Hybrid Physics-Based and Data-Driven Modeling of Vascular Bifurcation Pressure Differences

TL;DR

This work addresses inaccuracies in reduced-order cardiovascular models at vascular bifurcations by introducing a physics-guided, data-driven Resistor-Resistor-Inductor (RRI) junction that predicts the pressure difference between bifurcation inlet and outlet. The ΔP prediction is implemented as $\Delta P_{RRI} = R_{lin}(\mathcal{G}) Q + R_{quad}(\mathcal{G}) Q^2 + L(\mathcal{G}) \dot{Q}$, with geometry-driven coefficients learned from bifurcation geometry $\mathcal{G}$ using ML. The authors generate synthetic bifurcation geometries across three cohorts (isoradial, pulmonary, brachiocephalic) and train multiple regression models to predict $R_{lin}$, $R_{quad}$, and $L$ from geometry, evaluating steady and transient flows; results show steady RR with ML coefficients outperforms the Unified0D+ model, and transient predictions benefit from including the inductive term, with NN- or GPR-based predictors delivering the best accuracy. The framework integrates easily into existing ROM solvers, enables interpretable coefficient estimates, and demonstrates a path toward more accurate, real-time cardiovascular simulations by leveraging 3D CFD data to inform ROM corrections, while outlining future work to extend to more complex junctions via graph neural networks and broader datasets.

Abstract

Reduced-order models (ROMs) allow for the simulation of blood flow in patient-specific vasculatures without the high computational cost and wait time associated with traditional computational fluid dynamics (CFD) models. Unfortunately, due to the simplifications made in their formulations, ROMs can suffer from significantly reduced accuracy. One common simplifying assumption is the continuity of static or total pressure over vascular junctions. In many cases, this assumption has been shown to introduce significant error. We propose a model to account for this pressure difference, with the ultimate goal of increasing the accuracy of cardiovascular ROMs. Our model successfully uses a structure common in existing ROMs in conjunction with machine-learning techniques to predict the pressure difference over a vascular bifurcation. We analyze the performance of our model on steady and transient flows, testing it on three bifurcation cohorts representing three different bifurcation geometric types. We also compare the efficacy of different machine-learning techniques and two different model modalities.

Figures (11)

• Figure 1: 3D vascular bifurcation (left) and its representation in a ROM (center) including the proposed RRI bifurcation block, featuring a linear resistor, quadratic resistor, and inductor (right).
• Figure 2: Geometric parameters characterizing a bifurcation and used to predict the coefficients $R_{\text{quad}}$, $R_{\text{lin}}$, and $L$ which in turn govern the relationship between $Q$, $Q^2$, and $\dot{Q}$ and $\Delta P$ in the RRI model.
• Figure 3: Overview of the computation of a pressure difference over a vascular junction using the RRI model.
• Figure 4: Examples of pulmonary and brachiocephalic bifurcations in their surrounding vasculatures (top) and nominal idealized bifurcations from the isoradial, pulmonary, and brachiocephalic cohorts (bottom).
• Figure 5: Overview of data generation pipeline. First, we generated a bifurcation geometry based on a set of geometric features. Then, two steady simulations were run from which the coefficients $R_{\text{lin}}$ and $R_{\text{quad}}$ are determined by solving a simple system of equations containing the steady simulation results. Finally, a transient simulation was run from which the coefficient $L$ is determined using least squares. In the TO method, all three coefficients, $R_{\text{lin}}$, $R_{\text{quad}}$, and $L$ were determined from the transient simulation.