The saturable receptor-ligand model includes two tissue compartments. C1 represents the non-displaceable tissue compartment with free and non-specifically bound tracer, and C2 tracer bound to the target receptors. The model accounts for a saturation of receptor sites due to low specific activity Sact of the injected tracer. In this situation, k3 is given by kon(Bmax-C2(t)/Sact), and is therefore time-dependent. Bmax is the total receptor concentration, kon the bi-molecular association rate, and k4 the dissociation rate constant koff.
Differential Equation of the Mass Balance
with input curve Cp(t).
Operational Model Curve
with the concentration CB(t) of tracer in whole blood, and the blood volume fraction vB.
Parameter Fitting
This model alternative 2-Tissue Compartment Model, K1/k2, Bmax uses K1/k2 as a fitting parameter instead of k2. K1/k2 represents the distribution volume VND of the non-displaceable compartment C1. The advantage of this formulation is that in some situations VND can be assumed to be common among regions and estimated by a coupled fit. Alternatively, VND might already be known and can thus be fixed at a prior value. The other 5 fitable parameters vB, K1, k3on, k4, Bmax are the same as for the 2-Tissue Compartment Model, Bmax model.
Due to the high number of parameters, it is difficult to use the model for actual fitting. However, it may be valuable for generating synthetic data and assessing the effect of model simplification.