{"title":"肿瘤球体几乎具有周期性的营养和抑制剂供应","authors":"H. Díaz-Marín, O. Osuna","doi":"10.1002/zamm.202200228","DOIUrl":null,"url":null,"abstract":"We describe the time‐evolution of a tumor spheroid without necrotic core using the quasi‐stationary reaction–diffusion approach. We assume that inhibitor and nutrient supplies are time‐dependent and oscillating by incorporating continuous almost periodic functions in the model. The functional form of the intensity of the mitosis is supposed to be the product of two linear functions depending on the nutrient concentration σ and of the inhibitor concentration, β, respectively. Under some mild conditions, we give criteria predicting two possible global asymptotic limits: either the tumor oscillates converging towards a stable global almost periodic solution or the tumor shrinks as time increases.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Tumor spheroid with almost periodic nutrient and inhibitor supplies\",\"authors\":\"H. Díaz-Marín, O. Osuna\",\"doi\":\"10.1002/zamm.202200228\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe the time‐evolution of a tumor spheroid without necrotic core using the quasi‐stationary reaction–diffusion approach. We assume that inhibitor and nutrient supplies are time‐dependent and oscillating by incorporating continuous almost periodic functions in the model. The functional form of the intensity of the mitosis is supposed to be the product of two linear functions depending on the nutrient concentration σ and of the inhibitor concentration, β, respectively. Under some mild conditions, we give criteria predicting two possible global asymptotic limits: either the tumor oscillates converging towards a stable global almost periodic solution or the tumor shrinks as time increases.\",\"PeriodicalId\":23924,\"journal\":{\"name\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/zamm.202200228\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202200228","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Tumor spheroid with almost periodic nutrient and inhibitor supplies
We describe the time‐evolution of a tumor spheroid without necrotic core using the quasi‐stationary reaction–diffusion approach. We assume that inhibitor and nutrient supplies are time‐dependent and oscillating by incorporating continuous almost periodic functions in the model. The functional form of the intensity of the mitosis is supposed to be the product of two linear functions depending on the nutrient concentration σ and of the inhibitor concentration, β, respectively. Under some mild conditions, we give criteria predicting two possible global asymptotic limits: either the tumor oscillates converging towards a stable global almost periodic solution or the tumor shrinks as time increases.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.