Reconstructing cerebral hemodynamics from sparse data using Neural Operator Transformers

Cardiovascular diseases remain a major cause of mortality and disability, underscoring the need for improved analysis of brain hemodynamics. The Circle of Willis plays a crucial role in maintaining cerebral blood flow; however, conventional measurement and computational methods often lack the accuracy or speed required for real-time clinical application. We propose a novel computational framework that integrates a one-dimensional reduced-order blood flow model with two neural operator architectures: the General Neural Operator Transformer and the Variational Autoencoding Neural Operator. Synthetic data are first generated via finite-element simulations of the 1D system under a wide range of parameter and boundary-condition variations. The surrogate model learns to predict blood velocity, cross-sectional area, and pressure from sparse inputs, while the generative model provides a prior to ensure physiologically plausible parameter sampling. An inverse procedure is then employed to reconstruct full Circle of Willis hemodynamics from limited clinical-like observations, and subject-specific boundary conditions are derived from the reconstructed flow and pressure waveforms via an adaptive grid search fitting procedure. Across major vessels of the Circle of Willis, our surrogate model achieves below 1% mean relative error in velocity and area predictions while maintaining approximately 3.3% global error in reconstructing entire networks from sparse measurements. The adaptive boundary-condition estimation closely reproduces the original outlet pressures, facilitating case-specific parameter calibration. This neural-operator-based framework enables fast, accurate reconstruction of cerebral hemodynamics and boundary-condition inference from limited data, holding potential for real-time clinical integration and personalized digital-twin workflows in cerebrovascular diagnostics.