Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

Source containingpositron-emitterDD FIGURE22-22. Point source of positron-emittingradionuclide, in air, midway between two identicaldetectors.Efficiency in AnnihilationCoincidence DetectionConsider a point source of a positron-emitting radionuclide in air midway betweentwo identical detectors (Fig. 22-22) and assume that all positrons annihilate withinthe source. The true coincidence rate of the pair of detectors iswhere A is the activity of the source, G is the geometric efficiency of either detector,and E is the intrinsic efficiency of either detector. (Geometric and intrinsic efficiencyare defined in Chapter 20.) Because the rate of true coincidences detected is proportionalto the square of the intrinsic efficiency, maximizing the intrinsic efficiency isvery important in PET. For example, if the intrinsic efficiency of a single detector fora 51l-keV photon is 0.9, 81 % of the annihilation photon pairs emitted toward thedetectors have coincident interactions. However, if the intrinsic efficiency of a singledetector is 0.1, only 1% of pairs emitted toward the detectors has coincident interactions.As mentioned previously, most PET systems today use crystals ofBGO, becauseof its high attenuation coefficient. These crystals are typically about 3 cm thick. Asmentioned above (see Two and Three Dimensional Data Acquisition), increasing theaxial acceptance angle of annihilation photons greatly increases the efficiency.Attenuation in PET differs from attenuation in SPECT, because both annihilationphotons must escape the patient to cause a coincident event to be registered. Theprobability of both photons escaping the patient without interaction is the productof the probabilities of each escaping:(e-J.lX) . (e-~(d -x) = e-~d [22-3]where d is the total path length through the patient, x is the distance one photonmust travel to escape, and (d - x) is the distance the other must travel to escape (Fig.22-23). Thus, the probability of both escaping the patient without interaction isindependent of where on the line the annihilation occurred and is the same as theprobability of a single 511-keV photon passing entirely through the patient alongthe same path. (Equation 22-3 was derived for the case of uniform attenuation, butthis principle is valid for nonuniform attenuation as well.)Even though the attenuation coefficient for 511-keV annihilation photons insoft tissue (/lIp = 0.095 cm 2 /g) is lower than those of photons emitted by mostradionuclides used in SPECT (/lIp = 0.15 cm 2 /g for 140-keV gamma rays), theaverage path length for both to escape is much longer. For a 20-cm path in soft tissue,the chance of both annihilation photons of a pair escaping the tissue without