K1 and k2⁰⁰. The change with time in the tissue compartment, C1, could be described

by differential equation

dC1 tð Þ

dt

¼ K1C0 tð Þ
k2

00C1 tð Þ

ð16:2Þ

With this two-compartment model, one could quantify perfusion (blood flow, f )

with spontaneously diffusible tracers such as H2O with ¹⁵O, butanol [with both

possibilities ¹¹C and ¹⁵O], and fluoromethane [with ¹⁸F].

16.4.1.3 Three-Compartment Model (Two-Tissue Compartment Model)

The three-compartment model, also known as two tissue compartments (2TCM),

could be described by two differential equations:

dC1 tð Þ

dt

¼ K1C0 tð Þ
k2

0 þ k3

0

ð

ÞC1 tð Þ þ k4C2 tð Þ

ð16:3Þ

dC2 tð Þ

dt

¼ k3

0C1 tð Þ
k4C2 tð Þ

ð16:4Þ

Figure 16.7 shows an arrangement of three-compartment model defined by the

rate constants K1, k2⁰, k3⁰, and k4. These equations can be employed to analyze the

concentration curves in both of the tissue compartments. This three-compartment

model could be used to measure the transport of glucose and phosphorylation rate in

the brain. For irreversible tracer uptake, one can set k4 ¼ 0. This model could also be

used for analyzing brain receptor radioligands. The two parallel tissue compartments

are kinetically indistinguishable, and hence one could further simplify the model and

its constrained parameters.

The series configuration of tissue compartments could be applied in the metabo-

lism studies where perfusion uptake gets limited more than the transport across

capillary endothelium.

Fig. 16.6 Two-compartment

model

Fig. 16.7 Three-

compartment model

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K. Tankeshwar and S. Srivastava