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Mathematical representation of the vascular structure and applications
Conference proceeding

Mathematical representation of the vascular structure and applications

Jie Li, William Regli, Wei Sun and Jingjing Li
Proceedings of the 2007 ACM symposium on solid and physical modeling, pp 373-378
04 Jun 2007
DOI: https://doi.org/10.1145/1236246.1236300

Abstract

computational representation deformable model NURBS swept volumes vascular modeling
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. The work in this paper presents the initial steps toward creating computational models suitable for high-fidelity vascular modeling, design and analysis. The authors believe that improved computational modeling for biological structures will enable new applications in tissues engineering and biological analysis.

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