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.

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.