A statistical reconstruction algorithm for positronium lifetime imaging using time-of-flight positron emission tomography

TL;DR

This paper introduces a maximum likelihood estimation algorithm based on an exponentially modified Gaussian distribution for reconstructing positronium lifetime images from time-of-flight PET data, improving accuracy in tissue microenvironment analysis.

Contribution

It presents a novel EMG-based MLE method for 2D positronium lifetime imaging that outperforms traditional approaches and can handle multiple positron populations.

Findings

The EMG-MLE method produces quantitatively accurate lifetime images in simulations.

It outperforms traditional exponential likelihood and penalized surrogate methods.

The approach can be extended to datasets with multiple positron populations.

Abstract

Positron emission tomography (PET) is an important modality for diagnosing diseases such as cancer and Alzheimer's disease, capable of revealing the uptake of radiolabeled molecules that target specific pathological markers of the diseases. Recently, positronium lifetime imaging (PLI) that adds to traditional PET the ability to explore properties of the tissue microenvironment beyond tracer uptake has been demonstrated with time-of-flight (TOF) PET and the use of non-pure positron emitters. However, achieving accurate reconstruction of lifetime images from data acquired by systems having a finite TOF resolution still presents a challenge. This paper focuses on the two-dimensional PLI, introducing a maximum likelihood estimation (MLE) method that employs an exponentially modified Gaussian (EMG) probability distribution that describes the positronium lifetime data produced by TOF PET. We evaluate the performance of our EMG-based MLE method against \st{traditional} approaches using exponential likelihood functions and penalized surrogate methods. Results from computer-simulated data reveal that the proposed EMG-MLE method can yield quantitatively accurate lifetime images. We also demonstrate that the proposed MLE formulation can be extended to handle PLI data containing multiple positron populations.