2-Tissue Compartment Model, K1/k2

The 2-tissue compartment model separates tracer in tissue into two exchanging compartments C₁ and C₂ with a serial structure. The arterial plasma exchanges with the first tissue compartment C₁, which in turn exchanges with the second tissue compartment C₂. K₁ [ml/ccm/min] and k₂ [1/min] are the uptake and clearance rate constants, whereas k₃ [1/min] and k₄ [1/min] describe the exchange between the tissue compartments. The usual interpretation is that C₁ represents free and non-specifically bound tracer in tissue (non-displaceable compartment), and C₂ specifically bound tracer.

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 using K₁/k₂ instead of k₂

The 2-Tissue Compartment Model, K1/k2 model variant 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 four fitting parameters vB, K1, k3, k4 are the same as for the 2-Tissue Compartment Model.