{"title":"Physics-Informed Graph Neural Networks to solve 1-D equations of blood flow","authors":"","doi":"10.1016/j.cmpb.2024.108427","DOIUrl":null,"url":null,"abstract":"<div><h3>Background and Objective:</h3><div>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.</div></div><div><h3>Methods:</h3><div>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.</div></div><div><h3>Results:</h3><div>The accuracy was validated <em>in silico</em> with different arterial networks, where PIGNNs achieved a coefficient of determination (<span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>) consistently above 0.99, comparable to numerical methods like the discontinuous Galerkin scheme. Moreover, with <em>in vivo</em> data, the prediction reached <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> values greater than 0.80, demonstrating the method’s effectiveness in predicting flow and lumen dynamics using minimal data.</div></div><div><h3>Conclusions:</h3><div>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.</div></div>","PeriodicalId":10624,"journal":{"name":"Computer methods and programs in biomedicine","volume":null,"pages":null},"PeriodicalIF":4.9000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer methods and programs in biomedicine","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0169260724004206","RegionNum":2,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
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 () consistently above 0.99, comparable to numerical methods like the discontinuous Galerkin scheme. Moreover, with in vivo data, the prediction reached 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.
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.