Mathematical modeling of fluid dynamics in pulsatile cardiopulmonary bypass

The design criteria of an extracorporeal circuit suitable for pulsatile flow are quite different and more entangled than for steady flow. The time and costs of the design process could be reduced if mutual influences between the pulsatile pump and other extracorporeal devices were considered without experimental trial-and-error activities. With this in mind, we have developed a new lumped-parameter mathematical model of the hydraulic behavior of the arterial side of an extracorporeal circuit under pulsatile flow conditions. Generally, components feature a resistant-inertant-compliant behavior and the most relevant nonlinearities are accounted for. Parameter values were derived either by experimental tests or by analytical analysis. The pulsatile pump is modeled as a pure pulsatile flow generator. Model predictions were compared with flow rate and pressure tracings measured during hydraulic tests on two different circuits at various flow rates and pulse frequencies. The normalized root mean square error did not exceed 24% and the model accurately describes the changes that occur in the basic features of the pressure and flow wave propagating from the pulsatile pump to the arterial cannula.