A medical imaging system for reconstructing quantitative dynamic nuclear medicine images of a subject may include a three dimensional positron emission tomography (3D PET) scanner and a data processing system. The three dimensional positron emission tomography (3D PET) scanner may: perform scans of the subject at each of multiple bed positions, each scan being of only a sub-portion of the subject that is within an axial length covered by the scanner; and generate dynamic list-mode PET data that: represents a total number of photon pairs arriving at each of multiple detector pairs in the 3D PET scanner; and is organized in a list of elements, each element in the list including a detector pair index and an arrival time for each detected photon pair; and acquires PET data using a dynamic PET protocol with at least two scans at each of the multiple bed positions. The data processing system may: reconstruct Patlak slope and intercept images of the subject over an axial length of the subject that exceeds the axial length of each scan of the subject by optimizing a likelihood or penalized likelihood function using the list-mode PET data from at least two scans of the subject at each of the multiple bed positions; and store the reconstructed image in a storage device or displays the reconstructed image on a display system.