Hybrid physics-based and data-driven modeling of vascular bifurcation pressure differences

Reduced-order models allow for the simulation of blood flow in patient-specific vasculatures. They offer a significant reduction in computational cost and wait time compared to traditional computational fluid dynamics models. Unfortunately, due to the simplifications made in their formulations, reduced-order models can suffer from significantly reduced accuracy. One common simplifying assumption is that of continuity of static or total pressure over vascular bifurcations. In many cases, this assumption has been shown to introduce significant errors in pressure predictions. We propose a model to account for this pressure difference, with the ultimate goal of increasing the accuracy of cardiovascular reduced-order models. Our model successfully uses a structure common in existing reduced-order models 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 find that our model makes significantly more accurate predictions than other models for approximating bifurcation pressure losses commonly used in the reduced-order cardiovascular modeling community. We also compare the efficacy of different machine-learning techniques and observe that a neural network performs most robustly. Additionally, we consider two different model modalities: one in which the model is fit using both steady and transient flows, and one in which it is optimized for performance in transient flows. We discuss the trade-off between the physical interpretability associated with the first option and the improved accuracy in transient flows associated with the latter option. We also demonstrate the model's ability to generalize by testing it on a combined dataset containing two different bifurcation types. This work marks a step towards improving the accuracy of cardiovascular reduced-order models, thereby increasing their utility for cardiovascular flow modeling.