Corrections for Physical Factors - Correction Techniques in Emission Tomography - page 73

coincidence rate P Tij leads to an estimate of the true coincidence rate T Tij (in
addition to the scatter rate S Tij ):

T Tij + S Tij P Tij D Tij : (5.8)

Dead time effects are of no concern in this approach as both the prompt
and the delayed windows have the same dead time properties; however, as
the measured delayed rate is much lower than the singles rate, the calculated
randoms rate for a given line of response has much more variance as compared
to the singles-based method. This can be reduced by storing the collected
delayed events in a separate sinogram data set (besides the prompt sinogram
data set) instead of an online subtraction of delayed coincidences. The delayed
sinograms may then be processed by filtering steps (smoothing) to reduce the
variance before subtracting them from the prompt data [20]. This obviously
comes at the cost of computer memory and processing time, but helps to
reduce the signal-to-noise ratio in the reconstructed images as compared to
the simple online subtraction method [14].

5.4 Attenuation correction
A beam of monochromatic gamma rays that is passing through matter is
attenuated in intensity. Empirically, the intensity I after passing a homoge-
neous material of thickness r is found to be

e r ;

I(r) = I 0 · (5.9)

where I 0 is the incident intensity of the beam and is the total linear
attenuation coecient, a gamma energy- and material-dependent constant:
= (E ; material). In the case of an inhomogeneous material with spatially
variable linear attenuation coecients (r) (the so-called attenuation map or
-map), the transmitted intensity is

e R i (r)dr ;

I(r) = I 0 · (5.10)

with i denoting the line of the gamma ray.
This attenuation of intensity is due to interaction processes between the
photons and the atoms of the material. Basically, gamma photons discharged
in PET and SPECT can interact with matter by two processes known as
the Compton effect and the photoelectric effect. (A third process, electron-
positron pair production, is possible only at gamma energies above 1.022 MeV
which corresponds to twice the rest mass of electrons.)
Compton scattering is an inelastic scattering effect of photons interacting
with electrons, most probably those on the outer shell of atoms. The photon
transfers energy during the process to an electron and changes its traveling