Biomedical Engineering Reference
In-Depth Information
pends on several factors: intrinsic spatial resolution of the detector system and
the electronics, angular and linear sampling intervals, and the resolution of
the collimator. The latter is the dominant factor in most cases. The collima-
tor resolution depends on the geometry of the collimator, mainly the length
of the holes as well as their diameter. Besides the collimator characteristics,
the spatial resolution of the collimator depends on the distance between col-
limator and radiation source. For a point or line source this dependency can
be estimated by the following equation:
r coll;spatial d(l eff + source )
l eff
(4.7)
where d is the diameter of the collimator holes, l eff their effective length and
sources the distance between collimator and radiation source. The effective
length of the collimator holes is the length of the collimator holes reduced by
a correction term taking into account penetration of photons
l eff = l 2
(4.8)
with the linear attenuation coecient of the collimator material for the
appropriate photon energy.
Besides the effect for spatial resolution, the collimator reduces the number
of events measured in the detector, as photons are absorbed, attenuated or
scattered in the collimator material. The ratio of events that are detected
to the events that fall onto the collimator is called the collimator eciency.
This collimator eciency is only several percent in typical clinical settings.
It is improved if the collimator thickness is smaller (shorter holes) and if the
hole diameter is bigger. This means that improving the collimator eciency
always means decreasing the collimator resolution, as a bigger diameter d and
a shorter whole length l leads to an increased resolution according to Equation
4.7.
4.1.9 Positron range and annihilation (PET only)
In PET the position of the annihilation process of the positron with an
electron is measured. However, the localization of the annihilation is not equiv-
alent to the place of the positron emission from the radiotracer, which is the
location of interest. The reason for this is the excess beta decay energy which
manifests itself as kinetic energy of both positron and neutrino. As this decay
energy can be distributed between the neutrino and the positron differently,
the emitted positron has no specific kinetic energy, but an energy spectrum
with mean and maximum kinetic energy; the latter can be found in Table
4.2. The annihilation process finally takes place when the kinetic energy is
transferred to the surrounding matter. Due to the energy spectrum, the range
of the positrons is also not predetermined, but can be described by a distribu-
 
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