The plasma concentration of the unlabeled and unmetabolized ligand (denoted as C_a (t)) was estimated using the curve C_a^* (t) corresponding to the labeled ligand. The flux of [¹¹C]befloxatone from the arterial plasma compartment to the free compartment is given by K₁C_a^* (t). The free ligand can bind to an unoccupied specific receptor site, or escape back to the blood circulation with a rate constant k₂. The quantity of free labeled ligand present in 1 mL of the tissue volume is denoted by M_f^* (t). However, because of the obvious heterogeneity of the tissue, this concentration can be heterogeneous in the PET volume. To take into account this heterogeneity, the concept of reaction volume, denoted by V_R, has been introduced (Delforge et al, 1996). By definition, the value of V_R is such that M_f^* (t)/V_R is equal to the local free ligand concentration in the vicinity of the receptor sites. The specific binding is a saturable reaction that depends on the bimolecular association rate constant k_on, the free ligand concentration in the vicinity of the receptors sites M_f^* (t)/V_R, and the quantity of free receptors in 1 mL of tissue. This last quantity is equal to B′_max−M_b^* (t)−M_b (t). B′_max is the total receptor site concentration available for binding. M_b^* (t) and M_b (t) are the quantities of receptors sites in 1 mL of tissue already occupied by the labeled and unlabeled ligands, respectively. The rate constant for the dissociation of the specifically bound ligand is denoted by k_off. The in vivo equilibrium dissociation rate constant is denoted by K_dV_R, where K_d is the ratio k_off/k_on. The simulated PET data (denoted as M_TEP^* (t)) corresponding to the PET scan performed between time t_i and t_i+1 are given by the following equation: where C_b^* (t) is the whole blood time–concentration curve and where F_V represents the fraction of blood present in the tissue volume.

Simulations of the befloxatone kinetics in frontal cortex, after tracer injection and first co-injection (A), and after second co-injection (B). The befloxatone concentration is shown in all model compartments simulated using the model parameters given in Table 2 (experiment 3). Specifically bound ligand concentration: dotted line, free ligand concentration: dashed line, nonspecific binding concentration: dash-dot line, fitted PET befloxatone concentration: solid line. The left and right curves are from the same experiment, they are displayed on separates plots because of different y axis scales.

Study of the equilibrium states in the frontal cortex after tracer injection of [¹¹C]befloxatone (experiment 5). The dotted line (squares) represents the befloxatone concentration ratio in free over plasma compartment, the solid line (triangles) the befloxatone concentration ratio in bound over free compartment. Both curves reach a plateau at 30 mins indicating that the plasma, the free, and the bound ligand compartments are in equilibrium at this time.

Plasma and PET time–activity curves obtained in frontal cortex in baboon using a multi-injection protocol. Shown is the input function (plasma unchanged befloxatone, triangle and dashed line); the experimental PET data (circles symbols); and the simulated curve obtained from the estimated model parameters (solid line). The y axis has been truncated at 90 pmol/mL for a better visualization of the plasma curve.

Simulations of changes in cerebral blood flow and receptor concentration. Solid lines show the PET time–concentration curves simulated in the frontal cortex after a tracer injection (A) and a low SA injection (B) corresponding respectively to the first and the second injections of the experiment 1. Simulations are obtained with the same model parameters, except for the receptor concentration (dashed lines) or the parameter k₁ (dotted lines), which were increased or reduced by 20%.