photons of PET by applying a scaling factor defined by the ratio of mass
attenuation coefficient of 511-keV photons to that of 70-keV photons. This
factor is assumed to be the same for all tissues except bone, which has
a slightly higher mass attenuation coefficient. As mentioned in the
SPECT/CT section, the respiratory motion of the thorax during scanning
and intravenous contrast agents affect the CT attenuation factors. Use of
breath hold and water-based contrast agents helps mitigate these effects,
respectively.
Random Coincidences
Random coincidence events occur when two unrelated 511-keV photons,
arising from two different positron annihilation events, are detected by a
detector pair within the same time window (Fig. 13.8B). Random coinci-
dences are largely minimized in 2-D acquisition by septa, whereas in 3-D
acquisition in the absence of septa, their contribution is high causing loss
of image contrast. They increase with increasing pulse-height window, coin-
cidence time window, and activity [varies as the square of the activity; see
Eq. (13.7) below], and can be reduced by decreasing these variables. Also
increasing the ring diameter reduces the random coincidences.
Corrections for random coincidences can be made by separately mea-
suring two single count rates,R 1 and R 2 , of a radioactive source by each of
the detector pair and by using the following equation,
Rc= 2 tR 1 R 2 (13.7)where tis the coincidence time window and Rcis the random count rate
that is to be subtracted from the prompt count rate to obtain the true
coincidence count rate. In another method, two coincidence circuits
are employed in which one is set at a standard coincidence timing window
(e.g., 12 ns) and the other at a delayed time window (e.g., 55 ns that is,
counts arriving within 55 ns and 67 ns will be counted.), using the same
pulse-height window in both cases. The counts in the standard time window
contain true, scatter, and random events, whereas in the delayed time
window, only random events and no true or scatter coincidence events are
recorded, because true and scatter photons from the same annihilation
decay arrive at the detectors within the short coincidence time window. The
random counts will be the same in both coincidence and delayed coinci-
dence windows. The true counts are then obtained by subtracting the
delayed window counts from the standard window counts. Use of faster
electronics and a shorter coincidence time window are some of the physi-
cal techniques that are used to minimize random events. In another method,
a very high radioactive source is counted by the PET scanner over time
until the radioactivity is reduced to a level where no random event is
recorded. Random events are calculated by subtracting the low activity
counts (true plus scatter) from the high activity counts (true plus scatter
plus random).
Factors Affecting PET 199