Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5255_Библиотеки_им_академика_М_И_Перельмана
.pdf
142
Radiation Detection in vivo and gamma camera imaging
The selection of acquisition parameters depends upon the type of investigation. For
example, the static images are always collected in frame mode and the frame size is selected
keeping in view the attainable resolution. In dynamic images, the purpose is to follow the
uptake and clearance of radioactive tracer by an organ over a time period. The number of
frames acquired per unit time is selected depending upon a given situation and need (such as
perfusion, concentration of radiotracer and excretion from the organ).
The stored image can be displayed on the monitor screen as and when needed. The
display system has its own dedicated image memory. A smaller secondary memory known
as look up table or transformation table is used to display the image at desired intensity
levels (gray level). The gray scale can be altered without changing the actual image data.
Various parameters of the computer system have to be checked at the time of acceptance
and then at periodic intervals. The following parameters of the computer system can be
easily checked.
1. ADC linearity (Integral and differential)
2. Pixel size for all matrix sizes
3. Timing accuracy of data collection
ADC linearity
The quantitative assessment of ADC linearity needs a pulse generator. However, if the XADC and/or Y-ADC are non-linear the displayed image will show stripes and lines in the
digital image. The effect may be seen in X and/or Y direction depending upon which, axis is
affected. So we can check this parameter only qualitatively in the absence of a pulse generator
and can be corrected by the service personnel if needed. With modern systems ADCs nonlinearity is extremely uncommon.
Pixel size
Two point sources, separated by a distance say 300 mm are placed on the face of a commonly
used collimator (LEGPor LEHR). This is usually done by making two fine holes in a plastic
ruler. The holes are 300 mm apart and able to contain a small drop of radioactivity (
from a fine needle. The image is acquired as usual at 20% PHA window for 64x64, 128x128,
256x256 and higher matrix sizes if available both in X-X and Y-Y direction. The image
profile is taken and the number of pixels between these two point sources 300mm apart is
determined and then the pixel size for each matrix in mm is calculated.
Example: For 64x 64 matrix if 46 pixels=300 mm both in X and Y direction then 1 pixel
size is 6.52 mm (both in X and Y direction). The pixel size measurement for other matrix
size may be done in the same manner.
Software may be made to determine the center of gravity (COG) of the point sources.
The distance between two point sources can be calculated to the fraction of a pixel.
99m
Tc)
Radiation Detection in vivo and gamma camera imaging
143
Computer clock time
The simplest way of measuring/checking the clock time is by performing a dynamic study
using a uniform activity (flood source) phantom. Images of different frame lengths may be
acquired. The time of start and end of the study may be noted exactly with the help of a fine
stopwatch. The time elapsed should be exactly equal to the acquisition time of the study. It
should be born in mind that slightest error in starting and stopping the stopwatch would
cause error in the measurement of time. It is therefore, better
to start the stopwatch before starting the computer and only
note the time of start and end of the study.
One way of avoiding the possible error is to observe
counts in different frames. Acquire 10 frames of 1 second
each, 10 frames of 10 second each and one frame of 100
second. All the 10 frames of 1 second combined and one
frame of 10 second should have nearly equal counts. Similarly
10 frames of 10 second combined and one frame of 100
second should also give similar results. This however, does
not prove the accuracy of unit time (second).
Total performance test
Figures 18: Image of a
thyroid phantom. The hot and
cold lesions in the phantom
are distinctly visualized.
The total performance of the system may be checked by imaging the available phantoms.
The most commonly used collimator is mounted in place on the detector and the phantom is
filled with adequate amount of radionuclide (
99m
Tc) and all the parameters (PHA window
etc) are set as used in routine clinical studies. The phantom is kept on the collimator
covered with a polythene sheet at a reproducible position. The image is acquired for 1 to 2
million counts and kept as a reference image provided the image is good enough to show the
cold and hot areas of the phantom (Figure 18). Such an image may be recorded as acceptance
and reference image.
References
1. IAEA-TECDOC-602, Quality control of Nuclear medicine Instruments, Single and multi probe counting
systems for Gamma Radiation Measurements in vivo and rectilinear Scanner, Vienna 1991; pp 65-96:
97-133.
2. Hine GJ. Instrumentation in Nuclear Medicine, Academic Press, Thyroid Radioiodine Uptake
Measurements, New York 1967; pp 327-349.
3. Eberl S. Gamma Camera, (Instrumentation Part –2) Distance Assisted Training Program for Nuclear
Medicine Technologist ed: HE Patterson and BF Hutton IAEA page 8-10.
4. Tsui BM, Gullberg GT, Edgerton ER, Gilland DR, Perry JR and McCartney WH. Design and clinical
utility of a fan beam collimator for SPECT imaging of the head. J Nucl Med 1986; 27: 810-819.
5. Young KC, Kouris K, Awdeh M and Abdel-Dayem HM. Reproducibility and action levels for gamma
camera uniformity. Nucl Med Commun 1990; 11: 95-101.
144
Radiation Detection in vivo and gamma camera imaging
6. Performance measurements of scintillation cameras, NEMA standards Publications NUI-1986,
Washington, 1986.
7. Performance measurements of scintillation cameras, NEMA standards Publications NUI-1994,
Washington, 1994.
8. Muehllehner G, Colsher JG and Stoub EW. Correction for field nonuniformity in scintillation cameras
Through Removal of Spatial Distortion. J Nucl Med 1980; 21: 771-776.
9. Steidley JW and Kearns DS. Uniformity correction with the Micro Z processor. J Nucl Med 1978; 19:
712.
10. Halama JR, Henkin RE and Friend LE. Gamma camera radionuclide images: improved contrast with
energy-weighted acquisition. Radiology 1988; 169: 533-538.
11. Simmons GH. Gamma Camera Imaging Systems In R. Henkin (ed) Nuclear Medicine, Mosby-Year
Book Inc. 1996; pp 85-95.
12. Wicks R and Blau M. Effects of spatial distortion on Anger camera field-uniformity corrections:
concise communication. J Nucl Med 1979; 20: 252-254.
13. Short MD, Elliott AT and Barns KJ. Performance Assessment of Anger Camera, In Quality Control of
Nuclear Medicine Instrumentation (ed) R.F. Mould, HPA. London 1983; pp 1-20.
14. Chang W, Bruch P, Wesolowski CA et al. Performance of case collimator for SPECT imaging. J Nucl
Med 1985; 26: 44.
15. Chang W, LiSo, Williams JJ, Bruch PM, Wesolowski CA, Ehrhardt JC and Kirchner PT. New method
of examining gamma camera collimator. J Nucl Med 1988; 29: 676-683.
16. Busemann-Sokole E. Measurement of collimator hole angulation and camera head tilt for slant and
parallel hole collimators used in SPECT. J Nucl Med 1987; 28: 1592-1598.
17. Gerald JG. Nonisotropic PSF as a result of collimator design and manufacturing defect. J Nucl Med
1988; 29: 1096-1100.
18. Yoshizumi TT, Suneja SK, Teal JS, Sutton AM and Collyer D. Defective parallel-hole collimator
encountered in SPECT: A suggested approach to avoid potential problems. J Nucl Med 1990; 31:
1892-1893.
19. Keszthelyi-Landoori S. Nal(T1) camera crystals:Imaging capabilities of hydrated regions on the crystal
surface. Radiology 1986; 158: 823-826.
20. Lukes SJ, Grossman LW and Nishiyama H. Thallium-201 imaging artifacts not detected by Tc-99m
or Co-57 quality control testing. Radiology 1983; 146: 237-239.
Single Photon Emission Tomography
(SPECT)
G.S. Pant and H. Rajabi
A planar image is a 2-dimensional projection of a 3-dimensional structure with no depth
information. To have a depth perception of the normal or abnormal structures with human
eyes at least two planar views of the object, from two different angles are required. This
procedure is too complicated, imprecise and insufficient for a successful 3-dimensional
reconstruction. With present knowledge and technology the reconstruction procedure can be
performed using several views of an object from different angles. Different methods have
been developed for 3-D image reconstruction.
In single photon emission computed tomography (SPECT) the gamma camera, mounted on a
gantry, rotates around the patients’ body and collects counts (gamma photons) from different but
known directions. Three dimensional (SPECT) images are reconstructed from these projections.
The reconstruction software allows the user to generate slices of any thickness in transaxial,
coronal and sagittal plane of total image volume.
Though SPECT images are with poor spatial resolution as compared to CT and MRI but
provide valuable information on the physiological status of the organs imaged.
Basic Concepts
Before going in to the details of image reconstruction, let us understand few concepts that
are extremely important in understanding the SPECT reconstruction.
Frequency
Most confusing to many of us is the term spatial frequency. How frequency plays a role
when we are not dealing with a wave function? We also need to be familiar with the term Fourier
transform (FT) which is used in SPECT image reconstruction.
14 5
Single Photon Emission Tomography (SPECT)146
Let us take a simple example where a quadruple bar pattern is imaged as is usually done for
quality control (Figure 1). Identical line profiles are drawn over each quadrant with corresponding
line spread functions.
Figure 1: Change in frequency and amplitude of sine wave with change in bar spacing. The
frequency is more in C than in A whereas the amplitude changes in other way. The number of line
pairs in B and D is same and therefore the resultant wave patterns have identical frequency and
amplitude in X and Y direction.
As can be seen the line spread functions resemble sine wave patterns. As the bar spacing is
the same everywhere in a quadruplet, it can be said that the corresponding line spread function
can be represented by a sine wave of a given frequency. As the bar spacing changes from one
quadruplet to the other, the frequency and amplitude of the sinusoidal wave changes.
The frequency of the sine waves is obviously related to the number of bars per unit length. In
the quadruplet there are 9 bars along the profile, while in quadruplet C they are 15. Therefore the
frequency of the image in quadruplet C is more than that in A. It is now clear that a frequency
can be assigned to the images of each quadruplet. The amplitude of sine wave in quadruplet A is
higher than that in C. This is due to the fact the total counts in A, are distributed among 9 sine
waves while in C, it is in 15 sine waves (less counts result in smaller amplitude).
Now we can continue our discussion and extend these concepts into more realistic images.
Assuming a bar pattern of uneven but regular spacing, with little complicated situation as is seen
in figure 2. In such situation we can assume that the image profile is composed of several
frequencies of different amplitudes.
Figure 2: Image profile of a bar pattern with uneven but regular pattern
Single Photon Emission Tomography (SPECT) 147
In the above example the frequency changes only along the x-direction. In a more realistic
situation the frequency changes in both x and y directions (Figure 3). Therefore we will have
two-dimensional sine waves.
Figure 3: Image profile showing frequency and amplitude change both in X and Y direction
Let us now come to the real nuclear medicine image where instead of lead bars of regular
spacing there is an image, for example, of a physical phantom as shown in figure 4.
Figure 4: Image profile of a phantom along the line shown by arrows
This image is not much different from the image shown in figure 3. The only difference is
the regularity of objects in the phantoms. In figure 3 the object size and location changed in an
orderly manner unlike in figure 4 where the change has occurred without a regular order. Though
the sinusoidal waves are present in figure 4 but in an irregular manner.
When we go to a real patient image (Figure 5A), the irregularity further increases. The pixel
counts in various rows or columns in an image depend upon the uptake of radiopharmaceutical
in patients’ body. If we represent the variation in pixel counts along a line profile we may get a
graph as shown in figure 5B. This graph does not represent a periodic function with single
Single Photon Emission Tomography (SPECT)148
frequency. However it is composed of sinusoids of various frequencies and amplitude in irregular
order.
Figure 5: Real image (A) composed of various frequencies and amplitudes (B). The curve can be
used to determine the nyquist frequency in the real image.
Theoretically the graph may be rebuilt by many sine and cosine functions of different
frequencies and amplitudes. In nuclear medicine images, the variation in counts between two
consecutive pixels is too small at some places and reasonably high at other locations. When
gradient of the counts is high somewhere in the image we can say that this part represents high
frequency components of the data and similarly the low gradient represents the low frequency
components of the data. The amplitudes of the high or low frequencies depend on the count
density in corresponding location in the image.
Fourier transform (FT)
Based on the famous Fourier theorem, any continuous and periodic function may be decomposed
into a series of sinusoidal functions. Fourier presented some mathematical formula to decompose
a function into series of sine and cosine functions of harmonic frequencies. The Fourier transform
is an extension to Fourier series to include discrete data. Fourier transform is a mathematical
procedure, which transforms discrete data such as an image from spatial domain to frequency
domain. In other words, Fourier transform decomposes the frequency components of an image in
X and Y direction separately.
This type of conversion or transformation is very useful since one can remove some unwanted
frequency components of the data. The Fourier transform is a reversible operation and the
manipulated data can be brought back into spatial domain using inverse Fourier transform. The
Fast Fourier Transform refers to some algorithms that make the process fast.
The Fourier transformation is extremely useful mathematical technique and needs intense
study to understand it. Those who want to know little more on FT as relevant to nuclear
Single Photon Emission Tomography (SPECT) 149
medicine are suggested to go through a chapter on Fourier transformation in nuclear medicine in
this book.
Sampling theorem
In the real world most of physical quantities are in continuous form. For example time and
distance are continuous quantities. But when we use computers the data must be in discrete
form. To convert a continuous data into discrete form we bunch our data into separate bins. The
number of bins and bins interval is referred as sampling. However there are some rules to
perform sampling. Ideally the sampling must be done in such a way that the original continuous
data can be recovered with minimum error.
The Shannon sampling theorem states that a signal with a maximum frequency of B cycles/
unit distance can be reconstructed without error only if the samples are taken uniformly at a rate
of > 2B cycles per unit distance. This sampling frequency (2B cycles per unit distance in this
case) is called the Nyquist frequency )(
f . The corresponding sampling interval, T = 1/2B is
N
called the Nyquist interval. If the signal is sampled at less than 2B cycles/unit distance or
sampled at an interval T > 1/2B, it is said to be under sampled. Under sampling cannot retrieve
the original information correctly without losing some details that is interpreted as losing
resolution. This phenomenon in Fourier term is called aliasing. This is so called because some
high frequency components of the data appear as lower frequencies in Fourier domain. Though
in most of the cases, there is no need to retrieve the high frequency components of the data as
they normally represent noise but the Nyquist frequency must be considered to perform Fourier
transform.
Data in tomography
A gamma camera with a parallel hole collimator acquires the counts from all sources located
in front of the collimator surface, within a parallelopiped space of infinite length if the photons
are almost parallel to its hole axes (Figure 6). The imaging depth covered by a gamma camera is
therefore infinite (irrespective of blurring due to distance). When the camera rotates around an
object only a small cylindrical volume, which is the intercept of all the parallelopiped, is covered
from all the views. Therefore the image volume of SPECT is finite in space.
This space can virtually be divided into small cubic volume elements (voxels) that have the
size comparable to the picture element (pixels) in the planar image. Ideal reconstruction means
to calculate the real counts in all these imaginary voxels. There are three main approaches to
determine the counts in all voxels using the counts in planar views.
Single Photon Emission Tomography (SPECT)150
Figure 6: Image volume in planar gamma camera imaging is too large (infinite) whereas
such a volume is always finite in SPECT imaging.
Methods of Image reconstruction in SPECT
Multiple Linear Equations
Ignoring the attenuation, scatter, noise and partial volume effect, it can be assumed that the
counts in each pixel of a planar image is the sum of total counts in the voxels along an imaginary
line perpendicular to the image surface (Figure 7). Therefore for each pixel of a planar view one
linear equation can be considered. For a 6464 matrix size imaging there are 646464= 262144
known voxels in the image volume. For each voxel there should be equation. Solving all such
equations simultaneously solves our problem of reconstruction. The problem with this method is
the computation time, solving several hundred thousand simultaneous equations each with several
unknown variables is an intimidate task. Moreover systematic error caused by attenuation and
scattering and also random noise makes this approach unachievable.
Figure 7: Method of reconstruction using multiple linear equations
Single Photon Emission Tomography (SPECT) 151
R(S, ) = g(x, y).dL
Simple back-projection
The fastest and the simplest method of reconstruction is the simple back projection technique.
Before discussion on this we need to review some basic concepts of Radon transformation.
Radon Transformation
Johann Radon in 1917 introduced his mathematical tool to transform 2-dimensional images
into a domain of possible line parameters. Radon transform was originally used to extract lines
(curves in general) from very noisy images. It has now found numerous applications in the field
of image processing. In mathematical language a 2-dimensional image can be represented by a
2-dimensional function g(x,y). The Radon transform of the function g(x,y), denoted by R(S, ),
is defined as the line integral along a straight line L, defined by its distance S from the origin and
its angle of inclination from the x-axis (Figure 8). The Radon transform is actually the
projection of the image along a radial line oriented at a specific angle.
Figure 8: Coordinate system R (S, ) used in Radon transformation
In mathematical form the Radon transform is written as follows:
In simple words the Radon transform of an image at a given angle is just a lateral view of the
object. A full Radon transform of an image is actually the collection of many lateral views
aquired in order (Figure 9) and put juxtapose in the same order.
(1)
Соседние файлы в папке Библиотека им академика М.И. Перельмана