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