An inverse problem for equations of cerebral oxygen transport

• Published in: Applied mathematics and computation 2021-08, Vol.402, p.126154, Article 126154
• Main Authors: Kovtanyuk, Andrey, Chebotarev, Alexander, Turova, Varvara, Sidorenko, Irina, Lampe, Renée
• Format: Article
• Language: English
• Subjects: Cerebral oxygen transport; Inverse problem; Non-local solvability; Nonlinear boundary-value problem
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2021.126154

•An inverse problem for the continuum steady-state model of cerebral oxygen transport is studied.•The existence theorem is proved without assumptions of smallness.•The conditions for the uniqueness of the solution are established.•A numerical algorithm based on the Tikhonov regularization method is constructed and its convergence is shown by a numerical example. A continuum steady-state model of cerebral oxygen transport is considered. It consists of two semilinear elliptic equations describing the distributions of blood and tissue oxygen concentrations. The inverse problem is to find unknown intensities of the sources of the equation for the blood oxygen transport. As conditions of overdetermination, the average values of the blood oxygen concentration in some neighborhoods of the sources, are taken. In addition, the reconstruction of the blood and tissue oxygen concentrations are also required. The existence theorem is proved without assumptions of smallness. The conditions for the uniqueness of the solution are established. A numerical algorithm based on the Tikhonov regularization method is constructed and its convergence is shown by a numerical example.