Fang, Yan-Long;
Lesnic, Daniel;
Alosaimi, Moataz;
(2023)
Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion.
Inverse Problems
, 39
(6)
, Article 065008. 10.1088/1361-6420/acca42.
Preview |
Text
Paper446.pdf - Published Version Download (639kB) | Preview |
Abstract
Knowledge of the properties of biological tissues is essential in monitoring any abnormalities that may be forming and have a major impact on organs malfunctioning. Therefore, these disorders must be detected and treated early to save lives and improve the general health. Within the framework of thermal therapies, e.g. hyperthermia or cryoablation, the knowledge of the tissue temperature and of the blood perfusion rate are of utmost importance. Therefore, motivated by such a significant biomedical application, this paper investigates, for the first time, the uniqueness and stable reconstruction of the space-dependent (heterogeneous) perfusion coefficient in the thermal-wave hyperbolic model of bio-heat transfer from Cauchy boundary data using the powerful technique of Carleman estimates. Additional novelties consist in the consideration of Robin boundary conditions, as well as developing a mathematical analysis that leads to stronger stability estimates valid over a shorter time interval than usually reported in the literature of coefficient identification problems for hyperbolic partial differential equations. Numerically, the inverse coefficient problem is recast as a nonlinear least-squares minimization that is solved using the conjugate gradient method (CGM). Both exact and noisy data are inverted. To achieve stability, the CGM is stopped according to the discrepancy principle. Numerical results for a physical example are presented and discussed, showing the convergence, accuracy and stability of the inversion procedure.
| Type: | Article |
|---|---|
| Title: | Inverse problems of damped wave equations with Robin boundary conditions: an application to blood perfusion |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/1361-6420/acca42 |
| Publisher version: | http://doi.org/10.1088/1361-6420/acca42 |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10181220 |
Archive Staff Only
 |
View Item |
