Physical characteristics of the ECAT 953B/31: a new high resolution brain positron tomograph

A high spatial resolution brain positron tomograph, the ECAT 953B/31, is presented. The machine consists of two 76.5 cm diameter rings (patient port diameter: 36 cm) made of 24 8x8 BGO detector blocks each, each block being coupled to four 1 in(2) Hammamatsu phototubes. The machine has 15 9 cmx1 mm motorized removable septa, which allows reconstruction of 31 slices 3.375 mm apart. The transaxial resolution (FWHM) in the reconstructed image (with wobbling) is 4.5 mm at center, 5.2 mm (tangential) and 5.6 mm at 10 cm from center. With septa out of the field of view (FOV), the axial resolution degrades to 5.5 mm a center and 6.3 mm at 10 cm from center. At 1 muCi/cc with a 250 keV threshold and a 12 ns coincidence window, the sensitivity is 146100 true events, the ratio of randoms to trues is 0.10, the scatter fraction is 17% and the dead-time losses are 30%. With septa out of the FOV, the sensitivity is increased by a factor 3.6, while the scatter fraction reaches 0.9. Images obtained with (18 )F-DG and H(2)(15)O in human brains and (18 )F-DOPA in a baboon brain demonstrate that the ECAT 953B/31 will be suitable for high resolution and for low count rate brain studies.     

Efficient fully 3-D iterative SPECT reconstruction with Monte Carlo-based scatter compensation

Quantitative accuracy of single photon emission computed tomography (SPECT) images is highly dependent on the photon scatter model used for image reconstruction. Monte Carlo simulation (MCS) is the most general method for detailed modeling of scatter, but to date, fully three-dimensional (3-D) MCS-based statistical SPECT reconstruction approaches have not been realized, due to prohibitively long computation times and excessive computer memory requirements. MCS-based reconstruction has previously been restricted to two-dimensional approaches that are vastly inferior to fully 3-D reconstruction. Instead of MCS, scatter calculations based on simplified but less accurate models are sometimes incorporated in fully 3-D SPECT reconstruction algorithms. We developed a computationally efficient fully 3-D MCS-based reconstruction architecture by combining the following methods: 1) a dual matrix ordered subset (DM-OS) reconstruction algorithm to accelerate the reconstruction and avoid massive transition matrix precalculation and storage; 2) a stochastic photon transport calculation in MCS is combined with an analytic detector modeling step to reduce noise in the Monte Carlo (MC)-based reprojection after only a small number of photon histories have been tracked; and 3) the number of photon histories simulated is reduced by an order of magnitude in early iterations, or photon histories calculated in an early iteration are reused. For a 64 x 64 x 64 image array, the reconstruction time required for ten DM-OS iterations is approximately 30 min on a dual processor (AMD 1.4 GHz) PC, in which case the stochastic nature of MCS modeling is found to have a negligible effect on noise in reconstructions. Since MCS can calculate photon transport for any clinically used photon energy and patient attenuation distribution, the proposed methodology is expected to be useful for obtaining highly accurate quantitative SPECT images within clinically acceptable computation times.     

An approximation formula for the variance of PET region-of-interest values

An approximation formula for the variance of positron emission tomography (PET) region-of-interest (ROI) values has been developed, implemented, and evaluated. This formula does not require access to the original projection data and is therefore convenient for routine use. The formula was derived by applying successive approximations to the filtered-backprojection reconstruction algorithm. ROI variance is estimated from the product of mean pixel variance within the region and a term accounting for the intercorrelation of all pixel pairs inside the region. The formula accounts for radioactivity distribution, attenuation, randoms, scatter, deadtime, detector normalization, scan length, decay, and reconstruction filter. The algorithm was tested by comparison to the exact ROI variance as calculated with Huesman's algorithm. Tests with scan data from phantoms, animals, and humans obtained on the Scanditronix PC2048-15B tomograph showed the approximation formula to be accurate to within +/-10%     

2.5-D simultaneous multislice reconstruction by series expansion methods from Fourier-rebinned PET data

True three-dimensional (3-D) volume reconstruction from fully 3-D data in positron emission tomography (PET) has only a limited clinical use because of its large computational burden. Fourier rebinning (FORE) of the fully 3-D data into a set of 2-D sinogram data decomposes the 3-D reconstruction process into multiple 2-D reconstructions of decoupled 2-D image slices, thus substantially decreasing the computational burden even in the case when the 2-D reconstructions are performed by an iterative reconstruction algorithm. On the other hand, the approximations involved in the rebinning combined with the decoupling of the image slices cause a certain reduction of image quality, especially when the signal-to-noise ratio of the data is low. We propose a 2.5-D Simultaneous Multislice Reconstruction approach, based on the series expansion principle, where the volume is represented by the superposition of 3-D spherically symmetric bell-shaped basis functions. It takes advantage of the time reduction due to the use of the FORE (2-D) data, instead of the original fully 3-D data, but at the same time uses a 3-D iterative reconstruction approach with 3-D basis functions. The same general approach can be applied to any reconstruction algorithm belonging to the class of series expansion methods (iterative or noniterative) using 3-D basis functions that span multiple slices, and can be used for any multislice sinogram or list mode data whether obtained by a special rebinning scheme or acquired directly by a PET scanner in the 2-D mode using septa. Our studies confirm that the proposed 2.5-D approach provides a considerable improvement in reconstruction quality, as compared to the standard 2-D reconstruction approach, while the reconstruction time is of the same order as that of the 2-D approach and is clinically practical even on a general-purpose computer.     

An evaluation of exact and approximate 3-D reconstruction algorithms for a high-resolution, small-animal PET scanner

MicroPET is a low-cost, high-resolution positron emission tomography (PET) scanner designed for imaging small animals. MicroPET operates exclusively without septa, acquiring fully three-dimensional (3-D) data sets. The performance of the projection-reprojection (3DRP), variable axial rebinning (VARB), single slice rebinning (SSRB), and Fourier rebinning (FORE) methods for reconstruction of microPET data were evaluated. The algorithms were compared with respect to resolution, noise variance, and reconstruction time. Results suggested that the 3DRP algorithm gives the best combination of resolution and noise performance in 9 min of reconstruction time on a Sun UltraSparc I workstation. The FORE algorithm provided the most acceptable accelerated method of reconstruction, giving similar resolution performance with a 10%-20% degradation in noise variance in under 2 min. Significant degradation in the axial resolution was measured with the VARB and SSRB methods, offsetting the decrease in reconstruction time achieved with those methods. In-plane angular mashing of the 3-D data before reconstruction led to a 50% reduction in reconstruction time but also introduced unacceptable tangential blurring artifacts. This thorough evaluation of analytical 3-D reconstruction techniques allowed for optimal selection of a reconstruction method for the diverse range of microPET applications.     

Improved SPECT quantitation using fully three-dimensional iterative spatially variant scatter response compensation

The quality and quantitative accuracy of iteratively reconstructed SPECT images improves when better point spread function (PSF) models of the gamma camera are used during reconstruction. Here, inclusion in the PSF model of photon crosstalk between different slices caused by limited gamma camera resolution and scatter is examined. A three-dimensional (3-D) projector back-projector (proback) has been developed which models both the distance dependent detector point spread function and the object shape-dependent scatter point spread function of single photon emission computed tomography (SPECT). A table occupying only a few megabytes of memory is sufficient to represent this scatter model. The contents of this table are obtained by evaluating an analytical expression for object shape-dependent scatter. The proposed approach avoids the huge memory requirements of storing the full transition matrix needed for 3-D reconstruction including object shape-dependent scatter. In addition, the method avoids the need for lengthy Monte Carlo simulations to generate such a matrix. In order to assess the quantitative accuracy of the method, reconstructions of a water filled cylinder containing regions of different activity levels and of simulated 3-D brain projection data have been evaluated for technetium-99m. It is shown that fully 3-D reconstruction including complete detector response and object shape-dependent scatter modeling clearly outperforms simpler methods that lack a complete detector response and/or a complete scatter response model. Fully 3-D scatter correction yields the best quantitation of volumes of interest and the best contrast-to-noise curves.     

The design of an animal PET: flexible geometry for achievingoptimal spatial resolution or high sensitivity

Presents the design of a positron emission tomograph (PET) with flexible geometry dedicated to in vivo studies of small animals (TierPET). The scanner uses two pairs of detectors. Each detector consists of 400 small individual yttrium aluminum perovskite (YAP) scintillator crystals of dimensions 2×2×15 mm³, optically isolated and glued together, which are coupled to position-sensitive photomultiplier tubes (PSPMTs). The detector modules can be moved in a radial direction so that the detector-to-detector spacing can be varied. Special hardware has been built for coincidence detection, position detection, and real-time data acquisition, which is performed by a PC. The single-event data are transferred to workstations where the radioactivity distribution is reconstructed. The dimensions of the crystals and the detector layout are the result of extensive simulations which are described in this report, taking into account sensitivity, spatial resolution and additional parameters like parallax error or scatter effects. For the three-dimensional (3-D) reconstruction a genuine 3-D expectation-maximization (EM)-algorithm which can include the characteristics of the detector system has been implemented. The reconstruction software is flexible and matches the different detector configurations. The main advantage of the proposed animal PET scanner is its high flexibility, allowing the realization of various detector-system configurations. By changing the detector-to-detector spacing, the system is capable of either providing good spatial resolution or high sensitivity for dynamic studies of pharmacokinetics     

A projector/backprojector with slice-to-slice blurring forefficient three-dimensional scatter modeling

Scatter correction is an important factor in single photon emission computed tomography (SPECT). Many scatter correction techniques, such as multiple-window subtraction and intrinsic modeling with iterative algorithms, have been under study for many years. Previously, we developed an efficient slice-to-slice blurring technique to model attenuation and system geometric response in a projector/backprojector pair, which was used in an ML-EM algorithm to reconstruct SPECT data. This paper proposes a projector/backprojector that models the three-dimensional (3-D) first-order scatter in SPECT, also using an efficient slice-to-slice blurring technique. The scatter response is estimated from a known nonuniform attenuation distribution map. It is assumed that the probability of detection of a first-order scattered photon from a photon that is emitted in a given source voxel and scattered in a given scatter voxel is proportional to the attenuation coefficient value at that voxel. Monte Carlo simulations of point sources and an MCAT torso phantom were used to verify the accuracy of the proposed projector/backprojector model. An experimental Jaszczak torso/cardiac phantom SPECT study was also performed. For a 64 x 64 x 64 image volume, it took 8.7 s to perform each iteration per slice on a Sun ULTRA Enterprise 3000 (167 MHz, 1 Gbyte RAM) computer, when modeling 3-D scatter, attenuation, and system geometric response functions. The main advantage of the proposed method is its easy implementation and the possibility of performing reconstruction in clinically acceptable time.     

O(N3 log N) backprojection algorithm for the 3-D radon transform

We present a novel backprojection algorithm for three-dimensional (3-D) radon transform data that requires O(N3 log2 N) operations for reconstruction of an N x N x N volume from O(N2) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N5) computations under the same circumstances.     

Real-time image reconstruction for spiral MRI using fixed-point calculation

Because spiral magnetic resonance imaging (MRI) is more robust to motion artifacts than echo planar imaging (EPI), spiral imaging method is more suitable in real-time imaging applications where dynamic processes are to be observed. The major hurdle to use spiral imaging method in real-time applications is its slow reconstruction speed. Since spiral trajectories do not sample data on rectilinear grids, raw data must be regridded before inverse fast Fourier transform (FFT). At present, the computational cost for the spiral reconstruction algorithm is still too high and it is not fast enough to achieve the minimum speed requirement of 20 frames/s for real-time imaging applications. In this paper, we propose to replace floating-point calculations with fixed-point calculations in the reconstruction algorithm to remove the computational bottlenecks. To overcome the quantization and round-off errors introduced by fixed-point calculations, we devise a method to find the optimal precision for the fixed-point representation. Adding with a highly efficient vector-radix two-dimensional (2-D) FFT algorithm and modifications to speed up the gridding convolution, we have cut the reconstruction time by 42% and achieved real-time reconstruction at 30 frames/s for 128 x 128 matrices on low-cost PC's.     

Ultra fast symmetry and SIMD-based projection-backprojection (SSP) algorithm for 3-D PET image reconstruction

Remarkable progress in positron emission tomography (PET) development has occurred in recent years, in hardware, software, and computer implementation of image reconstruction. Recent development in PET scanners such as the high-resolution research tomograph (HRRT) developed by CTI (now Siemens) represents such a case and is capable of greatly enhanced resolution as well as sensitivity. In these PET scanners, the amount of coincidence line data collected contains more than 4.5 x 10(9) coincidence lines of response generated by as many nuclear detectors as 120 000. This formidable amount of data and the reconstruction of this data set pose a real problem in HRRT and have also been of the major bottle neck in further developments of high resolution PET scanners as well as their applications. In these classes of PET scanners, therefore, obtaining one set of reconstructed images often requires many hours of image reconstruction. For example, in HRRT with full data collection in a normal brain scan (using SPAN 3), the image reconstruction time is close to 80 min, making it practically impossible to attempt any list-mode-based dynamic imaging since the image reconstruction time would take many days (as much as 43 h or more for 32-frame dynamic image reconstruction). To remedy this data-handling problem in image reconstruction, we developed a new algorithm based on the symmetry properties of the projection and backprojection processes, especially in the 3-D OSEM algorithm where multiples of projection and back-projection are required. In addition, the single-instruction multiple-data (SIMD) technique also allowed us to successfully incorporate the symmetry properties mentioned above, thereby effectively reducing the total image reconstruction time to a few minutes. We refer to this technique as the symmetry and SIMD-based projection-backprojection (SSP) technique or algorithm and the details of the technique will be discussed and an example of the application of the technique to the HRRT's OSEM algorithm will be presented as a demonstration.     

3-D maximum a posteriori estimation for single photon emission computed tomography on massively-parallel computers

A fully three-dimensional (3-D) implementation of the maximum a posteriori (MAP) method for single photon emission computed tomography (SPECT) is demonstrated. The 3-D reconstruction exhibits a major increase in resolution when compared to the generation of the series of separate 2-D slice reconstructions. As has been noted, the iterative EM algorithm for 2-D reconstruction is highly computational; the 3-D algorithm is far worse. To accommodate the computational complexity, previous work in the 2-D arena is extended, and an implementation on the class of massively parallel processors of the 3-D algorithm is demonstrated. Using a 16000- (4000-) processor MasPar/DECmpp-Sx machine, the algorithm is demonstrated to execute at 2.5 (7.8) s/EM-iteration for the entire 64x64x64 cube of 96 planar measurements obtained from the Siemens Orbiter rotating camera operating in the high-resolution mode.     

Resolution and noise properties of MAP reconstruction for fully 3-D PET

We derive approximate analytical expressions for the local impulse response and covariance of images reconstructed from fully three-dimensional (3-D) positron emission tomography (PET) data using maximum a posteriori (MAP) estimation. These expressions explicitly account for the spatially variant detector response and sensitivity of a 3-D tomograph. The resulting spatially variant impulse response and covariance are computed using 3-D Fourier transforms. A truncated Gaussian distribution is used to account for the effect on the variance of the nonnegativity constraint used in MAP reconstruction. Using Monte Carlo simulations and phantom data from the microPET small animal scanner, we show that the approximations provide reasonably accurate estimates of contrast recovery and covariance of MAP reconstruction for priors with quadratic energy functions. We also describe how these analytical results can be used to achieve near-uniform contrast recovery throughout the reconstructed volume.     

A comparison of deconvolution and windowed subtraction techniques for scatter compensation in SPECT

Three procedures for the removal of Compton-scattered data in SPECT by constrained deconvolution are presented. The first is a deconvolution of a 2-D measured PSRF containing scatter from a single reconstructed transaxial image; the second is a deconvolution of a 2-D measured point-source response function (PSRF) from each frame of projection data prior to reconstruction; the third involves deconvolution of a 3-D measured PSRF from a stack of reconstructed slices. Results of applying these procedures to data obtained from a phantom containing cold cylinders and to data from a cold spot-resolution phantom are presented and are shown to be superior to the results of correcting for scatter by scatter-window substraction. Both 3-D deconvolution from reconstructed images and 2-D deconvolution from projection data show major improvements in image contrast, resolution, and quantitation. Improvements are especially marked for small (1.0-3.0 cm) cold sources.     

Novel scatter compensation of list-mode PET data using spatial and energy dependent corrections

With the widespread use of positron emission tomography (PET) crystals with greatly improved energy resolution (e.g., 11.5% with LYSO as compared to 20% with BGO) and of list-mode acquisitions, the use of the energy of individual events in scatter correction schemes becomes feasible. We propose a novel scatter approach that incorporates the energy of individual photons in the scatter correction and reconstruction of list-mode PET data in addition to the spatial information presently used in clinical scanners. First, we rewrite the Poisson likelihood function of list-mode PET data including the energy distributions of primary and scatter coincidences and show that this expression yields an MLEM reconstruction algorithm containing both energy and spatial dependent corrections. To estimate the spatial distribution of scatter coincidences we use the single scatter simulation (SSS). Next, we derive two new formulae which allow estimation of the 2-D (coincidences) energy probability density functions (E-PDF) of primary and scatter coincidences from the 1-D (photons) E-PDFs associated with each photon. We also describe an accurate and robust object-specific method for estimating these 1-D E-PDFs based on a decomposition of the total energy spectra detected across the scanner into primary and scattered components. Finally, we show that the energy information can be used to accurately normalize the scatter sinogram to the data. We compared the performance of this novel scatter correction incorporating both the position and energy of detected coincidences to that of the traditional approach modeling only the spatial distribution of scatter coincidences in 3-D Monte Carlo simulations of a medium cylindrical phantom and a large, nonuniform NCAT phantom. Incorporating the energy information in the scatter correction decreased bias in the activity distribution estimation by ~20% and ~40% in the cold regions of the large NCAT phantom at energy resolutions 11.5% and 20% at 511 keV, respectively, compared to when using the spatial information alone.     

Optimal CT scanning plan for long-bone 3-D reconstruction

Digital computed tomographic (CT) data are widely used in three-dimensional (3-D) construction of bone geometry and density features for 3-D modelling purposes. During in vivo CT data acquisition the number of scans must be limited in order to protect patients from the risks related to X-ray absorption. The aim of this work is to automatically define, given a finite number of CT slices, the scanning plan which returns the optimal 3-D reconstruction of a bone segment from in vivo acquired CT images. An optimization algorithm based on a Discard-Insert-Exchange technique has been developed. In the proposed method the optimal scanning sequence is searched by minimizing the overall reconstruction error of a two-dimensional (2-D) prescanning image: an anterior-posterior (AP) X-ray projection of the bone segment. This approach has been validated in vitro on 3 different femurs. The 3-D reconstruction errors obtained through the optimization of the scanning plan on the 3-D prescanning images and on the corresponding 3-D data sets have been compared. 2-D and 3-D data sets have been reconstructed by linear interpolation along the longitudinal axis. Results show that direct 3-D optimization yields root mean square reconstruction errors which are only 4%-7% lower than the 2-D-optimized plan, thus proving that 2-D-optimization provides a good suboptimal scanning plan for 3-D reconstruction. Further on, 3-D reconstruction errors given by the optimized scanning plan and a standard radiological protocol for long bones have been compared. Results show that the optimized plan yields 20%-50% lower 3-D reconstruction errors     

Comparison of 3-D maximum a posteriori and filtered backprojection algorithms for high-resolution animal imaging with microPET

We have evaluated the performance of two three-dimensional (3-D) reconstruction algorithms with data acquired from microPET, a high resolution tomograph dedicated to small animal imaging. The first was a linear filtered-backprojection algorithm (FBP) with reprojection of the missing data, and the second was a statistical maximum a posteriori probability algorithm (MAP). The two algorithms were evaluated in terms of their resolution performance, both in phantoms and in vivo. Sixty independent realizations of a phantom simulating the brain of a baby monkey were acquired, each containing three million counts. Each of these realizations was reconstructed independently with both algorithms. The ensemble of the 60 reconstructed realizations was used to estimate the standard deviation as a measure of the noise for each reconstruction algorithm. More detail was recovered in the MAP reconstruction without an increase in noise relative to FBP. Studies in a simple cylindrical compartment phantom demonstrated improved recovery of known activity ratios with MAP. Finally, in vivo studies also demonstrated a clear improvement in spatial resolution using the MAP algorithm. The quantitative accuracy of the MAP reconstruction was also evaluated by comparison with autoradiography and direct well counting of tissue samples and was shown to be superior.     

Characterization of dynamic 3-D PET imaging for functional brainmapping

Methods for optimizing the acquisition, reconstruction and analysis of positron emission tomography (PET) images for functional brain mapping have been investigated. The scatter fraction and noise-equivalent count rate characteristics were measured for the ECAT 951/31R PET scanner operating in septa-extended two-dimensional (2-D) and septa-retracted three-dimensional (3-D) modes. The 3-D mode is shown to provide higher signal-to-noise images than the 2-D mode at specific activities less than 30 kBq/ml. To enable increased temporal resolution in dynamic 3-D PET activation studies, a parallel version of the 3-D reconstruction algorithm was developed. Implementation of the reprojection algorithm on an 88 processor i860 supercomputer resulted in a more than tenfold increase in reconstruction speed compared to a single i860 processor system. An investigation of the optimal duration for imaging brain activations was undertaken in 12 normal subjects using repeated H₂¹⁵O slow infusions and a visually presented lexical decision task. The significance of change in regional cerebral blood flow (CBF) was determined using statistical parametric maps for images acquired during stimulation, immediately after stimulation, and commencing 1 min after cessation of the stimulus. Regions of CBF change were detected in all three images. Dynamic 3-D, or four-dimensional (4-D), PET activation scanning is shown to be practical and likely to further improve the sensitivity of PET for detection of subtle regional CBF changes in functional brain mapping research     

Exact and approximate rebinning algorithms for 3-D PET data

This paper presents two new rebinning algorithms for the reconstruction of three-dimensional (3-D) positron emission tomography (PET) data. A rebinning algorithm is one that first sorts the 3-D data into an ordinary two-dimensional (2-D) data set containing one sinogram for each transaxial slice to be reconstructed; the 3-D image is then recovered by applying to each slice a 2-D reconstruction method such as filtered-backprojection. This approach allows a significant speedup of 3-D reconstruction, which is particularly useful for applications involving dynamic acquisitions or whole-body imaging. The first new algorithm is obtained by discretizing an exact analytical inversion formula. The second algorithm, called the Fourier rebinning algorithm (FORE), is approximate but allows an efficient implementation based on taking 2-D Fourier transforms of the data. This second algorithm was implemented and applied to data acquired with the new generation of PET systems and also to simulated data for a scanner with an 18° axial aperture. The reconstructed images were compared to those obtained with the 3-D reprojection algorithm (3DRP) which is the standard “exact” 3-D filtered-backprojection method. Results demonstrate that FORE provides a reliable alternative to 3DRP, while at the same time achieving an order of magnitude reduction in processing time     

Implementation of a model-based nonuniform scatter correctionscheme for SPECT

Four scatter-compensation schemes are considered. The 4 schemes are all based on a previously developed two-dimensional (2-D) scatter model. Reconstruction is achieved using the iterative expectation-maximization maximum-likelihood (EM-ML) algorithm. The schemes consist of: (1) including the model in both the forward and back projector; (2) just including the model in the forward projector; (3) and (4) implementing the model in a subtraction and addition scheme, respectively. Monte Carlo simulated projection data are used to test the accuracy, convergence properties, and noise properties of the 4 scatter-compensation schemes. Data are simulated for both uniformly and nonuniformly attenuating objects. The results show that all 4 correction schemes yield images which are similar in terms of accuracy to that obtained from reconstructing scatter-free data. The subtraction scheme is shown to converge faster than the other compensation schemes, both in terms of iterations and actual time required for reconstruction. The scheme in which the model is only used in the forward-projector and the scatter-addition scheme both performs slightly better, in terms of signal-to-noise ratio (SNR), than the subtraction scheme. However, the forward projector scheme requires significantly more CPU time for reconstruction. The correction scheme in which the scatter model was included in both the forward and backprojectors is shown to produce accurate images with SNR's higher than even a perfect scatter rejection scheme. While the scatter correction scheme with the model in both the forward projector and backprojector has superior noise properties to the other algorithms, the results suggest that the faster subtraction/addition schemes will probably prove most useful for routine clinical scatter compensation