Reconstructing Blood Flow in Data-Poor Regimes: A Vasculature Network Kernel for Gaussian Process Regression

Blood flow reconstruction in the vasculature is important for many clinical applications. However, in clinical settings, the available data are often quite limited. For instance, Transcranial Doppler ultrasound (TCD) is a noninvasive clinical tool that is commonly used in the clinical settings to measure blood velocity waveform at several locations on brain's vasculature. This amount of data is grossly insufficient for training machine learning surrogate models, such as deep neural networks or Gaussian process regression. In this work, we propose a Gaussian process regression approach based on physics-informed kernels, enabling near-real-time reconstruction of blood flow in data-poor regimes. We introduce a novel methodology to reconstruct the kernel within the vascular network, which is a non-Euclidean space. The proposed kernel encodes both spatiotemporal and vessel-to-vessel correlations, thus enabling blood flow reconstruction in vessels that lack direct measurements. We demonstrate that any prediction made with the proposed kernel satisfies the conservation of mass principle. The kernel is constructed by running stochastic one-dimensional blood flow simulations, where the stochasticity captures the epistemic uncertainties, such as lack of knowledge about boundary conditions and uncertainties in vasculature geometries. We demonstrate the performance of the model on three test cases, namely, a simple Y-shaped bifurcation, abdominal aorta, and the Circle of Willis in the brain.

Physics-informed neural networks for improving cerebral hemodynamics predictions

Determining brain hemodynamics plays a critical role in the diagnosis and treatment of various cerebrovascular diseases. In this work, we put forth a physics-informed deep learning framework that augments sparse clinical measurements with fast computational fluid dynamics (CFD) simulations to generate physically consistent and high spatiotemporal resolution of brain hemodynamic parameters. Transcranial Doppler (TCD) ultrasound is one of the most common techniques in the current clinical workflow that enables noninvasive and instantaneous evaluation of blood flow velocity within the cerebral arteries. However, it is spatially limited to only a handful of locations across the cerebrovasculature due to the constrained accessibility through the skull's acoustic windows. Our deep learning framework employs in-vivo real-time TCD velocity measurements at several locations in the brain and the baseline vessel cross-sectional areas acquired from 3D angiography images, and provides high-resolution maps of velocity, area, and pressure in the entire vasculature. We validated the predictions of our model against in-vivo velocity measurements obtained via 4D flow MRI scans. We then showcased the clinical significance of this technique in diagnosing the cerebral vasospasm (CVS) by successfully predicting the changes in vasospastic local vessel diameters based on corresponding sparse velocities measurements. The key finding here is that the combined effects of uncertainties in outlet boundary condition subscription and modeling physics deficiencies render the conventional purely physics-based computational models unsuccessful in recovering accurate brain hemodynamics. Nonetheless, fusing these models with clinical measurements through a data-driven approach ameliorates predictions of brain hemodynamic variables.