脑内各向异性扩散传质与吸附反应过程数值分析

对脑组织内传质过程的机理及其影响因素进行了分析，建立了综合考虑脑内物质各向异性扩散、吸附和反应过程的数学模型，模型方程采用隐式控制容积法进行数值求解.计算结果表明:组织迂曲度越大，物质的扩散越慢，当某一方向迂曲度较小时，物质浓度明显增大，物质扩散变快，由于脑组织的非均质性，脑内物质的扩散传递存在着竞争现象；吸附与反应作用会抑制脑内物质传递，吸附速率越大，抑制现象越明显，对于脑内非线性的米氏反应过程，当反应速率常数增大时，稳定浓度会显著减小，同时米氏常数的增大则会使得稳定浓度值增大.相较于吸附过程，米氏过程的抑制性作用更为明显.

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.