Model-based estimation for dynamic cardiac studies using ECT

Direct List Mode Parametric Reconstruction for Dynamic Cardiac SPECT

Recently introduced stationary dedicated cardiac SPECT scanners provide new opportunities to quantify myocardial blood flow (MBF) using dynamic SPECT. However, comparing to PET, the low sensitivity of SPECT scanners affects MBF quantification due to the high noise level, especially for 201 Thallium (201Tl) due to its typically low injected dose. The conventional indirect method for generating parametric images typically starts by reconstructing a time series of frame images followed by fitting the time-activity curve (TAC) for each voxel or segment with an appropriate kinetic model. The indirect method is simple and easy to implement; however, it usually suffers from substantial image noise that could also lead to bias. In this paper, we developed a list mode direct parametric image reconstruction algorithm to substantially reduce noise in MBF quantification using dynamic SPECT and allow for patient radiation dose reduction. GPU-based parallel computing was used to achieve more than 2000-fold acceleration. The proposed method was evaluated in both simulation and in vivo canine studies. Compared with the indirect method, the proposed direct method achieved substantially lower image noise and variability, particularly at large number of iterations and at low-count levels.

Direct estimation of kinetic parametric images for dynamic PET

Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed.

Selection of weighting factors for quantification of PET radioligand binding using simplified reference tissue models with noisy input functions

Input function noise contributes to model-predicted values and should be accounted for during parameter estimation. This problem has been examined in the context of PET data analysis using a noisy image-derived arterial input function. Huesman and Mazoyer (1987 Phys. Med. Biol 32 1569-79) incorporated the effect of error in the measured input function into the objective function and observed a subsequent improvement in the accuracy of parameters estimated from a kinetic model of cardiac blood flow. Such a treatment has not been applied to the reference region models commonly used to analyze dynamic positron emission tomography data with receptor-ligand tracers. Here, we propose a strategy for selection of weighting factors that accounts for noise in the reference region input function and test the method on two common formulations of the simplified reference tissue model (SRTM). We present a simulation study which demonstrates that the proposed weighting approach improves the accuracy of estimated binding potential at high noise levels and when the reference tissue and target regions of interest are of comparable size. In the second simulation experiment, we show that using a small, homogeneous reference tissue with our weighting technique may have advantages over input functions derived from a larger (and thus less noisy), heterogeneous region with conventional weighting. A comparative analysis of clinical [(11)C]flumazenil data found a small but significant increase in estimated binding potential when using the proposed weighting method, consistent with the finding of reduced negative bias in our simulation study. The weighting strategy described here accounts for noise in the reference region input function and may improve the performance of the SRTM in applications where data are noisy and the reference region is relatively small. This technique may offer similar benefits to other models using reference region inputs, particularly those derived from the SRTM.

Direct 4D parametric imaging for linearized models of reversibly binding PET tracers using generalized AB-EM reconstruction

Due to high noise levels in the voxel kinetics, development of reliable parametric imaging algorithms remains one of most active areas in dynamic brain PET imaging, which in the vast majority of cases involves receptor/transporter studies with reversibly binding tracers. As such, the focus of this work has been to develop a novel direct 4D parametric image reconstruction scheme for such tracers. Based on a relative equilibrium (RE) graphical analysis formulation (Zhou et al 2009b Neuroimage 44 661-70), we developed a closed-form 4D EM algorithm to directly reconstruct distribution volume (DV) parametric images within a plasma input model, as well as DV ratio (DVR) images within a reference tissue model scheme (wherein an initial reconstruction was used to estimate the reference tissue time-activity curves). A particular challenge with the direct 4D EM formulation is that the intercept parameters in graphical (linearized) analysis of reversible tracers (e.g. Logan or RE analysis) are commonly negative (unlike for irreversible tracers, e.g. using Patlak analysis). Subsequently, we focused our attention on the AB-EM algorithm, derived by Byrne (1998, Inverse Problems 14 1455-67) to allow inclusion of prior information about the lower (A) and upper (B) bounds for image values. We then generalized this algorithm to the 4D EM framework, thus allowing negative intercept parameters. Furthermore, our 4D AB-EM algorithm incorporated and emphasized the use of spatially varying lower bounds to achieve enhanced performance. As validation, the means of parameters estimated from 55 human (11)C-raclopride dynamic PET studies were used for extensive simulations using a mathematical brain phantom. Images were reconstructed using conventional indirect as well as proposed direct parametric imaging methods. Noise versus bias quantitative measurements were performed in various regions of the brain. Direct 4D EM reconstruction resulted in notable qualitative and quantitative accuracy improvements (over 35% noise reduction, with matched bias, in both plasma and reference-tissue input models). Similar improvements were also observed in the coefficient of variation of the estimated DV and DVR values even for relatively low uptake cortical regions, suggesting the enhanced ability for robust parameter estimation. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomograph wherein the proposed method was shown across a variety of regions to outperform the conventional method in the sense that for a given DVR value, improved noise levels were observed.

Use of Cramer-Rao Lower Bound for Performance Evaluation of Different Monolithic Crystal PET Detector Designs

We have previously reported on continuous miniature crystal element (cMiCE) PET detectors that provide depth of interaction (DOI) positioning capability. A key component of the design is the use of a statistics-based positioning (SBP) method for 3D event positioning. The Cramer-Rao lower bound (CRLB) expresses limits on the estimate variances for a set of deterministic parameters. We examine the CRLB as a useful metric to evaluate the performance of our SBP algorithm and to quickly compare the best possible resolution when investigating new detector designs.In this work, the CRLB is first reported based upon experimental results from a cMiCE detector using a 50×50×15-mm(3) LYSO crystal readout by a 64-channel PMT (Hamamatsu H8500) on the exit surface of the crystal. The X/Y resolution is relatively close to the CRLB, while the DOI resolution is more than double the CRLB even after correcting for beam diameter and finite X (i.e., reference DOI position) resolution of the detector. The positioning performance of the cMiCE detector with the same design was also evaluated through simulation. Similar with the experimental results, the difference between the CRLB and measured spatial resolution is bigger in DOI direction than in X/Y direction.Another simulation study was conducted to investigate what causes the difference between the measured spatial resolution and the CRLB. The cMiCE detector with novel sensor-on-entrance-surface (SES) design was modeled as a 49.2×49.2×15-mm(3) LYSO crystal readout by a 12×12 array of 3.8×3.8-mm(2) silicon photomultiplier (SiPM) elements with 4.1-mm center-to-center spacing on the entrance surface of the crystal. The results show that there are two main causes to account for the differences between the spatial resolution and the CRLB. First, Compton scatter in the crystal degrades the spatial resolution. The DOI resolution is degraded more than the X/Y resolution since small angle scatter is preferred. Second, our maximum likelihood (ML) clustering algorithm also has limitations when developing 3D look up tables during detector calibration.

Dynamic single photon emission computed tomography--basic principles and cardiac applications

The very nature of nuclear medicine, the visual representation of injected radiopharmaceuticals, implies imaging of dynamic processes such as the uptake and wash-out of radiotracers from body organs. For years, nuclear medicine has been touted as the modality of choice for evaluating function in health and disease. This evaluation is greatly enhanced using single photon emission computed tomography (SPECT), which permits three-dimensional (3D) visualization of tracer distributions in the body. However, to fully realize the potential of the technique requires the imaging of in vivo dynamic processes of flow and metabolism. Tissue motion and deformation must also be addressed. Absolute quantification of these dynamic processes in the body has the potential to improve diagnosis. This paper presents a review of advancements toward the realization of the potential of dynamic SPECT imaging and a brief history of the development of the instrumentation. A major portion of the paper is devoted to the review of special data processing methods that have been developed for extracting kinetics from dynamic cardiac SPECT data acquired using rotating detector heads that move as radiopharmaceuticals exchange between biological compartments. Recent developments in multi-resolution spatiotemporal methods enable one to estimate kinetic parameters of compartment models of dynamic processes using data acquired from a single camera head with slow gantry rotation. The estimation of kinetic parameters directly from projection measurements improves bias and variance over the conventional method of first reconstructing 3D dynamic images, generating time-activity curves from selected regions of interest and then estimating the kinetic parameters from the generated time-activity curves. Although the potential applications of SPECT for imaging dynamic processes have not been fully realized in the clinic, it is hoped that this review illuminates the potential of SPECT for dynamic imaging, especially in light of new developments that enable measurement of dynamic processes directly from projection measurements.

A survey of approaches for direct parametric image reconstruction in emission tomography

The quantitative data obtained by emission tomography are decoded using a number of techniques and methods in sequence to provide physiological information. Conventionally, the data are reconstructed to produce a series of static images. Then, pharmacokinetic modeling techniques are applied, and kinetic parameters that have physiological or functional significance are derived. Although it is possible to optimize each estimation step in this process, many simplifying assumptions have to be introduced to make the methods that are used practicable. Published research has shown that if the kinetic parameters are estimated directly from the measured data, the parametric images will have higher quality and lower mean-squared error than if this was done indirectly. This review highlights some aspects of the methods that have been proposed for such direct estimation of pharmacokinetic information from raw emission data.

Level set method for positron emission tomography

In positron emission tomography (PET), a radioactive compound is injected into the body to promote a tissue-dependent emission rate. Expectation maximization (EM) reconstruction algorithms are iterative techniques which estimate the concentration coefficients that provide the best fitted solution, for example, a maximum likelihood estimate. In this paper, we combine the EM algorithm with a level set approach. The level set method is used to capture the coarse scale information and the discontinuities of the concentration coefficients. An intrinsic advantage of the level set formulation is that anatomical information can be efficiently incorporated and used in an easy and natural way. We utilize a multiple level set formulation to represent the geometry of the objects in the scene. The proposed algorithm can be applied to any PET configuration, without major modifications.

Tomographic reconstruction of dynamic cardiac image sequences

In this paper, we propose an approach for the reconstruction of dynamic images from a gated cardiac data acquisition. The goal is to obtain an image sequence that can show simultaneously both cardiac motion and time-varying image activities. To account for the cardiac motion, the cardiac cycle is divided into a number of gate intervals, and a time-varying image function is reconstructed for each gate. In addition, to cope with the under-determined nature of the problem, the time evolution at each pixel is modeled by a B-spline function. The dynamic images for the different gates are then jointly determined using maximum a posteriori estimation, in which a motion-compensated smoothing prior is introduced to exploit the similarity among the different gates. The proposed algorithm is evaluated using a dynamic version of the 4-D gated mathematical cardiac torso phantom simulating a gated single photon emission computed tomography perfusion acquisition with Technitium-99m labeled Teboroxime. We thoroughly evaluated the performance of the proposed algorithm using several quantitative measures, including signal-to-noise ratio analysis, bias-variance plot, and time activity curves. Our results demonstrate that the proposed joint reconstruction approach can improve significantly the accuracy of the reconstruction.

Image reconstruction

We give an overview of the role of Physics in Medicine and Biology in the development of tomographic reconstruction algorithms. We focus on imaging modalities involving ionizing radiation, CT, PET and SPECT, and cover a wide spectrum of reconstruction problems, starting with classical 2D tomography in the 1970s up to 4D and 5D problems involving dynamic imaging of moving organs.

Direct reconstruction of kinetic parameter images from dynamic PET data

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Polygonal and polyhedral contour reconstruction in computed tomography

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Vertice estimation is done without using a voxel approximation of the 3-D image. It is based on the construction and optimization of a regularized criterion that accounts for surface smoothness. We investigate original deterministic local algorithms, based on the exact computation of the line projections, their update, and their derivatives with respect to the vertice coordinates. Results are first derived in the two-dimensional (2-D) case, which consists of reconstructing a 2-D object of deformable polygonal contour from its tomographic data. Then, we investigate the 3-D extension that requires technical adaptations. Simulation results illustrate the performance of polygonal and polyhedral reconstruction algorithms in terms of quality and computation time.

Kinetic parameter estimation from renal measurements with a three-headed SPECT system: a simulation study

We present here a direct least-squares estimation (DLSE) method for the determination of renal kinetic parameters from sequences of very fast acquisitions performed with a three-headed single photon emission computed tomography (SPECT) system. A simple linear model for the behavior of the radiopharmaceutical, as well as a spatial model for its spatial distribution are defined. The model enables one to estimate the kinetic parameters directly from the projections, once the plasma concentration function is known. A new technique for the accurate reconstruction of time-radioactivity curves based on the direct reconstruction of the region-of-interest contents from a series of data from three-projections is presented. The technique is used to determine the plasma concentration function with a sub-second time resolution. The spatially-variant geometrical response is also included in the model to compensate for the spatial resolution of the SPECT system. Results obtained from simulations are presented. Basic spatial and time features of the simulations are derived from a patient study. Noise and segmentation errors are also simulated. The DLSE method is compared with the conventional one of deriving kinetic parameters from the time series of reconstructed images. The standard deviation of results given by DLSE is less than 2%, whereas with the conventional method it is between 5% and 6%. Within the limit of statistical fluctuations, DLSE results are unbiased whereas those of the conventional method are overestimated by 24%.

PET kinetic modeling of 11C-acetate from projections

Positron emission tomography (PET) image reconstruction techniques inevitably introduce inaccuracies in images. To avoid these inaccuracies in PET kinetic modeling, kinetic parameters can directly be obtained from the projections. The present work describes modeling 11C-acetate in the sinograms measured in normal and ischemic rats with the Sherbrooke small animal PET scanner. Each bin of the dynamic sinograms was decomposed in its basis functions using spectral analysis technique in conjunction with the 11C-acetate kinetic model. Homogeneous structures were clearly separated and reconstructed as well as the kinetic model parameters. Rate constants were well correlated to those obtained by means of curve fitting from images.

A curve evolution approach to object-based tomographic reconstruction

In this paper, we develop a new approach to tomographic reconstruction problems based on geometric curve evolution techniques. We use a small set of texture coefficients to represent the object and background inhomogeneities and a contour to represent the boundary of multiple connected or unconnected objects. Instead of reconstructing pixel values on a fixed rectangular grid, we then find a reconstruction by jointly estimating these unknown contours and texture coefficients of the object and background. By designing a new "tomographic flow", the resulting problem is recast into a curve evolution problem and an efficient algorithm based on level set techniques is developed. The performance of the curve evolution method is demonstrated using examples with noisy limited-view Radon transformed data and noisy ground-penetrating radar data. The reconstruction results and computational cost are compared with those of conventional, pixel-based regularization methods. The results indicate that the curve evolution methods achieve improved shape reconstruction and have potential computation and memory advantages over conventional regularized inversion methods.

4D maximum a posteriori reconstruction in dynamic SPECT using a compartmental model-based prior

A 4D ordered-subsets maximum a posteriori (OSMAP) algorithm for dynamic SPECT is described which uses a temporal prior that constrains each voxel's behaviour in time to conform to a compartmental model. No a priori limitations on kinetic parameters are applied; rather, the parameter estimates evolve as the algorithm iterates to a solution. The estimated parameters and time-activity curves are used within the reconstruction algorithm to model changes in the activity distribution as the camera rotates, avoiding artefacts due to inconsistencies of data between projection views. This potentially allows for fewer, longer-duration scans to be used and may have implications for noise reduction. The algorithm was evaluated qualitatively using dynamic 99mTc-teboroxime SPECT scans in two patients, and quantitatively using a series of simulated phantom experiments. The OSMAP algorithm resulted in images with better myocardial uniformity and definition, gave time-activity curves with reduced noise variations, and provided wash-in parameter estimates with better accuracy and lower statistical uncertainty than those obtained from conventional ordered-subsets expectation-maximization (OSEM) processing followed by compartmental modelling. The new algorithm effectively removed the bias in k21 estimates due to inconsistent projections for sampling schedules as slow as 60 s per timeframe, but no improvement in wash-out parameter estimates was observed in this work. The proposed dynamic OSMAP algorithm provides a flexible framework which may benefit a variety of dynamic tomographic imaging applications.

Performance of the dynamic single photon emission computed tomography (dSPECT) method for decreasing or increasing activity changes

Radionuclide imaging is now widely used whenever functional information is required. We present a new approach to dynamic SPECT imaging (dSPECT method) that uses a single slow rotation of a conventional camera and allows us to reconstruct a series of 3D images corresponding to the radiotracer distribution in the body at various times. Using simulations of various camera configurations and acquisition protocols, we have shown that this method is able to reconstruct washout half-lives with an accuracy greater than 90% when used with triple-head SPECT cameras. Accuracy decreases when using fewer camera heads, but dual-head geometries still give an accuracy greater than 80% for short and 90% for long half-lives and about 50-75% for single-head systems. Dynamic phantom experiments have yielded similar results. Presence of attenuation and background activity does not affect the accuracy of the dSPECT reconstructions. In all situations investigated satisfactory dynamic images were produced. A preliminary normal volunteer study measuring renal function was performed. The reconstructed dynamic images may be presented as a three-dimensional movie showing movement of the tracer through the kidneys and the measurement of the regional renal function can be performed. The time-activity curves determined from this dSPECT data are very similar to those obtained from dynamic planar scans.

Direct recovery of regional tracer kinetics from temporally inconsistent dynamic ECT projections using dimension-reduced time-activity basis

We present an algorithm of reduced computational cost which is able to estimate kinetic model parameters directly from dynamic ECT sinograms made up of temporally inconsistent projections. The algorithm exploits the extreme degree of parameter redundancy inherent in linear combinations of the exponential functions which represent the modes of first-order compartmental systems. The singular value decomposition is employed to find a small set of orthogonal functions, the linear combinations of which are able to accurately represent all modes within the physiologically anticipated range in a given study. The reduced dimension basis is formed as the convolution of this orthogonal set with a measured input function. The Moore-Penrose pseudoinverse is used to find coefficients of this basis. Algorithm performance is evaluated at realistic count rates using MCAT phantom and clinical 99mTc-teboroxime myocardial study data. Phantom data are modelled as originating from a Poisson process. For estimates recovered from a single slice projection set containing 2.5 x 10(5) total counts, recovered tissue responses compare favourably with those obtained using more computationally intensive methods. The corresponding kinetic parameter estimates (coefficients of the new basis) exhibit negligible bias, while parameter variances are low, falling within 30% of the Cramér-Rao lower bound.

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.

Relevance of accurate Monte Carlo modeling in nuclear medical imaging

Monte Carlo techniques have become popular in different areas of medical physics with advantage of powerful computing systems. In particular, they have been extensively applied to simulate processes involving random behavior and to quantify physical parameters that are difficult or even impossible to calculate by experimental measurements. Recent nuclear medical imaging innovations such as single-photon emission computed tomography (SPECT), positron emission tomography (PET), and multiple emission tomography (MET) are ideal for Monte Carlo modeling techniques because of the stochastic nature of radiation emission, transport and detection processes. Factors which have contributed to the wider use include improved models of radiation transport processes, the practicality of application with the development of acceleration schemes and the improved speed of computers. In this paper we present a derivation and methodological basis for this approach and critically review their areas of application in nuclear imaging. An overview of existing simulation programs is provided and illustrated with examples of some useful features of such sophisticated tools in connection with common computing facilities and more powerful multiple-processor parallel processing systems. Current and future trends in the field are also discussed.

Dynamic imaging and tracer kinetic modeling for emission tomography using rotating detectors

When performing dynamic studies using emission tomography the tracer distribution changes during acquisition of a single set of projections. This is particularly true for some positron emission tomography (PET) systems which, like single photon emission computed tomography (SPECT), acquire data over a limited angle at any time, with full projections obtained by rotation of the detectors. In this paper, an approach is proposed for processing data from these systems, applicable to either PET or SPECT. A method of interpolation, based on overlapped parabolas, is used to obtain an estimate of the total counts in each pixel of the projections for each required frame-interval, which is the total time to acquire a single complete set of projections necessary for reconstruction. The resultant projections are reconstructed using traditional filtered backprojection (FBP) and tracer kinetic parameters are estimated using a method which relies on counts integrated over the frame-interval rather than instantaneous values. Simulated data were used to illustrate the technique's capabilities with noise levels typical of those encountered in either PET or SPECT. Dynamic datasets were constructed, based on kinetic parameters for fluoro-deoxy-glucose (FDG) and use of either a full ring detector or rotating detector acquisition. For the rotating detector, use of the interpolation scheme provided reconstructed dynamic images with reduced artefacts compared to unprocessed data or use of linear interpolation. Estimates for the metabolic rate of glucose had similar bias to those obtained from a full ring detector.

Kinetic parameter estimation from SPECT cone-beam projection measurements

Kinetic parameters are commonly estimated from dynamically acquired nuclear medicine data by first reconstructing a dynamic sequence of images and subsequently fitting the parameters to time-activity curves generated from regions of interest overlaid upon the image sequence. Biased estimates can result from images reconstructed using inconsistent projections of a time-varying distribution of radiopharmaceutical acquired by a rotating SPECT system. If the SPECT data are acquired using cone-beam collimators wherein the gantry rotates so that the focal point of the collimators always remains in a plane, additional biases can arise from images reconstructed using insufficient, as well as truncated, projection samples. To overcome these problems we have investigated the estimation of kinetic parameters directly from SPECT cone-beam projection data by modelling the data acquisition process. To accomplish this it was necessary to parametrize the spatial and temporal distribution of the radiopharmaceutical within the SPECT field of view. In a simulated chest image volume, kinetic parameters were estimated for simple one-compartment models for four myocardial regions of interest. Myocardial uptake and washout parameters estimated by conventional analysis of noiseless simulated cone-beam data had biases ranging between 3-26% and 0-28%, respectively. Parameters estimated directly from the noiseless projection data were unbiased as expected, since the model used for fitting was faithful to the simulation. Statistical uncertainties of parameter estimates for 10,000,000 events ranged between 0.2-9% for the uptake parameters and between 0.3-6% for the washout parameters.

Block-iterative techniques for fast 4D reconstruction using a priori motion models in gated cardiac SPECT

We introduce a fast block-iterative maximum a posteriori (MAP) reconstruction algorithm and apply it to four-dimensional reconstruction of gated SPECT perfusion studies. The new algorithm, called RBI-MAP, is based on the rescaled block iterative EM (RBI-EM) algorithm. We develop RBI-MAP based on similarities between the RBI-EM, ML-EM and MAP-EM algorithms. RBI-MAP requires far fewer iterations than MAP-EM, and so should result in acceleration similar to that obtained from using RBI-EM or OS-EM as opposed to ML-EM. When complex four-dimensional clique structures are used in the prior, however, evaluation of the smoothing prior dominates the processing time. We show that a simple scheme for updating the prior term in the heart region only for RBI-MAP results in savings in processing time of a factor of six over MAP-EM. The RBI-MAP algorithm incorporating 3D collimator-detector response compensation is demonstrated on a simulated 99mTc gated perfusion study. Results of RBI-MAP are compared with RBI-EM followed by a 4D linear filter. For the simulated study, we find that RBI-MAP provides consistently higher defect contrast for a given degree of noise smoothing than does filtered RBI-EM. This is an indication that RBI-MAP smoothing does less to degrade resolution gained from 3D detector response compensation than does a linear filter. We conclude that RBI-MAP can provide smooth four-dimensional reconstructions with good visualization of heart structures in clinically realistic processing times.

Three-dimensional reconstructions from low-count SPECT data using deformable models

We demonstrate the reconstruction of a 3D, time-varying bolus of radiotracer from first-pass data obtained at the dynamic SPECT imager, FASTSPECT, built by the University of Arizona. The object imaged is a CardioWest Total Artificial Heart. The bolus is entirely contained in one ventricle and its associated inlet and outlet tracts. The model for the radiotracer distribution is a time-varying closed surface parameterized by 162 vertices that are connected to make 960 triangles, with uniform intensity of radiotracer inside. The total curvature of the surface is minimized through the use of a weighted prior in the Bayesian framework. MAP estimates for the vertices, interior intensity and background scatter are produced for diastolic and systolic frames, the only two frames analyzed. The strength of the prior is determined by finding the corner of the L-curve. The results indicate that qualitatively pleasing results are possible even with as few as 1780 counts per time frame (total after summing over all 24 detectors). Quantitative results will require correcting certain undesirable features of the reconstruction due to inappropriate assumptions in the model, e.g. inhomogeneities in the radiotracer distribution and smoothness of the surface at the tract/ventricle join.

The direct calculation of parametric images from dynamic PET data using maximum-likelihood iterative reconstruction

The aim of this work is to calculate, directly from projection data, concise images characterizing the spatial and temporal distribution of labelled compounds from dynamic PET data. Conventionally, image reconstruction and the calculation of parametric images are performed sequentially. By combining the two processes, low-noise parametric images are obtained, using a computationally feasible parametric iterative reconstruction (PIR) algorithm. PIR is performed by restricting the pixel time-activity curves to a positive linear sum of predefined time characteristics. The weights in this sum are then calculated directly from the PET projection data, using an iterative algorithm based on a maximum-likelihood iterative algorithm commonly used for tomographic reconstruction. The ability of the algorithm to extract known kinetic components from the raw data is assessed, using data from both a phantom experiment and clinical studies. The calculated parametric images indicate differential kinetic behaviour and have been used to aid in the identification of tissues which exhibit differences in the handling of labelled compounds. These parametric images should be helpful in defining regions of interest with similar functional behaviour, and with FDG Patlak analysis.

Equivalent methods to analyse dynamic experiments in which the input function is noisy

A comparison is made between two methods of parameter estimation for analysis of dynamic experiments in which the input function is noisy. Noise in the input function leads to uncertainties in the calculated model-predicted values, and therefore the covariance matrix of the residuals is a function of the model parameters. Statistical uncertainties in the model-predicted values significantly change the nature of the fitting process and the quality of the results. The initial method uses a weighted least-squares criterion where the weighting matrix is the inverse of the full covariance matrix of the residuals, incorporating both the noise in the output data and the noise in the input function. The methodology was applied to dynamic emission tomography studies of the heart, where the blood (input) and tissue (output) tracer concentrations at each time are derived from two regions of interest in the same tomographic section. The second method introduces additional parameters to describe the input function, and adds terms to the weighted sum of squares which comprise the criterion. Instead of only summing the weighted terms to account for differences between the model and the output function, there is a second set of terms to account for the differences between the model and the input function. The two methods have different theoretical bases and appear to optimize different criteria, but it is shown here that they are equivalent to one another. The criterion which they minimize is the same under certain matrix invertibility constraints, which must be satisfied to ensure the stability of either method.

Model-based estimation with boundary side information or boundary regularization [cardiac emission CT]

The authors have previously developed a model-based strategy for joint estimation of myocardial perfusion and boundaries using ECT (emission computed tomography). They have also reported difficulties with boundary estimation in low contrast and low count rate situations. Here they propose using boundary side information (obtainable from high resolution MRI and CT images) or boundary regularization to improve both perfusion and boundary estimation in these situations. To fuse boundary side information into the emission measurements, the authors formulate a joint log-likelihood function to include auxiliary boundary measurements as well as ECT projection measurements. In addition, they introduce registration parameters to align auxiliary boundary measurements with ECT measurements and jointly estimate these parameters with other parameters of interest from the composite measurements. In simulated PET O-15 water myocardial perfusion studies using a simplified model, the authors show that the joint estimation improves perfusion estimation performance and gives boundary alignment accuracy of <0.5 mm even at 0.2 million counts. They implement boundary regularization through formulating a penalized log-likelihood function. They also demonstrate in simulations that simultaneous regularization of the epicardial boundary and myocardial thickness gives comparable perfusion estimation accuracy with the use of boundary side information.