Figure 1.

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.