A method of 3D reconstruction of flow velocity fields from color-Doppler ultrasound

A method is proposed for quantitative reconstruction of the SD-velocity field from Color Doppler Ultrasound (CDUS) images, based on a physical model of flow. Given a small number of (spatially unrestricted) transversal CDUS cross sections of the artery, the 3D velocity field is reconstructed by numerically solving the Navier-Stokes and the Continuity equations for a steady flow of an incompressible Newtonian fluid at constant temperature, within a stiff pipe. The correct choice of the Penalty Parameter epsilon in the Finite Element Method (FEM) algorithm allows convergence to a feasible physical reconstruction of the field. Only two CDUS measurements are necessary to define the boundary conditions. Vessel's geometry, and therefore the velocity field reconstruction, improve with increasing number of B-mode cross sections.