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Recent work in the development of computerized phantoms has focused on the creation of ideal ldquohybridrdquo models that seek to combine the realism of a patient-based voxelized phantom with the flexibility of a mathematical or stylized phantom. We have been leading the development of such computerized phantoms for use in medical imaging research. This paper will summarize our developments dating from the original four-dimensional (4-D) mathematical cardiac-torso (MCAT) phantom, a stylized model based on geometric primitives, to the current 4-D extended cardiac-torso (XCAT) and mouse whole-body (MOBY) phantoms, hybrid models of the human and laboratory mouse based on state-of-the-art computer graphics techniques. This paper illustrates the evolution of computerized phantoms toward more accurate models of anatomy and physiology. This evolution was catalyzed through the introduction of nonuniform rational b-spline (NURBS) and subdivision (SD) surfaces, tools widely used in computer graphics, as modeling primitives to define a more ideal hybrid phantom. With NURBS and SD surfaces as a basis, we progressed from a simple geometrically based model of the male torso (MCAT) containing only a handful of structures to detailed, whole-body models of the male and female (XCAT) anatomies (at different ages from newborn to adult), each containing more than 9000 structures. The techniques we applied for modeling the human body were similarly used in the creation of the 4-D MOBY phantom, a whole-body model for the mouse designed for small animal imaging research. From our work, we have found the NURBS and SD surface modeling techniques to be an efficient and flexible way to describe the anatomy and physiology for realistic phantoms. Based on imaging data, the surfaces can accurately model the complex organs and structures in the body, providing a level of realism comparable to that of a voxelized phantom. In addition, they are very flexible. Like stylized models, they can easily b- e manipulated to model anatomical variations and patient motion. With the vast improvement in realism, the phantoms developed in our lab can be combined with accurate models of the imaging process (SPECT, PET, CT, magnetic resonance imaging, and ultrasound) to generate simulated imaging data close to that from actual human or animal subjects. As such, they can provide vital tools to generate predictive imaging data from many different subjects under various scanning parameters from which to quantitatively evaluate and improve imaging devices and techniques. From the MCAT to XCAT, we will demonstrate how NURBS and SD surface modeling have resulted in a major evolutionary advance in the development of computerized phantoms for imaging research.