T. Nakazawa, Sohei Tasaki, Kiyohiko Nakai, Takashi Suzuki
{"title":"血管生成的多细胞模型","authors":"T. Nakazawa, Sohei Tasaki, Kiyohiko Nakai, Takashi Suzuki","doi":"10.3934/bioeng.2022004","DOIUrl":null,"url":null,"abstract":"This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.","PeriodicalId":45029,"journal":{"name":"AIMS Bioengineering","volume":"112 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Multicellular model of angiogenesis\",\"authors\":\"T. Nakazawa, Sohei Tasaki, Kiyohiko Nakai, Takashi Suzuki\",\"doi\":\"10.3934/bioeng.2022004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.\",\"PeriodicalId\":45029,\"journal\":{\"name\":\"AIMS Bioengineering\",\"volume\":\"112 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Bioengineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/bioeng.2022004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"ENGINEERING, BIOMEDICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Bioengineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/bioeng.2022004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, BIOMEDICAL","Score":null,"Total":0}
This paper presents a mathematical model governing the dynamics of a morphogenetic vascular endothelial cell (EC) during angiogenesis, and vascular growth formed by EC. Especially, we adopt a multiparticle system for modeling these cells. This model does not distinguish a tip cell from a stalk cell. A formed vessel is modeled using phase-field equation to prevent capillary expansion with time stepping in particular. Numerical simulation reveals that all cells are moving in the direction of high concentration of vascular endothelial growth factor (VEGF), and that they are mutually repellent in cases in which they are closer than some threshold.
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