Comparison of two compartmental models for describing receptor ligand kinetics and receptor availability in multiple injection PET studies

Abstract

The goal of research with receptor ligands and PET is the characterization of an in vivo system that measures rates of association and dissociation of a ligand-receptor complex and the density of available binding sites. It has been suggested that multiple injection studies of radioactive ligand are more likely to identify model parameters than are single injection studies. Typically, at least one of the late injections is at a low specific activity (SA), so that part of the positron emission tomography (PET) curve reflects ligand dissociation. Low SA injections and the attendant reductions in receptor availability, however, may violate tracer kinetic assumptions, namely, tracer may no longer be in steady state with the total (labeled and unlabeled) ligand. Tissue response becomes critically dependent on the dose of total ligand, and an accurate description of the cold ligand in the tissue is needed to properly model the system. Two alternative models have been applied to the receptor modeling problem, which reduces to describing the time-varying number of available receptor sites. The first (Huang et al., 1989) contains only compartments for the hot ligand, 'hot only' (HO), but indirectly accounts for the action of cold ligand at receptor sites via SA. The second stipulates separate compartments for the hot and cold ligands, 'hot and cold' (HC), thus explicitly calculating available number of receptors. We examined these models and contrasted their abilities to predict PET activity, receptor availability, and SA in each tissue compartment. For multiple injection studies, the models consistently predicted different PET activities--especially following the third injection. Only for very high rate constants were the models identical for multiple injections. In one case, simulated PET curves were quite similar, but discrepancies appeared in predictions of receptor availability. The HO model predicted nonphysiological changes in the availability of receptor sites and introduced errors of 30-60% into estimates of B'max for test data. We, therefore, strongly recommend the use of the HC model for all analyses of multiple injection PET studies.