Numerical Analysis of Anisotropic Mass Diffusion, Adsorption and Chemical Reaction Processes in Brain Tissues

The mechanism and influence factors of mass transfer processes inside brain tissues were analyzed, and a modified mathematical model was built to comprehensively involve the adsorption, the chemical reaction and the anisotropic diffusion inside the brain tissues. Then the model equations were solved by means of the finite volume implicit scheme. The results indicate that, in the brain tissues, the mass diffuses more slowly as the tortuosity increases but spreads faster in a certain direction with a smaller tortuosity value. Owing to the heterogeneity of the brain tissues, a phenomenon of competition effect exists during the mass diffusion process inside the brain. The presences of adsorption and chemical reaction show an inhibitory action on the procedure of diffusion. The increase of the adsorption rate leads to a greater inhibition effect on the process. According to the Michaelis-Menten kinetics, the concentration value will significantly decrease with increment of the reaction rate constant, but increase with increment of the Michaelis-Menten constant. Furthermore, compared with the action of adsorption inside the brain, the Michaelis-Menten kinetics presents a more notable inhibitory effect on the concentration distribution towards the mass transfer process inside the brain tissues.