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Journal of Cerebral Blood Flow & Metabolism

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Research article

First published September 1990

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, and David R. ChristmanView all authors and affiliations

Volume 10, Issue 5

https://doi.org/10.1038/jcbfm.1990.127

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^t₀C_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.

References

Carson RE, (1986) Parameter estimation in positron emission tomography. In: Positron Emission Tomography and Autoradiography: Principles and Applications for the Brain and Heart (Phelps M, Mazziotta Schelbert H, eds), New York, Raven Press, pp. 347–390

Abstract

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