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.

在过去的十年中，高保真计算流体动力学（CFD）发现了在各种心血管应用中都存在高频流动不稳定性（大约100 s Hz）的情况。这些波动通常被记录为脉动速度-时间轨迹或快速傅立叶变换的功率频谱，通常来自单个点或最多几个点。最初受到其在频谱多普勒超声中使用的启发，在这里，我们展示了时频表示的最简单形式（频谱图）的实用性，它是可视化脉搏性心血管血流潜在谐波复杂性的更全面但仍直观的方法。在回顾了频谱图背后的基本理论之后，尤其是短时傅立叶变换（STFT），我们讨论了选择输入参数的方法，这些参数可以告知频谱图的外观和取舍。我们显示，使用STFT的频谱图能够突出频谱特征，并且代表了从更复杂的方法（例如连续小波变换（CWT））获得的频谱图。虽然显示的可视化属性（颜色图，滤波，平滑/插值）会影响光谱特征的醒目性，但显示的窗口属性（功能，大小，重叠）对最终的频谱图外观影响最大。使用一组脑动脉瘤CFD病例，我们表明，频谱图可以轻松揭示随时间变化的流动不稳定性的特定情况，无论是宽带，暗示间歇性湍流，窄带，暗示层流涡旋脱落或某种组合，其。