The Direct Robin Boundary Value Parabolic System of Time-Resolved Diffuse Optical Tomography with Fluorescence (Journal of Mathematical Study, 2019)
We consider a system of parabolic PDEs with measure data modelling aproblem of the time resolved diffuse optical tomography with a fluorescence term andRobin boundary conditions. We focus on the direct problem where the quantity ofinterest is the density of photons in the diffusion equations and which constitutes amajor step to solve the inverse problem of identifiability and reconstruction of diffusion, absorption and concentration of the fluorescent markers. We study the problemunder a variational form and its discretization with finite element method and we givesome numerical simulation results for verification purpose as well as simulations withreal data from a tomograph.