Biomedical Engineering Reference
In-Depth Information
as blood flow, glucose metabolism, oxygen utilization, protein synthesis, and
receptor or binding site density, etc. in the body. The concentration of the radio-
tracer introduced into the biologic system is assumed to be negligible so that it
does not perturb the natural process of the system. Otherwise, the measurement
does not represent the process we want to measure but the effect induced by the
introduction of the radiotracer. External measurable data is the time course of
total tissue activity concentration obtained from the PET images, and the time
course of blood (or plasma) activity concentration (i.e. the input function of the
compartment model), obtained from peripheral blood sampling. These curves
are described as
time-activity curves
(TACs), where the term “activity” refers
to
concentration
of the radiotracer rather than the tissue (or blood) activity.
Yet, the measured time course of tracer uptake and delivery does not directly
provide quantitative information about the biologic and physiologic processes
but the kinetic information of the radiotracer. Mathematical modeling of the
measured tracer kinetics is thus required to transform the kinetic information
into physiologically meaningful information, i.e. the physiologic parameters of
interest. This can be accomplished through the use of an analysis technique
commonly referred to as
compartmental
or
tracer kinetic modeling
.
Mathematical modeling of biologic processes and systems is well established
and a wide variety of models have been developed [61]. Although nonlinear
models should be used to study biological systems which are commonly non-
linear, linear compartmental models have properties which make them attrac-
tive for radiotracer experiments with PET and SPECT [62]. A given system
can be described by a compartment model, which consists of a finite num-
ber of interconnected compartments (or pools), each of which is assumed
to behave as a distinct component of the biologic system with well-mixed
and homogeneous concentration [63]. An example is shown in Fig. 2.9 for
[
18
F]fluorodeoxyglucose, which is the primary radiopharmaceutical used in PET
to assess glucose metabolism. A compartment can be a physical space, such as
plasma or tissue, or a chemical entity, where tracer may exist in different forms
k
1
k
3
FDG in tissue
C
e
(t)
FDG -6-P in
tissue C
m
(t)
FDG in plasma
C
p
(t)
k
k
Figure 2.9:
The three-compartment model for transport and metabolism of
[
18
F]fluorodeoxyglucose (FDG).
