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

Isotope specific resolution recovery image reconstruction in high resolution PET imaging

PURPOSE

Measuring and incorporating a scanner-specific point spread function (PSF) within image reconstruction has been shown to improve spatial resolution in PET. However, due to the short half-life of clinically used isotopes, other long-lived isotopes not used in clinical practice are used to perform the PSF measurements. As such, non-optimal PSF models that do not correspond to those needed for the data to be reconstructed are used within resolution modeling (RM) image reconstruction, usually underestimating the true PSF owing to the difference in positron range. In high resolution brain and preclinical imaging, this effect is of particular importance since the PSFs become more positron range limited and isotope-specific PSFs can help maximize the performance benefit from using resolution recovery image reconstruction algorithms.

METHODS

In this work, the authors used a printing technique to simultaneously measure multiple point sources on the High Resolution Research Tomograph (HRRT), and the authors demonstrated the feasibility of deriving isotope-dependent system matrices from fluorine-18 and carbon-11 point sources. Furthermore, the authors evaluated the impact of incorporating them within RM image reconstruction, using carbon-11 phantom and clinical datasets on the HRRT.

RESULTS

The results obtained using these two isotopes illustrate that even small differences in positron range can result in different PSF maps, leading to further improvements in contrast recovery when used in image reconstruction. The difference is more pronounced in the centre of the field-of-view where the full width at half maximum (FWHM) from the positron range has a larger contribution to the overall FWHM compared to the edge where the parallax error dominates the overall FWHM.

CONCLUSIONS

Based on the proposed methodology, measured isotope-specific and spatially variant PSFs can be reliably derived and used for improved spatial resolution and variance performance in resolution recovery image reconstruction. The benefits are expected to be more substantial for more energetic positron emitting isotopes such as Oxygen-15 and Rubidium-82.

Volumetric optoacoustic imaging with multi-bandwidth deconvolution

Optoacoustic (photoacoustic) imaging based on cylindrically focused 1-D transducer arrays comes with powerful characteristics in visualizing optical contrast. Parallel reading of multiple detectors arranged around a tissue cross section enables capturing data for generating images of this plane within micro-seconds. Dedicated small animals scanners and handheld systems using 1-D cylindrically focused ultrasound transducer arrays have demonstrated real-time cross-sectional imaging and high in-plane resolution. Yet, the resolution achieved along the axis perpendicular to the focal plane, i.e., the elevation resolution, is determined by the focusing capacities of the detector and is typically lower than the in-plane resolution. Herein, we investigated whether deconvolution of the sensitivity field of the transducer could lead to tangible image improvements. We showcase the findings on experimental measurements from phantoms and animals and discuss the features and the limitations of the approach in improving resolution along the elevation dimension.

Efficient fully 3D list-mode TOF PET image reconstruction using a factorized system matrix with an image domain resolution model

A factorized system matrix utilizing an image domain resolution model is attractive in fully 3D time-of-flight PET image reconstruction using list-mode data. In this paper, we study a factored model based on sparse matrix factorization that is comprised primarily of a simplified geometrical projection matrix and an image blurring matrix. Beside the commonly-used Siddon's ray-tracer, we propose another more simplified geometrical projector based on the Bresenham's ray-tracer which further reduces the computational cost. We discuss in general how to obtain an image blurring matrix associated with a geometrical projector, and provide theoretical analysis that can be used to inspect the efficiency in model factorization. In simulation studies, we investigate the performance of the proposed sparse factorization model in terms of spatial resolution, noise properties and computational cost. The quantitative results reveal that the factorization model can be as efficient as a non-factored model, while its computational cost can be much lower. In addition we conduct Monte Carlo simulations to identify the conditions under which the image resolution model can become more efficient in terms of image contrast recovery. We verify our observations using the provided theoretical analysis. The result offers a general guide to achieve the optimal reconstruction performance based on a sparse factorization model with an image domain resolution model.

Benefits of point-spread function and time of flight for PET/CT image quality in relation to the body mass index and injected dose

The PET image quality of overweight patients and patients who receive low injected doses deteriorates because of increases in statistical noise. The purpose of this study was to investigate the benefits of the point-spread function (PSF) and time-of-flight (TOF) for PET/CT image quality in such patients.

METHODS

The PET images were reconstructed using the baseline ordered-subsets expectation-maximization algorithm (OSEM), OSEM + PSF, OSEM + TOF, and OSEM + PSF + TOF. In the phantom study, we used a National Electrical Manufacturers Association body phantom with different radioactivity concentrations and analyzed image quality using the coefficient of variance in the background (CVphantom). In the clinical study, we retrospectively studied 39 patients who underwent clinical F-FDG PET/CT. The patients were classified into groups based on body mass index and injected dose. Image quality was evaluated using the CV in the liver (CVliver).

RESULTS

In the phantom study, PSF and TOF improved the CVphantom, especially in low-activity models. Among all of the reconstructions, the best CVphantom was obtained with OSEM + PSF + TOF. In the clinical study, the CVliver of the low-dose group with OSEM + PSF + TOF was comparable to that of the high-dose group with conventional OSEM.

CONCLUSIONS

Point-spread function and TOF improved PET/CT image quality for overweight patients who received a lower injected dose. Therefore, the use of PSF and TOF is suggested to maintain the image quality of such patients without extending scanning times. It is greatly beneficial to obtain sufficient image quality for larger patients, especially in delivery institutions where the injection dose cannot be easily increased.

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.

Influences of point-spread function and time-of-flight reconstructions on standardized uptake value of lymph node metastases in FDG-PET

PURPOSE

The purpose of this study was to investigate the effects of point-spread function (PSF) and time-of-flight (TOF) on the standardized uptake value (SUV) of lymph node metastasis in FDG-PET/CT.

MATERIALS AND METHODS

This study evaluated 41 lymph node metastases in 15 patients who had undergone (18)F-FDG PET/CT. The lesion diameters were 2.5 cm or less. The mean short-axis diameter of the lymph nodes was 10.5 ± 3.7 mm (range 4.6-22.8mm). The PET data were reconstructed with baseline OSEM algorithm, with OSEM+PSF, with OSEM+TOF and with OSEM+PSF+TOF. A semi-quantitative analysis was performed using the maximum and mean SUV of lymph node metastases (SUVmax and SUVmean) and mean SUV of normal lung tissue (SUVlung). We also evaluated image quality using the signal-to-noise ratio in the liver (SNRliver).

RESULTS

Both PSF and TOF increased the SUV of lymph node metastases. The combination of PSF and TOF increased the SUVmax by 43.3% and the SUVmean by 31.6% compared with conventional OSEM. By contrast, the SUVlung was not influenced by PSF and TOF. TOF significantly improved the SNRliver.

CONCLUSION

PSF and TOF both increased the SUV of lymph node metastases. Although PSF and TOF are considered to improve small-lesion detectability, it is important to be aware that PSF and TOF influence the accuracy of quantitative measurements.

Effects of Detector Thickness on Geometric Sensitivity and Event Positioning Errors in the Rectangular PET/X Scanner

We used simulations to investigate the relationship between sensitivity and spatial resolution as a function of crystal thickness in a rectangular PET scanner intended for quantitative assessment of breast cancers. The system had two 20 × 15-cm² and two 10 × 15-cm² flat detectors forming a box, with the larger detectors separated by 4 or 8 cm. Depth-of-interaction (DOI) resolution was modeled as a function of crystal thickness based on prior measurements. Spatial resolution was evaluated independent of image reconstruction by deriving and validating a surrogate metric from list-mode data (d_FWHM). When increasing crystal thickness from 5 to 40 mm, and without using DOI information, the d_FWHM for a centered point source increased from 0.72 to 1.6 mm. Including DOI information improved d_FWHM by 12% and 27% for 5- and 40-mm-thick crystals, respectively. For a point source in the corner of the FOV, use of DOI information improved d_FWHM by 20% (5-mm crystal) and 44% (40-mm crystal). Sensitivity was 7.7% for 10-mm-thick crystals (8-cm object). Increasing crystal thickness on the smaller side detectors from 10 to 20 mm (keeping 10-mm crystals on the larger detectors) boosted sensitivity by 24% (relative) and degraded d_FWHM by only ~3%/8% with/without DOI information. The benefits of measuring DOI must be evaluated in terms of the intended clinical task of assessing tracer uptake in small lesions. Increasing crystal thickness on the smaller side detectors provides substantial sensitivity increase with minimal accompanying loss in resolution.

Magnetic resonance-based motion correction for positron emission tomography imaging

Positron emission tomography (PET) image quality is limited by patient motion. Emission data are blurred owing to cardiac and/or respiratory motion. Although spatial resolution is 4 mm for standard clinical whole-body PET scanners, the effective resolution can be as low as 1 cm owing to motion. Additionally, the deformation of attenuation medium causes image artifacts. Previously, gating has been used to "freeze" the motion, but led to significantly increased noise level. Simultaneous PET/magnetic resonance (MR) modality offers a new way to perform PET motion correction. MR can be used to measure 3-dimensional motion fields, which can then be incorporated into the iterative PET reconstruction to obtain motion-corrected PET images. In this report, we present MR imaging techniques to acquire dynamic images, a nonrigid image registration algorithm to extract motion fields from acquired MR images, and a PET reconstruction algorithm with motion correction. We also present results from both phantom and in vivo animal PET/MR studies. We demonstrate that MR-based PET motion correction using simultaneous PET/MR improves image quality and lesion detectability compared with gating and no motion correction.

Noise propagation in resolution modeled PET imaging and its impact on detectability

Positron emission tomography imaging is affected by a number of resolution degrading phenomena, including positron range, photon non-collinearity and inter-crystal blurring. An approach to this issue is to model some or all of these effects within the image reconstruction task, referred to as resolution modeling (RM). This approach is commonly observed to yield images of higher resolution and subsequently contrast, and can be thought of as improving the modulation transfer function. Nonetheless, RM can substantially alter the noise distribution. In this work, we utilize noise propagation models in order to accurately characterize the noise texture of reconstructed images in the presence of RM. Furthermore we consider the task of lesion or defect detection, which is highly determined by the noise distribution as quantified using the noise power spectrum. Ultimately, we use this framework to demonstrate why conventional trade-off analyses (e.g. contrast versus noise, using simplistic noise metrics) do not provide a complete picture of the impact of RM and that improved performance of RM according to such analyses does not necessarily translate to the superiority of RM in detection task performance.

Accurate and efficient modeling of the detector response in small animal multi-head PET systems

In fully three-dimensional PET imaging, iterative image reconstruction techniques usually outperform analytical algorithms in terms of image quality provided that an appropriate system model is used. In this study we concentrate on the calculation of an accurate system model for the YAP-(S)PET II small animal scanner, with the aim to obtain fully resolution- and contrast-recovered images at low levels of image roughness. For this purpose we calculate the system model by decomposing it into a product of five matrices: (1) a detector response component obtained via Monte Carlo simulations, (2) a geometric component which describes the scanner geometry and which is calculated via a multi-ray method, (3) a detector normalization component derived from the acquisition of a planar source, (4) a photon attenuation component calculated from x-ray computed tomography data, and finally, (5) a positron range component is formally included. This system model factorization allows the optimization of each component in terms of computation time, storage requirements and accuracy. The main contribution of this work is a new, efficient way to calculate the detector response component for rotating, planar detectors, that consists of a GEANT4 based simulation of a subset of lines of flight (LOFs) for a single detector head whereas the missing LOFs are obtained by using intrinsic detector symmetries. Additionally, we introduce and analyze a probability threshold for matrix elements of the detector component to optimize the trade-off between the matrix size in terms of non-zero elements and the resulting quality of the reconstructed images. In order to evaluate our proposed system model we reconstructed various images of objects, acquired according to the NEMA NU 4-2008 standard, and we compared them to the images reconstructed with two other system models: a model that does not include any detector response component and a model that approximates analytically the depth of interaction as detector response component. The comparisons confirm previous research results, showing that the usage of an accurate system model with a realistic detector response leads to reconstructed images with better resolution and contrast recovery at low levels of image roughness.

Acceleration of image-based resolution modelling reconstruction using an expectation maximization nested algorithm

Recent studies have demonstrated the benefits of a resolution model within iterative reconstruction algorithms in an attempt to account for effects that degrade the spatial resolution of the reconstructed images. However, these algorithms suffer from slower convergence rates, compared to algorithms where no resolution model is used, due to the additional need to solve an image deconvolution problem. In this paper, a recently proposed algorithm, which decouples the tomographic and image deconvolution problems within an image-based expectation maximization (EM) framework, was evaluated. This separation is convenient, because more computational effort can be placed on the image deconvolution problem and therefore accelerate convergence. Since the computational cost of solving the image deconvolution problem is relatively small, multiple image-based EM iterations do not significantly increase the overall reconstruction time. The proposed algorithm was evaluated using 2D simulations, as well as measured 3D data acquired on the high-resolution research tomograph. Results showed that bias reduction can be accelerated by interleaving multiple iterations of the image-based EM algorithm solving the resolution model problem, with a single EM iteration solving the tomographic problem. Significant improvements were observed particularly for voxels that were located on the boundaries between regions of high contrast within the object being imaged and for small regions of interest, where resolution recovery is usually more challenging. Minor differences were observed using the proposed nested algorithm, compared to the single iteration normally performed, when an optimal number of iterations are performed for each algorithm. However, using the proposed nested approach convergence is significantly accelerated enabling reconstruction using far fewer tomographic iterations (up to 70% fewer iterations for small regions). Nevertheless, the optimal number of nested image-based EM iterations is hard to be defined and it should be selected according to the given application.

Design Study of a Whole-Body PET Scanner with Improved Spatial and Timing Resolution

Current state-of-art whole-body PET scanners achieve a system spatial resolution of 4-5 mm with limited sensitivity. Since the reconstructed spatial resolution and image quality are limited by the count statistics, there has not been a significant push for developing higher resolution whole-body PET scanners. Our goal in this study is to investigate the impact of improved spatial resolution together with time-of-flight (TOF) capability on lesion uptake estimation and lesion detectability, two important tasks in whole-body oncologic studies. The broader goal of this project is the development of a new state-of-art TOF PET scanner operating within an MRI while pushing the technology in PET system design. We performed Monte Carlo simulations to test the effects of crystal size (4 mm and 2.6 mm wide crystals), TOF timing resolution (300ps and 600ps), and 2-level depth-of-interaction (DOI) capability. Spatial resolution was calculated by simulating point sources in air at multiple positions. Results show that smaller crystals produced improved resolution, while degradation of resolution due to parallax error could be reduced with a 2-level DOI detector. Lesion phantoms were simulated to measure the contrast recovery coefficient (CRC) and area under the LROC curve (ALROC) for 0.5 cm diameter lesions with 6:1 activity uptake relative to the background. Smaller crystals produce higher CRC, leading to increased ALROC values or a reduction in scan time. Improved timing resolution provides faster CRC convergence and once again leads to an increase in ALROC value or reduced scan time. Based on our choice of timing resolution and crystal size, improved timing resolution (300ps) with larger crystals (4 mm wide) has similar ALROC as smaller crystals (2.6 mm wide) with 600ps timing resolution. A 2-level DOI measurement provides some CRC and ALROC improvement for lesions further away from the center, leading to a more uniform performance within the imaging field-of-view (FOV). Given a choice between having either an improved spatial resolution, improved timing resolution, or DOI capability, improved spatial or timing resolution provide an overall higher ALROC relative to a 2-level DOI detector.

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.

State of the Art in Cardiac Hybrid Technology: PET/MR

Simultaneous PET/MRI is an emerging technique combining two powerful imaging modalities in a single device. The wide variety of available tracers for perfusion and metabolic studies and the high sensitivity of positron emission tomography (PET) combined with the high spatial resolution and soft tissue contrast of magnetic resonance imaging (MRI) in depicting cardiac morphology and function as well as MRI's absence of ionizing radiation makes PET/MRI very attractive to radiologists and clinicians. Nevertheless, PET/MR scientific and clinical promise is to be considered in the context of numerous technical challenges that hinder its use in the clinical setting. For example, in order for a PET system to work correctly within an MR field, major changes are required to the photon detection chain such as the elimination of photomultiplier tubes, etc. Another significant limitation of PET/MRI is the lack of an electron density map (as is the case with PET-CT) that can be readily obtained from MRI (the latter measures proton not electron density) and used to correct PET data for attenuation. Moreover, as with PET-CT, cardiac and respiratory motions cause image degradations that affect image quality and accuracy both in static and dynamic PET imaging. As a result, overcoming these (and other) technical limitations is a very active area of research both in academic institutions as well as industry. In this paper, we review recent literature on cardiac PET/MRI, present the state-of-the-art of this technology, and explore promising preclinical and clinical cardiac applications where PET/MRI could play a substantial role.

Harmonizing SUVs in multicentre trials when using different generation PET systems: prospective validation in non-small cell lung cancer patients

Purpose

We prospectively evaluated whether a strategy using point spread function (PSF) reconstruction for both diagnostic and quantitative analysis in non-small cell lung cancer (NSCLC) patients meets the European Association of Nuclear Medicine (EANM) guidelines for harmonization of quantitative values.

Methods

The NEMA NU-2 phantom was used to determine the optimal filter to apply to PSF-reconstructed images in order to obtain recovery coefficients (RCs) fulfilling the EANM guidelines for tumour positron emission tomography (PET) imaging (PSF_EANM). PET data of 52 consecutive NSCLC patients were reconstructed with unfiltered PSF reconstruction (PSF_allpass), PSF_EANM and with a conventional ordered subset expectation maximization (OSEM) algorithm known to meet EANM guidelines. To mimic a situation in which a patient would undergo pre- and post-therapy PET scans on different generation PET systems, standardized uptake values (SUVs) for OSEM reconstruction were compared to SUVs for PSF_EANM and PSF_allpass reconstruction.

Results

Overall, in 195 lesions, Bland-Altman analysis demonstrated that the mean ratio between PSF_EANM and OSEM data was 1.03 [95 % confidence interval (CI) 0.94–1.12] and 1.02 (95 % CI 0.90–1.14) for SUV_max and SUV_mean, respectively. No difference was noticed when analysing lesions based on their size and location or on patient body habitus and image noise. Ten patients (84 lesions) underwent two PET scans for response monitoring. Using the European Organization for Research and Treatment of Cancer (EORTC) criteria, there was an almost perfect agreement between OSEM_PET1/OSEM_PET2 (current standard) and OSEM_PET1/PSF_EANM-PET2 or PSF_EANM-PET1/OSEM_PET2 with kappa values of 0.95 (95 % CI 0.91–1.00) and 0.99 (95 % CI 0.96–1.00), respectively. The use of PSF_allpass either for pre- or post-treatment (i.e. OSEM_PET1/PSF_allpass-PET2 or PSF_allpass-PET1/OSEM_PET2) showed considerably less agreement with kappa values of 0.75 (95 % CI 0.67–0.83) and 0.86 (95 % CI 0.78–0.94), respectively.

Conclusion

Protocol-optimized images and compliance with EANM guidelines allowed for a reliable pre- and post-therapy evaluation when using different generation PET systems. These data obtained in NSCLC patients could be extrapolated to other solid tumours.

Electronic supplementary material

The online version of this article (doi:10.1007/s00259-013-2391-1) contains supplementary material, which is available to authorized users.

Clinical evaluation of PET image reconstruction using a spatial resolution model

PURPOSE

PET image resolution is variable across the measured field-of-view and described by the point spread function (PSF). When accounting for the PSF during PET image reconstruction image resolution is improved and partial volume effects are reduced. Here, we evaluate the effect of PSF-based reconstruction on lesion quantification in routine clinical whole-body (WB) PET/CT imaging.

MATERIALS AND METHODS

41 oncology patients were referred for a WB-PET/CT examination (Biograph 40 TruePoint). Emission data were acquired at 2.5 min/bed at 1 hpi of 400 MBq [18F]-FDG. Attenuation-corrected PET images were reconstructed on 336 × 336-matrices using: (R1) standard AW-OSEM (4 iter, 8 subsets, 4 mm Gaussian) and (R2) AW-OSEM with PSF (3 iter, 21 subsets, 2 mm). Blinded and randomised reading of R1- and R2-PET images was performed. Individual lesions were located and counted independently on both sets of images. The relative change in PET quantification (SUVmax, SUVmean, volume) of lesions seen on R1 and R2 is reported as (R2-R1)/R1. Furthermore, SUVmax and SUVmean was measured for a 3 cm spherical norm region in the right lobe of the healthy liver for R1 and R2.

RESULTS

Clinical reading revealed 91 and 103 positive lesions for R1 and R2, respectively. For all lesions SUVmax (R2) was higher than SUVmax (R1). Regression analysis indicated that the relative increase in SUVmax (and SUVmean) decreased with lesion size, whilst it increased with increasing radial distance from the centre of the field of view (FOV). There was no significant difference in SUVmean in homogenous liver tissue between R1 and R2.

CONCLUSION

In whole-body FDG-PET/CT using routine clinical protocols, PSF-based PET reconstruction increases lesion detection and affects SUVmax measurements compared to standard AW-OSEM PET reconstruction.

Four-Dimensional Image Reconstruction Strategies in Cardiac-Gated and Respiratory-Gated PET Imaging

Cardiac and respiratory movements pose significant challenges to image quality and quantitative accuracy in PET imaging. Cardiac and/or respiratory gating attempt to address this issue, but instead lead to enhanced noise levels. Direct four-dimensional (4D) PET image reconstruction incorporating motion compensation has the potential to minimize noise amplification while removing considerable motion blur. A wide-ranging choice of such techniques is reviewed in this work. Future opportunities and the challenges facing the adoption of 4D PET reconstruction and its role in basic and clinical research are also discussed.

The use of zeolites to generate PET phantoms for the validation of quantification strategies in oncology

PURPOSE

In recent years, segmentation algorithms and activity quantification methods have been proposed for oncological (18)F-fluorodeoxyglucose (FDG) PET. A full assessment of these algorithms, necessary for a clinical transfer, requires a validation on data sets provided with a reliable ground truth as to the imaged activity distribution, which must be as realistic as possible. The aim of this work is to propose a strategy to simulate lesions of uniform uptake and irregular shape in an anthropomorphic phantom, with the possibility to easily obtain a ground truth as to lesion activity and borders.

METHODS

Lesions were simulated with samples of clinoptilolite, a family of natural zeolites of irregular shape, able to absorb aqueous solutions of (18)F-FDG, available in a wide size range, and nontoxic. Zeolites were soaked in solutions of (18)F-FDG for increasing times up to 120 min and their absorptive properties were characterized as function of soaking duration, solution concentration, and zeolite dry weight. Saturated zeolites were wrapped in Parafilm, positioned inside an Alderson thorax-abdomen phantom and imaged with a PET-CT scanner. The ground truth for the activity distribution of each zeolite was obtained by segmenting high-resolution finely aligned CT images, on the basis of independently obtained volume measurements. The fine alignment between CT and PET was validated by comparing the CT-derived ground truth to a set of zeolites' PET threshold segmentations in terms of Dice index and volume error.

RESULTS

The soaking time necessary to achieve saturation increases with zeolite dry weight, with a maximum of about 90 min for the largest sample. At saturation, a linear dependence of the uptake normalized to the solution concentration on zeolite dry weight (R(2) = 0.988), as well as a uniform distribution of the activity over the entire zeolite volume from PET imaging were demonstrated. These findings indicate that the (18)F-FDG solution is able to saturate the zeolite pores and that the concentration does not influence the distribution uniformity of both solution and solute, at least at the trace concentrations used for zeolite activation. An additional proof of uniformity of zeolite saturation was obtained observing a correspondence between uptake and adsorbed volume of solution, corresponding to about 27.8% of zeolite volume. As to the ground truth for zeolites positioned inside the phantom, the segmentation of finely aligned CT images provided reliable borders, as demonstrated by a mean absolute volume error of 2.8% with respect to the PET threshold segmentation corresponding to the maximum Dice.

CONCLUSIONS

The proposed methodology allowed obtaining an experimental phantom data set that can be used as a feasible tool to test and validate quantification and segmentation algorithms for PET in oncology. The phantom is currently under consideration for being included in a benchmark designed by AAPM TG211, which will be available to the community to evaluate PET automatic segmentation methods.

Immuno-SPET/CT and immuno-PET/CT: a step ahead to translational imaging

Malignant tumours have the remarkable property to express cell surface antigens. Pressman was first reporting that radiolabeled antibodies were capable of organ localization. It was a promising challenge but the expected success and the development of this imaging method was limited by a poor imaging resolution despite a rather good specificity of the antibodies used. Identification of key cell surface markers is opening a new era as potential molecular imaging biomarkers in oncologic applications. Antibodies production has been promoted by the development of engineered fragments with preserved immunological properties and pharmacokinetics optimized for molecular imaging. A good compromise has to be obtained between the biological properties of the antibody and the physical half-life of the radionuclide. Several positron emission tomography (PET) radionuclides such as iodine-124, copper-64, yttrium-86 or zirconium-89 have been the focus of recent immuno-PET studies with interesting informative images in preclinical and clinical studies. Thanks to the development of more sensitive new detectors and specific software, molecular imaging methods, particularly PET imaging, allow nowadays the detection of lesions smaller than 5 mm in human. Immuno-PET can potentially be used for tumour detection and identification at diagnosis, staging and restaging, for treatment selection and monitoring, and during follow-up. Moreover the availability of matched imaging or therapeutic radionuclide pairs, such as (124)I/(131)I, (64)Cu/(67)Cu and (86)Y/(90)Y, make easier the quantification of tissue uptake and dosimetry calculation for radioimmunotherapy.

Comparison of list-mode and DIRECT approaches for time-of-flight PET reconstruction

Early clinical results with time-of-flight (TOF) positron emission tomography (PET) systems have demonstrated the advantages of TOF information in PET reconstruction. Reconstruction approaches in TOF-PET systems include list-mode and binned iterative algorithms as well as confidence-weighted analytic methods. List-mode iterative TOF reconstruction retains the resolutions of the data in the spatial and temporal domains without any binning approximations but is computationally intensive. We have developed an approach [DIRECT (direct image reconstruction for TOF)] to speed up TOF-PET reconstruction that takes advantage of the reduced angular sampling requirement of TOF data by grouping list-mode data into a small number of azimuthal views and co-polar tilts and depositing the grouped events into histo-images, arrays with the sampling and geometry of the final image. All physical effects are included in the system model and deposited in the same histo-image structure. Using histo-images allows efficient computation during reconstruction without ray-tracing or interpolation operations. The DIRECT approach was compared with 3-D list-mode TOF ordered subsets expectation maximization (OSEM) reconstruction for phantom and patient data taken on the University of Pennsylvania research LaBr (3) TOF-PET scanner. The total processing and reconstruction time for these studies with DIRECT without attention to code optimization is approximately 25%-30% that of list-mode TOF-OSEM to achieve comparable image quality. Furthermore, the reconstruction time for DIRECT is independent of the number of events and/or sizes of the spatial and TOF kernels, while the time for list-mode TOF-OSEM increases with more events or larger kernels. The DIRECT approach is able to reproduce the image quality of list-mode iterative TOF reconstruction both qualitatively and quantitatively in measured data with a reduced time.

MRI-based nonrigid motion correction in simultaneous PET/MRI

Respiratory and cardiac motion is the most serious limitation to whole-body PET, resulting in spatial resolution close to 1 cm. Furthermore, motion-induced inconsistencies in the attenuation measurements often lead to significant artifacts in the reconstructed images. Gating can remove motion artifacts at the cost of increased noise. This paper presents an approach to respiratory motion correction using simultaneous PET/MRI to demonstrate initial results in phantoms, rabbits, and nonhuman primates and discusses the prospects for clinical application.

METHODS

Studies with a deformable phantom, a free-breathing primate, and rabbits implanted with radioactive beads were performed with simultaneous PET/MRI. Motion fields were estimated from concurrently acquired tagged MR images using 2 B-spline nonrigid image registration methods and incorporated into a PET list-mode ordered-subsets expectation maximization algorithm. Using the measured motion fields to transform both the emission data and the attenuation data, we could use all the coincidence data to reconstruct any phase of the respiratory cycle. We compared the resulting SNR and the channelized Hotelling observer (CHO) detection signal-to-noise ratio (SNR) in the motion-corrected reconstruction with the results obtained from standard gating and uncorrected studies.

RESULTS

Motion correction virtually eliminated motion blur without reducing SNR, yielding images with SNR comparable to those obtained by gating with 5-8 times longer acquisitions in all studies. The CHO study in dynamic phantoms demonstrated a significant improvement (166%-276%) in lesion detection SNR with MRI-based motion correction as compared with gating (P < 0.001). This improvement was 43%-92% for large motion compared with lesion detection without motion correction (P < 0.001). CHO SNR in the rabbit studies confirmed these results.

CONCLUSION

Tagged MRI motion correction in simultaneous PET/MRI significantly improves lesion detection compared with respiratory gating and no motion correction while reducing radiation dose. In vivo primate and rabbit studies confirmed the improvement in PET image quality and provide the rationale for evaluation in simultaneous whole-body PET/MRI clinical studies.

Small-animal imaging using clinical positron emission tomography/computed tomography and super-resolution

Considering the high cost of dedicated small-animal positron emission tomography/computed tomography (PET/CT), an acceptable alternative in many situations might be clinical PET/CT. However, spatial resolution and image quality are of concern. The utility of clinical PET/CT for small-animal research and image quality improvements from super-resolution (spatial subsampling) were investigated. National Electrical Manufacturers Association (NEMA) NU 4 phantom and mouse data were acquired with a clinical PET/CT scanner, as both conventional static and stepped scans. Static scans were reconstructed with and without point spread function (PSF) modeling. Stepped images were postprocessed with iterative deconvolution to produce super-resolution images. Image quality was markedly improved using the super-resolution technique, avoiding certain artifacts produced by PSF modeling. The 2 mm rod of the NU 4 phantom was visualized with high contrast, and the major structures of the mouse were well resolved. Although not a perfect substitute for a state-of-the-art small-animal PET/CT scanner, a clinical PET/CT scanner with super-resolution produces acceptable small-animal image quality for many preclinical research studies.

High Performance 3D PET Reconstruction Using Spherical Basis Functions on a Polar Grid

Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image space is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to reduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction is to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large number of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times. These two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared to non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing Unit (GPU) technology for speed and a precomputed Monte-Carlo-calculated SRM for accuracy. The reconstruction time achieved using spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than a CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of response ordering and constrained atomic writing. Small differences in image quality were observed between implementations.

Characterisation of partial volume effect and region-based correction in small animal positron emission tomography (PET) of the rat brain

Accurate quantification of PET imaging data is required for a useful interpretation of the measured radioactive tracer concentrations. The partial volume effect (PVE) describes signal dilution and mixing due to spatial resolution and sampling limitations, which introduces bias in quantitative results. In the present study we investigated the magnitude of PVE for volumes of interest (VOIs) in the rat brain and the effect of positron range. In simulated (11)C-raclopride studies we examined the influence of PVE on time activity curves in striatal and cerebellar VOIs and binding potential estimation. The performance of partial volume correction (PVC) was studied using the region-based geometric transfer matrix (GTM) method including the question of whether a spatially variant point spread function (PSF) is necessary for PVC of a rat brain close to the centre of the field of view. Furthermore, we determined the effect of spillover from activity outside the brain. The results confirmed that PVE is significant in rat brain PET and showed that positron range is an important factor that needs to be included in the PSF. There was considerable bias in time activity curves for the simulated (11)C-raclopride studies and significant underestimation of binding potential even for very small centred VOIs. Good activity recovery was achieved with the GTM PVC using a spatially invariant simulated PSF when no activity was present outside the brain. PVC using a simple Gaussian fit point spread function was not sufficiently accurate. Spillover from regions outside the brain had a significant impact on measured activity concentrations and reduced the accuracy of PVC with the GTM method using rat brain regions alone, except for the smallest VOI size but at the cost of increased noise. Voxel-based partial volume correction methods which inherently compensate for spillover from outside the brain might be a more suitable choice.

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.

Online detector response calculations for high-resolution PET image reconstruction

Positron emission tomography systems are best described by a linear shift-varying model. However, image reconstruction often assumes simplified shift-invariant models to the detriment of image quality and quantitative accuracy. We investigated a shift-varying model of the geometrical system response based on an analytical formulation. The model was incorporated within a list-mode, fully 3D iterative reconstruction process in which the system response coefficients are calculated online on a graphics processing unit (GPU). The implementation requires less than 512 Mb of GPU memory and can process two million events per minute (forward and backprojection). For small detector volume elements, the analytical model compared well to reference calculations. Images reconstructed with the shift-varying model achieved higher quality and quantitative accuracy than those that used a simpler shift-invariant model. For an 8 mm sphere in a warm background, the contrast recovery was 95.8% for the shift-varying model versus 85.9% for the shift-invariant model. In addition, the spatial resolution was more uniform across the field-of-view: for an array of 1.75 mm hot spheres in air, the variation in reconstructed sphere size was 0.5 mm RMS for the shift-invariant model, compared to 0.07 mm RMS for the shift-varying model.

Single scan parameterization of space-variant point spread functions in image space via a printed array: the impact for two PET/CT scanners

Incorporation of a resolution model during statistical image reconstruction often produces images of improved resolution and signal-to-noise ratio. A novel and practical methodology to rapidly and accurately determine the overall emission and detection blurring component of the system matrix using a printed point source array within a custom-made Perspex phantom is presented. The array was scanned at different positions and orientations within the field of view (FOV) to examine the feasibility of extrapolating the measured point source blurring to other locations in the FOV and the robustness of measurements from a single point source array scan. We measured the spatially-variant image-based blurring on two PET/CT scanners, the B-Hi-Rez and the TruePoint TrueV. These measured spatially-variant kernels and the spatially-invariant kernel at the FOV centre were then incorporated within an ordinary Poisson ordered subset expectation maximization (OP-OSEM) algorithm and compared to the manufacturer's implementation using projection space resolution modelling (RM). Comparisons were based on a point source array, the NEMA IEC image quality phantom, the Cologne resolution phantom and two clinical studies (carbon-11 labelled anti-sense oligonucleotide [(11)C]-ASO and fluorine-18 labelled fluoro-l-thymidine [(18)F]-FLT). Robust and accurate measurements of spatially-variant image blurring were successfully obtained from a single scan. Spatially-variant resolution modelling resulted in notable resolution improvements away from the centre of the FOV. Comparison between spatially-variant image-space methods and the projection-space approach (the first such report, using a range of studies) demonstrated very similar performance with our image-based implementation producing slightly better contrast recovery (CR) for the same level of image roughness (IR). These results demonstrate that image-based resolution modelling within reconstruction is a valid alternative to projection-based modelling, and that, when using the proposed practical methodology, the necessary resolution measurements can be obtained from a single scan. This approach avoids the relatively time-consuming and involved procedures previously proposed in the literature.

Noise propagation for iterative penalized-likelihood image reconstruction based on Fisher information

Iterative reconstruction algorithms have been widely used in PET and SPECT emission tomography. Accurate modeling of photon noise propagation is crucial for quantitative tomography applications. Iteration-based noise propagation methods have been developed for only a few algorithms that have explicit multiplicative update equations. And there are discrepancies between the iteration-based methods and Fessler's fixed-point method because of improper approximations. In this paper, we present a unified theoretical prediction of noise propagation for any penalized expectation maximization (EM) algorithm where the EM approach incorporates a penalty term. The proposed method does not require an explicit update equation. The update equation is assumed to be implicitly defined by a differential equation of a surrogate function. We derive the expressions using the implicit function theorem, Taylor series and the chain rule from vector calculus. We also derive the fixed-point expressions when iterative algorithms converge and show the consistency between the proposed method and the fixed-point method. These expressions are solely defined in terms of the partial derivatives of the surrogate function and the Fisher information matrices. We also apply the theoretical noise predictions for iterative reconstruction algorithms in emission tomography. Finally, we validate the theoretical predictions for MAP-EM and OSEM algorithms using Monte Carlo simulations with Jaszczak-like and XCAT phantoms, respectively.

A method for accurate modelling of the crystal response function at a crystal sub-level applied to PET reconstruction

Positron emission tomography (PET) images suffer from low spatial resolution and signal-to-noise ratio. Accurate modelling of the effects affecting resolution within iterative reconstruction algorithms can improve the trade-off between spatial resolution and signal-to-noise ratio in PET images. In this work, we present an original approach for modelling the resolution loss introduced by physical interactions between and within the crystals of the tomograph and we investigate the impact of such modelling on the quality of the reconstructed images. The proposed model includes two components: modelling of the inter-crystal scattering and penetration (interC) and modelling of the intra-crystal count distribution (intraC). The parameters of the model were obtained using a Monte Carlo simulation of the Philips GEMINI GXL response. Modelling was applied to the raw line-of-response geometric histograms along the four dimensions and introduced in an iterative reconstruction algorithm. The impact of modelling interC, intraC or combined interC and intraC on spatial resolution, contrast recovery and noise was studied using simulated phantoms. The feasibility of modelling interC and intraC in two clinical (18)F-NaF scans was also studied. Measurements on Monte Carlo simulated data showed that, without any crystal interaction modelling, the radial spatial resolution in air varied from 5.3 mm FWHM at the centre of the field-of-view (FOV) to 10 mm at 266 mm from the centre. Resolution was improved with interC modelling (from 4.4 mm in the centre to 9.6 mm at the edge), or with intraC modelling only (from 4.8 mm in the centre to 4.3 mm at the edge), and it became stationary across the FOV (4.2 mm FWHM) when combining interC and intraC modelling. This improvement in resolution yielded significant contrast enhancement, e.g. from 65 to 76% and 55.5 to 68% for a 6.35 mm radius sphere with a 3.5 sphere-to-background activity ratio at 55 and 215 mm from the centre of the FOV, respectively, without introducing additional noise. Patient images confirmed the usefulness of interC and intraC modelling for improving spatial resolution and contrast. Based on Monte Carlo simulated data, we conclude that four-dimensional modelling of the inter- and intra-crystal interactions during the reconstruction process yields a significantly improved contrast to noise ratio and the stationarity of the spatial resolution in the reconstructed images.

Geometrical and Monte Carlo projectors in 3D PET reconstruction

PURPOSE

In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under consideration involves an extensive model of the system response matrix based on Monte Carlo simulations and is computed off-line and stored on disk.

METHODS

Comparisons were performed using simulated and experimental data of the commercial small animal PET scanner rPET.

RESULTS

The results demonstrate that the orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions yield better images in terms of contrast and spatial resolution than those obtained after using the conventional method and the multiray-based S-RT. Furthermore, the Monte Carlo-based method yields slight improvements in terms of contrast and spatial resolution with respect to these geometrical projectors.

CONCLUSIONS

The orthogonal distance-based ray-tracer and Siddon ray-tracer using PSF image-space convolutions represent satisfactory alternatives to factorizing the system matrix or to the conventional on-the-fly ray-tracing methods for list-mode reconstruction, where an extensive modeling based on Monte Carlo simulations is unfeasible.

Characterization of the ringing artifacts in rotator-based reconstruction with Monte Carlo-based resolution compensation for PET

PURPOSE

Studies have shown that Monte Carlo-based reconstruction could effectively improve the image quality of positron emission tomography. The authors have previously used a Gaussian rotator-based algorithm to efficiently reduce the computational cost for system matrix (SM) calculation and to meet the large memory requirements for SM storage. However, pronounced ringing artifacts were observed in the reconstructed image. In this article, the authors investigated and characterized these artifacts.

METHODS

The authors proposed an "ideal" rotator and used it as a baseline in the artifacts evaluation. This ideal rotator produces perfectly rotated images. The Gaussian rotator method was evaluated by a full system model and a partial system model without positron range and acolinearity, which could be compensated for by the blurring of the Gaussian rotator for 18F studies. Noiseless data, Monte Carlo simulation data, as well as acquired experimental data were used to quantitatively characterize the behavior of the artifacts.

RESULTS

The study of the noiseless data indicated that the artifacts were mainly attributed to the rotator, which further blurred the simulated system responses. The simulation study suggested that the artifacts become less pronounced and not quantitatively significant in practice. This result is consistent with the experimental data study. Better contrast recovery was achieved with an over-compensated system model. Traditionally, an undercompensated system model was preferred to avoid artifacts. The authors' studies suggest that the Gaussian rotator with the full system model yields the best image quality among the evaluated methods with considerably reduced quantitative error and quantitatively insignificant artifacts in practice.

CONCLUSIONS

The authors' investigation indicated that a moderately overcompensated system model (about 2 mm FWHM in this study) yielded better contrast recovery and quantitatively insignificant artifacts in practice.

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.

Noise and signal properties in PSF-based fully 3D PET image reconstruction: an experimental evaluation

The addition of accurate system modeling in PET image reconstruction results in images with distinct noise texture and characteristics. In particular, the incorporation of point spread functions (PSF) into the system model has been shown to visually reduce image noise, but the noise properties have not been thoroughly studied. This work offers a systematic evaluation of noise and signal properties in different combinations of reconstruction methods and parameters. We evaluate two fully 3D PET reconstruction algorithms: (1) OSEM with exact scanner line of response modeled (OSEM+LOR), (2) OSEM with line of response and a measured point spread function incorporated (OSEM+LOR+PSF), in combination with the effects of four post-reconstruction filtering parameters and 1-10 iterations, representing a range of clinically acceptable settings. We used a modified NEMA image quality (IQ) phantom, which was filled with 68Ge and consisted of six hot spheres of different sizes with a target/background ratio of 4:1. The phantom was scanned 50 times in 3D mode on a clinical system to provide independent noise realizations. Data were reconstructed with OSEM+LOR and OSEM+LOR+PSF using different reconstruction parameters, and our implementations of the algorithms match the vendor's product algorithms. With access to multiple realizations, background noise characteristics were quantified with four metrics. Image roughness and the standard deviation image measured the pixel-to-pixel variation; background variability and ensemble noise quantified the region-to-region variation. Image roughness is the image noise perceived when viewing an individual image. At matched iterations, the addition of PSF leads to images with less noise defined as image roughness (reduced by 35% for unfiltered data) and as the standard deviation image, while it has no effect on background variability or ensemble noise. In terms of signal to noise performance, PSF-based reconstruction has a 7% improvement in contrast recovery at matched ensemble noise levels and 20% improvement of quantitation SNR in unfiltered data. In addition, the relations between different metrics are studied. A linear correlation is observed between background variability and ensemble noise for all different combinations of reconstruction methods and parameters, suggesting that background variability is a reasonable surrogate for ensemble noise when multiple realizations of scans are not available.