Reconstruction of scattered and unscattered PET coincidences using TOF and energy information

Fast Energy Dependent Scatter Correction for List-Mode PET Data

Improvements in energy resolution of modern positron emission tomography (PET) detectors have created opportunities to implement energy-based scatter correction algorithms. Here, we use the energy information of auxiliary windows to estimate the scatter component. Our method is directly implemented in an iterative reconstruction algorithm, generating a scatter-corrected image without the need for sinograms. The purpose was to implement a fast energy-based scatter correction method on list-mode PET data, when it was not possible to use an attenuation map as a practical approach for the scatter degradation. The proposed method was evaluated using Monte Carlo simulations of various digital phantoms. It accurately estimated the scatter fraction distribution, and improved the image contrast in the simulated studied cases. We conclude that the proposed scatter correction method could effectively correct the scattered events, including multiple scatters and those originated in sources outside the field of view.

Time of Flight in Perspective: Instrumental and Computational Aspects of Time Resolution in Positron Emission Tomography

The first time-of-flight positron emission tomography (TOF-PET) scanners were developed as early as in the 1980s. However, the poor light output and low detection efficiency of TOF-capable detectors available at the time limited any gain in image quality achieved with these TOF-PET scanners over the traditional non-TOF PET scanners. The discovery of LSO and other Lu-based scintillators revived interest in TOF-PET and led to the development of a second generation of scanners with high sensitivity and spatial resolution in the mid-2000s. The introduction of the silicon photomultiplier (SiPM) has recently yielded a third generation of TOF-PET systems with unprecedented imaging performance. Parallel to these instrumentation developments, much progress has been made in the development of image reconstruction algorithms that better utilize the additional information provided by TOF. Overall, the benefits range from a reduction in image variance (SNR increase), through allowing joint estimation of activity and attenuation, to better reconstructing data from limited angle systems. In this work, we review these developments, focusing on three broad areas: 1) timing theory and factors affecting the time resolution of a TOF-PET system; 2) utilization of TOF information for improved image reconstruction; and 3) quantification of the benefits of TOF compared to non-TOF PET. Finally, we offer a brief outlook on the TOF-PET developments anticipated in the short and longer term. Throughout this work, we aim to maintain a clinically driven perspective, treating TOF as one of multiple (and sometimes competitive) factors that can aid in the optimization of PET imaging performance.

Physics and technology of time-of-flight PET detectors

The imaging performance of clinical positron emission tomography (PET) systems has evolved impressively during the last ∼15 years. A main driver of these improvements has been the introduction of time-of-flight (TOF) detectors with high spatial resolution and detection efficiency, initially based on photomultiplier tubes, later silicon photomultipliers. This review aims to offer insight into the challenges encountered, solutions developed, and lessons learned during this period. Detectors based on fast, bright, inorganic scintillators form the scope of this work, as these are used in essentially all clinical TOF-PET systems today. The improvement of the coincidence resolving time (CRT) requires the optimization of the entire detection chain and a sound understanding of the physics involved facilitates this effort greatly. Therefore, the theory of scintillation detector timing is reviewed first. Once the fundamentals have been set forth, the principal detector components are discussed: the scintillator and the photosensor. The parameters that influence the CRT are examined and the history, state-of-the-art, and ongoing developments are reviewed. Finally, the interplay between these components and the optimization of the overall detector design are considered. Based on the knowledge gained to date, it appears feasible to improve the CRT from the values of 200-400 ps achieved by current state-of-the-art TOF-PET systems to about 100 ps or less, even though this may require the implementation of advanced methods such as time resolution recovery. At the same time, it appears unlikely that a system-level CRT in the order of ∼10 ps can be reached with conventional scintillation detectors. Such a CRT could eliminate the need for conventional tomographic image reconstruction and a search for new approaches to timestamp annihilation photons with ultra-high precision is therefore warranted. While the focus of this review is on timing performance, it attempts to approach the topic from a clinically driven perspective, i.e. bearing in mind that the ultimate goal is to optimize the value of PET in research and (personalized) medicine.

Modelling and Simulation of Compton Scatter Image Formation in Positron Emission Tomography

We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the Positron Emission Tomography. The formula of the forward model has been obtained using the Single Scatter Simulation approximation under simplified assumptions and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter physics. The numerical comparative study has been performed using a digital cylindrical phantom filled in with water and containing spherical sources of emission activity located at the central and several displaced positions. Good fits of the formula-based and statistically generated profiles of scatter projections are observed in the presented numerical results.

Algorithms for joint activity-attenuation estimation from positron emission tomography scatter

Background

Attenuation correction in positron emission tomography remains challenging in the absence of measured transmission data. Scattered emission data may contribute missing information, but quantitative scatter-to-attenuation (S2A) reconstruction needs to input the reconstructed activity image. Here, we study S2A reconstruction as a building block for joint estimation of activity and attenuation.

Methods

We study two S2A reconstruction algorithms, maximum-likelihood expectation maximization (MLEM) with one-step-late attenuation (MLEM-OSL) and a maximum-likelihood gradient ascent (MLGA). We study theoretical properties of these algorithms with a focus on convergence and convergence speed and compare convergence speeds and the impact of object size in simulations using different spatial scale factors. Then, we propose joint estimation of activity and attenuation from scattered and nonscattered (true) emission data, combining MLEM-OSL or MLGA with scatter-MLEM as well as trues-MLEM and the maximum-likelihood transmission (MLTR) algorithm.

Results

Shortcomings of MLEM-OSL inhibit convergence to the true solution with high attenuation; these shortcomings are related to the linearization of a nonlinear measurement equation and can be linked to a new numerical criterion allowing geometrical interpretations in terms of low and high attenuation. Comparisons using simulated data confirm that while MLGA converges largely independent of the attenuation scale, MLEM-OSL converges if low-attenuation data dominate, but not with high attenuation. Convergence of MLEM-OSL can be improved by isolating data satisfying the aforementioned low-attenuation criterion. In joint estimation of activity and attenuation, scattered data helps avoid local minima that nonscattered data alone cannot. Combining MLEM-OSL with trues-MLEM may be sufficient for low-attenuation objects, while MLGA, scatter-MLEM, and MLTR may additionally be needed with higher attenuation.

Conclusions

The performance of S2A algorithms depends on spatial scales. MLGA provides lower computational complexity and convergence in more diverse setups than MLEM-OSL. Finally, scattered data may provide additional information to joint estimation of activity and attenuation through S2A reconstruction.

Relationship between the image quality and noise-equivalent count in time-of-flight positron emission tomography

OBJECTIVE

The aim of this study was to investigate the relationship between the NEC and TOF-PET image quality.

METHODS

The National Electrical Manufactures Association and International Electrical Commission (NEMA IEC) body phantom with a 10-mm diameter sphere was filled with an 18F-FDG solution with a 4:1 radioactivity ratio. The PET data were acquired in the three-dimensional list mode for 20 min. We created frame data ranging from 1 to 5 min acquisition time, which were then reconstructed using the baseline ordered-subsets expectation maximization (OSEM), the OSEM + point spread function (PSF) algorithm, OSEM + time-of-flight (TOF) algorithm and OSEM + PSF + TOF algorithm. The PET images were analyzed according to the noise-equivalent count (NEC), the coefficients of variance of the background (CVBG), the maximum count (CVmax) and the contrast (CVCONT). The results were compared with the recommended value according to the guidelines for the oncology FDG-PET/CT protocol.

RESULTS

The NEC was higher than the recommended value at 3 min or longer acquisition time. The CVBG lower than 15% were obtained at 3 min acquisition time without TOF and at 2 min acquisition time with TOF. The CVBG of 10% or lower were obtained at 5 min or longer acquisition time without TOF and at 4 min or longer acquisition time with TOF. Both the CVmax and CVCONT lower than 10% were obtained at 3 min or longer acquisition time without TOF and at 1 min acquisition or longer with TOF. No particular relationships were observed between the frame number and degree of the variation in the image quality. The CVCONT significantly correlated with the NEC for the data reconstructed without TOF information, while there were no significant correlations between these useful metrics for the data reconstructed with TOF.

CONCLUSION

This study demonstrated that the NEC is not a useful metric for the evaluation of the image quality on TOF-PET images.

Attenuation correction in emission tomography using the emission data--A review

The problem of attenuation correction (AC) for quantitative positron emission tomography (PET) had been considered solved to a large extent after the commercial availability of devices combining PET with computed tomography (CT) in 2001; single photon emission computed tomography (SPECT) has seen a similar development. However, stimulated in particular by technical advances toward clinical systems combining PET and magnetic resonance imaging (MRI), research interest in alternative approaches for PET AC has grown substantially in the last years. In this comprehensive literature review, the authors first present theoretical results with relevance to simultaneous reconstruction of attenuation and activity. The authors then look back at the early history of this research area especially in PET; since this history is closely interwoven with that of similar approaches in SPECT, these will also be covered. We then review algorithmic advances in PET, including analytic and iterative algorithms. The analytic approaches are either based on the Helgason-Ludwig data consistency conditions of the Radon transform, or generalizations of John's partial differential equation; with respect to iterative methods, we discuss maximum likelihood reconstruction of attenuation and activity (MLAA), the maximum likelihood attenuation correction factors (MLACF) algorithm, and their offspring. The description of methods is followed by a structured account of applications for simultaneous reconstruction techniques: this discussion covers organ-specific applications, applications specific to PET/MRI, applications using supplemental transmission information, and motion-aware applications. After briefly summarizing SPECT applications, we consider recent developments using emission data other than unscattered photons. In summary, developments using time-of-flight (TOF) PET emission data for AC have shown promising advances and open a wide range of applications. These techniques may both remedy deficiencies of purely MRI-based AC approaches in PET/MRI and improve standalone PET imaging.

Evaluation of the Feasibility and Quantitative Accuracy of a Generalized Scatter 2D PET Reconstruction Method

Scatter degrades the contrast and quantitative accuracy of positron emission tomography (PET) images, and most methods for estimating and correcting scattered coincidences in PET subtract scattered events from the measured data. Compton scattering kinematics can be used to map out the locus of possible scattering locations. These curved lines (2D) or surfaces (3D), which connect the coincidence detectors, encompass the surface (2D) or volume (3D) where the decay occurs. In the limiting case where the scattering angle approaches zero, the scattered coincidence approaches the true coincidence. Therefore, both true and scattered coincidences can be considered similarly in a generalized scatter maximum-likelihood expectation-maximization reconstruction algorithm. The proposed method was tested using list-mode data obtained from a GATE simulation of a Jaszczak-type phantom. For scatter fractions from 10% to 60%, this approach reduces noise and improves the contrast recovery coefficients by 0.5–3.0% compared with reconstructions using true coincidences and by 3.0–24.5% with conventional reconstruction methods. The results demonstrate that this algorithm is capable of producing images entirely from scattered photons, eliminates the need for scatter corrections, increases image contrast, and reduces noise. This could be used to improve diagnostic quality and/or to reduce patient dose and radiopharmaceutical cost.