2-Tissue Compartment Model, k5

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2-Tissue Compartment Model, k5

In addition to uptake and washout the model handles two exchanging compartments C1 and C2 in tissue, as well as an efflux from C2.

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Differential Equation of the Mass Balance

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with input curve Cp(t), concentration C1(t) in the first and concentration C2(t) in the second compartment. 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 typical interpretation is that C1 represents free and non-specifically bound tracer in tissue (non-displaceable compartment), and C2 represents specifically bound tracer.

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

The model includes the 6 fitable parameters vB, K1, k2, k3, k4, k5. Usually, vB is fixed at a physiologic value of 3-5% to reduce the number of fitted parameters. Per default, k4=0 is fixed to model an efflux from the specific compartment rather than an exchange with the non-displaceable compartment.