Reconstruction of dual isotope PET using expectation maximization (EM) algorithm

Abstract

The dual-isotope (DI) imaging with positron emission tomography (PET) is particularly difficult because positron-electron annihilation always results in 511 keV photons, irrespective of the radioisotope. Therefore, differentiation of PET isotopes based on the energy discrimination is impossible. However, there are radioisotopes that in addition to a positron also emit at least one prompt high energy (HE) gamma (positron-gamma emitters). The detection of this gamma in coincidence with two annihilation photons tags this particular PET event as originating from the decay of the isotope with positron-gamma emissions. An example of such radioisotope is <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</sup> Cu which can be used in our approach for DI studies together with a pure positron emitter <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> F. Two data sets are acquired in DI-PET imaging. The first, standard PET dataset results from detections of two coincident 511 keV photons, and the second dataset - from detection of two 511 keV photons in coincidence with a HE gamma. The challenge is then to reconstruct two separate activities using the information contained in these two datasets. In this work, we developed an Expectation Maximization (EM) algorithm for the estimation of distributions of both isotopes. The EM update equations were derived and evaluated using synthetic data. We used Monte Carlo package GATE to simulate the dual-isotope acquisition with a standard PET camera. Realistic efficiencies were assumed for the HE gamma detection varying from 3% to 9%. A set of seven partially overlapping 3D objects filled with <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> F and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</sup> Cu was located at the center of a water phantom of 30 cm diameter. A low-count (250k decays of each <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> F and <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">60</sup> Cu) and a high-count (2.5M decays each) acquisitions were simulated. We found that the dual-isotope EM algorithm was able to successfully separate two PET tracers for all values of studied parameters. As expected the accuracy of this separation increased for higher HE gamma detection efficiency and higher total number of detected counts. A systematic analysis of the quantitative accuracy of these reconstructions is currently being performed.