PET image reconstruction using physical and mathematical modelling for time of flight PET-MR scanners in the STIR library.

This work demonstrates how computational and physical modelling of the positron emission tomography (PET) image acquisition process for a state-of-the-art integrated PET and magnetic resonance imaging (PET-MR) system can produce images comparable to the manufacturer. The GE SIGNA PET/MR scanner is manufactured by General Electric and has time-of-flight (TOF) capabilities of about 390 ps. All software development took place in the Software for Tomographic Image Reconstruction (STIR: http://stir.sf.net) library, which is a widely used open source software to reconstruct data as exported from emission tomography scanners. The new software developments will be integrated into STIR, providing the opportunity for researchers worldwide to establish and expand their image reconstruction methods. Furthermore, this work is of particular significance as it provides the first validation of TOF PET image reconstruction for real scanner datasets using the STIR library. This paper presents the methodology, analysis, and critical issues encountered in implementing an independent reconstruction software package. Acquired PET data were processed via several appropriate algorithms which are necessary to produce an accurate and precise quantitative image. This included mathematical, physical and anatomical modelling of the patient and simulation of various aspects of the acquisition. These included modelling of random coincidences using 'singles' rates per crystals, detector efficiencies and geometric effects. Attenuation effects were calculated by using the STIR's attenuation correction model. Modelling all these effects within the system matrix allowed the reconstruction of PET images which demonstrates the metabolic uptake of the administered radiopharmaceutical. These implementations were validated using measured phantom and clinical datasets. The developments are tested using the ordered subset expectation maximisation (OSEM) and the more recently proposed kernelised expectation maximisation (KEM) algorithm which incorporates anatomical information from MR images into PET reconstruction.

Data driven surrogate signal extraction for dynamic PET using selective PCA: time windows versus the combination of components.

Respiratory motion correction is beneficial in 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 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. The methods explored in this work include; a moving window approach (similar to the Kinetic Respiratory Gating method from Schleyer et al.), 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 18FFDG 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. 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. 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).

Use of non-Gaussian time-of-flight kernels for image reconstruction of Monte Carlo simulated data of ultra-fast PET scanners.

INTRODUCTION: Time-of-flight (TOF) positron emission tomography (PET) scanners can provide significant benefits by improving the noise properties of reconstructed images. In order to achieve this, the timing response of the scanner needs to be modelled as part of the reconstruction process. This is currently achieved using Gaussian TOF kernels. However, the timing measurements do not necessarily follow a Gaussian distribution. In ultra-fast timing resolutions, the depth of interaction of the γ-photon and the photon travel spread (PTS) in the crystal volume become increasingly significant factors for the timing performance. The PTS of a single photon can be approximated better by a truncated exponential distribution. Therefore, we computed the corresponding TOF kernel as a modified Laplace distribution for long crystals. The obtained (CTR) kernels could be more appropriate to model the joint probability of the two in-coincidenceγ-photons. In this paper, we investigate the impact of using a CTR kernel vs. Gaussian kernels in TOF reconstruction using Monte Carlo generated data. MATERIALS AND METHODS: The geometry and physics of a PET scanner with two timing configurations, (a) idealised timing resolution, in which only the PTS contributed in the CTR, and (b) with a range of ultra-fast timings, were simulated. In order to assess the role of the crystal thickness, different crystal lengths were considered. The evaluation took place in terms of Kullback-Leibler (K-L) distance between the proposed model and the simulated timing response, contrast recovery (CRC) and spatial resolution. The reconstructions were performed using STIR image reconstruction toolbox. RESULTS: Results for the idealised scanner showed that the CTR kernel was in excellent agreement with the simulated time differences. In terms of K-L distance outperformed the a fitted normal distribution for all tested crystal sizes. In the case of the ultra-fast configurations, a convolution kernel between the CTR and a Gaussian showed the best agreement with the simulated data below 40 ps timing resolution. In terms of CRC, the CTR kernel demonstrated improvements, with values that ranged up to 3.8% better CRC for the thickest crystal. In terms of spatial resolution, evaluated at the 60th iteration, the use of CTR kernel showed a modest improvement of the peek-to-valley ratios up to 1% for the 10-mm crystal, while for larger crystals, a clear trend was not observed. In addition, we showed that edge artefacts can appear in the reconstructed images when the timing kernel used for the reconstruction is not carefully optimised. Further iterations, can help improve the edge artefacts.

Effect of attenuation mismatches in time of flight PET reconstruction.

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).

PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence.

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.

Consensus Recommendations on the Use of 18F-FDG PET/CT in Lung Disease.

PET with 18F-FDG has been increasingly applied, predominantly in the research setting, to study drug effects and pulmonary biology and to monitor disease progression and treatment outcomes in lung diseases that interfere with gas exchange through alterations of the pulmonary parenchyma, airways, or vasculature. To date, however, there are no widely accepted standard acquisition protocols or imaging data analysis methods for pulmonary 18F-FDG PET/CT in these diseases, resulting in disparate approaches. Hence, comparison of data across the literature is challenging. To help harmonize the acquisition and analysis and promote reproducibility, we collated details of acquisition protocols and analysis methods from 7 PET centers. From this information and our discussions, we reached the consensus recommendations given here on patient preparation, choice of dynamic versus static imaging, image reconstruction, and image analysis reporting.

Effect of positron range on PET quantification in diseased and normal lungs.

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 (18F, 15O, 68Ga, 89Zr, 82Rb, 64Cu and 124I) 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.

Implementation and validation of time-of-flight PET image reconstruction module for listmode and sinogram projection data in the STIR library.

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.