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to those in the centre. This effect is fairly simple to
account for, since the degree of summing is always
known. However, it can complicate the process of cor-
recting for other effects if the summing is performed
prior to normalisation [10, 11].
Rotational Sampling
In a rotating system, LORs at the edge of the \ufb01eld of
view are sampled just once per half-rotation, while
those near the centre are sampled many times (see Fig.
5.5). As a result, sensitivity falls as radius increases.
Detector Efficiency Variations
In a block detector system, detector elements vary in
ef\ufb01ciency because of the position of the element in the
block, physical variations in the crystal and light
guides and variations in the gains of the photomulti-
plier tubes. These variations result in substantial high-
frequency non-uniformities in the raw data. In
particular there is a systematic variation in detector
ef\ufb01ciency with the crystal position within the block
(the \u201cblock pro\ufb01le\u201d) which results in signi\ufb01cant varia-
tions in the sensitivity of the tomograph in the axial
direction. Radially the effect is not so great, because
any one pixel in the image is viewed by many detectors
and there is a tendency for these effects to cancel out
during reconstruction. Nevertheless, failure to correct
for them leads to radial streaking in the image, and the
systematic block pro\ufb01le effects can reinforce during re-
construction, resulting in circular \u201csaw-tooth\u201d artefacts.
Detector ef\ufb01ciency, and in particular the block pro\ufb01le,
can be affected by count rate. One result of pulse pileup
within a block detector is the shifting of detected
events towards the centre of the block [12]. This is not
really a normalisation effect in the conventional sense,
but since it results in a systematic change in the appar-
ent ef\ufb01ciency of the lines of response with position in
the block it manifests itself in a very similar way. The
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98 Positron Emission Tomography
effect can be reduced by measuring normalisation
coef\ufb01cients at a similar count-rate to that used during
data acquisition, or by creating a rate-dependent look-
up table of normalization coef\ufb01cients [13].
If this is not possible, any resulting image artefacts
may be reduced by extracting systematic effects from the
raw data after normalisation but prior to reconstruction.
Geometric and Solid Angle Effects
Figure 5.6 shows that in a system with segmented detec-
tors, such as a block-detector based system, lines of re-
sponse close to the edge of the \ufb01eld of view are
narrower and more closely spaced than those at the
centre. This geometric effect is also apparent axially
and can be signi\ufb01cant for large area tomographs oper-
ating in 3D mode. The narrowing of the LORs results in
a tighter acceptance angle and in reduced sensitivity, al-
though in the transaxial plane this effect is partially
compensated by the fact that the separation between
opposing detectors is less towards the edge of the \ufb01eld
of view, so that the acceptance angle is changed in the
opposite direction. The narrowing of LORs also results
in reduced sampling distance. However, this effect is
easily describable analytically and can be corrected for
at reconstruction time \u2013 a process known as \u201carc cor-
rection\u201d. Arc correction may not be an issue for systems
that employ continuous detectors, as it is usually possi-
ble to bin the data directly into LORs of uniform width.
An effect that is relevant for systems employing
either continuous or discrete detectors, and that is not
so easy to describe analytically, is related to the angle
of incidence of the line of response at the detector face.
A photon entering a crystal at an angle will usually
have more material in its path than one entering nor-
mally, thus having an increased probability of interac-
tion. In the case of a ring scanner, this results in
measurable changes in sensitivity as the radial position
of the line of response is increased and is known as the
Quantitative Techniques in PET 99
Figure 55.5. Rotational sampling. (Left) Lines of response at the edge of the transaxial field of view are sampled once per detector half-rotation. (Right) lines of
response close to the centre of the field of view are sampled many times, as more detector elements are brought to bear.
Figure 55.6. Lines of response narrow as the radial distance increases.
radial, or transaxial, geometric effect (Fig. 5.7). However,
a photon entering a detector close to its edge and at an
angle may have signi\ufb01cantly less material along its path
and may therefore be more likely to escape. For block
detector systems this results in a pattern of sensitivity
change which varies both with radial position and with
the position of the line of response with respect to the
block (Fig. 5.8). This has become known as the \u201ccrystal
interference\u201d effect [10]. Again, similar effects can be
found in the axial direction [11].
It should be noted that the photon incidence angle is
most strongly correlated with the line of response for
true coincidences \u2013 these geometric effects would be
expected to be much weaker or non-existent for
random and scattered coincidences [14].
Time Window Alignment
For coincidence detection to work ef\ufb01ciently, timing
signals from each detector must be accurately synchro-
nised. Asynchronicity between detector pairs results in
an offset and effective shortening of the time window
for true and scattered (but not random) coincidences.
This, in turn, results in variations in the sensitivity to
true and scattered coincidences. For block detector
systems, the greatest source of such variations occurs
at the block level. Figure 5.9 shows the variations in
ef\ufb01ciency resulting from time alignment effects in a
block tomograph plotted as a sinogram. Each diamond
corresponds to a different block combination.
Structural Alignment
In a ring tomograph, the accuracy with which the de-
tectors are aligned in the gantry can affect line of re-
sponse ef\ufb01ciency. Such variations will manifest in
different ways depending on the exact design of the to-
mograph, the detectors and any casing in which the de-
tectors are contained. Frequently, block detectors are
mounted in modules or cartridges, each containing
100 Positron Emission Tomography
Radial Profiles
-45 -35 -25 -15 -5 5 15 25 35 45
LOR incidence angle (degrees)
Figure 55.7. Figure 5.7. Mean radial geometric profiles for three
block-detector tomographs \u2013 the Siemens/CTI ECAT 951, the
Siemens/CTI ECAT 962 and the GE Advance, measured using the
rotating transmission sources. The 951 data shows asymmetry
due to the fact that the centre of rotation of the transmission
sources is not coincident with the centre of the detector ring.
(From [11], with permission.)
Figure 55.8. Crystal interference factors for the Siemens/CTI ECAT 951.
(From [15], with permission.)
Figure 55.9. Time-window alignment factors for the Siemens/CTI ECAT 951.
The factors range in value from 0.872 to 1.120. (From [15], with permission.)
several units. Misalignments of these modules can have
noticeable affects on LOR sensitivity [11, 15]. Some
full-ring systems have a \u201cwobble\u201d feature designed to
improve spatial sampling \u2013 this feature allows the de-
tectors to describe a small orbit about the mean detec-
tor position. As a result, it is possible that the
transmission sources can rotate about a point which is
not actually the centre of the detector ring, and if they
are used to perform normalisation measurements, er-
roneous asymmetries can be introduced into the nor-
malisation coef\ufb01cients [11].
Septa can affect LOR sensitivity in a variety of ways.
They have a signi\ufb01cant shadowing effect on the detec-
tors, which can