MicroPET reconstruction with random coincidence correction via a joint Poisson model

Positron emission tomography (PET) can provide in vivo, quantitative and functional information for diagnosis; however, PET image quality depends highly on a reconstruction algorithm. Iterative algorithms, such as the maximum likelihood expectation maximization (MLEM) algorithm, are rapidly becoming the standards for image reconstruction in emission-computed tomography. The conventional MLEM algorithm utilized the Poisson model in its system matrix, which is no longer valid for delay-subtraction of randomly corrected data. The aim of this study is to overcome this problem. The maximum likelihood estimation using the expectation maximum algorithm (MLE-EM) is adopted and modified to reconstruct microPET images using random correction from joint prompt and delay sinograms; this reconstruction method is called PDEM. The proposed joint Poisson model preserves Poisson properties without increasing the variance (noise) associated with random correction. The work here is an initial application/demonstration without applied normalization, scattering, attenuation, and arc correction. The coefficients of variation (CV) and full width at half-maximum (FWHM) values were utilized to compare the quality of reconstructed microPET images of physical phantoms acquired by filtered backprojection (FBP), ordered subsets-expected maximum (OSEM) and PDEM approaches. Experimental and simulated results demonstrate that the proposed PDEM produces better image quality than the FBP and OSEM approaches.     

基于非线性统计估计技术的PET散射校正

散射事件是影响正电子发射断层扫描术 (Positron emission tomography,PET)图像重建质量的一个重要因素。我们根据投影图像的分布特征 ,基于泊松数据模型 ,利用最大似然期望值法 (Maximum likelihoodexpectation maximization,ML EM)对正弦图进行散射校正。比较采用 ML EM方法和去卷积法进行散射校正后的正弦图以及重建图像 ,结果表明我们的方法在进行散射补偿的同时 ,增加了图像的对比度 ,效果优于传统的校正方法     

Iterative deconvolution of simultaneous 99mTc and 201Tl projection data measured on a CdZnTe-based cardiac SPECT scanner

We present a method of correcting self-scatter and crosstalk effects in simultaneous technetium-99m/thallium-201 stress/rest myocardial perfusion (single photon emission computed tomography) SPECT scans. The method, which is in essence a hybrid between the triple energy window method and scatter modelling, is based on a model of spatial and spectral distribution of projection counts in several selected energy windows. The parameters of the model are determined from measurements of thin rod sources in air when no in-object scatter or attenuation effects are present. The model equations are solved using the iterative maximum likelihood expectation maximization algorithm in the projection space to find estimates of the primary photopeak counts of both radionuclides. The method has been developed particularly for a novel dedicated cardiac camera based on CdZnTe pixellated detectors, although it can also be adapted to a conventional scintillator camera. The method has been validated in anthropomorphic phantom experiments. Significant improvement in defect contrast has been observed with only moderate increase in image noise. The application of the method to patient data is illustrated.     

Acceleration of Monte Carlo-based scatter compensation for cardiac SPECT

Single proton emission computed tomography (SPECT) images are degraded by photon scatter making scatter compensation essential for accurate reconstruction. Reconstruction-based scatter compensation with Monte Carlo (MC) modelling of scatter shows promise for accurate scatter correction, but it is normally hampered by long computation times. The aim of this work was to accelerate the MC-based scatter compensation using coarse grid and intermittent scatter modelling. The acceleration methods were compared to un-accelerated implementation using MC-simulated projection data of the mathematical cardiac torso (MCAT) phantom modelling (99m)Tc uptake and clinical myocardial perfusion studies. The results showed that when combined the acceleration methods reduced the reconstruction time for 10 ordered subset expectation maximization (OS-EM) iterations from 56 to 11 min without a significant reduction in image quality indicating that the coarse grid and intermittent scatter modelling are suitable for MC-based scatter compensation in cardiac SPECT.     

Optimization of a fully 3D single scatter simulation algorithm for 3D PET

We describe a new implementation of a single scatter simulation (SSS) algorithm for the prediction and correction of scatter in 3D PET. In this implementation, out of field of view (FoV) scatter and activity, side shields and oblique tilts are explicitly modelled. Comparison of SSS predictions with Monte Carlo simulations and experimental data from uniform, line and cold-bar phantoms showed that the code is accurate for uniform as well as asymmetric objects and can model different energy resolution crystals and low level discriminator (LLD) settings. Absolute quantitation studies show that for most applications, the code provides a better scatter estimate than the tail-fitting scatter correction method currently in use at our institution. Several parameters such as the density of scatter points, the number of scatter distribution sampling points and the axial extent of the FoV were optimized to minimize execution time, with particular emphasis on patient studies. Development and optimization were carried out in the case of GSO-based scanners, which enjoy relatively good energy resolution. SSS estimates for scanners with lower energy resolution may result in different agreement, especially because of a higher fraction of multiple scatter events. The algorithm was applied to a brain phantom as well as to clinical whole-body studies. It proved robust in the case of large patients, where the scatter fraction increases. The execution time, inclusive of interpolation, is typically under 5 min for a whole-body study (axial FoV: 81 cm) of a 100 kg patient.     

Review and current status of SPECT scatter correction

Detection of scattered gamma quanta degrades image contrast and quantitative accuracy of single-photon emission computed tomography (SPECT) imaging. This paper reviews methods to characterize and model scatter in SPECT and correct for its image degrading effects, both for clinical and small animal SPECT. Traditionally scatter correction methods were limited in accuracy, noise properties and/or generality and were not very widely applied. For small animal SPECT, these approximate methods of correction are often sufficient since the fraction of detected scattered photons is small. This contrasts with patient imaging where better accuracy can lead to significant improvement of image quality. As a result, over the last two decades, several new and improved scatter correction methods have been developed, although often at the cost of increased complexity and computation time. In concert with (i) the increasing number of energy windows on modern SPECT systems and (ii) excellent attenuation maps provided in SPECT/CT, some of these methods give new opportunities to remove degrading effects of scatter in both standard and complex situations and therefore are a gateway to highly quantitative single- and multi-tracer molecular imaging with improved noise properties. Widespread implementation of such scatter correction methods, however, still requires significant effort.     

Joint estimation of dynamic PET images and temporal basis functions using fully 4D ML-EM

A fully 4D joint-estimation approach to reconstruction of temporal sequences of 3D positron emission tomography (PET) images is proposed. The method estimates both a set of temporal basis functions and the corresponding coefficient for each basis function at each spatial location within the image. The joint estimation is performed through a fully 4D version of the maximum likelihood expectation maximization (ML-EM) algorithm in conjunction with two different models of the mean of the Poisson measured data. The first model regards the coefficients of the temporal basis functions as the unknown parameters to be estimated and the second model regards the temporal basis functions themselves as the unknown parameters. The fully 4D methodology is compared to the conventional frame-by-frame independent reconstruction approach (3D ML-EM) for varying levels of both spatial and temporal post-reconstruction smoothing. It is found that using a set of temporally extensive basis functions (estimated from the data by 4D ML-EM) significantly reduces the spatial noise when compared to the independent method for a given level of image resolution. In addition to spatial image quality advantages, for smaller regions of interest (where statistical quality is often limited) the reconstructed time-activity curves show a lower level of bias and a lower level of noise compared to the independent reconstruction approach. Finally, the method is demonstrated on clinical 4D PET data.     

Evaluation of scatter compensation methods by their effects on parameter estimation from SPECT projections

Three algorithms for scatter compensation in Tc-99m brain single-photon emission computed tomography (SPECT) were optimized and compared on the basis of the accuracy and precision with which lesion and background activity could be simultaneously estimated. These performance metrics are directly related to the clinically important tasks of activity quantitation and lesion detection, in contrast to measures based solely on the fidelity of image pixel values. The scatter compensation algorithms were (a) the Compton-window (CW) method with a 20% photopeak window, a 92-126 keV scatter window, and an optimized "k-factor," (b) the triple-energy window (TEW) method, with optimized widths of the photopeak window and the abutting scatter window, and (c) a general spectral (GS) method using seventeen 4 keV windows with optimized energy weights. Each method was optimized by minimizing the sum of the mean-squared errors (MSE) of the estimates of lesion and background activity concentrations. The accuracy and precision of activity estimates were then determined for lesions of different size, location, and contrast, as well as for a more complex Bayesian estimation task in which lesion size was also estimated. For the TEW and GS methods, parameters optimized for the estimation task differed significantly from those optimized for global normalized pixel MSE. For optimal estimation, the CW bias of activity estimates was larger and varied more (-2% to 22%) with lesion location and size than that of the other methods. The magnitude of the TEW bias was less than 7% across most conditions, although its precision was worse than that of CW estimates. The GS method performed best, with bias generally less than 4% and the lowest variance; its root-mean square (rms) estimation error was within a few percent of that achievable from primary photons alone. For brain SPECT, estimation performance with an optimized, energy-based, subtractive correction may approach that of an ideal scatter-rejection procedure.     

Comparison of conventional, model-based quantitative planar, and quantitative SPECT image processing methods for organ activity estimation using In-111 agents

Accurate quantification of organ radionuclide uptake is important for patient-specific dosimetry. The quantitative accuracy from conventional conjugate view methods is limited by overlap of projections from different organs and background activity, and attenuation and scatter. In this work, we propose and validate a quantitative planar (QPlanar) processing method based on maximum likelihood (ML) estimation of organ activities using 3D organ VOIs and a projector that models the image degrading effects. Both a physical phantom experiment and Monte Carlo simulation (MCS) studies were used to evaluate the new method. In these studies, the accuracies and precisions of organ activity estimates for the QPlanar method were compared with those from conventional planar (CPlanar) processing methods with various corrections for scatter, attenuation and organ overlap, and a quantitative SPECT (QSPECT) processing method. Experimental planar and SPECT projections and registered CT data from an RSD Torso phantom were obtained using a GE Millenium VH/Hawkeye system. The MCS data were obtained from the 3D NCAT phantom with organ activity distributions that modelled the uptake of (111)In ibritumomab tiuxetan. The simulations were performed using parameters appropriate for the same system used in the RSD torso phantom experiment. The organ activity estimates obtained from the CPlanar, QPlanar and QSPECT methods from both experiments were compared. From the results of the MCS experiment, even with ideal organ overlap correction and background subtraction, CPlanar methods provided limited quantitative accuracy. The QPlanar method with accurate modelling of the physical factors increased the quantitative accuracy at the cost of requiring estimates of the organ VOIs in 3D. The accuracy of QPlanar approached that of QSPECT, but required much less acquisition and computation time. Similar results were obtained from the physical phantom experiment. We conclude that the QPlanar method, based on 3D organ VOIs and accurate models of the projection process, provided a substantial increase in accuracy of organ activity estimates from planar images compared to CPlanar processing and had accuracy approaching that of QSPECT.     

Dose calculation for asymmetric photon fields with independent jaws and multileaf collimators

We have developed a simple method for dose calculation in dual asymmetric open and irregular fields with four independent jaws and multileaf collimators. Our calculation method extends the scatter correction method of Kwa et al. [Med. Phys. 21, 1599-1604 (1994)] based on the principle of Day's equivalent-field calculation. The scatter correction factor was determined by the ratio of the derived doses of a smaller asymmetric open field or irregular field to a larger symmetric field. The algorithm with the scatter correction method can be calculated from output factors, tissue maximum ratios, and off-axis ratios for conventional symmetric fields. The doses calculated by this method were compared with the measured doses for various asymmetric open and irregular fields. The agreement between the calculated and measured doses for 4 and 10 MV photon beams was within 0.5% at the geometric center of the asymmetric open fields. For the asymmetric irregular fields with the same geometrical center, agreement within 1% was found in most cases.     

A Two-Stage Approach to the Correction of Ascertainment Bias in Complex Genetic Studies Involving Variance Components

Correction for ascertainment bias is a vital part of the analysis of genetic epidemiology studies that needs to be undertaken whenever subjects are not recruited at random. Adjustment often requires extensive numerical integration, which can be very slow or even computationally infeasible, especially if the model includes many fixed and random effects. In this paper we propose a two-stage method for ascertainment bias correction. In the first stage we estimate parameters that pertain to the ascertained population, that is the population that would be selected into the sample if the ascertainment criterion were applied to everyone. In the second stage we convert the estimates for the ascertained population into general population parameter estimates. We illustrate the method with simulations based on a simple model and then describe how the method can be used with complex models. The two-stage approach avoids some of the integration required in direct adjustment, hence speeding up the process of model fitting.     

PET energy-based scatter estimation and image reconstruction with energy-dependent corrections

In this paper we propose a comprehensive energy-based scatter correction approach for positron emission tomography (PET). We take advantage of the marked difference between the energy spectra of the unscattered and scattered photons, and use the detailed energy information that comes with the list-mode data for the estimation of the scattered events distribution in the data space. Also, inside the maximum-likelihood expectation maximization (ML-EM) image reconstruction algorithm, we introduce energy-dependent factors that individualize the correction terms for each event, given its position and energy information. The central piece of our approach is the two-dimensional detector energy response model represented as a linear combination of four components, each one representing a particular state a PET event can be found in: both photons unscattered, the second scattered while the first not, the first photon scattered while the second not and both photons scattered. For a set of events collected in the vicinity of a point in the projection space, the coefficient of each component is determined by applying a statistical estimator. As a result we obtain the number of scattered events that are in the given set. The model also gives us the variation of scatter fraction with the photon pair energies for that particular position in the data space. A simulation study that demonstrates the proposed methods is presented.     

Improved scatter correction using adaptive scatter kernel superposition

Accurate scatter correction is required to produce high-quality reconstructions of x-ray cone-beam computed tomography (CBCT) scans. This paper describes new scatter kernel superposition (SKS) algorithms for deconvolving scatter from projection data. The algorithms are designed to improve upon the conventional approach whose accuracy is limited by the use of symmetric kernels that characterize the scatter properties of uniform slabs. To model scatter transport in more realistic objects, nonstationary kernels, whose shapes adapt to local thickness variations in the projection data, are proposed. Two methods are introduced: (1) adaptive scatter kernel superposition (ASKS) requiring spatial domain convolutions and (2) fast adaptive scatter kernel superposition (fASKS) where, through a linearity approximation, convolution is efficiently performed in Fourier space. The conventional SKS algorithm, ASKS, and fASKS, were tested with Monte Carlo simulations and with phantom data acquired on a table-top CBCT system matching the Varian On-Board Imager (OBI). All three models accounted for scatter point-spread broadening due to object thickening, object edge effects, detector scatter properties and an anti-scatter grid. Hounsfield unit (HU) errors in reconstructions of a large pelvis phantom with a measured maximum scatter-to-primary ratio over 200% were reduced from -90 ± 58 HU (mean ± standard deviation) with no scatter correction to 53 ± 82 HU with SKS, to 19 ± 25 HU with fASKS and to 13 ± 21 HU with ASKS. HU accuracies and measured contrast were similarly improved in reconstructions of a body-sized elliptical Catphan phantom. The results show that the adaptive SKS methods offer significant advantages over the conventional scatter deconvolution technique.     

Improved activity estimation with MC-JOSEM versus TEW-JOSEM in 111In SPECT

We have previously developed a fast Monte Carlo (MC)-based joint ordered-subset expectation maximization (JOSEM) iterative reconstruction algorithm, MC-JOSEM. A phantom study was performed to compare quantitative imaging performance of MC-JOSEM with that of a triple-energy-window approach (TEW) in which estimated scatter was also included additively within JOSEM, TEW-JOSEM. We acquired high-count projections of a 5.5 cm3 sphere of 111In at different locations in the water-filled torso phantom; high-count projections were then obtained with 111In only in the liver or only in the soft-tissue background compartment, so that we could generate synthetic projections for spheres surrounded by various activity distributions. MC scatter estimates used by MC-JOSEM were computed once after five iterations of TEW-JOSEM. Images of different combinations of liver/background and sphere/background activity concentration ratios were reconstructed by both TEW-JOSEM and MC-JOSEM for 40 iterations. For activity estimation in the sphere, MC-JOSEM always produced better relative bias and relative standard deviation than TEW-JOSEM for each sphere location, iteration number, and activity combination. The average relative bias of activity estimates in the sphere for MC-JOSEM after 40 iterations was -6.9%, versus -15.8% for TEW-JOSEM, while the average relative standard deviation of the sphere activity estimates was 16.1% for MC-JOSEM, versus 27.4% for TEW-JOSEM. Additionally, the average relative bias of activity concentration estimates in the liver and the background for MC-JOSEM after 40 iterations was -3.9%, versus -12.2% for TEW-JOSEM, while the average relative standard deviation of these estimates was 2.5% for MC-JOSEM, versus 3.4% for TEW-JOSEM. MC-JOSEM is a promising approach for quantitative activity estimation in 111In SPECT.     

Material-specific analysis using coherent-scatter imaging

Coherent-scatter computed tomography (CSCT) is a novel imaging method we are developing to produce cross-sectional images based on the low-angle (<10 degrees) scatter properties of tissue. At diagnostic energies, this scatter is primarily coherent with properties dependent upon the molecular structure of the scatterer. This facilitates the production of material-specific maps of each component in a conglomerate. Our particular goal is to obtain quantitative maps of bone-mineral content. A diagnostic x-ray source and image intensifier are used to acquire scatter patterns under first-generation CT geometry. An accurate measurement of the scatter patterns is necessary to correctly identify and quantify tissue composition. This requires corrections for exposure fluctuations, temporal lag in the intensifier, and self-attenuation within the specimen. The effect of lag is corrected using an approximate convolution method. Self-attenuation causes a cupping artifact in the CSCT images and is corrected using measurements of the transmitted primary beam. An accurate correction is required for reliable density measurements from material-specific images. The correction is shown to introduce negligible noise to the images and a theoretical expression for CSCT image SNR is confirmed by experiment. With these corrections, the scatter intensity is proportional to the number of scattering centers interrogated and quantitative measurements of each material (in g/cm3) are obtained. Results are demonstrated using both a series of poly(methyl methacrylate) (PMMA) sheets of increasing thickness (2-12 mm) and a series of 5 acrylic rods containing varying amounts of hydroxyapatite (0-0.400 g/cm3), simulating the physiological range of bone-mineral density (BMD) found in trabecular bone. The excellent agreement between known and measured BMD demonstrates the viability of CSCT as a tool for densitometry.     

A convolution-subtraction scatter correction method for 3D PET

3D acquisition and reconstruction in positron emission tomography (PET) produce data with improved signal-to-noise ratios compared with conventional 2D slice-oriented methods. However, the sensitivity increase is accompanied by an increase in the number of scattered photons and random coincidences detected. This paper presents a scatter correction technique for 3D PET data where an estimate of the scattered photon distribution is subtracted from the data before reconstruction. The scatter distribution is estimated by iteratively convolving the photopeak projections with a mono-exponential kernel. The method accounts for the 3D acquisition geometry and nature of scatter by performing the scatter estimation on 2D projections. The assumptions of the method have been investigated by measuring the variation in the scatter fraction and the scatter function at different positions in a cylinder. Both parameters were found to vary by up to 50% from the centre to the edge of a large water-filled cylinder. Despite this, in a uniform cylinder containing water with different concentrations of radioactivity, scatter was reduced from 25% in a non-radioactive region to less than 5% using the convolution-subtraction method. In addition, the relative concentration of a cylinder containing an increased concentration, which was underestimated by almost 50% without scatter correction, was within 5% of the true concentration after correction.     

3.5D dynamic PET image reconstruction incorporating kinetics-based clusters

Standard 3D dynamic positron emission tomographic (PET) imaging consists of independent image reconstructions of individual frames followed by application of appropriate kinetic model to the time activity curves at the voxel or region-of-interest (ROI). The emerging field of 4D PET reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple frames within the image reconstruction task. Here we propose a novel reconstruction framework aiming to enhance quantitative accuracy of parametric images via introduction of priors based on voxel kinetics, as generated via clustering of preliminary reconstructed dynamic images to define clustered neighborhoods of voxels with similar kinetics. This is then followed by straightforward maximum a posteriori (MAP) 3D PET reconstruction as applied to individual frames; and as such the method is labeled '3.5D' image reconstruction. The use of cluster-based priors has the advantage of further enhancing quantitative performance in dynamic PET imaging, because: (a) there are typically more voxels in clusters than in conventional local neighborhoods, and (b) neighboring voxels with distinct kinetics are less likely to be clustered together. Using realistic simulated (11)C-raclopride dynamic PET data, the quantitative performance of the proposed method was investigated. Parametric distribution-volume (DV) and DV ratio (DVR) images were estimated from dynamic image reconstructions using (a) maximum-likelihood expectation maximization (MLEM), and MAP reconstructions using (b) the quadratic prior (QP-MAP), (c) the Green prior (GP-MAP) and (d, e) two proposed cluster-based priors (CP-U-MAP and CP-W-MAP), followed by graphical modeling, and were qualitatively and quantitatively compared for 11 ROIs. Overall, the proposed dynamic PET reconstruction methodology resulted in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) for parametric DV and DVR images. The method was also tested on a 90 min (11)C-raclopride patient study performed on the high-resolution research tomography. The proposed method was shown to outperform the conventional method in visual as well as quantitative accuracy improvements (in terms of noise versus regional DVR value performance).     

Scatter correction for positron emission mammography

In this paper we present a scatter correction method for a regularized list mode maximum likelihood reconstruction algorithm for the positron emission mammograph (PEM) that is being developed at our laboratory. The scatter events inside the object are modelled as additive Poisson random variables in the forward model of the reconstruction algorithm. The mean scatter sinogram is estimated using a Monte Carlo simulation program. With the assumption that the background activity is nearly uniform, the Monte Carlo scatter simulation only needs to run once for each PEM configuration. This saves computation time. The crystal scatters are modelled as a shift-invariant blurring in image domain because they are more localized. Thus, the useful information in the crystal scatters can be deconvolved in high-resolution reconstructions. The propagation of the noise from the estimated scatter sinogram into the reconstruction is analysed theoretically. The results provide an easy way to calculate the required number of events in the Monte Carlo scatter simulation for a given noise level in the image. The analysis is also applicable to other scatter estimation methods, provided that the covariance of the estimated scatter sinogram is available.     

Combining deterministic and Monte Carlo calculations for fast estimation of scatter intensities in CT

A side effect of increased volume coverage by using multi-row and flat-panel detectors in computed tomography (CT) is the concurrently growing contribution of scattered radiation to the measured signal. In order to investigate the effect of scatter on x-ray projections used for CT imaging, our study aimed at the development of a simulation tool for fast calculation of primary and scatter intensities. We developed a deterministic method to assess the contribution of single-scatter events to the measured signal. The investigation of multiple scatter by Monte Carlo simulations showed that it results in a smooth signal as compared to single scatter. A hybrid method is proposed in order to optimize the performance of the scatter simulation: a fast and exact analytical calculation of the single-scatter intensity combined with a coarse Monte Carlo (MC) estimate of multiple scatter to reduce overall computational expenses, while assuring an acceptable signal quality. The results of the hybrid simulation of total scatter were in excellent agreement with the corresponding MC only simulations, thereby allowing us to reduce computational time by orders of magnitude. Estimates of two-dimensional scatter distributions for flat-panel CT imaging took about 30-40 s (per projection). The hybrid method provides a realistic simulation of x-ray scatter and offers a basis for scatter correction approaches.     

EQPlanar: a maximum-likelihood method for accurate organ activity estimation from whole body planar projections

Optimizing targeted radionuclide therapy requires patient-specific estimation of organ doses. The organ doses are estimated from quantitative nuclear medicine imaging studies, many of which involve planar whole body scans. We have previously developed the quantitative planar (QPlanar) processing method and demonstrated its ability to provide more accurate activity estimates than conventional geometric-mean-based planar (CPlanar) processing methods using physical phantom and simulation studies. The QPlanar method uses the maximum likelihood-expectation maximization algorithm, 3D organ volume of interests (VOIs), and rigorous models of physical image degrading factors to estimate organ activities. However, the QPlanar method requires alignment between the 3D organ VOIs and the 2D planar projections and assumes uniform activity distribution in each VOI. This makes application to patients challenging. As a result, in this paper we propose an extended QPlanar (EQPlanar) method that provides independent-organ rigid registration and includes multiple background regions. We have validated this method using both Monte Carlo simulation and patient data. In the simulation study, we evaluated the precision and accuracy of the method in comparison to the original QPlanar method. For the patient studies, we compared organ activity estimates at 24 h after injection with those from conventional geometric mean-based planar quantification using a 24 h post-injection quantitative SPECT reconstruction as the gold standard. We also compared the goodness of fit of the measured and estimated projections obtained from the EQPlanar method to those from the original method at four other time points where gold standard data were not available. In the simulation study, more accurate activity estimates were provided by the EQPlanar method for all the organs at all the time points compared with the QPlanar method. Based on the patient data, we concluded that the EQPlanar method provided a substantial increase in accuracy of organ activity estimates from 24 h planar images compared to the CPlanar using 24 h SPECT as the golden standard. For other time points, where no golden standard is available, better agreement between estimated and measured projections was observed by using the EQPlanar method compared to the QPlanar method. This phenomenon is consistent with the improvement in goodness of fit seen in both simulation data and 24 h patient data. Therefore, this indicates the improved reliability of organ activity estimates obtained though the EQPlanar method.