The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence

The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence

Year:    2019

Author:    Zakaria Belhachmi, Guillaume Dollé, Christophe Prud'homme, Murielle Torregrossa

Journal of Mathematical Study, Vol. 52 (2019), Iss. 3 : pp. 341–358

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v52n3.19.07

Journal of Mathematical Study, Vol. 52 (2019), Iss. 3 : pp. 341–358

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Tomography scattering fluorescence contact non-contact.

Author Details

Zakaria Belhachmi

Guillaume Dollé

Christophe Prud'homme

Murielle Torregrossa

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