2-Tissue Compartment Model, K1/k2, Bmax

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 S_act of the injected tracer. In this situation, k₃ is given by k_on(B_max-C₂(t)/S_act), and is therefore time-dependent. B_max is the total receptor concentration, k_on the bi-molecular association rate, and k₄ 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. K₁/k₂ represents the distribution volume V_ND of the non-displaceable compartment C₁. 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.