The goal is to develop a 4D digital perfusion cardiac-torso (PCAT) phantom, a tracer kinetic extension of the XCAT phantom, by modeling the time activity curves (TACs) of individual organ regions in the phantom for dynamic perfusion PET and SPECT simulation studies. The PCAT phantom is based on a generalized compartmental model, which accepts the blood input function, multiple series or parallel compartments, the bidirectional rate constants between the compartments, the blood volume in the tissue, the extraction curves, and other properties of a specific tracer. Based on the kinetic differential equations of the compartmental model, the TACs of the targeted organ regions were determined. For a specific time point, a voxelized anatomical realistic phantom, which with or without the cardiac and respiratory motions, was generated and the activity concentrations in the organ regions were assigned according to the corresponding TACs. According to the dynamic scanning protocol, multiple phantoms at different acquisition time points, which could have uniform or non-uniform time intervals, were generated. When combining the dynamic phantoms with realistic projection simulator, realistic dynamic projection data could be generated by easily adopting to various scanning protocols and imaging systems. With the availability of the "known truth", the activity map of the targeted organ regions, the TACs, the estimated rate constants and other kinetic parameters, from the projection data and the reconstructed images could be quantitatively evaluated. We demonstrate the usefulness of the 4D PCAT phantom in initial simulation studies in dynamic myocardial perfusion PET imaging with different tracers. The PCAT phantom was found to be an important bridge between the creation of TACs and the generation of simulated projection data. It is a useful simulation tool to study different kinetic analysis methods, acquisition protocols, reconstruction methods, and imaging parameter settings.