Corrections for Physical Factors - Correction Techniques in Emission Tomography - page 69

Ideally, an emission tomography scanner should be able to address the fol-
lowing problems related to the physics of radioactive decay and the interaction
between radiation and tissue:

•Physical decay of the radionuclide;

• Loss of gamma photons by attenuation processes while traversing the

human body;

• Detection of gamma photons that changed direction due to scattering;

• Detection of coincident gamma photons that do not originate from the

same annihilation event (random coincidences).

Decay, attenuation and scatter affect both PET and SPECT imaging, while
random coincidences are a specifically PET-related problem. Figure 5.1 shows
the different types of events that are connected to these physical effects and
which can be measured in PET. (Not shown are multiple events which are
usually discarded and not taken into account.) In order to get absolute quan-
tifiable emission tomography data, one has to deal with all these effects to min-
imize their influence in the reconstructed images. Different correction methods
have been investigated since the introduction of emission tomography tech-
niques; the most important ones along with some interesting recent develop-
ment will be discussed in the following sections. As an exhaustive description
of correction techniques in both PET and SPECT (especially considering at-
tenuation and scatter correction) would go beyond the scope of this chapter,
the main focus will be put on PET correction techniques.

5.2 Decay correction
The most straightforward correction method in emission tomography is
the correction for the physical decay of the employed radionuclide. This is
especially necessary in dynamical studies where activity distribution values at
different points in time are to be measured. The main task then is to calculate
weighting factors that transform the measured activity values for every time
frame to values that would have been measured if the activity would have
remained constant in time.
A given radioactive decay process is governed by an exponential law:

e t ;

A(t) = A 0 · (5.4)

where A(t) denotes the activity of a radioactive sample at time t, A 0 is the
activity at time t = 0, and denotes the decay constant of the decay process
which is given by = ln(2)=T 1=2 (T 1=2 : half-life of the nuclide). A correction