Graphical Analysis of Reversible Radioligand Binding from Time—Activity Measurements Applied to [N-11C-Methyl]-(−)-Cocaine PET Studies in Human Subjects

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Abstract
A graphical method of analysis applicable to ligands that bind reversibly to receptors or enzymes requiring the simultaneous measurement of plasma and tissue radioactivities for multiple times after the injection of a radiolabeled tracer is presented. It is shown that there is a time t† after which a plot of f t0ROI( t') dt'/ROI( t) versus f t0 Cp( t') dt'/ROI( t) (where ROI and Cp are functions of time describing the variation of tissue radioactivity and plasma radioactivity, respectively) is linear with a slope that corresponds to the steady-state space of the ligand plus the plasma volume, Vp. For a two-compartment model, the slope is given by λ + Vp, where λ is the partition coefficient and the intercept is −1/[ k2(1 + Vp/λ)]. For a three-compartment model, the slope is λ(1 + Bmax/ Kd) + Vp and the intercept is −{(1 + Bmax/ Kd)/ k2 + [ koff(1 + Kd/ Bmax)]−1} [1 + Vp/λ(1 + Bmax/ Kd)]−1 (where Bmax represents the concentration of ligand binding sites and Kd the equilibrium dissociation constant of the ligand–binding site complex, koff ( k4) the ligand–binding site dissociation constant, and k2 is the transfer constant from tissue to plasma). This graphical method provides the ratio Bmax/ Kd from the slope for comparison with in vitro measures of the same parameter. It also provides an easy, rapid method for comparison of the reproducibility of repeated measures in a single subject, for longitudinal or drug intervention protocols, or for comparing experimental results between subjects. Although the linearity of this plot holds when ROI/ Cp is constant, it can be shown that, for many systems, linearity is effectively reached some time before this. This analysis has been applied to data from [ N-methyl-11C]-(–)-cocaine ([11C]cocaine) studies in normal human volunteers and the results are compared to the standard nonlinear least-squares analysis. The calculated value of Bmax/ Kd for the high-affinity binding site for cocaine is 0.62 ± 0.20, in agreement with literature values.