Scatter coincidences

The pulse height window cuts off a large fraction of the scattered radiations, which is limited by the width of the window. In 2D acquisition, the use of septa in multiring PET systems removes additional scattered events, whereas in 3D acquisition, they become problematic because of the absence of septa. Typically, the scatter fraction ranges from 15% in 2D mode to more than 40% in 3D mode for modern PET scanners. 

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Figure 3.1. (a) True coincidence events (b) Random coincidence events detected by two detectors connected in coincidence along the dotted line. The two 511-keV photons originated from different positron annihilations, (c) Scattered coincidence events. Two scattered photons with little loss of energy originating from two annihilation events may fall within PHA window and also within coincidence time window to be detected as a coincidence event by two detectors. 

Coincidence events detected by two detectors within the time window are termed prompt events. The prompts include true, random, and scatter coincidence events. In many PET systems, in an attempt to eliminate random and scatter photons discussed later, annular septa ( -1 mm thick and radial width... 

The projection data acquired in the form of sinograms are affected by a number of factors, namely variations in detector efficiencies between detector pairs, random coincidences, scattered coincidences, photon attenuation, dead time, and radial elongation. Each of these factors contributes to the sinogram to a varying degree depending on the 2D or 3D acquisition and needs to be corrected for prior to image reconstruction. These factors and their correction methods are described below. 

Describe the methods of correction for random coincidences and scatter coincidences in the acquired data for PET images. 

What are the contributing factors for the scatter coincidences in PET images ... 

Indicate how the true, random, and scatter coincidences vary with activity ... 

When do you apply various corrections (e.g., detection efficiency variations, noise components, random and scatter coincidences, attenuation) in the FBP and iterative methods of image reconstruction ... 

Note that the sensitivity of a PET scanner increases as the square of the detector efficiency, which depends on the scintillation decay time and stopping power of the detector. This is why LSO, LYSO and GSO detectors are preferred to Nal(Tl) or BGO detectors (see Table 2.1). In 2D acquisitions, system sensitivity is compromised because of the use of septa between detector rings, whereas these septa are retracted or absent in 3D acquisition, and hence the sensitivity is increased by a factor of 4-8. However, in 3D mode, random and scatter coincidences increase significantly, the scatter fraction being 30—40% compared to 15-20% in 2D mode. The overall sensitivities of PET scanners for a small-volume source of activity are about 0.2-0.5% for 2D acquisition and about 2-10% for 3D acquisition, compared to 0.01-0.03% for SPECT studies (Cherry et al, 2003). The greater sensitivity of the PET scanner results from the absence of collimators in data acquisition. 

To show this, it is necessary to insert the Fourier components E(q) of the dielectric permittivity tensor e( ) of the cholesteric into the general formula for the scattering cross section a oc (r s(q) f) as already discussed for nematics in Section 11.1.3. Here f and r are polarization vectors for the incident and reflected light, q is the wavevector of scattering coinciding in this simple geometry with the wavevector of the reflected wave [2]. 

FIGURE 11 Principle of coincidence detection. True coincidence (solid line), random coincidence (dashed line), and scattered coincidence (broken line) are indicated. 

Vi. Correction of random and scattered coincidences. Random coincidences can be corrected by two simple procedures. One is by using the delayed coincidence measurement with the same time window and the other, mentioned earlier, is by estimating random coincidences using Eq. (34). As stated above, random coincidences can be reduced either by minimizing the coincidence time window or by reducing the activity. 

Since the scattered coincidences are an inherent physical property, they cannot be easily reduced or eliminated as random coincidences. Because it is prompt in nature, differentiation between true and scatter simply by minimization of the time window is therefore difficult. In addition, the energy loss in small-angle scatter is so small that it is difficult to differentiate through the energy window. In the case of multilayer ring geometry in imaging multiple... 

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