Quantitative microdialysis: analysis of transients and application to pharmacokinetics in brain

The behavior of a microdialysis probe in vivo is mathematically described. A diffusion-reaction model is developed that not only accounts for transport of substances through tissues and probe membranes but also accounts for transport across the microvasculature and metabolism. Time-dependent equations are presented both for the effluent microdialysate concentration and for concentration profiles about the probe. The analysis applies either to measuring the tissue pharmacokinetics of drugs administered systemically, or for sampling of endogenously produced substances from tissue. In addition, an expression is developed for the transient concentration about the probe when it is used as an infusion device. All mathematical expressions are found to be a sum of an algebraic and an integral term. Theoretical prediction of time-dependent probe behavior in brain has been compared with experimental data for acetaminophen administered at 15 mg/kg to rats by intravenous bolus. Plasma and whole striatal tissue samples were used to describe plasma kinetics and to estimate a capillary permeability-area product of 0.07 min-1. Theoretical prediction of transient effluent dialysate concentrations exhibited close agreement with experimental data over 60 min. Terminal decline of the dialysate effluent concentration was slightly overestimated but theoretical concentrations still lay within the 95% confidence interval of the experimental data at 112 min. Microvasculature transport and metabolism play major roles in determining microdialysate transient responses. Extraction fraction (recovery) has been shown to be a declining function in time for five probe operating conditions. High rates of metabolism and/or capillary transport affect the time required to approach steady-state extraction, shortening the time as the rates increase. Conversely, for substances characterized by low permeabilities and negligible metabolism, experimental situations exist that are predicted to have very slow approaches to microdialysis steady state.