Reconstruction of vascular blood flow in a vessel from tomographic projections

In this work, we study the measurement of blood velocity with contrast enhanced computed tomography. The reconstruction is based on CT projections perpendicular to the main axis of the vessel and on a partial differential equation describing the propagation of the contrast agent. The inverse problem is formulated as an optimal control problem with the transport equation as constraint. The velocity field is obtained with stationary and unstationary Navier-Stokes equations and it is reconstructed with the adjoint method. The velocity and the density of the contrast agent are well reconstructed. The reconstruction results obtained are better for the axial component of the velocity than for transverse components.