Molecular imaging of small animals with a triple-head SPECT system using pinhole collimation.

Pinhole collimation yields high sensitivity when the distance from the object to the aperture is small, as in the case of imaging small animals. Fine-resolution images may be obtained when the magnification is large since this mitigates the effect of detector resolution. Large magnifications in pinhole single-photon emission computed tomography (SPECT) may be obtained by using a collimator whose focal length is many times the radius of rotation. This may be achieved without truncation if the gamma camera is large. We describe a commercially available clinical scanner mated with pinhole collimation and an external linear stage. The pinhole collimation gives high magnification. The linear stage allows for helical pinhole SPECT. We have used the system to image radiolabeled molecules in phantoms and small animals.

Determination of mechanical and electronic shifts for pinhole SPECT using a single point source.

The effects of uncompensated electronic and mechanical shifts may compromise the resolution of pinhole single photon emission computed tomography. The resolution degradation due to uncompensated shifts is estimated through simulated data. A method for determining the transverse mechanical and axial electronic shifts is described and evaluated. This method assumes that the tilt of the detector and the radius of rotation (ROR) are previously determined using another method. When this assumption is made, it is possible to determine the rest of the calibration parameters using a single point source. A method that determines the electronic and mechanical shifts as well as the tilt has been previously described; this method requires three point sources. It may be reasonable in most circumstances to calibrate tilt much less frequently than the mechanical shifts since the tilt is a property of the scanner whereas the mechanical shift may change every time the collimator is replaced. An alternative method for determining the ROR may also be used. Lastly, we take the view that the transverse electronic shift and the focal length change slowly and find these parameters independently.

Analytic determination of the pinhole collimator's point-spread function and RMS resolution with penetration.

Pinhole collimators are widely used to image small organs and animals. The pinhole response function (PRF) of knife-edge pinhole collimators has been estimated previously using geometric constructions without considering penetration and using "roll-off" models that employ an exponential model for the flux. An analytic expression for the PRF on the imaging plane that includes the effect of aperture penetration is derived in this paper by calculating the flux for photons passing through the aperture and those passing through the attenuating material. The PRF is then used to approximate the angular-dependent root-mean-square resolution in the directions parallel and perpendicular to the tilt of the point source. The corresponding aspect ratio is then obtained. The formulas are then compared with experimental data.

Modeling the axial extension of a transmission line source within iterative reconstruction via multiple transmission sources.

Reconstruction algorithms for transmission tomography have generally assumed that the photons reaching a particular detector bin at a particular angle originate from a single point source. In this paper, we highlight several cases of extended transmission sources, in which it may be useful to approach the estimation of attenuation coefficients as a problem involving multiple transmission point sources. Examined in detail is the case of a fixed transmission line source with a fan-beam collimator. This geometry can result in attenuation images that have significant axial blur. Herein it is also shown, empirically, that extended transmission sources can result in biased estimates of the average attenuation, and an explanation is proposed. The finite axial resolution of the transmission line source configuration is modeled within iterative reconstruction using an expectation-maximization algorithm that was previously derived for estimating attenuation coefficients from single photon emission computed tomography (SPECT) emission data. The same algorithm is applicable to both problems because both can be thought of as involving multiple transmission sources. It is shown that modeling axial blur within reconstruction removes the bias in the average estimated attenuation and substantially improves the axial resolution of attenuation images.

Relating radiation-induced regional lung injury to changes in pulmonary function tests.

PURPOSE: To determine whether the sum of radiotherapy (RT)-induced reductions in regional lung perfusion is quantitatively related to changes in global lung function as assessed by reductions in pulmonary function tests (PFTs). METHODS AND MATERIALS: Two hundred seven patients (70% with lung cancer) who received incidental partial lung irradiation underwent PFTs (forced expiratory volume in 1 s and diffusion capacity for carbon monoxide) before and repeatedly after RT as part of a prospective clinical study. Regional lung function was serially assessed before and after RT by single photon emission computed tomography perfusion scans. Of these, 53 patients had 105 post-RT evaluations of changes in both regional perfusion and PFTs, were without evidence of intrathoracic disease recurrence that might influence regional perfusion and PFT findings, and were not taking steroids. The summation of the regional functional perfusion changes were compared with changes in PFTs using linear regression analysis. RESULTS: Follow-up ranged from 3 to 86 months (median 19). Overall, a significant correlation was found between the sum of changes in regional perfusion and the changes in the PFTs (p = 0.002-0.24, depending on the particular PFT index). However, the correlation coefficients were small (r = 0.16-0.41). CONCLUSIONS: A statistically significant correlation was found between RT-induced changes in regional function (i.e., perfusion) and global function (i.e., PFTs). However, the correlation coefficients are low, making it difficult to relate changes in perfusion to changes in the PFT results. Thus, with our current techniques, the prediction of changes in perfusion alone does not appear to be sufficient to predict the changes in PFTs accurately. Additional studies to clarify the relationship between regional and global lung injury are needed.

Analytic determination of pinhole collimator sensitivity with penetration.

Pinhole collimators are widely used to image small organs and animals. The sensitivity of knife-edge pinhole collimators has been previously estimated using an "effective diameter" formulation and experimentally described using a sin(x) theta fit, where theta is the angle between the line segment from the center of the aperture to the photon source and its projection onto the plane of the aperture. An analytic form of the sensitivity of the pinhole collimator is derived in this paper. A numerical formula for predicting the sin(x) theta form of the sensitivity is calculated from the analytic form. Experimental data are compared with the theoretical estimate and the sin(x) theta prediction. The agreement is excellent.

Can we predict radiation-induced changes in pulmonary function based on the sum of predicted regional dysfunction?

PURPOSE: To determine whether changes in whole-lung pulmonary function test (PFT) values are related to the sum of predicted radiation therapy (RT)-induced changes in regional lung perfusion. PATIENTS AND METHODS: Between 1991 and 1998, 96 patients (61% with lung cancer) who were receiving incidental partial lung irradiation were studied prospectively. The patients were assessed with pre- and post-RT PFTs (forced expiratory volume in one second [FEV1] and diffusion capacity for carbon monoxide [DLCO]) for at least a 6-month follow-up period, and patients were excluded if it was determined that intrathoracic recurrence had an impact on lung function. The maximal declines in PFT values were noted. A dose-response model based on RT-induced reduction in regional perfusion (function) was used to predict regional dysfunction. The predicted decline in pulmonary function was calculated as the weighted sum of the predicted regional injuries: equation [see text] where Vd is the volume of lung irradiated to dose d, and Rd is the reduction in regional perfusion anticipated at dose d. RESULTS: The relationship between the predicted and measured reduction in PFT values was significant for uncorrected DLCO (P = .005) and borderline significant for DLCO (P = .06) and FEV1 (P = .08). However, the correlation coefficients were small (range,.18 to.30). In patients with lung cancer, the correlation coefficients improved as the number of follow-up evaluations increased (range,.43 to.60), especially when patients with hypoperfusion in the lung adjacent to a central mediastinal/hilar thoracic mass were excluded (range,.59 to.91). CONCLUSION: The sum of predicted RT-induced changes in regional perfusion is related to RT-induced changes in pulmonary function. In many patients, however, the percentage of variation explained is small, which renders accurate predictions difficult.

Receiver operating characteristic evaluation of iterative reconstruction with attenuation correction in 99mTc-sestamibi myocardial SPECT images.

UNLABELLED: The purpose of this study was to evaluate differences in myocardial defect detection between 99mTc-sestamibi myocardial SPECT images reconstructed using conventional filtered backprojection (FBP) without attenuation correction (AC) and those reconstructed using maximum-likelihood expectation maximization with nonuniform attenuation correction (MLAC). METHODS: An observer study and receiver operating characteristic (ROC) curve analysis were performed using simulated 99mTc-sestamibi SPECT data from a population of 24 mathematic anthropomorphic torso phantoms, which realistically modeled a wide range of anatomic variations. The phantoms modeled male patients with a flat diaphragm, male patients with a diaphragm raised to the level of the heart, and female patients with large breasts. Transmural, cold defects with a contrast of 0.25 were simulated in the left ventricular wall for 6 locations. Noisy projection data were generated from the phantoms and included the effects of nonuniform attenuation, collimator-detector response, and scatter. The data were then reconstructed using FBP and MLAC. Images were displayed in the short- and long-axis formats, as in clinical practice. Eight observers viewed blocks of FBP and MLAC images and, for each image, indicated on a continuous rating scale the probability that a defect was present. From the rating data, FBP and MLAC ROC curves were generated, and their areas (Az) were estimated and compared. RESULTS: In general, the FBP and MLAC ROC curves did not cross and the MLAC curve showed a higher Az than did the corresponding FBP curve. For male phantoms with a flat diaphragm, the average difference in Az was 0.04 and was not statistically significant (at the P = 0.05 level) for 6 of 8 observers. For male phantoms with a raised diaphragm, the average difference in Az was 0.22 and was statistically significant for 6 of 8 observers. For female phantoms with large breasts, the average difference in Az was 0.19 and was statistically significant for all 8 observers. CONCLUSION: This study showed an improvement in defect detection in myocardial SPECT images using MLAC in comparison with images using FBP without AC, particularly for patients with large breasts or with a diaphragm raised to the level of the heart.

The effect of patient-specific factors on radiation-induced regional lung injury.

PURPOSE: To assess the impact of patient-specific factors on radiation (RT)-induced reductions in regional lung perfusion. METHODS: Fifty patients (32 lung carcinoma, 7 Hodgkin's disease, 9 breast carcinoma and 2 other thoracic tumors) had pre-RT and > or = 24-week post-RT single photon emission computed tomography (SPECT) perfusion images to assess the dose dependence of RT-induced reductions in regional lung perfusion. The SPECT data were analyzed using a normalized and non-normalized approach. Furthermore, two different mathematical methods were used to assess the impact of patient-specific factors on the dose-response curve (DRC). First, DRCs for different patient subgroups were generated and compared. Second, in a more formal statistical approach, individual DRCs for regional lung injury for each patient were fit to a linear-quadratic model (reduction = coefficient 1 x dose + coefficient 2 x dose2). Multiple patient-specific factors including tobacco history, pre-RT diffusion capacity to carbon monoxide (DLCO), transforming growth factor-beta (TGF-beta), chemotherapy exposure, disease type, and mean lung dose were explored in a multivariate analysis to assess their impact on the coefficients. RESULTS: None of the variables tested had a consistent impact on the radiation sensitivity of regional lung (i.e., the slope of the DRC). In the formal statistical analysis, there was a suggestion of a slight increase in radiation sensitivity in the dose range >40 Gy for nonsmokers (vs. smokers) and in those receiving chemotherapy (vs. no chemotherapy). However, this finding was very dependent on the specific statistical and normalization method used. CONCLUSION: Patient-specific factors do not have a dramatic effect on RT-induced reduction in regional lung perfusion. Additional studies are underway to better clarify this issue. We continue to postulate that patient-specific factors will impact on how the summation of regional injury translates into whole organ injury. Refinements in our methods to generate and compare SPECT scans are needed.

Quantitative pulmonary single photon emission computed tomography for radiotherapy applications.

Pulmonary imaging using single photon emission computed tomography (SPECT) is the focus of current radiotherapy research, including dose-response analysis and three-dimensional (3D) radiation treatment planning. Improvement in the quantitative capability of SPECT may help establish its potential role in this application as well as others requiring accurate knowledge of pulmonary blood flow. The purposes of this study were to quantitatively evaluate SPECT filtered backprojection (FBP) and ordered subset-expectation maximization (OS-EM) reconstruction implementations for measuring absolute activity concentration in lung phantom experiments, and to incorporate quantitative SPECT techniques in 3D-RTP for lung cancer. Quantitative FBP (nonuniform iterative Chang attenuation compensation, scatter correction, and 3D postreconstruction Metz filtering) and OS-EM implementations were compared with a "clinical" implementation of FBP (uniform multiplicative Chang attenuation compensation and post-reconstruction von Hann filtering), for their ability to improve quantification of inactive and active spherical defects in the lungs of an anthropomorphic torso phantom. Activity concentration estimates were found to depend on many factors, such as region of interest size, scatter subtraction constant (k), postreconstruction deconvolution filtering and, in the case of OS-EM, total number of iterations. In general, reconstruction implementations incorporating compensation for nonuniform attenuation and scatter provided reduced bias relative to the clinical implementation. Potential applications to lung radiotherapy, including dose-functional histograms and treatment planning are also discussed. SPECT has the potential to provide accurate estimates of lung activity distributions that, together with improved image quality, may be useful for the study and prediction of therapeutic response.

Multimodality nuclear medicine imaging in three-dimensional radiation treatment planning for lung cancer: challenges and prospects.

The purpose of this study was to determine the utility of quantitative single photon emission computed tomography (SPECT) lung perfusion scans and F-18 fluorodeoxyglucose positron emission computed tomography (PET) during X-ray computed tomography (CT)-based treatment planning for patients with lung cancer. Pre-radiotherapy SPECT (n = 104) and PET (n = 35) images were available to the clinician to assist in radiation field design for patients with bronchogenic cancer. The SPECT and PET scans were registered with anatomic information derived from CT. The information from SPECT and PET provides the treatment planner with functional data not seen with CT. SPECT yields three-dimensional (3D) lung perfusion maps. PET provides 3D metabolic images that assist in tumor localization. The impact of the nuclear medicine images on the treatment planning process was assessed by determining the frequency, type, and extent of changes to plans. Pre-radiotherapy SPECT scans were used to modify 11 (11%) treatment plans; primarily altering beam angles to avoid highly functioning tissue. Fifty (48%) SPECT datasets were judged to be 'potentially useful' due to the detection of hypoperfused regions of the lungs, but were not used during treatment planning. PET data influenced 34% (12 of 35) of the treatment plans examined, and resulted in enlarging portions of the beam aperture (margins) up to 15 mm. Challenges associated with image quality and registration arise when utilizing nuclear medicine data in the treatment planning process. Initial implementation of advanced SPECT image reconstruction techniques that are not typically used in the clinic suggests that the reconstruction method may influence dose response data derived from the SPECT images and improve image registration with CT. The use of nuclear medicine transmission computed tomography (TCT) for both SPECT and PET is presented as a possible tool to reconstruct more accurate emission images and to aid in the registration of emission data with the planning CT. Nuclear medicine imaging techniques appear to be a potentially valuable tool during radiotherapy treatment planning for patients with lung cancer. The utilization of accurate nuclear medicine image reconstruction techniques and TCT may improve the treatment planning process.

Astigmatic single photon emission computed tomography imaging with a displaced center of rotation.

A filtered backprojection algorithm is developed for single photon emission computed tomography (SPECT) imaging with an astigmatic collimator having a displaced center of rotation. The astigmatic collimator has two perpendicular focal lines, one that is parallel to the axis of rotation of the gamma camera and one that is perpendicular to this axis. Using SPECT simulations of projection data from a hot rod phantom and point source arrays, it is found that a lack of incorporation of the mechanical shift in the reconstruction algorithm causes errors and artifacts in reconstructed SPECT images. The collimator and acquisition parameters in the astigmatic reconstruction formula, which include focal lengths, radius of rotation, and mechanical shifts, are often partly unknown and can be determined using the projections of a point source at various projection angles. The accurate determination of these parameters by a least squares fitting technique using projection data from numerically simulated SPECT acquisitions is studied. These studies show that the accuracy of parameter determination is improved as the distance between the point source and the axis of rotation of the gamma camera is increased. The focal length of the focal line perpendicular to the axis of rotation is determined more accurately than the focal length to the focal line parallel to this axis.

Transmission imaging for nonuniform attenuation correction using a three-headed SPECT camera.

UNLABELLED: Our objective was to build and test a new system for transmission CT (TCT) imaging on a three-headed SPECT camera. The TCT images are intended for use in nonuniform attenuation correction of cardiac SPECT data. METHODS: The system consists of a transmission line source mounted to the camera gantry at the focal line of a long focal length, asymmetric fanbeam collimator. The focal line is 114 cm from the collimator surface and shifted 20 cm from the detector midline. This asymmetric fanbeam geometry is used to reduce truncation artifacts in the reconstructed TCT image. The line source fixture accommodates a 25-cm long source and contains removable, variable thickness attenuator plates (copper or lead) to modulate the photon flux density and a slat collimator to collimate the TCT source beam in the axial direction. For the TCT reconstruction, an iterative maximum likelihood-expectation maximization algorithm is used that models the asymmetric fanbeam geometry. Our initial studies with this system used a 1850 MBq (50 mCi) 123mTe line source. The evaluation included TCT scans of a resolution phantom, an anthropomorphic thorax phantom and a human subject. For the thorax phantom and human subject, short (2-min) and long (14-min) scans were performed. The SPECT imaging performance of the fanbeam collimator was also characterized. RESULTS: For both phantom and human data, high quality TCT reconstructions were obtained with linear attenuation coefficients closely matching narrow beam values. In the images of the resolution phantom, the smallest rods (4.8-mm diam) were resolved. The long scan images of the thorax phantom and human subject demonstrated the high resolution nature of the system and contained no evidence of truncation artifacts. With smoothing to control noise, the short scan images generally retained the attenuation features of the lung and of soft tissue and may provide a practical approach for clinical application. The fanbeam collimator demonstrated high resolution SPECT performance. CONCLUSION: These results suggest this system may provide an effective and practical approach to TCT imaging for nonuniform attenuation correction on a three-headed SPECT camera.

An analytic model of pinhole aperture penetration for 3D pinhole SPECT image reconstruction.

Photons penetrate the attenuating material close to the aperture of pinhole collimators in nuclear medicine, broadening the tails of point spread functions (PSFs) and degrading the resolution of planar and SPECT images. An analytic approximation has been developed that models this penetration contribution to the PSF for knife-edge point pinhole apertures. The approximation has the form exp(-gamma r), where r is the distance on the detector surface from the projection of the point source through the pinhole. The rolloff coefficient gamma is a function of the photon energy, point source location and the design parameters of the collimator. There was excellent agreement between measured values of gamma from photon transport simulations of I-131 point sources (364 keV emission only) and theoretical predictions from the analytic formula. Predicted gamma values from the analytic formula averaged 25% greater than measured values from experimental I-131 point source acquisitions. Photon transport simulations were performed that modelled the 364 keV and less abundant 637 and 723 keV emissions and scatter within the scintillation crystal. Measured gamma values from these simulations averaged 12% greater than the experimental values, indicating that about half of the error between the analytic formula and the experimental measurements was due to unmodelled 637 and 723 keV emissions. The remaining error may be due in part to scatter in the pinhole region and backscatter from gamma camera components behind the scintillation crystal. The analytic penetration model was used in designing Metz filters to compensate for penetration blur and these filters were applied to the projection data as part of 3D SPECT image reconstruction. Image resolution and contrast were improved in simulated and experimental I-131 tumour phantom studies. This analytic model of pinhole aperture penetration can be readily incorporated into iterative 3D SPECT pinhole reconstruction algorithms.

Quantitative imaging of iodine-131 distributions in brain tumors with pinhole SPECT: a phantom study.

UNLABELLED: A method of quantitatively imaging 131I distributions in brain tumors from intratumoral administration of activity was developed and investigated using pinhole SPECT of brain tumor phantoms. METHODS: Pinhole SPECT sensitivity and resolution were characterized using 131I point-source acquisitions with high-resolution lead (1.4-mm diameter aperture) and tungsten (1.0-mm diameter aperture) pinhole inserts. SPECT scans were obtained from brain tumor phantoms in a water-filled cylinder. The tumor phantoms consisted of spheres filled with an 131I solution to model intratumoral administration of radiolabeled monoclonal antibodies. Two spheres were 20.5 and 97 ml, and two other concentric spheres modeled a tumor with a high-activity shell (71.5 ml) and a low-activity core (21 ml). The collimator focal length was 16 cm and the distance from the pinhole to the center of rotation was 13 cm. The filtered backprojection reconstruction algorithm incorporated scatter and attenuation compensation. SPECT tumor activities and concentrations were estimated using scaling factors from reference point-source scans. RESULTS: System sensitivities for point sources at the center of rotation were 28.4 cts/sec(-1) MBq(-1) (lead insert) and 13.6 cts/sec(-1) MBq(-1) (tungsten insert). SPECT resolutions (FWHM) at the center of rotation were 8.1-11.9 mm (lead) and 6.7-10.3 mm (tungsten). Total tumor activity estimates from SPECT were within 17% of the true activities. SPECT activity concentration estimates in small regions of interest (ROIs) averaged -20% for the 20.5-ml sphere, -11% for the 97-ml sphere, -39% for the shell and +20% for the core of the shell-core phantom. Activity spillover due to limited spatial resolution and the tails of the system response functions biased the estimates. The shell-to-core activity concentration ratio of 4.1 was better estimated with the tungsten insert (2.3) than with the lead insert (1.9) due to better resolution. CONCLUSION: Pinhole SPECT is a promising technique for imaging and quantifying total 131I activity in regions the size of brain tumors. Relative errors were greater for activity concentration estimates in small ROIs than for total activity estimates.

Effect of registration errors between transmission and emission scans on a SPECT system using sequential scanning.

UNLABELLED: The purpose of this study was to evaluate the effects of patient motion on nonuniform attenuation correction of cardiac SPECT when the transmission and emission scans were performed sequentially. By using a sequential protocol rather than doing the scans simultaneously, contamination from the emission scan into the transmission scan could be eliminated, but registration of the two scans become a concern. METHODS: Transmission and emission scans were acquired using both an anthropomorphic thorax phantom containing a cardiac insert and a human volunteer. The types of motion considered were transverse shifts, axial shifts and rotations that occur in the time period between the transmission and emission scan. For this study, the various types of motion were simulated in the data. Both the transmission and emission data were reconstructed using filtered backprojection. A single-iteration Chang algorithm, modified for nonuniform attenuation correction, was used to further process the emission data. To evaluate the effects of motion errors, circumferential profiles, all normalized to the same scale, were generated for each case. The cardiac images reconstructed using registered data were considered references. Error profiles were generated by subtracting misaligned images from the reference and then normalizing the difference by the reference. For comparison purposes, an error profile was generated for the case in which no attenuation correction was performed. RESULTS: It was found that, for transverse and axial shifts of 2.9 cm, the normalized myocardial SPECT activity was decreased in certain regions of the heart by 20%-35%. For a 12 degrees rotational shift, the error was on the order of 10%-20%, compared to a normalized variation of 20%-25% in the image with no attenuation correction. CONCLUSION: The results indicate that registration errors of 2-3 cm can seriously affect image quality in both the phantom and human images.

The effect of gamma ray penetration on angle-dependent sensitivity for pinhole collimation in nuclear medicine.

The sensitivity of a pinhole collimator for gamma ray imaging in nuclear medicine is dependent on the angle of incidence of the gamma rays. The effect of penetration near the pinhole aperture on angle-dependent sensitivity was investigated using experimental measurements and numerical modeling. Projection data measurements were acquired with Tc-99m and I-131 point sources using tungsten pinhole inserts with 1.0 to 4.0 mm diameter apertures. Curves of the form sinx theta, where theta is the angle of the incident ray with the surface of the detector crystal, were fit to sensitivity measurements from the projection data. Experimentally measured x values were between 3.3 and 4.1 for Tc-99m and between 5.1 and 7.2 for I-131. Penetration near the pinhole aperture was modeled using (1) an expression for effective pinhole diameter that is a generalization of Anger's formula for normally incident photons and (2) a photon transport simulation code. Experimentally measured sensitivity exponents x from new and previously reported experimental observations were modeled within 15% by the numerical simulations. For modeling using the generalized expression for effective diameter the average error was 1.4% and the standard deviation was 7.7%. For the photon transport simulation code the average error was 1.5% and the standard deviation also was 7.7%. The effect of pinhole aperture design parameters on angle-dependent sensitivity for high resolution pinhole apertures was modeled using a photon transport simulation code. The sensitivity exponents x were greater for 364 keV photons than for 140 keV photons and were greater for small aperture diameters, small acceptance angles, and large aperture channel heights. These results provide theoretical justification for incorporating sinx theta sensitivity corrections, with x greater than the value of 3 for an impenetrable pinhole, in filtered back projection and iterative reconstruction algorithms for single photon emission computed tomography (SPECT) pinhole imaging. Simulated I-131 SPECT studies for uniformly active cylinders showed that activity concentrations were underestimated toward the outside of the cylinders when a sin3 theta rather than the correct sinx theta sensitivity correction was applied in image reconstruction.

Fully Bayesian estimation of Gibbs hyperparameters for emission computed tomography data.

In recent years, many investigators have proposed Gibbs prior models to regularize images reconstructed from emission computed tomography data. Unfortunately, hyperparameters used to specify Gibbs priors can greatly influence the degree of regularity imposed by such priors and, as a result, numerous procedures have been proposed to estimate hyperparameter values from observed image data. Many of these procedures attempt to maximize the joint posterior distribution on the image scene. To implement these methods, approximations to the joint posterior densities are required, because the dependence of the Gibbs partition function on the hyperparameter values is unknown. In this paper, we use recent results in Markov chain Monte Carlo (MCMC) sampling to estimate the relative values of Gibbs partition functions and using these values, sample from joint posterior distributions on image scenes. This allows for a fully Bayesian procedure which does not fix the hyperparameters at some estimated or specified value, but enables uncertainty about these values to be propagated through to the estimated intensities. We utilize realizations from the posterior distribution for determining credible regions for the intensity of the emission source. We consider two different Markov random field (MRF) models-the power model and a line-site model. As applications we estimate the posterior distribution of source intensities from computer simulated data as well as data collected from a physical single photon emission computed tomography (SPECT) phantom.

Approximate 3D iterative reconstruction for SPECT.

Compared with slice-by-slice approaches for SPECT reconstruction, three-dimensional iterative methods provide a more accurate physical model and an improved SPECT image. Clinical application of these methods, however, is limited primarily to their computational demands. This paper investigates the methods for approximate 3D iterative reconstruction that greatly reduce this demand by excluding from the reconstruction the smaller magnitude elements of the system matrix. A new method is described which is designed to control the resulting bias in the SPECT image for a given reduction in computation. The approximate methods were compared to fully 3D iterative reconstruction in terms of SPECT image bias and visual quality. All methods were incorporated into the ML-EM algorithm and applied to data from 3D mathematical and experimental brain phantoms. The SPECT images reconstructed by the approximate methods exhibited a positive bias throughout the image that was in general smaller with the new method (in the rage of 2%-6%). The bias was smallest in locally hot regions and largest in locally cold regions. The high quality brain phantom images demonstrated the capability of the new method in realistic imaging contexts. The time per iteration for an entire 3D brain phantom on a modern workstation using the approximate 3D method was 7.0 s.