{"title":"使用 T-样条线等距计算法和晶格玻尔兹曼法的红血细胞计算模型","authors":"Yusuke Asai , Shunichi Ishida , Hironori Takeda , Gakuto Nakaie , Takuya Terahara , Yasutoshi Taniguchi , Kenji Takizawa , Yohsuke Imai","doi":"10.1016/j.jfluidstructs.2024.104081","DOIUrl":null,"url":null,"abstract":"<div><p>The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high-order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with T-splines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid–structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be <span><math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math></span> N/m, and the bending modulus is estimated to be <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup></mrow></math></span> J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.</p></div>","PeriodicalId":54834,"journal":{"name":"Journal of Fluids and Structures","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A computational model of red blood cells using an isogeometric formulation with T-splines and a lattice Boltzmann method\",\"authors\":\"Yusuke Asai , Shunichi Ishida , Hironori Takeda , Gakuto Nakaie , Takuya Terahara , Yasutoshi Taniguchi , Kenji Takizawa , Yohsuke Imai\",\"doi\":\"10.1016/j.jfluidstructs.2024.104081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high-order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with T-splines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid–structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be <span><math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></math></span> N/m, and the bending modulus is estimated to be <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>B</mi></mrow></msub><mo>=</mo><mn>4</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>19</mn></mrow></msup></mrow></math></span> J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.</p></div>\",\"PeriodicalId\":54834,\"journal\":{\"name\":\"Journal of Fluids and Structures\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Fluids and Structures\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0889974624000161\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fluids and Structures","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0889974624000161","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
A computational model of red blood cells using an isogeometric formulation with T-splines and a lattice Boltzmann method
The red blood cell (RBC) membrane is often modeled by Skalak strain energy and Helfrich bending energy functions, for which high-order representation of the membrane surface is required. We develop a numerical model of RBCs using an isogeometric discretization with T-splines. A variational formulation is applied to compute the external load on the membrane with a direct discretization of second-order parametric derivatives. For fluid–structure interaction, the isogeometric analysis is coupled with the lattice Boltzmann method via the immersed boundary method. An oblate spheroid with a reduced volume of 0.95 and zero spontaneous curvature is used for the reference configuration of RBCs. The surface shear elastic modulus is estimated to be N/m, and the bending modulus is estimated to be J by numerical tests. We demonstrate that for physiological viscosity ratio, the typical motions of the RBC in shear flow are rolling and complex swinging, but simple swinging or tank-treading appears at very high shear rates. We also show that the computed apparent viscosity of the RBC channel flow is a reasonable agreement with an empirical equation. We finally show that the maximum membrane strain of RBCs for a large channel (twice of the RBC diameter) can be larger than that for a small channel (three-quarters of the RBC diameter). This is caused by a difference in the strain distribution between the slipper and parachute shapes of RBCs in the channel flows.
期刊介绍:
The Journal of Fluids and Structures serves as a focal point and a forum for the exchange of ideas, for the many kinds of specialists and practitioners concerned with fluid–structure interactions and the dynamics of systems related thereto, in any field. One of its aims is to foster the cross–fertilization of ideas, methods and techniques in the various disciplines involved.
The journal publishes papers that present original and significant contributions on all aspects of the mechanical interactions between fluids and solids, regardless of scale.