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Accurate vascular geometry modeling is an essential task in computer assisted vascular surgery and therapy. This paper presents a vessel cross-section based implicit vascular modeling technique, which represents a vascular surface as a set of locally fitted implicit surfaces. In the proposed method, a cross-section based technique is employed to extract from each cross-section of the vascular surface a set of points, which are then fitted with an implicit curve represented as 2D radial basis functions. All these implicitly represented cross-section curves are then being considered as 3D cylindrical objects and combined together using a certain partial shape-preserving spline to build a complete vessel branch; different vessel branches are then blended using a extended smooth maximum function to construct the complete vascular tree. Experimental results show that the proposed method can correctly represent the morphology and topology of vascular structures with high level of smoothness. Both qualitative comparison with other methods and quantitative validations to the proposed method have been performed to verify the accuracy and smoothness of the generated vascular geometric models. [ABSTRACT FROM AUTHOR]

• A new tubular shape modeling technique based on implicit extrusion surfaces (IES) is developed for the accurate geometric modeling of vasculatures. • An implicit geometric editing technique is developed to modify the constructed vascular model with pathology for virtual stenting. • We conduct some blood flow simulations based on the reconstructed and corrected vessel models to illustrate the impact of blood flow dynamics on the diseased vascular wall and on the modified vascular model. High-quality vascular modeling is crucial for blood flow simulations, i.e., computational fluid dynamics (CFD). As without an accurate geometric representation of the smooth vascular surface, it is impossible to make meaningful blood flow simulations. The purpose of this work is to develop high-quality vascular modeling and modification method for blood flow computations. We develop a new technique for the accurate geometric modeling and modification of vasculatures using implicit extrusion surfaces (IES). In the proposed method, the skeleton of the vascular structure is subdivided into short curve segments, each of which is then represented implicitly locally as the intersection of two mutually orthogonal implicit surfaces defined by distance functions. A set of contour points is extracted and fitted with an implicit curve for accurately specifying the vessel cross-section profile, which is then extruded locally along the skeleton to fill the gaps between two vascular tube cross sections. We also present a new implicit geometric editing technique to modify the constructed vascular model with pathology for virtual stenting. Experimental results and validations show that accurate vascular models with highly smooth surfaces can be generated by the proposed method. In addition, we conduct some blood flow simulations to indicate the effectiveness of proposed method for hemodynamic simulations. The proposed technique can achieve precise geometric models of vasculatures with any required degree of smoothness for reliable blood flow simulations. [ABSTRACT FROM AUTHOR]