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.     

Fast transmission CT for determining attenuation maps using a collimated line source, rotatable air-copper-lead attenuators and fan-beam collimation

We describe a technique using a line source and a rotatable air-copper-lead assembly to acquire gamma transmission computed tomographic (TCT) data for determining attenuation maps to compensate SPECT emission scans. The technique minimizes problems associated with discriminating 99mTc transmission and 201Tl emission photons and requires only a modest increase in total study time. A 99mTc line source and a stacked foil ("multislat") collimator are placed near the focal line of a fan-beam collimator (114 cm focal length) mounted on one detector of a triple-camera SPECT system. We acquired TCT data of plastic rod and anthropomorphic thorax phantoms to investigate the capability of the line source and rotatable air-copper-lead attenuators to determine attenuation maps. The data were acquired with and without 5.4 MBq (145 microCi) of 201Tl placed in the myocardial chamber of the thorax phantom. Phantoms also were scanned using a curved transmission slab source mounted to a parallel-hole collimator. Fan-beam TCT images have improved resolution compared with parallel-beam TCT images. Two patient scans also were performed to evaluate the clinical usefulness of fan-beam TCT. The rotatable air-copper-lead attenuator method eliminates contamination of emission data by transmission photons and reduces spill-over of emission data into the transmission energy window for some cases. Results show the feasibility of using fast, sequential or interlaced transmission scans of a line source within a rotatable air-copper-lead attenuator assembly to obtain accurate attenuation maps for SPECT attenuation compensation.     

SPECT: Single Photon Emission Computed Tomography

Interest in single photon emission computed tomography (SPECT) has been renewed as a result of the successful application of transmission (x-ray) CT to diagnostic radiology. Many aspects of SPECT are different from those encountered in transmission CT, and often are more difficult to overcome. Examples of two major aspects encountered are 1) the limitations on the available photon flux imposed mainly by dose considerations to the patient and, 2) the internal attenuation of gamma rays within the patient prior to detection. Progress has been made recently in overcoming the quantum limitation by designing SPECT systems using special collimation and large active detector areas. High efficiency systems have been designed and built using both multiple-scanners and also using multiple large-field-of-view scintillation cameras. Much progress has also been made in compensating for the problem of gamma ray attenuation using iterative and analytical approaches. This paper reviews the history of single photon emission tomography, characterizes the physical attributes of SPECT, describes some solutions to the inherent problems encountered, and also reviews a few selected approaches in designing SPECT systems to provide high quality, artifact-free reconstructed images. It is anticipated that future developments will allow SPECT systems to more nearly attain the ultimate goal of determining absolute regional radionuclide concentration as a function of time. These systems, coupled with newly developed physiological radiopharmaceuticals, can provide useful research and clinical information.     

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.     

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.     

On Bayesian image reconstruction from projections: uniform and nonuniform a priori source information

A method that incorporates a priori uniform or nonuniform source distribution probabilistic information and data fluctuations of a Poisson nature is presented. The source distributions are modeled in terms of a priori source probability density functions. Maximum a posteriori probability solutions, as determined by a system of equations, are given. Interactive Bayesian imaging algorithms for the solutions are derived using an expectation maximization technique. Comparisons of the a priori uniform and nonuniform Bayesian algorithms to the maximum-likelihood algorithm are carried out using computer-generated noise-free and Poisson randomized projections. Improvement in image reconstruction from projections with the Bayesian algorithm is demonstrated. Superior results are obtained using the a priori nonuniform source distribution.     

Solid geometry-based object model for Monte Carlo simulated emission and transmission tomographic imaging systems

An object model based on combinations of object primitives is proposed for Monte Carlo simulated emission and transmission tomographic imaging systems. The primitives include ellipsoids, elliptic cylinders, tapered elliptic cylinders, rectangular solids, and their subsets: half, quarter, and eighth. The probability of a photon surviving interactions with the phantom medium is used as a weight for variance reduction. Calculation of the probability can be computationally intensive without properly organizing the inclusion of subregions within larger regions. A tree data structure is introduced to organize this inclusion relationship and used as the basis for two computationally efficient schemes for determining the intersection locations of a photon path with primitives and for identifying the attenuation coefficients for adjacent intersections for the survival probability computation. The approach has been validated by emission as well as transmission simulations. A thorax phantom containing overlapped ellipsoids and a heart composed of twelve overlapped quarter ellipsoids are employed to demonstrate the capability of the model.     

Physical and biological predictors of changes in whole-lung function following thoracic irradiation

PURPOSE: To develop methods of predicting the pulmonary consequences of thoracic irradiation (RT) by prospectively studying changes in pulmonary function following RT. METHODS AND MATERIALS: 100 patients receiving incidental partial-lung irradiation during treatment of tumors in or adjacent to the thorax had whole-lung function assessed via symptoms and pulmonary function tests (PFTs: FEV1-forced expiratory volume 1 s; DLCO-diffusion capacity) before and repeatedly 6-48 months following RT. All had computed tomography-based three-dimensional (3D) dose calculations with lung density heterogeneity corrections for dose-volume histogram (DVH) and normal tissue complication probability (NTCP) calculations. Functional DVHs (DVfH) based on SPECT (single photon emission computed tomography) lung perfusion scans, and serial transforming growth factor-beta (TGF-beta1) levels were available in 50 and 48 patients, respectively. The incidence and severity of changes in whole-lung function were correlated with clinical, physical, and biological factors. Exploratory statistical analyses were performed using chi-square, Pearson correlations, logistic regression, and multiple linear regression. RESULTS: RT-induced symptoms developed in 21 patients. In the overall group, the single best predictor for the development of symptoms was the NTCP (p < 0.05). Pre-RT PFTs alone were less predictive (p = 0.1 for FEV1, p = 0.08 for DLCO). A multivariate model based on pre-RT DLCO and CT-based NTCP was strongly predictive for the development of symptoms (p < 0.001). NTCPs based on SPECT-derived DVf Hs and TGF-beta1 levels did not appear to provide additional predictive value. The presence or absence of pulmonary symptoms was correlated with the decline in PFT 6 months following RT (p < 0.05). In the overall group, the degree of decline in PFTs was not well correlated with any of the dose-volume variables considered. In patients with "good" pre-RT PFTs, there was a relationship between the percent reduction in PFT and dose-volume parameters such as the percent of lung volume receiving > 30 Gy (p < 0.05). CONCLUSION: The extent of alteration in whole-lung function (symptoms or PFT changes) appears to be related to both dose-volume and pre-RT PFT parameters. The data suggest that no one variable is likely to be an adequate predictor and that multivariate predictive models will be needed. Additional studies are underway to develop better predictive models that consider physical factors such as the DVH and regional perfusion, as well as biological/clinical factors such as pre-RT PFTs and TGF-beta1.