Spectral models for 1D blood flow simulations

In this paper we introduce a new theoretical formulation for the description of the blood flow in the circulatory system. Starting from a linearized version of the Navier-Stokes equations, the Green's function of the propagation problem is computed in a rational form. As a consequence, the input-output transfer function relating the upstream and downstream pressure and blood flow is written in a rational form as well, leading to a time-domain state-space model suitable for transient analysis. The proposed theoretical formulation has been validated by pertinent numerical results.