The NURBS book
Biomedical computing and visualization software environments
Communications of the ACM - Bioinformatics
Approximate swept volumes of NURBS surfaces or solids
Computer Aided Geometric Design
A computational model of micro-vascular growth
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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Computational models have been used widely in tissue engineering research and have proven to be powerful tools for bio-mechanical analysis (i.e., blood flow, growth models, drug delivery, etc). This paper focuses on developing higher-fidelity models for vascular structures and blood vessels that integrate computational shape representations with biomedical properties and features. Previous work in computer-aided vascular modeling comes from two communities. For those in biomedical imaging, the goal of past research has been to develop image understanding techniques for the interpretation of x-ray, magnetic resonance imaging (MRI), or other radiological data. These representations are predominantly discrete shape models that are not tied to physiological properties. The other corpus of existing work comes from those interested in developing physiological models for vascular growth and behavior based on bio-medical attributes. These models usually either have a highly simplified shape representation, or lack one entirely. Further, neither of these representations are suitable for the kind of interactive modeling required by tissue engineering applications. This paper aims to bridge these two approaches and develop a set of mathematical tools and algorithms for feature-based representation and computer-aided modeling of vascular trees for use in computer-aided tissue engineering applications. The paper offers a multi-scale representation based on swept volumes and a feature-based representation that can attribute the geometric representation with information about blood flow, pressure, and other biomedical properties. The paper shows how the resulting representation can be used as part of an overall approach for designing and visualizing vascular scaffolds. As a real-world example, we show how this computational model can be used to develop a tissue scaffold for liver tissue engineering. Such scaffolds may prove useful in a number of biomedical applications, including the growth of replacement tissue grafts and in vitro study of the pharmacological affects of new drugs on tissue cultures.