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The 4D NURBS-based Cardiac-Torso (NCAT) phantom, which provides a realistic model of the normal human anatomy and cardiac and respiratory motions, is used in medical imaging research to evaluate and improve imaging devices and techniques, especially dynamic cardiac applications. One limitation of the phantom is that it lacks the ability to accurately simulate altered functions of the heart that result from cardiac pathologies such as coronary artery disease (CAD). The goal of this work was to enhance the 4D NCAT phantom by incorporating a physiologically based, finite-element (FE) mechanical model of the left ventricle (LV) to simulate both normal and abnormal cardiac motions. The geometry of the FE mechanical model was based on gated high-resolution x-ray multi-slice computed tomography (MSCT) data of a healthy male subject. The myocardial wall was represented as transversely isotropic hyperelastic material, with the fiber angle varying from -90 degrees at the epicardial surface, through 0 degrees at the mid-wall, to 90 degrees at the endocardial surface. A time varying elastance model was used to simulate fiber contraction, and physiological intraventricular systolic pressure-time curves were applied to simulate the cardiac motion over the entire cardiac cycle. To demonstrate the ability of the FE mechanical model to accurately simulate the normal cardiac motion as well abnormal motions indicative of CAD, a normal case and two pathologic cases were simulated and analyzed. In the first pathologic model, a subendocardial anterior ischemic region was defined. A second model was created with a transmural ischemic region defined in the same location. The FE based deformations were incorporated into the 4D NCAT cardiac model through the control points that define the cardiac structures in the phantom which were set to move according to the predictions of the mechanical model. A simulation study was performed using the FE-NCAT combination to investigate how the differences in contractile function between the subendocardial and transmural infarcts manifest themselves in myocardial SPECT images. The normal FE model produced strain distributions that were consistent with those reported in the literature and a motion consistent with that defined in the normal 4D NCAT beating heart model based on tagged MRI data. The addition of a subendocardial ischemic region changed the average transmural circumferential strain from a contractile value of 0.19 to a tensile value of 0.03. The addition of a transmural ischemic region changed average circumferential strain to a value of 0.16, which is consistent with data reported in the literature. Model results demonstrated differences in contractile function between subendocardial and transmural infarcts and how these differences in function are documented in simulated myocardial SPECT images produced using the 4D NCAT phantom. In comparison to the original NCAT beating heart model, the FE mechanical model produced a more accurate simulation for the cardiac motion abnormalities. Such a model, when incorporated into the 4D NCAT phantom, has great potential for use in cardiac imaging research. With its enhanced physiologically-based cardiac model, the 4D NCAT phantom can be used to simulate realistic, predictive imaging data of a patient population with varying whole-body anatomy and with varying healthy and diseased states of the heart that will provide a known truth from which to evaluate and improve existing and emerging 4D imaging techniques used in the diagnosis of cardiac disease.

The performance of the Channelized Hotelling Observer (CHO) was compared to that of human observers for determining optimum parameters for the iterative OS-EM image reconstruction method for the task of defect detection in myocardial SPECT images. The optimum parameters were those that maximized defect detectability in the SPECT images. Low noise, parallel SPECT projection data, with and without an anterior, inferior or lateral LV wall defect, were simulated using the Monte Carlo method. Poisson noise was added to generate noisy realizations. Data were reconstructed using OS-EM at 1 & 4 subsets/iteration and at 1, 3, 5, 7 & 9 iterations. Images were converted to 2D short-axis slices with integer pixel values. The CHO used 3 radially-symmetric, 2D channels, with varying levels of internal observer noise. For each parameter setting, 600 defect-present and 600 defect-absent image vectors were used to calculate the detectability index (dA). The human observers rated the likelihood that a defect was present in a specified location. For each parameter setting, the AUC was estimated from 48 defect-present and 48 defect-absent images. The combined human observer results showed the optimum parameter setting could be in the range 5-36 updates ([number of subsets]/iteration e number of iterations). The CHO results showed the optimum parameter setting to be 4-5 updates. The performance of the CHO was much more sensitive to the reconstruction parameter setting than was that of the human observers. The rankings of the CHO detectability values did not change with varying levels of internal noise.

With continuing improvements in spatial resolution of positron emission tomography (PET) scanners, small patient movements during PET imaging become a significant source of resolution degradation. This work develops and investigates a comprehensive formalism for accurate motion-compensated reconstruction which at the same time is very feasible in the context of high-resolution PET. In particular, this paper proposes an effective method to incorporate presence of scattered and random coincidences in the context of motion (which is similarly applicable to various other motion correction schemes). The overall reconstruction framework takes into consideration missing projection data which are not detected due to motion, and additionally, incorporates information from all detected events, including those which fall outside the field-of-view following motion correction. The proposed approach has been extensively validated using phantom experiments as well as realistic simulations of a new mathematical brain phantom developed in this work, and the results for a dynamic patient study are also presented. Index Terms--Positron emission tomography (PET) iterative reconstruction, motion correction, system response.

Rotating multisegment slant-hole (RMSSH) single photon emission computed tomography (SPECT) is suitable for detecting small and low-contrast breast lesions since it has much higher detection efficiency than conventional SPECT with a parallel-hole collimator and can image the breast at a closer distance. Our RMSSH SPECT reconstruction extends a previous rotation-shear transformation-based method to include nonuniform attenuation and collimator-detector response (CDR) compensation. To evaluate our reconstruction method, we performed two phantom simulation studies with 1) an isolated breast and 2) a breast phantom attached to the body torso. The reconstructed RMSSH SPECT images with attenuation and CDR compensation showed improved quantitative accuracy and less image artifacts than without. To evaluate the clinical efficacy of RMSSH SPECT mammography, we used a simulation study to compare with planar scintimammography in terms of the signal-to-noise ratio (SNR) value of a breast lesion. The RMSSH SPECT reconstruction images showed higher SNR value than the planar scintimammography images and even more so as we applied compensation for attenuation and collimator detector response. We conclude that attenuation and CDR compensation provide RMSSH SPECT mammography images with improved quality and quantitative accuracy.

To further improve pinhole single photon emission computed tomography (SPECT) imaging, there have been increasing interests in the use of nonstandard collimator designs and/or acquisition geometries. Homogeneous coordinates provide a compact and convenient framework to unify the geometric descriptions of the projection operators for these different imaging geometries, which may facilitate the implementation of iterative reconstruction algorithms and the investigation of crucial geometric calibration problems in pinhole SPECT. In this work, these advantages were demonstrated through three examples, namely, multipinhole SPECT, pinhole SPECT with a helical scanning orbit, and pinhole SPECT with dual detectors. Specifically, we showed adaptable implementations of iterative image reconstruction algorithms and translatable strategies for efficient geometric calibrations through unifying projection operators of the aforementioned imaging geometries. Notably, the unified geometric descriptions of multipinhole and single pinhole projection operators allowed us to derive that one can effectively calibrate a multipinhole geometry using only two point sources without measuring their distance. Experimental studies were performed to demonstrate the validity of our approaches, which may be extended to other pinhole SPECT and cone-beam X-ray computed tomography imaging geometries. Index Terms--Calibration, emission computed tomography, geometry, image reconstruction, single photon.

Receiver operating characteristic (ROC) analysis is well established in the evaluation of systems involving binary classification tasks. However, medical tests often require distinguishing among more than two diagnostic alternatives. The goal of this work was to develop an ROC analysis method for three-class classification tasks. Based on decision theory, we developed a method for three-class ROC analysis. In this method, the objects were classified by making the decision that provided the maximal utility relative to the other two. By making assumptions about the magnitudes of the relative utilities of incorrect decisions, we found a decision model that maximized the expected utility of the decisions when using log-likelihood ratios as decision variables. This decision model consists of a two-dimensional decision plane with log likelihood ratios as the axes and a decision structure that separates the plane into three regions. Moving the decision structure over the decision plane, which corresponds to moving the decision threshold in two-class ROC analysis, and computing the true class 1, 2, and 3 fractions defined a three-class ROC surface. We have shown that the resulting three-class ROC surface shares many features with the two-class ROC curve; i.e., using the log likelihood ratios as the decision variables results in maximal expected utility of the decisions, and the optimal operating point for a given diagnostic setting (set of relative utilities and disease prevalences) lies on the surface. The volume under the three-class surface (VUS) serves as a figure-of-merit to evaluate different data acquisition systems or image processing and reconstruction methods when the assumed utility constraints are relevant. Index Terms--Ideal observers, ROC analysis, three-class classification.

Partial volume (PV) effects degrade the quantitative accuracy of SPECT brain images. In this paper, we extended a PV compensation (PVC) method originally developed for brain PET, the geometric transfer matrix (GTM) method, to brain SPECT using iterative reconstruction-based compensations. In the GTM method a linear transform between the true regional activities and the measured results was assumed. Elements of the GTM were calculated by projecting and reconstructing maps with uniform regions representing different structures. However, with iterative reconstruction methods, especially when reconstruction-based compensation for detector response was applied, we found that it was important to treat the region maps as a perturbation to the reconstructed image in the estimation of the GTM. This modified method, termed perturbation-based GTM (pGTM) was evaluated using Monte Carlo (MC) simulated and experimentally acquired data. Results showed great improvement of the quantitative accuracy in brain SPECT imaging. For MC simulated data, PVC using pGTM reduced the underestimation of striatal activities from 30% to less than 1.2%. For experimental data, PVC using pGTM reduced the underestimation of striatal activities from 36% to less than 7.8%. The underestimation of the striatum to background activity ratio was also improved from 31% to 2.7%. Index Terms--Brain SPECT imaging, partial volume effect compensation, quantification.

In this paper, we apply the channelized Hotelling observer (CHO) using a defect detection task to the optimization and evaluation of three-dimensional iterative reconstruction-based compensation methods for myocardial perfusion single-photon emission computed tomography (SPECT). We used a population of 24 mathematical cardiac-torso phantoms that realistically model the activity and attenuation distribution in three classes of patients: females, and males with flat diaphragms and raised diaphragms. Projection data were generated and subsequently reconstructed using methods based on the ordered subsets-expectation maximization (OSEM) algorithm. The methods evaluated included compensation for attenuation, detector response blurring, and scatter in various combinations. We applied the CHO to optimize the number of iterations for OSEM and the cutoff frequency and order of a three-dimensional postreconstruction Butterworth filter. Using the optimal parameters, we then compared the compensation methods. The index of comparison in these studies was the area under the receiver operating characteristics curve (AUC) for the CHO. We found that attenuation compensation with either detector response or scatter compensation gave statistically significant increases in the AUC compared to attenuation compensation alone. The greatest increase in the AUC occurred when all three compensations were applied. These results indicate that compensation for detector response and scatter, in addition to attenuation compensation, will improve defect detectability in myocardial SPECT images. Index Terms--Attenuation compensation, mathematical observers, scatter compensation, SPECT.

We investigate the effects of initial conditions in the iterative maximum-likelihood (ML) reconstruction of fan-beam transmission projection data with truncation. In an iterative ML reconstruction, the estimate of the transmission reconstructed image in the previous iteration is multiplied by some factors to obtain the current estimate. Normally, a fiat initial condition (FIC) or an image with equal positive pixel values is used as initial condition for an ML reconstruction. Usage of FIC has also been perceived as a way of preventing any bias on the reconstruction which may have come from the initial condition. When projection data have truncation, we show that using an FIC in an ML iterative reconstruction can introduce a bias to the reconstruction inside the densely sampled region (DSR), whose projection data have no truncation at any angle. To reduce this bias, we propose to use the largest right singular vector (LRSV) of the system matrix as the initial condition, and demonstrate that the bias can be reduced with the LRSV. When data truncation is reduced, the LRSV approaches the FIC. This result does not contradict to the use of FIC when projection data are not truncated. We also demonstrate that the reconstructed transmission image using LRSV as initial condition provides a more accurate attenuation coefficient distribution than that using FIC. However, the improvement is mostly in the area outside the DSR. Index Terms - Fan beam, image reconstruction, initial condition, SPECT, transmission imaging.

Maximum a posteriori (MAP) reconstruction in SPECT has been shown to have significant advantages over traditional maximum likelihood (ML) methods in terms of noise performance, but these advantages are highly dependent on the choice of the distribution used to model the prior knowledge about the solution image. Several Gibbs prior distributions have been proposed in the literature, but there has been relatively little work comparing and contrasting the effects of these prior distributions on actual reconstructions. We demonstrate the effects of several of these prior distributions in terms of noise characteristics, edge sharpness, and overall quantitative accuracy of the final estimates obtained from an iterative MAP procedure applied to data from a realistic chest phantom. We also examine the effects of the adjustable parameters built into the prior distribution on these properties. We find that these parameter values influence the noise and edge characteristics of the final estimate and can generate reconstructions closer to the actual solution than ML. In addition, we find that the choice of the shape of the prior distribution affects the noise characteristics and edge sharpness in the final estimate.