Dynamic modeling of the outlet of a pulsatile pump incorporating a flow-dependent resistance

Outlet tube models incorporating a linearly flow-dependent resistance are widely used in pulsatile and rotary pump studies. The resistance is made up of a flow-proportional term and a constant term. Previous studies often focused on the steady state properties of the model. In this paper, a dynamic modeling procedure was presented. Model parameters were estimated by an unscented Kalman filter (UKF). The subspace model identification (SMI) algorithm was proposed to initialize the UKF. Model order and structure were also validated by SMI. A mock circulatory loop driven by a pneumatic pulsatile pump was developed to produce pulsatile pressure and flow. Hydraulic parameters of the outlet tube were adjusted manually by a clamp. Seven groups of steady state experiments were carried out to calibrate the flow-dependent resistance as reference values. Dynamic estimation results showed that the inertance estimates are insensitive to model structures. If the constant term was ignored, estimation errors for the flow-proportional term were limited within 16% of the reference values. Compared with the constant resistance, a time-varying one improves model accuracy in terms of root mean square error. The maximum improvement is up to 35%. However, including the constant term in the time-varying resistance will lead to serious estimation errors.