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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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Single Photon Emission Tomography (SPECT)162
( ) ( ) . ( ). . . . .
x x K C x Blur Atten R measured proj estimated proj
Figure 21: A simple block diagram to illustrate the iteration loop
Where the summation () performs the backprojection operation. The term 1/mean_ atten
in equation-14 serves to compensate for the attenuation introduced by the attenuation in
backprojection step. Wallis and Miller have also given the equation for the iterative methods
utilizing differences for the comparison step as follows:
1( ) ( )
k k
ˆ ˆ
u
(14)
Where R represents one dimensional convolution with a ramp filter prior to backprojection,
C(x) indicates a (spatially varying) multiplicative correction and K is a scaling factor. K could be
determined after the first iteration by comparing the total counts in first estimated and measured
projections.
Ordered Subset Expectation Maximization (OSEM)
The OSEM is a simplified version of ML EM but with the same objective of maximizing the
likelihood function. In OSEM projection data are grouped into a number of subsets. Standard
expectation maximization procedure is applied to each of these subsets. Within each iteration the
function is updated as many times as the number of subsets accelerating the convergence. The
optimization of subsets and number of iterations is required in real patient data for faster
convergence.
Row Action Maximum Likelihood Algorithm (RAMLA)
This is may be considered as a special case of OSEM that requires sequences of orthogonal
projections. It uses a parameter to control updating of the likelihood objective at each full
iteration cycle. This is one of most proposed methods for 3D reconstruction particularly in PET.
Single Photon Emission Tomography (SPECT) 163
3
Field size used Field size used
( )
matrix
( )
m matrix
The algorithm uses spherically symmetric volume elements (called blobs) instead of voxels. To
obtain almost uniform volume sampling, blobs are partially overlapped with neighboring ones
using proper weighting. Implementation of this method in 3D PET has produced good quality
images but the reconstruction time said to be quite long. This method has great potential for
future if the reconstruction time is reduced.
Image data acquisition in SPECT
While acquiring the SPECT image data following parameters have to be selected appropriately.
Pixel size (matrix)
Number of angular samples
Arc selection
Collimator
Acquisition time at each angle
Rotation mode
Pixel size (matrix)
According to sampling theorem at least 2 pixels per FWHM for planar imaging and 2.5 or 3
pixels per FWHM for SPECT need to be selected. Therefore the pixel size determination depends
on the spatial resolution required in the image. Once this is known, the matrix size for SPECT
acquisition can be estimated. Mathematically
Matrix size
For example if 15 mm resolution is expected from a 500x400 mm FOV detector the matrix
size should be:
500
15 3
/
So 128128 matrix size can be selected. It should be noted here that larger dimension in a
rectangular field of view has been selected for calculation. For circular FOV the diameter of the
detector is taken for field size. The matrix size for a circular detector of diameter 400 mm for
identical situation would be:
400
15 3
/
Here also one has to go for 128x128 matrix if 15 mm resolution is strictly required otherwise
a nearer available matrix size of 6464 can do the job.
100 100 100
80 80 80
pixel size FWHM
/
(15)
Single Photon Emission Tomography (SPECT)164
D r
d pixel size
100
Number of angular samples
As per sampling theorem we require about 3 pixels per FWHM for SPECT. The number of
angles should be more than
2
where D is diameter and r is radius of the object and d is the sampling interval. Thus for a
required resolution of 15 mm and object diameter as 200 mm (radius 100 mm) and pixel size of
6mm, the angular projections should be greater than:
(16)
2 100
6
Thus 120 or 128 projection angles may be used. The number of angular projections is
decided before starting the tomographic acquisition. The typical number of angular projections
used in SPECT may be calculated by the above mentioned method. More the number of projections
more is the time taken for a SPECT acquisition thereby giving a chance for motion artifacts
particularly in sick patients. Normally 60/64 or 120/128 projections are used in most of the
tomographic acquisition in nuclear medicine.
Arc selection
Acquisition is done over 180 or 360. Acquisition in 180 takes less time but there is risk of
getting artifacts in the image. Some of the acquisitions like cardiac SPECT are done only in 180
as complete rotation does not contribute significantly rather doubles the acquisition time. For
symmetric objects one can use 180 arc but for asymmetric objects it is advisable to go for 360
arc acquisition.
Collimator
If the count rate from the object is more than 2kcps then high resolution collimator should
be preferred. For lower count rates a general purpose collimator may be used. For small organs,
the best choice would be a focusing collimator (like fan beam collimator). Patient should be kept
as close to the collimator as possible for better resolution. In modern systems auto-contouring
facility is available which automatically brings the collimator as close to the patient as possible
in all projection views.
Acquisition time at each angle
Theoretically acquisition time should be as long as is necessary to acquire adequate counts
but practically it should not exceed 20-25 minutes. In sick patients, who cannot lie down in a
given position for long, the acquisition time has to be reduced. Commonly 25-40 seconds
acquisition time per projection is used depending upon the available count rate.
Single Photon Emission Tomography (SPECT) 165
Rotation mode
There are two types of modes of rotation available in SPECT systems; the Step and
shoot (SS) and continuous rotation (CR). In step and shoot motion the camera rotates by a
given angle, stays there for some pre-defined time to acquire static image data and then
rotates to the second position. The process continues till a complete rotation by a given
angle (180° or 360°) is complete. At each position the center of the camera points to the
same point in the patient (the center of rotation). The CR mode is more efficient due to
virtually no dead time and saves about 1 minute in 180° rotation. However, the spatial
resolution is believed to be slightly better in SS mode.
Performance evaluation of SPECT
Though the advantages of emission tomography are well understood and accepted but can
only be realized if its various performance parameters are maintained at their optimum level
(within tolerance limits). The performance characteristics of a plannar camera described in the
previous chapter are also equally applicable to a SPECT system. The following additional
parameters need to be checked for a SPECT system:
1. Tomographic uniformity
2. Centre of rotation (COR) offset values
3. Sensitivity and uniformity of the system at different angular projections
4. Tomographic contrast
5. Tomographic resolution
6. Linearity of tomographic response
7. Slice thickness
8. Total performance of SPECT system
The first and foremost task in quality control of SPECT system is the proper alignment of
gantry with the horizontal floor at the time of installation. Most of the non-alignments are
related to the mechanical maladjustments. The electronic components are now available with
good stability and are less troublesome. The mechanical stability of the gantry and detector head
plays a vital role in system performance during rotational motion. The detector plane should
remain perfectly parallel to the axis of rotation and the detector head should be stable (without
any jerk) during image acquisition. It is therefore, necessary to align the base exactly horizontal
and the gantry exactly vertical at the time of installation. The spirit labels of adequate dimensions
are helpful in checking the alignment of the system. In modern single or dual head SPECT
camera the gantry and the detector head both are very stable from all reputed manufacturers. The
suppliers have also improved the technique of making the base exactly horizontal on which the
system rests. This completely eliminates the alignment problem, which was faced in yester
years.
Single Photon Emission Tomography (SPECT)166
0 5 0 5
2 2
. .
1 2
( )/
COR offset
The center of axis rotation can be checked by keeping a point source near the center of
rotation and check the coordinates of its image at 0o and 180o as shown in figure 22. By
recording these coordinates one can calculate the COR offset. In fact to check the COR offset for
various locations of the point source, four point sources of radioactivity (
one within 2 cm of the axis of rotation, second at about 10 cm radially away from COR, third
and fourth within 5 cm of the edge of the field of view one along the positive and the other along
negative direction of Y. A normal tomographic acquisition is performed with the largest matrix
size (smallest pixel size) available. At least 10K counts should be collected at each projection.
The number of projections may be kept as small as possible (say 32) for 360o rotation. For each
image of the point source the centre of gravity (COG) may be estimated using software to
correctly represent the image location (2).
99m
Tc) may be positioned;
the COR offset (R0) may be determined as:
for R0.
Figure 22: Alignment and misalignment in coordinates at 0 o and 180 o for SPECT
The center of rotation will be
N
or
N
1
( )
depending upon whether the first pixel is designated as 0 or 1.
The x coordinate of center of gravity (COG) at 0o(X1) and then at 180o(X2) are recorded and
R N X X
0 1 2
(17)
The value can be determined for each pair of angles separated by 180o to have a set of values
Single Photon Emission Tomography (SPECT) 167
Determination of x and y offset values
The reconstructed image after tomography needs to be properly aligned so that projection of
axis of gantry rotation coincides with the center of the image. Incorrect adjustment of COR
results in the loss of contrast and distortion in the image. To realize this one can examine a point
source image reconstructed with an incorrect COR. The incorrect COR can easily be created by
giving a small tilt in detector head. After reconstruction the image first becomes broader and
then appears with annular rings for increasing error in COR.
The COR offset checking is done by placing a point source slightly away from the axis of
rotation (3 to 10 cm) and acquiring a SPECT image using 32 or 64 projections for 360o rotation
and with a minimum of 20 K counts per view. The software enables us to analyze the results of
the data and generates curves for x and y offset values against the angle of rotation. In an ideal
situation the x coordinate of the source is expected to move in a sinusoidal manner during a
complete rotation through 360o. The amplitude of the sine wave depends upon the distance of the
point source from the COR. The y direction is the direction of the image slice, so the y coordinate
is expected to remain the same during the entire rotational motion of the detector. One can
visually check x and y motion on the display monitor as well. The change in image position in x
direction can be seen horizontally whereas the y direction can be seen vertically (up and down)
on the image display monitor. The y offset particularly for a point source radially distant from
the central axis gives a good indication of the head tilt or possible angulation in collimator holes
(3). In normal situation the y offset plot should generate a flat (straight) line (4).
Figure 23: COR offset values for X-coordinates at each projection angle. During one complete
rotation of the camera X-coordinates follow a sine curve. The actual measured value of Xcoordinates may not exactly match with the expected (ideal) values (a), The difference between
expected and measured values show the actual offset in X-coordinates at each projection angle
(b), Computer records these values and makes necessary corrections (c).
The difference between the observed x values along the curve and the fitted sine wave
should be a straight line in case of perfect alignment (Figure 23). The deviation from the ideal
situations should be as small as possible. The average of x coordinate at a given angle and its
conjugate obtained after 180o rotation (i.e. and 180o + ) produces the center of rotation values
Single Photon Emission Tomography (SPECT)168
independent of source position. These values should not vary by more than a quarter of a pixel
for 6464 matrix. The COR offset values stored and used in the reconstruction of SPECT image.
The modern systems from all the suppliers have their own method for the determination of COR
offset values. After completion of COR acquisition it plots the x and y offset values for the
detectors and also indicates if they are within tolerance limits. The values may be subsequently
stored.
Figure 24a shows the COR offset values beyond tolerance limits. The necessary COR map
was acquired at three different ROR and then COR offset values were measured (Figure 24b)
where the values are well within allowed limits. The deviation and their allowed limits are
shown in some of the systems these days as can be seen in figure 24.
Figure 24: COR offset values beyond tolerance limits (a) After making necessary
COR build the values are well within tolerance limits (b)
Uniformity
The uniformity of the camera is initially checked the same way for planar and SPECT
system. Both integral and differential uniformity should be determined by the method already
described in the previous chapter. The best way to have a software which can provide information
on mean pixel counts, standard deviation and the coefficient of variation (COV). A COV value of
1% or less is ideal for SPECT imaging. For 6464 matrix, at least 30 million counts may be
acquired to check the system uniformity. The system uniformity should be checked for all
collimators that are likely to be used for SPECT imaging. The suitable flood phantom filled with
99m
Tc source in solution or 57CO flood sheet source may be used for this purpose. The uniformity
should also be checked for 128128 matrix size, which is now more frequently used in SPECT
Single Photon Emission Tomography (SPECT) 169
acquisition. These values are stored in the computer for uniformity correction. Again with
modern SPECT systems the manufacturers suggest the number of counts that need to be acquired
for a given matrix size for uniformity map.
Tomographic uniformity
The simplest way of determining tomographic uniformity is by filling a cylindrical phantom
(cylindrical portion of Jaszczak phantom can be used if available) with uniform solution of
radioactivity (
long axis of the phantom is parallel to the axis of rotation and the part to be imaged is projected
out of the imaging table towards the detector to avoid scatter from the table. A 360o tomographic
image is acquired with at least 64 angular projections in 6464 and 128128 matrix and for a
radius of rotation about 15 cm if possible. The counts at each projection should be more than
500K. The images with 4 pixel thick slices are reconstructed each containing at least 2 million
counts. The filter and attenuation correction are used as in routine clinical studies.
The transverse section is reviewed for any concentric ring or “bulls-eye” artifact, if any. The
uniformity may be determined quantitatively for each slice in terms of IU and DU. The central
round object (ring artifact) shows the tomographic non-uniformity. If there is non-uniformity in
a planar image then it gets amplified in a tomographic image (5, 6). The tomographic nonuniformity is inversely proportional to the distance from the axis of rotation. The non-uniformity
near the axis of rotation is many times greater than the planar non-uniformity. This test should be
repeated for a non-circular orbit if available with the system (7).
99m
Tc) and positioning it at the end of the imaging table in such a way that the
Electronic stability during rotation
All recently manufactured cameras have the incorporated magnetic shielding (mu metal) to
avoid interactions between the PMTs and weak magnetic fields in the vicinity either due to
earth’s magnet or some other electric fields. In addition to magnetic field effects the gravitationalmechanical effects may also change the camera sensitivity with gantry rotation. The uniformity
and sensitivity should not change during rotation beyond tolerance limits. Any change in these
two parameters can be checked at the time of acceptance and then periodically. Any change in
camera electronics during rotation caused by the above mentioned reasons may be responsible
for variation in uniformity and sensitivity during rotation.
The simple way to check this is to mount a 57Co flood source on the face of a collimator. The
source must be firmly attached so that it does not move/shift during rotation. A 20% PHA
window is centered on the photopeak. A 360o tomographic study in 64x64 matrix is acquired
using the smallest angular sampling that is used in any clinical study. The time for acquisition
should be selected in such a way that at least 1 million counts are acquired in each projection.
The mean counts per projection are calculated. The deviation in each projection may be calculated
and plotted against projection number/angle (Figure 25), which should be less than 1%. The
uniformity may also be calculated for each projection image. It is certainly time consuming, as
Single Photon Emission Tomography (SPECT)170
there may be 32 or 64 images to be processed. Usually (not strictly) if the uniformity does not
change during rotation then the sensitivity also remains unaffected. If this long procedure is not
followed then the sensitivity and uniformity should be measured at least at 4 projections; 0o, 90
o
180
and 270 o for any unacceptable deviation.
o
Figure 25: Change in detector sensitivity during camera rotation. The variation is negligible in
the system tested.
Collimators
The characteristics of collimator should be properly checked before they are put to use for
SPECT acquisition. Defective collimators may introduce artifacts in tomographic image (810,3). The procedure of collimator evaluation has already been described in detail in previous
chapter entitled “Radiation detection in vivo - Gamma Camera imaging”.
Tomographic contrast
The tomographic contrast is the ability of the system to detect a small change in activity
concentration. The method is to choose a sphere of known size and placed in a pool of uniform
activity. A normal tomogram is then taken. The contrast may then be calculated as:
Single Photon Emission Tomography (SPECT) 171
VV
bgdsph
VV
bgdsph
and
Contrast
V
Where
V
is the value of pixels in area outside the given volume (background). The contrast can
bgd
is the value of the pixels within the region corresponding to the given sphere
sph
also be checked qualitatively by the total performance phantom (such as Jaszczak phantom).
Tomographic resolution (NEMA)
This parameter also depends on various factors such as the collimator used, radius of rotation,
type of orbit used during acquisition and the type of filter used during reconstruction. The
resolution may be determined in air as well as with scatter by placing the point source in air near
the center of rotation (within 1 cm) and inside a resolution phantom respectively. A tomogram is
acquired with 15 cm radius and at least 10K counts per projection using the matrix size and
number of projections that are normally used in clinical studies.
Tomographic spatial resolution in air (without scatter)
The NEMA recommends acquisition of SPECT image of three point sources separated by
7.5 cm in x-direction and 5 cm in y -direction (Figure 26). For convenience one can make three
fine holes at respective locations in a perspex sheet and introduce a small amount of activity
99m
(
Tc) and place it on the imaging table parallel to the axis of rotation. SPECT acquisition is
done with the radius of rotation of 150.5 cm for at least 20 K counts in each of at least 120
projections over 360 using step and shoot mode. Image is reconstructed using FBP technique
with a ramp filter. One 130.5 cm thick transverse slice, 180.5 cm thick sagittal slice and 30.5
cm coronal slice are reconstructed centered on the central point source. It should be noted that
facility of reconstructing such thick slices is not available with the processing software. However,
facility to make composite images is available which may be used to reconstruct the slices of
desired thickness.
The transverse slice gives resolution in x and y direction, sagittal gives that in y and z and
coronal in x and z direction. From these values, average values of resolution in x, y and z
direction can be estimated. The average values are first calculated for the central point and then
for other two points. Thus the resolution in radial (x), tangential (y) and axial (z) directions is
reported. The measured values normally range from 12-13 cm in air.
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