Kinetic models for estimating occupancy from single-scan PET displacement studies

Abstract

The traditional design of PET target engagement studies is based on a baseline scan and one or more scans after drug administration. We here evaluate an alternative design in which the drug is administered during an on-going scan (i.e., a displacement study). This approach results both in lower radiation exposure and lower costs. Existing kinetic models assume steady state. This condition is not present during a drug displacement and consequently, our aim here was to develop kinetic models for analysing PET displacement data. We modified existing compartment models to accommodate a time-variant increase in occupancy following the pharmacological in-scan intervention. Since this implies the use of differential equations that cannot be solved analytically, we developed instead one approximate and one numerical solution. Through simulations, we show that if the occupancy is relatively high, it can be estimated without bias and with good accuracy. The models were applied to PET data from six pigs where [¹¹C]UCB-J was displaced by intravenous brivaracetam. The dose-occupancy relationship estimated from these scans showed good agreement with occupancies calculated with Lassen plot applied to baseline-block scans of two pigs. In summary, the proposed models provide a framework to determine target occupancy from a single displacement scan.

Keywords: Displacement; PET; drug occupancy; kinetic modelling; synaptic density.

Figure 1.

The left panel shows the occupancy function, ∂(t) as defined in equation (1), for 3 different choices of t_e. The middle panels show schematic diagrams of the intervention models for 2TCM and 1TCM, respectively. The right panels show time-activity curves originating from each compartmental model using the choices for ∂(t) depicted in the left panel.

Figure 2.

Results from simulating fast- (t_e $\hspace{0.17em}$ = $\hspace{0.17em}$ 5 min) and slow-acting (t_e $\hspace{0.17em}$ = $\hspace{0.17em}$ 30 min) drugs, displacing [¹¹C]UCB-J binding. Each panel shows histograms of occupancy (∂^max) estimates from the numerical solution (green) and single-step approximation (red). In each panel, the dashed black line corresponds to the true value for ∂^max.

Figure 3.

Displacement model fits (solid lines) to [¹¹C]UCB-J temporal cortex TACs (dots) from two pig scans in which brivaracetam was administered i.v. 60 minutes after radiotracer injection. The dashed lines show model curves in the absence of displacement. These curves were generated from the estimated model parameters, with occupancy set to zero. For the numerical solution, the model fits to all regions, including residuals, are presented in supplementary figures 13 and 14.

Figure 4.

Results from pig experiment. The two tiles show the estimated occupancies plotted against peak plasma brivaracetam concentrations for the numerical solution and single step solutions, respectively. In both, the Lassen-occupancies plotted against the peak plasma value during the block scans are also included.