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 & Murielle Torregrossa

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

Published online: 2019-09

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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.

  • Keywords

Tomography, scattering, fluorescence, contact, non-contact.

  • AMS Subject Headings

65N21, 65J22, 78A46

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zakaria.belhachmi@uha.fr (Zakaria Belhachmi)

guillaume.dolle@univ-reims.fr (Guillaume Dollé)

christophe.prudhomme@math.unistra.fr (Christophe Prud'homme)

m.torregrossa@unistra.fr (Murielle Torregrossa)

  • BibTex
  • RIS
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@Article{JMS-52-341, author = {Belhachmi , Zakaria and Dollé , Guillaume and Prud'homme , Christophe and Torregrossa , Murielle }, title = {The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence}, journal = {Journal of Mathematical Study}, year = {2019}, volume = {52}, number = {3}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v52n3.19.07}, url = {http://global-sci.org/intro/article_detail/jms/13302.html} }
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.

Zakaria Belhachmi, Guillaume Dollé, Christophe Prud'homme & Murielle Torregrossa. (2019). The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence. Journal of Mathematical Study. 52 (3). 341-358. doi:10.4208/jms.v52n3.19.07
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