Vitali Selivanov

Detector response models for statistical iterative image reconstruction in high resolution PET

One limitation in a practical implementation of statistical iterative image reconstruction is to compute a transition matrix accurately modeling the relationship between projection and image spaces. Detector response function (DRF) in positron emission tomography (PET) is broad and spatially-variant, leading to large transition matrices taking too much space to store. In this work, the authors investigate the effect of simpler DRF models on image quality in maximum likelihood expectation maximization reconstruction. The authors studied 6 cases of modeling projection/image relationship: tube/pixel geometric overlap with tubes centered on detector face; same as previous with tubes centered on DRF maximum; two different fixed-width Gaussian functions centered on DRF maximum weighing tube/pixel overlap; same as previous with a Gaussian of the same spectral resolution as DRF; analytic DRF based on linear attenuation of /spl gamma/-rays in detector arrays weighing tube/pixel overlap. The authors found that DRF oversimplification may affect visual image quality and image quantification dramatically, including artefact generation. They showed that analytic DRF yielded images of excellent quality for a small animal PET system with long, narrow detectors and generated a transition matrix for 2-D reconstruction that could be easily fitted into the memory of current stand-alone computers.

Performance Evaluation of the LabPET APD-Based Digital PET Scanner

The LabPETTM is a fully digital avalanche photodiode (APD) based PET scanner designed for state-of-the- art molecular and genomic imaging of small animals. Two versions of the scanner were evaluated, having 3.75 (LabPET4) and 7.5 cm axial FOV (LabPET8). The detectors are made of 2x2x10/12 mm3 LYSO and LGSO crystals assembled in phoswich pairs read out by an APD. After digital crystal identification, the average energy resolution is 24 plusmn 6% for LYSO and 25 plusmn 6% for LGSO. The scanner overall timing resolution is 6.6 ns for LYSO/LYSO and 10.7 ns for LGSO/LGSO coincidences after coarse timing alignment. The FBP reconstructed tangential/radial resolution is 1.3/1.4 mm FWHM (2.5/2.4 mm FWTM) at the FOV center and remains below 2.1 mm FWHM (3.6 mm FWTM) within the central 4-cm diameter FOV. MLEM reconstruction of a micro resolution phantom provided clear separation of the 1.35 mm spots and fair identification of 1 mm spots. With an energy window of 250-650 keV, the sensitivity is 1.1% for LabPET4 and 2.1% for LabPET8. The imaging capabilities of the scanner are demonstrated with in vivo images of rats and mice.

Cross-validation stopping rule for ML-EM reconstruction of dynamic PET series: effect on image quality and quantitative accuracy

A major shortcoming of the Maximum Likelihood Expectation Maximization (ML-EM) method for reconstruction of dynamic PET images is to decide when to stop the iterative process for image frames with largely different statistics and activity distributions. A widespread practice to overcome this problem involves over-iteration of an image estimate followed by smoothing. In this work, the authors investigate the qualitative and quantitative accuracy of the cross-validation procedure (CV) as a stopping rule, in comparison to over-iteration and post-filtering. For the reconstruction of phantom and small animal dynamic FDG-PET data acquired in 2-D mode. The CV stopping rule ensured visually acceptable image estimates with balanced resolution and noise characteristics. However, quantitative accuracy required more than 10/sup 5/ events per image. The effect of the number of ML-EM iterations on time-activity curves and metabolic rates of glucose extracted from image series is discussed. A dependence of the CV defined number of iterations on projection counts was found which simplifies reconstruction and reduces computation time.

Fast PET image reconstruction based on SVD decomposition of the system matrix

Data filtering based on matrix pseudo-inverse is a well known but not yet appreciated means of tomographic image reconstruction. Matrix pseudo-inversion step is very demanding in terms of numerical precision and necessary computing power. Ill conditioning of the system matrix in positron emission tomography (PET) results in solutions highly sensitive to noise in the experimental data. In the present work, the feasibility of image reconstruction based on singular value decomposition (SVD) of the system matrix for animal 2-D PET is demonstrated. Analytic detector response accounting for the non-invariant spatial system response is explicitly included into the system matrix. Regularization of the SVD-based solution with the singular spectrum truncation (TSVD solution) derived from spatial resolution analysis is proposed. TSVD reconstruction is fast except for the matrix decomposition step, which is performed once for a given scanner geometry. Reconstructed image quality and quantitation are compared to those obtained with filtered backprojection (FBP) and iterative maximum likelihood technique. TSVD image reconstruction may be a viable alternative to FBP for routine clinical applications.

Determination of blood curve and tissue uptake from left ventricle using FADS in rat FDG-PET studies

Blood input function is necessary for quantitative pharmacokinetic studies in Positron Emission Tomography (PET). However, external blood sampling from small animals presents many limitations. In this work, we show that the blood input function in rats can be extracted from the left ventricular blood pool using Factor Analysis of Dynamic Structures (FADS). Images of the heart from eight rats were acquired with the Sherbrooke animal PET scanner. A region of interest (ROI) was drawn around the left ventricle (LV) and decomposed into the blood pool and the myocardium tissue using FADS. The input curve (IC) obtained with FADS is comparable to that obtained from measured images for the first frames, while it significantly decreases with increasing time. The myocardium tissue segments present lower amplitude at early times and approximately no change at later times in comparison to the same ROIs obtained from measured images. On average, the variation of the total counts were about 18%, 19% and 43% in the IC, anterior and septal ROIs obtained from images reconstructed with maximum likelihood algorithm. IC and myocardium tissue uptake can be safely obtained from rat heart scans and corrected for spillover using FADS for images obtained with either iterative reconstruction or with the usual filtered backprojection.

Accelerated iterative image reconstruction methods based on block-circulant system matrix derived from a cylindrical image representation

Iterative image reconstruction methods based on an accurate and fully three-dimensional (3D) system probability matrix are well-known to provide images of higher quality. However, the size of the system matrix and the computation burden often make such methods impractical. To address this problem, we proposed to use a cylindrical image representation that preserves both in-plane and axial symmetries between the tubes of response for a given camera, leading to a system matrix having a block-circulant structure. For 3D image reconstruction, such a system matrix can be structured into a block-circulant matrix where blocks are themselves block-circulant. By storing only non-redundant parts of the block-circulant matrix, memory requirements can be reduced by a factor equivalent to the total number of system symmetries. The block-circulant system matrix can be stored in the Fourier domain representation to accelerate the forward and back projection steps of the iterative image reconstruction methods. When represented in the Fourier domain, the system matrix sparsity is reduced compared to the spatial domain representation, but some null values are still preserved.

Imaging performance of the LabPET™ APD-based digital PET scanner

The LabPET™ is an APD-based digital PET scanner with quasi-individual crystal readout and highly parallel digital architecture for high-performance in vivo molecular imaging of small animals. The scanner is built from LGSO and LYSO crystals (2×2×10/12 mm3) assembled side-by-side in a phoswich fashion and read out by an APD. The LabPET™ exists in two versions: LabPET4 (3.75 cm axial length) and LabPET8 (7.5 cm axial length). This paper focuses on advanced scanner characteristics such as count rate and imaging performance. After a global timing alignment and further optimization of APD operating bias, an overall timing resolution of 6.6 ns for LYSO-LYSO, 10.3 ns for LGSO-LGSO and 8.6 ns for mixed coincidences was measured. Using an energy window of 250–650 keV, scatter fraction is estimated to 18% and 28% for the NEMA mouse and rat phantoms, respectively. The peak NEC count rate with the same energy window is respectively 142/252 kcps at 207/131 MBq for the mouse phantom and 37/121 kcps at 245/168 MBq for the rat phantom with the LabPET4/LabPET8 scanners. When imaging an Ultra Micro Hot Spot Phantom for 1 hour with 33 MBq of 18F, 1 mm hot spots can be clearly distinguished in the MLEM reconstructed image. Recovery coefficients for 1.35 mm hot spots converge to 0.65 and to unity for 2 mm hot spots. The LabPET™ offers excellent capabilities and performance for molecular imaging of small animals.

Design of a prototype real-time image reconstruction system for PET imaging

Real-time reconstruction of the acquired data in positron emission tomography (PET) imaging would facilitate positioning of the subject and could serve to monitor image quality and detect potential problems during the acquisition. A real-time image reconstruction prototype was developed as an extension of the data acquisition system of the Sherbrooke Animal PET scanner using a network of field programmable gate arrays (FPGA), digital signal processors (DSP) and a fast PET image reconstruction algorithm based on SVD decomposition of the system matrix. Two different implementation of the reconstruction system were investigated in order to obtain the fastest reconstruction times for images of at least 64/spl times/64 pixels. Initial results demonstrate that the acquired image can be updated every second using a 600 MHz personal computer for the reconstruction calculations while using the DSPs to pre-process the incoming data.

MLEM Reconstructed Image Resolution from the LabPET Animal Scanner

Background: PET image resolution is a function of scanner intrinsic resolution and reconstruction method. The purpose of this study was to measure reconstructed image resolution vs. MLEM iterations on the new LabPET 3.6 animal scanner. Methods: A Micro Deluxetrade hot rods phantom filled with an 18F solution was scanned for 60 min, and images were reconstructed using 10 to 1000 MLEM iterations. To estimate the image resolution, peak activity values were measured for each rod and compared to the theoretical values of partial-volume recovery obtained by convolving a 2D-Gaussian model with circles of the known rod diameters. Results were confirmed visually by convolving the estimated Gaussian model with a high resolution CT image. Results: FWHM image resolution improved from 2.1 to 1.3 mm with 10 to 1000 MLEM iterations. CT image convolution with this Gaussian model faithfully reproduced the measured resolution in images reconstructed with 200 MLEM iterations. Conclusion: Initial measurement of the LabPET transverse image resolution is consistent with that expected from a system with individual detector readout.

Optimizing communications for parallel ML-EM image reconstruction on large clusters of processors

The ML-EM reconstruction algorithm is an iterative computation of tomographic images by maximization of a likelihood function of the Poisson emission rates. The method being time consuming, a parallel version can easily be implemented to distribute the reconstruction task on multiple processors. Since general-purpose supercomputers are costly and their parallel programming are platform-dependent, distributed ML-EM processing on a network of workstations is an attractive alternative. However, communications of the computed partial projections among processors are time consuming on typical networks such that there is a relatively low limit on the number of processors which can participate in the computation and still reduce reconstruction time. Optimizing the communication process by using efficient hardware and message passing interface, and by transferring sums of partial projections instead of the partial projections themselves over the network permits the distribution of the reconstruction task over a larger number of processors while reducing the overall reconstruction time.