Neuroreceptor Quantitation in vivo by the Steady-State Principle Using Constant Infusion or Bolus Injection of Radioactive Tracers

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Abstract
The approaches hitherto used for measuring the kinetic constants Kd and Bmax of neuroreceptors in vivo all violate the steady state of the system. This complicates the kinetic analysis as approximations must be made, introducing errors of unknown magnitude. The present study presents the theory for designing experiments in which the steady state is preserved. It is based on maintaining a constant degree of receptor binding (occupancy) throughout the experiment. This is achieved by administering by prolonged intravenous infusion the non-radioactive ligand one wishes to study. The fraction of receptor sites not occupied by the “cold” ligand is measured by using trace amounts of a radioactive ligand binding to the same receptor. A minimum of two studies at different occupancies must be performed. In this presentation it is proposed to make the second study at essentially zero receptor occupancy by administering the tracer alone. The pair of tracer studies, the one without and the other with infusion of cold ligand, allows calculation of the cold ligand's equilibrium dissociation constant Kd. In the special case when tracer and cold ligands are chemically identical, then Bmax can also be calculated. Two different modes of tracer administration can be used. If the tracer is also infused at a constant rate for a long time, then the occupancy of receptor sites by the cold ligand can be calculated by measuring the equilibrium tracer concentrations in brain and plasma. If the tracer is administered as an intravenous bolus injection, then the area under the brain and plasma radioactivity curves or compartmental analysis must be used. The bolus injection approach, described in this paper for the first time, has the highest overall counting efficiency and should therefore be particularly suited for studies in man using positron emission tomography (PET) or single photon emission tomography (SPECT). Tracer infusion is the method of choice for animal experiments, as only one set of values are needed, those at long time, as can be obtained post vivo by counting samples of brain or by using autoradiographic techniques. The steady-state principle shows that ligands with very low Kd values, i.e., with very high affinity, are not suited for receptor quantitation.

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