Physics-Informed Learning of Microvascular Flow Models using Graph Neural Networks

TL;DR

This work tackles the computational bottleneck of simulating microvascular blood flow in highly topologically complex networks. It introduces physics-informed Graph Neural Network surrogates trained on large sets of synthetic capillary graphs to predict nodal pressures, edge velocities, and, in nonlinear models, hematocrit, while enforcing mass conservation and constitutive laws. The authors develop an Encoder–Processor–Decoder GNN with message passing, trained against both data and physics residuals, and demonstrate strong generalization to anatomically realistic mouse cortex networks with real-time inference. The two-tier approach — fast synthetic network generation for scalable training and anatomically accurate networks for rigorous validation — shows potential for real-time digital-twin applications in vascular biomechanics and biomedical engineering.

Abstract

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a novel deep learning-based reduced-order modeling strategy, leveraging Graph Neural Networks (GNNs) trained on synthetic microvascular graphs to approximate hemodynamic quantities on anatomically realistic domains. Our method combines algorithms for synthetic vascular generation with a physics-informed training procedure that integrates graph topological information and local flow dynamics. To ensure the physical reliability of the learned surrogates, we incorporate a physics-informed loss functional derived from the governing equations, allowing enforcement of mass conservation and rheological constraints. The resulting GNN architecture demonstrates robust generalization capabilities across diverse network configurations. The GNN formulation is validated on benchmark problems with linear and nonlinear rheology, showing accurate pressure and velocity field reconstruction with substantial computational gains over full-order solvers. The methodology showcases significant generalization capabilities with respect to vascular complexity, as highlighted by tests on data from the mouse cerebral cortex. This work establishes a new class of graph-based surrogate models for microvascular flow, grounded in physical laws and equipped with inductive biases that mirror mass conservation and rheological models, opening new directions for real-time inference in vascular modeling and biomedical applications.

Figures (8)

• Figure 1: GNN complete architecture, consisting of an encoder, a processor, and a decoder.
• Figure 2: Message propagation and aggregation with edge features update.
• Figure 3: Example of an anatomically guided synthetic arterial tree generated via iCNS, showing the bifurcation optimization process in the CCO framework for each segment addition, adapted from linninger1linninger2.
• Figure 4: Visual comparison of pressure, velocity and hematocrit solutions (left, center, right panels, respectively) for GNN model 4 (top), compared with the respective high-fidelity approximations (bottom). In this test case, the $L^{2}$ pressure, velocity and hematocrit GNN errors are respectively $2.55\%$, $16.02\%$ and $4.14\%$.
• Figure 5: Pressure (top-left) and velocity (top-right) $L^{2}$ relative error comparison between the different models. Physics-based residuals of the constitutive law (bottom-left) and the mass balance law (bottom-right). The gray band highlights the interval of number of inlet nodes where the training data are located. These data show the ability of the model to generalize well beyond the vascular complexity of the training dataset.