Physics and Radiobiology of Nuclear Medicine

where mis the linear attenuation coefficient of the photon in tissue and x
is the depth of tissue traversed by the photon (Fig. 12.16). Photons origi-
nate from different depths of tissue, which are not exactly known. However,
in SPECT imaging, a solution to this problem is to obtain two counts in
opposite projections and then calculate the geometric mean of the two
counts. This is easily obtained in 360° data acquisition in SPECT. Thus the
geometric mean is given by

Ig=(Ia×Ib)1/2 (12.7)

where Iaand Ibare the measured attenuated counts in the opposite pro-
jections. Considering Figure 12.16Band applying Eq. (12.6), Eq. (12.7)
becomes

Ig=(Ia×Ib)1/2=(Ia 0 ×Ib 0 )1/2e−m(a +b)/2

=(Ia 0 ×Ib 0 )1/2e−mD/2 (12.8)

where Ia 0 and Ib 0 are the unattenuated counts detected in opposition and D
is the total thickness of the tissue. For parallel collimators, which are most
commonly used in SPECT imaging, the photon density does not change
with distance; that is,Ia 0 and Ib 0 are approximately equal. Then Eq. (12.8)
becomes

I 0 /Ig=emD/2 (12.9)

172 12. Single Photon Emission Computed Tomography

x 1 x 2

detector

A

x 3

D

ab

B

Detector at angle

f angle Detector at

f

+ 180

0

Ia Ib

patient

Fig. 12.16.A.Illustration of photons traveling different depths of tissue, thus suf-
fering variable attenuation.B.Two photons traversing distances aand bare detected
by the two detectors oriented at 180°. Attenuation correction can be applied by
taking the geometric mean of the two counts Iaand Iband using the total thickness
Dof the tissue in place of aand bseparately.