Abstract: Treatment targets such as tumors or lesions, located within an anatomical region that undergoes motion (which may be periodic with cycle P) are tracked. A 4D mathematical model may be established for the non-rigid motion and deformation of the anatomical region, from a set of CT or other 3D images. The 4D mathematical model relates the 3D locations of part(s) of the anatomical region with the targets being tracked, as a function of the position in time within P. Using non-rigid image registration between pre-operative and intra-operative images, the position of the target and/or other part(s) of the anatomical region may be determined.