An equivalent length model of microdialysis sampling

One of the critical issues in microdialysis sampling is how to predict the extraction fraction (E_d), based on transport properties of analytes in both tissues and probes. A one-dimensional (1-D) model has been used widely in previous studies to predict E_d at the steady state. However, this model is valid only for long probes. To this end, an equivalent length (EL) model was developed for probes with any length used in experiments. The key idea in the model was to replace the probe length (L) in the 1-D model with an equivalent length (L_E) when calculating transport resistance in surrounding tissues. The length difference, (L_E-L), was assumed to be proportional to the penetration depth of analytes (Γ). The proportionality constant (λ) was determined through minimizing the errors in predicted E_d. We found that, the EL model could accurately predict E_d when λ=0.369. The maximum error in EL model predictions was <6%, for model constants varying in the same ranges as those in microdialysis experiments. This error was one order of magnitude smaller than that in 1-D model predictions.