Intracerebral microdialysis: II. Mathematical studies of diffusion kinetics

The kinetics of intracerebral microdialysis are studied mathematically. In the microdialysis technique, a tubular membrane that is permeable to diffusion is implanted in the brain and perfused with an artificial cerebrospinal fluid. Molecular diffusion causes substances in the brain to enter the flowing perfusate. The perfusate is collected outside the brain and the content of various substances is determined. The mathematical problem of diffusion through the porous brain tissue into the flowing perfusate is formulated. Solutions for the concentration distributions in the brain and in the perfusate are derived. It is found that the factor limiting the transport is the diffusion through the brain and not through the membrane. A theoretical expression for the recovery ratio is also obtained. This ratio may be used to infer the extracellular concentration in the brain from the concentration in the collected perfusate.