An analytical algorithm for skew-slit imaging geometry with nonuniform attenuation correction

The pinhole collimator is currently the collimator of choice in small animal single photon emission computed tomography (SPECT) imaging because it can provide high spatial resolution and reasonable sensitivity when the animal is placed very close to the pinhole. It is well known that if the collimator rotates around the object (e.g., a small animal) in a circular orbit to form a cone-beam imaging geometry with a planar trajectory, the acquired data are not sufficient for an exact artifact-free image reconstruction. In this paper a novel skew-slit collimator is mounted instead of the pinhole collimator in order to significantly reduce the image artifacts caused by the geometry. The skew-slit imaging geometry is a more generalized version of the pinhole imaging geometry. The multiple pinhole geometry can also be extended to the multiple-skew-slit geometry. An analytical algorithm for image reconstruction based on the tilted fan-beam inversion is developed with nonuniform attenuation compensation. Numerical simulation shows that the axial artifacts are evidently suppressed in the skew-slit images compared to the pinhole images and the attenuation correction is effective.     

Analytical fan-beam and cone-beam reconstruction algorithms with uniform attenuation correction for SPECT

In this paper, we developed an analytical fan-beam reconstruction algorithm that compensates for uniform attenuation in SPECT. The new fan-beam algorithm is in the form of backprojection first, then filtering, and is mathematically exact. The algorithm is based on three components. The first one is the established generalized central-slice theorem, which relates the 1D Fourier transform of a set of arbitrary data and the 2D Fourier transform of the backprojected image. The second one is the fact that the backprojection of the fan-beam measurements is identical to the backprojection of the parallel measurements of the same object with the same attenuator. The third one is the stable analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan. The fan-beam algorithm is then extended into a cone-beam reconstruction algorithm, where the orbit of the focal point of the cone-beam imaging geometry is a circle. This orbit geometry does not satisfy Tuy's condition and the obtained cone-beam algorithm is an approximation. In the cone-beam algorithm, the cone-beam data are first backprojected into the 3D image volume; then a slice-by-slice filtering is performed. This slice-by-slice filtering procedure is identical to that of the fan-beam algorithm. Both the fan-beam and cone-beam algorithms are efficient, and computer simulations are presented. The new cone-beam algorithm is compared with Bronnikov's cone-beam algorithm, and it is shown to have better performance with noisy projections.     

Exact fan-beam and 4pi-acquisition cone-beam SPECT algorithms with uniform attenuation correction

This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4pi solid angle geometry. The cone-beam algorithm is also an exact algorithm.     

Quantitative multi-pinhole small-animal SPECT: uniform versus non-uniform Chang attenuation correction

Attenuation of photon flux on trajectories between the source and pinhole apertures affects the quantitative accuracy of reconstructed single-photon emission computed tomography (SPECT) images. We propose a Chang-based non-uniform attenuation correction (NUA-CT) for small-animal SPECT/CT with focusing pinhole collimation, and compare the quantitative accuracy with uniform Chang correction based on (i) body outlines extracted from x-ray CT (UA-CT) and (ii) on hand drawn body contours on the images obtained with three integrated optical cameras (UA-BC). Measurements in phantoms and rats containing known activities of isotopes were conducted for evaluation. In (125)I, (201)Tl, (99m)Tc and (111)In phantom experiments, average relative errors comparing to the gold standards measured in a dose calibrator were reduced to 5.5%, 6.8%, 4.9% and 2.8%, respectively, with NUA-CT. In animal studies, these errors were 2.1%, 3.3%, 2.0% and 2.0%, respectively. Differences in accuracy on average between results of NUA-CT, UA-CT and UA-BC were less than 2.3% in phantom studies and 3.1% in animal studies except for (125)I (3.6% and 5.1%, respectively). All methods tested provide reasonable attenuation correction and result in high quantitative accuracy. NUA-CT shows superior accuracy except for (125)I, where other factors may have more impact on the quantitative accuracy than the selected attenuation correction.     

An analytical reconstruction algorithm for multifocal converging-beam SPECT

Multifocal converging-beam collimation has been suggested for cardiac SPECT imaging to increase sensitivity over the heart without truncation of the activity distribution in the chest. In this study, an analytical reconstruction algorithm is derived for multifocal fan-beam and multifocal cone-beam tomography. In the algorithm, the projection data are differently weighted and filtered, depending on the distance from the detector. For a given image point, the set of filtered data corresponding to the distance between this point and detector is backprojected to determine the pixel value of the point. Thus, the backprojection is done only once at each projection view. To evaluate the algorithm, simulation studies are performed using a 3D Defrise slab phantom without considering photon attenuation and scatter, detector response, and statistical noise. Reconstructed images demonstrate that reasonable quality can be achieved with a modest focal-length variation rate and with a small radius of rotation. A collimator with a focal length increasing quickly near its centre provides better quality in the image region distant from the central plane of the cone geometry, but produces more severe artifacts at the centre of the reconstructed image, compared to a collimator with an initially slowly varying focal length.     

A spline-regularized minimal residual algorithm for iterative attenuation correction in SPECT.

In SPECT, regularization is necessary to avoid divergence of the iterative algorithms used for non uniform attenuation compensation. In this paper, we propose a spline-based regularization method for the minimal residual algorithm. First, the acquisition noise is filtered using a statistical model involving spline smoothing so that the filtered projections belong to a Sobolev space with specific continuity and derivability properties. Then, during the iterative reconstruction procedure, the continuity of the inverse Radon transform between Sobolev spaces is used to design a spline-regularized filtered backprojection method, by which the known regularity properties of the projections determine those of the corresponding reconstructed slices. This ensures that the activity distributions estimated at each iteration present regularity properties, which avoids computational noise amplification, thus stabilizing the iterative process. Analytical and Monte Carlo simulations are used to show that the proposed spline-regularized minimal residual algorithm converges to a satisfactory stable solution in terms of restored activity and homogeneity, using at most 25 iterations, whereas the non regularized version of the algorithm diverges. Choosing the number of iterations is therefore no longer a critical issue for this reconstruction procedure.     

An iterative transmission algorithm incorporating cross-talk correction for SPECT

Simultaneous emission/transmission acquisitions in cardiac SPECT with a Tc99m/Gd153 source combination offer the capability for nonuniform attenuation correction. However, cross-talk of Tc99m photons downscattered into the Gd153 energy window contaminates the reconstructed transmission map used for attenuation correction. The estimated cross-talk contribution can be subtracted prior to transmission reconstruction or incorporated in the reconstruction algorithm itself. In this work, we propose an iterative transmission algorithm (MLTG-S) based on the maximum-likelihood gradient algorithm (MLTG) that explicitly accounts for this cross-talk estimate. Clinical images were acquired on a three-headed SPECT camera, acquiring Tc99m emission and Gd153 transmission images simultaneously. Subtracting the cross-talk estimate prior to transmission reconstruction can result in negative and zero values if the estimate is larger than or equal to the count in the transmission projection bin, especially with increased attenuator size or amount of cross-talk. This results in inaccurate attenuation coefficients for MLTG reconstructions with cross-talk subtraction. MLTG-S reconstructions on the other hand, yield better estimates of attenuation maps, by avoiding the subtraction of the cross-talk estimate. Comparison of emission slices corrected for nonuniform attenuation reveals that inaccuracies in the reconstructed attenuation map caused by cross-talk can artificially enhance the extra-cardiac activity, confounding the ability to visualize the left-ventricular walls.     

Implementation and quantitative evaluation of analytical methods for attenuation correction in SPECT: a phantom study.

Three differing exact methods of inverting the two-dimensional (2D) exponential Radon transform were implemented and evaluated quantitatively with a phantom study. The phantom had the shape of a pie-chart divided into six cavities, each 480 ml in volume and 10 cm in height, that were symmetrically positioned in a cylinder that was 20 cm in diameter and 10 cm in height. This phantom tests for linearity between true activity concentration and measured activity concentration, and it is denoted as a linearity phantom in the present study. Each cavity contained a different concentration of a homogeneous solution of 99mTc (74, 148, 222, 296, 370 and 444 kBq ml(-1)). Data acquisition was performed with two energy windows: a 20% photopeak energy window set symmetrically over the 140 keV of 99mTc and a secondary 5% energy window set over the 122 keV peak. We optimized a triple-energy window scatter correction method for a gamma camera-collimator system to obtain accurate scatter-corrected projections. A circular ROI 3 cm in diameter was identified over each cavity region, and count density (counts per pixel) was calculated. This value was converted to activity concentration (kBq ml(-1)) using a cross-calibration coefficient between SPECT counts and the gamma well counter. The relation between true activity (x) and measured activity concentration (y) was fitted to a line using the least-squares method. Regression lines were y = 0.63 + 1.0255x (R2 = 0.9987), y = -2.62 + 1.0278x (R2 = 0.9995), and y = 0.092 + 1.0241x (R2 = 0.9989) for the Bellini, Inouye and Metz-Pan methods respectively. In another phantom study using two different types of phantoms, contrast of a cold region in the two was 96% and 101% for all three methods. Combined optimized scatter correction and analytical attenuation correction methods achieve good accuracy in quantification of activity distribution with a uniform attenuating medium.     

Image reconstruction algorithm for single-photon-emission computed tomography with uniform attenuation

A new method is presented for obtaining an analytical solution to the image-reconstruction problem in single-photon-emission computed tomography. The rigorous solution is introduced by applying an analytical continuation process to the two-dimensional Fourier transform of the image, which is derived from the one-dimensional Fourier transforms of projection functions. The calculations can be carried out in a short computation time without involving unstable procedures. Numerical simulations were made to demonstrate the effectiveness of the proposed method.     

Scatter correction in SPECT using non-uniform attenuation data

Quantitative assessment of activity levels with SPECT is difficult because of attenuation and scattering of gamma rays within the object. To study the effect of attenuation and scatter on SPECT quantitation, phantom studies were performed with non-uniform attenuation. Simulated transmission CT data provided information about the distribution of attenuation coefficients within the source. Attenuation correction was performed by an iterative reprojection technique. Scatter correction was done by convolution of the attenuation-corrected image and an appropriate filter. The filter characteristics depended on the attenuation and activity measurement at each pixel. The scatter correction could compensate completely for the 28% scatter component from a line source, and the 61% component from a thick, extended source. Accuracy of regional activity ratios and the linearity of the relationship between true radioactivity and the SPECT measurement were both significantly improved by these corrections. The present method is expected to be valuable for the quantitative assessment of regional activity.     

Analytical cone-beam SPECT reconstruction algorithm with non-uniform attenuation for general non-circular orbit

In single photon emission computed tomography (SPECT), due to the attenuation of gamma photons, the analytical reconstruction is complicated, where attenuation should be compensated to obtain quantitative results. We know that the resolution of SPECT is low. The cone-beam SPECT reconstruction can improve the photon density and spatial resolution of the reconstructed image. In practice, to minimize the effect of distance-dependent resolution variation (DDRV), the detector should be set as close as possible to the patient. Therefore it would be more efficacious for the orbit of the detector to be elliptical or another shape. In this paper, based on the Novikov's reconstruction formula and our Ray-driven Technology, we present an analytical cone-beam SPECT reconstruction algorithm for general non-circular orbit. The simulation results demonstrate the accuracy and robustness of our method.     

The cardiofocal collimator: a variable-focus collimator for cardiac SPECT

Investigators in nuclear medicine have long been in search of a practical method to increase the number of detected events in cardiac SPECT. A clinically practical method requires a simple data acquisition protocol, clinically acceptable reconstruction times, artifact levels near or below visual threshold, and the use of currently available cameras and computers. Towards this end, we have developed the Cardiofocal collimator, a variable-focus collimator for cardiac SPECT that increases the number of detected events from the heart by more than a factor of two compared to that of a parallel-hole collimator with equivalent resolution. In both the transverse and axial dimensions, the focusing is strongest at the centre of the collimator, and gradually relaxes to nearly parallel-hole collimation at the edge of the collimator. The variable-focus concept provides an increase in the number of counts from organs imaged near the centre of the collimator, where the heart will spend most of the time during a cardiac SPECT study, while adequately sampling enough of the background activity distribution to prevent truncation artifacts in the reconstructed images. Images are reconstructed in clinically acceptable times using a filtered backprojection reconstruction algorithm. The algorithm supports both full-scan (360 degrees) and short-scan (180 degrees plus the fan angle) acquisitions. The results of simulations and phantom studies are included to demonstrate the performance of the Cardiofocal collimator.     

A comparison of MR-based attenuation correction in PET versus SPECT

Attenuation correction (AC) is a critical step in the reconstruction of quantitatively accurate positron emission tomography (PET) and single photon emission computed tomography (SPECT) images. Several groups have proposed magnetic resonance (MR)-based AC algorithms for application in hybrid PET/MR systems. However, none of these approaches have been tested on SPECT data. Since SPECT/MR systems are under active development, it is important to ascertain whether MR-based AC algorithms validated for PET can be applied to SPECT. To investigate this issue, two imaging experiments were performed: one with an anthropomorphic chest phantom and one with two groups of canines. Both groups of canines were imaged from neck to abdomen, one with PET/CT and MR (n = 4) and the other with SPECT/CT and MR (n = 4), while the phantom was imaged with all modalities. The quality of the nuclear medicine reconstructions using MR-based attenuation maps was compared between PET and SPECT on global and local scales. In addition, the sensitivity of these reconstructions to variations in the attenuation map was ascertained. On both scales, it was found that the SPECT reconstructions were of higher fidelity than the PET reconstructions. Further, they were less sensitive to changes to the MR-based attenuation map. Thus, MR-based AC algorithms that have been designed for PET/MR can be expected to demonstrate improved performance when used for SPECT/MR.     

Calculation and validation of the use of effective attenuation coefficient for attenuation correction in In-111 SPECT

Nuclear medicine tracers using 111In as a radiolabel are increasing in their use, especially in the domain of oncologic imaging. In these applications, it often is critical to have the capability of quantifying radionuclide uptake and being able to relate it to the biological properties of the tumor. However, images from single photon emission computed tomography (SPECT) can be degraded by photon attenuation, photon scattering, and collimator blurring; without compensation for these effects, image quality can be degraded, and accurate and precise quantification is impossible. Although attenuation correction for SPECT is becoming more common, most implementations can only model single energy radionuclides such as 99mTc and 123I. Thus, attenuation correction for 111In is challenging because it emits two photons (171 and 245 keV) at nearly equal rates (90.2% and 94% emission probabilities). In this paper, we present a method of calculating a single "effective" attenuation coefficient for the dual-energy emissions of 111In, and that can be used to correct for photon attenuation in radionuclide images acquired with this radionuclide. Using this methodology, we can derive an effective linear attenuation coefficient Micro(eff) and an effective photon energy E(eff) based on the emission probabilities and linear attenuation coefficients of the 111In photons. This approach allows us to treat the emissions from 111In as a single photon with an effective energy of 210 keV. We obtained emission projection data from a tank filled with a uniform solution of 111In. The projection data were reconstructed using an iterative maximum-likelihood algorithm with no attenuation correction, and with attenuation correction assuming photon energies of 171, 245, and 210 keV (the derived E(eff)). The reconstructed tomographic images demonstrate that the use of no attenuation correction, or correction assuming photon energies of 171 or 245 keV introduces inaccuracies into the reconstructed radioactivity distribution when compared against the effective energy method. In summary, this work provides both a theoretical framework and experimental methodology of attenuation correction for the dual-energy emissions from 111In. Although these results are specific to 111In, the foundation could easily be extended to other multiple-energy isotopes.     

A Fourier reconstruction algorithm with constant attenuation compensation using 180 degrees acquisition data for SPECT

In this paper, we develop an approximate analytical reconstruction algorithm that compensates for uniform attenuation in 2D parallel-beam SPECT with a 180-degree acquisition. This new algorithm is in the form of a direct Fourier reconstruction. The complex variable central slice theorem is used to derive this algorithm. The image is reconstructed with the following steps: first, the attenuated projection data acquired over 180 degrees are extended to 360 degrees and the value for the uniform attenuator is changed to a negative value. The Fourier transform (FT) of the image in polar coordinates is obtained from the Fourier transform of an analytic function interpolated from an extension of the projection data according to the complex central slice theorem. Finally, the image is obtained by performing a 2D inverse Fourier transform. Computer simulations and comparison studies with a 360-degree full-scan algorithm are provided.     

Image reconstruction algorithm for a spinning strip CZT SPECT camera with a parallel slat collimator and small pixels

This paper discusses the use of small pixels in a spinning CdZnTe single photon emission computed tomography (SPECT) camera that is mounted with a parallel slat collimator. In a conventional slat collimation configuration, there is a detector pixel between two adjacent collimator slats. In our design, the pixel size is halved. That is, there are two smaller pixels to replace a regular pixel between two adjacent slats while the collimator remains unchanged. It has an advantage over our older design that uses tilted slats. In order to acquire a complete data set the tilted-slat collimator must spin 360 degrees at each SPECT view while the proposed design requires only 180 degrees at each SPECT view. Computer simulations and phantom experiments have been carried out to investigate the performance of the small-pixel configuration. It is observed that this design has the potential to increase the spatial resolution of the detector while keeping photon counts the same.     

CdZnTe strip detector SPECT imaging with a slit collimator

In this paper, we propose a CdZnTe rotating and spinning gamma camera attached with a slit collimator. This imaging system acquires convergent planar integrals of a radioactive distribution. Two analytical image reconstruction algorithms are proposed. Preliminary phantom studies show that our small CdZnTe camera with a slit collimator outperforms a larger NaI(Tl) camera with a pinhole collimator in terms of spatial resolution in the reconstructed images. The main application of this system is small animal SPECT imaging.     

Performance of a novel collimator for high-sensitivity brain SPECT

We assessed improvements in performance in detection and estimation tasks due to a novel brain single photon computed tomography collimator. Data were acquired on the CeraSPECT scanner using both new and standard collimators. The new variable focusing collimator SensOgrade samples the projections unequally, with central regions more heavily represented, to compensate for attenuation of counts from central brain structures. Furthermore, it utilizes more of the cylindrical crystal surface. Two phantom studies were performed. The first phantom was a 21-cm-diameter cylindrical background containing nine spheres ranging from 0.5 to 5 cm3 in volume. 99mTc sphere to background activity ratio was 10:1. Twenty-nine 10-min datasets were acquired with each collimator. The second phantom was the Radiology Support Devices (Long Beach, CA) striatal phantom with striatal-background ratios of 10:1 on the left and 5:1 on the right. Twenty-nine 4-min datasets were acquired with each collimator. Perfusion imaging using 99mTc-HMPAO was also performed in three healthy volunteers using both collimators under identical simulations. Projections were reconstructed by filtered backprojection with an unwindowed ramp filter. The nonprewhitening matched filter signal-to-noise ratio (NPW-SNR) was computed as a surrogate for human performance in detecting spherical lesions. Sphere activity concentration, radius, and location coordinates were simultaneously estimated by fitting images to an assumed model using an iterative nonlinear algorithm. Resolution recovery was implicit in the estimation procedure, as the point spread function was incorporated into the model. NPW-SNR for sphere detection was 1.5 to 2 times greater with the new collimator; for the striatal phantom the improvement in SNR was 54%. The SNR for estimating sphere activity concentration improved by 46 to 89% for spheres located more than 5 cm from the phantom center. Images acquired with the standard collimator were too noisy in the central regions to allow estimation of sphere activity. In 99mTc-HMPAO human studies, SNR was improved by 21 to 41% in the cortex, 66% in the basal ganglia, and 74% in the thalamus. The new collimator leads to substantially improved detection and estimation performance throughout the brain. The higher sensitivity will be particularly important for dynamic imaging.     

A three-dimensional ray-driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media

The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically accurate information.