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Objective. Respiratory motion correction is beneficial in positron emission tomography (PET), as it can reduce artefacts caused by motion and improve quantitative accuracy. Methods of motion correction are commonly based on a respiratory trace obtained through an external device (like the real time position management system) or a data driven method, such as those based on dimensionality reduction techniques (for instance principal component analysis (PCA)). PCA itself being a linear transformation to the axis of greatest variation. Data driven methods have the advantage of being non-invasive, and can be performed post-acquisition. However, their main downside being that they are adversely affected by the tracer kinetics of the dynamic PET acquisition. Therefore, they are mostly limited to static PET acquisitions. This work seeks to extend on existing PCA-based data-driven motion correction methods, to allow for their applicability to dynamic PET imaging. Approach. The methods explored in this work include; a moving window approach (similar to the Kinetic Respiratory Gating method from Schleyer et al (2014)), extrapolation of the principal component from later time points to earlier time points, and a method to score, select, and combine multiple respiratory components. The resulting respiratory traces were evaluated on 22 data sets from a dynamic [ 18 F]-FDG study on patients with idiopathic pulmonary fibrosis. This was achieved by calculating their correlation with a surrogate signal acquired using a real time position management system. Main results. The results indicate that all methods produce better surrogate signals than when applying conventional PCA to dynamic data (for instance, a higher correlation with a gold standard respiratory trace). Extrapolating a late time point principal component produced more promising results than using a moving window. Scoring, selecting, and combining components held benefits over all other methods. Significance. This work allows for the extraction of a surrogate signal from dynamic PET data earlier in the acquisition and with a greater accuracy than previous work. This potentially allows for numerous other methods (for instance, respiratory motion correction) to be applied to this data (when they otherwise could not be previously used)., (Creative Commons Attribution license.)

The assessment of the quality of synthesised/pseudo Computed Tomography (pCT) images is commonly measured by an intensity-wise similarity between the ground truth CT and the pCT. However, when using the pCT as an attenuation map (μ-map) for PET reconstruction in Positron Emission Tomography Magnetic Resonance Imaging (PET/MRI) minimising the error between pCT and CT neglects the main objective of predicting a pCT that when used as μ-map reconstructs a pseudo PET (pPET) which is as similar as possible to the gold standard CT-derived PET reconstruction. This observation motivated us to propose a novel multi-hypothesis deep learning framework explicitly aimed at PET reconstruction application. A convolutional neural network (CNN) synthesises pCTs by minimising a combination of the pixel-wise error between pCT and CT and a novel metric-loss that itself is defined by a CNN and aims to minimise consequent PET residuals. Training is performed on a database of twenty 3D MR/CT/PET brain image pairs. Quantitative results on a fully independent dataset of twenty-three 3D MR/CT/PET image pairs show that the network is able to synthesise more accurate pCTs. The Mean Absolute Error on the pCT (110.98 HU ± 19.22 HU) compared to a baseline CNN (172.12 HU ± 19.61 HU) and a multi-atlas propagation approach (153.40 HU ± 18.68 HU), and subsequently lead to a significant improvement in the PET reconstruction error (4.74% ± 1.52% compared to baseline 13.72% ± 2.48% and multi-atlas propagation 6.68% ± 2.06%)., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 The Author(s). Published by Elsevier B.V. All rights reserved.)

This special issue focuses on synergistic tomographic image reconstruction in a range of contributions in multiple disciplines and various application areas. The topic of image reconstruction covers substantial inverse problems (Mathematics) which are tackled with various methods including statistical approaches (e.g. Bayesian methods, Monte Carlo) and computational approaches (e.g. machine learning, computational modelling, simulations). The issue is separated in two volumes. This volume focuses mainly on algorithms and methods. Some of the articles will demonstrate their utility on real-world challenges, either medical applications (e.g. cardiovascular diseases, proton therapy planning) or applications in material sciences (e.g. material decomposition and characterization). One of the desired outcomes of the special issue is to bring together different scientific communities which do not usually interact as they do not share the same platforms (such as journals and conferences). This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Accurate regional brain quantitative PET measurements, particularly when using partial volume correction, rely on robust image registration between PET and MR images. We argue here that the precision, and hence the uncertainty, of MR-PET image registration is mainly driven by the registration implementation and the quality of PET images due to their lower resolution and higher noise compared to the structural MR images. We propose a dedicated uncertainty analysis for quantifying the precision of MR-PET registration, centred around the bootstrap resampling of PET list-mode events to generate multiple PET image realisations with different noise (count) levels. The effects of PET image reconstruction parameters, such as the use of attenuation and scatter corrections and different number of iterations, on the precision and accuracy of MR-PET registration were investigated. In addition, the performance of four software packages with their default settings for rigid inter-modality image registration were considered: NiftyReg, Vinci, FSL and SPM. Four distinct PET image distributions made of two early time frames (similar to cortical FDG) and two late frames using two amyloid PET dynamic acquisitions of one amyloid positive and one amyloid negative participants were investigated. For the investigated four PET frames, the biggest impact on the uncertainty was observed between registration software packages (up to 10-fold difference in precision) followed by the reconstruction parameters. On average, the lowest uncertainty for different PET frames and brain regions was observed with SPM and two iterations of fully quantitative image reconstruction. The observed uncertainty for the varying PET count-level (from 5% to 60%) was slightly lower than for the reconstruction parameters. We also observed that the registration uncertainty in quantitative PET analysis depends on amyloid status of the considered PET frames, with increased uncertainty (up to three times) when using post-reconstruction partial volume correction. This analysis is applicable for PET data obtained from either PET/MR or PET/CT scanners., (Copyright © 2021 The Author(s). Published by Elsevier Inc. All rights reserved.)

This paper presents a simulation framework for dynamic PET-MR. The main focus of this framework is to provide motion-resolved MR and PET data and ground truth motion information. This can be used in the optimisation and quantitative evaluation of image registration and in assessing the error propagation due to inaccuracies in motion estimation in complex motion-compensated reconstruction algorithms. Contrast and tracer kinetics can also be simulated and are available as ground truth information. To closely emulate medical examination, input and output of the simulation are files in standardised open-source raw data formats. This enables the use of existing raw data as a template input and ensures seamless integration of the output into existing reconstruction pipelines. The proposed framework was validated in PET-MR and image registration applications. It was used to simulate a FDG-PET-MR scan with cardiac and respiratory motion. Ground truth motion information could be utilised to optimise parameters for PET and synergistic PET-MR image registration. In addition, a free-breathing dynamic contrast enhancement (DCE) abdominal scan of a patient with hepatic lesions was simulated. In order to correct for breathing motion, a motion-corrected image reconstruction scheme was used and a Toft's model was fit to the DCE data to obtain quantitative DCE-MRI parameters. Utilising the ground truth motion information, the dependency of quantitative DCE-MR images on the accuracy of the motion estimation was evaluated. We demonstrated that respiratory motion had to be available with an average accuracy of at least the spatial resolution of the DCE-MR images in order to ensure an improvement in lesions visualisation and quantification compared to no motion correction. The proposed framework provides a valuable tool with a wide range of scientific PET and MR applications and will be available as part of the open-source project Synergistic Image Reconstruction Framework (SIRF).

While the pursuit of better time resolution in positron emission tomography (PET) is rapidly evolving, little work has been performed on time of flight (TOF) image quality at high time resolution in the presence of modelling inconsistencies. This works focuses on the effect of using the wrong attenuation map in the system model, causing perturbations in the reconstructed radioactivity image. Previous work has usually considered the effects to be local to the area where there is attenuation mismatch, and has shown that the quantification errors in this area tend to reduce with improved time resolution. This publication shows however that errors in the PET image at a distance from the mismatch increase with time resolution. The errors depend on the reconstruction algorithm used. We quantify the errors in the hypothetical case of perfect time resolution for maximum likelihood reconstructions. In addition, we perform reconstructions on simulated and patient data. In particular, for respiratory-gated reconstructions from a wrong attenuation map, increased errors are observed with improved time resolutions in areas close to the lungs (e.g. from 13.3% in non-TOF to up to 20.9% at 200 ps in the left ventricle).

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., (© 2019 The Authors. Medical Physics published by Wiley Periodicals, Inc. on behalf of American Association of Physicists in Medicine.)

Standard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified log-likelihood, and therefore break the data statistics. In this paper, we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer, which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors-which are characterized by cold regions surrounded by hot structures-while reconstructing similar activity values in hot regions.

In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.

The impact of positron range on PET image reconstruction has often been investigated as a blurring effect that can be partly corrected by adding an element to the PET system matrix in the reconstruction, usually based on a Gaussian kernel constructed from the attenuation values. However, the physics involved in PET is more complex. In regions where density does not vary, positron range indeed involves mainly blurring. However, in more heterogeneous media it can cause other effects. This work focuses on positron range in the lungs and its impact on quantification, especially in the case of pathologies such as cancer or pulmonary fibrosis, for which the lungs have localised varying density. Using Monte Carlo simulations, we evaluate the effects of positron range for multiple radionuclides ( 18 F, 15 O, 68 Ga, 89 Zr, 82 Rb, 64 Cu and 124 I) as, for novel radiotracers, the choice of the labelling radionuclide is important. The results demonstrate quantification biases in highly heterogeneous media, where the measured uptake of high-density regions can be increased by the neighbouring radioactivity from regions of lower density, with the effect more noticeable for radionuclides with high-energy positron emission. When the low-density regions are considered to have less radioactive uptake (e.g. due to the presence of air), the effect is less severe.

Respiratory motion is a major cause of degradation of PET image quality. Respiratory gating and motion correction can be performed to reduce the effects of respiratory motion; these methods require motion information, typically obtained from external tracking systems. Various groups have studied data-driven (DD) motion estimation methods. Recently, a DD respiratory motion estimation method was established by calculating the centroid of distribution (COD) of listmode events, which was then used with event-by-event respiratory motion correction (EBE-MC) and showed results comparable to those with an external motion tracking device. The EBE-MC method only corrected for rigid motion, so that non-rigid components still contributed to motion-induced blurring. A non-rigid respiratory motion correction (NRMC) was later developed to overcome this problem, but was only evaluated using signals from an external monitor. Thus, it is desirable to further develop DD motion estimation to achieve the best respiratory motion correction results. We evaluated two DD respiratory motion detection methods, COD and principal component analysis (PCA), by comparing the extracted motion trace to that acquired by the Anzai system in dynamic studies with two tracers. PCA was chosen as a preliminary study indicated that it produced stable results than other DD methods. We then developed and performed DD-EBE-NRMC using either COD- or PCA-derived respiratory motion information. DD correction results were compared with Anzai-based results. For all tested studies, both COD and PCA showed a good-to-excellent match with Anzai signals, with PCA showing a higher correlation with Anzai signals. The DD-EBE-NRMC results showed that both COD and PCA provide comparable image quality improvement to the Anzai-based correction. Although COD showed a lower correlation with Anzai than PCA, COD-based NRMC results are comparable to those of PCA, both of which showed great reduction in motion-induced blurring.

In this paper, we describe the implementation of support for time-of-flight (TOF) positron emission tomography (PET) for both listmode and sinogram data in the open source software for tomographic image reconstruction (STIR). We provide validation and performance characterization using simulated data from the open source GATE Monte Carlo toolbox, with TOF configurations spanning from 81.2 to 209.6 ps. The coincidence detector resolution was corrected for the timing resolution deterioration due to the contribution of the crystal length. Comparison between the reconstruction of listmode and sinogram data demonstrated good agreement in both TOF and non-TOF cases in terms of relative absolute error. To reduce the reconstruction time, we assessed the truncation of the TOF kernel along lines-of-response (LOR). Rejection of LOR elements beyond four times the TOF standard deviation provides significant acceleration of [Formula: see text] [Formula: see text] without compromising the image quality. Further narrowing of the kernel can provide extra time reduction but with the gradual introduction of error in the reconstructed images. As expected, TOF reconstruction performs better than non-TOF in terms of both contrast-recovery-coefficient (CRC) and signal-to-noise ratio (SNR). CRC achieves convergence faster with TOF, at lower noise levels. SNR with TOF was superior for early iterations, but with quick deterioration. Higher timing resolution further improved reconstruction performance, while TOF bin mashing was shown to have only a small impact on reconstructed images.

In PET imaging, patient motion due to respiration can lead to artifacts and blurring, in addition to quantification errors. The integration of PET imaging with MRI in PET/MRI scanners provides spatially aligned complementary clinical information and allows the use of high-contrast, high-spatial-resolution MR images to monitor and correct motion-corrupted PET data. On a patient cohort, we tested the ability of our joint PET/MRI-based predictive motion model to correct respiratory motion in PET and show it can improve lesion detectability and quantitation and reduce image artifacts. Methods: Using multiple tracers and multiple organ locations, we applied our motion correction method to 42 clinical PET/MRI patient datasets containing 162 PET-avid lesions. Quantitative changes were calculated using SUV changes in avid lesions. Lesion detectability changes were explored with a study in which 2 radiologists identified lesions in uncorrected and motion-corrected images and provided confidence scores. Results: Mean increases of 12.4% for SUV peak and 17.6% for SUV max after motion correction were found. In the detectability study, confidence scores for detecting avid lesions increased, with a rise in mean score from 2.67 to 3.01 (of 4) after motion correction and a rise in detection rate from 74% to 84%. Of 162 confirmed lesions, 49 showed an increase in all 3 metrics-SUV peak , SUV max , and combined reader confidence score-whereas only 2 lesions showed a decrease. We also present clinical case studies demonstrating the effect that respiratory motion correction of PET data can have on patient management, with increased numbers of detected lesions, improved lesion sharpness and localization, and reduced attenuation-based artifacts. Conclusion: We demonstrated significant improvements in quantification and detection of PET-avid lesions, with specific case study examples showing where motion correction has the potential to affect diagnosis or patient care., (© 2018 by the Society of Nuclear Medicine and Molecular Imaging.)

This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18 F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

PET/CT quantification of lung tissue is limited by several difficulties: the lung density and local volume changes during respiration, the anatomical mismatch between PET and CT and the relative contributions of tissue, air and blood to the PET signal (the tissue fraction effect). Air fraction correction (AFC) has been shown to improve PET image quantification in the lungs. Methods to correct for the movement and anatomical mismatch involve respiratory gating and image registration techniques. While conventional registration methods only account for spatial mismatch, the Jacobian determinant of the deformable registration transformation field can be used to estimate local volume changes and could therefore potentially be used to correct (i.e. Jacobian Correction, JC) the PET signal for changes in concentration due to local volume changes. This work aims to investigate the relationship between variations in the lung due to respiration, specifically density, tracer concentration and local volume changes. In particular, we study the effect of AFC and JC on PET quantitation after registration of respiratory gated PET/CT patient data. Six patients suffering from lung cancer with solitary pulmonary nodules underwent [Formula: see text]F-FDG PET/cine-CT. The PET data were gated into six respiratory gates using displacement gating based on a real-time position management (RPM) signal and reconstructed with matched gated CT. The PET tracer concentration and tissue density were extracted from registered gated PET and CT images before and after corrections (AFC or JC) and compared to the values from the reference images. Before correction, we observed a linear correlation between the PET tracer concentration values and density. Across all gates and patients, the maximum relative change in PET tracer concentration before (after) AFC was found to be 16.2% (4.1%) and the maximum relative change in tissue density and PET tracer concentration before (after) JC was found to be 17.1% (5.5%) and 16.2% (6.8%) respectively. Overall our results show that both AFC or JC largely explain the observed changes in PET tracer activity over the respiratory cycle. We also speculate that a second order effect is related to change in fluid content but this needs further investigation. Consequently, either AFC or JC is recommended when combining lung PET images from different gates to reduce noise.

Positron emission tomography (PET) images are degraded by a phenomenon known as the partial volume effect (PVE). Approaches have been developed to reduce PVEs, typically through the utilisation of structural information provided by other imaging modalities such as MRI or CT. These methods, known as partial volume correction (PVC) techniques, reduce PVEs by compensating for the effects of the scanner resolution, thereby improving the quantitative accuracy. The PETPVC toolbox described in this paper comprises a suite of methods, both classic and more recent approaches, for the purposes of applying PVC to PET data. Eight core PVC techniques are available. These core methods can be combined to create a total of 22 different PVC techniques. Simulated brain PET data are used to demonstrate the utility of toolbox in idealised conditions, the effects of applying PVC with mismatched point-spread function (PSF) estimates and the potential of novel hybrid PVC methods to improve the quantification of lesions. All anatomy-based PVC techniques achieve complete recovery of the PET signal in cortical grey matter (GM) when performed in idealised conditions. Applying deconvolution-based approaches results in incomplete recovery due to premature termination of the iterative process. PVC techniques are sensitive to PSF mismatch, causing a bias of up to 16.7% in GM recovery when over-estimating the PSF by 3 mm. The recovery of both GM and a simulated lesion was improved by combining two PVC techniques together. The PETPVC toolbox has been written in C++, supports Windows, Mac and Linux operating systems, is open-source and publicly available.

Patient motion due to respiration can lead to artefacts and blurring in positron emission tomography (PET) images, in addition to quantification errors. The integration of PET with magnetic resonance (MR) imaging in PET-MR scanners provides complementary clinical information, and allows the use of high spatial resolution and high contrast MR images to monitor and correct motion-corrupted PET data. In this paper we build on previous work to form a methodology for respiratory motion correction of PET data, and show it can improve PET image quality whilst having minimal impact on clinical PET-MR protocols. We introduce a joint PET-MR motion model, using only 1 min per PET bed position of simultaneously acquired PET and MR data to provide a respiratory motion correspondence model that captures inter-cycle and intra-cycle breathing variations. In the model setup, 2D multi-slice MR provides the dynamic imaging component, and PET data, via low spatial resolution framing and principal component analysis, provides the model surrogate. We evaluate different motion models (1D and 2D linear, and 1D and 2D polynomial) by computing model-fit and model-prediction errors on dynamic MR images on a data set of 45 patients. Finally we apply the motion model methodology to 5 clinical PET-MR oncology patient datasets. Qualitative PET reconstruction improvements and artefact reduction are assessed with visual analysis, and quantitative improvements are calculated using standardised uptake value (SUV(peak) and SUV(max)) changes in avid lesions. We demonstrate the capability of a joint PET-MR motion model to predict respiratory motion by showing significantly improved image quality of PET data acquired before the motion model data. The method can be used to incorporate motion into the reconstruction of any length of PET acquisition, with only 1 min of extra scan time, and with no external hardware required.

In this technical note we propose a rapid and scalable software solution for the processing of PET list-mode data, which allows the efficient integration of list mode data processing into the workflow of image reconstruction and analysis. All processing is performed on the graphics processing unit (GPU), making use of streamed and concurrent kernel execution together with data transfers between disk and CPU memory as well as CPU and GPU memory. This approach leads to fast generation of multiple bootstrap realisations, and when combined with fast image reconstruction and analysis, it enables assessment of uncertainties of any image statistic and of any component of the image generation process (e.g. random correction, image processing) within reasonable time frames (e.g. within five minutes per realisation). This is of particular value when handling complex chains of image generation and processing. The software outputs the following: (1) estimate of expected random event data for noise reduction; (2) dynamic prompt and random sinograms of span-1 and span-11 and (3) variance estimates based on multiple bootstrap realisations of (1) and (2) assuming reasonable count levels for acceptable accuracy. In addition, the software produces statistics and visualisations for immediate quality control and crude motion detection, such as: (1) count rate curves; (2) centre of mass plots of the radiodistribution for motion detection; (3) video of dynamic projection views for fast visual list-mode skimming and inspection; (4) full normalisation factor sinograms. To demonstrate the software, we present an example of the above processing for fast uncertainty estimation of regional SUVR (standard uptake value ratio) calculation for a single PET scan of (18)F-florbetapir using the Siemens Biograph mMR scanner.

This work is an extension of our recent work on joint activity reconstruction/motion estimation (JRM) from positron emission tomography (PET) data. We performed JRM by maximization of the penalized log-likelihood in which the probabilistic model assumes that the same motion field affects both the activity distribution and the attenuation map. Our previous results showed that JRM can successfully reconstruct the activity distribution when the attenuation map is misaligned with the PET data, but converges slowly due to the significant cross-talk in the likelihood. In this paper, we utilize time-of-flight PET for JRM and demonstrate that the convergence speed is significantly improved compared to JRM with conventional PET data.

This work provides an insight into positron emission tomography (PET) joint image reconstruction/motion estimation (JRM) by maximization of the likelihood, where the probabilistic model accounts for warped attenuation. Our analysis shows that maximum-likelihood (ML) JRM returns the same reconstructed gates for any attenuation map (μ-map) that is a deformation of a given μ-map, regardless of its alignment with the PET gates. We derived a joint optimization algorithm accordingly, and applied it to simulated and patient gated PET data. We first evaluated the proposed algorithm on simulations of respiratory gated PET/CT data based on the XCAT phantom. Our results show that independently of which μ-map is used as input to JRM: (i) the warped μ-maps correspond to the gated μ-maps, (ii) JRM outperforms the traditional post-registration reconstruction and consolidation (PRRC) for hot lesion quantification and (iii) reconstructed gated PET images are similar to those obtained with gated μ-maps. This suggests that a breath-held μ-map can be used. We then applied JRM on patient data with a μ-map derived from a breath-held high resolution CT (HRCT), and compared the results with PRRC, where each reconstructed PET image was obtained with a corresponding cine-CT gated μ-map. Results show that JRM with breath-held HRCT achieves similar reconstruction to that using PRRC with cine-CT. This suggests a practical low-dose solution for implementation of motion-corrected respiratory gated PET/CT.

Recently, there has been an increased interest in imaging different pulmonary disorders using PET techniques. Previous work has shown, for static PET/CT, that air content in the lung influences reconstructed image values and that it is vital to correct for this 'tissue fraction effect' (TFE). In this paper, we extend this work to include the blood component and also investigate the TFE in dynamic imaging. CT imaging and PET kinetic modelling are used to determine fractional air and blood voxel volumes in six patients with idiopathic pulmonary fibrosis. These values are used to illustrate best and worst case scenarios when interpreting images without correcting for the TFE. In addition, the fractional volumes were used to determine correction factors for the SUV and the kinetic parameters. These were then applied to the patient images. The kinetic parameters K1 and Ki along with the static parameter SUV were all found to be affected by the TFE with both air and blood providing a significant contribution to the errors. Without corrections, errors range from 34-80% in the best case and 29-96% in the worst case. In the patient data, without correcting for the TFE, regions of high density (fibrosis) appeared to have a higher uptake than lower density (normal appearing tissue), however this was reversed after air and blood correction. The proposed correction methods are vital for quantitative and relative accuracy. Without these corrections, images may be misinterpreted.

Positron Emission Tomography/Magnetic Resonance Imaging (PET/MR) scanners are expected to offer a new range of clinical applications. Attenuation correction is an essential requirement for quantification of PET data but MRI images do not directly provide a patient-specific attenuation map. Methods We further validate and extend a Computed Tomography (CT) and attenuation map (μ-map) synthesis method based on pre-acquired MRI-CT image pairs. The validation consists of comparing the CT images synthesised with the proposed method to the original CT images. PET images were acquired using two different tracers ((18)F-FDG and (18)F-florbetapir). They were then reconstructed and corrected for attenuation using the synthetic μ-maps and compared to the reference PET images corrected with the CT-based μ-maps. During the validation, we observed that the CT synthesis was inaccurate in areas such as the neck and the cerebellum, and propose a refinement to mitigate these problems, as well as an extension of the method to multi-contrast MRI data. Results With the improvements proposed, a significant enhancement in CT synthesis, which results in a reduced absolute error and a decrease in the bias when reconstructing PET images, was observed. For both tracers, on average, the absolute difference between the reference PET images and the PET images corrected with the proposed method was less than 2%, with a bias inferior to 1%. Conclusion With the proposed method, attenuation information can be accurately derived from MRI images by synthesising CT using routine anatomical sequences. MRI sequences, or combination of sequences, can be used to synthesise CT images, as long as they provide sufficient anatomical information.

Unlabelled: Respiratory motion during PET acquisition may lead to blurring in resulting images and underestimation of uptake parameters. The advent of integrated PET/MR scanners allows us to exploit the integration of modalities, using high spatial resolution and high-contrast MR images to monitor and correct PET images degraded by motion. We proposed a practical, anatomy-independent MR-based correction strategy for PET data affected by respiratory motion and showed that it can improve image quality both for PET acquired simultaneously to the motion-capturing MR and for PET acquired up to 1 h earlier during a clinical scan., Methods: To estimate the respiratory motion, our method needs only an extra 1-min dynamic MR scan, acquired at the end of the clinical PET/MR protocol. A respiratory signal was extracted directly from the PET list-mode data. This signal was used to gate the PET data and to construct a motion model built from the dynamic MR data. The estimated motion was then incorporated into the PET image reconstruction to obtain a single motion-corrected PET image. We evaluated our method in 2 steps. The PET-derived respiratory signal was compared with an MR measure of diaphragmatic displacement via a pencil-beam navigator. The motion-corrected images were compared with uncorrected images with visual inspection, line profiles, and standardized uptake value (SUV) in focally avid lesions., Results: We showed a strong correlation between the PET-derived and MR-derived respiratory signals for 9 patients, with a mean correlation of 0.89. We then showed 4 clinical case study examples ((18)F-FDG and (68)Ga-DOTATATE) using the motion-correction technique, demonstrating improvements in image sharpness and reduction of respiratory artifacts in scans containing pancreatic, liver, and lung lesions as well as cardiac scans. The mean increase in peak SUV (SUV(peak)) and maximum SUV (SUV(max)) in a patient with 4 pancreatic lesions was 23.1% and 34.5% in PET acquired simultaneously with motion-capturing MR, and 17.6% and 24.7% in PET acquired 50 min before as part of the clinical scan., Conclusion: We showed that a respiratory signal can be obtained from raw PET data and that the clinical PET image quality can be improved using only a short additional PET/MR acquisition. Our method does not need external respiratory hardware or modification of the normal clinical MR sequences., (© 2015 by the Society of Nuclear Medicine and Molecular Imaging, Inc.)

Monte Carlo (MC) simulation provides a flexible and robust framework to efficiently evaluate and optimize image processing methods in emission tomography. In this work we present Brain-VISET (Voxel-based Iterative Simulation for Emission Tomography), a method that aims to simulate realistic [ (99m) Tc]-SPECT and [ (18) F]-PET brain databases by including anatomical and functional information. To this end, activity and attenuation maps generated using high-resolution anatomical images from patients were used as input maps in a MC projector to simulate SPECT or PET sinograms. The reconstructed images were compared with the corresponding real SPECT or PET studies in an iterative process where the activity inputs maps were being modified at each iteration. Datasets of 30 refractory epileptic patients were used to assess the new method. Each set consisted of structural images (MRI and CT) and functional studies (SPECT and PET), thereby allowing the inclusion of anatomical and functional variability in the simulation input models. SPECT and PET sinograms were obtained using the SimSET package and were reconstructed with the same protocols as those employed for the clinical studies. The convergence of Brain-VISET was evaluated by studying the behavior throughout iterations of the correlation coefficient, the quotient image histogram and a ROI analysis comparing simulated with real studies. The realism of generated maps was also evaluated. Our findings show that Brain-VISET is able to generate realistic SPECT and PET studies and that four iterations is a suitable number of iterations to guarantee a good agreement between simulated and real studies.

Following continuous improvement in PET spatial resolution, respiratory motion correction has become an important task. Two of the most common approaches that utilize all detected PET events to motion-correct PET data are the reconstruct-transform-average method (RTA) and motion-compensated image reconstruction (MCIR). In RTA, separate images are reconstructed for each respiratory frame, subsequently transformed to one reference frame and finally averaged to produce a motion-corrected image. In MCIR, the projection data from all frames are reconstructed by including motion information in the system matrix so that a motion-corrected image is reconstructed directly. Previous theoretical analyses have explained why MCIR is expected to outperform RTA. It has been suggested that MCIR creates less noise than RTA because the images for each separate respiratory frame will be severely affected by noise. However, recent investigations have shown that in the unregularized case RTA images can have fewer noise artefacts, while MCIR images are more quantitatively accurate but have the common salt-and-pepper noise. In this paper, we perform a realistic numerical 4D simulation study to compare the advantages gained by including regularization within reconstruction for RTA and MCIR, in particular using the median-root-prior incorporated in the ordered subsets maximum a posteriori one-step-late algorithm. In this investigation we have demonstrated that MCIR with proper regularization parameters reconstructs lesions with less bias and root mean square error and similar CNR and standard deviation to regularized RTA. This finding is reproducible for a variety of noise levels (25, 50, 100 million counts), lesion sizes (8 mm, 14 mm diameter) and iterations. Nevertheless, regularized RTA can also be a practical solution for motion compensation as a proper level of regularization reduces both bias and mean square error.

We present a new version of STIR (Software for Tomographic Image Reconstruction), an open source object-oriented library implemented in C++ for 3D positron emission tomography reconstruction. This library has been designed such that it can be used for many algorithms and scanner geometries, while being portable to various computing platforms. This second release enhances its flexibility and modular design and includes additional features such as Compton scatter simulation, an additional iterative reconstruction algorithm and parametric image reconstruction (both indirect and direct). We discuss the new features in this release and present example results. STIR can be downloaded from http://stir.sourceforge.net.

Dynamic emission tomography measures the amount of the injected radiotracer through multiple consecutive time frames. The temporal information is used to estimate the pharmacokinetic properties of the radio-labeled molecules. One complicating factor is that the scanner measures the signal that is generated not only from the molecules in the tissues of interest, but also from those in the blood. This is usually corrected for by subtraction of the blood term from the radioactivity image before tracer kinetic modeling. However, some methods estimate the pharmacokinetic parameters directly from the measured data (e.g. sinograms) and in such cases the subtraction procedure for correcting the data cannot be applied. In other advanced direct reconstruction approaches, the blood radioactivity curve is included in the model. However, there may be models for tracers, which are not feasible as the blood volume component can be undistinguishable. In this study, we address these issues and show that these can be solved by viewing the blood radioactivity as a 'physiological' background term similar to the physical background (e.g. scatter and random counts). The proposed technique can be applied to any radiotracers in emission tomography, independent of the kinetic model.

A fully three-dimensional (3D) one-step late (OSL), maximum a posteriori (MAP) reconstruction algorithm based on the median root prior (MRP) was implemented and evaluated for the reconstruction of 3D positron emission tomography (PET) studies. The algorithm uses the ordered subsets (OS) scheme for convergence acceleration and data update during iterations. The algorithm was implemented using the software package developed within the EU project PARAPET (www.brunel.ac.uk/~masrppet). The MRP algorithm was evaluated using experimental phantom and real 3D PET brain studies. Various experimental set-ups in terms of activity distribution and counting statistics were considered. The performance of the algorithm was assessed by calculating figures of merit such as: contrast, coefficient of variation, activity ratio between two regions and full width at half of maximum for resolution measurements. The performance of MRP was compared with that of 3D ordered subsets-expectation maximisation (OSEM) and 3D re-projection (3DRP) algorithms. In all the experimental situations considered, MRP showed: (1) convergence to a stable solution, (2) effectiveness in noise reduction, particularly for low statistics data, (3) good preservation of spatial details. Compared with the OSEM and 3DRP algorithms, MRP provides comparable or better results depending on the parameters used for the reconstruction of the images.

We present an enhancement of the OSEM (ordered set expectation maximization) algorithm for 3D PET reconstruction, which we call the inter-update Metz filtered OSEM (IMF-OSEM). The IMF-OSEM algorithm incorporates filtering action into the image updating process in order to improve the quality of the reconstruction. With this technique, the multiplicative correction image--ordinarily used to update image estimates in plain OSEM--is applied to a Metz-filtered version of the image estimate at certain intervals. In addition, we present a software implementation that employs several high-speed features to accelerate reconstruction. These features include, firstly, forward and back projection functions which make full use of symmetry as well as a fast incremental computation technique. Secondly, the software has the capability of running in parallel mode on several processors. The parallelization approach employed yields a significant speed-up, which is nearly independent of the amount of data. Together, these features lead to reasonable reconstruction times even when using large image arrays and non-axially compressed projection data. The performance of IMF-OSEM was tested on phantom data acquired on the GE Advance scanner. Our results demonstrate that an appropriate choice of Metz filter parameters can improve the contrast-noise balance of certain regions of interest relative to both plain and post-filtered OSEM, and to the GE commercial reprojection algorithm software.

Quantitative determination of local radioactivity concentration in positron emission tomography (PET) requires a good attenuation correction procedure to reconstruct the emission image. Using a similar Maximum Likelihood (ML) algorithm as for the reconstruction of the emission image, a method is proposed to reconstruct a transmission image, i.e. a map of absorption coefficients. This reconstructed transmission image is then used to calculate the attenuation correction factors needed for the ML reconstruction of the emission image. This approach takes automatically into account the convolution step in the acquisition process (caused by various smoothing factors, e.g. the detector width). This results in appreciable noise suppression without loss of resolution due to filtering, thus making the reconstructed images easier to interpret. A comparison is made with other estimates for the measured attenuation correction using phantom studies.