Validity of the local nonlinear arterial flow theory: Influence of the upstream and downstream conditions

The “local flow” theory provides a simple way to take into account the nonlinear convective terms associated with blood flow in large arteries. The assumption that blood velocity profiles vary slowly with the longitudinal coordinate allows a simple nonlinear resolution via a mathematical approximation. Although validated in vitro by its authors, this theory still needs to be verified in accordance with the range of variation of the hemodynamical parameters. This constitutes the aim of this work where we assess the validity of two models issued from this theory: the “direct model” using the pressure-gradient as an input for the calculations and the “indirect model” using the centre-line velocity. The assessment of these models is made by comparing their solutions to those of the linear theory using numerical simulations. Our main conclusion is that the indirect model has a wide range of validity while the direct one fails in the presence of a strong reflected wave.