Biomedical Engineering Reference
In-Depth Information
accounts for the varying attenuation within the matter, and
d
is the distance
between the source and the detector (in cm). Therefore, in PET and SPECT,
attenuation artifacts can cause a significant reduction in measured counts, par-
ticularly for deep structures. For example, attenuation artifacts can resemble
hypoperfusion in the septal and inferior-posterior parts of the myocardium in
cardiac PET or SPECT study. Failure to correct for attenuation can cause se-
vere error in interpretation and quantitation. As the attenuation coefficient varies
with different tissue types, the extent of photon attenuation/absorption will also
vary even though the distance between the emission site of the photons and the
detector remains unchanged. Therefore, spatial distribution of attenuation co-
efficients, i.e. an attenuation map, is required for each individual patient in order
to correct for photon attenuation accurately.
Consider the attenuation in an object whose total thickness is
D
, measured
along the LoR, and the attenuation coefficient is
µ
, as shown in Fig. 2.7. If the
annihilation event occurs at position
x
, measured along the LoR, then the prob-
abilities for the two gamma rays to reach the opposing detectors are
e
−
µ
(
D
−
x
)
and
e
−
µ
x
, respectively. The probability of registering the coincidence event is
the product of the probabilities of detection of the gamma rays by the opposing
detectors, i.e.
e
−
µ
(
D
−
x
)
≡
e
−
µ
D
, which is independent of the source posi-
tion,
x
. This remains true when the attenuation coefficient is not uniform within
the cross-section of the body. Thus, the attenuation is always the same even if
the source position is outside the object.
The measured projection data will differ from the unattenuated projection
data in the same fashion. Suppose
µ
(
x
,
y
) denotes the attenuation coefficient
·
e
−
µ
x
Object
Detector
Detector
x
D
−
x
D
Figure 2.7:
Attenuation of the gamma rays in an object for a given line of
response.
