Can a Linear Electrical Analog Model of a Mechanical Valve Predict Flow by Using a Pressure Gradient?

The objective was to determine whether a previously developed technique for biological aortic valves could predict flow through a mechanical valve. An electrical analog model of the aortic valve that includes compliance, resistance, and inertance parameters, and corresponding second order differential equations was used to predict flow given a pressure gradient, as previously reported. Simulated pressures and flow were recorded by using a pulse duplicator system. The heart rate was varied from 60 to 180 bpm, and the stroke volume was varied from 22 to 67 cc. Resistance, inertance, and compliance parameters of the governing differential equation were estimated by using a least-squares fit to the measured flow at 120 bpm and 50 cc stroke volume. By using these parameter estimates, flow was calculated for other heart rates and stroke volumes. To achieve a better flow prediction, a nonlinear filter (third order polynomial range calibration equation) was applied to the output of the linear model (flow). The mean error, full-scale error, and spectral error in magnitude and phase between measured and predicted flow were compared. Error in mean flow ranged from 3% at medium flow rates to 90% at low flow rates. The maximum and minimum full scale errors were 12% and 5%, respectively. Error in the harmonics of measured and calculated flow ranged from 0% to 55%. Larger errors were usually present at the higher harmonics. The agreement between measured and calculated flow was better at normal and high flows but rather poor at low flows. The nonlinear filter (range calibration equation) was unable to account for the discrepancies between the measured and calculated flow over all flow ranges. It seems that this linear model and nonlinear filter have limited application, and an alternate nonlinear approach may produce better results.