Multi-ray-based system matrix generation for 3D PET reconstruction

Efficient image reconstruction for a small animal PET system with dual-layer-offset detector design

BACKGROUND

A compact PET/SPECT/CT system Inliview-3000B has been developed to provide multi-modality information on small animals for biomedical research. Its PET subsystem employed a dual-layer-offset detector design for depth-of-interaction capability and higher detection efficiency, but the irregular design caused some difficulties in calculating the normalization factors and the sensitivity map. Besides, the relatively larger (2 mm) crystal cross-section size also posed a challenge to high-resolution image reconstruction.

PURPOSE

We present an efficient image reconstruction method to achieve high imaging performance for the PET subsystem of Inliview-3000B.

METHODS

List mode reconstruction with efficient system modeling was used for the PET imaging. We adopt an on-the-fly multi-ray tracing method with random crystal sampling to model the solid angle, crystal penetration and object attenuation effect, and modify the system response model during each iteration to improve the reconstruction performance and computational efficiency. We estimate crystal efficiency with a novel iterative approach that combines measured cylinder phantom data with simulated line-of-response (LOR)-based factors for normalization correction before reconstruction. Since it is necessary to calculate normalization factors and the sensitivity map, we stack the two crystal layers together and extend the conventional data organization method here to index all useful LORs. Simulations and experiments were performed to demonstrate the feasibility and advantage of the proposed method.

RESULTS

Simulation results showed that the iterative algorithm for crystal efficiency estimation could achieve good accuracy. NEMA image quality phantom studies have demonstrated the superiority of random sampling, which is able to achieve good imaging performance with much less computation than traditional uniform sampling. In the spatial resolution evaluation based on the mini-Derenzo phantom, 1.1 mm hot rods could be identified with the proposed reconstruction method. Reconstruction of double mice and a rat showed good spatial resolution and a high signal-to-noise ratio, and organs with higher uptake could be recognized well.

CONCLUSION

The results validated the superiority of introducing randomness into reconstruction, and demonstrated its reliability for high-performance imaging. The Inliview-3000B PET subsystem with the proposed image reconstruction can provide rich and detailed information on small animals for preclinical research.

3D directional gradient L0 norm minimization guided limited-view reconstruction in a dual-panel positron emission mammography

BACKGROUND

Dual-panel PET is often used for local organ imaging, especially breast imaging, due to its simple structure, high sensitivity, good in-plane resolution, and straightforward fusion with other imaging modalities. Nevertheless, because of data loss caused by the dual-panel structure, using conventional image reconstruction methods results in limited-view artifacts and low image quality in dual-panel positron emission mammography (PEM), which may seriously affect the diagnosis. To mitigate the limited-view artifacts in the dual-panel PEM, we propose a 3D directional gradient L₀ norm minimization (3D-DL₀) guided reconstruction method.

METHODS

The detailed derivation and reasonable simplification of the 3D-DL₀ algorithm are given first. Using this algorithm, we then obtain a prior image with edge recovery but contrast loss. To limit the solution space, the 3D-DL₀ prior is introduced into the Maximum a Posteriori reconstruction. Meanwhile, a space-invariant point spread function is also implemented to restore image contrast and boundaries. Finally, the reconstructed images with limited-view artifact suppression are obtained. The proposed method was evaluated using the data acquired from physical phantoms and patients with breast tumors on a commercial dual-panel PET system.

RESULTS

The qualitative and quantitative studies for phantom data and the blind reader study for clinical data show that the proposed method is more effective in reaching a balance between artifact elimination and image contrast improvement compared with various limited-view reconstruction methods. In addition, the iteration process of the method is proved convergent numerically.

CONCLUSIONS

The image quality improvement confirms the potential value of the proposed reconstruction algorithm to address the limited-view problem, and thus improve diagnostic accuracy in dual-panel PEM imaging.

Super-resolution in brain Positron Emission Tomography using a real-time motion capture system

Super-resolution (SR) is a methodology that seeks to improve image resolution by exploiting the increased spatial sampling information obtained from multiple acquisitions of the same target with accurately known sub-resolution shifts. This work aims to develop and evaluate an SR estimation framework for brain positron emission tomography (PET), taking advantage of a high-resolution infra-red tracking camera to measure shifts precisely and continuously. Moving phantoms and non-human primate (NHP) experiments were performed on a GE Discovery MI PET/CT scanner (GE Healthcare) using an NDI Polaris Vega (Northern Digital Inc), an external optical motion tracking device. To enable SR, a robust temporal and spatial calibration of the two devices was developed as well as a list-mode Ordered Subset Expectation Maximization (OSEM) PET reconstruction algorithm, incorporating the high-resolution tracking data from the Polaris Vega to correct motion for measured line of responses (LORs) on an event-by-event basis. For both phantoms and NHP studies, the SR reconstruction method yielded PET images with visibly increased spatial resolution compared to standard static acquisitions, allowing improved visualization of small structures. Quantitative analysis in terms of SSIM, CNR and line profiles were conducted and validated our observations. The results demonstrate that SR can be achieved in brain PET by measuring target motion in real-time using a high-resolution infrared tracking camera.

Evaluation of applying space-variant resolution modeling to attenuation correction in PET

Attenuation correction aims to recover the underestimated tracer uptake and improve the image contrast recovery in positron emission tomography (PET). However, traditional ray-tracing-based projection of attenuation maps is inaccurate as some physical effects are not considered, such as finite crystal size, inter-crystal penetration and inter-crystal scatter. In this study, we evaluated the effects of applying resolution modeling (RM) to attenuation correction by implementing space-variant RM to complement physical effects which are usually omitted in the traditional projection model. We verified this method on a brain PET scanner developed by our group, in both Monte Carlo simulation and real-world data, in comparison with space-invariant Gaussian RM, average-depth-of-interaction, and multi-ray tracing methods. The results indicate that the space-variant RM is superior in terms of artifacts reduction and contrast recovery.

Hybrid model of photon propagation based on the analytical and Monte Carlo methods for a dual-head PET system

The construction of photon propagation has a close relationship with the quality of reconstructed images. The classical Monte Carlo (MC) based method can model the photon propagation precisely, but it is time-consuming. The analytical method can often quickly construct a model, but its precision is a problem. How to fully exploit the advantages of the MC simulation and analytical model is an open problem. Inspired by the characteristics of the depth of interaction (DOI) detectors, which can help confirm the deposited position of a photon with DOI-encoding technology, we virtually discretize each crystal into several subcrystals to obtain the statistical distribution by MC-based simulation. Then, the statistical distribution is combined with a spatially variant solid-angle model. This combination strategy provides a hybrid model to describe photon propagation with relatively high accuracy and low computational cost. Three discretization schemes are compared to optimize the constructed photon propagation model. Several experiments are carried out to evaluate the performance of the proposed hybrid method. The metrics of full width at half maximum (FWHM), contrast recovery (CR), and coefficient of variation (COV) are adopted to quantitate the imaging results. The classical MC-based method is compared as a gold-standard reference. When a crystal is divided into two discretized positions, the convergent tendencies of CRs and COVs are consistent with that based on MC simulation method, respectively. In terms of FWHMs, the resolutions of using the MC-based model and the proposed hybrid model are 0.71 mm and 0.68 mm in the direction parallel to the detector head, respectively. This indicates the potential of the proposed method in positron emission tomography imaging.

Preliminary Investigation of a Novel 18F Radiopharmaceutical for Imaging CB2 Receptors in a SOD Mouse Model

We successfully radiolabelled a novel prospective cannabinoid type 2 receptor ligand with 18F and tested its biodistribution in animal models by positron emission tomography (PET)/computed tomography (CT) imaging. The radiolabelling process was conducted on an alkyl mesylate fragment of the main naphthyridine core, using highly efficient microfluidic technology. No preliminary protection was needed, and the product was purified by semi-prep HPLC and SPE formulation, allowing the desired diastereomeric mixture to be obtained in 29% radiochemical yield and>95% radiochemically pure. SOD1G93A mice were used as model of overexpression of CB2 receptors; PET imaging revealed a significant increase of the tracer distribution volume in the brain of symptomatic subjects compared with the asymptomatic ones.

Evaluation of quantitative, efficient image reconstruction for VersaPET, a compact PET system

PURPOSE

Previously we developed a high-resolution positron emission tomography (PET) system-VersaPET-characterized by a block geometry with relatively large axial and transaxial interblock gaps and a compact geometry susceptible to parallax blurring effects. In this work, we report the qualitative and quantitative evaluation of a graphic processing unit (GPU)-accelerated maximum-likelihood by expectation-maximization (MLEM) image reconstruction framework for VersaPET which features accurate system geometry and projection space point-spread-function (PSF) modeling.

METHODS

We combined the ray-tracing module from software for tomographic image reconstruction (STIR), an open-source PET image reconstruction package, with VersaPET's exact block geometry for the geometric system matrix. Point-spread-function modeling of crystal penetration and scattering was achieved by a custom Monte-Carlo simulation for projection space blurring in all dimensions. We also parallelized the reconstruction in GPU taking advantage of the system's symmetry for PSF computation. To investigate the effects of PSF width, we generated and studied multiple kernels between one that reflects the true LYSO density in the MC simulation and another that reflects geometry only (no PSF). GATE simulations of hot and cold-sphere phantoms with spheres of different sizes, real microDerenzo phantom, and human blood vessel data were used to characterize the quantitative and qualitative performances of the reconstruction.

RESULTS

Reconstruction with an accurate system geometry effectively improved image quality compared to STIR (version 3.0) which assumes an idealized system geometry. Reconstructions of GATE-simulated hot-sphere phantom data showed that all PSF kernels achieved superior performance in contrast recovery and bias reduction compared to using no PSF, but may introduce edge artifact and lumped background noise pattern depending on the width of PSF kernels. Cold-sphere phantom simulation results also indicated improvement in contrast recovery and quantification with PSF modeling (compared to no PSF) for 5 and 10 mm cold spheres. Real microDerenzo phantom images with the PSF kernel that reflects the true LYSO density showed degraded resolving power of small sectors that could be resolved more clearly by underestimated PSF kernels, which is consistent with recent literature despite differences in scanner geometries and in approaches to system model estimation. The human vessel results resemble those of the hot-sphere phantom simulation with the PSF kernel that reflects the true LYSO density achieving the highest peak in the time activity curve (TAC) and similar lumped noise pattern.

CONCLUSIONS

We fully evaluated a practical MLEM reconstruction framework that we developed for VersaPET in terms of qualitative and quantitative performance. Different PSF kernels may be adopted for improving the results of specific imaging tasks but the underlying reasons for the variation in optimal kernel for the real and simulation studies requires further study.

Estimation of optimized timely system matrix with improved image quality in iterative reconstruction algorithm: A simulation study

The system matrix (SM) being a main part of statistical image reconstruction algorithms establishes relationship between the object and projection space. The aim was to determine it in a short duration time, towards obtaining the best quality of contrast images. In this study, a new analytical method based on Cavalieri's principle as subdividing common regions has been proposed in which the precision of the amounts of estimated areas was improved by increasing the number of divisions (NOD), and consequently the total SM's time was increased. An important issue is the tradeoff between the NODs and computational time. For this purpose, a Monte Carlo simulated Jaszczak phantom study was performed by the Monte Carlo N-Particle transport code version 5 (MCNP5) in which the tomographic images of resolution and contrast phantoms were reconstructed by maximum likelihood expectation maximization (MLEM) algorithm, and the influence of NODs variations was investigated. The results show that the lowest and best quality have been obtained at the NODs of 0 and 8, respectively and in the optimum case, the SM's total time at NOD of 8 was 925 s, which was much lower than those of the conventional Monte Carlo simulations and experimental test.

A Monte Carlo detector response model for the IRIS PET preclinical scanner

PET preclinical studies require high spatial resolution due to the limited size of the animal under investigation. To achieve this target, iterative image reconstruction algorithms are commonly preferred over the analytical methods because they offer the possibility of accurately modeling the whole imaging process. In this work, we propose an accurate factorized system matrix for the INVISCAN IRIS preclinical PET scanner to be used with an iterative algorithm. The model includes two components: the geometric component and the detector response of the system. The main innovative aspect of the work is the creation of the detector matrix using a Monte Carlo simulation, with a particular focus on the optimization of the simulation process to reduce the calculation time. The new system model is compared with the current IRIS model to evaluate the image quality, following the NEMA Standards NU 4-2008. The comparison showed an enhancement of the image quality, in terms of uniformity and recovery coefficients. This work confirms that the inclusion of the detector response into the system model leads to improved reconstruction results.

Enhancement of Partial Volume Correction in MR-Guided PET Image Reconstruction by Using MRI Voxel Sizes

Positron emission tomography (PET) suffers from poor spatial resolution which results in quantitative bias when evaluating the radiotracer uptake in small anatomical regions, such as the striatum in the brain which is of importance in this paper of neurodegenerative diseases. These partial volume effects need to be compensated for by employing partial volume correction (PVC) methods in order to achieve quantitatively accurate images. Two important PVC methods applied during the reconstruction are resolution modeling, which suffers from Gibbs artifacts, and penalized likelihood using anatomical priors. The introduction of clinical simultaneous PET-MR scanners has attracted new attention for the latter methods and brought new opportunities to use MRI information to assist PET image reconstruction in order to improve image quality. In this context, MR images are usually down-sampled to the PET resolution before being used in MR-guided PET reconstruction. However, the reconstruction of PET images using the MRI voxel size could achieve a better utilization of the high resolution anatomical information and improve the PVC obtained with these methods. In this paper, we evaluate the importance of the use of MRI voxel sizes when reconstructing PET images with MR-guided maximum a posteriori (MAP) methods, specifically the modified Bowsher method. We also propose a method to avoid the artifacts that arise when PET reconstructions are performed in a higher resolution matrix than the standard for a given scanner. The MR-guided MAP reconstructions were implemented with a modified Lange prior that included anatomical information with the Bowsher method. The methods were evaluated with and without resolution modeling for simulated and real brain data. We show that the use of the MRI voxel sizes when reconstructing PET images with MR-guided MAP enhances PVC by improving the contrast and reducing the bias in six different regions of the brain using regional metrics for a single simulated data set and ensemble metrics for ten noise realizations. Similar results were obtained for real data, where a good enhancement of the contrast was achieved. The combination of MR-guided MAP reconstruction with point-spread function modeling and MRI voxel sizes proved to be an attractive method to achieve considerable enhancement of PVC, while reducing and controlling the noise level and Gibbs artifacts.

An automatic algorithm to exploit the symmetries of the system response matrix in positron emission tomography iterative reconstruction

Positron emission tomography (PET) iterative 3D reconstruction is a very computational demanding task. One of the main issues of the iterative reconstruction concerns the management of the system response matrix (SRM). The SRM models the relationship between the projection and the voxel space and its memory footprint can easily exceed hundreds of GB. Moreover, in order to make the reconstruction fast enough not to hinder its practical application, the SRM must be stored in the random access memory of the workstation used for the reconstruction. This issue is normally solved by implementing efficient storage schemes and by reducing the number of redundant patterns in the SRM through symmetries. However, finding a sufficient number of symmetries is often non-trivial and is typically performed using dedicated solutions that cannot be exported to different detectors and geometries. In this paper, an automatic approach to reduce the memory footprint of a pre-computed SRM is described. The proposed approach was named symmetry search algorithm (SSA) and consists in an algorithm that searches for some of the redundant patterns present in the SRM, leading to its lossy compression. This approach was built to detect translations, reflections and coordinates swap in voxel space. Therefore, it is particularly well suited for those scanners where some of the rotational symmetries are broken, e.g. small animal scanner where the modules are arranged in a polygonal ring made of few elements, and dual head planar PET systems. In order to validate this approach, the SSA is applied to the SRM of a preclinical scanner (the IRIS PET/CT). The data acquired by the scanner were reconstructed with a dedicated maximum likelihood estimation maximization algorithm with both the uncompressed and the compressed SRMs. The results achieved show that the information lost due to the SSA compression is negligible. Compression factors up to 52 when using the SSA together with manually inserted symmetries and up to 204 when using the SSA alone, can be obtained for the IRIS SRM. These results come without significant differences in the values and in the main quality metrics of the reconstructed images, i.e. spatial resolution and noise. Although the compression factors depend on the system considered, the SSA is applicable to any SRM and therefore it can be considered a general tool to reduce the footprint of a pre-computed SRM.

New Digital Plug and Imaging Sensor for a Proton Therapy Monitoring System Based on Positron Emission Tomography

One of the most challenging areas of sensor development for nuclear medicine is the design of proton therapy monitoring systems. Sensors are operated in a high detection rate regime in beam-on conditions. We realized a prototype of a monitoring system for proton therapy based on the technique of positron emission tomography. We used the Plug and Imaging (P&I) technology in this application. This sensing system includes LYSO/silicon photomultiplier (SiPM) detection elements, fast digital multi voltage threshold (MVT) readout electronics and dedicated image reconstruction algorithms. In this paper, we show that the P&I sensor system has a uniform response and is controllable in the experimental conditions of the proton therapy room. The prototype of PET monitoring device based on the P&I sensor system has an intrinsic experimental spatial resolution of approximately 3 mm (FWHM), obtained operating the prototype both during the beam irradiation and right after it. The count-rate performance of the P&I sensor approaches 5 Mcps and allows the collection of relevant statistics for the nuclide analysis. The measurement of both the half life and the relative abundance of the positron emitters generated in the target volume through irradiation of 1010 protons in approximately 15 s is performed with 0.5% and 5% accuracy, respectively.

Carbon ions beam therapy monitoring with the INSIDE in-beam PET

In vivo range monitoring techniques are necessary in order to fully take advantage of the high dose gradients deliverable in hadrontherapy treatments. Positron emission tomography (PET) scanners can be used to monitor beam-induced activation in tissues and hence measure the range. The INSIDE (Innovative Solutions for In-beam DosimEtry in Hadrontherapy) in-beam PET scanner, installed at the Italian National Center of Oncological Hadrontherapy (CNAO, Pavia, Italy) synchrotron facility, has already been successfully tested in vivo during a proton therapy treatment. We discuss here the system performance evaluation with carbon ion beams, in view of future in vivo tests. The work is focused on the analysis of activity images obtained with therapeutic treatments delivered to polymethyl methacrylate (PMMA) phantoms, as well as on the test of an innovative and robust Monte Carlo simulation technique for the production of reliable prior activity maps. Images are reconstructed using different integration intervals, so as to monitor the activity evolution during and after the treatment. Three procedures to compare activity images are presented, namely Pearson correlation coefficient, Beam's eye view and overall view. Images of repeated irradiations of the same treatments are compared to assess the integration time necessary to provide reproducible images. The range agreement between simulated and experimental images is also evaluated, so as to validate the simulation capability to provide sound prior information. The results indicate that at treatment end, or at most 20 s afterwards, the range measurement is reliable within 1-2 mm, when comparing both different experimental sessions and data with simulations. In conclusion, this work shows that the INSIDE in-beam PET scanner performance is promising towards its in vivo test with carbon ions.

Sinogram Blurring Matrix Estimation From Point Sources Measurements With Rank-One Approximation for Fully 3-D PET

An accurate system matrix is essential in positron emission tomography (PET) for reconstructing high quality images. To reduce storage size and image reconstruction time, we factor the system matrix into a product of a geometry projection matrix and a sinogram blurring matrix. The geometric projection matrix is computed analytically and the sinogram blurring matrix is estimated from point source measurements. Previously, we have estimated a 2-D blurring matrix for a preclinical PET scanner. The 2-D blurring matrix only considers blurring effects within a transaxial sinogram and does not compensate for inter-sinogram blurring effects. For PET scanners with a long axial field of view, inter-sinogram blurring can be a major problem influencing the image quality in the axial direction. Hence, the estimation of a 4-D blurring matrix is desirable to further improve the image quality. The 4-D blurring matrix estimation is an ill-conditioned problem due to the large number of unknowns. Here, we propose a rank-one approximation for each blurring kernel image formed by a row vector of the sinogram blurring matrix to improve the stability of the 4-D blurring matrix estimation. The proposed method is applied to the simulated data as well as the real data obtained from an Inveon microPET scanner. The results show that the newly estimated 4-D blurring matrix can improve the image quality over those obtained with a 2-D blurring matrix and requires less point source scans to achieve similar image quality compared with an unconstrained 4-D blurring matrix estimation.

Spatially Variant Resolution Modelling for Iterative List-Mode PET Reconstruction

A spatially variant resolution modelling technique is presented which estimates the system matrix on-the-fly during iterative list-mode reconstruction. This is achieved by redistributing the endpoints of each list-mode event according to derived probability density functions describing the detector response function and photon acollinearity, at each iteration during the reconstruction. Positron range is modelled using an image-based convolution. When applying this technique it is shown that the maximum-likelihood expectation maximisation (MLEM) algorithm is not compatible with an obvious acceleration strategy. The image space reconstruction algorithm (ISRA), however, after being adapted to a list-mode based implementation, is well-suited to the implementation of the model. A comparison of ISRA and MLEM is made to confirm that ISRA is a suitable alternative to MLEM. We demonstrate that this model agrees with measured point spread functions and we present results showing an improvement in resolution recovery, particularly for off-centre objects, as compared to commercially available software, as well as the standard technique of using a stationary Gaussian convolution to model the resolution, for equal iterations and only slightly higher computation time.

Iterative reconstruction for pet scanners with continuous scintillators

Several technical developments have led to a comeback of the continuous scintillators in positron emission tomography (PET). Important differences exist between the resurgent continuous scintillators and the prevailing pixelated devices, which can translate into certain advantages of the former over the latter. However, if the peculiarities of the continuous scintillators are not considered in the iterative reconstruction in which the measured data is converted to images, these advantages will not be fully exploited. In this paper, we review which those peculiarities are and how they have been considered in the literature of PET reconstruction. In light of this review, we propose a new method to compute one of the key elements of the iterative schemes, the system matrix. Specifically, we substitute the traditional Gaussian approach to the so-called uncertainty term by a more general Monte Carlo estimation, and account for the effect of the optical photons, which cannot be neglected in continuous-scintillators devices. Finally, we gather in a single scheme all the elements of the iterative reconstruction that have been individually reformulated, in this or previous works, for continuous scintillators, providing the first reconstruction framework fully adapted to this type of detectors. The preliminary images obtained for a commercially available PET scanner show the benefits of adjusting the reconstruction to the nature of the scintillators.

Iterative reconstruction using a Monte Carlo based system transfer matrix for dedicated breast positron emission tomography

To maximize sensitivity, it is desirable that ring Positron Emission Tomography (PET) systems dedicated for imaging the breast have a small bore. Unfortunately, due to parallax error this causes substantial degradation in spatial resolution for objects near the periphery of the breast. In this work, a framework for computing and incorporating an accurate system matrix into iterative reconstruction is presented in an effort to reduce spatial resolution degradation towards the periphery of the breast. The GATE Monte Carlo Simulation software was utilized to accurately model the system matrix for a breast PET system. A strategy for increasing the count statistics in the system matrix computation and for reducing the system element storage space was used by calculating only a subset of matrix elements and then estimating the rest of the elements by using the geometric symmetry of the cylindrical scanner. To implement this strategy, polar voxel basis functions were used to represent the object, resulting in a block-circulant system matrix. Simulation studies using a breast PET scanner model with ring geometry demonstrated improved contrast at 45% reduced noise level and 1.5 to 3 times resolution performance improvement when compared to MLEM reconstruction using a simple line-integral model. The GATE based system matrix reconstruction technique promises to improve resolution and noise performance and reduce image distortion at FOV periphery compared to line-integral based system matrix 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.

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.

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.

Averaging and Metropolis iterations for positron emission tomography

Iterative positron emission tomography (PET) reconstruction computes projections between the voxel space and the lines of response (LOR) space, which are mathematically equivalent to the evaluation of multi-dimensional integrals. The dimension of the integration domain can be very high if scattering needs to be compensated. Monte Carlo (MC) quadrature is a straightforward method to approximate high-dimensional integrals. As the numbers of voxels and LORs can be in the order of hundred millions and the projection also depends on the measured object, the quadratures cannot be precomputed, but Monte Carlo simulation should take place on-the-fly during the iterative reconstruction process. This paper presents modifications of the maximum likelihood, expectation maximization (ML-EM) iteration scheme to reduce the reconstruction error due to the on-the-fly MC approximations of forward and back projections. If the MC sample locations are the same in every iteration step of the ML-EM scheme, then the approximation error will lead to a modified reconstruction result. However, when random estimates are statistically independent in different iteration steps, then the iteration may either diverge or fluctuate around the solution. Our goal is to increase the accuracy and the stability of the iterative solution while keeping the number of random samples and therefore the reconstruction time low. We first analyze the error behavior of ML-EM iteration with on-the-fly MC projections, then propose two solutions: averaging iteration and Metropolis iteration. Averaging iteration averages forward projection estimates during the iteration sequence. Metropolis iteration rejects those forward projection estimates that would compromise the reconstruction and also guarantees the unbiasedness of the tracer density estimate. We demonstrate that these techniques allow a significant reduction of the required number of samples and thus the reconstruction time. The proposed methods are built into the Teratomo system.

Patient-adaptive lesion metabolism analysis by dynamic PET images

Dynamic PET imaging provides important spatial-temporal information for metabolism analysis of organs and tissues, and generates a great reference for clinical diagnosis and pharmacokinetic analysis. Due to poor statistical properties of the measurement data in low count dynamic PET acquisition and disturbances from surrounding tissues, identifying small lesions inside the human body is still a challenging issue. The uncertainties in estimating the arterial input function will also limit the accuracy and reliability of the metabolism analysis of lesions. Furthermore, the sizes of the patients and the motions during PET acquisition will yield mismatch against general purpose reconstruction system matrix, this will also affect the quantitative accuracy of metabolism analyses of lesions. In this paper, we present a dynamic PET metabolism analysis framework by defining a patient adaptive system matrix to improve the lesion metabolism analysis. Both patient size information and potential small lesions are incorporated by simulations of phantoms of different sizes and individual point source responses. The new framework improves the quantitative accuracy of lesion metabolism analysis, and makes the lesion identification more precisely. The requirement of accurate input functions is also reduced. Experiments are conducted on Monte Carlo simulated data set for quantitative analysis and validation, and on real patient scans for assessment of clinical potential.

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.

Iterative reconstruction methods in X-ray CT

Iterative reconstruction (IR) methods have recently re-emerged in transmission x-ray computed tomography (CT). They were successfully used in the early years of CT, but given up when the amount of measured data increased because of the higher computational demands of IR compared to analytical methods. The availability of large computational capacities in normal workstations and the ongoing efforts towards lower doses in CT have changed the situation; IR has become a hot topic for all major vendors of clinical CT systems in the past 5 years. This review strives to provide information on IR methods and aims at interested physicists and physicians already active in the field of CT. We give an overview on the terminology used and an introduction to the most important algorithmic concepts including references for further reading. As a practical example, details on a model-based iterative reconstruction algorithm implemented on a modern graphics adapter (GPU) are presented, followed by application examples for several dedicated CT scanners in order to demonstrate the performance and potential of iterative reconstruction methods. Finally, some general thoughts regarding the advantages and disadvantages of IR methods as well as open points for research in this field are discussed.

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.

An outlook on future design of hybrid PET/MRI systems

Early diagnosis and therapy increasingly operate at the cellular, molecular, or even at the genetic level. As diagnostic techniques transition from the systems to the molecular level, the role of multimodality molecular imaging becomes increasingly important. Positron emission tomography (PET) and magnetic resonance imaging (MRI) are powerful techniques for in vivo molecular imaging. The inability of PET to provide anatomical information is a major limitation of standalone PET systems. Combining PET and CT proved to be clinically relevant and successfully reduced this limitation by providing the anatomical information required for localization of metabolic abnormalities. However, this technology still lacks the excellent soft-tissue contrast provided by MRI. Standalone MRI systems reveal structure and function but cannot provide insight into the physiology and/or the pathology at the molecular level. The combination of PET and MRI, enabling truly simultaneous acquisition, bridges the gap between molecular and systems diagnosis. MRI and PET offer richly complementary functionality and sensitivity; fusion into a combined system offering simultaneous acquisition will capitalize the strengths of each, providing a hybrid technology that is greatly superior to the sum of its parts. A combined PET/MRI system provides both the anatomical and structural description of MRI simultaneously with the quantitative capabilities of PET. In addition, such a system would allow exploiting the power of MR spectroscopy (MRS) to measure the regional biochemical content and to assess the metabolic status or the presence of neoplasia and other diseases in specific tissue areas. This paper briefly summarizes state-of-the-art developments and latest advances in dedicated hybrid PET/MRI instrumentation. Future prospects and potential clinical applications of this technology will also be discussed.

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.

A STAT3-mediated metabolic switch is involved in tumour transformation and STAT3 addiction

The pro-oncogenic transcription factor STAT3 is constitutively activated in a wide variety of tumours that often become addicted to its activity, but no unifying view of a core function determining this widespread STAT3-dependence has yet emerged. We show here that constitutively active STAT3 acts as a master regulator of cell metabolism, inducing aerobic glycolysis and down-regulating mitochondrial activity both in primary fibroblasts and in STAT3-dependent tumour cell lines. As a result, cells are protected from apoptosis and senescence while becoming highly sensitive to glucose deprivation. We show that enhanced glycolysis is dependent on HIF-1α up-regulation, while reduced mitochondrial activity is HIF-1α-independent and likely caused by STAT3-mediated down-regulation of mitochondrial proteins. The induction of aerobic glycolysis is an important component of STAT3 pro-oncogenic activities, since inhibition of STAT3 tyrosine phosphorylation in the tumour cell lines down-regulates glycolysis prior to leading to growth arrest and cell death, both in vitro and in vivo. We propose that this novel, central metabolic role is at the core of the addiction for STAT3 shown by so many biologically different tumours.

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.

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.

Improving the singles rate method for modeling accidental coincidences in high-resolution PET

Random coincidences ('randoms') are one of the main sources of image degradation in PET imaging. In order to correct for this effect, an accurate method to estimate the contribution of random events is necessary. This aspect becomes especially relevant for high-resolution PET scanners where the highest image quality is sought and accurate quantitative analysis is undertaken. One common approach to estimate randoms is the so-called singles rate method (SR) widely used because of its good statistical properties. SR is based on the measurement of the singles rate in each detector element. However, recent studies suggest that SR systematically overestimates the correct random rate. This overestimation can be particularly marked for low energy thresholds, below 250 keV used in some applications and could entail a significant image degradation. In this work, we investigate the performance of SR as a function of the activity, geometry of the source and energy acceptance window used. We also investigate the performance of an alternative method, which we call 'singles trues' (ST) that improves SR by properly modeling the presence of true coincidences in the sample. Nevertheless, in any real data acquisition the knowledge of which singles are members of a true coincidence is lost. Therefore, we propose an iterative method, STi, that provides an estimation based on ST but which only requires the knowledge of measurable quantities: prompts and singles. Due to inter-crystal scatter, for wide energy windows ST only partially corrects SR overestimations. While SR deviations are in the range 86-300% (depending on the source geometry), the ST deviations are systematically smaller and contained in the range 4-60%. STi fails to reproduce the ST results, although for not too high activities the deviation with respect to ST is only a few percent. For conventional energy windows, i.e. those without inter-crystal scatter, the ST method corrects the SR overestimations, and deviations from the true random rate are of the order of 1% or less. In addition, in the case of conventional energy window STi results reproduce ST results and therefore the former can be used to obtain the true random rate.

A practical way to improve contrast-to-noise ratio and quantitation for statistical-based iterative reconstruction in whole-body PET imaging

In whole-body positron emission tomography (PET) imaging, the detection of small uptake foci (i.e., around two or three times the tomograph's spatial resolution) is a critical issue. Indeed, spatial resolution is altered by postreconstruction smoothing operations used to reduce the noise introduced by (among other things) an inaccurate system matrix. The authors previously proposed a device-dedicated projector, easily applicable on a clinical gantry, based on point-source measurements, which introduces less noise than a geometrical model. In the present study, they took advantage of the lower noise levels by reducing the postfilter and then quantified the approach's impact on image quality. This study was performed on an IEC Body Phantom Set filled with 18F (sphere-to-background activity ratio: 4:1). The same 3 min acquisition was reconstructed with either (i) a clinical system based on a geometrical tomographic operator (OSEM_CL) or (ii) an OSEM algorithm using the suggested system matrix (OSEM_DR). In order to compare the resulting images, they set the 3D Gaussian postfilter (3DGPF) for OSEM_DR so as to obtain similar background signal-to-noise ratio (SNR) to that of OSEM_CL with a Gaussian postfilter full width at half maximum of 5 mm (as recommended for whole-body imaging on a Biograph6). They then assessed the contrast-to-noise ratio (CNR) and quantitation [contrast recovery (CR)] for the phantom's four smallest spheres (with internal diameters of 10, 13, 17, and 22 mm). Evaluation of 3DGPFs ranging from 2.2 to 2.6 mm showed that a value of 2.4 mm in OSEM_DR gave the closest background SNR to that of OSEM_CL with a 3DGPF of 5 mm. For all studied targets, the CNR was higher with OSEM_DR than with OSEM_CL. For the 10 and 13 mm spheres, OSEM_DR increased the size of the CNR peaks by 37% and 20%, relative to OSEM_CL. The OSEM_DR technique yielded higher CR values than OSEM_CL did. For the 10, 13, 17, and 22 mm spheres, the CR values at eight iterations were 0.5, 0.6, 1.1, and 1.0 for OSEM_DR and 0.3, 0.4, 0.9, and 0.8 for OSEM_CL. They evaluated a practical method for determining a device-dedicated system matrix based on point-source acquisitions. This tomographic operator is more realistic than geometrical system matrix and introduces less noise into PET images during statistical reconstruction; it thus reduces the extent of postfiltering operations required. Thus, spatial resolution is better maintained with OSEM_DR than with clinical reconstruction. They showed that this method improves the contrast-to-noise ratio and quantification of uptake foci (especially those that are at the system's limit of detection) and, in a clinical context, could allow better detection and earlier diagnosis.