Uncertainty analysis of measurement error in calculating vascular input impedance: how many harmonics can be resolved?

Vascular input impedance represents the hydraulic load seen by the ejecting ventricle and is represented by magnitude and phase components in the frequency domain derived from Fast Fourier Transform (FFT) of instantaneous vascular pressure and flow measurements. The resulting spectra consists of a mean or DC component and magnitude and phase information at harmonics of the fundamental frequency. The objective of this study was to determine how many harmonics could be faithfully reproduced as a function of measurement error associated with the instantaneous pressure and flow recordings using uncertainty analysis. Input impedance and uncertainty analysis algorithms were developed in Matlab. Simulated vascular pressure and flow waveforms were constructed by summing a series of sine waves of varying amplitude and phase to verify accuracy of the impedance and uncertainty m-files. Random normally distributed noise was injected into the simulated waveforms and a Monte Carlo analysis performed to verify the injected ´noise´ which fell within the bounded limits. Using aortic pressure and flow data obtained experimentally in an acute animal model, the uncertainty error associated with pressure, flow, and sampling time errors for up to ten harmonics was determined. These results indicate that given high-fidelity data, the DC and up to six harmonics can be faithfully resolved.