Positron Emission Tomography (PET) continues to have wide-ranging medical application and is based on the detection of gamma radiation emitted from the decay of certain types of radionuclides. Modern PET scanners produce three-dimensional (3D) images of the radiation source, in discrete time steps, using tomography analysis. Our work presents an application of PET for studying fluid mobility in pressurized low-permeability rock samples in the presence of natural fractures. This technique uses a high-resolution PET scanner and image reconstruction based on filtered back-projection. Traditional techniques have been limited to pressure measurement of fracture conductivity and effective permeability, but little is understood about the dynamic flow and velocity profiles within the fracture. The objective of our work was to investigate if we can measure the time-lapse distribution of the fluid flow as a function of the overburden stress. PET imaging was applied to the flow of brine solution, tagged with 18F positron emitting radionuclide, through non-fractured sandstone and naturally fractured shale cores. A special composite container was manufactured to sustain high-pressure conditions and minimize the absorption of emitted gamma rays. We describe the experimental apparatus and demonstrate that the 3D images obtained with a grid resolution of 2x2x2 mm3 allow clear determination of the fluid flow rate through the core as a function of overburden pressure and time. PET images are direct observations of the radiation source and allow an unambiguous determination of the fluid distribution in the core. The results of our research will be used to validate the numerical modeling of fluid flow through fractured rock matrices, enable more accurate estimates on the directionality of fractures from the fluid distribution as a function of time, and obtain more quantitatively sound estimates of fracture connectivity.