chapter 12 Counting Systems

Radiation counting systems are used for a variety of purposes in nuclear medicine. In vitro (from Latin, meaning “in glass”) counting systems are employed to measure radioactivity in tissue, blood, and urine samples; for radioimmunoassay and competitive protein binding assay of drugs, hormones, and other biologically active compounds; and for radionuclide identification, quality control, and radioactivity assays in radiopharmacy and radiochemistry. In vitro counting systems range from relatively simple, manually operated, single-sample, single-detector instruments to automated systems capable of processing hundreds of samples in a batch with computer processing of the resulting data.

In vivo (from Latin, meaning “in the living subject”) counting systems are employed for measuring radioactivity in human subjects or experimentally in animals. Different in vivo systems are designed for measuring localized concentrations in single organs (e.g., thyroid, kidney) and for measurements of whole-body content of radioactivity.

Most nuclear medicine counting systems consist of the following basic components: a detector and high voltage supply, preamplifier, amplifier, one or more single-channel analyzers (SCAs) or a multichannel analyzer (MCA) (“data analysis”), and a digital or analog scaler-timer, rate meter, or other data readout device. The majority of systems employ a computer or microprocessor for data analysis and readout.

At present, the most efficient and economical detector for counting γ-ray emissions * is a sodium iodide [NaI(Tl)] scintillation detector. The characteristics of various NaI(Tl) counting systems are discussed in Sections A and B in this chapter. Scintillation counters for β particles and low-energy x rays or γ rays are presented in Section C later in this chapter. Counting systems based on gas detectors and semiconductor detectors are discussed in Sections D and E, respectively. Section F deals with counting systems for in vivo applications, including thyroid uptake, sentinel node detection, and intraoperative probes.

A NaI(Tl) Well Counter

1 Detector Characteristics

The detector for a NaI(Tl) well counter is a single crystal of NaI(Tl) with a hole in one end of the crystal for the insertion of the sample (Fig. 12-1A). Dimensions of some commonly used well detectors are given in Table 12-1. The 4.5-cm diameter × 5-cm long crystal with 1.6-cm diameter × 3.8-cm deep well, the standard well-counter detector, is the most frequently used in nuclear medicine. It is designed for counting of samples in standard-size test tubes. Very large well-counter detectors, up to 13-cm diameter × 25-cm length, have been employed for counting very small quantities of high-energy γ-ray emitters (e.g., ⁴⁰K and ¹³⁷Cs). Most well-counter systems employ 5 cm or greater thickness of lead around the detector to reduce background counting levels. A typical manually loaded well-counter system is shown in Figure 12-1B.

FIGURE 12-1 A, Cross-sectional view of a well-counter detector containing a radioactive sample. B, Photograph of a manually loaded well counter with a digital readout and printer output.

(Courtesy Capintec, Inc., Ramsey, NJ.)

TABLE 12-1 DIMENSIONS OF TYPICAL NaI(Tl) WELL-COUNTER DETECTORS

Light transfer between the NaI(Tl) crystal and the photomultiplier (PM) tube is less than optimal with well-type detectors because of reflection and scattering of light by the well surface inside the detector crystal. Energy resolution is therefore poorer [10% to 15% full width at half maximum (FWHM) for ¹³⁷Cs] than obtained with optimized NaI(Tl) detector designs (approximately 6% FWHM) (see Chapter 10, Section B.7).

2 Detection Efficiency

The detection efficiency D (see Chapter 11, Section A) of the NaI(Tl) well counter for most γ-ray emitters is quite high, primarily because of their near 100% geometric efficiency g. The combination of high detection efficiency and low background counting levels makes the well counter highly suitable for counting samples containing very small quantities (Bq–kBq) of γ-ray-emitting activity. The geometric efficiency for small (1-mL) samples in the standard well counter is approximately 93% (see Fig. 11-3).

The intrinsic efficiency ε (Equation 11-8) of well-counter detectors depends on the γ-ray energy and on the thickness of NaI(Tl) surrounding the sample; however, the calculation of intrinsic efficiency is complicated because different thicknesses of detector are traversed by γ rays at different angles around the source. Calculated intrinsic efficiencies (i.e., all pulses counted) versus γ-ray energy for 1-mL sample volumes and for different NaI(Tl) well-counter detectors are shown in Figure 12-2. Intrinsic efficiency is close to 100% for 1.3- to 4.5-cm wall thickness and E_γ 150 keV, but at 500 keV the intrinsic efficiencies range from 39% to 82%.

FIGURE 12-2 Intrinsic efficiency (γ-ray absorption efficiency, Equation 11-9) vs. γ-ray energy for different NaI(Tl) well-counter detectors.

Intrinsic efficiency can be used to calculate the counting rate per kBq for a radionuclide if all pulses from the detector are counted; however, if only photopeak events are recorded, then the photofraction f_p also must be considered (see Chapter 11, Section A.4). The photofraction decreases with increasing γ-ray energy and increases with increasing well-detector size (Fig. 12-3). At 100 keV, f_p ≈ 100% for all detector sizes. At 500 keV, f_p ranges from 48% to 83% from the smallest to the largest common detector sizes (Table 12-1).

FIGURE 12-3 Photofraction versus γ-ray energy for different NaI(Tl) well-counter detectors.

The intrinsic photopeak efficiency ε_p is the product of the intrinsic efficiency and photofraction

(12-1)

This may be used to estimate photopeak counting rates. Figure 12-4 shows ε_p versus γ-ray energy.

FIGURE 12-4 Intrinsic photopeak efficiency vs. γ-ray energy for different NaI(Tl) well-counter detectors.

Table 12-2 lists some detection efficiencies, expressed as counts per minute (cpm) per becquerel, for full-spectrum counting of different radionuclides in the standard well counter. These values apply to 1-mL samples in standard test tubes.

TABLE 12-2 COUNTING EFFICIENCY FOR 1-mL SAMPLES IN A STANDARD SODIUM IODIDE WELL COUNTER (ASSUMING ALL PULSES COUNTED)

3 Sample Volume Effects

The fraction of γ rays escaping through the hole at the end of the well depends on the position of the source in the well. The fraction is only about 7% near the bottom of the well but increases to 50% near the top and is even larger for sources outside the well. Thus the geometric efficiency of a well counter depends on sample positioning. If a small volume of radioactive solution of constant activity in a test tube is diluted progressively by adding water to it, the counting rate recorded from the sample in a standard well detector progressively decreases, even though total activity in the sample remains constant (Fig. 12-5). In essence, the geometric efficiency for the sample decreases as portions of the activity are displaced to the top of the well.

FIGURE 12-5 A, Change in counting rate in a standard NaI(Tl) well counter for a sample of constant activity but diluted to increasing sample volume in a test tube. B, Change in counting rate with volume for constant concentration.

If the volume of a sample is increased by adding radioactive solution at a constant concentration, the counting rate first increases linearly with sample volume (or activity) but the proportionality is lost as the volume approaches and then exceeds the top of the well. Eventually there is little change with increasing sample volume, although the total activity is increasing (see Fig. 12-5). For example, an increase of sample volume in a standard test tube from 7 to 8 mL, a 14% increase in volume, increases the counting rate by only about 1%.

Thus sample volume has significant effects on counting rate with well counters. Sample volumes should be the same when comparing two samples. One technique that is used when adequate sample volumes are available is to fill the test tubes to capacity because with full test tubes, small differences in total volume have only minor effects on counting rate (curve B in Fig. 12-5); however, this requires that identical test tubes be used for all samples, so that the volume of activity inside the well itself does not differ between samples.

Absorption of γ rays within the sample volume or by the walls of the test tube is not a major factor except when low-energy sources, such as ¹²⁵I (27-35 keV) are counted. Identical test tubes and carefully prepared samples of equal volume should be used when comparing samples of these radionuclides.

4 Assay of Absolute Activity

A standard NaI(Tl) well counter can be used for assay of absolute activity (Bq or Bq/mL) in samples of unknown activity using the calibration data given in Table 12-2. Alternatively, one can compare the counting rate of the unknown sample to that of a calibration source (see Chapter 11, Section A.6). “Mock” sources containing long-lived radionuclides are used to simulate short-lived radionuclides, for example, a mixture of ¹³³Ba (356- and 384-keV γ rays) and ¹³⁷Cs (662-keV γ rays) for “mock ¹³¹I.” Frequently, such standards are calibrated in terms of “equivalent activity” of the radionuclide they are meant to simulate. Thus if the activity of a mock ¹³¹I standard is given as “A(Bq) of ¹³¹I,” then the activity of a sample of ¹³¹I of unknown activity X would be obtained from

(12-2)

where R(¹³¹I) and R(mock ¹³¹I) are the counting rates recorded in the well counter for the sample and the calibration standard, respectively.

Another commonly used mock standard is ⁵⁷Co (129 and 137 keV) for ^99mTc (140 keV). If the ⁵⁷Co is calibrated in “equivalent Bq of ^99mTc,” then Equation 12-2 can be used for ^99mTc calibrations also. If it is calibrated in becquerels of ⁵⁷Co, however, one must correct for the differing emission frequencies between ⁵⁷Co and ^99mTc (0.962 γ rays/disintegration vs. 0.889 γ rays/disintegration, respectively). The activity X of a sample of ^99mTc of unknown activity would then be given by

(12-3)

where A is the calibrated activity of the ⁵⁷Co standard and R(^99mTc) and R(⁵⁷Co) are the counting rates recorded from the ^99mTc sample and the ⁵⁷Co standard, respectively.

5 Shielding and Background

It is desirable to keep counting rates from background radiation as low as possible with the well counter to minimize statistical uncertainties in counting measurements (see Chapter 9, Section D.4). Sources of background include cosmic rays, natural radioactivity in the detector (e.g., ⁴⁰K) and surrounding shielding materials (e.g., radionuclides of Rn, Th, and U in lead), and other radiation sources in the room. Additional sources of background in a hospital environment include patients who have been injected with radionuclides for nuclear medicine studies or for therapeutic purposes. These sources of radiation, although usually located some distance from the counter, can produce significant and variable sources of background. External sources of background radiation are minimized by surrounding the detector with lead. The thickness of the lead shielding is typically 2.5-7.5 cm; however, even with lead shielding it is still advisable to keep the counting area as free as possible of unnecessary radioactive samples.

In well counters with automated multiple-sample changers (Section A.9), it also is important to determine if high-activity samples are producing significant backgrounds levels in comparison with activity samples in the same counting rack. In many nuclear medicine procedures, background counting rates are measured between samples, but if the background counting rate becomes large (e.g., from a radioactive spill or contamination of the detector), it can produce significant statistical errors even when properly subtracted from the sample counting rate (see Chapter 9, Section D.4).

6 Energy Calibration

Energy selection in a well counter usually is accomplished by an SCA (Chapter 8, Section C.2). Commercial well-counter systems have push-button or computer selection of the appropriate SCA window settings for different radionuclides. In these systems compensation has been made by the manufacturer for the nonlinear energy response of the NaI(Tl) detector. However, because of the possibility of drifts in the electronics and the PM tube gain with time, the response of the well counter should be checked regularly with a long-lived standard source, such as ¹³⁷Cs, as a quality assurance measure. Some modern well counters incorporate MCAs, allowing the entire spectrum to be measured and analyzed.

7 Multiple Radionuclide Source Counting

When multiple radionuclides are counted simultaneously (e.g., from tracer studies with double labels), there is “crosstalk” interference because of overlap of the γ-ray spectra of the two sources, as shown in Figure 12-6 for ^99mTc and ⁵¹Cr. If SCA windows are positioned on the ^99mTc (window 1) and ⁵¹Cr (window 2) photopeaks, a correction for the interference can be applied as follows: A sample containing only ⁵¹Cr is counted and the ratio R₁₂ of counts in window 1 to counts in window 2 is determined. Similarly, a sample containing only ^99mTc is counted and the ratio R₂₁ of counts in window 2 to counts in window 1 is determined. Suppose then that a mixed sample containing unknown proportions of ^99mTc and ⁵¹Cr is counted and that N₁ counts are recorded in the ^99mTc window (window 1) and that N₂ counts are recorded in the ⁵¹Cr window (window 2). Suppose further that room and instrument background counts are negligible or have been subtracted from N₁ and N₂. Then the number of counts from ^99mTc in window 1 [N₁(^99mTc)] can be calculated from

FIGURE 12-6 Window settings used for simultaneous measurement of ^99mTc and ⁵¹Cr in a mixed sample. Crosstalk from ⁵¹Cr into the ^99mTc window must be corrected for, using methods described in the text.

(12-4)

and the number of counts from ⁵¹Cr in window 2 [N₂(⁵¹Cr)] from

(12-5)

Equations 12-4 and 12-5 permit calculation of the number of counts that would be recorded in the photopeak window for each radionuclide in the absence of crosstalk interference from the other radionuclide. These equations can be used for other combinations of radionuclides and window settings with appropriate changes in symbols. For greatest precision, the ratios R₁₂ and R₂₁ should be determined to a high degree of statistical precision (e.g., ±1%) so that they do not add significantly to the uncertainties in the calculated results. The technique is most accurate when crosstalk is small, that is, R₁₂ and/or R₂₁ 1. Generally, the technique is not reliable for the in vivo measurements described in Section F, because of varying amounts of crosstalk caused by Compton scattering within body tissue.

Example 12-1

A mixed sample containing ^99mTc and ⁵¹Cr provides 18,000 counts in the ^99mTc window and 8000 counts in the ⁵¹Cr window. A sample containing ⁵¹Cr alone gives 25,000 counts in the ⁵¹Cr window and 15,000 crosstalk counts in the ^99mTc window, whereas a sample containing ^99mTc alone gives 20,000 counts in the ^99mTc window and 1000 crosstalk counts in the ⁵¹Cr window. What are the counts due to each radionuclide in their respective photopeak windows? Assume that background counts are negligible.

8 Dead Time

Because NaI(Tl) well counters have such high detection efficiency, only small amounts of activity can be counted (typically 10² to 10⁴ Bq). If higher levels of activity are employed, serious dead time problems can be encountered (see Chapter 11, Section C). For example, if the dead time for the system (paralyzable) is 4 µsec, and 50 kBq of activity emitting one γ ray per disintegration is counted with 100% detection efficiency, then the true counting rate is 50,000 cps; however, the recorded counting rate would be approximately 41,000 cps because of 18% dead time losses (see Equation 11-18).

9 Automated Multiple-Sample Systems

Samples with high counting rates require short counting times and provide good statistical precision with little interference from normal background radiation. If only a few samples must be counted, they can be counted quickly and conveniently using manual techniques; however, with long counting times or large numbers of samples, the counting procedures become time consuming and cumbersome. Systems with automated sample changers have been developed to alleviate this problem (Fig. 12-7). Typically, these systems can accommodate 100 or more samples, and each sample is loaded automatically into the counter in a sequential manner.

FIGURE 12-7 A NaI(Tl) well counter with automated sample-changing capabilities. Hundreds of samples can be loaded and measured in a single run. This system also incorporates a multichannel analyzer for spectral analysis.

(Courtesy PerkinElmer, Inc. Waltham, MA.)

Most multiple sample systems use a variation of the well-counter detector known as the “through-hole” detector. As shown in Figure 12-8, the sample hole passes through the entire length of the NaI(Tl) crystal, and the PM tube is connected to the side of the scintillator. A key advantage of the through-hole detector is that samples can be automatically positioned at the center of the NaI(Tl) crystal, irrespective of sample volume. This results in the highest detection efficiency and minimizes efficiency changes with volume. Figure 12-9 shows the smaller changes in efficiency with volume for a through-hole versus a well-type counter for ⁵⁹Fe.