Interactions and Exponential Attenuation

For a photon—whether gamma ray from technetium (^99mTc) or x-ray subsequent to the decay of thallium (²⁰¹Tl)—to become part of a cardiac image, it must first escape the body (see photon A in Fig. 6-1). The chances of this occurring are reduced in proportion to the likelihood that it will interact in the patient’s body before it can escape. At the photon energies of interest in nuclear cardiology, the major interactions in tissues are Compton scattering and photoelectric absorption.^8,9 In Compton scattering, a photon interacts with an electron that is loosely bound compared to the photon’s energy. The result of this interaction is the ejection of the electron from the atom and the creation of a new photon having a lower energy and different direction (see photons B and C in Fig. 6-1). The probability of interaction per unit path length (characterized by the linear attenuation coefficient for Compton scattering) depends on the tissue density and number of electrons per gram and decreases slowly with increasing photon energy. In photoelectric absorption, the photon imparts all of its energy to an electron, which is then ejected from the atom. The ejected photoelectron carries a kinetic energy that is equal to the energy of the incident photon minus the binding energy with which it was held to the atom. No scattered photon is emitted in the photoelectric interaction (see photon D in Fig. 6-1). However, characteristic radiation will likely be emitted when the electrons of the atom rearrange to fill the vacancy left by the photoelectron. The linear attenuation coefficient for photoelectric absorption increases as the cube of the atomic number of the atom, depends on tissue density, and decreases as the inverse cube of the photon energy.

Figure 6-1 Illustration of photon interactions of interest in patient for cardiac imaging. A, Transmitted photon originating in myocardium. B, Compton scattered photon originating in myocardium that collimator stops from striking crystal. C, Compton scattered photon originating in the liver that collimator allows to pass and results in the detection of an event that apparently originated in the myocardium. D, Photoelectrically absorbed in bone, which originated in myocardium.

Mathematically, the fraction of photons that will be transmitted through an attenuator or the transmitted fraction (TF) is given by:

(1)

where μ is the linear attenuation coefficient (sum of all the coefficients for individual interactions) and x is the thickness of the attenuator the photons pass through. If the attenuator is made up of a number of materials of various compositions, then the product μx in Eq. 1 is replaced by a sum of the attenuation coefficient for each material times the thickness of the material the transmitted photons pass through (path length the photons travel in the material). As a result of the differences in attenuation coefficient with type of tissue, the TF will vary with the materials traversed, even if the total patient thickness between the site of the emission and the camera is the same. Thus, one needs to have patient-specific information on the spatial distribution of attenuation coefficients (an attenuation map) to calculate the attenuation, which decreases the probability of photon detection.

Attenuation Artifacts (See Chapter 6)

The change in TF with direction of the photons and between different locations in the patient results in a variation in attenuation. This can be visualized in planar images as, for example, breast shadows and decreased counts in the presence of an elevated diaphragm. In SPECT slices, these artificial shadows are difficult to recognize; however, there is a pattern of altered relative counts consistent with the influence of attenuation in the mean bull’s eye polar maps of patients with a low likelihood of CAD. Eisner and colleagues reported decreased relative counts in the anterior wall of ²⁰¹Tl polar maps for females due to breast attenuation, and a relative decrease in the inferior wall of males, which may be due to diaphragmatic attenuation.¹⁰ The problem is that the location, extent, and severity of these reduced-count regions vary from patient to patient as a function of their anatomy. Thus, the variation in the pattern of apparent localization in disease-free patients is increased, resulting in more false-positive results (lower specificity) at any given level of true-positive results (sensitivity).

The types of changes in the reconstructed activity distributions when attenuation is present are illustrated in Figure 6-2. The top row of this figure shows what can be expected in the simple case of an elliptically shaped uniform-activity distribution without and with the presence of attenuation caused by a uniform attenuation distribution within the object. Note that attenuation causes a scaling of the reconstructed activity distribution such that there is a decrease by more than a factor of 2 at the outside, and a further decrease as one moves toward the center or most attenuated portion of the distribution. Hence an extended object that has a uniform distribution to begin with would have a loss in uniformity dependent on the relative depths of locations within it. The middle row of the figure shows the more complex case of a uniform source distribution that is attenuated by a non-uniform attenuation distribution simulating that of a cross-section through a female patient. This attenuation distribution and subsequent source and attenuator distributions the employed in the figures of this chapter were obtained from the mathematic cardiac-torso (MCAT) digital anthropomorphic phantom.¹¹ Notice that because the lungs have an attenuation coefficient approximately one-third that of soft tissue, there is now less attenuation within them than would have occurred had the entire cross-section consisted of soft tissues. Thus with attenuation, there appears to be a higher concentration of activity within them than the surrounding soft tissue, when actually the concentration was uniform. Notice also the sharp transition in apparent concentration of activity between the medial boundary of the lung and the heart region. The heart lateral wall is attenuated significantly more than the lung next to it. This explains why AC correction is very sensitive to having the correct registration between emission imaging and attenuation maps. A small movement can cause a big difference in the correction applied. The bottom row shows the even more complex case of both non-uniform source and attenuation distributions from the MCAT phantom simulating that of ^99mTc-sestamibi imaging. At the far left, in the absence of attenuation, the distribution of activity within the heart wall is uniform; however, when attenuation is included, a non-uniform distribution results, with the apex and lateral wall being brighter than the deeper lateral wall. Notice also that with attenuation present, there is now a mild change in the size and shape of the heart, as well as a significant distortion of the liver. With attenuation, there now is activity reconstructed as being outside the body. Such geometric distortion is greater for 180-degree reconstruction (as performed for these slices) than 360-degree reconstruction, owing to the greater inconsistencies in the emission profiles in the absence of their averaging by combining conjugate views.¹² The positive and negative tails from hot sources, which result from the incomplete cancellation of the inconsistent data in the emission profiles, can also lead to significant distortions in cardiac wall counts when there is significant extracardiac localization, such as with hepatic uptake. Germano and colleagues showed in phantom studies that an apparent reduction in counts occurs with the presence of a “hot” liver in the slices with the heart.¹³ Nuyts and colleagues¹⁴ observed that use of 360 degrees as opposed to 180 degrees with filtered backprojection (FBP) reconstruction reduced the magnitude of the artifact. The artifact was further reduced by use of attenuation compensation with maximum-likelihood expectation-maximization (MLEM) reconstruction.

Figure 6-2 Transverse slices showing examples of the distortion in apparent activity distribution caused by attenuation for (top) uniform activity and attenuation distributions, (middle) non-uniform attenuation and a uniform attenuation distribution, and (bottom) non-uniform attenuation and activity distributions. Top left shows a comparison of a slice through an elliptically shaped uniform-activity distribution and its reconstruction when attenuation is included in the creation of the SPECT data used in reconstruction. The attenuation distribution used to simulate attenuation during acquisition was also assumed to be uniform, with an attenuation coefficient equal to that of water for (^99mTc) photons. Notice that there is a significant decrease in the apparent activity in the reconstructed slice as one goes from the outside toward the center. The plots at the upper right are count profiles at the level indicated by the superimposed horizontal lines to the left for the original activity distribution (red) and the apparent distribution post reconstruction (blue). These graphically illustrate the impact of attenuation on the originally uniform activity distribution. Note that the scaling of the two count profiles is different, and that attenuation decreases the counts, even at the edge of the original distribution. Middle left shows a non-uniform attenuation distribution from the mathematic cardiac-torso phantom simulating that of a cross-section through a female patient, and the resulting apparent activity distribution when a uniform activity distribution is simulated as having been present in the patient. The outermost portion of the apparent distribution is again hotter, but now the lungs—which have a significantly lower attenuation coefficient than soft tissues—are also hotter. Note also the false presence of activity beyond the anterior surface of the body. Middle right shows overlaid plots of a horizontal profile through the attenuation map (red) and through the apparent activity distribution (blue), which clearly illustrate the impact of the less attenuating lungs. Bottom left shows 180-degree filtered backprojection reconstructed activity distribution that simulated that of ^99mTc-sestamibi imaging for the cases of first, no attenuation and then, use of the attenuation distribution of the attenuation map, shown in the middle row. Notice the loss of uniformity of activity distribution within the walls of the heart, the presence of activity outside the body, and the significant distortion of the liver, with the inclusion of attenuation when simulating the SPECT data. Bottom right shows count profiles at the level indicated by the horizontal lines of the slices, showing the increased non-uniformity in wall apparent uptake when attenuation is included during simulation of the SPECT data.

The artifactual decrease in apparent activity within the heart walls due to nearby extracardiac activity is further illustrated in the short-axis slices and circumferential count profiles at the top of Figure 6-3 for 180-degree reconstruction of Monte Carlo simulations¹⁵ of the MCAT phantom.¹¹ The top set of slices are with the liver uptake simulated as the same as that of the background. The next lower set of three slices shows the artifactual decrease in the inferior wall caused by the alteration of the liver activity to be the same as that of the heart. This alteration is illustrated graphically in the plots of the maximum count circumferential count to the right. There, one sees the typical pattern of a decrease in activity in the inferior versus the anterior wall due to the greater depth of the inferior wall, but this difference is dramatically accentuated by the increase in liver activity. This alteration in the apparent distribution of activity within the slices can be understood by the theory of the impact of attenuation on positron emission tomography (PET) and SPECT slices developed by Nuyts et al.,¹⁶ Bai et al.,¹⁷ and Bai and Shao.¹⁸ By this theory, attenuation causes a scaling of the counts at a given position, as illustrated in Figure 6-2, and a shifting of the local counts due to the attenuation of the other activity within the slice. It is this shifting that creates a negative bias that is the cause of the artifactual decrease in the inferior wall of the heart.

Figure 6-3 Comparison of Monte Carlo–simulated short-axis slices and circumferential profiles illustrating the impact of attenuation, attenuation correction (AC), and the inclusion of scatter. The two sets of three short-axis slices at the upper left show the uniformity of the activity within the LV wall when reconstructing 180 degrees of data using filtered back projection (FBP) without AC. The simulated acquisitions included the presence of non-uniform attenuation and camera distance-dependent spatial resolution but do not include scattered photons. In the first of these two sets, the concentration of activity within the liver was set to that of the background. In the second, it was set to be equal to that of the heart. Notice that the presence of a significant concentration of activity within the liver causes a significant apparent decrease in the inferior wall of the LV. This change is further demonstrated in the plots at the upper right, which show the maximum-count circumferential profiles from these short-axis slices. The middle of the five sets of short-axis slices shows the impact of using AC as part of maximum-likelihood expectation maximization reconstruction on the uniformity of the counts in the heart wall for acquisitions, with the liver activity concentration equaling that of the heart. The dramatic improvement in wall uniformity seen in the slices can be seen graphically by comparing the maximum-count circumferential profile plot for these slices at the lower right with those at the upper right for reconstruction without AC. The fourth set of three short-axis slices at the lower left illustrates the impact of the inclusion of scattered photons in imaging when the liver activity concentration is the same as in the heart. Notice that the apparent inferior-wall decrease seen without AC is now turned into an elevation in apparent inferior-wall counts with AC but no correction for scatter. This elevation is quantitatively demonstrated in the maximum-count circumferential profiles at the lower right. The bottom set of three short-axis slices is the reconstruction of solely the scatter contribution in the fourth set. Notice that scatter contributes to all regions of the slices, reducing wall contrast and apparent separation between the inferior heart wall and the liver.

That AC, when included within iterative reconstruction, can correct this artifactual decrease as illustrated in the middle set of three short-axis slices at the left in Figure 6-3, and in the corresponding circumferential profile at the right. Notice that with AC, the wall now becomes fairly uniform in uptake. Notice also that the liver now becomes more intense than the heart, even though they were simulated as having the same concentration of activity. The reason for the apparent difference is the partial volume effect (PVE),⁹ which causes structures smaller in any dimension than two to three times the full-width-at-half-maximum (FWHM) measure of the system spatial resolution to be blurred such that their apparent activity is less than the actual value.

Broad Beam Attenuation and Scatter

Equation 1 is accurate only (1) for a beam of photons with the same energy and (2) under the “good geometry condition” that, as soon as a photon undergoes any interaction, is no longer counted as a member of the beam.^8,9 Attenuation coefficients measured subject to these conditions are the “good-geometry” attenuation coefficients. Compton scattered photons, even though they are reduced in energy, are not necessarily excluded from being counted, owing to the finite width of the energy windows used because of the limited ability to distinguish different energy photons (finite energy resolution) of the cameras (Fig. 6-4). In fact, the ratio of scattered photons included in the energy window to primary photons in the energy window (scatter fraction) is typically 0.34 for ^99mTc¹⁹ and 0.95 for ²⁰¹Tl²⁰ for cardiac SPECT. Thus, Eq. 1 has to be modified to match the “broad beam” attenuation, which actually occurs in emission imaging by the inclusion of the buildup factor B, which is dependent on both μ and x. The result is^8,9:

Figure 6-4 Illustration of the energy distribution of primary and scattered photons for a technetium (^99mTc) point source in an attenuating medium. Shown also are the locations of the photopeak and Compton scatter windows.

(2)

Numerically, the buildup factor is the ratio between the sum of primary and scatter counts over the primary counts only, or the relative increase in counts due to the inclusion of scattered photons. It thus depends on variables such as location in the attenuator, geometry and composition of the attenuator, energy of the photon, energy resolution of the camera, and energy window used in imaging.

When scatter is not removed from the emission profiles before reconstruction, or its presence is incorporated into the reconstruction process itself, an overcorrection will occur. This is illustrated by the three sets of short-axis slices and the circumferential profiles at the bottom of Figure 6-3. As discussed previously, the top row of these slices illustrates how successful AC included within MLEM reconstruction can be at correcting the artifactual change in apparent uptake of the inferior wall of the row of slices just above it. However, the success of AC returning this slice to an apparent uniform concentration of activity within the walls is due in part to just primary photons being present. When the scattered photons acquired within the photopeak of the simulated acquisition are included, the short-axis slices next to the bottom are obtained. Notice how scatter has caused the inferior wall to now appear brighter than the anterior wall, which is the opposite of the effect of attenuation. The presence of scatter has also decreased wall contrast compared to the heart chamber region and visually decreased the separation of the heart from the liver. The bottom row of short-axis slices shows this is due to the non-uniform presence of scatter being concentrated closer to the liver. The circumferential profiles at the bottom right in the figure show that quantitatively, scatter has added approximately 30% more counts to the heart wall and that the inferior wall was increased the most.

Finite and Distance-Dependent Spatial Resolution

The third source of degradation discussed in this chapter is the finite, distance-dependent spatial resolution of the imaging system. When imaging in air, the system spatial resolution consists of two independent sources of blurring.⁹ The first is the intrinsic resolution of the detector and electronic components of the camera head. The second is the spatially varying geometric acceptance of the photons through the holes of the collimator. The collimator is the “lens” of the gamma camera; however, unlike optical lenses that form images by bending the light photons, collimators work by stopping all but the few photons that can pass through their holes without being absorbed by the septa of the collimator (absorptive collimation). This is illustrated in Figure 6-5, which shows two images of a very small point source of ^99mTc at the same location 10 cm from the detector face, first with no collimator and then with a low-energy high-resolution (LEHR) parallel-hole collimator on the camera head. The obvious need for the collimator is made clear by this figure, and so is the price paid for the use of the collimator in terms of loss in detection efficiency. Without the collimator, 7.2 million counts were collected in 1 minute. With the collimator, only 18,000 counts were collected in 1 minute, or 0.25% of that when the collimator was not on the system. The actual difference is greater because when the collimator was off, the count rate was near the maximum count rate of the system, so the recorded number of counts was depressed by resolving time count losses.⁹

Figure 6-5 Images of a (^99mTc) point source 10 cm in air from the face of the camera detector. A, No collimator on the camera head. B, Low-energy high-resolution collimator on the camera head.

As good as the image of the point source looks in Figure 6-5B compared to 6-5A, the ideal response would have been significantly better, since the point source was approximately only 1 mm in any dimension, and its bright representation in Figure 6-5B is larger than 10 mm across. The image resulting from imaging a point source of activity such as illustrated in Figure 6-5B is called a point spread function (PSF),⁹ and it portrays how a very small source of activity is blurred out during the course of imaging. Figure 6-6A illustrates plots through the center of Monte Carlo–simulated PSFs for an increasing distance of the point source in air from the face of a LEHR parallel-hole collimator. Notice how the PSF changes significantly in width and height as a function of distance. However, the area under the curves stays constant, consistent with no change in sensitivity with distance in air from the face of a parallel-hole collimator.

Figure 6-6 Illustration of the change in the spatial resolution with distance from the face of a low-energy high-resolution parallel-hole collimator for a (^99mTc) point source as depicted by the system point spread function (PSF), and the impact of this change in spatial resolution on one coronal slice through the heart and liver of the mathematic cardiac-torso (MCAT) phantom. A, Variation in Monte Carlo–simulated PSFs with distance for a point source in air (no contribution of scatter is included). Since sensitivity does not change with distance for a parallel-hole collimator, the area under all of the PSFs is the same. Thus, as the blurring becomes greater (the PSF wider), the maximum of the PSF decreases. This illustrates that increasingly lower fractions of the counts are left in place (not blurred) as one moves farther from the collimator. B, Coronal slices of the MCAT phantom. From upper left, the source distribution, upper right imaged as 10 cm distant in air from the face of the collimator, lower left imaged as 20 cm distant, and lower right imaged as 30 cm distant. Notice that as the distance away from the camera increases, the activity distribution is increasingly blurred, as exemplified by the heart and liver becoming increasingly smoothed together.

Figure 6-6B illustrates the impact of distance-dependent spatial resolution on one coronal slice through the MCAT phantom. As illustrated at the upper left in this figure, the concentrations of activity in the wall of the left ventricle (LV) and liver were the same, and that of the general tissue background was set to one-tenth that of the heart. All other organs had a concentration of activity of zero, as illustrated by the lungs, blood pool, and bones showing up as black. The slice at the upper right is that of the upper left blurred as if it were 10 cm from the face of a camera, as imaged with a LEHR collimator. The lower left slice is blurred as if acquired at 20 cm from the face of the collimator, and the lower right is 30 cm from the face. The FWHMs of the PSFs at these distances were 0.8 cm, 1.34 cm, and 1.88 cm. Notice how with increasing distance, the heart wall appears to become thicker and of apparently lower concentration relative to the liver. The apparent change in concentration is an illustration of the PVE or dependence of the apparent concentration of a structure on its size relative to the extent of blurring (FWHM).⁹ Note that the thickness of the wall in the slice varies due to the angulation of the heart relative to the coronal plane. Thus, the PVE causes the heart wall to appear as though it does not have a uniform concentration, when it actually had to begin with. Notice also that with increased distance, the liver and heart blur together to an increasing extent.

Basic Transmission Configurations

The basic transmission source and camera collimator configurations currently offered commercially are illustrated in Figure 6-7 for a 40-cm field of view (FOV) SPECT system imaging a 50-cm diameter patient. The first configuration illustrated in Figure 6-7A is that of a scanning line source.²¹ The camera head opposed to the line source is electronically windowed to store only the events detected in a narrow region opposed to the line source in the transmission image. This results in significant reduction in the amount of scattered transmission radiation from the source itself, imaged compared to having a stationary planar source opposite the camera. It also decreases (but does not eliminate) the cross-contamination from emission photons, because only the portion of the camera face where there is a high likelihood of a transmission photon being detected is used to form the transmission image. The emission images can also be electronically windowed to store counts only when the transmission source is not opposed to the location of the detected event. This simplifies the correction for down-scatter from a higher-energy transmission source to a lower-energy emission source window if different radionuclides are used or for self-correction if the same radionuclide is used for both emission and transmission imaging. This type of system is susceptible to problems in the mechanical motion of the line source and coordination of mechanical scanning with electronic scanning. Therefore, as part of one’s quality-control plan for attenuation compensation with such units, checks of the proper operation of the source scanning mechanism should be made frequently (daily) by performing a “blank” scan, which is a transmission scan with nothing, including the table, between the line source and camera head. One should also check individual patient transmission scans for signs of non-uniform motion in the axial (scanning) direction, truncation of the patient’s body within the FOV of the system, significant crosstalk from the emission-to-transmission source, and excessive attenuation of the transmission source by extra-large patients or weak sources.²² The merits of this configuration have made it the most widely available configuration for transmission imaging.

Figure 6-7 Four configurations of transmission sources and collimators for use in transmission imaging. In each case, a 40-cm camera field of view (FOV) is shown imaging a patient with a 50-cm major axis. Truncation will vary with camera FOV, patient size, and focal distance for converging collimation.

The second configuration, which is shown in Figure 6-7B, is that of the multiple line-source array.²³ With this configuration, the transmission flux comes from a series of collimated line sources aligned parallel to the axis of rotation of the camera. The spacing and activity of the line sources are tailored to provide a greater flux near the center of the FOV, where the attenuation from the patient is greater. As the line sources decay, new line sources are inserted into the center of the array. The rest of the lines are moved outward and the weakest is removed. The transmission profiles result from the overlapping irradiation of the individual lines, which varies with the distance of the source from the detector. The multiple line-source array provides full irradiation across the FOV of the parallel-hole collimator employed for emission imaging, without the need for translation of the source. An advantage of the configuration is that no scanning motion of the sources is required. A disadvantage of this system is the amount of crosstalk between the emission and transmission photons. Thus, attenuation maps formed with this system when imaging ^99mTc-labeled agents should be checked for apparent decreases in the attenuation coefficients (display intensity) in regions of significant ^99mTc accumulation, such as the heart and liver. Also, the down-scatter of the transmission source to the ²⁰¹Tl x-ray window makes the use of sequential or interleaved emission and transmission imaging favors. Another disadvantage is the high cost of replacing the line sources at short time intervals.

The first commercial transmission imaging system employed a line source at the focal distance of a fan-beam collimator.²⁴ The major problem with using fan-beam collimation for estimation of attenuation maps is that of truncation. Truncation of attenuation profiles results in the estimated attenuation maps exhibiting the “cupping artifact,” or pile-up of information in the truncated region near its edge when the reconstruction is limited to reconstructing only the region within the FOV at every angle, or fully sampled region (FSR). If the reconstruction is not limited to the FSR, the area outside the FSR is distorted, and the inside is slightly reduced in value. Truncation can be eliminated, or at least dramatically reduced, by imaging with an asymmetric as opposed to a symmetric fan-beam collimator.^25–28 The use of asymmetric collimation results in one side of the patient being truncated instead of both. By rotating the collimator and source 360 degrees around the patient, conjugate views will fill in the region truncated. If a point source with electronic collimator is employed instead of a line source, then a significant improvement in crosstalk can be obtained.²⁹ The problem, however, is that fan-beam collimators acquire the emission profiles, which makes it difficult for physicians to use in cine-mode to check for attenuation artifacts when reading the patient studies. This difficulty is overcome by the third commercial method of transmission imaging currently being marketed, as illustrated in Figure 6-7C, by using photons from a medium-energy scanning point source to create an asymmetric fan-beam transmission projection through a parallel-hole collimator by penetrating the septa of the collimator.³⁰ With this strategy, transmission imaging is performed sequentially after emission imaging to prevent transmission photons from contaminating the emission data. This lengthens the time the patient must remain motionless on the imaging table, thereby decreasing patient throughput and increasing the potential for patient motion. In particular, there is a change in motion of the heads between emission and subsequent transmission imaging, which can lead patients to momentarily relax, thinking the study is over, and thereby cause a misalignment between the emission data and attenuation map. Use of dual display in which the reconstructed emission slices are displayed in color “on top of” the reconstructed attenuation map displayed in grayscale, is recommended with this system to check for a possible misalignment.

High-resolution images from another modality can be imported and registered with the patient’s SPECT data.^31,32 Of course, the task is made a lot simpler by acquiring the high-resolution slices while the patient is on the same imaging table.³³ The inclusion of a computed tomography (CT) system on the SPECT gantry is the fourth transmission imaging option currently being offered commercially³⁴ and is illustrated in Figure 6-7D. The use of a CT to estimate attenuation maps and provide anatomic correlation has essentially replaced the use of radionuclide-based transmission imaging in PET.³⁵ CT overcomes the noise limitations of radionuclide transmission imaging through use of the x-ray tube and a separate block of detectors for x-ray imaging. However, the x-ray beam is made up of photons of many different energies. Thus appropriate care must be taken in scaling the attenuation map measured with this polychromatic photon beam to that of the energy of the emission radionuclide.³⁶ Besides their use for attenuation maps, these images can also provide anatomic contexts for the emission distributions and compensation for the PVE.³⁷ Because different detectors are employed, the CT and SPECT acquisitions are performed sequentially. Thus, as with the scanning medium-energy point source, care must be taken to assess the possibility of patient motion between the two, and imaging time is protracted.

There are two types of CT scanners in hybrid SPECT/CT. The first type is with a low-output x-ray tube and a slow gantry rotation cycle.^34,38,39 A typical CT scan is taken with the x-ray tube current of 2.5 mA and the gantry rotation cycle of 23 seconds. It can be a single- or multiple-detector row CT scanner. It uses 13.6 seconds of data (little over half of a gantry rotation, due to fan-beam detector geometry) for reconstruction of a CT image. The CT image is not for diagnosis; rather, it is intended for attenuation correction of the SPECT data. The radiation dose of the slow CT is about 5 mGy, which is significantly less than that of CT when used for diagnostic imaging.³⁹ Studies have demonstrated its effectiveness for this purpose.⁴⁰ However, a recent study suggested caution when performing AC with this technology for evaluation of perfusion defects; the SPECT slices after AC might be compromised by misregistration between the attenuation map derived from the CT slices and the SPECT data.³⁸ In this study, motion resulted in 42% of the 60 patients having moderate to severe misregistration of the heart between the CT and the SPECT data. Since most respiratory cycles are in the range of 4 to 6 seconds,⁴¹ the scan duration of 13.6 seconds for each CT image slice may not be slow enough to reduce reconstruction artifacts and subsequent misregistration. This is compounded by a possible change in respiration between emission and CT imaging, as well as a shifting in position of the patient. A recent study of using slow CT for respiratory gating suggested the gantry rotation cycle might have to be over 3 minutes to reduce the artifact caused by respiration.⁴² This is to ensure that there is one respiratory cycle of data taken at each CT projection angle.

The second type of CT scanner is diagnostic-quality CT, capable of producing thin slices of high spatial and temporal resolutions with a fast gantry rotation cycle of less than 0.6 seconds. The number of detector rows is 2, 6, 16, 40, or 64. The CT scanner can be potentially used for imaging the coronary arteries. However, the 64-detector row CT with 0.35 second or faster gantry rotation cycle produces the best image quality for the coronary artery, owing to its larger coverage and higher temporal resolution. The combination of CT for imaging coronary arteries and SPECT for evaluation of myocardial perfusion provides a noninvasive evaluation of the heart in both anatomy and function. Calcium scoring can also be obtained from this type of CT scanner to provide long-term risk assessment.^43,44 Although the quality of CT is very good, it still poses problems in registration of the heart between CT and SPECT, because the CT image is taken in less than 1 second. Misregistration normally occurs when the CT image is taken at the end-inspiration phase, which is very different from the average respiration SPECT data of over several minutes. Recent development of “average CT” by averaging the CT images taken over one respiratory cycle may provide a solution.^41,45 Average CT is promising in cardiac PET/CT⁴⁶ and potentially useful for cardiac SPECT/CT. This approach uses a fast gantry rotation of less than 0.5 second to acquire CT images that are almost motion free in respiration, and averaging brings temporal resolution of the CT images to that of SPECT images. Acquisition of average CT data should be at least one respiratory cycle and can be carried out at a low tube current such as 10 mA and fast gantry rotation cycle of 0.5 seconds. The radiation dose of average CT is also about 5 mGy.⁴¹ Since the patient is scanned sequentially, re-registration of the CT and SPECT data manually is necessary if the patient moves between the CT and SPECT scans.^46,47

Statistically Based Reconstruction Methods

The statistically based reconstruction algorithms start with a model for the noise in the emission data and then derive an estimate of the source distribution based on some statistical criterion. Many times they are named so that the first part of their name tells the statistical criterion that is to be optimized, and the second part of the name tells the mathematical algorithm employed to achieve optimization. For example, in MLEM,^52,53 the statistical criterion is to determine the source distribution in the slices with the maximum likelihood (ML) of having resulted in the measured SPECT projection data, given that the noise fluctuations in the acquisitions follow the Poisson distribution. The expectation maximization algorithm is employed for finding this ML solution. The success of this method of reconstruction is reflected by its becoming the standard for comparison against other reconstruction methods.

Conceptually, the MLEM algorithm works by iteratively refining an initial guess as to the distribution of the counts in the slices until the distribution is found that has the greatest likelihood of having resulted in the measured SPECT acquisitions. The rule or algorithm followed can be summarized as⁵¹:

(4)

where Slices^new is the resulting estimate of the counts in the voxels after the completion of one iteration during which the estimate of every voxel is updated, and Slices^old is the current guess going into the iteration as to the counts in the slices. The initial guess is typically a uniform count in each voxel of the slice.

The algorithm starts on the bottom right hand side of Eq. 4 by mathematically emulating SPECT imaging of the current estimate (making projections from Slices^old). This is where the physics of imaging can come into play and is one of the major advantages of iterative methods over FBP reconstruction. One can include as much information as to how the estimated counts contribute to the acquired projections as one has the ability to mathematically model (and is willing to spend the computer time so doing) during each iteration. For example, given an aligned attenuation map for a slice, one could include attenuation by starting with the voxel on the side opposite the projection being created, and multiplying its value by the TF for passing through one-half the voxel distance of an attenuator of the given attenuation coefficient in the attenuation map. The value of half the pixel dimension is usually used as an approximation for the self-attenuation of the activity in the voxel. One would then move to the next voxel along the direction of projection, and add its value after correction for self-attenuation to the current projection sum attenuated by passing through the entire thickness of the voxel. One would then continue this process until having passed through all voxels along the path of projection. The result would be the discrete approximation to the calculation of the line integral through the emission estimate, with each voxel location corrected for attenuation. Similarly, one can include modeling of scatter-dependent and distance-dependent spatial resolution. It is our experience that the better one does at accurately mathematically modeling the imaging of the patient, the better the resulting image quality will be. Of course, without clever approximations, such modeling can be quite time-consuming, even with today’s computers. Thus implementations of MLEM will vary, depending on the extent to which the physics is modeled and the approximations are employed in implementation.

The second step in the MLEM algorithm, as shown by the division on the right side of Eq. 4, is to divide the estimated projection values into the values actually measured. The ratio of the two indicates whether the voxel values along the given path of projection are too large (ratio less than 1), just right (ratio of 1), or too small (ratio larger than 1). These ratios are then backprojected as indicated in Eq. 4 to create an update matrix. That is, the ratios are combined for each slice voxel according to the probability they contributed to the projections from which the ratios were formed. This update matrix is then normalized by dividing by the backprojection of 1.0s to account for some ratios contributing more than others to the update matrix, based on the physics of imaging. The normalized update matrix is then multiplied voxel-by-voxel times the old estimate of the slice values to create the new estimate. This step is typically repeated until a set number of iterations has been performed. Ordered subset expectation maximization (OSEM)^48,49 and block iterative methods⁵⁰ accelerate reconstruction by forming and applying the update matrix from subsets of the projection set that are selected in an ordered fashion. The result is a reduction in the number of iterations by a factor approximately equal to the number of subsets used.⁵⁴ If fewer than four angles spaced as far apart as possible are used in forming subsets, then a loss in image quality with OSEM can result.⁵⁵

Figure 6-8 shows a comparison of the transverse slices, short-axis slices, and polar maps for reconstructions of simulations of the MCAT phantom.¹¹ In the first column on the right are image slices and the polar map for the case FBP reconstruction over 360 degrees of Monte Carlo–simulated acquisition images created as imaged by a LEHR collimator but without inclusion of attenuation, scatter, or additional noise. Because no noise was added to the high-count Monte Carlo simulation, no low-pass smoothing was included with reconstruction. These images thus represent the case of ideal attenuation and scatter correction. Notice that the counts at the apex of the LV in the transverse slice and in the apical region of the polar map are not uniform. The non-uniformity reflects the impact of the PVE on wall counts due to the inclusion of apical thinning in the MCAT source distribution. This shows that even with ideal attenuation and scatter correction, one should not expect to obtain uniform counts in the polar maps. The following columns show what happens when attenuation and scatter in addition to distance-dependent spatial resolution are included in the Monte Carlo–simulated projections. Additionally, a noise level equivalent to that seen clinically is simulated, thus requiring low-pass filtering of the reconstructed slices. In the first column of these (second column of images from the left) are shown the results for FBP reconstruction of projection data that include attenuation acquired over the 180 degrees centered on the heart. A two-dimensional pre-reconstruction Butterworth filter with an order of 5 and a cutoff frequency of 0.25 cycle/cm was used to suppress noise. Notice the significant count fall off as one moves basally (deeper into the patient) along the myocardial walls, especially for the inferior wall. Also notice the distortion in shape of the walls, especially near the base. The center column of images shows the result of one iteration of OSEM reconstruction that employed 15 subsets of 4 angles each and included AC as described in the proceeding paragraphs. Additionally, three-dimensional (3D) post-reconstruction Gaussian filtering was applied to reduce noise. Notice that the shape of the LV walls is improved with AC, and the decrease in counts inferiorly is replaced with an increase septally and inferiorly. This overcorrection is due to the presence of scattered photons in the projections, which add counts to the projection data such that the decrease due to attenuation is moderated. The correction of attenuation is usually based on correcting the losses of primary counts. When these losses are corrected and scatter has not been removed, an apparent overcorrection by attenuation correction occurs.

Figure 6-8 Comparison of transverse slices (top row), short-axis slices (middle row), and maximum count polar maps (bottom row) of mathematical cardiac-torso (MCAT) phantom simulations. First column from the left shows slices and polar map for OSEM reconstruction without attenuation, scatter, or noise included when creating the projections. Instead solely the influence of distance-dependent spatial resolution of a LEHR parallel-hole collimator is present. Shown are slices reconstructed by FBP with no post-reconstruction smoothing included in reconstruction because of no noise having been included in the simulated projections. This thus represents the ideal case of attenuation and scatter compensation. Second column shows slices and polar map for FBP reconstruction without attenuation correction when simulation included the influence of distance-dependent resolution, attenuation, and scatter with clinically equivalent noise. It represents how reconstruction is typically performed presently. Third column shows slices and polar map for OSEM reconstruction, which included modeling of attenuation in projection and back projection. Fourth column shows slices and polar map obtained with OSEM reconstruction which included attenuation and scatter correction. Final column shows slices and polar map for OSEM reconstruction which includes correction for attenuation, scatter, and distance-dependent spatial resolution.