{"title":"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","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":"23 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":\"23 1\",\"pages\":\"\"},\"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}","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}
Retrieving the time-dependent blood perfusion coefficient in the thermal-wave model of bio-heat transfer
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.
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