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.