{"title":"分数阶粘弹性血管网络的一维血流动力学模型","authors":"Ruslan Yanbarisov, Timur Gamilov","doi":"10.1515/rnam-2023-0024","DOIUrl":null,"url":null,"abstract":"Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"213 1","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity\",\"authors\":\"Ruslan Yanbarisov, Timur Gamilov\",\"doi\":\"10.1515/rnam-2023-0024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.\",\"PeriodicalId\":49585,\"journal\":{\"name\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"volume\":\"213 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Numerical Analysis and Mathematical Modelling\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/rnam-2023-0024\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Numerical Analysis and Mathematical Modelling","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rnam-2023-0024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity
Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.
期刊介绍:
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.
Topics:
-numerical analysis-
numerical linear algebra-
finite element methods for PDEs-
iterative methods-
Monte-Carlo methods-
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.