{"title":"红细胞在剪切流动中飞盘运动的理论研究","authors":"T. Mignon, S. Mendez","doi":"10.1051/MMNP/2021014","DOIUrl":null,"url":null,"abstract":"The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.","PeriodicalId":18285,"journal":{"name":"Mathematical Modelling of Natural Phenomena","volume":" ","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2021-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A theoretical investigation of the frisbee motion of red blood cells in shear flow\",\"authors\":\"T. Mignon, S. Mendez\",\"doi\":\"10.1051/MMNP/2021014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.\",\"PeriodicalId\":18285,\"journal\":{\"name\":\"Mathematical Modelling of Natural Phenomena\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2021-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling of Natural Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/MMNP/2021014\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICAL & COMPUTATIONAL BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling of Natural Phenomena","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/MMNP/2021014","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICAL & COMPUTATIONAL BIOLOGY","Score":null,"Total":0}
A theoretical investigation of the frisbee motion of red blood cells in shear flow
The dynamics of a single red blood cell in shear flow is a fluid–structure interaction problem that yields a tremendous richness of behaviors, as a function of the parameters of the problem. A low shear rates, the deformations of the red blood cell remain small and low-order models have been developed, predicting the orientation of the cell and the membrane circulation along time. They reproduce the dynamics observed in experiments and in simulations, but they do not simplify the problem enough to enable simple interpretations of the phenomena. In a process of exploring the red blood cell dynamics at low shear rates, an existing model constituted of 5 nonlinear ordinary differential equations is rewritten using quaternions to parametrize the rotations of the red blood cell. Techniques from algebraic geometry are then used to determine the steady-state solutions of the problems. These solutions are relevant to a particular regime where the red blood cell reaches a constant inclination angle, with its membrane rotating around it, and referred to as frisbee motion. Comparing the numerical solutions of the model to the steady-state solutions allows a better understanding of the transition between the most emblematic motions of red blood cells, flipping and tank-treading.
期刊介绍:
The Mathematical Modelling of Natural Phenomena (MMNP) is an international research journal, which publishes top-level original and review papers, short communications and proceedings on mathematical modelling in biology, medicine, chemistry, physics, and other areas. The scope of the journal is devoted to mathematical modelling with sufficiently advanced model, and the works studying mainly the existence and stability of stationary points of ODE systems are not considered. The scope of the journal also includes applied mathematics and mathematical analysis in the context of its applications to the real world problems. The journal is essentially functioning on the basis of topical issues representing active areas of research. Each topical issue has its own editorial board. The authors are invited to submit papers to the announced issues or to suggest new issues.
Journal publishes research articles and reviews within the whole field of mathematical modelling, and it will continue to provide information on the latest trends and developments in this ever-expanding subject.