2-Tissue Compartment Model

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2-Tissue Compartment Model

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 Cp(t).

Operational Model Curve


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

Parameter Fitting

The model includes the 5 fitable parameters vB, K1, k2, k3, k4. Usually, vB is fixed at a physiologic value of 3-5% to reduce the number of fitted parameters. An alternative is to fit vB with a TAC from a big representative VOI, and fix it for the TACs from smaller VOIs. For irreversible tracers with trapping in the second compartment, k4 is fixed: k4=0. Please inspect the %SE standard error to get information about the reliability of the parameter estimates.

Alternative Models with VND and VS Fit Parameters

There are two alternative models available which have the same structure but use distribution volumes as fit parameters. The advantage of the reformulation is that in some situations distribution volumes can be assumed to be common among regions and estimated by a coupled fit, or they might already be known and can thus be fixed at a prior value.