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Brain Imaging with a Coded
Pinhole Mask
WUWEI REN
Master of Science Thesis in Medical Engineering Stockholm, Sweden 2012
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Brain Imaging with a Coded Pinhole Mask
Wuwei Ren
Supervisor: Massimiliano Colarieti Tosti Examiner: Andras Kerek
TRITA 2012:34
School of Technology and Health Royal Institute of Technology Stockholm, Sweden, 2012
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Abstract
In this study, we present a novel design of Multi-‐Layer Pinhole Collimator (MLPC), which is a pre-‐requisite for the development of a mobile stationary SPECT with large field of view (FOV). The 4-‐layer MLPC structure consists of three mask-‐detector groups. All three groups have different focal points but share similar hexagonal pattern with a phase difference of π/6. For a specific group of detector and pinhole mask, it is assumed that an optimal imaging area exists, where a good balance between sensitivity and resolution is achieved. Both resolution measurement and Derenzo phantom test are performed in GATE, a Monte Carlo simulator. The raw data is processed using NORA decoding method, a fast and non-‐iterative reconstruction method, based on Matlab. After evaluating the reconstruction results, we find that MLPC is able to diminish the resolution variation in large FOV with improved sensitivity of 86,0 cps/MBq, and decent image resolution of 5 mm compared with parallel-‐hole collimator and classic 7-‐pinhole mask. A three-‐dimensional object is reconstructed without rotating a gantry.
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Content
Abstract ......................................................................................................................................... 3 Content .......................................................................................................................................... 4 Abbreviations ............................................................................................................................. 5 1. Introduction ....................................................................................................................... 6
1.1 Nuclear Imaging ....................................................................................................... 6 1.2 Collimation of Gamma Camera .......................................................................... 8 1.3 Scope of the thesis ................................................................................................. 13
2 Monte Carlo simulation in GATE .............................................................................. 15 2.1 Geant4 Application for Tomographic Emission (GATE) ....................... 15 2.2 Physics process of gamma radiation ............................................................. 15 2.3 Basic Setup for Physics in GATE ...................................................................... 16 2.4 Structure of simulation files ............................................................................. 17
3 Geometry description of MLPC ................................................................................. 19 3.1 Individual Pinhole Collimator .......................................................................... 19 3.2 Multi-‐Layer Pinhole Collimator ....................................................................... 20
4 Image Reconstruction and Analysis ........................................................................ 24 4.1 Development of PinholeViewer ........................................................................ 24 4.2 Digitization ............................................................................................................... 25 4.3 Reconstruction ....................................................................................................... 25 4.4 Deblurring ................................................................................................................ 27 4.5 Visualization ............................................................................................................ 28
5 System Optimization ...................................................................................................... 29 5.1 Energy Window ...................................................................................................... 29 5.2 Collimator Thickness ........................................................................................... 29 5.3 Pinhole Shape .......................................................................................................... 30 5.4 Layer Positioning ................................................................................................... 31
6 Imaging with MLPC ........................................................................................................ 35 6.1 Reconstruction resolution without scattering .......................................... 35 6.2 System volume sensitivity ................................................................................. 37 6.3 Derenzo Phantom study ..................................................................................... 38
7 Conclusion and Future work ...................................................................................... 41 7.1 Conclusion ................................................................................................................ 41 7.2 Future work ............................................................................................................. 42
8 Reference ............................................................................................................................ 43 Appendix I: Paper submitted .............................................................................................. 45
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Abbreviations
ACD: Annihilation Coincidence Detection FDG: Fluorodeoxyglucose FOV: Field of View FWHM: Full width at half maximum GATE: Geant4 Application for Tomographic Emission GUI: Graphical User Interface ICU: Intensive Care Unit LEP: Low Energy Electromagnetic Processes MF: Magnification Factor MLPC: Multi-‐Layer Pinhole Collimator MPA: Multiple Pinhole Array NORA: Non-‐overlapping Redundant Array PET: Positron Emission Tomography PSF: Point Spread Function SEP: Standard Energy Electromagnetic Processes SNR: Signal to Noise Ratio SPECT: Single Photon Emission Computed Tomography Tc-‐99m: Technetium 99m
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1. Introduction
Modern nuclear imaging technology including Positron Emission Tomography (PET) and Single Photon Emission Computer Tomography (SPECT) plays a vital role in both clinical practice and biomedical research. Nuclear imaging visualizes the distribution of radioactive compounds in the subjects, patients or experimental animal. Balancing factors such as equipment costs, resolution requirement, infrastructure, sensitivity and availability of the radioactive agents, PET and SPECT are considered to be complementary for various purposes[1]. In spite of relatively low sensitivity and limited resolution, SPECT has several advantages over PET. Most SPECT radionuclides have lower production costs than PET. Besides, spatial resolution of PET is limited by the inevitable positron range and non-‐collinearity of annihilation photons, which are not seen in SPECT. In SPECT, a collimator is designed to permit photons following certain trajectories to reach the detector. The collimator design has been an important issue for two reasons: first, the geometry of collimator controls the trade-‐off between sensitivity and resolution; second, some special collimation patterns introduce additional tomographic information. These will be discussed further in section 1.2. In this study, we investigated the theoretical feasibility of Multiple Pinhole Array (MPA) collimators for developing a SPECT system without rotating or moving elements. A four-‐layer arrangement is proposed and the system performance is evaluated using the simulation toolkit GATE[2]. We are able to image a field of view (FOV) of the order of a human brain (a sphere of radius 100 mm). The system sensitivity is 86,0 cps/MBq while the overall resolution is estimated as 5 mm. The Performance of the MPA collimator is comparable with traditional parallel-‐hole collimator.
1.1 Nuclear Imaging
Nuclear imaging produces images of the distribution of radionuclides in experimental subjects. Gamma rays, characteristic x-‐rays or annihilation photons are used to form images. A typical radiopharmaceutical consists of carrier molecules, such as ligands or antibodies and its coupled radioactive moieties. When the radiotracer is injected into a patient’s body, gamma photons are emitted proportional to the distribution of the in vivo tracers. These photons are thus recorded and a two-‐dimensional (2D) or three-‐dimensional (3D) image is obtained via various imaging modalities. The functional information provided by PET or SPECT makes nuclear imaging a diagnostic tool in clinical practice. The body handles substances differently when
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there is pathology. Some good examples include myocardial perfusion scan, parathyroid scan and pulmonary ventilation scan. Thanks to the high sensitivity of PET, early tumor prediction is possible using 18F-‐FDG[3]. Nuclear imaging can be subdivided into two categories: planar imaging and tomography. Planar imaging provides a 2D projection of the real 3D distribution of tracers. In this way, the 3D information is lost since planar imaging adds up all the radioactivity values along the projection direction. Tomography provides solution to reconstruct the 3D volume by sampling numerous projection data from different angles around the object. SPECT and PET are distinguished by the different radionuclides and collimation methods. The following explains the detailed principles for these two modalities. Positron Emission Tomography (PET): The basic mechanism behind PET is annihilation coincidence detection (ACD). When the radioisotope, such as 11C, 13N, 15O and 18F, decays, a positron particle (β＋) is generated and annihilates with an electron (e) in the surround material after travelling a certain distance ranging from 0.5 mm to 3 mm. The annihilation event results in two 511 keV photons that are emitted in early opposite directions. When the pair of photons is detected simultaneously within a ring of detectors surrounding the target, it is presumed that this annihilation occurred on the line between the two registered positions in the ring.
Figure 1: Annihilation event happens to the radionuclides in subjects (left); Schematic diagram of PET
ring detector shows how the coincidence is detected (right) [1]
.
Single Photon Emission Computed Tomography (SPECT): In SPECT the gamma rays emitted by radionuclides, such as 99mTc, 123I and 201Tl, obey a uniform angular probability distribution. To create a correspondence between points of target and those of detector plane, a mechanical collimator is needed. A SPECT system samples projections from various angles. The most commonly used collimator is the parallel-‐hole collimator. Other specialized collimators such as fan-‐beam collimator find their application mainly in brain imaging.
27
(a) (b)
Nucleus
e-E+
511 keV
511 keV
J
J
object
ring detector
coincidencecircuitry
Figure 1-1. (a) Annihilation reaction. (b) Schematic diagram of PET ring detector.
addition, positron-emitting isotopes of carbon, nitrogen, oxygen, and fluorine occur
naturally in many biological systems and pharmaceutical compounds; this permits
incorporation of positron emitters into a wide variety of useful radiopharmaceuticals to
investigate specific physiological functions (Ollinger and Fessler, 1997). For example,
18F-FDG (fluorodeoxyglucose) is a commonly used PET radiopharmaceutical, which is a
chemical analog of glucose with replacement of the oxygen at the C-2 position with 18-
fluorine. When 18F-FDG is introduced into blood stream, it localizes through glucose
metabolism and thus can be used to study the metabolic process of glucose in the organ
of interest (Opie and Hesse, 1997).
The major disadvantages of PET are its equipment and radiopharmaceutical costs.
Since the half-lives of positron emitters are generally short, an on-site or nearby cyclotron
is required to produce the necessary radioisotopes. PET scanners are also significantly
more expensive than SPECT instruments in general. In addition, the spatial resolution of
PET has some fundamental physical limitations, such as non-zero positron range after
8
Figure 2: Planar imaging with a parallel-‐hole collimator (left); Schematic diagram of a triple-‐head
SPECT scanner (right) [1].
PET vs. SPECT: We compare these two imaging modalities from several perspectives: sensitivity, resolution and cost. First of all, PET has a higher sensitivity than SPECT due to different collimation methods. The ACD applies electronic collimation, which avoids much loss of events during detection. However, SPECT uses a mechanical way to find the correspondence. This method is less efficient since only small fraction of emitting gamma particles arrive in the scintillator. The improvement of sensitivity for SPECT depends largely on the optimization of collimator geometry. Secondly, the resolution of PET is limited by two factor, namely positron range and photon non-‐collinearity. Positron range is the distance the positron travels before it can reach thermal energies in order to be annihilated. This range differs from isotope to isotope due to different energy distribution. Non-‐collinearity means deviation from 180o between the trajectories of the two emitted photons due to conservation of momentum. On the contrary, the resolution of SPECT is mainly limited by technology, mainly collimator design. For example, some of small animal SPECT systems achieve sub-‐millimeter resolution using specialized pinhole collimator [10]. Finally, high cost to build an on-‐site cyclotron for generating PET radionuclides has limited the widespread of this efficient technique. The average cost to do PET scan in Sweden scan is over 10,000 SEK[4], which is more expensive than SPECT. The radionuclides in SPECT have relatively longer life and make transporting to hospitals easier. From what we have discussed above, it is convincing that the study in the collimation of SPECT is salient.
1.2 Collimation of Gamma Camera
Classification of collimators:
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(a) (b)
object detector
parallel-holecollimator
object
detector
rotationorbit
Figure 1-2. (a) Gamma-ray imaging with a parallel-hole collimator. (b) Schematic diagram of a triple-head SPECT scanner.
To accomplish SPECT imaging, sufficient projections from different views must be
collected to allow tomographic reconstruction. This can be done by rotating the object in
front of the detector or by rotating the collimator-detector combination around the object.
SPECT systems usually comprise a gantry with one or more movable camera heads or
multiple detectors in a closed ring or polygon. More detectors lead to higher system
sensitivity but also higher cost. A triple-head SPECT system design is shown in Fig. 1-
2(b) and the dotted circle indicates the rotation orbit of detectors. Each head needs to
cover 120° in this system.
In contrast to the flourishing developments of dedicated small-animal PET scanners,
most of the early small-animal SPECT studies were accomplished with clinical gamma
cameras. Conventional clinical gamma cameras with parallel-hole collimators only
provide spatial resolution around 6 to 10 mm, which is too low for small-animal imaging.
However, high-resolution imaging can be achieved by using specialized pinhole apertures.
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The purpose of introducing mechanical collimators in gamma camera is to find the point-‐to-‐point correspondence between object and image. The collimators are made of high atomic number materials, usually lead or tungsten. According to their geometry, we can generally classify collimators into four types, namely parallel-‐hole, pinhole, converging and diverging. The parallel-‐hole collimators are the most commonly used. This type of collimators contains thousands of parallel holes. The shape of individual hole varies. Most of parallel-‐hole collimators use hexagonal holes. The partitions between the neighboring holes are called septa. The septa must be thick enough to stop the photons from neighboring holes. The size of image is the same as the object. Generally speaking, the pinhole collimator is only suitable for small FOV because the variation of both sensitivity and resolution can be large in a big FOV. A magnification factor is defined as the ratio between image and its corresponding object. This factor is determined by the relative positions of object, collimator and detector. A large magnification factor is always applied in order complement the detector resolution. Today, most small animal SPECT systems are using pinhole collimation. A converging collimator induces magnification of the object and thus is useful in imaging small object. On the contrary, the diverging type minifies the object on the image plane and can be used in developing a mobile scintillation camera in Intensive Care Unit (ICU) in hospitals.
Figure 3: There are four types of collimators: Parallel-‐hole (upper left), Pinhole (upper right),
converging (lower left) and diverging (lower right)[4].
Image in crystal
LTtTTTlT1llT1TT. .
. .
Parallelhole
Image in crystal
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the-art collimators have hexagonal holes and are usually made from lead foil,although some are cast. The partitions between the holes are called septa. The septamust be thick enough to absorb most of the photons incident upon them. For thisreason, collimators designed for use with radionuclides that emit higher-energyphotons have thicker septa. There is an inherent compromise between the spatialresolution and efficiency (sensitivity) of collimators. Modifying a collimator toimprove its spatial resolution (e.g., by reducing the size of the holes or lengtheningthe collimator) reduces its efficiency. Most scintillation cameras are provided with aselection of parallel-hole collimators. These may include "low-energy, high-sensitiv-ity," "low-energy, all-purpose" (LEAP), "low-energy, high-resolution", "medium-energy" (suitable for Ga-67 and In-Ill), "high-energy" (for 1-131), and "ultra-high-energy" (for F 18) collimators. The size of the image produced by a parallel-hole collimator is not affected by the distance of the object from the collimator.However, its spatial resolution degrades rapidly with increasing collimator-to-objectdistance.
A pinhole collimator (Fig. 21-6) is commonly used to produce magnified viewsof small objects, such as the thyroid or a hip joint. It consists of a small (typically3- to 5-mm diameter) hole in a piece of lead or tungsten mounted at the apex of aleaded cone. Its function is identical to the pinhole in a pinhole photographic cam-era. As shown in the figure, the pinhole collimator produces a magnified imagewhose orientation is reversed. The magnification of the pinhole collimator decreasesas an object is moved away from the pinhole. If an object is as far from the pinhole
as the pinhole is from the crystal of the camera, the object is not magnified and, if
10
Pinhole collimator: As we mentioned above, pinhole collimation brings two major benefits: (1) control of trade-‐off between resolution and sensitivity and (2) Additional tomographic information. According to the theory of photon quantum noise, a large pinhole size improves the signal to noise ratio (SNR) and sensitivity, but blurs the image; On the contrary, with a small pinhole, the SNR declines because fewer photons are detected, but higher resolution is achieved. To maintain both good resolution and high sensitivity, the concept of Multiple Pinhole Array (MPA) is proposed. Each hole in MPA generates a projection with high fidelity and the total amount of photons from all the holes contributes to the decent improvement of sensitivity. The MPA also makes 3D reconstruction possible. Every pinhole provides a unique pattern of projection from a certain angle. Therefore, it is feasible to reconstruct the object according to the central slice theory.
Figure 4: A tradeoff between spatial resolution and sensitivity can be controlled by the diameter of a
pinhole (upper). The concept of Multiple Pinhole Array is proposed to maintain both good resolution
and high sensitivity (lower)[5].
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The idea of using MPA dates back to very early years of planar scintigraphy. In 1974, Chang suggested a method using an aperture of multiple pinholes to produce a coded image and decoded it with a diffuse light source and the original aperture to produce the image[15]. Vogel and his colleagues proposed a 7-‐pinhole mask coupled with an Anger scintillation camera. The lateral resolution is 1.0 cm and depth resolution is 1.5 cm[16][17].
Figure 5: Chang used an early MPA and a corresponding optical decoding method (left). Vogel and his
colleagues proposed a 7-‐pinhole collimator for heart imaging (right).
A stationary SPECT using pinhole collimation is built at the University of Arizona[6]. In Barrett’s group, a hemispherical SPECT imager is proposed to produce three-‐dimensional images of the brain. The system constitutes a hemispherical MPA and 20 modular cameras. The system sensitivity is 36 cps/μCi and the resolution is 4.8 mm.
CHANG, KAPLAN, MACDONALD, PEREZ-MENDEZ, AND SHIRAISHI
properly aligned, the decoded image comes intosharp focus at an image plane where it can be directlyobserved on a second ground-glass screen and subsequently photographically recorded.
RESULTS AND DISCUSSION
An image of a Picker thyroid phantom taken withthe 27 nonredundant pinhole-coded aperture isshown in Fig. 1A. The shadowgram consisting of540,000 dots was recorded on Kodak Ektapan film.The reconstructed image as shown in Fig. lB wasprinted on high-contrast paper to reduce the background of light and enhance the contrast. The rightand left lobes differed in activity and this differencecan be seen in the reconstruction. The smallest ofthe cold nodules is 5 mm in diameter and is clearlyimaged.The tomographic capability of this coded aperture
is shown in Fig. 2. Figure 2A shows the shadowgram of a radioactive phantom consisting of threegeometric patterns labeled with 1251 (a cross, a tnangle, and a circle) which were separated by a distance of 2.5 cm in depth. A total of I million gammaswas recorded on the shadowgram. Figures 2B, C,and D are the reconstructions of each of the patternsobtained by adjusting the mask-to-image plane distance in the reconstructions so as to bring eachpattern into sharp focus. Each of the in-focus imagesis superimposed on a background arising from theplanes at other depths in the phantom. Since nomovement of the detector is necessary and all theinformation of the shape and size of the object isrecorded in a single picture, dynamic studies arepossible.
CODEDP1510LIAPEITSIE[
OBJECT @-@ â€w,'@pp.7v/st
IMAGEPLANE
PINNatEMASK
A
[lOUTSOUUCE
B
COPED55*5000kM
DIFFUSINCSCUllS
FIG. 1. (A)Compositediagramof imagingsystemshowsspatial placement of various components depicting 27 nonredundantpinhole array and actual shadowgram of Picker thyroid phantom.(B) Composite diagram of reconstruction system shows decodedimage of shadowgram.
a single pinhole, and is given by S = d( 1 + S,/S2)where d is the diameter of the pinhole and S and S@are as shown in Fig. IA. The depth resolution isgiven by@ = 2(d/D) S@(l + S1/S2) where D isthe largest lateral distance between any two pinholesof the array. This calculation for the depth resolutionassumes that 50% of the light from the out-of-focusplanes overlaps the light from the in-focus plane.The coded aperture consists of 27 2-mm-diam
pinholes drilled into a flat sheet of lead 2 mm thickand was designed to work with gammas up to 140-keV energy. In this application, the radiation wasthe 28-keV x-rays emitted by a â€25I-filledthyroidphantom. The resolution of the system is limited bythe 2-mm-diam size of the individual pinholes and,thus, for a typical imaging geometry in which S@=52, the overall lateral resolution is 4 mm.The reconstruction system is shown in Fig. IB.
An intense, uniform, and diffuse light source is madeby focusing the light from a slide projector onto aground-glass screen. The rays of light emitted fromthe screen are further transmitted through the transparency of the shadowgram and through a maskthat is a duplicate of the original nonredundant pinhole array. When the shadowgram and mask are
cJ..S@ . , ..
;@-@:@@@@@ @-.@
C
FIG.2. (A)CodedshadowgramofPatterns were spaced 2.5 cm in depthReconstructedimagesof each pattern.
cross, triangle, and circle.from one another. (B,C,D)
1064 JOURNAL OF NUCLEAR MEDICINE
IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. MI-4, NO. 2, JUNE 1985
Improved Tomographic Reconstruction inSeven-Pinhole Imaging
JOHN W. VAN GIESSEN, MAX A. VIERGEVER, AND CORNELIS N. DE GRAAF, MEMBER, IEEE
Abstract-Cardiac emission tomography using a seven-pinhole colli-mator has received only little appreciation as a diagnostic imaging tech-nique. The main reasons are the limited angular sampling of the seven-
pinhole device and the difficulties encountered in properly positioningthe patient relative to the collimator/camera system. In order to over-
come these problems, we have developed a modified ART3 algorithmfor reconstruction of the radioactivity distribution in the heart. Themethod is very appropriate for seven-pinhole tomography, as demon-strated by the quality of the reconstructions, by the excellent point sourceresolution of the system response, and by a comparison to two othersuitable reconstruction techniques, viz., SMART and SIRT.
I. INTRODUCTION
EVEN-pinhole (7P) tomography is a method of my-ocardial perfusion imaging introduced by Vogel and
co-workers [1]. It is a low-cost method because it onlyrequires a simple collimator in addition to a conventionalgamma camera system. Yet, seven-pinhole imaging hasnot gained wide appreciation in nuclear cardiology prac-tice. The limited angular samipling of the device has pre-vented reconstructed images from having a quality com-parable to full angle tomography [2]. Also, positioning ofthe patient relative to the collimator is critical for success-ful reconstructions.The purpose of this paper is to discuss whether the po-
tentialities of 7P tomography have been fully investigated.We start by formulating the reconstruction problem inmathematical terms; both a continuous version and a dis-crete version of the problem are presented. We then arguethat feasible reconstruction methods should be sought inthe class of discrete iterative techniques. Up to now, re-construction of 7P images has been performed almost ex-clusively on the basis of the SMART algorithm, which hasbeen proposed by the designers of the 7P device [3]. Toanswer the question as to whether this algorithm is the bestreconstruction method for this application, we compare itto two other iterative techniques, namely SIRT (to whichSMART bears some similarities) and a modified versionof ART3. Furthermore, we introduce a new operator topostprocess the reconstructed tomograms.Our intention is to convey that the ART3-based recon-
struction algorithm, extended with the postreconstruction
Manuscript received November 29, 1984; revised February 25, 1985.J. W. van Giessen and M. A. Viergever are with the Department of
Mathematics and Informatics, Delft University of Technology, 2628 BLDelft, The Netherlands.
C. N. de Graaf is with the Institute of Nuclear Medicine, UniversityHospital Utrecht, 3511 GV Utrecht, The Netherlands.
optical axLs(z-axis)
*-z=O
Fig. 1. Schematic representation of the imaging system and the reconstruc-tion volume. Dimensions are given in the text. The division of the re-construction volume into slices parallel to the detector face, which ischaracteristic of longitudinal tomography, is also outlined. For simplici-ty's sake we show here a division into three slices; in the computationseight slices are used.
operator, renders it worthwhile to reconsider the use of 7Ptomography as a standard clinical imaging technique forthe heart.
II. IMAGING SYSTEM AND PROCESSING SYSTEMThe collimator consists of a lead pinhole plate, located
at 127 mm from the camera crystal, with seven pinholesof 7 mm diameter. The center of the central pinhole issituated on the optical axis of the system (see Fig. 1). Thispinhole has a conical 530 field of view, perpendicular tothe crystal face. The six peripheral pinholes are spacedevenly at 63.5 mm from the axis; they have a conical 450field of view, converging inwards at 26.50. The seven-pin-hole collimator is used in combination with a wide-field(380 mm effective diameter) Anger camera with an intrin-sic resolution of 4.0 mm. Following intravenous injectionof a suitable radionuclide (i.e., 201T1), this configurationrecords seven projected images of the radioactivity distri-
0278-0062/85/0600-0091$01.00 1985 IEEE
91
12
Figure 6: The hemispherical multiple-‐pinhole SPECT at University of Arizona (left) and its
reconstruction result in simulation (right).
However, the hemispherical suffers a series of problems such as the resolution variation and low sensitivity. During the last decade, most studies regarding MPA concentrate on small animal imaging. Most small animal multiple-‐pinhole SPECTs can be classified as trans-‐axial computer tomography, which contains a cylindrical cavity and ring-‐shaped detectors. Several small animal pinhole SPECTs are described in the reference ([9]-‐[14]). The resolution can be less than 0,5 mm and the FOV is large enough for small animals, such as rodents, but is too small for bigger human organs like brain. If one wants to achieve an equally high image quality for human body using the same principle, the size of the whole machine will be extremely huge and thus not practical.
Figure 7: The design of a typical pinhole SPECT, U-‐SPECT-‐I[10], contains 75 gold pinhole apertures. 15
pinholes are distributed in each ring (left) with a total of nine rings (right).
Our design is mainly based on the early 7-‐pinhole collimator. However, this 7-‐pinhole design has several drawbacks: firstly, the geometric efficiency of pinhole collimators deteriorates with increasing source-‐to-‐aperture distance; secondly, spatial resolution varies with the changed distance between source
the N-element vector f. The corresponding SPEC!' data set isassumed to consist of M discrete picture elements (pixels) withcounts given by the elements of the M-element vector g. Thesystem is modeled by the M x N-element H matrix, whichrepresents the spatially variant response function of the system.The simulation routine used a numerical model of the imaging
system to generate independently the system matrix H and datavector g for each system configuration studied. Both sets of dataincluded effects due to radiometry, photon noise, finite pinholesize, object attenuation and the spatial resolution of the detector. Scatteranddetectorenergyresolutionwere not modeledbythe simulation. The system matrix was produced by simulatinga calibration procedure whereby a small point source wasmoved to each of the voxels within the FOV. The response ofthe imaging system to each of these source positions was recorded as a single column of the H matrix. The FOV used in allof the simulations was a 40 x 30 x 20voxel region in which eachvoxel was a 5 mm cube.The simulated data vector g was synthesized by a weighted
sum of the projection data produced by each of the voxelscontained in a three-dimensional digital phantom, where theweighting factor was proportional to the activity level of eachvoxel. A coarsely-sampled version of the digital brain phantomused during the simulation study is shown in Figure 2A. Thisversion consists of 24,000 voxels, each a 5-mm cube, and isrepresented in the figure as 20 slices of 40 x 30 pixels. In orderto better approximate a realistic, continuous object, the phantom that was actually used in the simulations was more finelysampled, consisting of 68 x 51 x 34 voxels with a voxel spacing
Eq.1
In this formulation, the object is modeled as N discrete volumeelements (voxels) with activity levels given by the elements of
@40:4@$.Iâ€*II•
,@:•*4*l@
*
FIGURE 1. Conceptualsketchof the UAbrainimagerdesigned to perform three-dimensionalSPECT imaging with nosystemmotion.The imager consists of a lead-alloyhemispherical multiple-pinhole coded aperture and 20 modular gammacameras.
SimulationStudy of the Brain ImagerThe imaging characteristics of the three-dimensional brain
imager can be described by a linear-systems model of the following form:
g = Hf.
—@—@.“ --@-.
@ â€@ *@ @â€@ , @@.-
p@&@I,
@ @-@h@―
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FIGURE 2. (A)Twenty slices through adigital brain phantomsimilarto the oneusedfor the simulationstudies.Eachsliceconsists of 40 x 30 voxels, each 5 x 5 x 5mm. The base of the brain phantom isshownintheupperleftcornerandconsecutive slices are arrangedIna rasterpatternwith the apex of the brain shown in thelower right corner of the Image. (B) Projection data of the digital brain phantom ascollectedby the 20 modularcamerasIn asimulated imagingsystemsimilar to FigureI . The aperturehemispherehada radiusof15 cm and contained 100 pinholes, each1.4 mm square. The cameras were axranged tangent to a 22-cm radius hemisphere. (C) Reconstruction of the digitalbrain phantomthat was producedusingtheprojection data described in (B). Both theprojection data and the system matrix Included effectsdue to photon noise and attenuation.
I•::@@
@;
Three-DimensionalSPECT,CodedAperturesandBrainImaging•Roweetal. 475
!@
the N-element vector f. The corresponding SPEC!' data set isassumed to consist of M discrete picture elements (pixels) withcounts given by the elements of the M-element vector g. Thesystem is modeled by the M x N-element H matrix, whichrepresents the spatially variant response function of the system.The simulation routine used a numerical model of the imaging
system to generate independently the system matrix H and datavector g for each system configuration studied. Both sets of dataincluded effects due to radiometry, photon noise, finite pinholesize, object attenuation and the spatial resolution of the detector. Scatteranddetectorenergyresolutionwere not modeledbythe simulation. The system matrix was produced by simulatinga calibration procedure whereby a small point source wasmoved to each of the voxels within the FOV. The response ofthe imaging system to each of these source positions was recorded as a single column of the H matrix. The FOV used in allof the simulations was a 40 x 30 x 20voxel region in which eachvoxel was a 5 mm cube.The simulated data vector g was synthesized by a weighted
sum of the projection data produced by each of the voxelscontained in a three-dimensional digital phantom, where theweighting factor was proportional to the activity level of eachvoxel. A coarsely-sampled version of the digital brain phantomused during the simulation study is shown in Figure 2A. Thisversion consists of 24,000 voxels, each a 5-mm cube, and isrepresented in the figure as 20 slices of 40 x 30 pixels. In orderto better approximate a realistic, continuous object, the phantom that was actually used in the simulations was more finelysampled, consisting of 68 x 51 x 34 voxels with a voxel spacing
Eq.1
In this formulation, the object is modeled as N discrete volumeelements (voxels) with activity levels given by the elements of
@40:4@$.Iâ€*II•
,@:•*4*l@
*
FIGURE 1. Conceptualsketchof the UAbrainimagerdesigned to perform three-dimensionalSPECT imaging with nosystemmotion.The imager consists of a lead-alloyhemispherical multiple-pinhole coded aperture and 20 modular gammacameras.
SimulationStudy of the Brain ImagerThe imaging characteristics of the three-dimensional brain
imager can be described by a linear-systems model of the following form:
g = Hf.
—@—@.“ --@-.
@ â€@ *@ @â€@ , @@.-
p@&@I,
@ @-@h@―
r@,_ @F,@
$ , ,-:@râ€@
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FIGURE 2. (A)Twenty slices through adigital brain phantomsimilarto the oneusedfor the simulationstudies.Eachsliceconsists of 40 x 30 voxels, each 5 x 5 x 5mm. The base of the brain phantom isshownintheupperleftcornerandconsecutive slices are arrangedIna rasterpatternwith the apex of the brain shown in thelower right corner of the Image. (B) Projection data of the digital brain phantom ascollectedby the 20 modularcamerasIn asimulated imagingsystemsimilar to FigureI . The aperturehemispherehada radiusof15 cm and contained 100 pinholes, each1.4 mm square. The cameras were axranged tangent to a 22-cm radius hemisphere. (C) Reconstruction of the digitalbrain phantomthat was producedusingtheprojection data described in (B). Both theprojection data and the system matrix Included effectsdue to photon noise and attenuation.
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Three-DimensionalSPECT,CodedAperturesandBrainImaging•Roweetal. 475
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multi-pinhole SPECT imaging using dedicated detectorsprovides a combination (and not trade-off) of highresolution and high sensitivity, and furthermore, con-siderably enhances possibilities of dynamic imaging.However, one may add that these systems would stilllikely require axial translation schemes since they cover avery limited FoV.
Finite resolution effects in SPECTIn SPECT, the image generated from a point source isdegraded by a number of factors related to collimatorsand detectors in gamma cameras, thus referred to as thecollimator–detector response (CDR). Therefore, for anyparticular SPECT camera, the CDR can be a measure ofthe image resolution; however, this is valid only if nofurther compensation is included. In recent years, a greatdeal of work has gone into developing methods tocompensate for the CDR [33].
The CDR is determined by the following four factors:
(1) Intrinsic response Aside from the effect of collimators,the detector system itself demonstrates an intrinsicuncertainty in position estimation of incident gammarays. This is caused by two factors: (a) the statisticalsignal variation (noise) in signal output of PMTs usedfor position estimation, and (b) change/spread insignal energy deposition in the detector due toscattering (especially for higher energy isotopes, e.g.,111In).
(2) Geometric response Collimator dimensions define theacceptance angle within which incident photons areaccepted. Subsequently, the geometric responsefunction becomes wider with increasing distancefrom the collimator surface, and strongly depends onthe particular design of each collimator.
(3) Septal penetration The CDR is further degraded owingto the penetration of some photons through thecollimator septa. No analytical treatment of thiseffect appears to exist in the literature, and MonteCarlo simulation techniques have been used instead(e.g., Cot et al. [34], Du et al. [35] and Staelens et al.[36]).
(4) Septal scatter This effect is caused by photons thatscatter in the collimator septa and still remain withinthe detection energy window. Similar to septalpenetration, this effect may also be computed usingMonte Carlo simulation techniques.
Analytical methods taking into account the distancedependence of the CDR function (CDRF) have beenproposed in the literature (see Frey and Tsui [37] for areview of both related analytical and statistical methods).However, compared to statistical methods, analyticalmethods suffer from (1) a general lack of ability to treatstatistical noise in the data, and (2) making specificapproximations, for instance with regards to the shapeand/or distance dependence of the CDRF, in order toarrive at analytical solutions.
With the increasing realization of the power of statisticalmethods in nuclear medicine, and particularly with thedevelopment of convenient and fast rotation-basedprojectors in SPECT [38–40], as shown in Fig. 3, iterativereconstruction methods incorporating distance-depen-dent CDRFs are increasing in popularity. The use ofGaussian diffusion methods [41,42] can further increasethe speed of rotation-based projectors.
Incorporation of CDR modelling in reconstruction algo-rithms (especially statistical methods) has been shown toresult in improvements in spatial resolution [41], noise
Fig. 3
Rotate
CDRFs
Rotation-based projector methods incorporating distant-dependentCDRFs make use of the fact that, for parallel-beam geometries, theCDRF is spatially invariant in rows (planes) parallel to the collimatorface. Thus, each row (plane) may be convolved with the appropriatedistance-dependent CDRF.
Fig. 2
The design of U-SPECT-I contains a total of 75 gold pinhole apertures:15 pinholes in each ring (left) with a total of nine rings (right). Notshown here is that pinhole positions in adjacent rings are rotatedtransaxially with respect to each other by 81 in order to increase thevariety of angles at which each voxel is observed. Reprinted withpermission from Beekman and Vastenhouw [31].
196 Nuclear Medicine Communications 2008, Vol 29 No 3
Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.
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and pinhole along central axis; finally, the whole system resolution is limited by the resolution of detectors besides the geometry of pinhole aperture. A proper magnification factor should be chosen which means the distance between collimators and scintillators should be large enough in order to achieve decent resolution of projection, which in turn results in an uncompact and less mobile system. In the new design of our project, we are able to eliminate almost all drawbacks in the old 7-‐pinhole collimator.
1.3 Scope of the thesis
The focus of the thesis work is development of a new type of collimation method, namely Multi-‐Layer Pinhole Collimator (MLPC) based on Monte Carlo Simulation using GATE. Generally, the computer aided design cycle includes mainly three stages: (1) Monte Carlo simulation, (2) Image reconstruction and analysis and (3) Evaluation and optimization, as shown in the following figure.
Figure 8: the design process for developing MLPC.
Monte Carlo simulation: The design process initiates with creation of collimation in GATE (Chapter 2). The geometry of collimator plays a key role herein, which consists of many aspects, such as arrangement, shapes and titled angles of pinholes (Chapter 3). A virtual experiment is established in addition to the collimator. At the end of simulation, raw data is obtained. Image reconstruction and analysis: the raw data from GATE simulation is digitized for further analysis, similar with the process of peripheral circuit
GATE Simulation
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readout. After digitization, reconstruction is performed. The last two steps include deblurring and 3D visualization of the reconstructed volume. The whole decoding procedure is done in Matlab. (Chapter 4) Evaluation and optimization: we analyze the performance of the testing setup from several perspectives, namely system sensitivity, resolution, mobility and feasibility. We try to alter the geometry of collimator if any improvement needed after each experiment. (Chapter 5) In the end, we use the optimized collimator to do phantom studies, such as point response and Derenzo phantom (Chapter 6). Conclusion and discussion are given in the last chapter (Chapter 7).
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2 Monte Carlo simulation in GATE
When we want to test certain geometry of collimator, it is both expensive and time consuming to build a real system. The inaccuracy of manufacturing new collimators and measurement errors of readout components both complicate the problem of trying a new geometry. In the very early stage of developing a new method of collimation, we use computer simulation. In this case, we choose the Monte Carlo method in the platform of GATE[2], a simulation toolkit. The central idea behind Monte Carlo method is repeated random sampling. Several related physics processes are introduced here and these processes are simulated with Monte Carlo method. The basic parameter settings regarding the physics are also given in this chapter. Finally we show the structure of our simulation files in GATE.
2.1 Geant4 Application for Tomographic Emission (GATE)
GATE is a worldwide used Monte Carlo toolkit for performing Emission Computer Tomography including SPECT and PET. In GATE, the validated physics modeling, geometry description and 3D rendering are well combined with unique features in medical imaging. It is able to synchronize all time-‐dependent components during the acquisition process. GEANT4 interaction histories can mimic realistic detector output and thus it is possible to get an output file for further utilization. The application of GATE has gained validations for several PET and SPECT scanners. The simulations involved in the project need strong calculation power and thus we used a cluster of 24 dual-‐core PCs to accelerate the process. The tasks were distributed between the nodes using Sun Grid Engine software.[24] We use Scientific Linux system as the platform.
2.2 Physics process of gamma radiation
For gamma radiation interactions in this project, there are three major types of interactions of photons with surrounding materials: (1) Rayleigh scattering, (2) Compton scattering and (3) photoelectric absorption[4]. (1) Rayleigh scattering: there is no energy loss and only a slight change in direction occurs during Rayleigh scattering. Less than 5% of interactions belong to this category and thus it is infrequent in gamma radiation. (2) Compton scattering: it is also called inelastic scattering, which implies energy loss in the process. When an outer shell electron absorbs part of the incident photon energy, the electron is ejected from the atom while the photon is
16
scattered with some reduction in energy. Compton scattering is predominant for gamma photons. (3) Photoelectric absorption: a photon may interact by transferring all of its energy to an inner shell electron. This results in an ejection from the atom.
2.3 Basic Setup for Physics in GATE
In GATE, there are two types of packages to simulate electromagnetic processes, namely Standard Energy Electromagnetic Processes (SEP) and Low Energy Electromagnetic Processes (LEP). Since the gamma rays in our case have the power of 140 keV and SEP is used to simulate interactions with energy higher than 10 keV, we choose SEP here. As we have mentioned above, the interactions in our project are Rayleigh scattering, Compton scattering and photoelectric absorption. Since Rayleigh scattering only counts for less than 5%, we omit this interaction to speed up our simulation. Thus we have the process list below:
/gate/physics/gamma/selectPhotoelectric standard /gate/physics/gamma/selectCompton standard /gate/physics/gamma/selectRayleigh inactive /gate/physics/gamma/selectPhotoelectric standard /gate/physics/gamma/selectGammaConversion inactive
Besides, we also set the cut for the electrons, X-‐ray and Delta-‐ray. Since the dimension of our camera is about 0.8m×0.8m×0.8m, we set the range of electron to 1m. The gamma rays in the case have the energy of about 140 keV, the energy cut of X-‐ray and Delta-‐ray is typically set as 1 GeV. Therefore, we have the following list:
/gate/physics/setElectronCut 1. m /gate/physics/setXRayCut 1. GeV /gate/physics/setDeltaRayCut 1. GeV
Technetium 99m (Tc-‐99m) is the major radionuclide used in SPECT. The gamma rays emitted from Tc-‐99m have a characteristic energy of 140,5 keV. In the macro file regarding the radioactive source, we set the particle type as “gamma”. The energy mode is “Mono”, which only contains energy of 140 keV. The source emits isotropic rays and the half-‐life time is 21600 seconds that is the real value for Tc-‐99m. The energy window for detector is 20%. The crystal selected is NaI.
17
2.4 Structure of simulation files
Since our simulation contains too many components, it is not wise to run it under the interactive mode although this mode provides convenient communication between users and computer. One practical way to conduct our experiment is to choose a Batch mode with parameterized Macros [2]. All the files are divided into three levels. We list the structure of files herein. Level I only contains a Main.mac file which acts like a main function in most programing languages, such as C or C++. In Level II, all the steps mentioned are crystalized into specific files. These files can also be divided into “PerInit>mode” and “IBLE>mode”. Level III provides selections of different phantoms and 4 detailed layer geometries in the scanner considering its complexity.
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Level File Name Description of functions
I Main.mac Manage all macro files and parameters needed for a complete simulation.
II
Initialization Setup
Visualization.mac Visualize detector geometry, source distribution and phantom shapes before running a simulation.
SetWorld.mac Set a suitable size for the “world”, which is the boundary of the experiment.
Scanner.mac Construct a multiple-‐layer pinhole collimator. It contains four layers and for each layer we build a separate file due to its complicated structure.
Phantom.mac Create a spherical phantom with a radius of 100 mm. The material is set as air, which neglects the attenuation correction problem in the project.
Physics.mac Set the physics parameters such as the interaction types needed.
Ran_Gen.mac Generate random seeds to trigger a simulation. Running Setup
Source.mac Define the distribution, shape and radioactivity of the source. There are four kinds of sources to choose from.
Digitizer.mac Simulate the behavior of the scanner’s detectors and signal processing.
Output.mac Specify the output format. In this case. ASCII file is chosen for further analysis.
Start.mac Start the acquisition with a proper time slice parameter.
III
Source selections Point_Source.mac Define a point source. Point_Array.mac Define an 11-‐point one-‐dimensional array. Derenzo.mac Define a Derenzo Phantom.
Round_Matrix.mac Define a three-‐dimensional matrix with a spherical boundary. Scanner layers
Layer_1.mac Define the geometry of Layer 1. Layer_2.mac Define the geometry of Layer 2. Layer_3.mac Define the geometry of Layer 3. Layer_4.mac Define the geometry of Layer 4.
Table 1: Structure of simulation files.
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3 Geometry description of MLPC
To avoid resolution variation in large FOV, we use multiple layers of mask-‐detector groups instead of a single mask-‐detector combination. The basic principle of MLPC is that a specific volume in FOV can be optimally reconstructed if a proper combination of pinhole mask and detector is selected. Before the mechanism of MLPC, a single pinhole mask involved in the system is described below.
3.1 Individual Pinhole Collimator
As we mentioned in Section 1.2, for each pinhole the magnification factor is crucial for pinhole collimator. This factor is determined by the ratio between the detector-‐collimator distance (d1) and the collimator-‐object distance (d2). Magnification Factor (MF) is given by d1/d2. When MF is larger than 1, the image on the detector plane is bigger than the original object. On the contrary, the image is zoomed out. A large MF compensates the low resolution of detector but also sacrifice the FOV for a given size of detector. Controlling MF value is important in this project. In our case, MF ranges from 0,3 to 1,0.
Figure 9: magnification for pinhole collimator. MF is given by d1/d2.
The individual pinhole mask has a similar pattern as a classic 7-‐pinhole mask[16]. Though different layers in our system vary, they share almost the same pattern. Generally speaking, 6 or 7 pinholes are distributed hexagonally on a round lead collimator. Each pinhole is keel-‐shaped with a tilting angle θ. All pinholes have the same focal point and the length is denoted as f. The opening angle α determines how large the detector can see through the pinhole. The thickness of collimator is 4 mm. Last but not least, r, the radius of pinhole, affects the final resolution mostly. We will explain the optimization of designing the pinhole shape and collimator thickness later in Chapter 5.
D1 D2
NaI Detector Pinhole Collimator
Object
DetectorSingle pinhole
Detector
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Figure 10: Frontal and side views of one MPA (left and middle) and individual pinhole geometry
(right).
3.2 Multi-‐Layer Pinhole Collimator
In MLPC system, the large FOV is divided into several small subsets by specific layer of pinhole mask and detector. These sub-‐FOVs also have smaller resolution variation compared with the original one. In our system, the structure has 4 layers making up 3 detector-‐mask groups with different patterns and focal points. The four layers are round and have the same radius of 400 mm. The whole MLPC has a length of 300mm. This size of our MLPC system is smaller than common clinical SPECT systems. The distances between layer 1 and 2, 2 and 3, 3 and 4 are denoted as D1, D2 and D3 respectively. They will be optimized later in Chapter 5. The detectors are distributed in layer 2, 3, 4 while the pinholes are in layer 1, 2. If pinholes exist in a layer, they follow the same pattern and tilting-‐hole design as mentioned above. Grouping is crucial for improving the image quality within FOV. Group I consists of 6 pinholes in peripheral of the first layer and 6 separate detectors in the second layer. They focus on the backside of object with a focal point located in the tail of FOV; Group II is composed of 6 pinholes in the layer 2 and 6 separate detectors in the third layer. The photons passing through the central large hole of the first layer will be partially captured; Group III is made up of 7 pinholes in the middle of the second layer and the whole forth layer, which is a pure detector without pinholes.
θα
tr
d
21
Figure 11: Two-‐dimensional sketch of MLPC system (upper) and cross-‐sectional structures of different
layers (from middle to lower).
Mask
Detector
Group I II III
4 3 2 1
1 2
3 4
30cm
4 3 2 1
Mask
Detector
FOV
80cm 20cm
D3 D2 D1
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Figure 12: building up procedure in GATE simulation.
Group n r/mm z/mm f/mm θ/deg α/deg d/mm I 6 1 D1 200 48,4 23 225 II 6 1 D2 D1+100 45 23 200 III 7 1 D2+D3 100 36,9 45 75
Table 2: important parameters of mask-‐detector groups (n, the number of pinholes; r, radius of
pinhole; z, the distance between detector and pinhole mask; f, the distance between pinhole mask
and focal point; θ, tilting angle of pinhole; α: opening angle of pinhole; d, the distance between two
adjacent pinholes).
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We removed all unnecessary components including detector sections and lead protection in the MLPC structure in order to reduce the weight and increase the mobility considering its clinical application. Within a mask-‐detector group the pattern of detectors is always determined by the distribution of pinholes in the front layer. This results in a same hexagonal pattern of detector distribution as pinholes. Since we create the pinhole masks with a phase difference of π/6 between layer 1 and layer 2, the arrangement of detectors in layer 2 and layer 3 are thus effected which means they also have the same phase difference.
Figure 13: Phase difference between Layer 2 (left) and Layer 3 (right)
Detector Pinhole Shielding
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4 Image Reconstruction and Analysis
Data decoding is done after we get raw data from every simulation. Four steps are done here as we mentioned in figure 8. They are digitization, reconstruction, deblurring and visualization. A software called PinholeViewer is developed to integrate all the steps needed in image reconstruction and analysis.
4.1 Development of PinholeViewer
PinholeViewer is designed to integrate the four major steps and also some other useful functions such as calculation of sensitivity during the decoding procedure. It is based on Matlab Graphical User Interface (GUI). The GUI style facilitates the evaluation of the each MLPC design. We can get better and faster feedback from the results of each simulation. We list the functions of PinholeViewer below. l Digitization from raw data towards matrix l Switch among different color maps (JET, HOT, GREY) l Switch among different detectors l Display and Output l Sensitivity calculation l Reconstruction
Figure 14: GUI design of PinholeViewer, the image shown here is the result of 9-‐pinhole collimator in
JET scale.
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4.2 Digitization
The output file generated after each simulation is in the format of ‘dat’, which only contains 4 columns of data. The first column stands for energy of the captured photons. The rest three mean x, y and z coordinate values respectively. We screened other unrelated information such as time in order to reduce redundancy and speed up simulation. This “ASCII” table is not interpretable for reconstruction, thus a digitization process must be done in the beginning of decoding. We first assume that the pixel size is 1 mm�1 mm considering the fact that the pinhole radius is 1 mm and the PSF should be larger than 2 mm. Hence the pixel size will not limit the performance of our collimator. We count the number of photons registered within the pixel size and map the whole FOV. After counting the photons in each pixel, we get a matrix with the same size as the detector plane. Different color maps can be applied here. In the following example of a circle plane source response, we used the grey scale.
Figure 15: Registered photons in side view (left). The digitized result in grey scale (right).
4.3 Reconstruction
The tomographic reconstruction algorithm we choose here is called Non-‐overlapping Redundant Array (NORA) decoding method[21]. As will be showed in what follows, this simple, direct, and non-‐iterative method, initially designed for x-‐ray imaging system, is very suitable for our MLPC system. During each time of decoding, the algorithm is applied to only one pinhole mask and its coupled detectors. That is to say, the same algorithm with different parameters will be used for three times since we have 3 groups and finally three objects will be reconstructed and merged in the end assigned with weighting factors.
After digitization
0 0 0 0 0 0 0
0 1 0 0 1 0 0
0 0 0 0 0 1 0
0 2 1 2 2 0 1
3 0 3 4 2 1 0
3 7 28 74 26 7 1
2 27 167 216 177 27 1
1 81 211 226 209 72 6
3 27 182 184 177 17 1
0 1 25 66 23 1 6
2 2 0 1 3 3 0
0 0 2 0 3 1 0
0 0 1 0 1 0 0
0 0 0 0 0 0 0
1 1 0 0 1 0 0
The data in the center
x (mm) y (mm)
z (mm)
Whole image
Magnified image
For a larger object
We put a larger object, whose radius is 5mm.
Parameters:
Radioactivity of 0.2 mm diameter circle is 0.00005Ci. 180 degree emission angle (all possible
directions) in front of the pinhole.
Exposure time: 10s
Pinhole size: 2-mm-diameter&1-mm-diameter.
Distance: Detector-50mm-mask-50mm-object
Detector size: 400mm diameter.
Pixel size: 1mm*1mm
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Figure 16: a scheme for Reconstruction
Figure 17: Projections from Group I (left), II (middle) and III (right).
Basic principles: The basic principles of NORA algorithm can be explained using a simplified 1-‐D sketch with three infinitely small pinholes and two point sources denoted as S1 and S2 in the following figure. For each coupled array and detector, we can apply correlation process to gain tomograms. When reconstructing a specific plane z1, we simply correlate the magnified NORA with the detected image. The magnification factor of the template is m1=(z1+f)/z1. During the correlation we use a single operator, which is generated from two constraints[21] and takes the smallest count, including zero among the template pinholes. The same process is applied to z2 plane with a different magnification parameter m2.
NORA Decoding
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27
Figure 18: 1-‐D sketch for explaining NORA algorithm.
In real situations, each pinhole has a finite size and one ideal point source corresponds to a round area with radius of r�m. Therefore during correlation, we should zoom not only the adjacent distance between pinholes but also their sizes on the template. Besides, due to photon statistics and scattering, background counts always exist on real detector plane. These background counts will cause both degradation and artifacts in the final image. To eliminate the effect, we will sample a quiet region and subtract the average from all pixels before NORA decoding. Another subtle assumption in NORA decoding is that each point in the source contributes equally through all pinholes. Thus an obliquity factor of (z+f)-‐2cos3θ should be assigned to all the pixels on the detector, where θ is the angle between the normal to the detector and the direction of ray.
4.4 Deblurring
Since we know the shape of each pinhole and the magnification factor during reconstruction at specific depth, The PSF can be estimated. The estimated PSF can be used as a further step to improve the image quality. This process is called deconvolution, which is used for reversing the effect of convolution on recorded data. If we treat the detected image as the result of convolution between PSF and the object, namely the distribution of Tc-‐99m, with the influence of noise, we can present the formula below.
Obj*PSF+Noise=Img (convolution is denoted as * )
Obj is denoted as object and Img is the image detected. PSF is can be estimated
Plane 2 Plane 1 Collimator Detector
Z1
Z2 f
Plane 1
S2
S1 Reconstruction
28
with the pinhole radius and magnification factor, while the noise can be derived by measuring a quiet detector area where background noise can be sampled properly. In our case, we chose Richardson-‐Lucy Deconvolution method to store each slice. This algorithm is an iterative procedure for restoring the image that has been affected by a known PSF. The basic idea is to maximize the likelihood of the resulting image being an instance of the original image under Poisson statistics.
Figure 19: Reconstructed slice before (left) and after deblurring (right).
4.5 Visualization
After reconstruction with NORA decoding method, all the slices are saved and stacked in a 3D matrix. This 3D matrix represents the final result. We can visualize the matrix slice by slice in 2D form. Alternatively, 3D visualization can be used. In this case, we choose to show the surface information of a reconstructed volume by setting a threshold, which eliminates the effect of noise.
Decoding in Matlab
● Deblurring
– Estimate the PSF
– Apply Richardson–Lucy algorithm
Before deblurring After deblurring
Decoding in Matlab
● Deblurring
– Estimate the PSF
– Apply Richardson–Lucy algorithm
Before deblurring After deblurring
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5 System Optimization
When we have the initial geometry of MLPC system, it is necessary to make slight changes to achieve better efficiency and accuracy. This chapter is viewed as the additional part for Chapter 3. We optimize our camera by adjusting the four aspects: energy window, collimator thickness, pinhole shape and layer positioning. The optimization procedure contains several experiments, which are different from imaging experiments using an optimized MLPC system in Chapter 6.
5.1 Energy Window
After setting the material for the detector, we need to choose the energy window since not all the registered photons represent the correct information. Here we compare the windows of 10% and 20%. As we can observe from the figure below, there is no big difference between them. Hence to increase the sensitivity, we choose the 20% window.
Figure 20: registered positions in three dimensions of the crystal and energy spectrum for energy
windows of 10% and 20%
There is a trade-‐off between detector resolution and efficiency when deciding the thickness of the crystal. Normally, the thickness in a conventional gamma camera is around 10 mm. In our case, we set this value with 12 mm.
5.2 Collimator Thickness
A pinhole collimator is usually thinner than a conventional parallel-‐hole one. The thickness of the collimator influences the sensitivity and its corresponding FOV for individual pinholes. For example, if the radius of pinhole is given, a thinner
30
collimator will allow more photons going through but also take a risk of leaking photons resulting in a lower SNR. To balance the trade-‐off between sensitivity and noise level, we should choose a proper value for the collimator thickness. We conducted a simulation, in which 1,85�106 photons are emitted towards a lead plate without pinholes. The detector records the number of photons penetrating the plate. We tried a series of thickness ranging from 5 mm to 2 mm and compared the leakage rate with the noise level, mainly the quantum photon noise. Accordingly, the noise is dominated by the photon quantum noise, which is the square root of the total coming photons. In our case, the noise level is 7,6�10-‐2 %. The leakage rate is defined as the ratio between detected photons and total emitting photons. The minimum value to control the leakage below quantum photon noise is 4 mm.
Thickness (mm) Leakage (counts) Leakage rate (%) 5 4 2,3�10-‐4
4 51 2,9�10-‐3 3 746 4,4�10-‐2 2 9799 5,8�10-‐1
No mask 1,71�106 92,4 Table 3: leakage record with changing thickness.
5.3 Pinhole Shape
The shape we apply here is keel-‐shaped instead of cylindrical type. As we can observe from the figure below, two point sources are emitting gamma particles to two detectors with different pinhole shapes. For conventional cylindrical shape, we can record photons from S1 but not S2. However, since the keel shape has a larger opening angle, it is able to image both points with similar PSF.
Figure 21: cylindrical pinhole (left) and keel pinhole (right)
Cylindrical shape Keel shape
Detector
S1
S2
Detector
S1
S2
31
Figure 22: The performance with Cylindrical (left) and Keel (right) pinhole collimators.
5.4 Layer Positioning
At this stage, we neglect attenuation problem and set the material of phantom as air. To optimize the positions of layers, we put the 11 equidistant point sources (the position is z=0, 20, …200 mm) on the central axis of FOV and evaluate the reconstruction results. Each mask-‐detector group generates a unique responding profile to the point sources. We initiated the layer position with D1=D2=D3=100 mm and fixed both Layer 1 and 4 while moving Layer 2 and 3 simultaneously towards Layer 1 until D1= 60 mm. The step is 5 mm and for each setup, all three profiles will be recorded. Intensity and resolution were evaluated finally.
Figure 23: test to optimize the positions of 4 layers
We first reconstruct all raw data with different groups. All results are presented in 3D format (figure 24). As we observe below (figure 25), curves with colors represent different groups. Each group gives unique information regarding
Experiments & Results
● 2D-Plane5) Pinhole shape: Cylinder Vs Keel(FOV)
Cylinder Keel
x
y
z
Point source
32
different ranges along the 11-‐point array. It is convincing to say that D1=75 mm is the optimal position. Because when you shorten the D1, the magnification factors of Group II and III increase while that of Group I decreases. Besides, the system sensitivity will increase if D1 is shorter. If D1 is large, Group II and III provide almost same information and the resolution in the middle part is bad. In contrast, a small D1 will bring blurring to the Group I.
Figure 24: 3D reconstruction results of Depth Resolution test from Group I (left), Group II (middle) and
Group III (right).
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D1=60
D1=65
D1=70
D1=75
D1=80
34
Figure 25: Depth Profile at D1 (Ranging from 60 mm to 100 mm).
Figure 26: Optimized geometry of MLPC visualized in GATE: side view (left) and frontal view (right).
D1=85
D1=90
D1=95
D1=100
35
6 Imaging with MLPC
After optimization, we start evaluation of the system performance. Very similar with what we did in optimization, we simulated the camera responses to a phantom constituted of 11 point-‐sources in order to test the system resolution. Both lateral and depth resolution results are obtained by placing the 11 point sources in two directions. The sensitivity is also estimated by putting a round phantom with the same size as the FOV. In the last phantom study, we put two Derenzo phantoms in different planes and reconstructed these two planes.
6.1 Reconstruction resolution without scattering
To test the depth resolution, we designed a phantom made of 11 point sources, 20 mm apart from each other, positioned on the central axis of the FOV perpendicular to the MLPC system and starting from layer 1. Each point source mentioned has a radioactivity of 1�10-‐4 Ci and exposure time of 10 seconds. The same phantom was also positioned parallel to the MLPC system in the center of the FOV. The phantom is shown below.
Figure 27: the 11-‐point-‐source phantom is positioned in different directions in order to test both
depth and lateral resolution
We present the results of reconstruction here. Both real positions of point sources and reconstruction profiles are shown in the following figures. We also displayed the misplacement of the sources as a function of distance from Layer 1 in our MLPC system when testing depth resolution test. When testing lateral resolution, we obtained a function of distance from the center of FOV.
x
y
z
Point source
36
Figure 28: Reconstructed profile of 11 point sources, along z through the center of FOV (upper, in
blue); Reconstructed profile of 11 point sources, along x through the center of FOV (lower, in blue);
The real position of each point source are described as a red circle.
Figure 29: Depth resolution vs z (upper) and lateral resolution vs x (lower).
37
As we observe from above, we are able to reconstruct all the points. For depth resolution, the minimum resolution value is 3 mm and there is no monotonous trend with distance. The reason is that the FOV is divided in subsets imaged by different combination of pinholes and detector sensitive areas. For the lateral resolution, the minimum resolution is also around 3 mm. The lateral resolution function is much symmetrical due to the symmetrical design of our camera. The best lateral resolution is achieved in the central point of FOV. Besides the central vertical and horizontal line of point sources, we also place the 11 point sources perpendicular to the MLPC system but 25 mm off the central z-‐axis. This setup is more general case. We present the results below.
Figure 30: z-‐axis profile and resolution function for the point sources positioned 20 mm off the central
axis of the FOV.
Here we are still able to reconstruct the 11 points, the general trend of depth resolution function is almost the same as the previous result in figure 29. One thing we should point out is that the last two points, which is furthest from the MLCP, in figure 30 have more than 8 mm resolution, which is not so good. However, those two points is out of FOV. Therefore, the blurring of last two points will not affect the image quality.
6.2 System volume sensitivity
The next step in measuring the sensitivity of our system. We used a radioactive round ball to measure the system sensitivity. The most photons are accepted by Group III, while Group I is least sensitive. Because the solid angle for the third
38
group is the largest among all three groups. Another reason is that the first group is mainly responsible for the distal part of object thus receives a smaller fraction of total emitting photons.
Figure 31: System volume sensitivity test
Group Counts Sensitivity/cps�MBq-‐1 Ratio to the system/% I 14775 9,1 10,6 II 32976 20,2 23,5 III 92258 56,7 65,9
Whole system 140009 86,0 100 Table 4: System sensitivity
6.3 Derenzo Phantom study
Finally, we created a double Derenzo Phantom with a diameter of 100 mm. The two Derenzo Phantoms share the same shape but lie in different planes parallel to the our MLPC system. The diameters of the rods are: 2.4 mm, 3.2 mm, 4.8 mm, 6.4 mm, 8 mm, 10 mm. The thickness of cylinders is 20 mm. For each cylinder, the radioactivity is 1�10-‐4 Ci and exposure time is 10 seconds. The Derenzo planes were placed at the depth of 100 mm and 50 mm simultaneously.
x
y
z
spherical source
39
Figure 32: Double Derenzo Phantom study
Figure 33: Visualization of distribution of rods and double Derenzo Phantoms in GATE. The diameters
of rods in Derenzo phantom are 2.4 mm, 3.2 mm, 4.8 mm, 6.4 mm, 8 mm, 10 mm. The first phantom
lies at 50 mm while the second one 100 mm.
The two phantoms are reconstructed at different levels and the results are shown below.
Figure 34: Results of Phantom reconstruction at D1=50mm (left) and 100mm (right)
x
y
z
Derenzo phantom
50 mm50 mm
100 mm
Fig. 3. Derenzo phantoms position (upper). Image of the Derenzo at for50 mm distance (centre). Image of the Derenzo phantom at 100 mm distance(lower).
of the sources is also indicated.
E. Conclusions
Our simulations show that a SPECT system with no movingelements can image a FOV of the size of a human brainwith acceptable resolution and good sensitivity. The resultsare encouraging regarding the possibility of designing a morerealistic system with smaller detectors and realistic read out.
REFERENCES
[1] S. Jan, G. Santin, D. Strul, S. Staelens, K. Assie, D. Autret, S. Avner,R. Barbier, M. Bardies, P. M. Bloomfield, D. Brasse, V. Breton,P. Bruyndonckx, I. Buvat, A. F. Chatziioannou, Y. Choi, Y. H. Chung,
!
!!"#$%&'$!())&*+,!!
!
!
!!"#$%&'$!())&*+,!!
!
Fig. 4. Point spread function of 11 point sources, 20 mm apart, along z
through the centre of FOV (upper). Point spread function of 11 point sources,20 mm apart, along x through the centre of of FOV (lower) .
!"#$%&#&'()(")(*&)+"',&-&'+&)$.$&-)
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!!3/)!&/%+,+/4!%'+0,!+4!5$,()$5!)(%/5.,+/4!,(%,6!789!2($4%!,'(!)(:/4%,).:,(-!&/+4,!+%!/4!,'(!)+;',!%+-(!/0!,'(!)($5!/4(!+0!</.!/=%()>(!=('+4-!:$2()$6!>+:(!>()%$#!!
!!3/)!&/%+,+/4!%'+0,!+4!-(&,'!)(%/5.,+/4!,(%,6!7?9!2($4%!,'(!)(:/4%,).:,(-!&/+4,!+%!/4!,'(!+44()!%+-(!/0!,'(!)($5!/4(!)(5$,+>(!,/!,'(!:$2()$6!>+:(!>()%$#!!:4 !*.';&6)(")(*&)-&.%)9.(.).'9)-&+"'6(-7+(8"')+"#$.-86"'),8;7-&4)!@+,'!$))/*%A!
!"#$%&#&'()(")(*&)+"',&-&'+&)$.$&-)
!"# /012!$!%&'()(!*+,'!$!)$-+.%!/0!"11!22#! !!34 5&6"%7(8"')(")986(.'+&),7'+(8"'4)
!!3/)!&/%+,+/4!%'+0,!+4!5$,()$5!)(%/5.,+/4!,(%,6!789!2($4%!,'(!)(:/4%,).:,(-!&/+4,!+%!/4!,'(!)+;',!%+-(!/0!,'(!)($5!/4(!+0!</.!/=%()>(!=('+4-!:$2()$6!>+:(!>()%$#!!
!!3/)!&/%+,+/4!%'+0,!+4!-(&,'!)(%/5.,+/4!,(%,6!7?9!2($4%!,'(!)(:/4%,).:,(-!&/+4,!+%!/4!,'(!+44()!%+-(!/0!,'(!)($5!/4(!)(5$,+>(!,/!,'(!:$2()$6!>+:(!>()%$#!!:4 !*.';&6)(")(*&)-&.%)9.(.).'9)-&+"'6(-7+(8"')+"#$.-86"'),8;7-&4)!@+,'!$))/*%A!
Fig. 5. Depth resolution vs z (upper) and lateral resolution vs x (lower).
C. Comtat, D. Donnarieix, L. Ferrer, S. J. Glick, C. J. Groiselle,D. Guez, P.-F. Honore, S. Kerhoas-Cavata, A. S. Kirov, V. Kohli,M. Koole, M. Krieguer, D. J. van der Laan, F. Lamare, G. Largeron,C. Lartizien, D. Lazaro, M. C. Maas, L. Maigne, F. Mayet, F. Melot,C. Merheb, E. Pennacchio, J. Perez, U. Pietrzyk, F. R. Rannou,M. Rey, D. R. Schaart, C. R. Schmidtlein, L. Simon, T. Y. Song,J.-M. Vieira, D. Visvikis, R. V. de Walle, E. Wieers, and C. Morel,“GATE: a simulation toolkit for PET and SPECT,” Physics in Medicineand Biology, vol. 49, no. 19, p. 4543, 2004. [Online]. Available:http://stacks.iop.org/0031-9155/49/i=19/a=007
[2] L. T. Chang, S. N. Kaplan, B. Macdonald, V. Perez-Mendez, andL. Shiraishi, “A method of tomographic imaging using a multiple pinhole-coded aperture,” Journal of Nuclear Medicine, vol. 15, pp. 1063–1065,1974.
[3] R. K. Rowe, “A system for three-dimensional SPECT without motion,”Ph.D. dissertation, University of Arizona, 1991. [Online]. Available:http://hdl.handle.net/10150/185409
[4] L. I. Yin and S. M. Seltzer, “Tomographic decoding algorithm for anonoverlapping redundant array,” Applied Optics, vol. 32, pp. 3726–3735,1993.
#Figure'8:'Results'of'phantom'test:'cross'section'of'reconstructed'Derenzo'Phantom'
Discussion"and"Conclusion:"
The#depth#response#curve# is#extremely# important# for# the#system.#On#one#hand,# this#curve#does#not#exist#in#traditional#parallel3hole#gamma#cameras.#Fast#3D#reconstruction#is#thus#possible#for#our#system.#On#the#other#hand,#the#previous#73pinhole#camera#actually#has#this#kind#of#curve.#We#can# predict# that# the# shape# is# almost# the# same# as# the# red# curve# provided# by# the# third# group,#because#one#can#treat#the#third#group#as#an#independent#73pinhole#system.#
Acknowledgments:"
References:" "
##
40
As we see here, both phantoms are reconstructed with our MLPC system. The camera is able to distinguish phantoms at different distance from the collimator. This function is impossible for a normal planar gamma camera. Rods with diameter ranging from 10 mm to 3,2 mm are resolved and 2,4 mm cannot be resolved here. It is convincing to say that MLPC system might have a resolution of about 3 mm at 50 mm and 100 mm distance.
41
7 Conclusion and Future work
7.1 Conclusion
The thesis concentrates on exploring the feasibility of developing MLPC, a new collimator for a small stationary SPECT. The framework of development contains three stages: (1) Monte Carlo simulation, (2) Image reconstruction and analysis and (3) Evaluation and optimization. Optimization of collimator geometry has been done according to the evaluation and several system properties, such as system resolution and sensitivity, have been investigated using specified phantoms. The MLPC proposed here has the following strength: 1. Both decent resolution and improved sensitivity are achieved. An important
benefit of introducing pinhole collimation is the controlling of the trade-‐off between sensitivity and resolution. In our setup, a sensitivity of 86,0 cps/MBq and an overall resolution of 5 mm have been estimated, indicating that performances are expected to be comparable to traditional parallel-‐hole collimator. The sensitivity is improved due to multiple layers of MPA applied in the system. The following layers can detect more photons, which go through previous layers.
2. MLPC is able to reconstruct 3D volume instead of 2D plane without moving or rotating elements. Another benefit of pinhole collimation is the additional projection data, which can be used in 3D reconstruction. In the MLPC system, we have 19 projections in total for a single object. These projections finally build the 3D volume. For parallel-‐hole collimator in a single head gamma camera, for each imaging session, only one projectile data is obtained, which is impossible to do tomography without rotation. In our double Derenzo Phantom study, two separate planes are reconstructed at different distance from MLPC. This study is hard to do with a conventional parallel-‐hole collimator.
3. The small size of MLPC system facilitates its mobility. The dimension of our
MLPC is around 800mm�800mm�300m, which is little bigger than normal gamma camera but much smaller than a normal SPECT machine. It will be convenient to move the new MLPC camera as a fast 3D imaging modality in hospitals.
4. MLPC images a large FOV of the order of a human brain. The strategy of
dividing the FOV into sublets with multiple combinations of detector and collimators reduces the variation in both sensitivity and resolution. The most
42
obvious evidence is the trend of the function of depth resolution with changing z. One can find two inflection points in that curve, which is different from that of using only one MPA.
However, MLPC has its several drawbacks. For example, the assumption of putting so many layers of detectors together is that the thickness of individual detector is less 20 mm. The readout part should also be compact. The fabrication is a big problem; we did not reduce the variation of lateral resolution in FOV, although this problem is not as serious as the depth resolution. Despite of these shortcomings, MLPC still demonstrates its potential to be used as a fast 3D gamma imaging modality.
7.2 Future work
This new type of tomographic collimation method shows encouraging results in the above. According to the system drawbacks, several works can be done in the future. More reconstruction methods can be applied. The NORA decoding method applied here is a fast non-‐iterative algorithm. The result we obtained from NORA decoding can be used as initial guess for a more complex iterative algorithm, such as Maximum-‐Likelihood Reconstruction, which might provide more accurate results. Resolution can be improved and artifacts can be eliminated. During reconstruction, attenuation correction can be done. More phantom studies can be done. We can create more phantoms with different configurations. In this thesis, we neglected the attenuation coefficients of the materials (the phantom is made of air). In the next step, we can test a complex phantom filled with materials have similar properties as human soft issue and bones. New geometries of MPA can be designed. A curved collimator can be designed to take place of the planar type in this project. A curved collimator might be useful in sampling more projection with wider angles. Modular detector-‐collimator combination can be tried to reduce the system cost. Realistic machine design and experiments can be conducted. We can start real camera design from building a 7-‐pinhole camera. The designs and experiments can refer the simulation process. Readout components and the technology to create titled pinholes with certain diameters will be very challenging. With its encouraging potentials displayed above, the continuous research of MLPC system will play an important role in dynamic 3D imaging of human organs in the future.
43
8 Reference
[1] Y. C. Chen, System calibration and image reconstruction for a new small-‐animal SPECT system, PhD dissertation from the University of Arizona, 2006
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[3] M. Rudin, Molecular Imaging: Basic Principles and Applications in Biomedical Research, 2005
[4] J. T. Bushberg, J. A. Seibert, The Essential Physics of Medical Imaing, 1994 [5] M. C. Tosti, Master thesis project proposal: brain imaging with a coded pinhole mask, 2010 [6] R. K. Rowe, John N. Aarsvold, etc., A Stationary Hemispherical SPECT Imager for
Three-‐Dimensional Brain Imaging, Journal of Nuclear Medicine, Vol. 34, No. 30, 474-‐480, 1993
[7] H. H. Barrett, Fresnel zone plate imaging in nuclear medicine, Journal of Nuclear Medicine, Vol. 13, No 6: 382-‐385, 1972
[8] R. K, Rowe, A system for three-‐dimensional SPECT without motion, PhD dissertation from the University of Arizona, 1991
[9] A. Rahmim, H. Zaidi, PET versus SPECT: strengths, limitations and challenges, Nuclear Medicine Communications, Vol. 29, 193-‐207, 2008
[10] F. J. Beekman, B. Vastenhouw, Design and simulation of a high-‐resolution stationary SPECT system for small animals, Physics in Medicine and Biology. Vol. 4, 4579-‐4592, 2004
[11] F. J. Beekman, F. V. Have, etc., U-‐SPECT-‐I: A Novel System for Submillimeter-‐Resolution Tomography with Radiolabeled Molecules in Mice, Journal of Nuclear Medicine, Vol. 46, No 7, 1194-‐1200, 2005
[12] F. Have, B. Vastenhouw, etc., U-‐SPECT-‐II: An Ultra-‐High-‐Resolution Device for Molecular Small-‐Animal Imaging, Journal of Nuclear Medicine, v 50, No. 4, 599–605, 2008
[13] N. U. Schramm, G. Ebel, etc., High-‐resolution SPECT using multipinhole collimation, IEEE Transactions on Nuclear science, Vol. 50 No. 3, 315-‐320, 2003
[14] T. Funk, P. Despres, A Multipinhole Small Animal SPECT System with Submillimeter Spatial Resolution, Medical Physics. Vol. 33, 1259-‐1269, 2006
[15] L. T. Chang, S. N. Kaplan, etc., A method of tomographic imaging using a multiple pinhole-‐coded aperture, Journal of Nuclear Medicine, Vol. 15, No. 11, 1063-‐1065, 1974
[16] R. A. Vogel, D. Kirch, etc., A New Method of Multiplanar Emission Tomography using a Seven Pinhole Collimator and an Anger Scintillation Camera, Journal of Nuclear Medicine, Vol. 19, No. 6, 648-‐654, 1978
[17] W. L. Rogers, K. F. Koral, etc., Coded-‐Aperture Imaging of the Heart, Journal of Nuclear Medicine, Vol. 21, No. 4, 371-‐378, 1979
[18] M. T. LeFree, R.A. Vogel, etc., Seven-‐Pinhole Tomography: A Technical Description, Journal of Nuclear Medicine, Vol. 22, No. 1, 48-‐54, 1981
[19] T. F. Budinger, Physical attributes of Single Photon tomography, Journal of Nuclear Medicine, Vol 21, No. 6, 579-‐592, 1980
[20] F. D. Rollo, J. A. Patton etc., Perspectives on Seven Pinhole Tomography, Journal of Nuclear Medicine, Vol. 21, No. 9, 888-‐889, 1980
44
[21] L. Yin, S. M. Seltzer, Tomographic decoding algorithm for a nonoverlapping redundant array, Applied optics, Vol. 32, No. 20, 3726-‐3734, 1992
[22] V. Giessen, M. A. Viergever, etc., Improved Tomographic Reconstruction in Seven-‐Pinhole Imaging, IEEE Transactions on Medical Imaging, Vol. MI-‐4, No. 2, 91-‐103, 1985
[23] P. Nillius, M. Danielsson, Theoretical Bounds and Optimal Configurations for Multi-‐Pinhole SPECT, Nuclear Science Symposium Conference Record, 2008
[24] I. Valastyan, Software Solutions for Nuclear Imaging Systems in Cardiology, Small Animal Research and Education, PhD dissertation from Royal Institute of Technology, Sweden, 2010
45
Appendix I: Paper submitted
The paper ‘Stationary SPECT with Multi-‐Layer Multi-‐Pinhole-‐Array’ has been submitted to 2012 IEEE Nuclear Science Symposium and Medical Imaging Conference (2012 NSS/MIC).
Stationary SPECT with Multi-LayerMultiple-Pinhole-Arrays
Wuwei Ren, Student Member, IEEE, Ivan Valastyan and Massimiliano Colarieti-Tosti, Member, IEEE
Abstract—The potential of Multiple Pinhole Arrays (MPA)collimators for developing a Single Photon Emission ComputerTomography (SPECT) system without rotating or moving ele-ments is investigated. A four layer arrangement is proposedand the system performance is evaluated using the simulationtoolkit GATE [1]. For a camera with a field of view (FOV) ofthe order of a human brain (a sphere of radius 100 mm), asensitivity of 86, 0 cps/MBq and a overall resolution of 5 mmhave been estimated, indicating that performances comparableto traditional parallel-hole-collimator cameras can be achieved.
I. SUMMARY
A. Introduction
A SPECT system that does not need moving elements im-plies less maintenance, drift and production costs (no rotationgantry, less bulky), allows for list-mode data acquisition andopens up for the possibility of camera mobility. Pioneeringwork in using stationary Multiple Pinhole Arrays (MPA) forthree-dimensional imaging started already in the ’70 by L-TChang and his collaborators [2] and has recently undergonea renaissance thanks to the excellent work by the group ofH. H. Barret (see ref. [3] and references therein for a review).In this paper we propose a SPECT camera with a 4-layerdetector/MPA structure and investigate its performance inimaging a FOV of size comparable to that of a human brain.
B. Camera Design
Fig. 1 shows schematically our camera design. The leadingstrategy is a divide-et-impera-like approach: The FOV isdivided in subsets, each imaged by a specific combination ofpinholes and sensitive detector areas. This allows keeping thedepth resolution deterioration with distance inside acceptablelimits. In our simulations the sensitive part of the detectoris made of 12 mm thick NaI crystals with ideal read out.The back-side of the NaI crystals is shielded by 4 mm lead.The MPA-layers are made of 4 mm thick lead and the singlepinholes geometry is shown in Fig. 2.
C. Image reconstruction
Image decoding was performed using the algorithm pro-posed by Yin and Seltzer in Ref. [4].
W. R. I. V. and M. C. T. are with the Department of Medical Engineering,School of Technology and Health, Royal Institute of Technology (KTH),Stockholm, Alfred Nobels Alle 10, SE-141 52 Huddinge, Sweden (telephone:+46-8-7904861, e-mail: [email protected]).
I. V. is also with the Institute of Nuclear Research of the HungarianAcademy of Sciences, Bem ter 18/c, H-4026 Debrecen, Hungary and with(e-mail: [email protected]).
Fig. 1. Two-dimensional sketch of FOV subdivision (a) and cross-sectionalstructures of the different layers (b).
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Fig. 2. Frontal and side view of one MPA (left and centre) and individualpinhole geometry (right).
D. Results
1) Sensitivity: The sensitivity of the camera was estimatedby GATE simulations with a spherical source of radius 100mm and an activity of 100 µCi. The camera sensitivity resultedto be of the order of 86,0 cps/MBq.
2) Imaging performance: In Fig. 3 the reconstructed im-ages from data generated when two Derenzo phantoms are putin the camera at distances 50 mm and 100 mm respectivelyare shown. The capability of the proposed system to showthree-dimensionality is evident.
We also simulated the camera response to a phantomconstituted of 11 point sources, 20 mm apart from each other,positioned on the central axis of the FOV perpendicular tothe MPA-plane and starting at layer 1. The camera responseis shown in Fig. 4 (upper). The same phantom was alsopositioned parallel to the MPA-planes in the centre of theFOV. The camera response is shown in Fig. 4 (lower). Fromthe above two simulations the camera resolution has beenestimated and is shown, as a function of distance from the firstlayer in Fig. 5 (upper) and as a function of distance from thecentre of FOV (lower). In the same figures the misplacement
46
Fig. 3. Derenzo phantoms position (upper). Image of the Derenzo at for50 mm distance (centre). Image of the Derenzo phantom at 100 mm distance(lower).
of the sources is also indicated.
E. Conclusions
Our simulations show that a SPECT system with no movingelements can image a FOV of the size of a human brainwith acceptable resolution and good sensitivity. The resultsare encouraging regarding the possibility of designing a morerealistic system with smaller detectors and realistic read out.
REFERENCES
[1] S. Jan, G. Santin, D. Strul, S. Staelens, K. Assie, D. Autret, S. Avner,R. Barbier, M. Bardies, P. M. Bloomfield, D. Brasse, V. Breton,P. Bruyndonckx, I. Buvat, A. F. Chatziioannou, Y. Choi, Y. H. Chung,
!
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Fig. 4. Point spread function of 11 point sources, 20 mm apart, along z
through the centre of FOV (upper). Point spread function of 11 point sources,20 mm apart, along x through the centre of of FOV (lower) .
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Fig. 5. Depth resolution vs z (upper) and lateral resolution vs x (lower).
C. Comtat, D. Donnarieix, L. Ferrer, S. J. Glick, C. J. Groiselle,D. Guez, P.-F. Honore, S. Kerhoas-Cavata, A. S. Kirov, V. Kohli,M. Koole, M. Krieguer, D. J. van der Laan, F. Lamare, G. Largeron,C. Lartizien, D. Lazaro, M. C. Maas, L. Maigne, F. Mayet, F. Melot,C. Merheb, E. Pennacchio, J. Perez, U. Pietrzyk, F. R. Rannou,M. Rey, D. R. Schaart, C. R. Schmidtlein, L. Simon, T. Y. Song,J.-M. Vieira, D. Visvikis, R. V. de Walle, E. Wieers, and C. Morel,“GATE: a simulation toolkit for PET and SPECT,” Physics in Medicineand Biology, vol. 49, no. 19, p. 4543, 2004. [Online]. Available:http://stacks.iop.org/0031-9155/49/i=19/a=007
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