Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The current processing performed by commercial instruments to obtain the time-frequency representation (TFR) of pulsed-wave Doppler signals may not be adequate to characterize turbulent flow motions. The assessment of the intensity of turbulence is of high clinical importance and measuring high-frequency (small-scale) flow motions, using Doppler ultrasound (US), is a difficult problem that has been studied very little. The objective was to optimize the performance of the spectrogram (SPEC), autoregressive modeling (AR), Choi-Williams distribution (CWD), Choi-Williams reduced interference distribution (CW-RID), Bessel distribution (BD), and matching pursuit method (MP) for mean velocity waveform estimation and turbulence detection. The intensity of turbulence was measured from the fluctuations of the Doppler mean velocity obtained from a simulation model under pulsatile flow. The Kolmogorov spectrum, which is used to determine the frequency of the fluctuations and, thus, the scale of the turbulent motions, was also computed for each method. The best set of parameters for each TFR method was determined by minimizing the error of the absolute frequency fluctuations and Kolmogorov spectral bandwidth measured from the simulated and computed Doppler spectra. The results showed that different parameters must be used for each method to minimize the velocity variance of the estimator, to optimize the detection of the turbulent frequency fluctuations, and to estimate the Kolmogorov spectrum. To minimize the variance and to measure the absolute turbulent frequency fluctuations, four methods provided similar results: SPEC (10-ms sine-cosine windows), AR (10-ms rectangular windows, model order = 8), CWD (w(N) and w(M) = 10-ms rectangular windows, sigma = 0.01), and BD (w(N) = 10-ms rectangular windows, alpha = 16). The velocity variance in the absence of turbulence was on the order of 0.04 m/s (coefficient of variation ranging from 8.0% to 14.5%, depending on the method). With these spectral techniques, the peak of the turbulence intensity was adequately estimated (velocity bias < 0.01 m/s). To track the frequency of turbulence, the best method was BD (w(N) = 2-ms rectangular windows, alpha = 2). The bias in the estimate of the -10 dB bandwidth of the Kolmogorov spectrum was 354 +/- 51 Hz in the absence of turbulence (the true bandwidth should be 0 Hz), and -193 +/- 371 Hz with turbulence (the simulated -10-dB bandwidth was estimated at 1256 Hz instead of 1449 Hz). In conclusion, several TFR methods can be used to measure the magnitude of the turbulent fluctuations. To track eddies ranging from large vortex to small turbulent fluctuations (wide Kolmogorov spectrum), the Bessel distribution with appropriate set of parameters is recommended.