Total arterial inertance as the fourth element of the windkessel model

In earlier studies we found that the three-element windkessel, although an almost perfect load for isolated heart studies, does not lead to accurate e stimates of total arterial compliance. To overcome this problem, we introdu ce an inertial term in parallel with the characteristic impedance. In seven dogs we found that ascending aortic pressure could be predicted better fro m aortic flow by using the four-element windkessel than by using the three- element windkessel: the root-mean-square errors and the Akaike information criterion and Schwarz criterion were smaller for the four-element windkesse l. The three-element windkessel overestimated total arterial compliance com pared with the values derived from the area and the pulse pressure method ( P = 0.0047, paired t-test), whereas the four-element windkessel compliance estimates were not different (P = 0.81). The characteristic impedance was u nderestimated using the three-element windkessel, whereas the four-element windkessel estimation differed marginally from the averaged impedance modul us at high frequencies (P = 0.0017 and 0.031, respectively). When applied t o the human, the four-element windkessel also was more accurate in these sa me aspects. Using a distributed model of the systemic arterial tree, we fou nd that the inertial term results from the proper summation of all local in ertial terms, and we call it total arterial inertance. We conclude that the four-element windkessel, with all its elements having a hemodynamic meanin g, is superior to the three-element windkessel as a lumped-parameter model of the entire systemic tree or as a model for parameter estimation of vascu lar properties.