Biomedical Engineering Reference
In-Depth Information
in a quantitative PET study. After radiopharmaceutical administration, PET data
is acquired at a predefined sampling schedule and individual voxel values in the
reconstructed images represent the localized radiotracer time-activity concen-
tration in the body upon correction for some degrading factors (e.g. attenuation
and scatter) and cross-calibration. A vector formed by extracting a voxel curve
from the sequence of images corresponds to a tissue TAC, which represents the
response of the local tissue as a function of time after the tracer administration.
Alternatively, the tissue TAC can be obtained by manual delineation of region
of interest (ROI) on the reconstructed PET images. Plasma tracer concentra-
tion is typically measured by means of arterial blood sampling. A mathematical
model is applied to the tissue and the plasma tracer concentration to estimate
the physiological parameters of interest. Kinetic modeling approaches based
on the framework of tracer kinetic modeling could be applied to estimate the
physiologic parameters. The same analysis procedures can also be applied to
dynamic SPECT without loss of generality, although the challenges tend to be
much greater in SPECT.
2.14.2 Compartmental Model Fitting
As the rate of tracer exchanges is assumed to be proportional to the amount
of tracer in the compartment, a system of first-order differential equations can
be derived. Compartmental model fitting performs the mathematical estimation
process to seek the values for the rate constant parameters that provide a best
fit for the observed tissue and blood (or plasma) TAC to the predefined com-
partmental model. The general solution to the system of first-order differential
equations has the form
N
j
=
1
α
j
e
β
j
t
C
T
(
t
)
=
(1
−
V
B
)
⊗
C
p
(
t
)
+
V
B
C
a
(
t
)
(2.22)
where
C
T
(
t
) is the measured time course of total tissue activity concentration (or
tissue TAC) in the FOV,
C
p
(
t
) is the input function of the compartment model,
C
a
(
t
) is the tracer concentration in whole blood,
N
is the number of tissue
compartments assumed for the radiotracer,
α
j
and
β
j
are the fitted parameters
from which the rate constant parameters,
k
i
, of the compartment model can
be derived,
V
B
is the fraction of the measured volume occupied by the blood
pool (0
≤
V
B
≤
1), and
⊗
is the convolution operator. It is assumed that
C
p
(
t
)
