied in this work and, in particular, some simulations have been carried out in order to study the behaviour of the main PET components in a magnetic eld. The PET insert is the MADPET4 prototype, that is being developed at the Klinikum rechts der Isar, in collaboration with the Technische Universität München (TUM) in Munich, Germany.
In this chapter, the MADPET4 prototype and the MRI scanner are pre-sented.
4.1 The MADPET4 prototype
The MADPET4 is a PET insert prototype for a 7 Tesla MRI Agilent/GE Discovery MR 901, an MRI scanner for preclinical small animal studies. The MADPET4 prototype is being developed by the research group of prof. Sibylle Ziegler at the Technische Universität München (TUM). The goals of the MADPET4 prototype are MRI compatibility, high spatial resolution (< 1.5 mm), homogeneous sensitivity and usability of the FOV up to 90% of the ring diameter. The MADPET4 PET insert will be used for medical and Biological research topics in combination with the 7 Tesla MRI Scanner, in particular for preclinical studies on mice and rats. One focus will be metabolic studies in tumours: for this topic simultaneous PET and MRI acquisitions with hyperpolarized13C and FDG will be performed; moreover
FDG will be used also in simultaneous scans of PET and MR for studies of mouse brain metabolism. Studies of hypoxia with a new PET tracer called FMISO ( uoromisonidazole, a molecule of misonidazole, radiosensitizer for tumour cells marked with 18F radiotracer) may be performed, and other
several studies are planned once the scanner will be fully operational. The simulations carried out in this thesis work analyse three particular
topics regarding the MADPET4 development:
the uniformity of the static B0 magnetic eld in the presence of the
PET insert components;
the uniformity of the RF B1 magnetic eld in the presence of the PET
components;
the eects of the RF B1 eld on the PET components, in particular
the heating eect given by the induced currents in conductors.
In the following sections, geometry and components of the MADPET4 prototype are shown.
4.1.1 The MADPET4 geometry
The MADPET4 insert is a dual layer PET detector designed in a ring shape of 91 mm inner diameter and 146 mm outer diameter, with a detector layer placed in the inner ring and composed of 132 scintillator crystals, and a detector layer placed in the outer ring composed of 198 scintillator crystals. The entire PET detector is structured in 8 axial rings with 2.6 mm pitch, covering 19.7 mm in axial direction with a total of 2640 channels. The FOV of the prototype is 19.7 mm in the axial direction and 81 mm of diameter in the transaxial plane.
The complete structure is made of a 3D-printed ring-shaped UV cur-able acrylic plastic board where the inner and outer crystals are embedded and optically insulated from each other. The crystals have an end face of 1.5 × 1.5 mm2 and a length in the radial direction of 6 mm and 14 mm for inner and outer crystals, respectively. The crystals in each ring are placed equidistant to their neighbours, making the system highly symmetric; they are not arranged in arrays or blocks but they are all facing the center of the FOV (Figure 4.1(a)).
The inner and outer detector layers are designed with solid state light detectors placed on a readout Printed Circuit Board (PCB): the detectors are arranged in a matrix of 8 rows (one per ring) and 3 columns in the outer ring and in a matrix of 8 rows and 2 columns of detectors for the inner ring: thus the single basic module of detection is a sector of 3 outer and 2 inner crystals (cf. Figure 4.1(b)). The PCBs are held to the 3D-printed plastic structure by 3D-printed screws (two for each PCB) in a way that the solid state detectors are xed to the end face of the correspondent crystals (Figure 4.2(c) and Figure 4.2(d)).
4.1.2 The MADPET4 components
The crystals chosen in this module is the Lutetium Yttrium Oxiorthosilicate (LYSO), a state of the art scintillator for PET and appropriate for operations
(a) (b)
Figure 4.1: Left: Single PET ring of MADPET4, with the 330 crystals (grey) and SiPMs (green) on the front-end face of each crystals. In the zoom, the basic module of the ring (violet) is shown. Right: Schematic of the basic detector module [50].
inside MRI. The dimensions reported in 4.1.1 have been chosen for high count rate capability and direct interaction localization as well as its full magnetic compatibility.
The light detectors of choice are the SiPMs, since they are already proven to work as PET detectors and to be unaected by the magnetic eld. They are compact as well, and thus appropriate to accommodate the MRI space limitations (the bore of the scanner). Because of their high gain (∼ 106),
the SiPMs do not need a preampli cation and thus no additional electronic PET components inside the bore. The SiPMs used in the MADPET4 module are non-magnetic nickel free KETEK PM1150 (see Figure 4.2(b)), with an active area of 1.2 × 1.2 mm2 and 50 µm cells; their gain is very stable to the
temperature variations (< 1%/K) as well as the bias voltage (∼ 18mV/K), the dimensions are very small (2.45×1.95×1.8 mm3) and the PhotoDetection
E ciency (PDE) is very high (55% at 420 nm).
The SiPMs are xed on a PCB (outer 52×1.6×6 mm3, inner 48×1.6×4
mm3) that is held on the plastic structure of the PET module. At the other end of the PCB there is a USLS connector (KEL Corporation Japan, www.kel.jp, 0.4 mm pitch) with 30 pins for the outer and 20 pins for the inner PCB, and 6 layers of copper wires connect the SiPMs to the USLS connector (Figure 4.2(a)). Such connector provides the common bias voltage for the SiPMs and receives the individual signal of each SiPMs. Very thin 1.5 m coaxial cables (one for each USLS connector pin) connect the PCB to the readout PET electronics and the power supply, both placed outside the MRI to avoid electromagnetic interferences.
(a) (b)
(c) (d)
Figure 4.2: Top left: Outer PCB (top) with 24 SiPM and USLS connector of 30 pins and inner PCB (bottom) with 16 SiPM and USLS connector of 20 pins. Top right: The KETEK PM 1150 used in the MADPET4 module. Bottom-left: Assembly of PCBs with SiPMs to the 3D-printed plastic structure, which houses the crystals inside. Bottom-right: Close-up of the mounted inner PCB [50].
displaced as can be seen in Figure 4.2(c), and 8 coaxial bre bundles (4 for the inner PCB 4 for the outer PCBs) connected to the PCBs connectors. This con guration has been used so far to study the energy resolution of the prototype, and to acquire rst coincidence images of two22Na point sources
with dierent activities. The MADPET4 prototype in its nal con guration (Figure 4.3) will be ready probably at the end of February: once completely mounted, simultaneous measurements and images acquisitions in the MRI scanner will be performed.
4.2 The 7 Tesla GE/Agilent Discovery MR 901
scan-ner for small animals
The MADPET4 prototype is designed to work inside 7 Tesla GE/Agilent Discovery MR 901 scanner for small animals. The scanner has a cylindrical shape given by the superconductive coil, with a length of 1636 mm and an overall diameter of 1690 mm. The internal bore of the magnet is 310 mm, that becomes 210 mm with the gradient coil, and with the RF coil it further reduces to 146 mm: this is the bore where the MADPET4 is inserted.
Figure 4.3: 3D model of the nal con guration of the MADPET4 prototype, consisting of 66 outer PCBs and 44 inner PCBs, mounted on the inner and outer ring. The same number of bre boundles (66 for the outer ring and 44 for the inner ring) will connect the PCBs to the readout PET electronics, placed outside the MRI scanner [50].
The main component of this MR scanner is the superconductive coil, that allows to reach a 7 Tesla static magnetic eld with high uniformity (drift less than 0.05 ppm). The coil is actively shielded, and is cooled with liquid helium and liquid nitrogen: the maximum magnetic eld is reached through a current of 262 A that ows in the coil. Other important components for the main magnetic eld are the shim coils: their task is to adjust the homogeneity of the main magnetic eld through the variable currents that ow within them. This MRI scanner is provided with ten superconductive shim coils, that adjust the static magnetic eld along the main axis of the magnet and in the transaxial plane. Gradient coils along the z-axis and the transaxial plane are provided for the imaging processes. The main gradient coil (along the z-axis) is a removable component and is able to generate at most 300 mT/m of gradient strength. Finally, the RF coil is a transmitter and receiver birdcage coil that works at 300 MHz, the Larmor frequency of the hydrogen at 7 Tesla.
The scanner is developed for small animal studies. In particular, 2D and 3D images can be acquired through several sequences, as Spin Echo, Fast Spin Echo, Gradient Echo and Spoiled Gradient Echo; some imag-ing options are available, like respiratory compensation, ow compensation, cardiac compensation, fat/water spectral chemical saturation. Neuro 2D and 3D studies can be performed, through dierent sequences, like Multi-Echo Recombined Gradient Multi-Echo, Multi-Echoplanar Imaging or functional MRI. The scanner has also additional cardiac and angiographic functionalities, as 2D/3D Phase Contrast MR angiography, 2D/3D Gated Time-of-Flight and Fast Time-of-Flight MR angiography, black blood Double or Triple Fast Spin
Echo and time-resolved imaging of contrast kinetics. Finally, spectroscopy functionalities are available.
Chapter 5
Simulation with the
MADPET4 components in the
MRI elds
The simulations in this work have been carried out with COMSOL Multiphysics (www.comsol.com), a dedicated simulation software platform for modelling and simulating physical-based problems. COMSOL is able to solve 1D, 2D and 3D-physical problems by the nite element method and, with its user-friendly interface, is possible to set the geometry, the physical phenomena involved in the model, the materials which the model is made of, and the meshing parameters (the mesh is necessary for the nite element calculus). To understand the simulations done with COMSOL Multiphysics, an intro-duction to the nite element method is reported in Appendix A.
Simulations realized can be divided in three main groups:
1. study of the uniformity of the 7T magnetic eld with the MADPET4 components inside the bore;
2. study of the uniformity of the RF magnetic eld generated by the RF coil with the MADPET4 components inside the bore;
3. study of the heating inducted by the RF magnetic eld in the MAD-PET4 components.
For each group of simulations these steps have to be carefully followed: de nition of the geometry; of the materials in the dierent domains of the geometry; of the physical processes that have to be studied; of the mesh and of the type of study to apply to the model (this last choice also changes the equations of the physical model).
As can be seen in Figure 5.1, COMSOL provides a graphic interface where the simulation set-up can be modi ed and continuously monitored.
Figure 5.1: Example of the COMSOL interface. The user can see the model in the graphic window (on the right) and set the simulations in the left (Model Builder) and central (Settings). The progress bar and warning or error messages are shown in the bottom right row.
Referring to Figure 5.1, in the rst column on the left, called Model Builder, the user can select one of the dierent options of the simulation (Global Def-initions, Model, Study and Results). In the Global De nitions, the user can de ne constants or variables or functions of the model. In the Model node the user can nd many subnodes where all the aspects of the model can be de ned: Geometry, Materials, Physics and Mesh. Choosing the Geometry subnode, the user can add, remove or visualize all the domains (volumes in 3D model, planes in 2D model, lines in 1D model); in the Materials subnode, the materials can be de ned for each domain; in the Physics node, the user can add one or more of the various already-built physical processes: they can be gathered in 4 main categories (electrical, mechanical, uid and chem-ical) and, once the desired physics is chosen, the user can add, remove and visualize all the options related to that particular physical process; in the Mesh subnode the user can select the type of meshing desired, geometrical forms and many options about the dimensions of the elements; the Study node allows to choose the type of study, and therefore the physical equations in the Physics node, the model is solved for (Stationary study, Time Depen-dent study, Frequency Analysis study, etc.), and the solver options, like the algorithm (direct or iterative) for the research of solution of the nite ele-ment method; the Result node is used to analyse the solutions and physical quantities calculated by the simulation, through many dierent types of 3D, 2D and 1D graphs.
Builder: once one of the nodes or subnodes is selected in the Model Builder, the user can set or modify, in the Setting column, values, parameters, func-tions or geometrical domains or boundaries related to the particular node or subnode chosen. Moreover, in this column the physical equations used in the model can be visualized.
In the graphic window, on the right of the interface, the user can visualize and monitor the 3D, 2D or 1D model built in the Geometry node and select domains, boundaries or lines when requested in the settings column. Also, the results and graphs are shown here.
The last row in the bottom-right of the interface shows the warning and error messages during the building of the model, and the progresses and errors of the simulation.
In order to study the magnetic compatibility of the MADPET4, only the SiPM and PCB have been recreated in a 3D model, while the plastic structure and the LYSO crystals have not been taken into account: this choice has been made because the SiPM and the PCB are the only components that present electrical parts that could interfere with the magnetic eld since the LYSO crystals and the plastic are made of non-magnetic materials. Every simulation has been carried out with only one component at a time, due to the limited performances of the computer used; for the same reason, the simulation of the entire MADPET4 module was not possible.
5.1 The 3D models of the main MADPET4
com-ponents
It has to be pointed out that, to de ne a 3D model in COMSOL, the geomet-rical informations of the element (or elements) of interest in the space are not enough: also the informations about the materials the element is com-posed of are necessary. In COMSOL a material is de ned by the values of its physical constants (e.g. density, heat capacity at constant pressure, electri-cal conductivity, magnetic permeability, etc.), and the constants needed in the simulation are those who appear in the equations of the physical process chosen (e.g. if a process of electrical currents induced by a magnetic eld is simulated, the physical constants that must be de ned are relative permit-tivity, electrical conductivity and relative permeability for each material), or clearly the simulation cannot be computed. The program COMSOL pro-vides a large Material Library, where materials of common use are already built in and, if a constant requested by the physical equations is not de ned in the material, the user can add it manually. Moreover, the user can de- ne a completely new material if he is able to indicate all the values of the constants that appear in the physical equations.
As said before, the PCB and SiPM are the MADPET4 components cho-sen for the simulations: their 3D models used in this work can be observed
(a) SiPM model (b) PCB model, all made of copper
(c) PCB model, one layer of copper (d) PCB model, 6 layers of copper Figure 5.2: 3D models of the MADPET4 components simulated in this work. Top Left:
the SiPM 3D model of KETEK PM1150; Top Right: the PCB model entirely made of copper; Bottom Left: the PCB model with a 35µm layer of copper on the plastic substrate; Bottom Right: the PCB model with 6 layers of copper, each 35µm of thickness, inside the plastic.
in Figure 5.2. These models had been used during all the simulations re-ported in this work. The SiPM model was already provided by the KETEK company and it has been simply acquired in COMSOL. Once available, the materials have to be de ned according with the datasheet of the SiPM (Fig-ure 5.2(a)). Silicon crystal have been chosen for both the active area (it has not been possible to de ne the silicon doped material) and the silicon sub-strate (the SiPMs are actually made by a silicon crystal that is conveniently doped and upon which the cells are lithographed). For the plastic layer under the silicon substrate, the FR4 has been chosen (that is the plastic the Printed Circuit Boards are made of), while the epoxy resin has been selected for the transparent capsule that covers the active area (cf. Figure 4.2(b)). Finally, copper has been chosen for the ve electrical connectors at the bottom of the SiPM.
Regarding the PCB, an already-built le with its structure does not exist and the real structure is too complicated to build by hand: as reported in 4.1.2, PCB is made of FR4 of 1.6 mm thickness, inside which 6 layers of copper connections 35 µm thick connect the SiPMs to the USLS connector.
In order to study the behaviour of the PCB in the magnetic resonance system, three approximations steps have been chosen: the "zero order", where all the PCB is made of copper (Figure 5.2(b)): this is the worst possibility, where the interferences between copper and RF magnetic eld are maximum; the " rst order", where a 35 µm thick copper layer is built upon an FR4 support in a way that the total thickness is again 1.6 mm (Figure 5.2(c)): this is like all the wires were on the PCB surface; the "second order", where the PCB is built alternating around 0.2 mm thick FR4 layers and six 35 µm thick copper layers (that simulates the six layers of copper wires), the layers at the top and at the bottom are made of FR4 (Figure 5.2(d)) and the thickness of the whole structure is again 1.6 mm: this is approximately the real situation. The dimensions of the PCB are those of the outer one (52×1.6×6 mm3): this
decision has been taken in order to consider the worst case, because the ux of the magnetic eld is higher in the outer PCB (due to the larger surface) than the inner one, so if the eects of interferences observed in the simulation are very low, the eects in the inner PCB will be even lower. Unfortunately, the USLS connectors cannot be added in the model: an already-built le of the connectors currently exists, but it has been impossible to mesh in COMSOL, making the simulation with the connector model impossible to carry out.
About the meshing of the SiPM model, several steps have been followed, that can be observed in Figure 5.3. Firstly, a grid of squares has been built on the surface of the domain corresponding to the active area (Figure 5.3(a)), then a swept process has been de ned in order to carry the grid de ned before through the domain, until the surface opposed to the active area: in this way the domain is divided in prisms with a squared base (Figure 5.3(b)). The same meshing has been de ned for the four rectangular connectors on the base of the SiPM (Figure 5.3(c)). The round connector has been meshed in a similar way: a grid of triangles has been created on the free face and , through the swept process, has been passed through the connector until the face opposed to the free one, thus the connector is divided in prisms with a triangular base (Figure 5.3(d)). This kind of mesh is strongly recom-mended by COMSOL developers when the domain to be meshed has one of the dimensions smaller than the other two, and is very useful to obtain an highly-uniform meshing, specially on the surfaces of such domains. Finally, all the squares and rectangles have been converted in triangles by adding one or two diagonals and all the prisms in tetrahedrons (Figure 5.3(e)), because COMSOL can work only with tetrahedrons and triangles. Finally, the re-maining domains of the SiPM have been meshed directly with tetrahedrons (Figure 5.3(f)). Due to the dierent computational weight of each physical model used in this work, the dimensions of the meshing elements (squares, triangles, tetrahedrons, etc.) have been de ned each time in each simulation, in order to not exceed the computational features of the computer used, but at the same time trying to reach a suitable level of approximation.
