Fast point spread function computation from aperture functions in high-resolution positron emission tomography

Imaging performance of LabPET APD-based digital PET scanners for pre-clinical research

The LabPET is an avalanche photodiode (APD) based digital PET scanner with quasi-individual detector read-out and highly parallel electronic architecture for high-performance in vivo molecular imaging of small animals. The scanner is based on LYSO and LGSO scintillation crystals (2×2×12/14 mm3), assembled side-by-side in phoswich pairs read out by an APD. High spatial resolution is achieved through the individual and independent read-out of an individual APD detector for recording impinging annihilation photons. The LabPET exists in three versions, LabPET4 (3.75 cm axial length), LabPET8 (7.5 cm axial length) and LabPET12 (11.4 cm axial length). This paper focuses on the systematic characterization of the three LabPET versions using two different energy window settings to implement a high-efficiency mode (250–650 keV) and a high-resolution mode (350–650 keV) in the most suitable operating conditions. Prior to measurements, a global timing alignment of the scanners and optimization of the APD operating bias have been carried out. Characteristics such as spatial resolution, absolute sensitivity, count rate performance and image quality have been thoroughly investigated following the NEMA NU 4-2008 protocol. Phantom and small animal images were acquired to assess the scanners' suitability for the most demanding imaging tasks in preclinical biomedical research. The three systems achieve the same radial FBP spatial resolution at 5 mm from the field-of-view center: 1.65/3.40 mm (FWHM/FWTM) for an energy threshold of 250 keV and 1.51/2.97 mm for an energy threshold of 350 keV. The absolute sensitivity for an energy window of 250–650 keV is 1.4%/2.6%/4.3% for LabPET4/8/12, respectively. The best count rate performance peaking at 362 kcps is achieved by the LabPET12 with an energy window of 250–650 keV and a mouse phantom (2.5 cm diameter) at an activity of 2.4 MBq ml−1. With the same phantom, the scatter fraction for all scanners is about 17% for an energy threshold of 250 keV and 10% for an energy threshold of 350 keV. The results obtained with two energy window settings confirm the relevance of high-efficiency and high-resolution operating modes to take full advantage of the imaging capabilities of the LabPET scanners for molecular imaging applications.

Development and evaluation of a LOR-based image reconstruction with 3D system response modeling for a PET insert with dual-layer offset crystal design

In this study we present a method of 3D system response calculation for analytical computer simulation and statistical image reconstruction for a magnetic resonance imaging (MRI) compatible positron emission tomography (PET) insert system that uses a dual-layer offset (DLO) crystal design. The general analytical system response functions (SRFs) for detector geometric and inter-crystal penetration of coincident crystal pairs are derived first. We implemented a 3D ray-tracing algorithm with 4π sampling for calculating the SRFs of coincident pairs of individual DLO crystals. The determination of which detector blocks are intersected by a gamma ray is made by calculating the intersection of the ray with virtual cylinders with radii just inside the inner surface and just outside the outer-edge of each crystal layer of the detector ring. For efficient ray-tracing computation, the detector block and ray to be traced are then rotated so that the crystals are aligned along the X-axis, facilitating calculation of ray/crystal boundary intersection points. This algorithm can be applied to any system geometry using either single-layer (SL) or multi-layer array design with or without offset crystals. For effective data organization, a direct lines of response (LOR)-based indexed histogram-mode method is also presented in this work. SRF calculation is performed on-the-fly in both forward and back projection procedures during each iteration of image reconstruction, with acceleration through use of eight-fold geometric symmetry and multi-threaded parallel computation. To validate the proposed methods, we performed a series of analytical and Monte Carlo computer simulations for different system geometry and detector designs. The full-width-at-half-maximum of the numerical SRFs in both radial and tangential directions are calculated and compared for various system designs. By inspecting the sinograms obtained for different detector geometries, it can be seen that the DLO crystal design can provide better sampling density than SL or dual-layer no-offset system designs with the same total crystal length. The results of the image reconstruction with SRFs modeling for phantom studies exhibit promising image recovery capability for crystal widths of 1.27-1.43 mm and top/bottom layer lengths of 4/6 mm. In conclusion, we have developed efficient algorithms for system response modeling of our proposed PET insert with DLO crystal arrays. This provides an effective method for both 3D computer simulation and quantitative image reconstruction, and will aid in the optimization of our PET insert system with various crystal designs.

Resolution modeling in PET imaging: theory, practice, benefits, and pitfalls

In this paper, the authors review the field of resolution modeling in positron emission tomography (PET) image reconstruction, also referred to as point-spread-function modeling. The review includes theoretical analysis of the resolution modeling framework as well as an overview of various approaches in the literature. It also discusses potential advantages gained via this approach, as discussed with reference to various metrics and tasks, including lesion detection observer studies. Furthermore, attention is paid to issues arising from this approach including the pervasive problem of edge artifacts, as well as explanation and potential remedies for this phenomenon. Furthermore, the authors emphasize limitations encountered in the context of quantitative PET imaging, wherein increased intervoxel correlations due to resolution modeling can lead to significant loss of precision (reproducibility) for small regions of interest, which can be a considerable pitfall depending on the task of interest.

Simultaneous attenuation and scatter corrections from the projections in small animal PET imaging

Attenuation and scatter corrections are important in quantitative positron emission tomography (PET) imaging even in small animals such as mice and rats. In this work we describe a simple and efficient model to correct for both scatter and attenuation in a single operation. The model aims to solve the equation M=(A+F) P for the primaries P, corrected for attenuation and scatter, based on the measured coincidences M, the matrix of compensation for attenuation A and on the scatter fractions F issued from all emitting sources and contributing to M. The scatter functions are analytically calculated using Klein-Nishina formula, the scanner geometry and the detection efficiencies. This method was applied in measured data of line sources and hot spots phantoms as well as in rat heart and tumors and compared to Monte Carlo based simulations and to the single scatter simulation model developed by Watson et al. The corrected data showed a quantitative contrast and signal to noise ratio enhancement with respect to the uncorrected data. In terms of results, our method is comparable to that of Watson et al. The Monte Carlo simulations, where the primaries and the scattered events were separately registered, confirmed the accuracy of the new approach.

A comparison of a Monte Carlo-based detection probability matrix with analytical probability matrix for small animal PET scanners

Positron Emission Tomography (PET) offers the possibility to quantitatively measure the radiotracer distribution in tissues. In order to obtain images of these tissues, the detection probability matrix (DPM) must be accurately determined. Usually, DPM is analytically calculated. However, this approach does not take into account the whole probabilistic interactions of the photons. On the other hand, Monte Carlo simulations (MC) are more accurate to calculate the DPM as they selectively consider diverse photon interactions. In this work, MC DPM (MCDPM) and analytically calculated DPM (ACDPM) were compared in terms of image quality. The results showed that the images obtained from the MCDPM were qualitatively better resolved and provided a significant improvement of the signal-to-noise ratio (SNR). The MCDPM yielded to an increase of up to 40% in SNR and up to 25% in contrast in comparison with ACDPM. On the other hands, MCDPM enhanced the counts distribution by more than 12% with respect to ACDPM.

Fast and efficient fully 3D PET image reconstruction using sparse system matrix factorization with GPU acceleration

Statistically based iterative image reconstruction has been widely used in positron emission tomography (PET) imaging. The quality of reconstructed images depends on the accuracy of the system matrix that defines the mapping from the image space to the data space. However, an accurate system matrix is often associated with high computation cost and huge storage requirement. In this paper, we present a method to address this problem using sparse matrix factorization and graphics processor unit (GPU) acceleration. We factor the accurate system matrix into three highly sparse matrices: a sinogram blurring matrix, a geometric projection matrix and an image blurring matrix. The geometrical projection matrix is precomputed based on a simple line integral model, while the sinogram and image blurring matrices are estimated from point-source measurements. The resulting factored system matrix has far less nonzero elements than the original system matrix, which substantially reduces the storage and computation cost. The smaller matrix size also allows an efficient implementation of the forward and backward projectors on a GPU, which often has a limited memory space. Our experimental studies show that the proposed method can dramatically reduce the computation cost of high-resolution iterative image reconstruction, while achieving better performance than existing factorization methods.

Image reconstruction for PET/CT scanners: past achievements and future challenges

PET is a medical imaging modality with proven clinical value for disease diagnosis and treatment monitoring. The integration of PET and CT on modern scanners provides a synergy of the two imaging modalities. Through different mathematical algorithms, PET data can be reconstructed into the spatial distribution of the injected radiotracer. With dynamic imaging, kinetic parameters of specific biological processes can also be determined. Numerous efforts have been devoted to the development of PET image reconstruction methods over the last four decades, encompassing analytic and iterative reconstruction methods. This article provides an overview of the commonly used methods. Current challenges in PET image reconstruction include more accurate quantitation, TOF imaging, system modeling, motion correction and dynamic reconstruction. Advances in these aspects could enhance the use of PET/CT imaging in patient care and in clinical research studies of pathophysiology and therapeutic interventions.

Non-Gaussian space-variant resolution modelling for list-mode reconstruction

Partial volume effect is an important source of bias in PET images that can be lowered by accounting for the point spread function (PSF) of the scanner. We measured such a PSF in various points of a clinical PET scanner and modelled it as a product of matrices acting in image space, taking the asymmetrical, shift-varying and non-Gaussian character of the PSF into account (AMP modelling), and we integrated this accurate image space modelling into a conventional list-mode OSEM algorithm (EM-AMP reconstruction). We showed on the one hand that when a sufficiently high number of iterations are considered, the AMP modelling lead to better recovery coefficients at reduced background noise compared to reconstruction where no or only partial resolution modelling is performed, and on the other hand that for a small number of iterations, a Gaussian modelling gave the best recovery coefficients. Moreover, we have demonstrated that a deconvolution based on the AMP system response model leads to the same recovery coefficients as the corresponding EM-AMP reconstruction, but at the expense of an increased background noise.

Evaluation of the spatial dependence of the point spread function in 2D PET image reconstruction using LOR-OSEM

PURPOSE

The use of positron emission tomography (PET) imaging has proved beneficial in the staging and diagnosis of several cancer disease sites. Additional applications of PET imaging in treatment planning and the evaluation of treatment response are limited by the relatively low spatial resolution of PET images. Including point spread function (PSF) information in the system matrix (SM) of iterative reconstruction techniques has been shown to produce improved spatial resolution in PET images.

METHODS

In this study, the authors sampled the spatially variant PSF at over 6000 locations in the field of view for a General Electric Discovery ST PET/CT (General Electric Healthcare, Waukesha, WI) scanner in 2D acquisition mode. The authors developed PSF blurred SMs based on different combinations of the radial, depth, and azimuthal spatial dependencies to test the overall spatial dependence of the PSF on image quality. The PSF blurred SMs were included in a LOR-OSEM reconstruction algorithm and used for image reconstruction of geometric phantoms. The authors also examined the effect of sampling density on PSF characterization to design a more efficient sampling scheme.

RESULTS

The authors found that depth dependent change in the amplitude of the detector response was the most important factor affecting image quality. A SM created from a PSF that introduced r (perpendicular to the LOR), d (parallel to the LOR), or r and d dependent blurring across the radial lines of response led to visually identifiable improvements in spatial resolution and contrast in reconstructed images compared to images reconstructed with a purely geometric SM with no PSF blurring. Images reconstructed using a SM with r and d dependent blurring across the radial lines of response showed improved spatial resolution and contrast-noise ratios compared to images reconstructed with a SM that had only r dependent blurring. Additionally, the authors determined that the PSF could be adequately characterized with roughly 85% fewer samples through the use of a better optimized sampling scheme.

CONCLUSIONS

PET image reconstruction using a SM made from an accurately characterized PSF that accounts for r and d dependencies results in improved spatial resolution and contrast-noise relations, which may aid in lesion boundary detection for treatment planning or quantitative assessment of treatment response.

Application and evaluation of a measured spatially variant system model for PET image reconstruction

Accurate system modeling in tomographic image reconstruction has been shown to reduce the spatial variance of resolution and improve quantitative accuracy. System modeling can be improved through analytic calculations, Monte Carlo simulations, and physical measurements. The purpose of this work is to improve clinical fully-3-D reconstruction without substantially increasing computation time. We present a practical method for measuring the detector blurring component of a whole-body positron emission tomography (PET) system to form an approximate system model for use with fully-3-D reconstruction. We employ Monte Carlo simulations to show that a non-collimated point source is acceptable for modeling the radial blurring present in a PET tomograph and we justify the use of a Na22 point source for collecting these measurements. We measure the system response on a whole-body scanner, simplify it to a 2-D function, and incorporate a parameterized version of this response into a modified fully-3-D OSEM algorithm. Empirical testing of the signal versus noise benefits reveal roughly a 15% improvement in spatial resolution and 10% improvement in contrast at matched image noise levels. Convergence analysis demonstrates improved resolution and contrast versus noise properties can be achieved with the proposed method with similar computation time as the conventional approach. Comparison of the measured spatially variant and invariant reconstruction revealed similar performance with conventional image metrics. Edge artifacts, which are a common artifact of resolution-modeled reconstruction methods, were less apparent in the spatially variant method than in the invariant method. With the proposed and other resolution-modeled reconstruction methods, edge artifacts need to be studied in more detail to determine the optimal tradeoff of resolution/contrast enhancement and edge fidelity.

Simultaneous attenuation and scatter corrections in small animal PET imaging

The aim of this work is to simultaneously correct for attenuation and scatter in PET by analytically assessing the distribution of the scattered photons using the emission and the transmission images, the probability of scatter interactions and the detection efficiency. Above the usual lower energy threshold of 350 keV, the attenuated photons are dominantly those which have undergone a Compton scattering. By considering that each pixel in the image is the measurement of the transmitted photons through the subject, added to the contribution from the other sources by means of their scatter at this position, a simple equation is established accounting for the primaries by simultaneously correcting the data for attenuation and scatter for all emitting sources. This new method was applied in Monte Carlo simulated and measured data with the Sherbrooke small animal PET scanner in line sources, hot spot phantoms, and in rat hearts and tumors, and was compared to the approach developed by Watson et al.

Analytic system matrix resolution modeling in PET: an application to Rb-82 cardiac imaging

This work explores application of a novel resolution modeling technique based on analytic physical models which individually models the various resolution degrading effects in PET (positron range, photon non-collinearity, inter-crystal scattering and inter-crystal penetration) followed by their combination and incorporation within the image reconstruction task. In addition to phantom studies, the proposed technique was particularly applied to and studied in the task of clinical Rb-82 myocardial perfusion imaging, which presently suffers from poor statistics and resolution properties in the reconstructed images. Overall, the approach is able to produce considerable enhancements in image quality. The reconstructed FWHM for a Discovery RX PET/CT scanner was seen to improve from 5.1 mm to 7.7 mm across the field-of-view (FoV) to approximately 3.5 mm nearly uniformly across the FoV. Furthermore, extended-source phantom studies indicated clearly improved images in terms of contrast versus noise performance. Using Monte Carlo simulations of clinical Rb-82 imaging, the resolution modeling technique was seen to significantly outperform standard reconstructions qualitatively, and also quantitatively in terms of contrast versus noise (contrast between the myocardium and other organs, as well as between myocardial defects and the left ventricle).

Improved quantitation for PET/CT image reconstruction with system modeling and anatomical priors

Accurate quantitation of positron emission tomography (PET) tracer uptake levels in tumors is important for staging and monitoring response to treatment. Quantitative accuracy in PET is particularly poor for small tumors because of system partial volume errors and smoothing operations. This work proposes a reconstruction algorithm to reduce the quantitative errors due to limited system resolution and due to necessary image noise reduction. We propose a method for finding and using the detection system response in the projection matrix of a statistical reconstruction algorithm. In addition, we use aligned anatomical information, available in PET/CT scanners, to govern the penalty term applied during each image update. These improvements are combined with Fourier rebinning in a clinically feasible algorithm for reconstructing fully three-dimensional PET data. Results from simulation and measured studies show improved quantitation of tumor values in terms of bias and variance across multiple tumor sizes and activity levels with the proposed method. At common clinical image noise levels for the detection task, the proposed method reduces the error in maximum tumor values by 11% compared to filtered back-projection and 5% compared to conventional iterative methods.

Modeling and incorporation of system response functions in 3-D whole body PET

Appropriate application of spatially variant system models can correct for degraded resolution response and mispositioning errors. This paper explores the detector blurring component of the system model for a whole body positron emission tomography (PET) system and extends this factor into a more general system response function to account for other system effects including the influence of Fourier rebinning (FORE). We model the system response function as a three-dimensional (3-D) function that blurs in the radial and axial dimension and is spatially variant in radial location. This function is derived from Monte Carlo simulations and incorporates inter-crystal scatter, crystal penetration, and the blurring due to the FORE algorithm. The improved system model is applied in a modified ordered subsets expectation maximization (OSEM) algorithm to reconstruct images from rebinned, fully 3-D PET data. The proposed method effectively removes the spatial variance in the resolution response, as shown in simulations of point sources. Furthermore, simulation and measured studies show the proposed method improves quantitative accuracy with a reduction in tumor bias compared to conventional OSEM on the order of 10%-30% depending on tumor size and smoothing parameter.

An improved analytical detector response function model for multilayer small-diameter PET scanners

The optimization of spatial resolution is a critical consideration in the design of small-diameter positron emission tomography (PET) scanners for animal imaging, and is often addressed with Monte Carlo simulations. As a faster and simpler solution, we have developed a new analytical model of the PET detector response function, and implemented the model for a small single-slice, multilayer PET scanner. The accuracy of the model has been assessed by comparison with both Monte Carlo simulations and experimental measurements published in the literature. Results from the analytical model agreed well with the Monte Carlo method, being noise free and two to three orders of magnitude faster. The only major discrepancy was a slight underestimation of the width of the point spread function by the analytical method as inter-crystal scatter is neglected. We observed good agreement between the predictions of the model and experimental measurements. For two large-diameter scanners additional discrepancies were seen due to photon acollinearity, which is not considered in the model. We have shown that the simple and fast analytical detector response function model can provide accurate estimates of spatial resolution for small-diameter PET scanners, and could be a useful tool for several applications, complementing or cross-validating other simulation methods.

Detector response restoration in image reconstruction of high resolution positron emission tomography

A mathematical method was studied to model the detector response of high spatial-resolution positron emission tomography systems consisting of close-packed small crystals, and to restore the resolution deteriorated due to crystal penetration and/or nonuniform sampling across the field-of-view (FOV). The simulated detector system had 600 bismuth germanate crystals of 3.14 mm width and 30 mm length packed on a single ring of 60 cm diameter. The space between crystals was filled up with lead (i.e., septa). Each crystal was in coincidence with 200 opposite crystals so that the FOV had a radius of 30 cm. The detector response was modeled based on the attenuating properties of the crystals and the septa, as well as the geometry of the detector system. The modeled detector-response function was used to restore the projections from the sinogram of the ring-detector system. The restored projections had a uniform sampling of 1.57 mm across the FOV. The crystal penetration and/or the nonuniform sampling were compensated in the projections. A penalized maximum-likelihood algorithm was employed to accomplish the restoration. The restored projections were then filtered and backprojected to reconstruct the image. A chest phantom with a few small circular "cold" objects ( approximately 4 mm diameter) located at the center and near the periphery of FOV was computer generated and used to test the restoration. The reconstructed images from the restored projections demonstrated resolution improvement off the FOV center, while preserving the resolution near the center.

Effect of detector weighting functions on the point spread function of high-resolution PET tomographs: a simulation study

The point spread function (PSF) of a ring PET tomograph is known to be spatially variant and difficult to obtain because it must be reconstructed from projections. A mathematical model was developed to simulate the data acquisition from a point source and to reconstruct the PSF, taking into account weighting functions to describe the detector response functions. In order to investigate the effect of the detector weighting function on the PSF, the reconstruction, based on the filtered backprojection algorithm, was implemented with three classes of weighting functions of decreasing complexity: exact, locally invariant, and constant. Significant differences are observed to result from the three hypotheses, and this is shown to lead to distorted PSFs and to erroneous estimates of the intrinsic resolution off the center of the tomograph.

Study of the resolution performance of an array of discrete detectors with independent readouts for positron emission tomography

The intrinsic resolution characteristics of an original detection system for very high resolution positron emission tomography (PET) based on arrays of small discrete crystals individually coupled to solid state photodetectors are evaluated. The results obtained demonstrate the excellent three-dimensional (3-D) resolving capability of a detection system based on the EG&G/RCA C30994 detector module. The analysis of the various components contributing to the resolution has shown that the geometry of the detector and the intercrystal scattering both contribute to limit the achievable intrinsic resolution. The geometrical component is dominant off the central region of the camera field as a result of intercrystal penetration when the array is irradiated at an angle. Intercrystal scattering must be properly rejected to achieve the intrinsic resolution determined by the detector geometry.