Performance of Fourier-based activation function in physics-informed neural networks for patient-specific cardiovascular flows.

BACKGROUND AND OBJECTIVES: Physics-informed neural networks (PINNs) can be used to inversely model complex physical systems by encoding the governing partial differential equations and training data into the neural network. However, neural networks are known to be biased towards learning less complex functions, called spectral bias. This has important implications in modeling cardiovascular flows, where spatial frequencies can vary substantially across anatomies and pathologies (e.g., aneurysms or stenoses). Recent evidence suggests that Fourier-based activation functions have desirable properties, and can potentially reduce spectral bias; however, the performance and adequacy of such Fourier activation functions have not yet been evaluated in patient-specific cardiovascular flow applications. METHODS: The performance of sine activation function was evaluated against tanh and swish activation functions in a 1D advection-diffusion problem, an eccentric 2D stenosis model (Re=5000), and a patient-specific 3D aortic model (Re=823) under pulsatile flow conditions. CFD simulations were performed at high spatio-temporal resolution and data points were extracted for training the neural network. The number of training data points were normalized by L/D. The performance of the PINNs framework was evaluated with increasing number of training data points and across all three activation functions. RESULTS: Our results demonstrate that sine activation function presents desirable characteristics, such as monotonic reduction in errors, relatively faster convergence, and accurate eigen spectra at higher modes, compared to tanh and swish activation functions. Interestingly, for all activation functions, the domain-averaged errors tended to asymptote at ≈15-20% despite substantial increase in training point density. For 2D eccentric stenosis, errors asymptoted at a sensor point density of 40L/D. For 3D patient-specific aorta, this asymptote was achieved at 180L/D for all three activation functions with an error of ≈15% although sine activation function demonstrated relatively faster convergence. CONCLUSIONS: We have demonstrated that Fourier-based activation functions have higher performance in terms of accuracy and convergence properties for cardiovascular flow applications; however, inherent challenges of neural networks (e.g., spectral bias) can limit the accuracy to ≈15% under physiological, 3D patient-specific blood flow conditions.

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.

Undetected common variable immune deficiency in a young adult of Pakistani descent.

Common variable immune deficiency (CVID) is a syndrome which is due to deficiency of humoral immune response resulting in increased susceptibility to infections We report a case of CVID in a 24-year-old male whopresented with a history of recurrent pneumonias.