Basic Principles of Computed Axial Tomography

Transcription

1 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- OMOGRAPHY, both transaxial and longi- T tudinal, 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 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. Ter- Pogossian, Ph.D., Mallinckrodt Institute of Radiology, Washington University School of Medicine, 510 South Kingshighway, St. Louis, Mo by Grune & Stratton, Inc. 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. 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. Seminars in Nuc/ear Medicine, Vol, VII, No. 2 (April)

2 1 10 MICHEL M, TER-POGOSSIAN X-RAY TUBE / X-RAY TUBE 1 / 1 1 COMPUTER ] \ ~:~.!~ : FILM 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 / \ -RAY TUBE \\\\ \ \ \ \ N \ \ Fig. 2. Transaxial "blurring tomography. (Courtesy Seminars in Radiology). CRT MONITOR U 0 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 kvp with a tube current of 30 ma. The beam of radiation thus produced is

3 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 detector 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 forct devices. CT IMAGE RECONSTRUCTION The radiation transmission profiles which are acquired by the CT detector 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 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 projected, 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 cruddy 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 contrast 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

4 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 different angles. (Courtesy Seminars in Radiology)..k VOlues o~ I! VO/UO $ B4CK pro d Fig. 5, Convolution or filtration of a radiation transmission profile represented on the left. The filtered profile (right) contains negative as well as positive values, (Courtesy Seminars in Radiology). - ~ ~ ~. PRO,Js N

5 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.

6 114 MICHEL M. TER-POGOSSIAN X- RAY TUBE ~" ----~ /?i~ ETEcTORS \ C OETEC'~m 1 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.)

7 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 1 15 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 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-

8 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 Mark 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).

9 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 1 17 clear medicine, because of the unavailability of a broad spectrum of radiographic contrast 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). PROFILE ~._~..ECTOR ~,~ Igl CRT MONITOR f COMPUTER I 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-applied back projection.

10 1 18 MICHEL M, TER-POGOSSlAN 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. 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. GAMMA 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

11 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 119 the reconstructed 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. Mark IV gamma ray emission CT system. {Courtesy D. E. Kuhl). ~a. A -/" + Fig. 12. Illustration of the problems presented by the variation of the collimator field of view and by radiation attenuation in gamma 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 radiation detector varies with depth, seriously impede the practical application of this methodology. 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 "seen" 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

12 120 MICHEL M. TER-POGOSSIAN 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 are used, 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 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 as 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.

13 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 121 Positrons are positively charged electrons, usually emitted by radionuclides, which are unstable because they include an excess of neutrons with respect to a stable 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 "electronic" collimator, 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 demonstrated 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 REGION I WHERE---"~ EVENTSARE ANNIHILATION DETECTED )(t i~( tl I DETECTED BY ~ 9 i COINCIDENCE ) [ I RE~ECTEO... {,; I, J f I P s I P I J RADIATION ~OETECTOR r.f COINCIDENCE CIRCUIT 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 traversed, and u the linear attenuation coefficient for the annihilation radiation. Similarly, the probability of the other annihilation photon escaping the absorber while traveling towards B is proportional to e -ub, 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 property 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 absorption by placing a positron-emitting 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).

14 122 MICHEL M. TER-POGOSSIAN I-- Z -~ 8 0 (J! i tl 0 6 n- Z "~:E 4 I' I~oRS ' (cm) uj ~ 2.J e,- 0 "~DISTANCE FROM = AXIS, (cm) sep OrOliOn octet t~ Detector separotion : 53 cm ca d (J Z < I- (n.j ee uj k- <.J 9 i, _, ; ' ~ 0 ~ - z 0 _ ~ : _: : ;: ;.-i o o--,,._ o~" ' : '.--so---? 9,~ I I I I I 1 I I I I I i I I I I I I I i I I I I I [~> 12 JO I0 12 DISTANCE FROM CENTER BETWEEN DETECTORS, (cm) 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 CIRCUIT ] I ~..~:===:=..~ j SOURCE OF [ i ~ ~,.~s /.J ~!i!iii!!!ii~<~ ~ ~, L. jradiation ~ f DETECTOR !?... RADIATIONoETECTOR Fig. 15. Illustration of the constancy of the radiation attenuation effect for coincidence detection of the annihilation radiation.

15 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 123 i RADIATION Fig. 17. Photograph of MGH (Massachusetts General Hospital) camera. (Courtesy G. L. Brownell. 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.

16 124 MICHEL M. TER-POGOSSIAN \ J/ -:% / Fig. 18. Diagram of PETT IV _r E ~ IOOC I-- o - 20 cm dia I0 Mbyte T 64 K, 16 bit memory! ~ 9trock. 800 BP! ic tape drive E P E T T ~ ~C~ Grophical ~~Video kcps/ml Fig. 19. Relationship between the numerical response of the PETT system and activity concentrations for two 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 with the PETT III system: (A) Transmission CT images from a patient with 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 with 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. Amount: 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.

17 III m C"--..,, -. 50% of max

18 126 MICHEL M. TER-POGOSSIAN 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- 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-

19 BASIC PRINCIPLES OF COMPUTED AXIAL TOMOGRAPHY 127 tion by providing the third dimension (Fig. 21), with the concomitant enormous improvement in image contrast, and by providing a truly quantitative method for the regional and in vivo assessment of the concentration of radionuclides. The latter property might prove to be of fundamental importance in nuclear medicine functional studies, 1. Hounsfield G, Ambrose J, Perry J, et al: Computerized transverse axial scanning. Br J Radiol 46:1016, Bracewell RN, Riddle AC: Inversion of fan beam scans in radioastronomy. Astrophys J 150(2):427, Ter-Pogossian MM, Phelps ME, Hoffman EJ, et al: The extraction of the yet unused wealth of information in diagnostic radiology. Radiology 113:515, Cho ZH: General views on 3-D image reconstruction and computerized transverse axial tomography. IEEE Trans Nucl Sci NS-21, No. 3:44, Brooks RA, Di Chiro G: Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging: Review article. Phys Med Biol 21:689,732, Ramachandran GN, Lakshminarayanan AV: Threedimensional reconstruction from radiographs and electron micrographs: Application of convolutions instead of Fourier transforms. Proc Natl Acad Sci USA 68:2236, Shepp LA, Logan BF: The Fourier reconstruction of a head section. IEEE Trans Nucl Sci NS-21:21, Freedman GS, ed. Tomographic Imaging in Nuclear Medicine. New York, Society of Nuclear Medicine, Kuhl DE, Edwards RQ: Image separation radioisotope scanning. Radiology 80:653, Kuhl DE, Edwards RQ, Ricci AR, et al: Quantitative section scanning, in Medical Radioisotope Scintigraphy, Vol. 1, IAEA, Vienna 1973, pp Kuhl DE, Hale J, Eaton WL: Transmission scanning: A useful adjunct to conventional emission scanning for accurately keying isotope deposition to radiographic anatomy. Radiology 87:278, Bowley AR, Taylor CG, Causer DA, et al: A radioisotope scanner for rectilinear, arc, transverse section and longitudinal section scanning: (ASS--the Aberdeen Section Scanner). Br J Radio146:262, Patton JA, Brill AB, King PH: Transverse section brain scanning with a multicrystal cylindrical imaging device, in GS, Freedman (ed): Tomographic Imaging in Nuclear Medicine. New York, Society of Nuclear Medicine, Tanaka E: Multi-crystal section imaging device and its data processing. Proc XIII Int Cong Radiol Madrid, October 15-20, Kuhl DE, Edwards RQ: The Mark IV system for emission computerized tomography and quantitative re- REFERENCES construction of brain radioactivity. J Nucl Med 16:543, 1975 (Abstr) 16. Kay DB, Keyes JW, Simon W: Radionuclide tomographic image reconstruction using Fourier transform techniques. J Nucl Med 15:981, Budinger TF, Gullberg GT: Three-dimensional reconstruction of isotope distributions. Phys Med Biol 19: , Chesler DA: Positron tomography and three-dimensional reconstruction technique, Freedman GS, (ed): in Tomographic Imaging in Nuclear Medicine. New York, Society of Nuclear Medicine, 1973, pp Muehllehner G: Section imaging by computer calculation. J Nucl Med 12:76 84, Cormack AM: Reconstruction of densities from their projections, with applications in radiological physics. Phys Med Biol 18: , Keyes WI: A practical approach to transversesection gamma-ray imaging. Br J Radiol 49:62, Chesler DA: Three-dimensional activity distribution from multiple positron scintigraphs. J Nucl Med 12: , 1971 (Abstr) 23. Robertson JS, Marr RB, Rosenblum Met al: 32 Crystal positron transverse section detector, in Freedman GS, (ed): Tomographic Imaging in Nuclear Medicine, New York, Society of Nuclear Medicine, 1973, pp Ter-Pogossian MM, Phelps ME, Hoffman E3, et al: A positron-emission transaxial tomograph for nuclear imaging (PETT). Radiology 114:89 98, Phelps ME, Hoffman E J, Mullani NA, et al: Application of annihilation coincidence detection to transaxial reconstruction tomography. J Nucl Med 16: , Cho ZH, Eriksson L, Chan J: A circular ring transverse axial positron camera, in Ter-Pogossian MM, (ed): Reconstructive Tomography in Diagnostic Radiology and Nuclear Medicine. Baltimore, University Park Press, (in press) 27. Derenzo SE, Zaklad H, Budinger TF: Analytical study of a high-resolution positron ring detector system for transaxial reconstruction tomography. J Nucl Med 16: , Lim CB, Chu D, Kaufman L, et al: Initial characterization of a multiwire proportional chamber positron camera. 1EEETrans Nucl Sci 22:388, Brownell GL, Burnham CA, Hoop B Jr, et al: Positron scintigraphy with short-lived cyclotron produced radiopharmaceuticals, in Medical Radioisotope Scintigraphy, Vol. 1, IAEA, Vienna, 1973, pp