Retrieving the time-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer

IF 1.5 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
M. Alosaimi, D. Lesnic
{"title":"Retrieving the time-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer","authors":"M. Alosaimi, D. Lesnic","doi":"10.1108/ec-01-2024-0013","DOIUrl":null,"url":null,"abstract":"<h3>Purpose</h3>\n<p>In order to include the non-negligible lag relaxation time feature that is characteristic of heat transfer in biological bodies, the classical Fourier's law of heat conduction has to be generalized as the Maxwell–Cattaneo law resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the unknown time-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from (non-intrusive) measurements of the temperature on an accessible sub-portion of the boundary that may be taken with an infrared scanner.</p><!--/ Abstract__block -->\n<h3>Design/methodology/approach</h3>\n<p>The nonlinear and ill-posed problem is reformulated as a nonlinear minimization problem of a Tikhonov regularization functional subject to lower and upper simple bounds on the unknown coefficient. For the numerical discretization, an unconditionally stable direct solver based on the Crank–Nicolson finite-difference scheme is developed. The Tikhonov regularization functional is minimized iteratively by the built-in routine <em>lsqnonlin</em> from the MATLAB optimization toolbox. Numerical results for a benchmark test example are presented and thoroughly discussed, shedding light on the performance and effectiveness of the proposed methodology.</p><!--/ Abstract__block -->\n<h3>Findings</h3>\n<p>The inverse problem of obtaining the time-dependent blood perfusion coefficient and the temperature in the thermal-wave model of bio-heat transfer from extra boundary temperature measurement has been solved. In particular, the uniqueness of the solution to this inverse problem has been established. Furthermore, our proposed computational method demonstrated successful attainment of the perfusion coefficient and temperature, even when dealing with noisy data.</p><!--/ Abstract__block -->\n<h3>Originality/value</h3>\n<p>The originalities of the present paper are to account for such a more representative thermal-wave model of heat transfer in biological bodies and to investigate the possibility of determining its time-dependent blood perfusion coefficient from non-intrusive boundary temperature measurements.</p><!--/ Abstract__block -->","PeriodicalId":50522,"journal":{"name":"Engineering Computations","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Computations","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1108/ec-01-2024-0013","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0

Abstract

Purpose

In order to include the non-negligible lag relaxation time feature that is characteristic of heat transfer in biological bodies, the classical Fourier's law of heat conduction has to be generalized as the Maxwell–Cattaneo law resulting in the thermal-wave model of bio-heat transfer. The purpose of the paper is to retrieve the unknown time-dependent blood perfusion coefficient in such a thermal-wave model of bio-heat transfer from (non-intrusive) measurements of the temperature on an accessible sub-portion of the boundary that may be taken with an infrared scanner.

Design/methodology/approach

The nonlinear and ill-posed problem is reformulated as a nonlinear minimization problem of a Tikhonov regularization functional subject to lower and upper simple bounds on the unknown coefficient. For the numerical discretization, an unconditionally stable direct solver based on the Crank–Nicolson finite-difference scheme is developed. The Tikhonov regularization functional is minimized iteratively by the built-in routine lsqnonlin from the MATLAB optimization toolbox. Numerical results for a benchmark test example are presented and thoroughly discussed, shedding light on the performance and effectiveness of the proposed methodology.

Findings

The inverse problem of obtaining the time-dependent blood perfusion coefficient and the temperature in the thermal-wave model of bio-heat transfer from extra boundary temperature measurement has been solved. In particular, the uniqueness of the solution to this inverse problem has been established. Furthermore, our proposed computational method demonstrated successful attainment of the perfusion coefficient and temperature, even when dealing with noisy data.

Originality/value

The originalities of the present paper are to account for such a more representative thermal-wave model of heat transfer in biological bodies and to investigate the possibility of determining its time-dependent blood perfusion coefficient from non-intrusive boundary temperature measurements.

在生物传热的热波模型中检索随时间变化的血液灌注系数
目的 为了包括生物体内热传导所特有的不可忽略的滞后弛豫时间特征,必须将经典的傅里叶热传导定律概括为麦克斯韦-卡塔尼奥定律,从而形成生物热传导的热波模型。本文的目的是通过红外扫描仪(非侵入式)测量可接近的边界子部分的温度,在这种生物热传导的热波模型中检索未知的随时间变化的血液灌注系数。设计/方法/途径将非线性问题重新表述为 Tikhonov 正则化函数的非线性最小化问题,该函数受制于未知系数的简单下限和上限。在数值离散化方面,开发了基于 Crank-Nicolson 有限差分方案的无条件稳定直接求解器。Tikhonov 正则化函数通过 MATLAB 优化工具箱中的内置例程 lsqnonlin 进行迭代最小化。研究结果解决了从额外的边界温度测量中获取随时间变化的血液灌注系数和生物传热热波模型中温度的逆问题。特别是,该逆问题解的唯一性已经确定。此外,我们提出的计算方法表明,即使在处理噪声数据时,也能成功获得血液灌流系数和温度。 原创性/价值本文的原创性在于解释了生物体中热传导的这种更具代表性的热波模型,并研究了从非侵入式边界温度测量中确定随时间变化的血液灌流系数的可能性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Engineering Computations
Engineering Computations 工程技术-工程:综合
CiteScore
3.40
自引率
6.20%
发文量
61
审稿时长
5 months
期刊介绍: The journal presents its readers with broad coverage across all branches of engineering and science of the latest development and application of new solution algorithms, innovative numerical methods and/or solution techniques directed at the utilization of computational methods in engineering analysis, engineering design and practice. For more information visit: http://www.emeraldgrouppublishing.com/ec.htm
×
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