The SNR of time-of-flight positron emission tomography data for joint reconstruction of the activity and attenuation images

Objective.Measurement of the time-of-flight (TOF) difference of each coincident pair of photons increases the effective sensitivity of positron emission tomography (PET). Many authors have analyzed the benefit of TOF for quantification and hot spot detection in the reconstructed activity images. However, TOF not only improves the effective sensitivity, it also enables the joint reconstruction of the tracer concentration and attenuation images. This can be used to correct for errors in CT- or MR-derived attenuation maps, or to apply attenuation correction without the help of a second modality. This paper presents an analysis of the effect of TOF on the variance of the jointly reconstructed attenuation and (attenuation corrected) tracer concentration images.Approach.The analysis is performed for PET systems that have a distribution of possibly non-Gaussian TOF-kernels, and includes the conventional Gaussian TOF-kernel as a special case. Non-Gaussian TOF-kernels are often observed in novel detector designs, which make use of two (or more) different mechanisms to convert the incoming 511 keV photon to optical photons. The analytical result is validated with a simple 2D simulation.Main results.We show that if two different TOF-kernels are equivalent for image reconstruction with known attenuation, then they are also equivalent for joint reconstruction of the activity and the attenuation images. The variance increase in the activity, caused by also jointly reconstructing the attenuation image, vanishes when the TOF-resolution approaches perfection.Significance.These results are of interest for PET detector development and for the development of stand-alone PET systems.

MR-based Attenuation Correction for Brain PET Using 3D Cycle-Consistent Adversarial Network

Attenuation correction (AC) is important for the quantitative merits of positron emission tomography (PET). However, attenuation coefficients cannot be derived from magnetic resonance (MR) images directly for PET/MR systems. In this work, we aimed to derive continuous AC maps from Dixon MR images without the requirement of MR and computed tomography (CT) image registration. To achieve this, a 3D generative adversarial network with both discriminative and cycle-consistency loss (Cycle-GAN) was developed. The modified 3D U-net was employed as the structure of the generative networks to generate the pseudo CT/MR images. The 3D patch-based discriminative networks were used to distinguish the generated pseudo CT/MR images from the true CT/MR images. To evaluate its performance, datasets from 32 patients were used in the experiment. The Dixon segmentation and atlas methods provided by the vendor and the convolutional neural network (CNN) method which utilized registered MR and CT images were employed as the reference methods. Dice coefficients of the pseudo-CT image and the regional quantification in the reconstructed PET images were compared. Results show that the Cycle-GAN framework can generate better AC compared to the Dixon segmentation and atlas methods, and shows comparable performance compared to the CNN method.

Practical joint reconstruction of activity and attenuation with autonomous scaling for time-of-flight PET

Recent research has showed that attenuation images can be determined from emission data, jointly with activity images, up to a scaling constant when utilizing the time-of-flight (TOF) information. We aim to develop practical CT-less joint reconstruction for clinical TOF PET scanners to obtain quantitatively accurate activity and attenuation images. In this work, we present a joint reconstruction of activity and attenuation based on MLAA (maximum likelihood reconstruction of attenuation and activity) with autonomous scaling determination and joint TOF scatter estimation from TOF PET data. Our idea for scaling is to use a selected volume of interest (VOI) in a reconstructed attenuation image with known attenuation, e.g. a liver in patient imaging. First, we construct a unit attenuation medium which has a similar, though not necessarily the same, support to the imaged emission object. All detectable LORs intersecting the unit medium have an attenuation factor of e -1≈ 0.3679, i.e. the line integral of linear attenuation coefficients is one. The scaling factor can then be determined from the difference between the reconstructed attenuation image and the known attenuation within the selected VOI normalized by the unit attenuation medium. A four-step iterative joint reconstruction algorithm is developed. In each iteration, (1) first the activity is updated using TOF OSEM from TOF list-mode data; (2) then the attenuation image is updated using XMLTR-a extended MLTR from non-TOF LOR sinograms; (3) a scaling factor is determined based on the selected VOI and both activity and attenuation images are updated using the estimated scaling; and (4) scatter is estimated using TOF single scatter simulation with the jointly reconstructed activity and attenuation images. The performance of joint reconstruction is studied using simulated data from a generic whole-body clinical TOF PET scanner and a long axial FOV research PET scanner as well as 3D experimental data from the PennPET Explorer scanner. We show that the proposed joint reconstruction with proper autonomous scaling provides low bias results comparable to the reference reconstruction with known attenuation.

PET-enabled dual-energy CT: image reconstruction and a proof-of-concept computer simulation study

Standard dual-energy computed tomography (CT) uses two different x-ray energies to obtain energy-dependent tissue attenuation information to allow quantitative material decomposition. The combined use of dual-energy CT and positron emission tomography (PET) may provide a more comprehensive characterization of disease states in cancer and other diseases. However, the integration of dual-energy CT with PET is not trivial, either requiring costly hardware upgrades or increasing radiation exposure. This paper proposes a different dual-energy CT imaging method that is enabled by PET. Instead of using a second x-ray CT scan with a different energy, this method exploits time-of-flight PET image reconstruction via the maximum likelihood attenuation and activity (MLAA) algorithm to obtain a 511 keV gamma-ray attenuation image from PET emission data. The high-energy gamma-ray attenuation image is then combined with the low-energy x-ray CT of PET/CT to provide a pair of dual-energy CT images. A major challenge with the standard MLAA reconstruction is the high noise present in the reconstructed 511 keV attenuation map, which would not compromise the PET activity reconstruction too much but may significantly affect the performance of the gamma-ray attenuation image for material decomposition. To overcome the problem, we further propose a kernel MLAA algorithm to exploit the prior information from the available x-ray CT image. We conducted a computer simulation to test the concept and algorithm for the task of material decomposition. The simulation results demonstrate that this PET-enabled dual-energy CT method is promising for quantitative material decomposition. The proposed method can be readily implemented on time-of-flight PET/CT scanners to enable simultaneous PET and dual-energy CT imaging.

Total Body PET: Why, How, What for?

PET instruments are now available with a long axial field-of-view (LAFOV) to enable imaging the total-body, or at least head and torso, simultaneously and without bed translation. This has two major benefits, a dramatic increase in system sensitivity and the ability to measure kinetics with wider axial coverage so as to include multiple organs. This manuscript presents a review of the technology leading up to the introduction of these new instruments, and explains the benefits of a LAFOV PET-CT instrument. To date there are two platforms developed for TB-PET, an outcome of the EXPLORER Consortium of the University of California at Davis (UC Davis) and the University of Pennsylvania (Penn). The uEXPLORER at UC Davis has an AFOV of 194 cm and was developed by United Imaging Healthcare. The PennPET EXPLORER was developed at Penn and is based on the digital detector from Philips Healthcare. This multi-ring system is scalable and has been tested with 3 rings but is now being expanded to 6 rings for 140 cm. Initial human studies with both EXPLORER systems have demonstrated the successful implementation and benefits of LAFOV scanners for both clinical and research applications. Examples of such studies are described in this manuscript.

Estimation of Crystal Timing Properties and Efficiencies for the Improvement of (Joint) Maximum-Likelihood Reconstructions in TOF-PET

With increasing improvements in the time of flight (TOF) resolution of positron emission tomography (PET) scanners, an accurate model of the TOF measurements is becoming increasingly important. This work considers two parameters of the TOF kernel; the relative positioning of the timing data-bins and the timing resolution along each line of response (LOR). Similar to an existing data-driven method, we assume that any shifts of data-bins along lines of response can be modelled as differences between crystal timing offsets. Inspired by this, timing resolutions of all LORs are modelled as the hypotenuse of timing resolutions of the crystal-pairs in coincidence. Furthermore, in order to mitigate the influence of potential inaccuracies of detector-pair sensitivities on crystal timing resolutions, relative LOR sensitivities are modelled as the product of efficiency factors for the two crystals in coincidence. We validate estimating maps of crystal timing offsets, timing resolutions and efficiencies from the emission data using noisy simulations of a brain phantom. Results are shown for phantom and patient data scanned on clinically available TOF-PET scanners. We find that the estimation of crystal timing resolutions is more sensitive to the data statistics than the estimation of crystal timing offsets. As a result, estimation of crystal timing properties could either be limited to high count emission data, or be obtained utilizing additional regularizations on the estimates. Using a more accurate model of the TOF acquisition, improvements are observed in standard activity reconstructions as well as joint reconstructions of activity and attenuation.

PET/MRI attenuation estimation in the lung: A review of past, present, and potential techniques

Positron emission tomography/magnetic resonance imaging (PET/MRI) potentially offers several advantages over positron emission tomography/computed tomography (PET/CT), for example, no CT radiation dose and soft tissue images from MR acquired at the same time as the PET. However, obtaining accurate linear attenuation correction (LAC) factors for the lung remains difficult in PET/MRI. LACs depend on electron density and in the lung, these vary significantly both within an individual and from person to person. Current commercial practice is to use a single‐valued population‐based lung LAC, and better estimation is needed to improve quantification. Given the under‐appreciation of lung attenuation estimation as an issue, the inaccuracy of PET quantification due to the use of single‐valued lung LACs, the unique challenges of lung estimation, and the emerging status of PET/MRI scanners in lung disease, a review is timely. This paper highlights past and present methods, categorizing them into segmentation, atlas/mapping, and emission‐based schemes. Potential strategies for future developments are also presented.

A Quantitative Evaluation of Joint Activity and Attenuation Reconstruction in TOF PET/MR Brain Imaging

Time-of-flight (TOF) PET data provide an effective means for attenuation correction (AC) when no (or incomplete or inaccurate) attenuation information is available. Since MR scanners provide little information on photon attenuation of different tissue types, AC in hybrid PET/MR scanners has always been challenging. In this contribution, we aim at validating the activity reconstructions of the maximum-likelihood ordered-subsets activity and attenuation (OSAA) reconstruction algorithm on a patient brain data set. We present a quantitative comparison of joint reconstructions with the current clinical gold standard-ordered-subsets expectation maximization-using CT-based AC in PET/CT, as well as the current state of the art in PET/MR, that is, zero time echo (ZTE)-based AC. Methods: The TOF PET emission data were initially used in a preprocessing stage to estimate crystal maps of efficiencies, timing offsets, and timing resolutions. Applying these additional corrections during reconstructions, OSAA, ZTE-based, and the vendor-provided atlas-based AC techniques were analyzed and compared with CT-based AC. In our initial study, we used the CT-based estimate of the expected scatter and later used the ZTE-based and OSAA attenuation estimates to compute the expected scatter contribution of the data during reconstructions. In all reconstructions, a maximum-likelihood scaling of the single-scatter simulation estimate to the emission data was used for scatter correction. The reconstruction results were analyzed in the 86 segmented regions of interest of the Hammers atlas. Results: Our quantitative analysis showed that, in practice, a tracer activity difference of +0.5% (±2.1%) and +0.1% (±2.3%) could be expected for the state-of-the-art ZTE-based and OSAA AC methods, respectively, in PET/MR compared with the clinical gold standard in PET/CT. Conclusion: Joint activity and attenuation estimation methods can provide an effective solution to the challenging AC problem for brain studies in hybrid TOF PET/MR scanners. With an accurate TOF-based (timing offsets and timing resolutions) calibration, and similar to the results of the state-of-the-art method in PET/MR, regional errors of joint TOF PET reconstructions are within a few percentage points.

Time efficient scatter correction for time-of-flight PET: the immediate scatter approximation

Utilization of time-of-flight (TOF) information allows us to improve image quality and convergence rate in iterative PET image reconstruction. In order to obtain quantitatively correct images accurate scatter correction (SC) is required that accounts for the non-uniform distribution of scatter events over the TOF bins. However, existing simplified TOF-SC algorithms frequently exhibit limited accuracy while the currently accepted reference method-the TOF extension of the single scatter simulation approach (TOF-SSS)-is computationally demanding and can substantially slow down the reconstruction. In this paper we propose and evaluate a new accelerated TOF-SC algorithm in order to improve this situation. The key idea of the algorithm is the use of an immediate scatter approximation (ISA) for scatter time distribution calculation which speeds up estimation of the required TOF scatter by a factor of up to five in comparison to TOF-SSS. The proposed approach was evaluated in dedicated phantom measurements providing challenging high activity contrast conditions as well as in representative clinical patient data sets. Our results show that ISA is a viable alternative to TOF-SSS. The reconstructed images are in excellent quantitative agreement with those obtained with TOF-SSS while overall reconstruction time can be reduced by a factor of two in whole-body studies, even when using a listmode reconstruction not optimized for speed.

Generation of PET Attenuation Map for Whole-Body Time-of-Flight 18F-FDG PET/MRI Using a Deep Neural Network Trained with Simultaneously Reconstructed Activity and Attenuation Maps

We propose a new deep learning-based approach to provide more accurate whole-body PET/MRI attenuation correction than is possible with the Dixon-based 4-segment method. We use activity and attenuation maps estimated using the maximum-likelihood reconstruction of activity and attenuation (MLAA) algorithm as inputs to a convolutional neural network (CNN) to learn a CT-derived attenuation map. Methods: The whole-body ¹⁸F-FDG PET/CT scan data of 100 cancer patients (38 men and 62 women; age, 57.3 ± 14.1 y) were retrospectively used for training and testing the CNN. A modified U-net was trained to predict a CT-derived μ-map (μ-CT) from the MLAA-generated activity distribution (λ-MLAA) and μ-map (μ-MLAA). We used 1.3 million patches derived from 60 patients' data for training the CNN, data of 20 others were used as a validation set to prevent overfitting, and the data of the other 20 were used as a test set for the CNN performance analysis. The attenuation maps generated using the proposed method (μ-CNN), μ-MLAA, and 4-segment method (μ-segment) were compared with the μ-CT, a ground truth. We also compared the voxelwise correlation between the activity images reconstructed using ordered-subset expectation maximization with the μ-maps, and the SUVs of primary and metastatic bone lesions obtained by drawing regions of interest on the activity images. Results: The CNN generates less noisy attenuation maps and achieves better bone identification than MLAA. The average Dice similarity coefficient for bone regions between μ-CNN and μ-CT was 0.77, which was significantly higher than that between μ-MLAA and μ-CT (0.36). Also, the CNN result showed the best pixel-by-pixel correlation with the CT-based results and remarkably reduced differences in activity maps in comparison to CT-based attenuation correction. Conclusion: The proposed deep neural network produced a more reliable attenuation map for 511-keV photons than the 4-segment method currently used in whole-body PET/MRI studies.