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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)172
(a)
Figure 26: NEMA three point sources to determine spatial resolution in air (a), SPECT images of
these three point sources are shown as transverse, sagittal and coronal slices of 130 mm, 180m
and 30 mm respectively (b). Since only Ramp filter has been used, high frequency noise is clearly
seen in these images.
Tomographic spatial resolution with scatter (NEMA phantom)
A water filled acrylic NEMA phantom with inner diameter of 20 cm and containing three
axial line sources with a diameter 1 mm (Figure 27) is used for this purpose. The phantom is
placed with its axis along the axis of rotation. The phantom is imaged with radius of rotation as
150.5 cm over 360. At least 100K counts at each of at least 120 different projections are
acquired using step and shoot mode. One transverse slice, 10.3 cm thick is constructed through
the center of the phantom with FBP technique using ramp filter. Two additional transverse slices,
each 10.3 cm thick is reconstructed in the same manner centered at 4 cm on either side from
the center. The spatial resolution is reported in tangential and radial directions for central and
peripheral sources.
Single Photon Emission Tomography (SPECT) 173
(a)
(b)
Figure 27: NEMA cylindrical phantom with three line sources to determine spatial resolution in
radial and tangential direction (a). The SPECT transaxial slices of three point sources
with scatter (b)
Alternatively a profile is drawn through the reconstructed image of a point source (2) and the
FWHM is measured both in x and y direction. The FWHM should be same in x and y direction.
The FWHM for a given tomographic image should not exceed by more than 10% (or 2mm) of
the corresponding static image in air. The spatial resolution with scatter should not be worse than
about 16 mm for a radius of 15 cm. And the background at the edge should not exceed 10% of
the peak of the reconstructed point source (2). If these tolerance limits exceeded then the system
is not properly centered. This test is very useful to ensure that the system is accurately centered.
System volume sensitivity (NEMA)
A cylindrical phantom is filled with radioactivity (
same manner as for NEMA phantom. About 10K counts per projection at 20% photopeak
symmetrical energy window. Calculate the average counts per minute for the SPECT acquisition
(A) by dividing the total counts imaged by the total elapsed time. Calculate the source activity
concentration (Be) at time T halfway through the 360 SPECT acquisitions by applying the
proper source decay correction factor for the radionuclide used.
99m
Tc). Image acquisition is done in the
Single Photon Emission Tomography (SPECT)174
3
( /min)
( / )
B kBq cm
The system volume sensitivity (SVS) is then calculated as:
A cts
e
(20)
SVS
Linearity of activity (IAEA)
This test is done to show that an area of more activity should contain more counts than that
of less activity and the difference should be in proportion to the activity contained in them. This
is checked by placing a series of objects of different but known activities in the central field of
view of the camera in such a way that they remain in the FOV during SPECT acquisition. After
reconstruction the counts per pixel or per slice is plotted against the known activity with minimum
activity object first and then in increasing order or vice versa. The result should be straight line
for a linear response of the system with activity. Scatter and attenuation cause considerable
deviation in the linear response. It is therefore, advisable to use these corrections during
reconstruction.
Slice thickness (IAEA TECHDOC)
The slice thickness is estimated usually at the center of the slice in the central field of view.
A small point source is placed within 1 cm of the central axis and a tomographic acquisition is
performed exactly the same way as for tomographic resolution in air. The profile is drawn
through the reconstructed image both in horizontal and vertical direction. The pixel with maximum
number of counts is recorded in a slice in which the point source is seen clearly. The counts in
adjacent slices at the same location are recorded including those containing up to 5% of the
maximum. A profile is generated along the z-axis using these values and FWHM of the profile is
calculated. The FWHM here should match (within 10 %) with the tomographic resolution for the
same radius of rotation.
Total performance for SPECT
The total performance test is done to check the performance of the system under conditions
identical or nearly identical to those used in clinical situations. The Jaszczak or Carlson phantoms
are normally used for this purpose. The Jaszczak phantom allows to check almost all the main
performance parameters of the system e.g. tomographic resolution, uniformity, etc. and overall
performance of the SPECT system. The phantom image is reconstructed using FBP and then
with attenuation and uniformity correction.
The image of total performance phantom is shown in figure 28 after reconstruction. One can
also check the ability to resolve the objects with high and low contrast and uniformity in
tomographic slices using total performance phantom.
Single Photon Emission Tomography (SPECT) 175
Figure 28: SPECT image of Jaszczak phantom. The transverse slice at the level of 6 cold spheres
is shown. Such an image can be taken at different levels to check the resolution, linearity and
uniformity.
References
1. Wallis JW and Miller TR, Rapidly converging iterative reconstruction algorithm in single photon
emission tomography. J Nucl Med 1993; 34: 1793-1800.
2. SPECT systems in quality control of nuclear medicine instruments, IAEA-TECDOC-602, 1991; pp
253-301.
3. Busemann-Sokole E. Measurement of collimator hole angulation and camera head tilt for slant and
parallel hole collimator used in SPECT. J Nucl Med 1987; 28:1592-1598.
4. Lonn AHR, Rowbotham, GD and Holman LA. Monitoring rotating gamma camera performance for
emission tomography, In Quality control of nuclear medicine instrumentation (ed) R.F. Mould, HPA,
London, 1983; 92-100.
5. Rogers WL, Clinthorne NH, Harkness BA, et al. Field uniformity requirements for emission computed
tomography with an Anger camera. J Nucl Med 1982; 28:1592-1598.
6. O’connor MK and Vermeersch C. Critical examination of the uniformity requirements for single
photon emission computed tomography. Med Phys 1991; 13: 190-197.
7. Gulberg GT. An analytical approach to quantify uniformity artifacts for circular and non-circular
detector motion in SPECT imaging. Med Phys 1987; 14: 105-114.
8. Chang W, Bruch P, Wesoloski C, et al. Performance of case collimators for SPECT imaging. J Nucl
Med 1985; 26: 44.
9. Chang W, Li SO, Williams JJ, et al. New Method of examining gamma camera collimators. J Nucl
Med 1988; 29: 676-683.
10. Malmin RE, Stanley PC and Guth WR. Collimator angulation error and its effect on SPECT. J Nucl
Med 1990; 31: 655-659.
Additional suggested reading:
1. Zubal IG and Wisniewski G. Understanding Fourier space and filter selection. J Nucl Cardiol 4, 234-
243: 1997.
Single Photon Emission Tomography (SPECT)176
2. Heideman MT, Johnson DH, and Burrus CS, “Gauss and the history of the fast Fourier transform,”
IEEE ASSP Magazine 1984; 4: 14–21.
3. H. Nyquist, “Certain topics in telegraph transmission theory”, Trans. AIEE, vol. 47, pp. 617-644,
Apr. 1928 Reprint as classic paper in: Proc. IEEE, Vol. 90, No. 2, Feb 2002.
4. Eisner, RL. Principles of instrumentation in SPECT. J Nucl Med Technol 1985;13:23-31.
5. Ficken V and McCartney W. SPECT quality control: A programme recommended by the American
college of nuclear physicians and the ACNP corporate committee, J Nucl Med Technol 1994; 22: 205-
210.
6. Harkness BA, Rogers WL, Clinthrone NH and Keyes JW. Quality control procedures and artifact
identifications, J Nucl Med Technol 1983; 11:55-60.
7. Nowak DJ, Eisner RL and Fajman, WA. Distance weighted backprojection: A SPECT reconstruction
technique, Radiology 1986; 159:531-536.
Image Filtering in Nuclear Medicine
H. Rajabi and A.K. Pandey
A digital image is a two dimensional matrix of single color elements. Each element of
picture is called pixel. A digital image is formed by displaying a matrix of pixels in the
proper order on the computer screen (monitor) (Figure 1). It is saved in computer memory
in binary form. To save an image in binary form an instruction is required to guide the
computer. There are almost 44 different types of instructions to register an image into a
binary file. However there are two basic methods for a computer to store and display an
image; vector and raster graphic formats.
Figure 1: A digital image is a matrix of color elements
In vector format, the image information is saved as actual mathematical vectors rather
than pixels of different colors. An image in vector format can be shown in any scale and
resolution without distortion. The vector format has no application in nuclear medicine.
CorelDraw (CDR), Hewlett-Packard G~aphics Language (HOL), and Windows Metafiles
(EMF) are a few examples of vector format.
There are many versions of raster formats such as Bitmap, OIF, and JPEO. Bitmap is the
standard file format for Microsoft Windows operating system. Almost all operating systems
support this format. Bitmap may be regarded as a classic example of raster format. We will
have some few words on the structure of bitmap format.
A typical bitmap file usually contains the following blocks of data:
Bitmap Header: It is composed of 14 bytes that stores general information about the
17 7
Image Filtering in Nuclear Medicine178
file including; type and size of image file.
Bitmap Information: It is composed of 20 bytes that stores detailed information about
the bitmap image; including the height, width, depth of image and color palette.
Color Palette: This block stores the definition of the colors being used in the image.
The purpose of the color palette is to apply actual color of each of pixel in the image.
Bitmap Data: This block stores the actual image, pixel by pixel. Pixels are arranged
from the bottom to the top and from the left to the right. Each pixel is described using one
or more bytes. If the amount of bytes matching a horizontal line in the image is not a
quadruple, the line is padded with null-bytes
A typical bitmap file uses the RGB color system. In this system, a color is created by
mixing different intensities of red (0-255), green (0-255) and blue (0-255). The RGB system
needs 24 or 32 bits allocated to each pixel. The 24 bit RGB system can generate up to
16,777,216 different colors. There are other versions of bitmap that use 1, 8, 16 and 48 bits
allocated to each pixel. Bitmap format is a very well documented format and free of patents.
Nuclear medicine image
A nuclear medicine image is the distribution map of radiopharmaceutical in the patient’s
organ/body. During data acquisition, the field of view of imaging system is divided into
small parts called voxels. The imaging system detects the photons emitted from each voxel
and registers them into memory units individually allocated to that voxel (Figure 2). The
image data is essentially two-dimensional matrix of pixels (picture elements) representing
the relative distribution of activity in the patients’ body. In mathematics such data are
usually presented using 2D bar chart (Figure 3), which is not the method of choice in
nuclear medicine. Conventionally nuclear medicine data (radiopharmaceutical distribution)
are shown as images (Figure 4). For conversion of nuclear medicine data (i.e. a two
dimensional matrix) into image an instruction is needed to relate the pixel values to a color.
This is done by color table that should be put in color palette in bitmap file.
Image Filtering in Nuclear Medicine 179
Figure 2: Gamma Camera Frame Mode Acquisition
Figure 3: One frame of a renal dynamic study presented in 3D form
Figure 4: A nuclear medicine image
Noise in nuclear medicine image
Each elements of nuclear medicine image (raw data) is actually the result of a measurement
of number of disintegration in a given part of patient’s body. It is just like measuring a
sample activity placed in a well counter. If we put a small amount of activity in a vial and
measure it in a well counter many times, we won’t get similar values in all the measurements.
But why that is so?
Generally there are two types of possible errors with every measurement; systematic and
random. Systematic error includes all types of error that is potentially avoidable if we are
attentive during measurement. The other type of error - random error - includes all types of
unavoidable error. For example a photon emitted from a source may not interact with the
detector or, may lose the energy in multiple collisions. In both the cases, energy of the
signal is less than the threshold value and the event is lost. On the other hand two photons
Image Filtering in Nuclear Medicine180
may simultaneously interact with the detector and as a result very strong signal is produced
that is out of energy windows therefore these two events are also lost. Moreover the
disintegration is a random phenomenon in nature and in a given time interval the number of
disintegrations are not equal. Therefore there are always uncertainties in the pixel values
(counts). From the statistical point of view there is always random error in the pixel values.
The amount of error in each pixel is unpredictable, therefore uncorrectable. Moreover the
error in one pixel is quite independent of the other pixels.
The term random error is used to refer the uncertainty in a single measurement. A
nuclear medicine image is composed of thousands independent measurements (pixel values).
The special term to refer to this type of error is known as noise. Noise in nuclear medicine
images is the random errors in the pixel values.
Noise distribution in nuclear medicine image data
An image in nuclear medicine is composed of thousands of pixels. In each pixel there is
random error. Statistically we deal with a large population of random numbers. Since noise
in all pixels have similar nature, these random numbers must obey a certain statistical
distribution. The disintegration itself obeys Poisson distribution.
Other phenomena such as photon absorption in source, photon interaction in detector,
number of light photons produced, number of light photons entering the PMTs, and electron
multiplication in PMTs more or less follow Poisson statistics. However the uncertainties in
electronic equipment have different distribution.
From the statistical point of view, we are dealing with so many types of distributions.
Based on the central limit theorem (the most famous theorem in statistics) the overall
distribution of several trivial events tends towards the Gaussian distribution. With a good
approximation it can be assumed that noise in raw nuclear medicine image data obeys the
Gaussian distribution. However there is a dilemma here. The Gaussian distribution is only
valid for continuous types of data while nuclear medicine data are always in discrete form.
This is a simple fact that is usually overlooked. Moreover it is always assumed that the
standard deviation of noise in nuclear medicine data is equal to the square root of the mean
value while this is the unique property of Poisson distribution.
Anyhow, there is practically not much difference if we assume a Gaussian distribution in
which the standard deviation is approximately equal to the mean value. From the above
discussion two points are very important to remember.
When we say that noise in a nuclear medicine image obeys the Gaussian distribution it
should not be misinterpreted that the level of noise is the same in all pixel. The relative
amount of uncertainty depends on the absolute pixel value. Pixels with high counts are less
noisy than the pixels with low counts.
The above reasoning about the noise distribution in nuclear medicine is only valid for
Image Filtering in Nuclear Medicine 181
intact raw data. Any type of manipulation changes the noise distribution significantly.
Reconstructed images are not raw data therefore noise distribution is different in tomographic
images than in the corresponding raw data. The type of noise is very much dependent on the
method of reconstruction. As a rule of thumb noise in each pixel of tomographic image is
dependent on both absolute count value and the location of pixel over the image.
All the processing must be performed on raw data not on the image. It is important to
note that whenever the data is transferred for processing in any other system it should be
raw data and not the images.
How to deal with random error?
Whenever we want to be sure about the results of a measurement we repeat the measurement
few times and average the values. The average is always assumed to be better than a single
value. A simple reasoning is that the measured values are randomly distributed around the
real value. When we average, the big and small values come closer to the real value.
Suppose we measure a sample activity of 100 MBq in a counter five times with values as
(say) 97, 94, 101, 105 and 83. Averaging just decreases the range of dispersion or range of
random error. It does not mean that the average value is more accurate.’ Averaging just
improves precision not accuracy. If the original readings are inaccurate the average is also
inaccurate.
Figure 5: Normal distribution
How to deal with noise?
Noise is nothing but random error in each data point. Our data may be in one- dimensional
(e.g. activity time curves) or in two-dimensional form (e.g. images). We have to deal with
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