Volume 52, Issue 3
The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence

Zakaria Belhachmi ,  Guillaume Dollé ,  Christophe Prud'homme and Murielle Torregrossa


J. Math. Study, 52 (2019), pp. 341-358.

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  • Abstract

We consider a system of parabolic PDEs with measure data modelling a problem of the time resolved diffuse optical tomography with a fluorescence term and Robin boundary conditions. We focus on the direct problem where the quantity of interest is the density of photons in the diffusion equations and which constitutes a major step to solve the inverse problem of identifiability and reconstruction of diffusion, absorption and concentration of the fluorescent markers. We study the problem under a variational form and its discretization with finite element method and we give some numerical simulation results for verification purpose as well as simulations with real data from a tomograph.

  • History

Published online: 2019-09

  • AMS Subject Headings

65N21, 65J22, 78A46

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