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

arXiv: https://arxiv.org/abs/2403.09758 · HTML: https://mlsanity.com/paper/2403.09758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 55 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Builds on (most cited first, 14 of 14)

- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [Multi-fidelity Bayesian Neural Networks: Algorithms and Applications](https://mlsanity.com/paper/2012.13294/) (2020)
- [Kernel Flows: from learning kernels from data into the abyss](https://mlsanity.com/paper/1808.04475/) (2018)
- [Inferring solutions of differential equations using noisy multi-fidelity data](https://mlsanity.com/paper/1607.04805/) (2016)
- [Neural-net-induced Gaussian process regression for function approximation and PDE solution](https://mlsanity.com/paper/1806.11187/) (2018)
- [Physics-Informed CoKriging: A Gaussian-Process-Regression-Based Multifidelity Method for Data-Model Convergence](https://mlsanity.com/paper/1811.09757/) (2018)
- [Deep Multi-fidelity Gaussian Processes](https://mlsanity.com/paper/1604.07484/) (2016)
- [Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI](https://mlsanity.com/paper/2302.12835/) (2023)
- [Automatic Segmentation, Feature Extraction and Comparison of Healthy and Stroke Cerebral Vasculature](https://mlsanity.com/paper/2002.11208/) (2020)
- [Uncertainty quantification of a three-dimensional in-stent restenosis model with surrogate modelling](https://mlsanity.com/paper/2111.06173/) (2021)
- [Parametric Gaussian Process Regression for Big Data](https://mlsanity.com/paper/1704.03144/) (2017)
- [Predictive and diagnosis models of stroke from hemodynamic signal monitoring](https://mlsanity.com/paper/2306.05289/) (2023)

## Abstract (arXiv)

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.