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

Communications in Applied and Industrial Mathematics Pub Date : 2019-01-01 DOI:10.2478/caim-2019-0006

Sara Garbarino, G. Caviglia

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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。

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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.

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来源期刊

Communications in Applied and Industrial Mathematics Mathematics-Applied Mathematics

CiteScore

1.30

自引率

0.00%

发文量

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 Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments.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.