Numerical Investigation Of Mass Transfer In Brain Tissues

Brain tissue is a kind of biological porous media.From the standpoing of energy and mass transfer,the realization of the advanced capabilities of the brain is based on these transfer processes which are efficiently going on within the brain tissues.The studies on the mass transfer and clearance phenomena in brain tissues are of great importance to the decipherment of the mechanism of advanced functions of the brain,to the diagnosis and treatment of encephalopathy,and to the development of new drugs and treatment projects.Currently,the research on the mass transfer and clearance process inside the brain has become a new direction and hot topic in the brain science.Based on a detailed analysis and discussion on the brain tissue structure and the related mechanism and influence factors in the transfer and clearance processes in the brain tissue,by applying the volume averaging method and porous media theory,a mathematical model describing the process is proposed,and then numerical simulations are separately performed for the anisotropic mass diffusion,adsorption and chemical reaction process in brain,and drug delivery process in brain tumor,and some meaningful results are gained.For the process of the anisotropic mass diffusion,adsorption and chemical reaction in brain,the model equations are solved by using the finite volume implicit scheme,and the effects of the structural factors such as porosity,tortuosity and adsorption,chemical reaction on the process are obtained.The results indicate that,in the brain tissues,the mass diffuses more slowly as the tortuosity increases and spreads faster in a certain direction that has a small tortuosity value.Owing to the heterogeneity of the brain tissues,a phenomenon of competitive effect exists during the mass diffusion process inside the brain tissues.Moreover,the presences of adsorption and reaction show an inhibitory action in the procedure of diffusion.The increase of the adsorption rates leads to a greater inhibition effect in the process.In addition,for the Michaelis-Menten kinetics(a type of chemical reaction in the brain),the concentration values will significantly increase with higher reaction rate constants,and so does the Michaelis-Menten constant.Furthermore,compared with the action of adsorption inside the brain tissues,the Michaelis-Menten kinetics presents an apparently stronger inhibitory effect on the concentration distribution inside the brain tissue.Taking into account the significant advantage of the simple diffusion delivery method(SDD)in the treatment of brain tumor,a mathematical model for the drug transfer and clearance in the brain tumor is established,and,based on the spherical structure of the brain tumor,a discretization scheme in the spherical coordinate system is derived.Through numerical evaluation,the effects of the structural characteristics of the brain tumor and two different modes of administration on the SDD process are analyzed.The numerical results show that the structure of brain tumor obviously affects the drug concentration,and the drug concentration goes down as the tortuosity increases.For the two different methods of drug injection,the concentration increases more rapidly in continuous injection mode than in one-time injection.Meanwhile,the value of the drug concentration is obviously higher in continuous injection method.But considering the edema and other adverse reactions possibly caused by long time continuous injection,in order to maximize the advantages of the SDD and attain the purpose of low dose,appropriate concentration and minimal invasive treatment,how to balance the drug injection duration and concentration distribution should be investigated.Finally,the main contents of this work are summarized,and the future works of the mass transfer and clearance in brain tissue are prospected.