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Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
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q
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∑
12 Single Photon Emission Computed Tomography
For ASIRT:
pa
−
n
+
1
k
=+
j
1
k
q
j
∑
n
i
a
ij
i
ij jkij
j
m
a
ij
j
(12.6)
where k is the iteration number. In the MLEM method, the data are considered a Poisson distribution and in the ASIRT method, they are assumed to be a Gaussian distribution. A ow chart of sequential steps of the iterative method is shown in Fig.12.14.
The main feature of the iterative method is to update the estimated image during each iteration to agree with the measured image, and requires many iterations to achieve a satisfactory agreement, demanding a lengthy computation time. To expe­dite the iteration process, the ordered subset expectation maximization (OSEM) algorithm has been introduced, which is a modication of MLEM, in that projec­tions are grouped into a number of subsets separated by some xed projection angles. The number of projections are grouped equally in each subset. For example, if there are 48 projections, they can be divided into eight subsets, each containing six projections. The projections in each subset are not contiguous but are spread over all angular projections so that the rst subset will contain projections 1, 7, 13, 19, and so on, and the second set will have projections 2, 8, 14, 20, and so on, and so goes for the remaining subsets. For each subset, MLEM is applied, and the expected projection values are computed from the estimation of pixel values in all projections in the subset and compared with the measured image. The variance in
pi/qi or (pi−qi) is applied to the pixel values to give the next subset. This is repeated
for all subsets. After all subsets are processed, a single iteration is considered com­plete. Such iteration is repeated until an expected agreement is achieved between the estimated and measured images. It has been shown that if there are n subsets
Fig. 12.14 A ow chart of sequential steps in the iterative reconstruction algorithm
12.2 Single Photon Emission Computed Tomography
187
and, once all subsets are used in a single iteration of OSEM, an estimate is produced which is similar to that obtained by n iterations of MLEM using all projections (Hudson and Larkin 1994). It is this property of OSEM that accelerates the compu­tation process, and, in general, the computation time decreases when more projec­tions are included in each subset. However, there is a tendency of having more image variance with increasing number of subsets when compared to MLEM. So an optimum number of subsets need to be chosen.
To illustrate the OSEM method, consider an example of a 2× 2 true image whose pixel values are 2, 4, 6, and 8, which are not known and need to be deter­mined (Fig.12.15). However, the measured pi values at 4 projection angles (6 and 14 at 90°, 10 at 45°, 8 and 12 at 0°, and 10 at 135°) are known. In the OSEM method, initially the rst estimate of the image is assumed with some arbitrary
Fig. 12.15 Illustration of iterative reconstruction of an image represented by a 2 × 2 image. Known are ith bin values (sum), 8 and 12 at 0° projection, 10 at 45° projection, 14 and 6 at 90° projection, and 10 at 135° projection. Initially, an estimate of the image in a 2×2 matrix is assumed to have arbitrary values of 4in each pixel. From these values, the estimated ith bin values are calculated for a given projection, e.g., 8 and 8 at 0° projection. The ratios of true to estimated values are calculated as 1.0 and 1.5, which are then applied to update the estimated image, which becomes the rst subset. The estimated ith bin values are calculated for the next projection (90° projection) and the ratios are calculated and applied to generate the next subset. When a compari­son of all bin values of all projections is made, an iteration is complete. Iterations are repeated until an acceptable agreement is achieved between the estimated image and measured image
188
ab
12 Single Photon Emission Computed Tomography
values of, say, 4, 4, 4, and 4in each pixel. Instead of 4, any other positive values can be assigned. The pixel values in the two columns at the 0° projection are added to give qi values of 8 and 8. The ratios, pi/qi, are calculated as 8/8=1.0 and 12/8=1.5 (comparison). The pixel values in each column are then corrected by these ratios (backprojection): 4×1=4, 4×1=4; and 4×1.5=6 and 4×1.5=6, resulting in the rst subset. Next, the qi values are calculated for the 90° projection by adding the pixel values in each row, that is, 4+6=10 and 4+6=10 and the pi/qi values are 6/10=0.6 and 14/10=1.4. The pixel values are corrected to give the second subset with values as 4×0.6=2.4, 6×0.6=3.6, 4×1.4=5.6 and 6×1.4=8.4. For the third subset, the diagonal pixel values at 45° and 135° projections are added, the pi/qi values calculated and corrections are applied. This is the end of the rst iteration, and iterations are repeated for better agreement. Refer to the references (Hudson and Larkin 1994; Shepp and Vardi 1982) for a detailed description of the iterative methods.
Corrections for detection efciency variations, noise component, random coinci­dences, scatter coincidences, and photon attenuation are made prior to reconstruc­tion in the FBP method. In the MLEM or OSEM method, these factors are incorporated a priori in the estimated image and need not be applied separately. In general, iterative reconstruction methods do not produce artifacts that are observed with the FBP method and provide a better signal-to-noise ratio in regions of low tracer uptake (Fig.12.16). Overall, iterative methods provide high-quality images and are routinely used in image reconstruction in PET and SPECT.Despite many improvements in the OSEM method, it is a big challenge to have good-quality images in obese patients.
Another algorithm, the row-action maximum likelihood algorithm (RAMLA), has been proposed as a special case of OSEM requiring sequences of orthogonal projections, which lead to faster convergence than OSEM itself.
Fig. 12.16 Comparison of (a) ltered backprojection and (b) iterative OSEM method with attenuation correction

12.3 SPECT/CT Scanner

189
12.3 SPECT/CT Scanner
Accurate medical diagnosis of human disease can be made if both the anatomical and functional status of the patient’s disease are known. In the interpretation of nuclear medicine studies, physicians always like to have a comparison between high-resolution CT or MR images and low-resolution PET or SPECT images for accurate localization of lesions. In PET and SPECT imaging, invivo measurement of organ physiology, cellular metabolism, and perfusion, and other functional status of the organ is made. However, these studies have poor resolution due to poor pho­ton ux and lack anatomical detail. On the other hand, computed tomography (CT) or magnetic resonance (MR) imaging provides excellent spatial resolution with high anatomical detail, but little functional information.
Efforts are made to co-register the two sets of images, in which the matrix size, voxel intensity, and rotation are adjusted to establish one-to-one spatial correspon­dence between the two images. Various techniques of such alignment are employed, and co-registered images are displayed side by side with a linked cursor indicating spatial correspondence, or may be overlaid or fused using the gray or color scale. The major drawback of these alignment techniques arises from positional variations of the patient scanned on different equipment and at different times. Furthermore, patient motion, voluntary or involuntary, adds to the uncertainty in the co­registration. Even with the sophisticated algorithm, a misalignment of 2–3mm is not uncommon.
To overcome the problem of positional variations in alignment of images from different equipment, a dual-modality system has been introduced, in which a SPECT camera and a CT scanner are combined into a single system for imaging the patient in the same clinical setting. Both units are mounted on the same gantry, with the SPECT camera in the front and the CT scanner in the back, and use a common imaging table. The two units are mounted xed; therefore, the centers of the scan elds of SPECT and CT scanners are separated by a xed distance, called the dis­placement distance. The axial travel range of the scanning table varies with different designs of the manufacturers. The scan eld is limited by the maximum travel range of the table minus the displacement distance.
The details of CT scanners are found in standard textbooks on CT and only a brief summary is given here. The CT scanner consists of an x-ray producing tube that contains a cathode lament and a rotating tungsten anode. When a high voltage (kV) is applied to the lament, electrons are emitted from it, which strike the rotat­ing anode producing brehmsstrahlung and characteristic K X-rays. These radiations are then focused onto an intense beam to project toward the object of irradiation. The beam energy typically ranges from 70 to 140keV in energy depending on the high voltage applied. When a beam is projected through a patient, the transmitted beam is detected by detectors on the opposite side of the body and processed to produce signals that are stored in a matrix of choice (64×64, 128×128, etc.) in a computer. The stored data are further processed to form the image of differ­ent organs.
190
ab
12 Single Photon Emission Computed Tomography
The detectors in CT scanners are made of materials such as ceramics, gadolin­ium oxysulde, and gemstone, and in some units, xenon gas. X-rays interact with these detector materials and produce visible light that is processed by a photodiode, producing a signal. Normally, a large number of such detectors are arranged in a full ring or in a partial ring in the form of an arc around the patient. In the full ring sys­tem, the detectors are xed in 360° around the patient and the x-ray tube rotates around (Fig.12.17a), whereas in the partial ring, both the detectors and the x-ray tube are mechanically tied together in 180° opposition in the gantry and the two together rotate around the patient (Fig.12.17b). The detected data are acquired in seconds and stored in a matrix of choice (64×64, 128×128, etc.) in a computer. The stored data are then processed to reconstruct subject images in different projec­tions. Currently, multislice CT scanners are available, providing 6, 16, 64, or 128 slices. In helical or spiral CT scanners, the patient table moves along the body while the x-ray tube rotates around the body, resulting in a spiral pattern of motion of the x-ray tube around the subject. This technique reduces the time of scanning to a few seconds.
When x-rays are projected through the patient’s body, they are attenuated by the tissues to varying degrees depending on the density of the tissues. The transmitted beam produces different shadows of the tissues on the detection system (x-ray lm, computer, etc.) due to varied attenuation, which are often obscured by the shadow of the adjacent organs or tissues. This problem can be overcome by having separate images at two x-ray energies, e.g., 70 and 140keV, and removing the shadow inten­sity from the intended image by coregistration using a software algorithm. However, to avoid performing duplicate studies in different settings, manufacturers install two x-ray tubes in the same CT scanner (Siemen’s Somatom) to operate at two energies separately or in some CT scanners (GE Healthcare’s Lightspeed) with a single x-ray tube, which can be switched between two energies in a fraction of a second. These
Fig. 12.17 (a) Full ring x-ray unit. (b) Partial ring x-ray unit
12.3 SPECT/CT Scanner
191
dual energy CT scanners reduce scan time, lessening the radiation exposure to the patient, and provide high contrast images.
Commercial SPECT/CT scanners are marketed by GE Healthcare (Discovery NM/CT 670), Philips Healthcare (BrightView XCT), Siemens Healthcare (Symbia T16), and Digirad (Cardius X-ACT). Some features of SPECT/CT scanners from three manufacturers are presented in Table12.2, and Siemens Healthereen SYMBIA Pro specta SPECT CT scanner is illustratd in Fig.12.18.
Either CT or SPECT imaging can be performed rst, followed by the other. For example, CT images are taken rst with the organ of interest in the CT eld of view. Next, the scan table with the patient in the same position is moved to the center of
Table 12.2 Some features of SPECT/CT scanners from three manufacturerers
Manucturerer GE healthcare Model Innia Hawkeye 4 BrightView
Detector characteristics
Crystal dimension, cm
Crystal thickness, inch
Diameter =, in (cm)
Number of PMTs Attenuation corr. Ye s CT-AC CT-AC UFOV, cm 54×40 40.6×54 53.3×38.7 Maximum count
rate, cps Dead time, μsec 0.5 1.3 N/A
Intrinsic spatial resol, mm
FWHM, CFOV 3.8/4.5
FWHM, UFOV 3.9/4.5
FWTM, CFOV 7.1/8.3
FWTM, UFOV 7.2/8.5
System Sensitivity (LEHR)
Integral UFOV 3.60% 2.50% <3.7% (uncorrected) Differential
UFOV
59.7×45.7 52×64 59.1×44.5
3.8″×1″ (9.5mm or 25.4mm)
59(3/8″) or 95 (1″)
460 350 310 at 15%
170
2.30% 2.00% <2.7% (uncorrected)
Philips heathcare Siemens healthineer
XCT
9.5 or 19.1
59 59
3/8″–3.3mm; 3/4″–4.3mm
3/8″–3.3mm; 3/4″–4.3mm
3/8″–6.3mm; 3/4″–8.0mm
3/8″–6.3mm; 3/4″–8.0mm
3/8″–277; 3/4″–311
Symbia Pro Specta Q3
3.8″ or 5/8″(9.5 or
15.9mm) 3 or 2 (7.6 or 5.1)
≤3.8mm (3/8); ≤4.5mm (5/8)
≤3.9mm (3/8); ≤4.6mm (5/8)
≤7.5mm (3/8); ≤8.7mm (5/8)
≤7.7mm (3/8); ≤8.9mm (5/8)
203cpm/μCi (3/8); 225cpm/μCi (5/8)
(continued)
192
12 Single Photon Emission Computed Tomography
Table 12.2
Manucturerer GE healthcare
CT physical assembly
Type of detector CdWO4 mounted on a slip-ring High res fat
Number of channls
Generator output 350 watts 32kWmin;
Gantry weight, kg, (lb)
LC resolution (20cm Catph./ surface)
Scan feld, cm 45cm, 56.5cm WFOV SW Optic 47 50cm/70cm with
Number of slices 4 140 @ 1cm
Slice thickness, mm5 0.33–2.00+ 0.6, 0.8, 1, 1.5, 2, 3,
CTDI (dose/100 mAs) B/16cm Phant
Max HC resolution (2% MTF)
Std HC resolution (2% MTF)
Adapted from ‘SPECT-CT Systems Comparison Chart’, February 5, 2024, Imaging Technology News (ITN), Reprinted with permission
(continued)
Philips heathcare Siemens healthineer
panel
1536 786,432 12,288
50kW max
6172 (2800) 2041 (4500) 3710.8 (8180.8)
4mm 5.0mm @
B(32cm phant) CTDIvol=3m(16cm phant. CTDIvol=4.3mGy; & 2.5mA max available current, 140kV, helical scan
3 lp/cm 15 lp/cm @
4 lp/cm 5 lp/cm @
https://www.itnonline.com/chart/spect- ctsystems. Copyright 2024 by Wainscot Media
0.5%
thick
3mGy/100 mAs
10% MTF
10% MTF
Stellar detector
32kW; equivalent 80kW maximum generator power with SAFIRE
5mm
HD FoV Pro 32
4, 5, 6, 7, 8, 10
13.4/14.9
15.0 lp/cm
the SPECT FOV, and images are taken. Both CT (anatomical) and SPECT (func­tional) images are reconstructed and then fused together by applying appropriate alignment algorithms. Various vendors provide commercially available fusion soft­ware, namely, Syngo of Siemens Healthcare, Extended Brilliance Workspace of Philips Healthcare, MIM of MIMVISTA, and Centricity of GE Healthcare. Because the position of the patient on the table does not change, both CT and SPECT images are aligned very accurately, and the overall accuracy is improved by 20–25% com­pared to either modality alone.
0
12.4 Factors Aecting SPECT
Fig. 12.18 Siemens Healthereen SYMBIA Pro specta SPECT CT scanner. (Courtesy of Siemens Medical Solutions USA, Inc.)
193
A major advantage of including CT in the dual-modality is that the CT data can be utilized in attenuation correction of SPECT data, which is particularly useful in cardiac perfusion imaging. Apparent perfusion defects are often seen in the anterior wall in women due to breast position and in the inferior wall in men, and soft-tissue attenuation also shifts between rest and stress images. As will be described later, attenuation correction using CT transmission data compensates for these artifacts more accurately in a shorter time than using the conventional sealed source trans­mission data. Such CT transmission attenuation correction can be applied to other organ imaging as well.

12.4 Factors Affecting SPECT

12.4.1 Photon Attenuation

γ-Ray photons are attenuated in body tissue while passing through a patient. The degree of attenuation depends on the photon energy, the thickness of tissue, and the linear attenuation coefcient of the photons in the tissue. If I0 is the number of pho­tons emitted from an organ, and I is the number of photons detected by the gamma camera, then
µx
−
IIe
=
where μ is the linear attenuation coefcient of the photon in tissue and x is the depth of tissue traversed by the photon (Fig.12.19b). Photons originate from different depths of tissue, which are not exactly known, and so are attenuated to different extents (Fig.12.19a). Attenuation causes a gradual decrease of count density from the edge to the center of the image (Fig.12.20a). If SPECT images are reconstructed from these attenuated proles without correction, artifacts are seen. Attenuation corrections are difcult to apply to the attenuated photons due to lack of knowledge about I and x in Eq. (12.7). Attempts have been made over the years to devise
(12.7)
194
a b
detector patient
I
II
ab
+
()
2
I
gab
()
12/
X
X
1
2
Fig. 12.19 (a) Illustration of photons traveling different depths of tissue, thus suffering variable attenuation. (b) Two photons traversing distances a and b are detected by the two detectors ori­ented at 180°. Attenuation correction can be applied by taking the geometric mean of the two counts I
and Ib and using the total thickness D of the tissue in place of a and b separately
a
X
3
12 Single Photon Emission Computed Tomography
D
l
a
*
b a
l
b
methods of attenuation correction in SPECT imaging, with particular attention to estimate the values of I and x, and given below is a brief description of the com­monly used ones.

12.4.2 Attenuation Correction Methods

In SPECT imaging, two techniques are employed to estimate I0. One is to obtain two counts in opposite projections and then taking the arithmetic mean of the two, or secondly, taking their geometric mean. This is accomplished by acquiring SPECT data in 360° and sorting the counts in opposite projections to calculate the arithme­tic or geometric mean. The arithmetic mean is given by
=
where Ia and Ib are the measured attenuated counts in the opposite projections. Similarly, the geometric mean is given by
t
IxI
=
(12.8)
(12.9)
()
()
−−
()
µµ
I Ie
2//
=
µ
I
Di
=−
()
−
µ
µ
Object profile with
12.4 Factors Aecting SPECT
195
Considering Fig.12.19 and applying Eqs. (12.7 and 12.9) becomes
/
IIxI
=
gab
=×
Ie Ie
a
00
=×
II e
()
ab
00
=
III e
×
()
ab
00
12
/
/
b
2
12
b
−+
µ
ab
−//
µ
D
12
2
/
2
(12.10)
a
I
where Ia0 and Ib0 are the unattenuated counts detected in opposition and D is the total thickness of the tissue. For parallel-hole collimators, which are most commonly used in SPECT imaging, the photon intensity does not change with distance, i.e., Ia0 and Ib0 are approximately equal. Then Eq. (12.10) becomes
gD0
(12.11)
Equation (12.11) is the attenuation correction factor that is applied to the geo­metric mean counts to obtain the unattenuated correct counts. For the arithmetic mean, assuming a uniform uptake of the tracer and a constant μ value for all tissues, the attenuation correction factor is
ID e
ti
0
1//
(12.12)
Equations (12.11) and (12.12) are applied for attenuation corrections using geo­metric and arithmetic means of SPECT projection data. For
99m
Tc studies, a value of
0.12cm−1 is assumed for μ, and Di is empirically estimated from standard body shape and size. Corrections are applied to the measured projections, which are then used for reconstruction of the images by ltered backprojection. A simulated pic­ture of attenuation corrected image is shown in Fig.12.20b.
Fig. 12.20 (a) Object prole without attenuation correction showing decreased distribution of activity at the center. (b) The same object prole with attenuation correction
Object profile
wiithout AC
AC