In ultra filtration processes the deposition of organic or inorganic substances leads to fouling on or in a membrane and therefore to a loss in productivity and increase in maintenance and operating costs. This prevents a wider application of this promising technology for water treatment. There are still models missing for the description of the fouling process which describe morphological changes of the porosity in the membrane as well as the forming of a layer on the membrane. Furthermore, at the moment there are no measurements available from the filtration process in the porous media. Imaging techniques such as magnetic resonance imaging (MRI) and computer tomography (CT) are limited in terms of spatial resolution and required image contrast. The main objective of this pro-posal is to close this gap by developing a fundamentally new method, the model- and simulation-based flow-MRI (CFD-MRI). For this purpose, a flow model is used to exclude unphysical meas-urement results, to eliminate measurement artifacts and to increase the spatial resolution, which finally leads to a more accurate description of flow and biofilm morphology on the membrane walls.The CFD-MRI is realized by formulating and efficiently solving a topology optimization problem, which minimizes the measurement to simulation result error. For it, gradient-based algorithms are used those kernel is a further development of the recently discovered Adjoint Lattice Boltzmann Methods (ALBM). Advantages of this approach are on the one hand, the underlying mesoscopic modeling of the flow, so that the particle distributions can be directly calculated and correlated with the measured MRI values, and, on the other hand, the efficiency of the parallel algorithm. Finally, the method is applied to the filtration process, which enables to compute the distribution of the per-meability and the fluid flow dynamics inside the membrane. At the end of the project, a characteri-zation tool for fluid flow dynamics in complex geometries is obtained, which also promises to pro-vide new findings for other applications.