Modeling Analysis of [ 11 C]Flumazenil Kinetics Studied by PET: Application to a Critical Study of the Equilibrium Approaches

The multi-injection modeling approach was used for the in vivo quantitation of benzodiazepine receptors in baboon brain using positron emission tomography (PET) and [¹¹C]flumazenil (RO 15-1788) as a specific ligand. The model included three compartments (plasma, free, and bound ligand) and five parameters (including the benzodiazepine receptor concentration). The plasma concentration after correction for the metabolites was used as the input function. The experimental protocol consisted of four injections of labeled and/or unlabeled ligand. This protocol allows the evaluation, from a single experiment, of the five model parameters in various regions of interest. For example, in the temporal cortex, the concentration of receptor sites available for binding (B′_max) and the equilibrium dissociation constant (K_d) were estimated to be 70 ± 15 pmol/ml and 15.8 ± 2.2 nM, respectively. The validity of the equilibrium approach, which is the most often used quantitation method, has been studied from simulated data calculated using these model parameters. The equilibrium approaches consist of reproducing in PET studies the experimental conditions that permit the use of the usual in vitro methods such as Scatchard analysis. These approaches are often open to criticism because of the difficulty of defining the notion of equilibrium in in vivo studies. However, it appears that the basic relation of Scatchard analysis is valid over a broader range of conditions than those normally used, such as the requirement of a constant bound/free ratio. Simulations showed that the values of the receptor concentration (B′_max) and the equilibrium dissociation constant (K_d) found using Scatchard analysis are always underestimated. These simulations also suggest an explanation concerning the dependency of B′_max and K_d on the time point employed for the Scatchard analysis, a phenomenon found by several authors. To conclude, we propose new protocols that allow the estimation of the B′_max and K_d parameters using a Scatchard analysis but based on a protocol including only one or two injections. These protocols being entirely noninvasive, it thus becomes possible to investigate possible changes in receptor density and/or affinity in patients.