Download Basic Principles of Computed Axial Tomography

Basic Principles of Computed Axial Tomography
Michel M. Ter-Pogossian
Computer tomography (CT) is a radiological imaging
method which yields transverse tomographic images reflecting with high accuracy the spatial distribution of x-ray attenuation in the part examined. The contrast resolution
achieved by CT permits the visualization of soft tissue structure heretofore invisible with conventional radiographic procedure, The CT image is reconstructed by a computer
applied algorithm, from a series of x-ray attenuation
measurements obtained at different angles around the subject, by means of radiation detectors. The signal to noise
ratio for these measurements is optimized by reducing the
contribution of scattered radiation and of system noise. The
CT principle of image reconstruction is also applicable in nuclear medicine imaging, with the goal of achieving contrast
improvement and quantitative assessment of radionuclide
distribution over conventional "projection" techniques. In
this application, however, the attenuation of the radiation in
the tissues interposed between the radionudide and the de-
rector must be taken into account to yield quantitatively accurate images. Furthermore, the variation of the field of view
of the collimator as a function of distance contributes
another unwanted variable to the reconstruction process. A
mathematically rigorous tomographic reconstruction which
would account for these variables is unavailable for gamma
ray-emitting radionuclides, although approximate solutions
of that problem have led to the satisfactory images of the
head. Images of larger inhomogoneous organs are less quantitative. The detection of coincidence annihilation counting
of positron-emitting radionuclides allows the accurate correction for the attenuation of that radiation in tissues and
permits depth independent collimation which renders these
radionuclides particularly suitable for their imaging by CT. A
number of CT devices designed for the imaging of positron
emitting radionuclides are yielding nuclear medicine images
of quality and potential clinical usefulness unequaled by
more conventional projection techniques.
OMOGRAPHY, both transaxial and longitudinal, has been widely used in diagnostic
radiology since the 1930s. Today, the term
"computed (axial) tomography" (CT) most
often refers to a new diagnostic radiological procedure which provides images of transverse sections of the body. As in other radiographic
procedures, the CT image reflects variations in
the attenuation of x-rays in the object imaged.
Computed tomography, as it is presently used in
diagnostic radiology, was developed by Godfrey
Hounsfield of EMI Ltd. in the early 1970s, ~ although its fundamental principles had been previously described and tested. In an astonishingly
short period of time, the use of CT became
widespread: There are over 1000 CT units in use
in the world today. The success of CT can be
traced to its ability to discern minute
differences in x-ray attenuation, thus allowing
the visualization of structures heretofore invisible with conventional diagnostic radiological
procedures. Furthermore, CT permits, for the
first time, the accurate and noninvasive quantitative determination of the x-ray absorption
properties of tissues buried deeply in the human
body.
The principle of image reconstruction utilized
in CT is not specific to diagnostic radiology.
Well before its medical application, that principle was applied in astronomy? The principle
of image reconstruction used in computed
tomography can be utilized for the visualization
of anatomical structures by the modulation of
forms of energy other than x-radiation, and it is
also used in the field of nuclear medicine for the
visualization of organs containing gamma- or
positron-emitting radionuclides. This latter
form of computed tomography is called
emission computed tomography, in contrast to
transmission computed tomography, in which
the sectional images represent the spatial distribution of the attenuation of x-rays in the
tissues examined.
While overlying structures are superimposed
on the images provided by most diagnostic
radiological procedures, CT sections provide
the unencumbered third dimension and the
quantitatively correct distribution of x-ray attenuation. However, the exquisite contrast
sensitivity displayed in CT images is not accompanied by the same high spatial resolution that
is commonly expected in conventional radiographic procedures.
T
From The Edward Mallinckrodt Institute of Radiology,
Washington University School of Medicine, St. Louis, Mo.
Michel M. Ter-Pogossian, Ph.D.: The Edward
Mallinckrodt Institute of Radiology, Washington
University School of Medicine, St. Louis, Mo.
Reprint requests should be addressed to M. M. TerPogossian, Ph.D., Mallinckrodt Institute of Radiology,
Washington University School of Medicine, 510 South
Kingshighway, St. Louis, Mo. 63110.
9 1977 by Grune & Stratton, Inc.
Seminars in Nuc/ear Medicine, Vol, VII, No. 2 (April). 1977
109
1 10
MICHEL M, TER-POGOSSIAN
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Fig. 1. Transversal or linear "blurring" tomography,
(Courtesy Seminars in Radiology).
PRINCIPLE OF OPERATION OF CT
The ability of CT to distinguish quantitatively
minute differences in x-ray attenuation
properties of structures in the human body
stems from the combined application of three
unrelated approaches: (1) The reconstruction of
a sectional image from a series of projections
taken at different angles around an object; (2)
the collection of data under narrow x-ray beam
conditions with the concomitant reduction of
the contrast-depressing effect of scattered
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Fig. 2. Transaxial "blurring tomography. (Courtesy
Seminars in Radiology).
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Fig. 3. Computerized axial (or transaxial) tomography.
(Courtesy Seminars in Radiology),
radiation to a low value; (3) the minimization of
noise in the CT data (detected x-ray photons) by
utilizing a large number of photons to reduce
the proportion of statistical fluctuations in their
number, and by utilizing low noise detectors.
In CT, a transaxial sectional image is reconstructed from a series of radiographic projections taken at different angles around the object imaged. This reconstruction method and
the results obtained may seem similar to those
of conventional x-ray tomography (sometimes
called "in-focus" or "blurring" tomography).
There are, however, profound differences
between CT and blurring tomography. In blurring tomography, be it longitudinal or transversal (Figs. 1 and 2), the source of radiation
and the film are moving in a related fashion during x-ray exposure so that a selected plane in
the patient remains in focus on the film, while
the projections of overlying and underlying
structures are blurred. Thus, the structures
contained in planes other than that of interest
are recorded on the radiograph in a blurred
form, and their contribution depresses image
contrast. Blurring tomography, although highly
useful in diagnostic radiology, provides relatively low-contrast images containing no accurate quantitative information about the x-ray
absorption properties of the structures imaged.
The method of data acquisition in CT can
best be illustrated in its simple form, first
developed by EMI (Fig. 3). An x-ray tube of
conventional design is energized at a potential of
about 120-140 kVp with a tube current of 30
mA. The beam of radiation thus produced is
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHu
collimated to a rectangle a few millimeters wide
and about 13 mm long. This beam passes
through the patient and, after further collimation, impinges upon a scintillation d e t e c t o r
consisting of a luminescent crystal optically
coupled to a photomultiplier tube. The latter is
connected to electronic circuitry suitable for the
measure of direct current. The x-ray tube and
the detector are connected rigidly, and the object to be examined is scanned in a linear translational motion. After one scan, the gantry supporting the tube and the detector is rotated by
1~ about an axis perpendicular to the section to
be imaged, and another scan is performed.
Typically, this operation is repeated 180 times
for a total of 180 ~ The data collected by this
method consists of a series of profiles of the attenuation of x-rays in the tissues traversed at
180 different angles. It is from these profiles
that the tomographic section is reconstructed
by a computer-applied algorithm. The data required for the reconstruction of the image is derived solely from the information contained in
these profiles, and any difference in x-ray attenuation to be reconstructed in the image must
appear in the profiles. Great care is taken to insure that the profiles faithfully reflect even
minute differences in x-ray attenuation. The
optimization of the CT data acquisition is such
that differences in x-ray attenuation of a fraction of a percent for resolution elements approximately 1.5 mm x 13 mm are elicited. In
conventional radiography, the contrast perceptibility is limited to about 2% due to the
combined effect of scattered radiation and film
screen combination noise. 3 (As these factors
vary with field size, subject thickness and type
of film and screen used, this assessment is approximate.) However, in diagnostic radiology,
the spatial resolution achieved is of the order of
0.1 to 0.3 mm, as compared to 1 to 2 mm f o r C T
devices.
CT IMAGE RECONSTRUCTION
The radiation transmission profiles which are
acquired by the CT d e t e c t o r system are
recorded in a digital form by a computer system. From these data, the CT computer system
generates the image of the section through the
application of a suitable algorithm. A number of
different algorithms have been used in tomographic reconstruction; 4,~ however, a discussion
111
of the relative merits of these algorithms is outside the scope of this work. The method of reconstruction which is currently used in most CT
devices is conceptually quite simple. Called
either the "convolution" or the "filtered back
projection" reconstruction method, 5-7 it can be
illustrated as follows: Assume that the object to
be imaged is a small area of higher x-ray attenuation (Fig. 4A) than the surrounding circle,
which is assumed to be transparent to x-rays.
The radiation profile for this object is recorded
as a peak, whose ordinate is proportional to the
radiation attenuation in the object. The information contained in this single profile is that
somewhere along a line corresponding to the abscissa of the peak the x-ray attenuation is
represented by the ordinate of the peak (which
is the line integral of x-ray attenuations along
the line). This information is displayed in what
eventually will be the image of the section as a
strip with a density proportional to the ordinate
of the peak (Fig. 4A). This form of display,
which is called "back projection," represents
the projection of the profile onto a two-dimensional image. If a series of profiles recorded at
different angles are back p r o j e c t e d , the
resultant image will be as shown in Fig. 4B. Two
remarks can be made about the image thus obtained: (1) the presence of the object can be
c r u d d y identified, and (2) the presence of the
object casts spurious densities in regions of the
image where they do not belong. The method of
reconstruction which has so far been described
as back projection is conceptually akin to blurring tomography. It provides low c o n t r a s t
images and does not yield accurate quantitative
information. The fundamental difference between computed tomography and back projection blurring tomography is that the former is
capable of removing the artifactual contributions of the image, and of yielding a quantitative
representation of the object. The transition between back projection and CT is accomplished
as follows. Assume that the profile shown in Fig.
4A, which contains only positive values, is converted as shown in Fig. 5 to exhibit a series of alternatively positive and negative values, which
decrease in amplitude as the distance from the
object increases. This operation convolves or filters the shape of the object by a filter function,
endowing the profile of the object with negative
and positive values which extend outside the
1 12
MICHEL M. TER-POGOSSIAN
Fig. 4. (A) Back projection of a radiation
transmission profile. (B) Series of back projections of radiation transmission profiles obtained
at d i f f e r e n t angles. ( C o u r t e s y S e m i n a r s in
Radiology).
.k VOlues
o~
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Fig. 5, Convolution or filtration of a
radiation transmission profile represented on the left. The filtered profile
(right) contains negative as well as posit i v e v a l u e s , ( C o u r t e s y S e m i n a r s in
Radiology).
- ~ ~ ~. PRO,Js
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BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
113
Fig. 6. (A) Beck projection
of a filtered radiation transmission profile, (B) Back projections of a series of filtered profiles taken at different angles
around the object to be image,
(Courtesy
Seminars
in
Radiology).
shadow cast by the object, and which contribute
to the total image. The back projection of the
filtered profile is shown in Fig. 6A, and is called
filtered back projection. This process is repeated for a number of profiles taken at
different angles, as in Fig. 6B, and the negative
values of the filter profiles are subtracted from
the positive values so as to remove their unwanted contribution, thus restoring the true appearance of the object. This approach, which
might appear simplistic, is based on sound
mathematical considerations. The design of the
filter function is determined by a number of factors, some imposed by counting statistics,
others involving a compromise between resolution and contrast. The filter function can also be
shaped to permit image processing, such as
edge enhancement. It should be noted that, in
practice, the filter function used presently in
many CT devices convolves the positive pulse to
exhibit only negative values outside the pulse itself, as shown in Fig. 7. Note that the selection
of the filter function is often guided by trial and
error and is somewhat subjective.
TRANSMISSION CT DATA
ACQUISITION SYSTEMS
The data acquisition system of the first transmission CT device (Fig. 3) utilizes only a small
fraction of the radiation emitted by the tube,
and, at any point in time, only a small percentage of the tissues to ultimately be imaged
are probed for their attenuation properties by
the scanning x-ray beam. These inefficiencies
result in a long data acquisition time, typically 5
rain, with the resultant degradation of the
quality of the image through motion artifacts,
which are either physiological, such as heartbeat, blood vessel pulsations, respiration, and
peristalsis, or due to patient movement.
114
MICHEL M. TER-POGOSSIAN
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TUBE
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Fig. 7. (A) Scanning and rotating fan beam CT system. (B) Rotating fan beam CT system. (C) Rotating x-ray tube CT system.
(Courtesy Seminars in Radiology).
Extended examination times are also burdensome to the patient and encumber equipment
which is expensive to operate. For these
reasons, a number of different CT devices have
been developed with the purpose of speeding up
data acquisition, and the original single beam
device is now superseded by faster systems.
These faster CT devices can be divided into
three categories, based on the configuration of
their data acquisition system: (1) scanning and
rotating fan beam, (2) rotating fan beam, and
(3) rotating x-ray tube.
The principle of operation of the scanning and
rotating fan beam configuration is shown in Fig.
7A. In this design, the beam of x-rays is fan
shaped, with a typical angle of about 10~ and a
thickness of about I cm. The radiation transmitted through the subject is measured by several
scintillation detectors (typically 30). The x-ray
beam is made to scan across the patient in a
manner similar to that used for the single beam
device at a number of angles (typically 18) for
180 ~ around the subject. During each scan, the
response of the detectors is normalized to compensate for possible drifts, either in the source
of radiation or in the detector response. The
data acquisition time of such a system is about
20 sec. This design offers a number of highly desirable features: (1) the repeated normalization
of the system during each scan provides highly
consistent data for image reconstruction; (2) the
combined scanning and rotation method of data
acquisition spreads the contribution of each of
the detectors over the whole image in such a
fashion that artifacts produced by minimal
sensitivity drift in the detectors influence image
quality only minimally; (3) the spatial resolution
in data collection and in the resulting image can
be varied by adjusting the distance scanned to
the size of the object imaged.
The major disadvantage of the above design is
the complexity of the mechanical system required for the combination of translation and
rotation. This results in a costly system, which
is relatively slow and subject to misalignment.
While it is possible that the data acquisition
time of such a system could be speeded up
somewhat, it is unlikely that scanning times of
less than 10 sec could be achieved. In spite of
these disadvantages, and because of its numerous desirable features, a large number of
manufacturers have adopted this design (Fig. 8).
Fig. 8. Photograph of a cranial CT device. (C 1010
Courtesy Emitronics, Inc.)
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
The mode of operation of the rotating fan
beam design is shown in Fig. 7B. A fan-shaped
beam of x-rays with an angle of approximately
40 ~ is measured as it emerges through the
patient by a series of radiation detectors. The
source of x-rays and the detectors are rotated
around a common axis for 360 ~ during data acquisition. No translation is used. The radiation
sensors, typically 300 in number, are gas detectors filled With xenon at high pressure. Xenon
detectors are preferred in this configuration because of their high stability, convenient dimensional properties, and lower cost as compared to
scintillation detectors. The main advantage of
this design is its high speed (typically 5 sec),
which can be achieved due to the mechanical
simplicity of this system. This design suffers
from two disadvantages: (1) the radiation detectors cannot be conveniently normalized during
data acquisition, and since each radiation detector always measures the same x-ray "line," detector drift results in a circular artifact in the
reconstructed image; (2)no matter what the object size is, the spatial resolution of the system
is limited by the distance between the radiation
detectors. Several commercial companies have
developed CT systems based on this principle.
The third CT configuration is shown in Fig.
7C. The x-ray tube rotates within a ring of stationary scintillation detectors, typically 600 in
number. This design, which has been adopted by
one commercial company, embodies some of
the advantages of both systems described
above. It shares with the scanning fan beam
concept the advantage of variable resolution,
the method by which the contribution of one detector is distributed over the image, and also the
ability of normalizing the detectors during data
acquisition. It shares with the rotating fan beam
geometry design its mechanical simplicity. The
disadvantages of this design are: (1) large
number of detectors, which raises the cost and
complexity of the system; (2) difficulty in removing the radiation scattered by the patient by
collimation; and (3) relatively inefficient utilization of the radiation impinging upon the patient.
It should be noted that the advantages and disadvantages of this system are difficult to assess
at the present time because of the paucity of information about its performance. The results
obtained with this device are encouraging in the
1 15
sense that high quality CT images are provided
in a few seconds.
At this time, the CT devices based on the
scanning fan beam design are in wide clinical
use and provide CT images of quality unexcelled
as yet by other designs. Several CT systems
which utilize the rotating fan beam design are
presently undergoing clinical trials in several institutions, and although results obtained are
highly encouraging, some difficulties of this
design have not yet been entirely solved. The
rotating x-ray tube device is currently at the
prototype testing stage and has already provided some very promising results.
ADVANTAGES OF CT IN NUCLEAR MEDICINE
The main advantages of CT in diagnostic
radiology are as follows: (1) CT adds the third
dimension to radiological examinations; (2) the
sectional images provided by CT are unencumbered by the contrast-reducing superimposition of structures normally seen in conventional projection examinations; and (3) CT provides a quantitatively accurate distribution of
x-ray attenuation in the section imaged.
The application of CT to nuclear medicine
imaging invests the above advantages with an
even greater importance. In nuclear medicine,
the images of organs and structures containing
a gamma-emitting radionuclide are severely distorted by (1) the contribution of activity in
planes overlying and underlying the region of
interest; (2) the variation with depth of the field
of view of most collimators used in nuclear
medicine imaging; and (3) the fact that the attenuation of the gamma radiation in tissues
located between the plane of interest and the
radiation detector cannot, for all practical purposes, be accounted for. These three factors
reduce contrast perceptibility to the point
where only gross differences in radionuclide
concentration can be perceived and render
quantitative determinations in most instances
all but impossible. In comparison to the above
described situation in nuclear medicine imaging,
in radiography and resolution of the examination varies only minimally with depth. Furthermore, in radiography, the attention of the
x-radiation in tissues is the variable providing
the image. Also, in radiography, quantitative
measures are perhaps less important than in nu-
1 16
MICHEL M. TER-POGOSSIAN
Fig. 9. (A)Diagram illustrating the method of data acquisition and image formation utilized by Kuhl for emission transverse
section scanning (Courtesy David E. Kuhl), (B) Photograph of M a r k II emission scanner, [This instrument was used by Kuhl and
coworkers in their original emission computed tomography and transmission transverse tomography work, D, E. Kuhl, private
communication) (Courtesy D. E. Kuhl).
BASICPRINCIPLESOF COMPUTEDAXIALTOMOGRAPHY
clear medicine, because of the unavailability of
a broad spectrum of radiographic c o n t r a s t
media with organ specificity, in comparison with
the wealth of radiopharmaceuticals used in nuclear medicine.
The recognition of the possible usefulness of
tomography in nuclear medicine has led to the
development of several tomographic systems, s
Conceptually, many of these systems belong in
the category of blurring tomographs because
the images of structures in planes other than
that of interest are blurred out, while the structures in the plane of interest remain in focus. It
should be noted that the converging collimator,
which is widely used in rectilinear nuclear scanners, provides a tomographic effect (particularly when used with large detectors) because
structures located outside the zone of convergence of the collimator holes yield out of
focus images. However, blurring tomographs,
even of particularly ingenious design, have so
far not demonstrated the obvious clinical usefulness of those in use in diagnostic radiology.
In 1963, Kuhl and Edwards .9 described a nuclear medicine tomographic imaging approach
called transverse section scanning, and which
exhibited several conceptual similarities to
transmission CT, but applied to emission CT.
Their system consisted of a collimated radiation
detector which scanned in a transversal linear
motion across the object to be imaged (Fig. 9).
A number of such scans were performed in
equal angular increments around the object.
The data acquired in each of the translational
motions consisted of profiles of activity, and the
image was reconstructed by back projecting
these profiles using an oscilloscope and a suitable electronic circuit. The final cross-sectional
image was integrated by recording the oscilloscope image on photographic film.
The method described by Kuhl and Edwards
is conceptually identical in its data acquisition
phase to that of computed tomography. The
method of reconstruction, however, differs from
reconstruction tomography in that it consists of
a back projection technique in which the information from any point is spread over the
whole section imaged, resulting in low contrast
*The methods for longitudinal and transverse section
emission scanning were worked out by Kuhl in late 1958
(Kuhl, DE, private communication).
117
PROFILE
~._~__..ECTOR ~ , ~
f COMPUTERI
MONITOR
Igl
CRT
Fig. 10.
Principle of operation of a gamma ray emission
CT system,
and no lirlear relationship between the counts in
the section matrix and the radioactivity in the
patient. 1~ In this respect, their original device
was akin to a blurring tomographic system.
Later, Kuhl et al. ~~modified their section scanning system by the introduction of a computer
applied correction which enabled their system
to yield quantitative data. This latter version of
their device was conceptually identical to CT
systems.*
EMISSION COMPUTED TOMOGRAPHY
Conceptually, it is easy to extrapolate from
the basic principles of transmission CT scanning
to nuclear medicine imaging, where the image
reflects the distribution of a radionuclide rather
than the distribution of x-ray attenuation
coefficients. Emission CT scanning can be
illustrated as follows. Assume a small concentration of a radionuclide (Fig. 10) in a circular
object otherwise free of activity. The data are
collected by means of a narrowly collimated
radiation detector scanning across the object,
and are in the form of counts per unit time as a
function of the position of the detector with
respect to the object. These data can be displayed as a profile in which the ordinate
represents the counting rate and the abscissa
the position of the scanner. This operation is repeated for a number of angles around the object, and the image can be reconstructed by the
application of a suitable algorithm, for example,
*It is interesting to note that in 1966 Kuhl et al."
proposed the use of transmission transverse section scanning using an americium source which scanned across the
object to be imaged by computer-appliedback projection.
1 18
by the filtered back projection method
described above.
Unfortunately, while this straightforward approach to CT applies successfully to transmission tomography, it would yield a poor
quality image in emission tomography, because
the latter is severely complicated by factors
which either do not exist or which play only a
minor role in transmission tomography. The
most important of these factors are: (1) the attenuation of the gamma radiation in the tissues
between its source and the detectors, and (2)
the variation of the resolution of the radiation
detector, determined by the collimator, as a
function of distance.
In a comparison of transmission and emission
CT, an important difference in the data acquired by these two modalities must be emphasized. In transmission CT, the profiles used
in image reconstruction represent, with relatively minor distortions, the attenuation of
x-rays in the tissues traversed, and it is this variable which constitutes the reconstructed image.
In emission CT, the profiles represent the distribution of activity in the scanned tissues, altered by the attenuation of the radiation between its source and the detector. Yet the
image reconstructed from these profiles must
reflect the distribution of activity unaltered by
attenuation. The extent of radiation attenuation
depends upon the tissues interposed between
the detector and the source of radiation, and
upon the energy of the gamma radiation emitted
by the radionuclide to be imaged. It is usually
far from negligible and, if not accounted for,
may distort the reconstructed image devastatingly by providing the reconstruction algorithm
with data containing two variables. Another
difficulty contributed by attenuation to emission
tomography is the fact that those portions of the
object to be imaged which are most distant from
the detector and consequently suffer maximum
attenuation contribute particularly noisy data to
the profile due to statistical fluctuations, and,
therefore, they provide little useful data to the
reconstruction algorithm. Thus, in emission
tomography the attenuation of radiation, which
plays a greater role in the imaging of the larger
structures and particularly for lower energy
radiation, presents a serious impediment to reconstruction, and this variable must be corrected for.
MICHEL M, TER-POGOSSlAN
An additional serious difficulty encountered
in emission tomography and of minimal importance in transmission tomography is the fact
that the field of view and the sensitivity of the
radiation detector collimator used in emission
CT vary with distance. The reconstruction
process in CT assumes that the field of view of
the radiation detector is invariant throughout
the object to be imaged, and if this condition is
not fulfilled or accounted for, truly quantitative
measurements are impossible. In transmission
CT, the cross section of the beam of radiation
traversing the object does vary slightly due to
beam divergence, but this slight divergence
from the ideal condition only minimally affects
the reconstruction process. Unfortunately, in
emission tomography, this effect is more pronounced and more detrimental to the quality of
the image obtained.
The application of CT to nuclear medicine
imaging can be regarded as consisting of two
phases: (1) the application of the general principle of CT which has been discussed above, and
(2) the minimization of the obstacles to the application of the CT principle of reconstruction
to nuclear medicine, namely, the attenuation of
the radiation in tissues and the variation of the
field of view of the collimators used. The approach to the solution to these two problems is
very different from the computed tomography
of radionuclides decaying by the emission of
gamma rays and for that of radionuclides emitting positrons and imaged through the annihilation radiation. Because of this difference, the
following discussion of emission tomography
will be divided into two parts: gamma ray
emission CT and positron emission CT.
G A M M A RAY EMISSION CT
CT devices designed for nuclear medicine
imaging of gamma-ray emitting radionuclides
consist essentially of a mechanical gantry that
supports the radiation detector or detectors and
which incorporates the mechanical system required to provide the motion or motions for the
acquisition of profiles at different angles around
the patient, who is usually supported by a
couch. The CT system also includes suitable
electronic circuitry for the operation of the
radiation detector and a computer system which
records the data provided by the detector, applies the reconstruction algorithm, and displays
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
the r e c o n s t r u c t e d image for inspection or
further manipulation. The computer system will
be described below. The radiation detectors almost universally used for this purpose are scintillation counters fitted with activated sodium
iodide detectors, although ,xenon detectors have
also been used. In its simplest form, a gamma
ray emission CT system consists of a single
collimated detector which is animated by a
translational and rotational motion (Fig. 10). In
the attempt to improve the radiation collection
efficiency of the system, additional detectors
can be placed around the patient. 12-'4 The
recently developed Mark IV system of Kuhl
and Edwards incorporates a detector system
consisting of 32 collimated scintillation detectors fitted with activated sodium iodide crystals
(Fig. 11). 15 In this system, which is specifically
designed for the examination of the head, the
crystals are disposed in a square array (eight
detectors per side), and each set of eight detectors is displaced with respect to the center of
the side on which it is placed in such a fashion
that during rotation the detectors in fact undergo a translational motion to scan across the
object and provide suitable profiles. Scintillation
Fig. 11. M a r k IV gamma
{Courtesy D. E. Kuhl).
ray emission CT system.
119
~a.
A
-/"
+
Fig. 12. Illustration of the problems presented by the
variation of the collimator field of view and by radiation attenuation in g a m m a ray emission CT: as the detector is
moved for position A to position B the solid angle subtended
at the detector at point P varies from (~ to ~ and the amount
of tissues traversed by the radiation varies from a to b.
cameras also have been used as radiation detectors for this purpose. '6-'9 With such a positioning sensitive detector (as is also the case for
multiwire xenon counters) no translational motion is required, and only rotation is needed for
CT reconstruction.
A number of ingenious apparatus have been
conceived and constructed to carry out CT
imaging in nuclear medicine with gamma-ray
emitting radionuclides. Unfortunately, as has
been discussed by Cormack, 2~ the two factors
that have been discussed above, namely, the attenuation of the radiation in the tissues interposed between the source of radiation and the
detector, and the fact that the field of view of
the r a d i a t i o n d e t e c t o r varies with d e p t h ,
seriously impede the practical application of
this m e t h o d o l o g y . This difficulty can be
illustrated as follows. Figure 12 represents the
plane of the section to be imaged and the radiation detector, D. Let us assume that the line L is
" s e e n " by the detector, and assume the
presence of a point P, containing a certain
amount of activity placed somewhere along line
L. At first, let us assume ideal conditions in
which no attenuation of radiation takes place in
the object, and the solid angle subtended by the
detector (collimator field of view) is constant
along line L. These ideal conditions would be
fulfilled with point P being placed in the vacuum
and with the radiation detector located at an infinitely great distance from the object to be
120
imaged. Under such ideal conditions, the counting rate recorded by the detector would be independent of the position of point P along line L,
and the position of point P and the amount of
activity at P could be unequivocally obtained by
CT reconstruction from a series of profiles
taken at different angles and, consequently,
from a series of integral lines traversing point P.
Consider the real situation, in which the radiation emitted by point P is attenuated as it
travels in the direction of the detector, and the
solid angle subtended by the detector varies as a
function of the position of point P along line L.
Under these circumstances, the solid angle and
the attenuation of the radiation can indeed be
calculated for any point P on line L, but the
same factors will yield different values for the
same point P on a different line. Thus, the combination of solid angle and absorption factors
cannot define a single value function of position
of the point P in the object. 2~ Under such circumstances, CT reconstruction-for gamma-ray
emitting radionuclides cannot yield a correct
representation of radiation distribution in the
imaged section. This pessimistic statement,
dictated by mathematical rigor, does yield to a
more optimistic assessment of gamma-ray
emission CT if some compromises are tolerated
in the precision and accuracy of the results obtained. As pointed out by Budinger, 17 the solid
angle subtended at the detector by points in the
object to be imaged does not vary widely, and,
under the circumstances, through the application of a suitable attenuation correction the CT
image of the distribution of a gamma-ray emitting radionuclide can be achieved with the use of
a suitable algorithm. It should be noted that in
this approach iterative reconstruction schemes
a r e u s e d , 17 rather than the convolution algorithm discussed above. Thus, gamma ray
emission CT works only as a result of the use of
optimized radiation detectors with as uniform a
field of view as permitted by counting statistics,
and the application of some ad hoc corrections
designed to remove the effect of radiation attenuation from the reconstruction process.
The Aberdeen group ~1 has met the problems
of radiation attenuation and collimator field
variability by using long focused collimators
with an intercollimator distance of about 40 cm,
and by combining the effect of collimator field
and attenuation into a single function of total
MICHEL M. TER-POGOSSIAN
thickness of absorbing media. The thickness of
the object imaged is incorporated into the reconstruction algorithm by assuming that the object is represented by an ellipse of homogeneous
material. The conclusion of this group is that, in
practice, a quantitative estimate is achieved if
the concentration of the activity does not vary
significantly over the thickness of the section,
and if the thickness of the section viewed by the
collimation system is reasonably constant over
the plane of the section. Kuhl and co-workers 1~
utilized an attenuation correction based on the
normalization of the individual measurements
taken to the total amount of activity recorded
for the section imaged. The application of this
simple attenuation correction yields quantitative results in objects the size of the human
head. ~o
Thus, it appears well documented now in numerous publications that gamma ray CT yields
images which often provide more information
than perceivable on conventional projection
scintiscans. In smaller objects, such as the
human head, which exhibit a relatively uniform
attenuation to gamma rays, CT yields quantitative values for the distribution of gamma-emitting radionuclides. For larger parts of the body,
such as the chest or abdomen, however, particularly in situations where the distribution of the
concentration of the radionuclide varies significantly throughout the section, gamma ray CT is
no longer quantitative and does not yield faithful
images. Still, this technique appears valuable in
assisting in tomographic imaging and approximate quantitation of three-dimensional distributions of radionuclides. The application of
gamma ray CT to the visualization of lower
energy gamma ray emitters such a s 99mTc in
larger parts of the body is seriously impeded by
the high attenuation suffered by this radiation in
the tissues traversed.
POSITRON EMISSION CT
A number of radionuclides decay through the
emission of positrons. One physical characteristic of these particles is highly serendipitous
for the CT imaging of the radionuclides which
emit them. This characteristic, positron annihilation, provides a very effective solution to the
major problem of emission CT, that of the combination of detector field of view variation and
radiation attenuation.
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
Positrons are positively charged electrons,
usually emitted by radionuclides, which are unstable because they include an excess of
n e u t r o n s with r e s p e c t to a s t a b l e state.
Positrons lose their kinetic energy in matter in a
manner similar to that of electrons. However,
when positrons are brought to rest, they undergo the phenomenon of annihilation, whereby
the positron interacts with an electron, the two
particles undergo annihilation, and the masses
are converted into energy in the form of two
photons called the annihilation radiation. These
two photons travel at 180 ~ from each other and
each carry an energy of approximately 511 keV.
It is through the simultaneous detection of the
two annihilation photons that positron-emitting
radionuclides are of significance in CT reconstruction.
The annihilation radiation can be uniquely detected by two scintillation detectors connected
to a coincidence circuit (Fig. 13). In this
scheme, a count is recorded only if both detectors detect the annihilation photons simultaneously. This method of detection provides an
" e l e c t r o n i c " c o l l i m a t o r , since annihilation
events occurring outside a straight line joining
the two detectors cannot be recorded because
the annihilation photons are emitted at 180 ~
from each other. Thus, two detectors operated
in coincidence establish a field of view encompassed by the lines joining them. It is of particular importance in the detection of the annihilation radiation, and particularly in the application of that detection to CT, that the field
of view (or sensitivity) of such coincidence
collimation is nearly uniform in a wide region
located between the two detectors. Typically,
for two cylindrical scintillation detectors (Fig.
14) 2 inches in diameter and separated by 1 m,
the full width at half maximum of the line
spread function does not vary by more than 10%
over a distance of 60 cm. It is apparent that this
property eliminates one of the difficulties encountered in emission CT.
A second characteristic of coincidence annihilation detection that can be exploited profitably
for emission CT can be d e m o n s t r a t e d as
follows: Assume an absorber (Fig. 15) containing a point source of positron activity P located
on a line joining two radiation detectors, A and
B, operated in coincidence. If a positron undergoes annihilation at P in such a fashion that one
121
REGION
I
WHERE---"~
ANNIHILATION
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tlI
DETECTED BY~
9
COINCIDENCE
) [
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COINCIDENCE
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RADIATION
~OETECTOR
Fig. 13. Principle of "electronic" collimation by the coincidence detection of the annihilation radiation.
photon travels toward A, the other photon will
travel towards B. The probability of the photon
traveling towards A escaping the absorber without undergoing an interaction is proportional to
e -ua , where a is the thickness of material
t r a v e r s e d , and u the linear a t t e n u a t i o n
coefficient for the annihilation radiation. Similarly, the probability of the other annihilation
photon escaping the absorber while traveling
towards B is proportional to e - u b , and the
combined probability for the two photons escaping the absorber is e -ua + e ub = e-,<a+b). Note
that the latter probability depends only on the
total amount of material traversed and is independent of the position of point P within the
absorber. This p r o p e r t y of the annihilation
radiation can be exploited in emission CT to
correct for the attenuation of the radiation. Indeed, to apply such a correction it is sufficient
either to calculate or to measure the attenuation of 511 keV photons along any coincidence
line and to correct the coincidence counting rate
by this value. The attenuation can be calculated
either by measuring the thickness of the object
traversed if the assumption can be made that
the absorber is uniform, or by measuring its
a b s o r p t i o n by placing a p o s i t r o n - e m i t t i n g
source outside the object along the integral line.
The latter method of correction is valid even for
inhomogeneous absorbers such as the chest.
A third advantage of the annihilation radiation in emission CT is its high energy (511 keV),
which renders it penetrating in tissue equivalent
material (HVL for 51l keV about 7 cm in water
versus 4 cm for 140 keV photons).
122
MICHEL M. TER-POGOSSIAN
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Fig. 14. Uniformity of depth response (top: line spread functions; bottom: isocount curves; photopeak only) for the
electronic collimation of the annihilation radiation. (Courtesy of Radiology).
The advantages of positron emission CT have
been recognized by a number of investigators, 2~
and several systems have been designed and tested. The overwhelming majority
of these designs incorporate scintillation detectors, although multiwire chambers have also
been used for positron imaging. 28 In its simplest
form, a positron emission CT system consists of
two detectors scanning across the object at
different angles. In order to achieve high
efficiency in collecting the radiation, more detectors can be placed around the object (Fig.
16A). Another design for this purpose consists
of a circle of detectors rotating around the object to be imaged (Fig. 16B). It should be noted
that the tomographic visualization of an organ
requires several tomographic sections. Thus,
tomographs capable of yield!ng only one section
COINCIDENCE
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Fig. 15.
Illustration of the constancy of
the radiation attenuation effect for coincidence detection of the annihilation radiation.
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
123
i
RADIATION
Fig. 17. Photograph of MGH (Massachusetts General
Hospital) camera. (Courtesy G. L. B r o w n e l l | .
Fig. 16. (Top) Diagram representing the method of
operation of the PETT system utilizing translation and rotation of the detectors. (Bottom) Diagram representing a
positron emission CT device.
at a time must be operated sequentially with a
relative motion of the tomograph with respect
to the patient between sections. This approach
is wasteful of radiation, time-consuming, and
often unsuitable for the study of time-dependent
dynamic phenomena throughout the organ
imaged. Furthermore, the accurate indexing of
the apparatus with respect to the patient is
difficult. To alleviate this difficulty, state-of-theart positron imaging systems incorporate the
ability to provide several sections simultaneously. Thus, the MGH positron camera
(Fig. 17) does provide a number of simultaneous
CT sections? ~ A more recent design (Fig. 18) incorporates a signal positioning logic for
elongated detectors which provide four tomographic sections simultaneously. Positron
emission tomography yields sectional images of
the distribution of positron-emitting radionuelides which are extremely faithful and highly
quantitative (Fig. 19), regardless of the size of
the part to be imaged. The faithfulness of these
reconstructions is unaffected by the presence of
radiation absorption inhomogeneities, such as
bone or lung.
Positron emission CT exhibits two disadvantages as compared to gamma ray CT: (l)
positron emission CT is inherently limited to
positron-emitting radionuclides, and (2) the
dose of radiation delivered to the patient from
the administration of a positron-emitting radionuclide includes, in addition to the contribution
from the annihilation radiation, that contributed
by the kinetic energy of the positrons. However,
the advantages of positron emission CT are
strikingly illustrated by the fact that, in the past
few years, more positron emission CT devices
have been developed and tested than gammaray emission CT systems.
COMPUTER SYSTEM
A number of functions essential to the application of computed tomography are normally
implemented by a computer system. These
functions include: (1) storage of data collected
by the radiation detector or detectors in a quantitative form; (2) application of the data thus
collected for the reconstruction of the tomographic section using a suitable mathematical
algorithm; and (3) display of the reconstructed
section for its diagnostic interpretation either in
an analogue form as an image or as a numerical
printout. Additional functions such as further
image processing, comparison of numerical
values in different regions of interest, correction
for radioactive decay or for attenuation, etc.,
may also be performed by the computer system.
124
MICHEL M. TER-POGOSSIAN
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Fig. 18.
Diagram of PETT IV.
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Fig. 19. Relationship between the numerical response of
the PETT system and activity concentrations for t w o cylindrical phantoms: 30 and 20 cm diameter). (Courtesy J. O.
Eichling).
Fig. 20.
Diagram of computer system for PETT IV.
Fig. 21. Examples of images obtained w i t h the PETT III system: (A) Transmission CT images from a patient w i t h a recent
occlusion of the right internal carotid artery. Carbon-1 I-labeled carboxyhemoglobin was administered by inhalation to measure
regional cerebral blood volume. Gallium-68-EDTA, 13N-ammonia, and lZC-glucose were administered intravenously to assess regional changes in the blood-brain barrier, perfusion, and metabolism, respectively. The study shows an obvious defect in regional perfusion (13NH3) in the right hemisphere w i t h associated reactive hyperemia (z]C-carboxyhemoglobin), disruption of the
blood-brain barrier (SSGa-EDTA), and altered glucose metabolism. (B) Upper right--Emission CT image of the heart of a normal
subject. Radiopharmaceutical: ]lC-palmitate. A m o u n t : 6.2 mCi. Scanning time: 8 min. Total number of counts: 384,000. The
density to the left of the heart is interpreted as the upper portion of the liver. (Upper left) Transmission CT image reconstructed
from the data used for the attenuation correction applied to the image on the right. (Lower left) Numerical printout of the
emission image shown. (Lower right) Section of a cadaver at approximately the same level as the emission image.
III
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126
The computer systems used for transmission
and emission CT can be, for all practical purposes, identical.
The CT computer system (Fig. 20) consists of
the computer per se, or the central processing
unit (CPU), and of computer peripherals. The
peripherals are usually comprised of the interface which links the computer to the detectors,
one or several computer magnetic discs, a magnetic tape recorder, an image display system,
and a line printer. Various other peripherals
also can be added. The fundamental functions of
the CPU are to interact (sometimes control) the
motion of the radiation detectors during data
collection, to collect the data, to sort the data
into a form suitable for reconstruction, to reconstruct the image and to assist in displaying
it. The reconstruction operation, which consists
of applying calculations to the results of a large
number of measurements taken at many angles
from the object imaged, is a time-consuming,
number-handling operation of considerable
magnitude. In transmission CT, the pixels in the
reconstructed image represent a resolution of
approximately 1 mm, and are reconstructed
from approximately 10~ transmitted x-ray
photons, whereas in emission CT, due to limitations imposed by the radiation exposure to the
patient, the image pixel is reconstructed from
only 103 gamma ray photons for a typical resolution of about 1 cm. Under these circumstances, the requirements placed upon the computer system by transmission CT are more
stringent than for emission CT. However, for all
practical purposes, these different requirements
are translated into minor differences in the computer systems.
To reduce the time required for the required
for the reconstruction and display of the CT
image, powerful computers capable of short
cycle times and endowed with large memories
are most often used. The magnetic discs provide
a Iarge amounL of rapidly accessible memory
where CT unprocessed data and reconstructed
images may be temporarily stored for easy access by the CPU. Computer discs, because of
their high cost, are not used for long-term
storage of the CT images; this function is
usually fulfilled by magnetic tape, which can be
either computer tape or conventional "sound"
tape cassettes. Some CT units incorporate rela-
MICHEL M. TER-POGOSSIAN
tively inexpensive "floppy" discs capable of
storing several images.
The line printer provides the numerical printout of the image in a grid form. The numbers
represent the quantitative values of the distribution of the radionuclide in the section imaged.
The data display system converts the reconstructed virtual "image," stored either on
magnetic tape or on a computer disc, into an
analogue optical image displayed either on a
cathode ray tube or, more often, on a television
monitor. Often the data display system
embodies interactive capabilities, which allow
operations such as the display of specific isocount contours or comparison of activity in
different regions of interest. In some applications, multicolor displays have been found useful.
In spite of the use of powerful computers, the
time required to provide an image after the
completion of the scan may be as long as several
minutes. To shorten this time period, some CT
devices incorporate electronic circuits to
perform some of the mathematical calculations
normally carried out by the CPU.
CONCLUSION
The principle of image reconstruction which
is utilized so successfully in transmission CT
can also be applied in nuclear medicine imaging
as emission CT. However, the application of CT
to nuclear medicine is considerably complicated
by the combined effects of gamma ray attenuation and by the variation in the field of view of
the radiation collimator as a function of
distance. In gamma ray emission, CT compromise solutions to these difficulties yield
images which represent the quantitative distribution of the radionuclide, but only in relatively small structures, such as the head, which
exhibit a uniform attenuation to gamma rays.
For larger-inhomogeneous structures, gamma
ray emission CT yields images that are useful,
although quantitatively inaccurate. Positron
emission CT satisfactorily resolves the above
difficulties and yields highly quantitative images
of any part of the body; however, this approach
is limited to the use of a small number of
positron-emitting radionuclides.
The application of CT in nuclear medicine
imaging has profoundly improved data acquisi-
BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY
tion by p r o v i d i n g t h e t h i r d d i m e n s i o n (Fig. 21),
with t h e c o n c o m i t a n t e n o r m o u s i m p r o v e m e n t in
i m a g e c o n t r a s t , a n d by p r o v i d i n g a t r u l y
q u a n t i t a t i v e m e t h o d for t h e r e g i o n a l and in vivo
127
assessment of the concentration of radionuclides. T h e l a t t e r p r o p e r t y m i g h t p r o v e to be o f
f u n d a m e n t a l i m p o r t a n c e in n u c l e a r m e d i c i n e
functional studies,
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