Decomposition of Velocity Field Along a Centerline Curve Using Frenet-Frames: Application to Arterial Blood Flow Simulations

Abstract

This paper presents a novel method for the evaluation of three-dimensional blood-flow simulations based, on the decomposition of the velocity field into localized coordinate systems along the vessels centerline. The method is based on the computation of accurate centerlines with the Vascular Modeling Toolkit (VMTK) library, to calculate the localized Frenet-frames along the centerline and the morphological features, namely the curvature and torsion. Using the Frenet-frame unit vectors, the velocity field can be decomposed into axial, circumferential and radial components and visualized in a diagram along the centerline. This paper includes case studies with four idealized geometries resembling the carotid siphon and two patient-specific cases to demonstrate the capability of the method and the connection between morphology and flow. The proposed evaluation method presented in this paper can be easily extended to other derived quantities of the velocity fields, such as the wall shear stress field. Furthermore, it can be used in other fields of engineering with tubular cross-sections with complex torsion and curvature distribution.