The goal of this research is to dramatically improve PET image quality using real time motion information provided by simultaneous MR imaging in PET-MR scanners. PET imaging of the thorax is significantly limited by poor spatial resolution due to voluntary as well as internal, i.e., cardiac and respiratory, motion. Prototype small bore simultaneous PET-MR systems now exist, and whole-body PET-MR systems are under development. We are developing a novel iterative PET reconstruction framework that models the MR-derived 3D non-rigid motion field in the emission and attenuation maps.  We are also evaluating the performance of the methods to be developed in realistic Monte Carlo simulations of small thoracic tumors and atherosclerotic plaques.