Graphical Evaluation of Blood-to-Brain Transfer Constants from Multiple-Time Uptake Data. Generalizations

TLDR

The study presents a simplified derivation and general equations for analyzing tissue uptake data when blood‑plasma concentrations are difficult to measure or trapping is incomplete. The derivations are configuration‑agnostic, relying on reversible compartments in steady state, and are illustrated for a system with one reversible and one irreversible region. The expanded graphical method for irreversible trapping yields equations with at least one fewer nonlinear term than direct compartmental analysis.

Abstract

The method of graphical analysis for the evaluation of sequential data (e.g., tissue and blood concentrations over time) in which the test substance is irreversibly trapped in the system has been expanded. A simpler derivation of the original analysis is presented. General equations are derived that can be used to analyze tissue uptake data when the blood-plasma concentration of the test substance cannot be easily measured. In addition, general equations are derived for situations when trapping of the test substance is incomplete and for a combination of these two conditions. These derivations are independent of the actual configuration of the compartmental system being analyzed and show what information can be obtained for the period when the reversible compartments are in effective steady state with the blood. This approach is also shown to result in equations with at least one less nonlinear term than those derived from direct compartmental analysis. Specific applications of these equations are illustrated for a compartmental system with one reversible region (with or without reversible binding) and one irreversible region.