Graphical analysis of reversible radioligand binding from time-activity measurements applied to [N-11C-methyl]-(-)-cocaine PET studies in human subjects

Jean Logan, Joanna S. Fowler, Nora D. Volkow, Alfred P. Wolf, Stephen L. Dewey, David J. Schlyer, Robert R. MacGregor, Robert Hitzemann, Bernard Bendriem, S. John Gatley, David R. Christman

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1243 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)740-747
Number of pages8
JournalJournal of Cerebral Blood Flow and Metabolism
Issue number5
StatePublished - 1990
Externally publishedYes


  • Cocaine
  • Compartmental modeling
  • Graphical analysis
  • PET
  • Receptors
  • Transfer constants

ASJC Scopus subject areas

  • Neurology
  • Clinical Neurology
  • Cardiology and Cardiovascular Medicine


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