Direct least-squares estimation of spatiotemporal distributions from dynamic SPECT projections using a spatial segmentation and temporal B-splines

Artifacts can result when reconstructing a dynamic image sequence from inconsistent, as well as insufficient and truncated, cone beam single photon emission computed tomography (SPECT) projection data acquired by a slowly rotating gantry. The artifacts can lead to biases in kinetic model parameters estimated from time-activity curves generated by overlaying volumes of interest on the images. However, the biases in time-activity curve estimates and subsequent kinetic parameter estimates can be reduced significantly by first modeling the spatial and temporal distribution of the radiopharmaceutical throughout the projected field of view, and then estimating the time-activity curves directly from the projections. This approach is potentially useful for clinical SPECT studies involving slowly rotating gantries, particularly those using a single-detector system or body contouring orbits with a multidetector system. We have implemented computationally efficient methods for fully four-dimensional (4-D) direct estimation of spatiotemporal distributions from dynamic SPECT projection data. Temporal B-splines providing various orders of temporal continuity, as well as various time samplings, were used to model the time-activity curves for segmented blood pool and tissue volumes in simulated cone beam and parallel beam cardiac data acquisitions. Least-squares estimates of time-activity curves were obtained quickly using a workstation. Given faithful spatial modeling, accurate curve estimates were obtained using cubic, quadratic, or linear B-splines and a relatively rapid time sampling during initial tracer uptake. From these curves, kinetic parameters were estimated accurately for noiseless data and with some bias for noisy data. A preliminary study of spatial segmentation errors showed that spatial model mismatch adversely affected quantitative accuracy, but also resulted in structured errors (projected model versus raw data) that were easily detected in our simulations. This suggests iterative refinement of the spatial model to reduce structured errors as an area of future research.     

Normal and pathological NCAT image and phantom data based on physiologically realistic left ventricle finite-element models

The four-dimensional (4-D) 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 4-D 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 multislice computed tomography (MSCT) data of a healthy male subject. The myocardial wall was represented as a transversely isotropic hyperelastic material, with the fiber angle varying from -90 degrees at the epicardial surface, through 0 degrees at the midwall, 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 as the 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 4-D 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 Single photon emission computed tomography (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 4-D NCAT beating heart model based on tagged magnetic resonance imaging (MRI) data. The addition of a subendocardial ischemic region changed the average transmural circumferential strain from a contractile value of -0.09 to a tensile value of 0.02. The addition of a transmural ischemic region changed average circumferential strain to a value of 0.13, 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 4-D NCAT phantom. Compared with 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 4-D NCAT phantom, has great potential for use in cardiac imaging research. With its enhanced physiologically based cardiac model, the 4-D 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 4-D imaging techniques used in the diagnosis of cardiac disease.     

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm

Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigen-values. This paper also investigates the effects when unmatched projector/backprojector pairs are used.     

Constitutive expression of the Wilms'' tumor gene (WT1) in the leukemic cell line U937 blocks parts of the differentiation program

OBJECTIVE: To characterize relationships among blood pressure, pulse rate, vitamin C status and other protective and risk factors for older British people, from a national survey. DESIGN: A cross-sectional analysis of survey data. SETTING: A population study, representative of mainland Britain. SUBJECTS: Among 914 people of both sexes living in the community, 373 were taking blood-pressure-lowering drugs and were therefore excluded from the analyses. INTERVENTIONS: Completion of an interview on health, lifestyle and dietary habits, recording of a 4-day dietary record, anthropometry and taking of a blood sample to determine haematological and biochemical status. MAIN OUTCOME MEASURES: Systolic and diastolic blood pressures, pulse rate, indices of micronutrient status including plasma ascorbate concentration, nutrient intake and haematology. RESULTS: Plasma ascorbate concentration was inversely correlated to systolic and diastolic blood pressures and pulse rate. Other covariates of blood pressure included age, sex, domicile, plasma retinol, fibrinogen and gamma-tocopherol concentrations, erythrocyte count, prothrombin time and urine sodium: creatinine ratio. Covariates of pulse rate included sex, domicile, plasma fibrinogen and platelet count. Blood pressure was also correlated to intake of vitamin C. CONCLUSIONS: Plasma ascorbate concentration and intake of vitamin C are covariates of blood pressure in older people living in Britain. New intervention studies are now needed, to test for possible causalities.     

An SVD study of truncated transmission data in SPECT

Even though a noiseless, band-limited function is uniquely determined by its values in a local region, single photon emission computed tomography (SPECT) projections are not band-limited, and unmeasured projections may not be possible to be exactly estimated from the measured data. Projections from all views should be considered simultaneously and are modeled as a set of linear equations. The singular value decomposition (SVD) method is used to analyze and solve the equations. It is shown that truncation does not always result in an underdetermined problem, yet the problem may be ill-conditioned. An inaccurate pixel model may cause reconstruction artifacts via mismatch between the measured data and the modeled projections     

Helical SPECT using axially truncated data

In this study, use of a helical orbit in performing a long object SPECT scan with parallel, cone, fan, rotated fan, varying focal-length cone, divergent, and astigmatic collimators is proposed. Sufficient-data scanning helical orbits for these collimation geometries are developed. Both a single-detector system and a multi-detector system are considered. In order to verify the authors' orbit design requirement, the iterative ML-EM algorithm is used to reconstruct images of a long Defrise phantom. The phantom height is five times the height of the detectors. Computer simulations are performed and exact reconstructions are obtained. The proposed sufficient helical orbit pitch will facilitate performing whole body SPECT and PET scans that demand an exact reconstruction     

Correction for ambiguous solutions in factor analysis using a penalized least squares objective

Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of factor analysis of dynamic structures (FADS) is that the solution is not mathematically unique when only nonnegativity constraints are used to determine factors and factor coefficients. In this paper, a method to correct for ambiguous FADS solutions has been developed. A nonambiguous solution (to within certain scaling factors) is obtained by constructing and minimizing a new objective function. The most common objective function consists of a least squares term that when minimized with nonnegativity constraints, forces agreement between the applied factor model and the measured data. In our method, this objective function is modified by adding a term that penalizes multiple components in the images of the factor coefficients. Due to nonuniqueness effects, these factor coefficients consist of more than one physiological component. The technique was tested on computer simulations, an experimental canine cardiac study using 99mTc-teboroxime, and a patient planar 99mTc-MAG3 renal study. The results show that the technique works well in comparison to the truth in computer simulations and to region of interest (ROI) measurements in the experimental studies.     

Fan-beam reconstruction algorithm for a spatially varying focal length collimator

Fan-beam collimators are used in single-photon-emission computed tomography (SPECT) to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself, producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constructed so that the shortest focal lengths are located at the center of the collimator and the longest focal length is located at the periphery. The focal length is assumed to increase monotonically toward the edge of the collimator. A reconstruction algorithm for this type of fan-beam collimation, expressed as an infinite series of convolutions followed by one backprojection, is presented. Simulations show that only a small number of N terms in the series is needed to obtain high-quality reconstructions. Computer simulations showed that if the focal length function is smooth, the reconstructions are free of artifacts.     

Lobbying friends and foes in climate policy: The case of business and environmental interest groups in the European Union

Drawing on two conflicting hypotheses from the theoretical literature on lobbying, I consider the strategies applied by interest groups lobbying to influence climate policy in the European Union (EU). The first hypothesis claims that interest groups lobby their ‘friends’, decision-makers with positions similar to their own. The second claims that interest groups lobby their ‘foes’, decision-makers with positions opposed to their own. Using interviews with lobbyists and decision-makers, I demonstrate that in the field of climate policy, interest groups in the EU lobby both friends and foes, but under different conditions. Moreover, I find that the interest groups’ motives are not always in line with the theoretical hypotheses. Interest groups lobby their friends on single policy decisions to exchange information, to further a common cause and to exert pressure, and their foes because a foe on one issue might prove to be a friend on another issue. Interest groups direct general lobbying towards both friends and foes. This paper provides a new empirical contribution to a literature that has so far been heavily dominated by studies focusing on lobbying in the US.