The saturable receptor-ligand model includes two tissue compartments. C_{1} represents the non-displaceable tissue compartment with free and non-specifically bound tracer, and C_{2} tracer bound to the target receptors. The model accounts for a saturation of receptor sites due to low specific activity S_{act} of the injected tracer. In this situation, k_{3} is given by k_{on}(B_{max}-C_{2}(t)/S_{act}), and is therefore time-dependent. B_{max} is the total receptor concentration, k_{on} the bi-molecular association rate, and k_{4} the dissociation rate constant k_{off}.

Differential Equation of the Mass Balance

with input curve C_{p}(t).

Operational Model Curve

with the concentration C_{B}(t) of tracer in whole blood, and the blood volume fraction v_{B}.

Parameter Fitting

This model alternative **2-Tissue Compartment Model, K1/k2, Bmax **uses **K1/k2** as a fitting parameter instead of **k2**. K_{1}/k_{2} represents the distribution volume V_{ND} of the non-displaceable compartment C_{1}. The advantage of this formulation is that in some situations V_{ND} can be assumed to be common among regions and estimated by a coupled fit. Alternatively, V_{ND} 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.