Rational macromodeling of 1D blood flow in the human cardiovascular system.

In this paper, we present a novel rational macromodeling approach for the description of 1D blood flow in the human cardiovascular system, which is suitable for time-domain simulations. Using the analogy of the blood flow propagation problem with transmission lines and considering the hypothesis of linearized Navier-Stokes equations, a frequency-domain rational macromodel for each arterial segment has been built. The poles and the residues of each arterial segment macromodel have been calculated by means of the Vector Fitting technique. Finally, the rational macromodel of the whole cardiovascular system is obtained by properly combining the macromodels of the single arterial segments using an interconnect matrix. The rational form of the proposed cardiovascular model leads to a state-space or electrical circuit model suitable for time-domain analysis. The stability and passivity properties of the global cardiovascular model are discussed to guarantee stable time-domain simulations. The proposed macromodeling approach has been validated by pertinent numerical results.