Mathematical Model of Hippocampal Microdialysis: Validation of in vivo Methodology

Microdialysis is a well-established method for in vivo neurochemical measurements of small molecules, with implanted concentric-design probes offering minimized tissue damage and good temporal and spatial resolution. However, the large majority of measurements do not allow the perfusate to reach equilibrium with the brain, so that inferential methods of sample concentration correction such as zero-net-flux must be used to determine actual brain extracellular fluid glucose concentrations. In order for such methods to be valid, steady-state transfer of the analyte of interest within the brain is required, but this situation has not previously been confirmed. A first-principles mathematical model of fluid flow and analyte diffusion around an implanted microdialysis probe was developed and implemented in COMSOL in order to validate the zero-net-flux approach, using measurement of extracellular brain glucose levels as a well-explored example system against which to compare the model. Results from the model accurately reproduced and predicted results from in vivo experiments. Importantly, the model predicts that the time for an implanted probe to achieve steady-state equilibrium with the surrounding extracellular fluid is on the order of one to two minutes, supporting the validity of this technique for quantitative measurement of in vivo neurochemistry.