Determination of a space-dependent source in the thermal-wave model of bio-heat transfer
Determination of a space-dependent source in the thermal-wave model of bio-heat transfer
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DOI：
10.1016/j.camwa.2022.10.026
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
M. Alosaimi;D. Lesnic
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文献类型：
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作者：
M. Alosaimi;D. Lesnic
我们考虑线性但不适定的反问题，包括从最终时间或时间平均温度测量的生物热传递的热波模型中找到未知的空间相关源。与以往的抛物型生物传热模型的研究不同，本文研究的是生物医学工程中更复杂、更实用的双曲型模型。首先，建立了线性源反问题的唯一可解性。然后，反问题被改写为变分问题，允许最小二乘目标泛函的梯度导出。后者的问题迭代求解共轭梯度法结合差异原则。最后，反演算法进行了测试，确定一维和二维空间相关的源。
We consider linear but ill-posed inverse problems consisting of finding the unknown space-dependent source in the thermal-wave model of bio-heat transfer from final-time or time-average temperature measurements. In contrast to the previous research on parabolic bio-heat transfer models, this work concerns a more involved and practical hyperbolic model used in biomedical engineering. First, the unique solvability of the linear inverse source problems is established. Then, the inverse problems are recast as variational problems, allowing the gradients of the least-squares objective functionals to be derived. These latter problems are solved iteratively using the conjugate gradient method combined with the discrepancy principle. Finally, the inversion algorithm is tested on identifying one- and two-dimensional space-dependent sources.