Neurological diseases such as cancer, damage blood brain barrier and consequently cause more permeability in tissues. In general if there is damage to the brain tissues, the contrast agent used in MRI, diffuses outside the capillaries and the MRI picture brightness changes. The purpose of this paper is to show the effects of different parameters on the contrast agent diffusion in the brain capillary. In this study, the lattice Boltzmann method with multi-relaxation time (MRT) is used to simulate the flow in the capillary and porous media around it. The results show that the porosity in extravascular tissues (it shows the tissue damage), the kind of contrast agent and capillaries curvature have impact on the contrast agent diffusion in the tissues. The presented results show the effects of curvature on shear stress and thus on mass transfer in the capillary. It should be noted that the presented results have been evaluated by previous statistical and analytical results for flow in the damaged brain capillary with different permeability. It has been shown that the lattice Boltzmann method is able to simulate the complex problems especially in porous media.