Direct 6D List-Mode Maximum-Likelihood Expectation-Maximization Reconstruction for Dynamic Cardiac SPECT

SPECT is the foundation of cardiac nuclear stress testing in the medical imaging industry. To achieve its full potential, one needs to be able to accurately calculate myocardial blood flow (MBF) and coronary flow reserve (CFR) from clinical slowly rotating gamma cameras with algorithms that are able to correct for cardiac and respiratory motion. Implementing dynamic cardiac imaging with conventional slowly rotating clinical SPECT scanners, the emitted photons are detected and recorded continuously by the camera detector as it rotates. Acquiring the data in list mode with information of angle and bin location, in addition to information of cardiac and respiratory phases, allows for more flexibility in modeling the physiological processes of the time varying activity changes and cardiac and respiratory motion. It is known that for a slowly rotating gamma camera it is difficult to obtain consistent tomographic data to solve dynamic inverse problems frame-by-frame. However, by estimating coefficients of spatiotemporal basis functions directly from projection measurements one can fairly accurately measure the wash-in and wash-out kinetics of a myocardial perfusion SPECT tracer. Here we develop a direct 6D list-mode (LM) maximum-likelihood expectation-maximization (LM-ML-EM) reconstruction algorithm. Our spatiotemporal image reconstruction uses splines to explicitly model the temporal change of the tracer and Gaussian basis functions to model cardiac and respiratory motion. The varying change in the projected activity distribution is a non-homogeneous Poisson process in contrast with homogeneous Poisson processes characteristic of imaging biological systems at equilibrium. Using an appropriate likelihood function for the measured projections and an appropriate likelihood function for the "complete" data space, an equivalent algorithm is developed form these two formulations that provides an iterative update for the coefficients of a tensor product of the spatiotemporal basis functions.