Tissue Engineering, the science and engineering of creating functional tissues and organs for transplantation, integrates a variety of scientific and engineering disciplines to produce physiologic ldquoreplacement partsrdquo for the development of viable substitutes which restore, maintain or improve the function of human tissues. In the success of tissue engineering, three-dimensional (3D) scaffolds play important roles as extra-cellular matrices onto which cells can attach, grow, and form new tissues. Modeling, design and fabrication of tissue scaffolds to meet multiple biological and biophysical requirements is always a challenge in regenerative tissue engineering. BioCAD in tissue engineering is broadly classified into the following three major applications: 1) computer-aided tissue modeling, including 3D anatomic visualization, 3D reconstruction, computer-aided design (CAD) of tissue models and bio-physical modeling for surgical planning and simulation; 2) computer-aided tissue scaffold informatics and biomimetics; and 3) bio-manufacturing for tissue and organ regeneration.

The complexity and diversity of the vascular system makes it difficult to perform quantitative blood vessel modeling and analysis. Emerging applications in biomedical modeling, bio-mimetic manufacturing and tissue engineering necessitate the development of new approaches to computational modeling of vascular structures. In this paper, we address the computational representation of realistic vascular objects to enable deformable blood vessels. First, we construct a swept volume based vascular model from a physiological vascular model. Second, we construct the NURBS surface based on deformable circles, i.e., the primitive of swept volume, as the boundary of the swept volumes. The approach of NURBS surface construction can also be extended to reconstruct medical image based vasclar models. In the end, potential applications of the mathematical representation of vascular structure including blood flow simulation in scaffold are discussed. As a computational representation, our vascular model enables multiscale visualization of a realistic vascular system.