The rate constant, K1, represents the delivery rate which defines the unidirectional

transport of the tracer from plasma or blood compartment to the first tissue compart-

ment. Using the Fick principle and Renkin-Crone model, K1 depends on perfusion,

f (mL  mL
¹  min
¹), and the product of capillary permeability P (cm/min) and

capillary surface area S (cm²/cm³), P  S:

K1 ¼ f 1
e
^PSf



ð16:5Þ

Transport must happen during the time that the blood stays in the capillaries

(1–3 s). Even if tracer resides in both blood plasma and blood cells, for many

radioligands only the ligand that is in blood plasma is available for transport; then

K1 depends on plasma flow instead of blood flow. The rate constant k2 represents

unidirectional transport back from tissue to the blood and is defined in terms of K1

and distribution volume, V1, of the tracer in the first tissue compartment:

k2

00 ¼ K1V1

ð16:6Þ

Both K1 and k2 depend on perfusion. In the case of central nervous system, if K1

gets strongly limited by the value of P  S of the capillary endothelium owing to the

blood-brain barrier, one can assume the first tissue compartment (C1) to denote the

interstitial and intracellular spaces, whereas the second tissue compartment (C2) can

indicate a metabolic or a receptor-bound compartment within the tissue. Rate

constant defines the fractional tracer leaving the compartment per unit time measured

in units of s
¹. For a zero concentration, the rate constant can have values over 1.0

because if flow of material is zero, then the quantity of material transferred per unit

time is given by the product of rate constant as well as the amount of tracer in the

initiating compartment. K1 takes into account the perfusion-dependent component

expressed in units of milliliter plasma (or blood) per minute per milliliter tissue

(mL min
¹ mL
¹), whereas k2⁰, k3⁰,. . . represents fraction of mass transferred per

unit time with unit min
¹.

Compartmental modeling with the two-tissue model has been implemented in

syngo MBF which is an FDA-approved commercial software package.

16.4.1.4 Perfusion Limited Uptake

For blood flow limited uptake, if P  S  f, it reduces e
^PS/f to zero and hence

K1 ¼ f. This further leads to, k2 ¼ f/V1, and CV(t) ¼ C1(t)/V1. With one-tissue

compartmental model, i.e., when all tissue compartments are lumped into one, this

would equal the model for radiowater where rapid diffusion of water takes place in

the tissues. In the case of liver with large openings of capillary endothelium, the

organ is largely porous to all radiotracers. Therefore, blood flow is the first restrictive

feature for uptake, and the first tissue compartment (C1) represents extracellular

volume which comprises of both vascular and interstitial space. The second tissue

compartment (C2) characterizes the intracellular space in hepatocytes. Thus, K1 ¼ f,

and rate constants k3 and k4 denote the transport rates among extracellular and

intracellular compartments. Comparable models could be applied to tissues where

16

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