Biomedical Engineering Reference
In-Depth Information
y
Q
B
Q
B
P
B
P
B
P
B
x
z
Q
A
Q
A
P
A
P
A
P
A
Transaxial view
Axial view
FIGURE 9.4: Representation of the ane transformation applied to a de-
tected LOR. The scanner detector ring is approximated by a cylinder with a
radius corresponding to the distance between the surface of a crystal and the
PET system axis. The list mode output contains the detection coordinates
of the coincidence photons, vectors
P
A
, and
P
B
. The ane transformation is
applied on each of the individual lines of response, that is to say on the vec-
tors
P
A
and
P
B
. The corrected LOR is fully described by the two transformed
detected coordinate vectors
P
0
A
and
P
0
B
. A geometric model of the scanner is
used to determine the intersections of the transformed LOR with the detec-
tor ring. If the modified LOR intersects the detector ring, the transformed
detection coordinates
Q
A
and
Q
B
(intersection of the transformed LOR with
the detector ring) are written in a corrected list mode file, otherwise the LOR
is rejected. This method is repeated for each event of the detected list mode
data sets.
long as the uptake in the heart is sucient [11]. In PET/CT imaging, thanks
to the CT images, the movement of each organ during the respiratory cycle
is known. For each time interval of the respiratory cycle, the corresponding
transformation is applied to each detected line of coincidence [45]; the LOR
is moved back to the location it should have been detected if the patient had
not moved. It is important to note that an ane (or rigid) transformation
transforms a line into a line, therefore the use of such a deformation model
does not modify the principle of backprojection. A geometric model of the
imaging device is finaly required to determine the new detection points which
correspond to the intersection between the scanner detection ring formed by
the crystals and the new motion-corrected LOR [39, 29] (see Figure 9.4).
This work, based on the use of an ane transformation of list mode data
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