TY - JOUR T1 - The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence AU - Belhachmi , Zakaria AU - Dollé , Guillaume AU - Prud'homme , Christophe AU - Torregrossa , Murielle JO - Journal of Mathematical Study VL - 3 SP - 341 EP - 358 PY - 2019 DA - 2019/09 SN - 52 DO - http://doi.org/10.4208/jms.v52n3.19.07 UR - https://global-sci.org/intro/article_detail/jms/13302.html KW - Tomography, scattering, fluorescence, contact, non-contact. AB -

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.