Tracer in tissue is attributed to two different compartments in the following linear configuration. Tracer is taken up (K_{1}) from arterial plasma into compartment C_{1}. A fraction of it diffuses back to plasma (k_{2}), another fraction moves further to compartment C_{2} (k_{3)}. Unless tracer is trapped in the C_{2} compartment (k_{4}=0), transfer back to the intermediate compartment is also going on.
The typical interpretation is that C_{1} represents free and non-specifically bound tracer in tissue (non-displaceable compartment), and C_{2} represents specifically bound tracer.
System of differential equations:
In the auxiliary 2-tissue compartment models a direct model parameter (rate constant) is replaced by a combination of the basic parameters:
2-Tissue Compartment Model, K1/k2 |
The parameter K_{1}/k_{2} (DV, distribution volume of free tracer and non-specific binding) is used as a fit parameter instead of k_{2}, and k_{2} is derived from the estimated K_{1} and K_{1}/k_{2}. |
2-Tissue Compartment Model, K1/k2 & DVs |
The parameters K_{1}/k_{2} and K_{1}/k_{2}*k_{3}/k_{4} (DVs, distribution volume of specific binding) are used as fit parameters instead of k_{2} and k_{4}; k_{2} and k_{4 }are derived from the fit results. |
This approach allows using the non-specific distribution volume K_{1}/k_{2} and DVs as common parameters in a coupled fit, as well as for the generation of synthetic curves with fixed DV and DVs.
FDG 2 Tissue Compartment Model
The FDG model is a standard 2-tissue compartment model with two additional input parameters, the lumped constant (LC) and the plasma glucose concentration (PG). In combination with the estimated K_{1}, k_{2}, and k_{3} parameters they allow to calculate the metabolic rate of glucose. When switching back and forth with the Patlak model, LC and PG are maintained, if the checkbox Model conversion in the Configuration menu is enabled.
Note: In the FDG model k_{4} is initially set to 0 assuming metabolic trapping, but can also be fitted.