Biomedical Engineering Reference
In-Depth Information
9.2 Parameter identification
In comparison to many other medical imaging techniques, positron emis-
sion tomography (PET) allows the monitoring of physiological instead of
anatomical information. Physiological processes over time can often be de-
scribed by intuitive mathematical models relating physiological parameters
to measured PET activity. Typical applications for parameter estimation are,
e.g., the determination of tumor or myocardial perfusion [51, 23, 33, 25, 1, 63,
7], or ligand-receptor-binding in the brain [19].
Although algorithms for direct parametric reconstruction go back to the
mid-1980s [12], combined parameter identification and reconstruction meth-
ods did not become popular for a long period. Due to the complexity of those
combined methods, these still time-demanding approaches could not be re-
alized on the hardware available. Thus, in the early stages the parameter
identification process was rather treated as a two-step procedure. First, PET
reconstructions were computed for several periods in time. Subsequently, the
obtained frames were preprocessed via a fitting of the desired parameters to
these frames with respect to the specific model. As we will discover in the
upcoming section, these models usually incorporate the temporal dependency
between the frames. The drawback of the two-step procedure was the loss of
temporal correlation between the PET-data sets. The combination of recon-
struction and parameter identification methods has recently become a major
field of interest in scientific research.
In the following we are going to present state-of-the-art compartment mod-
els used to describe physiological processes, and we are going to present recent
progress in combined parameter identification/reconstruction methods.
9.2.1 Compartment modeling
Underlying models describing physiological processes such as myocardial
perfusion are usually variants of so-called compartment models. Basically,
compartments are homogeneous spatial regions (e.g., a voxel) for which ra-
dioactive tracer concentrations can be described as functions in time. Figure
9.1(a) shows the simplest of all compartment models, the one-compartment
model. The single compartment consists of two regions, e.g., blood and tissue,
with underlying radioactive concentrations. Here h(t) represents the tracer
concentration in blood, while f(t) denotes the tracer concentration in tissue.
For the specific compartment the radioactive concentration can exchange be-
tween these regions. The exchange over time can be described via the ordinary
differential equation
d
dt f(t) = a h(t) b f(t) ,
(9.1)
 
Search WWH ::




Custom Search