Biomedical Engineering Reference
In-Depth Information
voxel curves make the compartmental model fitting approach unappealing. A
number of “fast” estimation techniques have been developed to reduce the com-
putational load and improve the reliability of estimating images whose voxels
represent parameters of interest, commonly known as
parametric images
.A
brief description of these estimation techniques follows.
2.14.5 Linearization Approaches
Linearization approaches reformulate the model equations so that (1) a linear
relationship exists between the transformed data and the primary physiological
parameter of interest, or (2) the reformulated model equations contain only
linear parameters. In these circumstances, estimation of parameters can be
accomplished by a simple linear regression or by linear least-squares (LLSs)
techniques.
A number of
graphical techniques
that aim at transforming the measured
data into a plot which is linear after a certain “transformed time” have been
proposed for specific tracer studies, including the Patlak [75, 76], Logan [77, 72],
and Yokoi [78, 79] plots. Applications of the techniques depend on the tracer
studies and parameter of interest. The Patlak plot [75] was initially developed
for estimating the influx rate constant of radiotracer accumulation in an irre-
versible compartment, and was extended to allow for slow clearance from the
irreversible compartment [76]. When employed in FDG studies, the influx rate
constant is directly proportional to the regional metabolic rate of glucose. The
Logan plot [77, 72] was primarily developed for estimation of parameters re-
lated to receptor density such as binding potential and volume of distribution
for neuroreceptor studies and the radiotracers can have reversible uptake. The
Yokoi plot [78, 79] has been proposed as a rapid algorithm for cerebral blood
flow measurements with dynamic SPECT. Although all these methods permit
the estimation of physiologic parameter in rapid succession and have been used
extensively because of their computational simplicity, the bias introduced into
the physiologic parameters is significant in the presence of statistical noise in
the image data.
The use of linearized model equations was first proposed by Blomqvist [80]
for the Kety-Schmidt one-compartment model used for measuring cerebral
blood flow [81] and was extended by Evans [82] for the three-compartment
model (as shown in Fig. 2.9) to measure cerebral metabolic rate of glucose.
The key idea is that by reformulating and integrating the model equations, the
