GRAPHICAL ANALYSIS OF REVERSIBLE RADIOLIGAND BINDING FROM TIME ACTIVITY MEASUREMENTS APPLIED TO [N-C-11-METHYL]-(-)-COCAINE PET STUDIES IN HUMAN-SUBJECTS

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 ∫0tROI(t′)dt′/ROI(t) versus ∫0tCp(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/Kp) + Vmax and the intercept is -{(1 + Bmax/Kd)/k2 + (koff(1 + Kd/Bmax)]-1} [1 + Vp/λ(1 + BmaxKd)]-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.