Quantitative myocardial perfusion SPECT

REVIEW Quantitative myocardial perfusion SPECT Benjamin M. W. Tsui, PhD, a,b Eric C. Frey, PhD, a,b Karen J. LaCroix, PhD, a David S. Lalush, PhD, a,b William H. McCartney, MD, b Michael A. King, PhD, c and Grant T. Gullberg, PhD d In recent years, there has been much interest in the clinical application of attenuation compensation to myocardial perfusion single photon emission computed tomography (SPECT) with the promise that accurate quantitative images can be obtained to improve clinical diagnoses. The different attenuation compensation methods that are available create confusion and some misconceptions. Also, attenuation-compensated images reveal other image-degrading effects including collimator-detector blurring and scatter that are not apparent in uncompensated images. This article presents basic concepts of the major factors that degrade the quality and quantitative accuracy of myocardial perfusion SPECT images, and includes a discussion of the various image reconstruction and compensation methods and misconceptions and pitfalls in implementation. The differences between the various compensation methods and their performance are demonstrated. Particular emphasis is directed to an approach that promises to provide quantitative myocardial perfusion SPECT images by accurately compensating for the 3-dimensional (3-D) attenuation, collimator-detector response, and scatter effects. With advances in the computer hardware and optimized implementation techniques, quantitatively accurate and highquality myocardial perfusion SPECT images can be obtained in clinically acceptable processing time. Examples from simulation, phantom, and patient studies are used to demonstrate the various aspects of the investigation. We conclude that quantitative myocardial perfusion SPECT, which holds great promise to improve clinical diagnosis, is an achievable goal in the near future. (J Nucl Cardiol 1998;5:507-22) Key Words: attenuation compensation • collimator-detector response compensation • scatter compensation • single photon emission computed tomography

INTRODUCTION Single photon emission computed tomography (SPECT) with 2°1T1 chloride and 99mTc-labeled sestamibi (99mTc-sestamibi) has been widely used to assess myocardial perfusion and to provide diagnostic and From the aDepartment of Biomedical Engineering and bDepartment of Radiology, The University of North Carolina at Chapel Hill, CDepartment of Nuclear Medicine, University of Massachusetts Medical Center, Worcester, and aDepartment of Radiology, University of Utah. Supported in part by the US Public Health Service grant No CA39463 of the Cancer Institute. The contents of this work are solely the responsibility of the authors. Reprint requests: Benjamin M. W. Tsui, PhD, CB #7575, 152 MacNider Hall, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-7575; [email protected]. Copyright © 1998 by American Society of Nuclear Cardiology. 1071-3581/98/$5.00 + 0 43/1/92922

prognostic information regarding coronary artery disease (CAD). 1A typical commercial SPECT system consists of 1 or more scintillation cameras that are rotated around the patient. The scintillation cameras acquire planar images of the 3-dimensional (3-D) distribution of a radioactivelabeled perfusion agent at different projection views. Traditionally, the planar or projection images have been subsequently used in image reconstruction to obtain multiple 2-dimensional (2-D) transaxial images forming a 3D image set. Ideally, the 3-D-reconstructed image set provides exact information about the 3-D distribution of the perfusion agent. In practice, however, the acquired projection data are affected by various image-degrading factors. They include physical factors such as photon attenuation and scatter in the patient, instrumentation factors such as blurring caused by the collimator-detector, and patient factors such as heart and patient motions. 2,3 Furthermore, because of practical restrictions on the 507

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Figure 1. Flow chart of an iterativereconstructionmethod that uses the maximum-likelihood (ML) expectation-maximization (EM) algorithm. Central to the iterative compensation method is the model of the imaging process that is used in the projection and backprojection steps of the iterative algorithm. amount of injected dose and the length of imaging time, the projection data are degraded by statistical noise fluctuations that propagate to the reconstructed images. When the degraded projection data are used in image reconstruction, the resulting myocardial perfusion SPECT images do not accurately represent the distribution of the perfusion agent in the myocardium. To obtain high-quality and quantitatively accurate myocardial perfusion SPECT images, efforts must be made to minimize such image-degrading factors. Because noise fluctuations and the image-degrading effects cannot be totally eliminated, methods must be developed that will reduce or compensate for them. The development of quantitative reconstruction methods for myocardial SPECT has been an active area of research. Most of these methods consist of 2 parts, namely, an image-reconstruction algorithm and a specific compensation method designed to reduce image noise or to compensate for a particular image-degrading effect. Alternatively, quantitative reconstruction methods have been developed to incorporate compensation of the degrading effects in the image reconstruction process. Photon attenuation is perhaps the most important image-degrading factor in SPECT. It results in a loss of detected photons and its effect increases with a lower photon energy or with higher density and greater thickness of the attenuating medium. In myocardial SPECT, the effects of attenuation are complicated by the different attenuation properties of water-based tissue (muscle, blood etc), lung, and bones. When combined with the variations in anatomy, the effects of attenuation are complex and patient dependent. Attenuation effects related to anatomy often are manifest as a regional decrease in myocardial count density that may be mistaken as a perfusion defect.4-7 There are other complications in the image-degrading effects. The collimator-detector response (CDR)

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function broadens with increased distance from the collimator. The distance-dependent blurring produces special artifacts in the reconstructed images. The scatter response function broadens with increased distance from the collimator and depth in the scattering medium. Also, it is a complex function of the radioactive source distribution, the photon energy, the energy window and collimator response used in data acquisition, and the attenuation distribution and anatomy of the patient. These effects further complicate the quantitative accuracy of myocardial SPECT images. This article provides a discussion of the characteristics of the major degrading factors including statistical noise, photon attenuation, CDR, and scatter and their specific effects on myocardial SPECT images. A review of the compensation methods designed for the different degrading factors is presented. We also emphasize the general approaches used in these methods and their performance characteristics. In particular, we clarify some of the confusion and misconceptions that have resulted from the proliferation of compensation methods. In addition, we discus some important pitfalls that may occur in their implementation: Finally, we discuss a reconstruction approach that will provide high-quality and quantitatively accurate myocardial SPECT images. Although the approach is computationally intensive, with the advance of computer hardware and the development of highly optimized implementations, the processing time can be brought to a level that is clinically acceptable. Results from simulation, experimental, and patient studies are presented to highlight the discussion.

MAJOR DEGRADING FACTORS Photon Attenuation In myocardial perfusion SPECT, photon attenuation results in decreased detected count density in the projection data. A localized decrease in count density in the projection data results in a regional decrease in image intensity in the reconstructed image. If this regional decrease in image intensity occurs along the myocardiurn, it may be mistaken for a regional myocardial perfusion defect and may result in a false-positive diagnosis. Also, attenuation artifacts may obscure a real myocardial perfnsion defect and result in a false-negative diagnosis. The effect of attenuation is complicated by anatomic structure and nonuniform attenuation properties in the chest region.8,9 The heart is largely surrounded by soft tissue and by the lungs which in turn are surrounded by the ribs, the spine, and the sternum. Outside the rib cage, there is a layer of soft tissue and skin. The attenuation coefficients of the soft tissue, lungs, and bones are very different. For example, the average attenuation coeffi-

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cient of lung tissue is about one third of that of the soft tissue in healthy individuals. This varies greatly among patients (eg, smokers and nonsmokers), and when patients are at rest and stress. 10 The degree of attenuation depends on the size and shape of the lungs and the thickness and shape of the outer layer of soft tissue. For example, 2 patients with the same body size may have very different degrees of attenuation effect because of differences in the size and shape of their lungs. As a result, the degree and characteristics of attenuation effects on photons emitted from the heart will be quite complex and patient specific. The heart and lungs are situated on top of the diaphragm. Beneath the diaphragm are the liver, stomach, and other abdominal organs. Since there is a marked difference between the attenuation coefficients of the lungs and tissues below the diaphragm, the shape of the diaphragm has a profound effect on attenuation. For instance, patients with a raised diaphragm (especially the left diaphragm) exhibit a larger attenuation effect in the inferior portion of the myocardium than patients with a diaphragm that is nearly flat. 4,5-7 This artifactual decrease of count density in inferior region of the myocardium is often referred to as diaphragmatic attenuation. Breast tissue is a significant source of attenuation artifacts in female patients.4,5,7,11 It is thought to be the major cause of false-positive diagnosis of CAD in female patients. In general, breast attenuation results in an image intensity decrease in the anterior region of the myocardium. However, the exact characteristics of breast attenuation vary from patient to patient and depend on the size, shape, and location of the breasts with respect to the heart. The artifactual decrease of image intensity in the anterior region of the myocardium is often referred to as breast attenuation.

Geometry and Imaging Characteristics of the Collimator -Detector In a typical SPECT system based on rotating cameras, the collimator is the most important factor in determining detection efficiency and spatial resolution of the system. It is the major factor that contributes to general blurring of SPECT images. For all conventional camera collimators, including the parallel-hole, fan-beam, and cone-beam collimators, the spatial resolution of the collimator-detector degrades with increasing distance from the collimator face. When a circular orbit is used in data acquisition, the spatial resolution at the center of rotation (COR) is radially symmetric or isotropic. At a location other than the COR, the varying spatial resolution of the collimator detector results in anisotropic spatial resolution in the reconstructed image. 12 More specifically, the spatial resolution along the radial direction is fairly constant, but along the tangential direction it improves with an increas-

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Figure 2. Top, Three-dimensionalsurface-renderedimage of the 3D Mathematical CArdiac Torso (MCAT)phantom. The outside skin and muscle layers have been removed to show the different organs in the torso region. Sample 2-D transaxial slice of the 3-D attenuation coefficient distribution (bottom left) and the corresponding uptake distribution (bottom right) for 99mTc-sestamibiin different organs. ing distance from the COR. The degree of asymmetry is proportional to the rate of change of collimator-detector spatial resolution with distance. For example, for a given spatial resolution collimators with longer holes produce less asymmetric spatial resolution in the reconstructed images compared with collimators with shorter holes. In myocardial perfusion SPECT the varying collimator-detector spatial resolution may produce another type of artifact when an elliptical orbit is used. As the eccentricity of the elliptical orbit increases (eg, the ratio of the long to short axis increases), the count density along the lateral sides of the myocardium may decrease. 13

Scatter Scatter is perhaps the most complicated physical factor that affects the quality and quantitative accuracy of myocardial perfusion SPECT images. The effect of scatter on the left ventricular (LV) wall is complicated by the activity in the adjacent organs, the shapes and relative positions of the organs, and their different tissue densities. For example, scatter photons originated from radioactivity uptake in the right ventricular (RV) wall contribute to the apparent uptake in the septal wall of the LV. In some patients, the diaphragm is raised such that the liver and other abdominal organs are close to the infe-

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Chang

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Figure 3. Comparison of performance of different iterative reconstruction algorithms using noise-free (A) and noisy data (B) from the 3-D MCAT phantom. The number of iterations is indicated in the upper left c o m e r of each image.

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rior wall of the myocardium. 14 Scatter artifacts resulting from high radioactivity uptake in these organs (commonly found in 99mTc-sestamibi studies) manifest themselves as increased count density in the inferior wall region. 15,16 The artifactual increase in the inferior LV wall may be partially compensated for by the diaphragmatic attenuation described in the last section. The negative side lobe from filtered backprojection reconstruction may also contribute to the partial compensation. 15 When attenuation compensation is applied and the attenuation artifact is removed, the scatter contribution becomes apparent, thus creating a new set of artifacts. The enhancement of scatter artifacts in attenuation-compensated images is sometimes referred to as overcompensation by the attenuation-compensation method. It is a major concern in the clinical implementation of attenuation compensation.

COMPENSATION METHODS FOR DEGRADING FACTORS As described in the previous section, several physical factors cause degradations in the myocardial perfusion SPECT projection data that affect 2 major aspects of the reconstructed images--quantitative accuracy and image quality.2,3 Most importantly, they hinder the accurate detection of perfusion defects and may inadvertently affect clinical diagnosis. Hence, to improve the accuracy of myocardial defect detection and potentially, the clinical diagnosis of CAD, it is important to increase the quantitative accuracy and improve the quality of the reconstructed images. Steps have been taken to achieve these goals and to develop methods for reducing the effects of such image-degrading factors. The following sections provide a brief summary of these compensation methods for myocardial perfusion SPECT and their implementation. First, we present conventional compensation methods that offer only approximate or partial compensation. Then we describe a relatively new class of 3-D quantitative reconstruction methods that hold promise to provide accurate compensation for the degrading factors.

Conventional Compensation Methods Attenuation Compensation. Attenuation compensation has been an active area of research in SPECT. 17 Depending on their application, attenuation compensation methods can be divided into 2 general categories. The first category assumes that the attenuation coefficient is uniform throughout the body. The uniform attenuation compensation methods 18-2°have been applied to SPECT imaging of the brain and the abdomen. In these applications, the attenuation coefficients of the different soft tissue organs are very similar. The relative size of denser bone structures

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is relatively small and the amount of air-filled structure is negligible. The application of uniform attenuation compensation techniques to myocardial SPECT can provide relatively accurate compensation for small patients with little attenuation, but is inaccurate for larger patients with larger attenuation effect and therefore is unacceptable. The second category of attenuation compensation methods takes into account the fact that the attenuation coefficient is nonuniform throughout the body. The most important application of these methods is myocardial perfusion SPECT since the attenuation coefficient in the torso region is very nonuniform. The analytical SPECT reconstruction problem with nonuniform attenuation is difficult to solve and its analytical solution has not yet been found. The most common nonuniform attenuation compensation methods involve the use of iterative reconstruction techniques and knowledge of the attenuation coefficient distribution in the patient's body. 21 These methods have been used in myocardial perfusion SPECT and are described in more detail.

Collimator-Detector Response Compensation. Several approaches have been developed to compensate for the effects of CDR in myocardial SPECT. The first approach assumes that the CDR is constant or stationary. By using a stationary CDR function, a deconvolution filter can be applied to process the projection data or the reconstructed images. 22 However, since the CDR varies with distance its compensation using the deconvolution method is only approximate. Furthermore, the deconvolution method is limited by the tradeoff between resolution enhancement and noise smoothing. Analytical approaches to solve the SPECT reconstruction problem with the distance varying CDR have been attempted. However, solutions to the problem have only been obtained by approximating either the shape of the CDR function to a special function23 or by assuming collimator design parameters that are not fully met in practical collimators. 24 Alternatively, compensation for the distance vaffing CDR can be achieved using the frequency distance principal (FDP). 25 This technique allows separation of the projection data in sinogram frequency space as a function of the distance from the collimator. The CDR function can be compensated for by applying appropriately chosen distance-dependent functions. Although these methods are relatively fast, they give only approximate compensation and care must be taken to prevent amplification of high-frequency noise. Another approach for accurate compensation of the effect of CDR is the incorporation of the nonstationary CDR function into iterative reconstruction methods. This method allows accurate compensation of the fully 3-D CDR resulting in improved spatial resolution and image noise. 26 This approach is described in more detail later in this article.

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Average transmission counts/pixel

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Figure 4. A, Transmission CT images obtained from projection data at 3 different average count densities using raw data (left column) and processed data where the zero counts have been handled properly (right column). B, The attenuation-compensated SPECT images using attenuation maps generated from the processed transmission CT images with different total emission counts (left to right columns). The results show that where noise is handled properly, the noise in the transmission CT is not a problem as long as noise in the emission data is the dominant factor.

Scatter Compensation. As described previously, the complex scatter response function depends on the energy of the emitted photon, the energy window used, the CDR function, the source location, and the shape and composition of the scattering medium. 27-3° Because of these complexities, most scatter compensation methods for myocardial perfusion SPECT are based on an approximation of the scatter response function. In general, they can be divided into 3 main categories: scatter subtraction, scatter deconvolution, and reconstruction-based methods. In subtraction-based methods, the idea is to estimate the scatter and subtract it from the projection data. The scatter estimate can be obtained by use of spatial information or measurements made in other energy windows. An example is the convolution subtraction method that estimates the scatter using spatial information. 31 In the energy window-based subtraction methods the scatter component is estimated using one 32 or two 33 energy windows or using a ratio of detected counts in different energy windows. 34 Scatter compensation methods using three 35 and more energy windows 36,37 have also been proposed. However, because of variations in the shape of the scatter response as a function of energy, these methods can provide only approximate scatter compensation. 38,39 In addition, an increase in image noise resulted from the scatter subtraction methods. The second class of methods is based on deconvolution techniques. These methods assume that the scatter

response function is spatially invariant and use restoration filtering methods to deconvolve the scatter response function from the reconstructed image or the projection data. In some implementations, only the scatter response function is deconvolved, 4° whereas in others both scatter and CDR compensation are included.41, 42 These methods are fast and require only a single energy window. However, because of the assumption that the scatter response is spatially invariant, these methods result in inaccurate scatter compensation. Another class of methods incorporates scatter compensation into the reconstruction algorithm. The simplest method for doing this is to reduce the attenuation coefficients used in attenuation compensation. Although the method accounts for the increased amount of scatter from sources deeper in the scattering medium, it does not account for the different spatial distribution of the scatter response function. Another approach incorporates the scatter estimate, usually obtained from energy window information, into an iterative reconstruction algorithm. 43,44 Although this approach reduces noise amplification, the scatter compensation is approximate because of errors in the scatter estimate. A newer and more accurate class of scatter compensation methods is to include the spatially varying, patient-dependent scatter response function in an iteratire reconstruction algorithm. 45-47 This method is described in more detail in the following section.

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Sample slice through 3D MCAT phantoms

Bull's-eye plot of LV wall of phantoms

Bull's-eye plot from FBP images

Bull's-eye plot from Chang with AC

Bull's-eye plot from ML-EM with AC

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Figure 5. Comparison between the performance of the popular Chang and the iterative ML-EM algorithm for lateral body widths,from left to right column, of 30 cm, 36 cm, 42 cm and 48 cm, respectively. Top row: Transmission CT images; second row: bull's-eye plots of LV count density of the 3-D MCAT phantom; third row: bull's-eye plots of from the FBP-reconstructed images without any compensation;fourth row: bull'seye plots from the reconstructed images obtained using the Chang algorithm with compensation of the nonuniform attenuation; fifth row: bull's-eye plots from the reconstructed images obtained using the MLEM algorithm with compensation of the nonuniform attenuation. The results show that the ML-EM algorithm is more robust than the Chang algorithm in attenuation compensation for different body sizes.

Quantitative Compensation Methods Quantitative compensation methods in myocardial perfusion SPECT imaging attempt to compensate accurately for the complex image-degrading factors. Currently, the most promising approach is the use of an iterative reconstruction method, which consists of an iterative reconstruction algorithm and models of the imaging process that include the image-degrading factors. The following section describes how the iterative reconstruction methods work and their application in quantitative myocardial perfusion SPECT imaging.

lterative Reconstruction Algorithms. Figure 1 shows the flow chart of a typical iterative reconstruction method that uses the maximum-likelihood (ML) expectation-maximization (EM) algorithm. 43 The first step is to make an initial estimate of the reconstructed image. It is often a nonzero uniform image that the same total projection counts as the measured projection data. The next step is to calculate projection data that would have resulted from this initial estimate. Here, the model of the imaging process is incorporated in the generation of the projection data. The ratio of the measured and calculated projection

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FBP Image w! smoothing wlo compensation)

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Figure 6. Reconstructed images obtained from a sample short slice of a patient 2°IT1SPECT study. A, FBP-reconstructed image without any compensation, postprocessed using a Butterworth smoothing filter. B, Reconstructed images from 4 different image reconstruction and compensation methods. Top row: Reconstructed images using 2-D image-reconstruction and compensation techniques applied to each image slice; bottom row: reconstructed images using 3-D image-reconstruction and compensation techniques applied to a stack of image data simultaneously. Left column: Reconstructed images using approximation compensation methods including the Chang attenuation compensation method and Metz filtering for CDR compensation; right column: reconstructed images using 100 iterations of the ML-EM algorithm with accurate compensation for both attenuation and CDR. data (the difference between the measured and calculated projection data may be used in other algorithms) is determined. The ratio (or difference) data are then backprojected to obtain the correction image. The model of the imaging process is also used in the backprojection process. The initial image estimate is then multiplied by (or added to) the correction image estimate to form a new image estimate. The new image estimate is then tested using a specific criterion. If the criterion is not met, the new image estimate is used to generate the calculated projection data and the iterative steps repeat. If the criterion is met, the new image estimate is considered the final image estimate and the iteration stops. In the ML-EM algorithm, the criterion that is often used is a comparison between a preselected small value and the difference between the previous and new image estimates. If the model of the imaging process accurately includes the image-degrading factors, such as attenuation, and CDR and scatter responses, the iterative process will converge to an image estimate that approaches the true radioactivity distribution. When this is achieved, the degrading factors have been compensated for. An iterative algorithm has 2 main characteristics: the statistical model used and the rate of convergence. For example, the popular ML-EM algorithm 43 is derived from the assumption that the noise in the measured projection

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data follow Poisson statistics. In the ML-EM reconstructed image, the variance of the noise fluctuations (ie, square of the standard deviation) is approximately proportional to the mean counts. Thus, unlike the filtered backprojection (FBP) images, the noise level in the ML-EM images is lower in regions of lower image intensity.48, 49 This results in the generally superior noise properties of the ML-EM-reconstructed images compared with those obtained from other algorithms. Also, the ML-EM algorithm guarantees the image pixel values are nonnegative. A major disadvantage of the ML-EM algorithm is its slow convergence rate. For clinical myocardial SPECT data, it has been found that about 30 to 60 iterations are required for the ML-EM to reach a stable, final image estimate. Because each iteration step requires a projection and a backprojection operation, the intensive computation involved has been a major deterrent in the clinical application of the iterative ML-EM reconstruction method. Although fast algorithms, such as the weighted least-squares conjugate gradient (WLS-CG) algorithm, 5°-51 Chang, t9,52 iterative filtered backprojection (IFPB) algorithm53, 54-55 and other heuristic algorithms have convergence rates as much as 10 times faster than the ML-EM algorithm, the higher image noise level of these obtained by using algorithms preclude their use in clinical applications. 56 Recently an ordered-subset expectation-maximization (OS-EM) algorithm 57 has been proposed that provides similar noise characteristics but much faster convergence rates compared with the ML-EM algorithm (up to -15 to 30 times faster). The OS-EM algorithm is similar to the ML-EM algorithm except that the projection data are divided into subsets each containing 2 or more projections arranged in a specific order. In turn, each subset is used in the iterative step to update the reconstructed image estimate. As a result, the OS-EM algorithm converges to the final image estimate in as few as 3 to 5 iterations and produces reconstructed images that are comparable in quality to those from the ML-EM algorithm. The fast OSEM algorithm in combination with the new generation of fast computers has significantly reduced the processing time while maintaining good image quality for quantitative SPECT image reconstruction. Iterative Attenuation Compensation. Iterative reconstruction methods have been gaining increased acceptance in compensating for the nonuniform attenuation of the patient's chest region in myocardial perfusion SPECT. 17,21,58 Here, the attenuation coefficient distribution is modeled in the imaging process shown in Figure 1. The clinical implementation of the method involves both a determination of the attenuation coefficient distribution in the patient's chest region using a transmission computed tomography (TCT) technique and an iterative reconstruction algorithm.

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Figure 7. Typical transaxial SPECT images from a 2°iT1 patient study obtained using the conventional FBP-reconstmction algorithm without any compensation.

Various methods for TCT data acquisition have been proposed, t7 Although the x-ray TCT technique has the potential to provide an effective and low-cost means for acquiring attenuation coefficient information, most of the TCT methods used in SPECT attenuation compensation are based on a radionuclide source, t7 The radionuclide TCT methods can be implemented using either parallel or fanbeam collimation geometries. In the parallel-beam collimation geometry, a scanning line source59,60 or a set of multiple line sources 6t are used to cover the full field of view of a parallel-hole collimator. The main advantages of the parallel-beam collimation geometry are the use of the conventional parallel-hole collimator and a TCT resolution that is similar to that of the SPECT system. 62 The main disadvantage is the requirement of a scanning mechanism or multiple line sources to cover the full field of view of the collimator and higher activity concentration in the line source compared with the converging-beam collimation geometry. The effectiveness of the iterative attenuation compensation method has been evaluated using limited simulation and patient data. In a computer simulation study, 7 the 99mTc-sestamibi data were generated from a populations of phantoms modeling male patients with relatively flat and raised diaphragms and female patients with breasts of different sizes and shapes. Results from ROC studies indicated that the attenuation compensation method provided little improvement in male patients with flat diaphragms. However, they showed major improvements in male patients with raised diaphragms (greater diaphragmatic attenuation) and in female patients with breast attenuation. 7 Initial clinical evaluation of iterative

attenuation compensation method is encouraging. 63 The results reveal that although the attenuation effect is compensated for, the effects of other image degrading factors such as scatter may become dominant and can sometimes affect clinical diagnoses. An important example is the contribution of scatter from the radioactivity uptake in the adjacent liver to the inferior region of the myocardiurn. This effect is especially important in 99mTc-sestamibi studies where high levels of subdiaphragmatic activity is common. 16 lterative CDR Compensation. The distance-varying CDR function can be modeled in the imaging process of the iterative reconstruction algorithm shown in Figure 1 for spatial resolution recovery alone or in combination with attenuation compensation 64 for both attenuation and spatial resolution recovery. In 2-D reconstruction where 1-D projection data are used, the 1-D CDR function is used. The 2-D CDR function can also be used with the iterative reconstruction algorithm for fully 3-D spatial resolution recovery. 26,65,66 It is found that fully 3-D reconstruction provides both improved spatial resolution recovery and lower noise levels compared with 2-D reconstruction. 26 Although iterative spatial resolution recovery yields improved overall spatial resolution when compared with FBP, the reconstructed image resolution remains asymmetric. 67 lterative Scatter Compensation. The application of iterative reconstruction methods to scatter compensation has been complicated by the complex dependence of the scatter response function on various imaging parameters. Early models of scatter response functions incorporated

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Figure 8. A, Transmission CT images from a patient obtained using a pair of scanning line sources installed on the GE Optima dual-camera SPECT system. B, Corresponding SPECT reconstructed images obtained with 30 iterations of the ML-EM algorithm With attenuation compensation using the attenuation map derived from A.

dependence on the collimator-detector used, the distance from the collimator-detector, source depth, and source location in the scattering medium.46,68, 69 More recent scatter response models take into account the nonuniform attenuation distribution. 30,70,71 The scatter response can be combined with the nonuniform attenuation and CDR to form an accurate model of the imaging process to be used in the iterative reconstruction algorithm as shown in Figure 1 for accurate SPECT image reconstruction.

Implementation Methods and Processing Time. The intensive computations involved in the quantitative

iterative reconstruction methods have been major deterrents in the application of the 3-D quantitative reconstruction for clinical use. The major difficulty in decreasing the processing time is in modeling of the large spatial extent of the collimator-detector and scatter response functions and the complexity of the accurate scatter models. Much effort has been devoted to this area of development. F o r example, rotation of the reconstructed i m a g e matrix may be used in fast methods for modeling the distance-dependent collimator response 72 and object dependent scatter response functions.46, 68 Recently efforts have

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been made to further improve the speed of iterative reconstruction-based scatter compensation. 73,74 Since the scatter response consists of mostly low-frequency components, a coarser voxel size can be used during the scatter calculations: 74 Also, the complex scatter response is included only in the projection operation 73 and intermittently in the iterative process, holding the scatter estimate constant in other iterations. 74 With these optimized implementation techniques, quantitative myocardial perfusion SPECT images can be obtained in clinically acceptable times. For example, using a DEC Alpha 500 MHZ computer workstation, the total processing time for 5 iterations of OS-EM reconstruction of a 32-slice volume of 64 x 64-reconstructed images from 64 projection views is about 3.6 minutes.

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MISCONCEPTIONS AND PITFALLS With increased interest in quantitative myocardial SPECT imaging, there are some misconceptions about the different degrading factors, their compensation methods, the iterative algorithms, and their performance characteristics. Also, the implementation of the quantitative reconstruction methods has some pitfalls. The following section covers some of these important misconceptions and sources of error.

lterative Image Reconstruction Algorithms. Because of its accurate model of the statistics of noise fluctuations in the acquired projection data, the iterative MLEM algorithm provides much improved reconstructed noise characteristics. Also, the positivity constraint of the algorithm does not generate negative pixel values in the reconstructed image in contrast to the FBP algorithm. Despite the improved image quality, the ML-EM algorithm alone does not provide compensation for the other degrading factors such as attenuation, CDR, and scatter. Conversely, given the same TCT data for use in attenuation compensation, different iterative reconstruction algorithms perform differently. Fast iterative reconstruction algorithms have received much research interest as a substitute for the slow ML-EM algorithm. However, these heuristic algorithms often show poor noise characteristics and have a tendency to fluctuate around the final estimate. 56 To control these problems, special filtering and regularization techniques are needed. Unfortunately, these techniques have to be tailored to specific patient data in order to be successful. To evaluate the performance of various iterative reconstruction algorithms, we used a 3-D Mathematical CArdiac Torso (MCAT) phantom, 6,75 developed at the University of North Carolina at Chapel Hill. Figure 2, top, shows a 3-D volume-rendered image of the current 3-D MCAT phantom with the skin and outer muscle tissue removed to reveal the internal organs. The phantom

B

Figure 9. Results from 2°IT1 study of normal male patient. A, Sample short-axis images obtained using the FBP reconstruction algorithm without any compensation showing a diaphragmatic attenuation artifact in the inferior region of the LV wall. B, Corresponding short-axis images obtained using 30 iterations of the ML-EM algorithm with attenuation compensation show substantial reduction of the diaphragmatic attenuation artifact.

can be used to simulate the attenuation coefficient distribution of and radioactivity uptakes in different organs. Figures 2, bottom left and bottom right, show the same transaxial image slice through the 3-D attenuation coefficient and radioactivity uptake distributions, respectively. Two-dimensional transmission and emission projection data can be generated from the 3-D attenuation and radioactivity distributions using simulation techniques to include the effects of attenuation, collimator-detector blurring, and scatter. Poisson noise fluctuations can then be added to simulate the acquired data. Using the data generated from the 3-D MCAT phantom, we compared the performance of several iterative reconstruction algorithms (Figure 3). The reconstructed images demonstrate the superior quality generated by the ML-EM and OSEM algorithms compared with the other fast heuristic algorithms. Also, the OS-EM algorithm has a much faster convergence rate than the ML-EM algorithm.

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Figure 10. Results from 2°iT1 studyof normal female patient. A, Sample short-axis images obtained using the FBP reconstruction algorithm without any compensation show the breast attenuation artifact in the superior region of the LV wall. B, Corresponding short-axis images obtained using 30 iterations of the ML-EM reconstruction algorithm with attenuation compensation show substantial reduction of the breast attenuation artifact.

TCT Methods. The common misconceptions about the TCT methods using radionuclides relate to their imaging characteristics and their influence on the performance of attenuation compensation of the myocardial SPECT data. These include the requirements of spatial resolution and count density of the TCT images. It is often believed that superior TCT image spatial resolution is required for attenuation compensation. This has to do with the better spatial resolution in TCT images obtained with the fan-beam collimator geometry and stationary line source compared with that obtained with the parallel-beam collimation geometry and scanning line source. However, it has been shown that comparable attenuation compensated images can be obtained using TCT with spatial resolution that is better or about the same as that of the SPECT images. 76 Image artifacts are found when the spatial resolution TCT is almost perfect or much worse than that of the SPECT images. The

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results are consistent with what was found in attenuation compensation of positron emission tomography (PET) images. Figure 4, A, shows the TCT images at three different average count densities. At low count densities, the quality and accuracy of the transmission TCT images is severely compromised. This is related to the large number of projection data with zero counts that must be handled properly. With appropriate processing techniques, the quality of the transmission TCT images can be improved except at extremely low count levels. Figure 4, B, shows the attenuation-compensated SPECT images using attenuation maps generated from the processed TCT images. At the higher transmission count densities where the noise can be handled properly, the noise in the TCT is not a problem as long as noise in the emission data is the dominant factor. The effect of noise in the TCT data on the attenuation-compensated images has been studied in detail. 77 Attenuation Compensation. An important component in the attenuation compensation method is the image reconstruction algorithm used. As shown in Figure 3, the choice of reconstruction algorithms affects the processing speed and noise characteristics of the attenuation compensation method. In addition, the choice also affects the accuracy of the compensation. For example, Figure 5 shows a comparison between the performance of the popular Chang19, 52 and the iterative ML-EM 43 algorithms for different body sizes using the simulated data from the 3-D MCAT phantom. In both cases, the nonuniform attenuation distribution is used in the reconstruction. The results indicate that both compensation methods work well with smaller body sizes. As the body size increases, the Chang algorithm gradually breaks down and produces inaccurate attenuationcompensated SPECT images. In contrast, the iterative ML-EM algorithm is more robust compared with the Chang algorithm in producing accurate attenuationcompensated SPECT images for different body sizes. Attenuation and CDR Compensation. The effectiveness of the iterative CDR compensation is demonstrated in Figure 6 with data from a patient 20aT1SPECT study. The same projection data were processed using the FBP algorithm without any compensation and using approximate and quantitative 2-D and 3-D image reconstruction and compensation methods. The approximate compensation methods include the Chang attenuation compensation technique and Metz filtering for CDR compensation. The quantitative reconstruction methods use iterative reconstruction algorithms and accurate models of attenuation and CDR. Reconstructed images obtained using the 3-D quantitative reconstruction methods show improvements in both spatial resolution and noise compared with those obtained using the 2-D technique and those obtained using the approximate compensation methods.

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CLINICAL RESULTS Attenuation Compensation. Figure 7 shows typical SPECT images from a 2roT1 patient study obtained using the conventional FBP reconstruction algorithm without any compensation for the degrading factors. The patient was injected with 2.5 mCi of 2°1T1 and projection data were acquired with a GE Optima dual-camera SPECT system. The detectors are connected at a right angle. Sixty-four projection views that range from 45 degrees left posterior oblique (LPO) to 45 degrees right anterior oblique (RAO) were acquired by 90-degree rotation of the dual-camera SPECT system. The set of projection data was digitized into 64 x 64 matrices and reconstructed into a stack of 64 × 64 x 64 images. The images show the typical image noise, artifacts due to the effect of nonuniform attenuation, blurring, and loss of image contrast due to the effects of CDR and scatter. Figure 8, A, shows the TCT images obtained using a pair of 153Gd scanning line sources mounted on the GE Optima dualcamera SPECT system. They were transformed to the attenuation coefficient maps for the average 201T1photon energies. Figure 8, B, shows the attenuation-compensated SPECT images obtained using the ML-EM algorithm and the attenuation maps obtained from TCT images shown in Figure 8, A. Note that the reconstructed images show reduced image artifacts and improved quality and quantitative accuracy resulting from accurate attenuation compensation compared with the FBP-reconstructed images. Figure 9 shows results from a 2mT1 myocardial perfusion SPECT study of a normai male patient. Figure 9, A, shows short-axis images from the conventional FBPreconstructed images without any compensation. They demonstrate the typical decreased image intensity in the inferior region of the LV wail caused by diaphragmatic attenuation. The diaphragmatic attenuation artifact is substantially reduced in the attenuation-compensated images shown in Figure 9, B, using 30 iterations of the ML-EM algorithm with an attenuation map obtained from the same patient. Figure 10 shows results from a 2°1T1 myocardial SPECT study of a normal female patient. Figure 10, A; shows short-axis images from conventional FBP reconstructed without any compensation. They demonstrate the typical decreased image intensity in the anterior region of the LV wall caused by breast attenuation. The breast attenuation artifact is significantly reduced in the attenuation compensated images shown in Figure 10, B, using 30 iterations of the ML-EM algorithm with attenuation map obtained from the same patient. Attenuation, CDR, and Scatter Compensation. Figure 11 shows results from a 99mTc-sestamibi study of a normal male patient. Figure 11, A, shows a long-

Vertical long-axis slices

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Figure 11. Results from 99mTc-sestamibi study of normal male patient. A, Sample vertical long-axis (top row) and short-axis images (bottom row) obtained using the FBP-reconstruction algorithm without any compensation (left column), 5 iterations of OSEM algorithm with attenuation compensation (middle column), and 5 iterations of OS-EM algorithm with attenuation and CDR compensation (right column). The image with attenuation compensation shows increased uptake in the inferior region of the LV wall due to scatter from the high liver uptake. B, Images in the left column were obtained using projection data that had been compensated for scatter using the dual-energy window subtraction method and reconstructed using 5 iterations of OS-EM algorithm with 3-D attenuation and collimator-detector response compensation. Images in the right column were reconstructed using 5 iterations of the OS-EM algorithm with accurate 3-D model of the attenuation, and collimator-detector and scatter response functions. These images show substantially reduced inferior wall scatter artifact.

and a short-axis slice from an image set reconstructed with the FBP algorithm without any compensation (left column), 5 iterations of the OS-EM algorithm with attenuation compensation alone (middle column), and 5 iterations of OS-EM algorithm with both attenuation and collimator-detector compensation (right column). The images reconstructed with attenuation compensa-

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tion alone and with both attenuation and CDR compensation show an increased count density in the inferior wall of the myocardium that is not seen in the FBPreconstructed image. Figure 11, B, shows reconstructed images obtained using 2 scatter compensation methods. The images in the left column were obtained using projection data corrected for scatter using the dual-energy window subtraction method and were reconstructed using 5 iterations of OS-EM algorithm with both 3-D attenuation and CDR compensation. The images in the fight column were obtained using 5 iterations of OSEM algorithm with accurate 3-D compensation of attenuation, collimator-detector, and scatter response. Figure I 1, B, shows that improved image quality and quantitative accuracy are achieved when the full scatter model is implemented. In particular, the artifactual increase in the image intensity of the inferior wall of the left ventricle related to subdiaphragmatic radioactivity is more accurately compensated for compared with that offered by the dual-energy window scatter subtraction method.

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and have been developed during the last decade. The implementation of these methods has been deterred because of the intensive computations involved and the resulting long processing time using the previous generations of iterative reconstruction algorithms and computer hardware. With the advances of a new generation of fast robust iterative reconstruction algorithms, computer hardware, and optimized implementations, the 3-D quantitative image reconstruction methods can now be obtained in clinically acceptable processing time. Substantial improvements in quality and quantitative accuracy over conventional myocardial SPECT images are now achievable in clinical practice. These improvements have great potential for more accurate clinical diagnoses and management of heart disease. We thank G. E. DePuey, MD, of the St. Luke's-Roosevelt Hospital, for providing 99mTc-sestamibi study data.

References DISCUSSION Image-degrading factors including statistical noise, attenuation, CDR, and scatter are known to affect the quality and quantitative accuracy of myocardial SPECT images. Attenuation is the most important imagedegrading factor. Diaphragmatic and breast attenuation are major artifacts that often manifest themselves as artifactual myocardial defects or obscure true myocardial defects leading to an overall lowering of specificity in clinical diagnosis of cardiac disease. The search for effective compensation methods of these degrading factors has been an active area of research. However, most of the conventional compensation methods are only approximations and provide only partial compensation. This is due largely to the complex effects of the degrading factors. Accurate attenuation compensation using TCT method is gaining broader acceptance. However, effective attenuation compensation often reveals the effects of the collimator-detector response and scatter. An important example is scatter from high radioactivity uptake in the liver that is in close proximity to the heart. This results in an artifactual count density increase in the inferior region of the LV wall. Conventional CDR and scatter compensation methods only provide approximate and partial compensation despite their computational efficiency. The quantitative 3-D image reconstruction methods described in this article provide accurate myocardial perfusion SPECT images with substantially reduced artifacts, improved image quality, and increased quantitative accuracy. These methods are the work of many investigators

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