•

One could make use of linear, first-order ordinary differential equations (ODE) to

describe these compartmental models.

In a given tissue compartment, variation in tracer concentration could be

expressed as a linear function of the concentrations in remaining compartments:

dCi tð Þ

dt

¼ f i C0 tð Þ, C1 tð Þ, C2 tð Þ, . . .

ð

Þ

ð16:1Þ

Hence, by taking the convolution of the tracer input function and the response

function, kinetic measurements could be carried out. By employing the measured

kinetics of the system, one can obtain the response function by de-convolving the

input function.

The compartment model could be classified into two types:

1. Catenary model: Here one considers series connection of one-dimensional chain

of compartments.

2. Mammillary model consists of a central compartment surrounded by other

parallel-connected compartments. In nuclear medicine, one has to work with

mixed mammillary/catenary models.

16.4.1.1 Applications

Simulation studies of given tissue data can be carried out with the help of this

compartmental model and hence could be employed to

1. Examine simplified analysis methods and software.

2. Calculate parameters of compartmental model by making use of available

PET data.

The parameters of a model which define the dynamic progressions could be

calculated from available dynamic PET data and metabolite corrected arterial

blood curve starting from the time of injection and covering all observed significant

modifications in tracer kinetics. With good sufficient information, one could calcu-

late all the parameters of dynamic processes which would include reaction rate,

perfusion, transport, blood volume involved in tissue vasculature, specific binding,

etc. However, most of the time only one key parameter is required to correlate with

the desired property under normal conditions.

16.4.1.2 Two-Compartment Model

The two-compartment model, as shown in Fig. 16.6, is the simplest compartmental

model where the input function (measured) is given to the first compartment which

could be plasma or blood curve. The second compartment could be used for the

isotope label in tissue. It is also known as one-tissue compartmental model (1TCM).

Connection between the two compartments could be defined by two rate constants,

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