{"title":"抗血管生成治疗与放疗的集值分析","authors":"Amine Moustafid","doi":"10.53391/mmnsa.2022.015","DOIUrl":null,"url":null,"abstract":"The aim of the paper is to study a cancer model based on anti-angiogenic therapy and radiotherapy. A set-valued analysis is carried out to control the tumor and carrying capacity of the vasculature, so in order to reverse tumor growth and augment tumor repair. The viability technique is used on an augmented model to solve the control problem. Obtained control is a selection of set-valued map of regulation and reduces tumor volume to around zero. A numerical simulation scheme with graphical representations and biological interpretations are given.","PeriodicalId":210715,"journal":{"name":"Mathematical Modelling and Numerical Simulation with Applications","volume":"60 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Set-valued analysis of anti-angiogenic therapy and radiotherapy\",\"authors\":\"Amine Moustafid\",\"doi\":\"10.53391/mmnsa.2022.015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of the paper is to study a cancer model based on anti-angiogenic therapy and radiotherapy. A set-valued analysis is carried out to control the tumor and carrying capacity of the vasculature, so in order to reverse tumor growth and augment tumor repair. The viability technique is used on an augmented model to solve the control problem. Obtained control is a selection of set-valued map of regulation and reduces tumor volume to around zero. A numerical simulation scheme with graphical representations and biological interpretations are given.\",\"PeriodicalId\":210715,\"journal\":{\"name\":\"Mathematical Modelling and Numerical Simulation with Applications\",\"volume\":\"60 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-09-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling and Numerical Simulation with Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.53391/mmnsa.2022.015\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Numerical Simulation with Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53391/mmnsa.2022.015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Set-valued analysis of anti-angiogenic therapy and radiotherapy
The aim of the paper is to study a cancer model based on anti-angiogenic therapy and radiotherapy. A set-valued analysis is carried out to control the tumor and carrying capacity of the vasculature, so in order to reverse tumor growth and augment tumor repair. The viability technique is used on an augmented model to solve the control problem. Obtained control is a selection of set-valued map of regulation and reduces tumor volume to around zero. A numerical simulation scheme with graphical representations and biological interpretations are given.
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