A new nonlinear two-dimensional model of blood motion in tapered and elastic vessels.

An original mathematical model for the local study of blood motion in tapered and distensible arteries was developed. The theory takes into account the nonlinear terms of the Navier-Stokes equations, as well as wall motion and instantaneous taper angle, and allows the calculation of axial and radial velocity profiles with low computational complexity. The relationship between instantaneous flow and the pressure gradient in steady and dynamic conditions is evaluated by means of the mathematical model. The results obtained by simulation agree with experimental evidence and also indicate that the anatomic tapering of arteries and pulsatile changes in diameter highly influence blood motion.