Regularization of blood motion fields by modified Navier-Stokes equations

A technique for the regularization of incompressible fluid motion fields based on the use of modified Navier-Stokes equations is presented. It is shown that the technique belongs to the class of Tikhonov-type regularization methods. The technique was applied to an analytically known fluid-dynamic problem (Couette flow). Noisy and scattered versions of the analytical velocity field were generated, and the accuracy in reconstructing the analytical field was evaluated. It was found that accuracy depends on the value of a regularization parameter, and its optimal value depends on the entity of noise and scattering. When the optimal value is selected, the accuracy of the regularization technique is excellent, even for consistent noise and scattering levels. The technique was finally applied to echocardiographic data in order to estimate the blood velocity field within the left ventricle.