Count rate performance refers to the finite time it takes the system to process detected photons. After a photon is detected in the crystal, a series of optical

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Figure 3.17. The energy spectra for single photons for a BGO PET system. The air and scatter measurements are of a 68Ge line source in air and in a 20 cm-diameter water-filled cylinder respectively, while the distributed source is for a solution of 18F in water in the same cylinder, to demonstrate the effect on energy spectrum of a distribution of activity. The respective energy resolutions are: air - 16.4%, line source in scatter - 19.6%, and distributed source - 21.6%.

Figure 3.17. The energy spectra for single photons for a BGO PET system. The air and scatter measurements are of a 68Ge line source in air and in a 20 cm-diameter water-filled cylinder respectively, while the distributed source is for a solution of 18F in water in the same cylinder, to demonstrate the effect on energy spectrum of a distribution of activity. The respective energy resolutions are: air - 16.4%, line source in scatter - 19.6%, and distributed source - 21.6%.

Figure 3.18. The "true" coincidence energy spectrum of a BGO full-ring scanner is shown for a 68Ge line source measured in air. The spectrum is obtained by having one photon energy window set from 100-850 keV and the opposing detector window stepped in small increments of 25 keV to yield an integral coincidence spectrum. The derivative of the integral spectrum results in the above graph.

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Figure 3.18. The "true" coincidence energy spectrum of a BGO full-ring scanner is shown for a 68Ge line source measured in air. The spectrum is obtained by having one photon energy window set from 100-850 keV and the opposing detector window stepped in small increments of 25 keV to yield an integral coincidence spectrum. The derivative of the integral spectrum results in the above graph.

and electronic processing steps results, each of which requires a finite amount of time. As these combine in series, a slow component in the chain can introduce a significant delay. Correction for counting losses due to dead time are discussed in detail in Ch. 6. In this section we will restrict ourselves to the determination of count rate losses for PET systems for the purposes of comparing performance.

The most common method employed in PET for count rate and dead time determinations is to use a

Figure 3.19. Count rate curves are shown for the measured parameters of true (unscattered plus scattered) coincidences, random coincidences, and multiple coincidences (three events within the time window), and the derived curves for expected (no counting losses) and noise equivalent count rate (NEC). The data were recorded on a CTI ECAT 953B PET camera using a 20 cm-diameter water-filled cylinder filled with 11C in water.

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source of a relatively short-lived tracer (e.g., 18F, 11C) in a multi-frame dynamic acquisition protocol and record a number of frames of data of suitably short duration over a number of half-lives of the source. Often, a cylinder containing a solution of 18F in water is used. From this, count rates are determined for true, random, and multiple events. The count rates recorded at low activity, where dead time effects and random event rates should approach zero, can then be used to extrapolate an "ideal" response curve with minimal losses (observed = expected count rates). An example of the counting rates achieved for a BGO-based scanner in 2D mode is shown in Fig. 3.19.

It is possible to apply appropriate models to calculate dead time parameters. The data in Fig. 3.19 were characterized by modelling as a cascaded non-paralysable/

paralysable system (Fig. 3.20) [20]. From this analysis, the non-paralysable dead-time component (Tnp) and the paralysable dead-time component (tp) were found to be approximately 3^s and 2^s respectively. Clearly, this is very different to the coincidence timing window duration (in this case 2t = 12ns). The purposes of such parameter determinations might be to derive a dead-time correction factor from the observed counting rates.

The purpose of defining count rate performance is motivated by the desire to assess the impact of increasing count rates on image quality. Much of the theory behind measuring image quality derives from the seminal work of Dainty and Shaw with photographic film [21] and has been applied in a general theory of quality of medical imaging devices to measure detector quantum efficiency [22]. In PET an early suggestion for

Figure 3.20. The true coincidence count rate for a 16-ring BGO scanner modelled as a combined paralysable and non-paralysable system produces the above fit to the data. From this, estimates of the dead time components can be derived.

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Figure 3.21. Log-linear count rate profiles from sinograms of a line source of 68Ge in air (left) and centered in a 20 cm-diameter water-filled cylinder (right) demonstrate the additive scatter component outside of the central peak in the measurement in the cylinder. Interpolation of this section permits an estimate of the scatter fraction to be made. Both measurements were in 2D mode.

the use of such a figure of merit defined an '"effective" image event rate, Q to be:

where dj,dS,and dA are the count rates per cm from the center of a uniform cylinder containing radioactivity for the unscattered, scattered, and accidental (random) coincidences respectively, DI is the total unscattered coincidence rate and (d7/dT) is the contrast. It was suggested that "... Q may also be called an 'effective'image event rate, since the same signal-to-noise ratio would be obtained in an ideal tomograph " [2].

This has been further developed in recent years. Comparison of the count rate performance of different tomographs, or of the same scanner operating under different conditions (e.g., 2D and 3D acquisition mode) have been difficult to make because of the vastly different physical components of the measured data (e.g., scatter, randoms) and the strategies for dealing with these. These effects necessitate a comparison which can take account of these differences. The noise equivalent count (NEC) rate [23] provides a means for making meaningful inter-comparisons that incorporate these effects. The noise equivalent count rate is that count rate which would have resulted in the same signal-to-noise ratio in the data in the absence of scatter and random events. It is always less than the observed count rate.

The noise equivalent count rate is defined as:

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where rtotal is the observed count rate (including scattered events), T and S are the unscattered and scattered event rates respectively, f is the "random event field fraction", the ratio of the source diameter to the tomograph's transaxial field-of-view, and R is the random coincidence event rate. This calculation assumes that the random events are being corrected by direct measurement and subtraction from the prompt event rate and that both measurements contain noise, hence the factor of 2 in the denominator (see Ch. 6). The NEC rate is shown, along with the data from which it was derived, in Fig. 3.19.

Some caution is required when comparing NECs from various systems, namely what scatter fraction was used and how it was determined, how the randoms fraction (R) was determined and how randoms subtraction was applied (delay-line method, estimation from single event rates, etc). However, the NEC does provide a parameter which can permit comparisons of count rate, and therefore an index of image quality, between systems.

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