Arterial Wall Shear Stress Of The Hilbert-huang Transform And Its Applications

The analysis of the signals of arterial wall shear stress (WSS) plays an important role in the study of the relationship between WSS and arterial remodeling. Due to the regulation of other systems such as nervous and respiratory systems, arterial WSS is actually a nonstationary and nonlinear pulsatile signal rather than a strict stationary periodic one. In previous investigations, Fourier Transform (FT) or Fast Fourier Transform (FFT), which is very effective for stationary periodic signals, has extensively adopted to determine and analyze the WSS signals.In this thesis, at first, the nonstationary signals of arterial wall shear stress were numerically determined; The WSS signals were analyzed by Hilbert-Huang Transform (HHT). Furthermore, the mean frequency and the mean energy density of Intrinsic Mode Function (IMF) by Empirical Mode Decomposition (EMD) were calculated. By analyzing the characteristics of the mean frequency and the mean energy density, the different frequency characteristics of WSS signals between Spontaneously Hypertensive Rats (SHRs) and Wistar Kyoto Rats (WKYs) at different ages were compared, respectively. It was demonstrated that HHT is more effective than FFT in distinguishing the frequency characteristics of arterial WSS between SHR and WKY by comparing the results from HHT to those from FFT.The main conculsions of the thesis are shown as follows:The signals of wall shear stress in the common carotid arteries in rats were numerically determined and analyzed by Hilbert-Huang Transform (HHT). By carefully analyzing the HHT spectra, it was shown that the WSS signal is nonstationary but not strict stationary periodic one;While the FFT of arterial WSS results in the transfer of energy from a low frequency band to a high frequency band in the Fourier space, the HHT of arterial WSS results in the concentration of energy in the marginal Hilbert space;The EMD of arterial WSS acts as aλrank filter bank. In other words, the frequency of the next IMF will beλtimes smaller than the former one's in each EMD processing. Here the values of X is not equal to 2 but around 1.5～1.8, which can be regarded as an index reflecting the intrinsic frequency characteristics of WSS;Compared with the well known FFT, the mean frequency and the mean energy density of IMFs have significant advantages in distinguishing the frequency characteristics of arterial WSS between SHR and WKY at different ages.