Validation of a novel nonlinear black box Wiener System model for arterial pulse transmission

Abstract

Numerous linear dynamic models exist for describing the arterial pulse transmission phenomenon. We introduce a novel Wiener system based model in which a linear filter representing large arteries is coupled with a hysteresis-free nonlinear function representing complex wave transmission of branching arteries and the periphery. Experimental datasets (n = 7) are used to first estimate the Wiener model with linear, quadratic and cubic function for the aorta to radial artery pulse transmission and aorta to femoral artery pulse transmission. To model the nonlinear memoryless monotonic function in the Wiener System model, a correlation study is performed for linear finite impulse response (FIR) filter simulated peripheral pressure vs. measured peripheral pressure waveform. Each of this correlation curves were fitted to linear, quadratic and cubic polynomial equation. Wiener model is then simulated for aortic-to-radial artery as well as aortic-to-femoral artery to reconstruct radial and femoral pressure waveform. It was found that Wiener model with 3rd order polynomial function yielded better modeling accuracy (with average RMSE = 2.187 mmHg for radial and 4.281 mmHg for femoral pressure) than that from 2nd order polynomial function (with average RMSE = 2.242 mmHg for radial and 4.355 mmHg for femoral pressure) which in turn was better than mere linear FIR filter (with average RMSE = 2.604 mmHg for radial and 4.810 mmHg for femoral pressure).