On the spectrographic representation of cardiovascular flow instabilities

In the past decade, high-fidelity computational fluid dynamics (CFD) has uncovered the presence of high-frequency flow instabilities (on the order of 100 s of Hz) in a variety of cardiovascular applications. These fluctuations are typically reported as pulsatile velocity-time traces or fast-Fourier-transformed power-frequency spectra, often from a single point or at most a handful of points. Originally inspired by its use in spectral Doppler ultrasound, here we demonstrate the utility of the simplest form of time-frequency representation - the spectrogram - as a more comprehensive yet still-intuitive means of visualizing the potential harmonic complexity of pulsatile cardiovascular flows. After reviewing the basic theory behind spectrograms, notably the short-time Fourier transform (STFT), we discuss the choice of input parameters that inform the appearance and trade-offs of spectrograms. We show that spectrograms using STFT were able to highlight spectral features and were representative of those obtained from more complex methods such as the Continuous Wavelet transforms (CWT). While visualization properties (colourmap, filtering, smoothing/interpolation) are shown to affect the conspicuity of spectral features, the window properties (function, size, overlap) are shown to have the greatest impact on the resulting spectrogram appearance. Using a set of cerebral aneurysm CFD cases, we show that spectrograms can readily reveal the case-specific nature of the time-varying flow instabilities, whether broadband, suggesting intermittent turbulent-like flow, or narrowband, suggesting laminar vortex shedding, or some combination thereof.