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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5255_Библиотеки_им_академика_М_И_Перельмана
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272
Medical Cyclotron: Basic Principles and Operation
3. Satyamurthy N. Electronic Generators, In PET: Molecular Imaging and its Biological applications,
eds Michael E. Phelps, UCLA, pp 217, 2004.
4. Thomas LH. The paths of ions in the cyclotron. I. Orbits in the magnetic field. Phys. Rev. 1938;54:
580-588.
5. Evans, Robely D., The Atomic Nucleus. McGraw-Hill Book Co. New York 1955.
6. Deconninck, G. (1978) Introduction to Radioanalytical Physics, Nuclear Methods Monographs No.1
Elsevier Scientific Publishing Co. Amsterdam.
7. Qaim SM (1989) Target development for medical radioisotope production at a cyclotron. Nuclear
Instruments and Methods in Physical Research A282, 289-295.
GSPant\Newbook\Final-2008\17-chp\272
Positron Emission Tomography:
Physical Principles, Instrumentation
and Performance Evaluation
G.S. Pant and S. Senthamizhchelvan
Positron emission tomography (PET) is a modern imaging technique that utilizes the
annihilation coincidence detection (ACD) of two 511 keV gamma photons emitted from
positron emitting radionuclides. The most commonly used positron emitters (11C,
and 18F) are produced ina cyclotron and few (68Ge-68Ga) are eluted from the generators. The
desired positron emitting radionuclides are subjected to chemical process to synthesize the
desired radiopharmaceuticals for visualization and quantitative assessment of physiologic
and biochemical processes within the human body (1). It has significant role in detection
and quantification of metabolic abnormalities of disease processes (1-3).
The first application of PET for medical imaging was realized as early as in 1950 (4,5).
Michael Ter-Pogossian, considered as father of PET, did the pioneering research in PET
during 1950s (6). Since then dramatic improvements have taken place in detector technology
and design of PET to improve spatial resolution and sensitivity (7). Although PET began to
demonstrate its clinical utility as early as in mid 1980s, it became popular after its role in
oncology was established in 1990s. After the introduction of the integrated PET/CT system,
images acquired by CT and PET are fused to obtain both anatomic and physiologic
information. Since both CT and PET are in the same gantry the fusion/co-registration is
much easier and accurate in comparison to that obtained from two different imaging systems.
13
N, 15O
The PET facility needs a medical cyclotron with radiochemistry laboratory either onsite
or nearby for producing positron emitting radionuclides and synthesizing positron emitting
radiopharmaceuticals such as 18F-FDG. Practically one cyclotron facility can distribute 18FFDG to many PET imaging centers that are easily approachable within couple of hours. In
this chapter the physical principles of PET imaging, advances in instrumentation, future
scope and performance evaluation have been described in brief.
27 3
274
Positron emission tomography: physical principles, instrumentation and performance evaluation
Physics of PET
PET is based on the detection of two 511 keV photons in coincidence that are originated
from the annihilation of a positron with an atomic electron at rest (8,9). The annihilation
photons travel opposite to each other (180° apart) and strike the opposite pair of detectors in
coincidence. A line (or volume) joining the opposite pair of
detectors in coincidence is called the line of response (LOR)
as shown in figure 1.
The system may detect any number of events produced
along the LOR. The electronic coincidence detection
intrinsically implies alignment and avoids the need of
physical collimation. This increases the detection efficiency
of PET significantly as compared to single-photon emission
computed tomography (SPECT). Each registered coincident
511 keV photon is referred as an event (single) and when
detected by the opposite pair of detectors along the LOR is
known as a (coincident) true event (Figure 2a). However
there are undesirable events as well caused by random, and
scatter coincidences (Figure 2b,c). The random and scatter coincidences deteriorate the
image quality due to misplacement of the position of events.
Figure 1: Schematic diagram
showing the annihilation coincidence detection of two gamma
photon
Figure 2: (a) Detection of true coincidence event, (b) Detection of random coincidence event, (c)
Detection of scatter coincidence event
It is possible that the two photons created by annihilation may not be detected
instantaneously by the opposite detector pair due to the reason that a) they may not reach
the respective detectors at exactly same time (though time difference may be negligible), b)
the light emission and its decay in respective detectors may slightly vary and c) the signal
processing time in electronic circuitry of two opposing detectors may be slightly different.
In view of these reasons a finite timing window is used for the detection of annihilation
photons. Within this electronic time window, there is possibility of some random events to
be registered (10). The randoms rate (R) depends upon the rate of singles in each detector
Positron emission tomography: physical principles, instrumentation and performance evaluation
1 2
S S
275
(S1 and S2) and the coincidence time window (c). The relationship may be expressed
mathematically as:
R =
2
c
(1)
From this equation it is clear that increase in the amount of radioactivity administered to
the patient will have quadratic increase in randoms. However, smaller the timing window,
lesser will be the chance for detection of random coincidence events. The timing windows
are normally set in the range of 6-10 ns. With faster detectors like lutetium oxyorthosilicate
(LSO) the timing window has been reduced to as low as 4.5 ns.
The minimization of the scattered photons by narrowing the photopeak energy window
is not practical in PET due to poor energy resolution of the detectors. In 2D acquisition
mode the lead/tungsten septa reduces the scattered events considerably. In 3D mode
computationally intensive statistical methods such as Monte Carlo simulation is used to
minimize the scatter. The energy window is normally kept wider (~400 to ~650) to record
most of the true events. This has been successfully implemented in most of the scanners.
Detector materials for PET
The performance of a PET scanner is strongly influenced by the detector material (scintillator)
used. The most important characteristics of scintillators for PET application include density,
effective atomic number, decay time, attenuation coefficient for 511 keV photons, emission
wavelength, relative light output, cost and easy availability (11,12). An ideal detector material
satisfies most of these requirements. The characteristics of some of the scintillators used in
PET are given in Table 1. Higher density and atomic number for efficient gamma ray
detection results in improved overall system sensitivity. Short scintillation light decay time
is another important characteristic that substantially improves the detector efficiency and
temporal resolution facilitating a large reduction in the detection of random coincidences.
Table 1: Physical characteristics of scintillators for PET scanners
Scintillator Density Z
material (g/cm3) Time (ns) coefficient wavelength [% relative to
NaI(Tl) 3.67 51 230 0.35 410 100
BGO 7.1 75 300 0.95 480 15
LSO 7.4 66 40 0.86 420 75
GSO 6.7 59 60 0.70 430 30
LGSO 7.23 65 60 0.84 420 40
LYSO 7.1 65 42 0.83 400 75
LuAP 8.3 64.9 18 0.87 365 30
YAP 5.5 32 27 0.37 350 40
(Most of these values are from Muehllehner and Karp, Phys Med Biol 2006)
eff
Decay Attenuation Emission light output
for 511 keV (nm) NaI (Tl)]
(cm–1)
276
Positron emission tomography: physical principles, instrumentation and performance evaluation
Bismuth germanate (BGO) has been successfully used as PET detector for many years
(13,14). However, low light output and long decay time of BGO may not support it to be the
choice of detector for long particularly with modern fast scanners. Detectors like lutetium
oxyorthosilicate (LSO), gadolinium oxyorthosilicate (GSO), and lutetium yttrium
oxyorthosilicate (LYSO) are now being used in commercially available scanners. These
detectors enable a significant reduction in the detection of scatter and random coincidences
in comparison to BGO-based detectors (15-18). In direct comparison, although LSO has a
higher stopping power and faster decay time than GSO, its intrinsic non-linearity leads to
relatively poorer energy resolution.
Scintillation detectors require an electronic device to convert scintillation light into an
electric signal. The most common device used for this purpose is the photomultiplier tube
(PMT), which provides several stages of charge amplification to achieve a typical gain of
the order of more than 106. In animal PET detectors, multi-channel or position-sensitive
PMT (PS-PMT) or semiconductor detectors (that convert light photons to electron hole
pairs) are used (19). Recently the avalanche photodiodes (APD) have shown great potential
for future PET applications (20,21). Multi-channel and position sensitive APD have been
used in the design of high-resolution PET detectors by several research groups (20-24). The
primary advantage of APD is its compactness, which increases flexibility in design of highresolution PET detector systems. With higher quantum efficiency, APD-based detectors can
have superior energy resolution compared to PMT-based detectors. The cost of APD, which
is a major factor today, could come down if produced in large quantities depending upon the
demand in the future.
Detector Configuration
In modern PET scanners the detectors are arranged in the form of multiple rings in the
gantry. Each ring has several blocks and each block has several detector elements. A block
consists of a large number of detector elements by partially cutting and filling the cuts with
reflective material to make them opaque to light from other detector elements. The depth of
the cuts is less at the centre and proportionately increases towards the edge (depth of cut at
centre is nearly half that at the edge). The spatial resolution is better with smaller crystal
elements.
In the Biograph (Siemens medical solutions), one detector block consists of 88 elements
each with dimensions of 6.456.4525 mm. A total of 144 blocks are arranged in 12 buckets
as shown in figure 3. Each bucket consists of 12 blocks (34). There are 3 blocks arranged
side by side around the gantry to make 24 (38) rings. The GE Health care, in their LYSO
based PET/CT (Discovery RX) used 96 blocks of crystal array. Each block is coupled to
4-anode, square PMT. Eight blocks are grouped in a module in 24 arrangement (25).
The TruePoint (True V) system designed by Siemens is an extended axial field of view
PET/CT scanner that has an axial FOV of 21.6 cm. The detector blocks are made of 1313
Positron emission tomography: physical principles, instrumentation and performance evaluation
277
elements each with dimensions of 4420 mm. It has as many as 52 detector in the rings
with more than 100 image planes in one bed position. The system is said to have high
sensitivity (increased noise equivalent count rate). When using such a system with large
AFOV and high sensitivity systems for scanning, one can either decrease the radioactive
dose to the patient or reduce the scan time considerably.
Figure 3: Schematic diagram showing Siemens Biograph 2 detector configuration. There are 12
buckets numbered from 0 to 11. In each bucket there are 12 blocks (0 to 11) as can be clearly
seen in the figure. Each block has 8x8 (=64) detector elements. (Courtesy Siemens Medical
Solutions, Molecular Imaging)
Spatial Resolution
There are several factors, which influence the spatial resolution in PET images such as
positron range, noncolliearity of annihilation photons, and radial position of the source and
detector dimensions.
Positrons travel some distance in the medium (tissue) before coming to rest and annihilate
(Figure 4). It is the annihilation sites, and not the site of the positron emitting atoms, which
are imaged in PET due to finite range of positrons. Some blurring is therefore introduced in
the image. The amount of this blurring depends on the energy with which the positrons are
emitted and is therefore radionuclide-dependent. The second factor, non-colinearity, is a
result of nonzero momentum of the positron and electron at the time of annihilation, resulting
278
Positron emission tomography: physical principles, instrumentation and performance evaluation
in a slight angular deviation of the 2
annihilation photons about the expected 180°
(Figure 4). The amount of blurring due to noncolinearity is roughly equal to 0.022 × detector
separation (26). The detector separation
increases with ring diameter therefore larger
ring diameter causes more blurring. The third
factor is detector geometry. A detector of width
‘d’ results in a triangular coincidence response
function with a full width at half maximum
(FWHM) of d/2 at the center between two
opposite detectors (Figure 5). The resolution
deteriorates as one moves radially from center
towards either of the detector pair.
FWHM =d/2
Figure 4: Schematic diagram showing spatial
resolution degradation due to finite positron
range and non-colinearity in the detection of
two 511 keV gamma photons. ‘D’ shows the
detector separation (ring diameter)
d
Figure 5: Spatial resolution for discrete detectors is a triangle at mid plane with FWHM = d/2.
The thickness of the detector also has
some influence on spatial resolution through
parallax errors (Figure 6). In a typical scanner
with ring-geometry, this influence leads to
degradation of spatial resolution as one move
radially from the central axis of the scanner.
The fourth factor is the size of detector
elements. Spatial resolution improves with
reduction in the size of detector elements but
up to a certain limit. In addition to these four
factors there is Compton interaction from 511
keV photons with the detector that needs to
be considered. The photon undergoing
Compton scattering deposit some of its energy
in the detector and change direction with a
significant probability of interacting in
adjacent detectors thereafter. Thus, the energy
is deposited at two or more locations in the
scanner, and there is no simple way to
Figure 6: Apparent width of detector element,
d¢, increases with increasing radial offset in a
circular array PET scanner. This parallax error
depends on the diameter of the scanner, D, the
length of crystal x and width of detector
elements, d.
Positron emission tomography: physical principles, instrumentation and performance evaluation
2
r
T S R
279
determine the first point of interaction that corresponds to the desired positional information
(27, 28). This is one of the reasons for accepting wider energy window in PET data
acquisition. The result is some additional data blurring that depends on the scintillator
material and its thickness.
Sensitivity of PET detecting system
The sensitivity (recorded true events per unit activity) in PET depends upon the detector
(crystal) efficiency and scanner geometry. In an ideal situation the source of radioactivity
should be surrounded by the detector assembly to maximize the sensitivity, but unfortunately
it is not possible in practice (29). The most practical detector geometry is cylindrical for
which sensitivity is defined as follows
2
Sensitivity =
Where A is detector area seen by each point of the volume to be imaged, is single
detector efficiency and is the attenuation factor and r is the radius of detector ring.
Increase in single (individual) detector efficiency will increase the sensitivity in a quadratic
manner.
A
4
(2)
Noise Equivalent Count Rate (NECR)
The noise-equivalent count rate (NECR), is an important parameter of practical PET
performance (sensitivity) and is defined as follows:
2
NECR =
where T, S, and R are the trues, scatter, and randoms count rates, respectively. The maximum
NECR is thus the optimal count rate for a particular scanner. For 2D scanners, the interdetector septa effectively reduce the contribution of the scatter and randoms count rates
such that the NECR is essentially equivalent to the trues rate. Thus, for 2D scanners, the
NECR increases linearly with activity and there is no optimal count rate or activity. For 3D
scanners, on the other hand, the trues and scatter count rates are proportional to the activity
while the randoms count rate is proportional to the square of the activity. Thus, there exists
a well-defined optimum activity (around 370 MBq) for 3D scanners for which NECR reaches
a plateau and does not increase with increase in activity (27). The faster the detectors, the
shorter the coincidence timing window resulting in lower randoms count rate for a given
activity with increased NECR. A plot of the trues, randoms, and NECR versus activity (to
make the concept clear but not bases on measurement) is shown in figure 7 for a 3D PET
scanner.
T
(3)
280
Positron emission tomography: physical principles, instrumentation and performance evaluation
Figure 7: A plot of the trues, randoms, and NECR versus activity is for a 3D scanner (Plot not to
scale)
It is important to realize that peak NECR occurs at lower activity concentrations in
patients than it does in phantom studies. One should not decide optimum activity based on
NECR value from phantom measurement. The NECR determined from phantom measurement
may however be taken as a guide for determining optimal doses of radioactivity to be
injected to the patient.
Image data acquisition (2D/3D)
PET scanners capable of data acquisition in 2D mode employ lead or tungsten septa
typically of 1mm thick, positioned between the detector elements (27). In this arrangement,
known as 2D PET, these inter-ring annular septa largely eliminate out-of-plane annihilation
-rays (Figure 8). By minimizing the contribution of out-of-plane randoms and scatter,
image quality is optimized, especially for large-volume sources (27). However, 2D PET also
eliminates most trues and thus reduces sensitivity considerably (27). Sensitivity can be
increased substantially by removing the septa altogether and including coincidence events
from all of the LORs among all the detectors as can be seen in figure 8. This is known as
three-dimensional (3D) PET, and is widely used in most of the modern PET scanners (14,15,
27). Sensitivity is increased approximately fivefold in 3D relative to 2D PET, but with a
considerable increase in the randoms and scatter count rates. Further increase in count rate
results in dead time losses. To compensate for the increase in scatter count rates, detectors
(such as LSO and LYSO) with better energy resolution and accurate scatter-correction
algorithms are required for 3D PET (30). Data processing time, for 3D PET is about an
order of magnitude longer than for 2D PET. In contrast to the relatively uniform axial
sensitivity for 2D PET, the axial sensitivity profile for a 3D PET scanner is triangular and
peaked at the center of the field of view. Thus, whole body 3D PET studies require
considerable overlap of adjacent bed positions during image acquisitions to yield the
sensitivity as uniform as possible over the resulting whole-body images (27). Though the
Positron emission tomography: physical principles, instrumentation and performance evaluation
281
intrinsic spatial resolution of the current generation PET scanners is small (4-6 mm), the
reconstructed spatial resolution in clinical studies lies somewhere in the 8 to 12 mm range
with acceptable signal-to-noise ratios (SNRs) for diagnostic interpretation (28).
Figure 8: The 2D acquisition system employs lead/tungsten septa. It permits direct and cross
plane acquisition as shown on left side. The axial sensitivity profile is shown at the bottom on the
left side. The 3D acquisition and sensitivity profile is shown on the right side. Because of the
non-uniform axial sensitivity in 3D acquisition, bed positions are overlapped.
Image Reconstruction in PET
The image reconstruction from raw data (sinogram) can be done either by filtered back
projection or by iterative reconstruction methods or by both. The filtered back projection
(FBP) technique is simple, and fast but suffers from artifacts caused by a combination of
low statistics and sampling considerations. The method also gives the same weight to
projection elements with high counts and those containing fewer counts (31). On the other
hand iterative reconstruction algorithms weigh the data according to their statistical quality
and has the capability of incorporating physics such as attenuation, scatter, depth dependent
resolution etc. Generally, iterative methods result in reconstructed images that eliminate
streak artifacts effectively and have a more favorable tradeoff between signal to noise ratio
(SNR) and spatial resolution. Iterative reconstruction algorithms with their faster versions
(such as OSEM) are readily available and widely adopted today in PET (32-35). For 2D
acquisition the reconstruction is straightforward but for 3D acquisition 3D reconstruction
algorithms such as 3D FPB or row action maximum likelihood algorithm (RAMLA) is
required. Alternatively 3D data rebinning algorithm may be used to convert the 3D data into
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