Physics-Informed Graph Neural Networks to solve 1-D equations of blood flow

IF 4.9 2区 医学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computer methods and programs in biomedicine Pub Date : 2024-09-20 DOI:10.1016/j.cmpb.2024.108427
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Abstract

Background and Objective:

Computational models of hemodynamics can contribute to optimizing surgical plans, and improve our understanding of cardiovascular diseases. Recently, machine learning methods have become essential to reduce the computational cost of these models. In this study, we propose a method that integrates 1-D blood flow equations with Physics-Informed Graph Neural Networks (PIGNNs) to estimate the propagation of blood flow velocity and lumen area pulse waves along arteries.

Methods:

Our methodology involves the creation of a graph based on arterial topology, where each 1-D line represents edges and nodes in the blood flow analysis. The innovation lies in decoding the mathematical data connecting the nodes, where each node has velocity and lumen area pulse waveform outputs. The training protocol for PIGNNs involves measurement data, specifically velocity waves measured from inlet and outlet vessels and diastolic lumen area measurements from each vessel. To optimize the learning process, our approach incorporates fundamental physical principles directly into the loss function. This comprehensive training strategy not only harnesses the power of machine learning but also ensures that PIGNNs respect fundamental laws governing fluid dynamics.

Results:

The accuracy was validated in silico with different arterial networks, where PIGNNs achieved a coefficient of determination (R2) consistently above 0.99, comparable to numerical methods like the discontinuous Galerkin scheme. Moreover, with in vivo data, the prediction reached R2 values greater than 0.80, demonstrating the method’s effectiveness in predicting flow and lumen dynamics using minimal data.

Conclusions:

This study showcased the ability to calculate lumen area and blood flow rate in blood vessels within a given topology by seamlessly integrating 1-D blood flow with PIGNNs, using only blood flow velocity measurements. Moreover, this study is the first to compare the PIGNNs method with other classic Physics-Informed Neural Network (PINNs) approaches for blood flow simulation. Our findings highlight the potential to use this cost-effective and proficient tool to estimate real-time arterial pulse waves.
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用物理信息图神经网络求解一维血流方程
背景与目的:血液动力学计算模型有助于优化手术方案,并提高我们对心血管疾病的认识。最近,机器学习方法已成为降低这些模型计算成本的关键。在这项研究中,我们提出了一种将一维血流方程与物理信息图神经网络(PIGNN)相结合的方法,用于估算血流速度和管腔面积脉搏波沿动脉的传播。创新之处在于解码连接节点的数学数据,每个节点都有速度和管腔面积脉搏波形输出。PIGNNs 的训练方案涉及测量数据,特别是从入口和出口血管测量的速度波,以及从每个血管测量的舒张管腔面积。为了优化学习过程,我们的方法将基本物理原理直接纳入损失函数。这种全面的训练策略不仅利用了机器学习的力量,还确保了 PIGNNNs 遵循流体动力学的基本规律。结果:PIGNNNs 的准确性在不同的动脉网络中得到了验证,其决定系数(R2)始终高于 0.99,可与非连续加勒金方案等数值方法相媲美。结论:这项研究展示了在给定拓扑结构下,通过将一维血流与 PIGNNs 无缝整合,仅使用血流速度测量值计算血管内腔面积和血流量的能力。此外,本研究还首次将 PIGNNNs 方法与其他用于血流模拟的经典物理信息神经网络(PINNs)方法进行了比较。我们的研究结果凸显了使用这种经济高效、功能强大的工具来估算实时动脉脉搏波的潜力。
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来源期刊
Computer methods and programs in biomedicine
Computer methods and programs in biomedicine 工程技术-工程:生物医学
CiteScore
12.30
自引率
6.60%
发文量
601
审稿时长
135 days
期刊介绍: To encourage the development of formal computing methods, and their application in biomedical research and medical practice, by illustration of fundamental principles in biomedical informatics research; to stimulate basic research into application software design; to report the state of research of biomedical information processing projects; to report new computer methodologies applied in biomedical areas; the eventual distribution of demonstrable software to avoid duplication of effort; to provide a forum for discussion and improvement of existing software; to optimize contact between national organizations and regional user groups by promoting an international exchange of information on formal methods, standards and software in biomedicine. Computer Methods and Programs in Biomedicine covers computing methodology and software systems derived from computing science for implementation in all aspects of biomedical research and medical practice. It is designed to serve: biochemists; biologists; geneticists; immunologists; neuroscientists; pharmacologists; toxicologists; clinicians; epidemiologists; psychiatrists; psychologists; cardiologists; chemists; (radio)physicists; computer scientists; programmers and systems analysts; biomedical, clinical, electrical and other engineers; teachers of medical informatics and users of educational software.
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