1. A method of performing elastography of a volume of tissue of a patient with a CT scanner, comprising: applying, by a vibration source, a periodic excitation wave to the volume of tissue, the periodic excitation wave having a plurality of phases that each correspond to a respective one of a plurality of deformation states of the volume of tissue; acquiring by the CT scanner a first plurality of CT projections at a first phase corresponding to a first deformation state of the volume of tissue, the first plurality of CT projections comprising a first CT projection set; acquiring by the CT scanner a second plurality of CT projections at a second phase corresponding to a second deformation state of the volume of tissue, wherein the second phase is different than the first phase, the second plurality of CT projections comprising a second CT projection set; determining, based on the first CT projection set and the second CT projection set, at least one of a tissue deformation field and a tissue mechanical property of the volume of tissue.