Navier-Stokes Equations With Fuzzy EmbeddedConditions Applied To Regularization Of ArterialBlood Velocity Profile Distribution

A new approach to regularize blood velocity profile distribution in an arterial vessel segment is presented. The knowledge of the velocity field in a limited set of points within the vessel segment is assumed. This reduced velocity data set has been used as fuzzy embedded conditions to solve the Navier-Stokes equations. The reduced data set represents a noisy scattered velocity field, in such a way as can be measured by means of noninvasive techniques (Doppler, NMR). In the proposed approach, the data set has been used to compute the velocity field in all the points of the domain. Moreover, the data set is regularized in order to satisfy the constraints imposed through the Navier-Stokes equations with an added extra forcing term. The approach has been preliminary applied to a simple analytically known problem: the stationary Poiseuille flow in a two dimensional pipe. In order to generate the reduced data set, the analytical solution has been sampled and altered by adding a gaussian noise. After regularization, the percentage difference between analytical and regularized velocity has been computed in each point: in the worst cases, the mean and the standard deviation of this difference remain respectively less than 15% and 30%. It can be claimed that the regularization method reconstructs the analytical velocity distribution with good accuracy.