Vascular imaging by ultrasound: 3D reconstruction of flow velocity fields for endothelial shear stress calculation

A new method for quantitative reconstruction of a three dimensional (3D) velocity field from ultrasound color doppler mapping (USCDM) images is used here to calculate the shear stress distribution on the endothelial layer of an artery. Measurements of a few spatially unrestricted USCDM transverse cross sectional images of the artery, and of several echo-ultrasound B-mode images of the same area, are required for reconstructing the geometry of the vessel's endothelial surface. The calculation is based on assuming a physical model of flow, and solving the Continuity and the Navier-Stokes equations numerically for a steady flow of an incompressible Newtonian fluid at constant temperature within a non-flexible tube. The correct choice of the penalty parameter in the finite element method (FEM) algorithm provides proper convergence of the reconstruction. The endothelial shear stress is calculated from the gradient of the velocity field at each point of the vessel's inner surface.