Irreversible 2-Tissue Compartment Model, Flux

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Irreversible 2-Tissue Compartment Model, Flux

The irreversible 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 where the tracer is trapped. K1 [ml/ccm/min] and k2 [1/min] are the uptake and clearance rate constants, whereas k3 [1/min] describes the trapping. The usual interpretation is that C1 represents free and non-specifically bound tracer in tissue (non-displaceable compartment), and C2 irreversibly bound or metabolized tracer.

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An important parameter of an irreversible configuration is net influx rate Ki, the unidirectional uptake rate constant that incorporates both net inward transport and trapping of the tracer in tissue.

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Another macroparameter "lambda*k3" as been used in the context of enzymatic reactions, where k3 is supposed to be proportional to enzyme concentration.

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Logan et al. [1] have shown in simulations that lambda*k3 is preferable to k3 alone in terms of bias and precision.

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

The model includes the 4 fitable parameters vB, K1, Flux, k3, and calculates the LambdaK3 macroparameter. Usually, vB is fixed at a physiologic value of 3-5% to reduce the number of fitted parameters.

Parameter Fitting using Flux instead of k2

The Irreversible 2-Tissue Compartment Model, Flux model variant uses Flux as a fitting parameter instead of k2. The advantage of the reformulation is that the Flux can be calculated as a regression slope with the robust Patlak model, and used as a fixed parameter in the compartment model fit. If the Model Conversion option is enabled, the Flux will be copied when switching from the Patlak model to the Irreversible 2-Tissue Compartment Model, Flux model.

Reference

1.Logan J, Fowler JS, Ding YS, Franceschi D, Wang GJ, Volkow ND, Felder C, Alexoff D: Strategy for the formation of parametric images under conditions of low injected radioactivity applied to PET studies with the irreversible monoamine oxidase A tracers [11C]clorgyline and deuterium-substituted [11C]clorgyline. J Cereb Blood Flow Metab 2002, 22(11):1367-1376. DOI