多元正则牛顿法与Levenberg-Marquardt法:动力学框架下肿瘤缺氧合成数据的比较

IF 0.3 Q4 MATHEMATICS
Sara Garbarino, G. Caviglia
{"title":"多元正则牛顿法与Levenberg-Marquardt法:动力学框架下肿瘤缺氧合成数据的比较","authors":"Sara Garbarino, G. Caviglia","doi":"10.2478/caim-2019-0006","DOIUrl":null,"url":null,"abstract":"Abstract In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multivariate Regularized Newton and Levenberg-Marquardt methods: a comparison on synthetic data of tumor hypoxia in a kinetic framework\",\"authors\":\"Sara Garbarino, G. Caviglia\",\"doi\":\"10.2478/caim-2019-0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.\",\"PeriodicalId\":37903,\"journal\":{\"name\":\"Communications in Applied and Industrial Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2478/caim-2019-0006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/caim-2019-0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

摘要本文提出了一种新的算法来优化描述肿瘤缺氧的分区问题的参数。该方法基于多元牛顿方法,具有Tikhonov正则化,可以很容易地应用于具有不同统计分布的数据。本文模拟了[18F]−氟咪唑正电子发射断层扫描颈部肿瘤缺氧动态数据,并采用双室室模型描述了肿瘤内示踪剂的流动。我们通过多元正则牛顿方法对模型的参数进行优化,并与标准Levenberg-Marquardt方法得到的结果进行验证。该算法在保留数据统计分布的同时,返回更接近真实值的参数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Multivariate Regularized Newton and Levenberg-Marquardt methods: a comparison on synthetic data of tumor hypoxia in a kinetic framework
Abstract In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
1.30
自引率
0.00%
发文量
3
审稿时长
16 weeks
期刊介绍: Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信