Graphical Analysis of Reversible Radioligand Binding from Time—Activity Measurements Applied to [N-¹¹C-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 f ^t₀ROI( t') dt'/ROI( t) versus f ^t₀ 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/[ k₂(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)/ k₂ + [ 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 ( k₄) the ligand–binding site dissociation constant, and k₂ 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-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 B_max/ K_d for the high-affinity binding site for cocaine is 0.62 ± 0.20, in agreement with literature values.