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

TLDR

The study introduces a graphical method that yields the Bmax/Kd ratio from the slope, enabling rapid comparison with in vitro values and assessment of reproducibility across subjects and time. The method uses time‑activity curves of plasma and tissue radioactivity to construct a plot whose linear slope equals the ligand’s steady‑state space plus plasma volume, with specific expressions for two‑ and three‑compartment models. Applied to [11C]cocaine PET data, the method produced a Bmax/Kd of 0.62 ± 0.20, consistent with literature, and matched the standard nonlinear least‑squares analysis while achieving linearity before the full steady state.

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 t 0 ROI( t') dt'/ROI( t) versus f t 0 C p ( t') dt'/ROI( t) (where ROI and C p 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, V p . For a two-compartment model, the slope is given by λ + V p , where λ is the partition coefficient and the intercept is −1/[ k 2 (1 + V p /λ)]. For a three-compartment model, the slope is λ(1 + B max / K d ) + V p and the intercept is −{(1 + B max / K d )/ k 2 + [ k off (1 + K d / B max )] −1 } [1 + V p /λ(1 + B max / K d )] −1 (where B max represents the concentration of ligand binding sites and K d the equilibrium dissociation constant of the ligand–binding site complex, k off ( k 4 ) the ligand–binding site dissociation constant, and k 2 is the transfer constant from tissue to plasma). This graphical method provides the ratio B max / K d 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/ C p 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- 11 C]-(–)-cocaine ([ 11 C]cocaine) studies in normal human volunteers and the results are compared to the standard nonlinear least-squares analysis. The calculated value of B max / K d for the high-affinity binding site for cocaine is 0.62 ± 0.20, in agreement with literature values.