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

Abstract

A theoretical model of blood–brain exchange is developed and a procedure is derived that can be used for graphing multiple-time tissue uptake data and determining whether a unidirectional transfer process was dominant during part or all of the experimental period. If the graph indicates unidirectionality of uptake, then an influx constant ( K_i) can be calculated. The model is general, assumes linear transfer kinetics, and consists of a blood–plasma compartment, a reversible tissue region with an arbitrary number of compartments, and one or more irreversible tissue regions. The solution of the equations for this model shows that a graph of the ratio of the total tissue solute concentration at the times of sampling to the plasma concentration at the respective times ( C_p) versus the ratio of the arterial plasma concentration–time integral to C_p should be drawn. If the data are consistent with this model, then this graph will yield a curve that eventually becomes linear, with a slope of K_i and an ordinate intercept less than or equal to the vascular plus steady-state space of the reversible tissue region.