2-Tissue Compartment Model, K1/k2

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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.

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Differential Equation of the Mass Balance

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with input curve Cp(t).

Operational Model Curve

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with the concentration CB(t) of tracer in whole blood, and the blood volume fraction vB.

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 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 four fitting parameters vB, K1, k3, k4 are the same as for the 2-Tissue Compartment Model.