A reduced model of pulsatile flow in an arterial compartment

Abstract

In this article we propose a reduced model of the input–output behaviour of an arterial compartment, including the short systolic phase where wave phenomena are predominant. The objective is to provide basis for model-based signal processing methods for the estimation from non-invasive measurements and the interpretation of the characteristics of these waves. Due to phenomena such that peaking and steepening, the considered pressure pulse waves behave more like solitons generated by a Korteweg–de Vries (KdV) model than like linear waves. So we start with a quasi-1D Navier–Stokes equation taking into account radial acceleration of the wall: the radial acceleration term being supposed small, a 2scale singular perturbation technique is used to separate the fast wave propagation phenomena taking place in a boundary layer in time and space described by a KdV equation from the slow phenomena represented by a parabolic equation leading to two-elements windkessel models. Some particular solutions of the KdV equation, the 2 and 3-soliton solutions, seems to be good candidates to match the observed pressure pulse waves. Some very promising preliminary comparisons of numerical results obtained along this line with real pressure data are shown.