Computational geometry for patient-specific reconstruction and meshing of blood vessels from MR and CT angiography

Abstract

Investigation of three-dimensional (3-D) geometry and fluid-dynamics in human arteries is an important issue in vascular disease characterization and assessment. Thanks to recent advances in magnetic resonance (MR) and computed tomography (CT), it is now possible to address the problem of patient-specific modeling of blood vessels, in order to take into account interindividual anatomic variability of vasculature. Generation of models suitable for computational fluid dynamics is still commonly performed by semiautomatic procedures, in general based on operator-dependent tasks, which cannot be easily extended to a significant number of clinical cases. In this paper, we overcome these limitations making use of computational geometry techniques. In particular, 3-D modeling was carried out by means of 3-D level sets approach. Model editing was also implemented ensuring harmonic mean curvature vectors distribution on the surface, and model geometric analysis was performed with a novel approach, based on solving Eikonal equation on Voronoi diagram. This approach provides calculation of central paths, maximum inscribed sphere estimation and geometric characterization of the surface. Generation of adaptive-thickness boundary layer finite elements is finally presented. The use of the techniques presented here makes it possible to introduce patient-specific modeling of blood vessels at clinical level.