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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5545_Библиотеки_им_академика_М_И_Перельмана.pdf
becomes prominent when the energy of the photon is less than about 200 keV,
ENERGY (keV)
because, at energies above 200keV, the iodine escape peak would fall within the
width of the photopeak, due to the small differences between the two peaks.
8.4.6 Positron Annihilation Peak
γ-rays with energy greater than 1.02MeV may undergo pair production in the detector in which a positive–negative electron pair is produced. The β+-particles are annihilated to produce two 511-keV photons, which appear as photopeaks in the γ-ray
spectrum. If, however, one of the 511-keV photons escapes from the detector, then
a peak, called the single-escape peak, corresponding to the primary photon energy
minus 511keV, will appear in the spectrum. If both annihilation photons escape,
then a double-escape peak results, corresponding to the primary photon energy
minus 1.02 MeV. Larger detectors can prevent the escape of the annihilation
radiations.
8.4.7 Coincidence Peak
A coincidence or sum peak results when more than one photon is absorbed simultaneously in the detector to be considered as a single event. The peak equals the sum
of the energies of the photons. Such situations occur with radionuclides that have
short-lived isomeric states and thus emit γ-rays in cascade. For example,
171- and 245-keV photons, which can result in a sum peak of 416keV (Fig.8.5).
Sum peaks are also caused by counting high-activity samples in which two photons
may strike the detector at the same time. These peaks can be reduced by counting
the samples at larger distances between the source and the detector or by using
smaller detectors so that the likelihood of two photons striking the detector at the
same time is reduced. In the case of high-activity samples, the level of activity has
to be reduced either by dilution or allowing to decay, in order to reduce the sum peak.
111
In emits
Fig. 8.5 A spectrum of
111
In with 171- and
245-keV photons showing
a coincidence (sum) peak
at 416keV
70
60
50
40
30
20
10
80 160 240 320 400
8.5 Liquid Scintillation Counter
Scaler
Freezer
Low-energy β−-particles are normally absorbed within the source and in the window
and walls of the detectors, and therefore β−-emitters are difcult to detect in gas or
solid detectors. For this reason, β−-emitting radionuclides are counted using the
liquid scintillation technique in which the radioactive sample is mixed with a scintillating material. A sample vial containing the liquid scintillator and the radioactive
sample of interest is placed between two PM tubes connected in coincidence
(Fig.8.6). Each PM tube receives the light photons emitted by the interaction of the
β−-particle with the scintillator and converts them into a pulse, which is further
amplied by an amplier. The amplitude of the pulses is proportional to the energy
of the β−-particles. The amplied pulses are then delivered to the coincidence circuit
that contains a PHA to analyze the pulse height for acceptance. A count is registered
in the scaler if two pulses of the same height are recorded in both PM tubes simultaneously. Such coincidence counting reduces the background counts due to noise,
including terrestrial and cosmic radiations, radioactive patients, etc.
The liquid scintillation solution is prepared by dissolving a primary scintillating
solute or uor and often a secondary uor in a solvent. The radioactive sample is
added to and thoroughly mixed with the scintillating solution for counting. The
primary uors include 2,5-diphenyloxazole (PPO), 2,5 bis-2-(5-T-
butylbenzoxazolyl)-thiophene (BBOT), and p-terphenyl, of which PPO is most
commonly used in a concentration of 5g/L.
Toluene, xylene, and dioxane are the most common solvents that easily dissolve
the primary uor and often the radioactive sample, which is a requirement for a
good solvent. These solvents, however, are poorly miscible in water, and therefore
their disposal in the sewer system is restricted. For this reason, biodegradable
Amplifier
Pre-
amplifier
Fig. 8.6 A schematic diagram of a liquid scintillation counting system. Light photons emitted
from the sample strike the two photomultiplier tubes to produce pulses. Only coincident pulses
are counted
Coincidence
Circuit
Radioactive sample
Amplifier
PM tubePM tube
Pre-
amplifier
solvents such as linear alkylbenzene and phenyl xylyl ethane are widely used.
Counting vials are usually glass or plastic, but the latter is not used when toluene or
xylene is used as a solvent because the solvent tends to dissolve plastic.
When radiations pass through the solvent, electrons are released from the solvent
molecules after absorption of radiation energies. These electrons transfer energy to
primary uor molecules, which then emit light photons for further processing by
PM tubes and associated electronics. The wavelength of these light photons may be
somewhat shorter than required for the spectral sensitivity of the photocathode of
the PM tube. This mismatch is rectied by adding a secondary uor or solute, called
the wavelength shifter, to the scintillating solution. The wavelength shifter absorbs
the light photons emitted by the primary uor and reemits them with a longer wavelength, which is more suitable for the photocathode of the PM tube. The compound
1, 4-bis-2-(5-phenyloxazolyl)-benzene (POPOP) is most commonly used as a secondary solute in a concentration of about 0.1%.
An attempt is always made to keep the radioactive sample in solution in the liquid scintillator. Solubilizing agents are added to improve dissolution of specic
samples, and the common example is the hydroxide of Hyamine 10-X used in
counting tissue samples.
8.5.1 Quenching
In liquid scintillation counting, quenching is a problem caused by interference with
the production and transmission of light, which ultimately reduces the detection
efciency of the system. Quenching can be of the following types:
1. Chemical type, resulting from interference in energy transfer by substances such
as samples or extraneous materials (e.g., dissolved O2).
2. Color type, resulting from absorption of light photons by colored substances,
such as hemoglobin, before striking the PM tube.
3. Dilution type, resulting from relatively large dilution of the scintillation mixture,
in which case many light photons may be absorbed by the diluted sample.
4. Optical type, resulting from absorption of light by a dirty vial containing frost or
ngerprints.
Quenching must be corrected to obtain accurate counting of samples, and three
methods have been adopted for this purpose, namely, internal standard method,
channel ratio method, and external standard method. The readers are asked to refer
to physics books for details of these methods.
A problem with liquid scintillation counting is the noise due to spontaneous thermal emission of electrons from the photocathode of the PM tube. Background noise
also arises from the interaction of light with scintillation solution. Thermal emission
of electrons is reduced by refrigeration of the counting chamber to keep the PM
tubes at low temperature. But the coincidence counting is the most effective method
to reduce the noise.
The liquid scintillation counting systems are provided with automatic sample
E
nX
FWHM
E
100
changers for counting as many as 500 samples. Also, one to ve PHAs are available
on a liquid scintillation counter, so that β−-particles of different energies can be
counted simultaneously by using different baselines and windows on each PHA. The
β−-emitters, 3H, 14C, 32P, and 35S, are commonly detected by liquid scintillation
counting. Whereas, the counting efciencies of 3H (E
(E
=1.71MeV) are ∼60–70% and ∼100% respectively, they are negligible for
max
= 0.018 MeV) and 32P
max
γ- and x-rays.
8.6 Characteristics ofCounting System
Detection of radiation and therefore counting of radioactive samples is affected by
different characteristics of the detector and the associated electronics. The following is a discussion of these properties.
8.6.1 Energy Resolution
As already mentioned, even though γ-rays of the same energy are absorbed in the
NaI(Tl) detector by the photoelectric effect, pulses of different amplitudes are produced because of the statistical variations in the production of light photons in the
detector and photoelectrons and electrons in the PM tube. This results in the broadening of the photopeak. The width of the peak or the sharpness of the peak (i.e., the
energy resolution of the detector) predicts the ability of the NaI(Tl) spectrometer to
discriminate between the γ-ray photons of dissimilar energies. A similar situation
exists for semiconductor detectors where the number of ionizations may vary from
one γ-ray to another of the same energy, leading to the broadening of the peak.
The energy resolution of a system is given by the full width at half-maximum
(FWHM) amplitude of the photopeak expressed as a percentage of the photon
energy as follows:
nergyresolutio
%
(8.1)
where Eγ is the energy of the γ-ray photon. In Fig.8.7, FWHM is 55 keV for the
662-keV peak of
137
Cs; therefore,
Energy resolution%
55
662
.%
83
100
The energy resolution depends on the photon energy. The higher the photon
energy, the better the energy resolution (i.e., smaller FWHM), because of the
decrease in the percentage of statistical variations in the pulse production. The
energy resolution of NaI(Tl) detectors is about 7–10% for the 662-keV γ-ray of
70
ENERGY (keV)
V
Fig. 8.7 The full width at
Efficiency ff fN
ipgi
half maximum (FWHM) of
the 662-keV γ-ray of
in a NaI(Tl) detector
137
Cs
60
50
40
30
20
10
137
Cs and 10–14% for the 140-keV γ-ray of
FWHM =
99m
Tc. In contrast, the energy resolution
800 700 600 500 300 200 100 400
∆E = 55 ke
in Ge(Li) detectors is about 0.42% for 140-keV γ-rays and about 0.2% for photons
of more than 1MeV.
8.6.2 Detection Efficiency
The detection efciency of a counter is given by the observed count rate divided by
the disintegration rate of a radioactive sample. The count rate of a sample differs
from the disintegration rate because of several factors. Radiations from a source are
emitted isotropically around 4π steridians, but only a fraction of all photons emitted
strikes the detector, depending on the solid angle subtended by the detector on the
source. Also, only a fraction of all photons striking the detector may interact in the
detector and produce pulses. Only a fraction of all pulses produces a single photopeak. Furthermore, the count rate is affected by the abundance of a particular radiation from a radionuclide. Considering these factors, the overall counting efciency
of a counter for a radiation is given by the following expression:
(8.2)
where fi is the intrinsic efciency; fp is the photopeak efciency, or photofraction; fg
is the geometric efciency; and Ni is the abundance of the radiation in question. Ni
is available in literature on Tables of Isotopes.
8.6.2.1 Intrinsic Efficiency
The fraction of all radiations of a given type and energy impinging on the detector
that interacts with it to produce pulses is called the intrinsic efciency, fi, of the
detector:
No of radiations detected bythe detector
Allcounts under the photopeak
Gamma ray energy (keV)
fi=
.
No of radiations
.
impingingon the detector
Allcounts under the entire spect=rrum
No of radiations impinging on the detector.
(8.3)
It includes all photons undergoing both photoelectric absorption and Compton
scattering. Intrinsic efciency depends on the type and energy of the radiation and
the linear attenuation coefcient (μ) and thickness of the detector. The dependence
of intrinsic efciency on the photon energy and the detector thickness is illustrated
in Fig.8.8. The value of fi is almost 1 for low-energy γ-rays and thicker detectors.
The fi tends to 0 for high-energy γ-rays and thinner detectors. These conditions
apply to all solid scintillation detectors. The intrinsic efciency of gas detectors is
almost unity for α- and β-particles but is about 0.01 (1%) for γ- and x-rays.
8.6.2.2 Photopeak Efficiency or Photofraction
The fraction of all detected γ-rays that contributes only to the photopeak is called
the photopeak efciency, or photofraction (fp). It is given as the total photopeak area
divided by the total area under the entire spectrum:
fp=
All photons detected by the deetector
(8.4)
This value is affected by all factors that inuence photoelectric effect, such as the
size and composition of the detector and γ-ray energy, but is primarily determined
by the discriminator settings on the PHA. The fp increases with increasing window
width of the PHA.
Fig. 8.8 Dependence of
intrinsic efciency on
photon energy and detector
thickness
100
75
50
25
Nal(TI)
thickness
1.3 cm
0.6 cm
70 140 210
280
8.6.2.3 Geometric Efficiency
r
R
2
4
a
b
c
Radiations from a source are emitted uniformly with equal intensity in all directions. If a source of radiation is placed at a distance from a detector, then only a
fraction of all radiations emitted from the source will be detected by the detector.
This fraction is determined by the solid angle subtended by the detector on the
source. The geometric efciency, fg, is equal to the number of radiations striking the
detector divided by the total number of radiations emitted by the source.
Thus,
No of radiations striking the detector
fg=
Total number of r
.
aadiations emittedbythe source
(8.5)
For a circular detector with radius r, it is equal to the area πr2 of the detector
divided by the total spherical area 4πR2, where R is the distance between a point
source S and the detector D (Fig.8.9).
f
g
2
(8.6)
As the distance R between the source and the detector increases, the fg decreases,
according to the inverse square law, that is, fg∝1/R2 (Fig.8.9a). Thus the fg at 2R is
one fourth of the fg at R. The value of fg increases with the size of the detector. Also,
the nite size of the radiation source affects the fg values.
When the source and the detector are in close contact, the fg tends to be about 50%
(Fig.8.9b). In the case of gamma well counters and liquid scintillation counters, the
fg approaches 100% (Fig.8.9c).
Fig. 8.9 Illustration of
geometric efciency, fg, of
a detector D with a circular
2
area, πr
, where r is the
radius of the detector. (a)
The detector D placed at a
distance R from the point
source S has an f
times greater than the f
when the detector is placed
at a distance 2R. (b) When
the source and the detector
are in close contact, the f
is about 50%. (c) When the
source is well inside the
detector as in a well
counter, the f
approaches 100%
four
g
g
g
g
S D
S
SD
R
r
2R
r
D D
8.6.3 Dead Time
RR R
to o
/1
Each counting system takes a certain amount of time to process a radiation event,
starting from interaction of radiation with the detector all the way up to forming a
pulse and ultimately recording it. The counter remains insensitive to a second event
for this period of time, that is, if a second radiation arrives during this time, the
counter cannot process it. This period is called the dead time. When the counter
recovers after this period, only then can a second radiation be detected. Thus the
second event arriving during the dead time is lost. Counts lost during the dead time
are called the dead-time loss. In scintillation detectors, radiations may arrive at the
same time and be processed simultaneously to form a single event of amplitude that
is equal to the sum of the amplitudes of both events. This is referred to as pulse
pileup. If one or both of the events were photopeaks originally, then the combined
peak will fall outside the PHA window setting and be lost. Dead time loss at high
count rates is a serious problem for any counting system and is more so for scintillation cameras due to pulse pileup (see Chap. 11).
The dead time of a counting system may arise from different components of the
entire counting system: detector, PHA, PM tube, scaler, computer interface, and so
on. While Geiger–Müller (GM) detectors have a longer dead time of 80–500μs, the
typical values for NaI(Tl) and semiconductors are of the order of 0.5–10μs and for
liquid scintillators, ∼0.1–1 μs (Cherry etal. 2012).
Based on how successive pulses are processed owing to the dead time, the counting systems fall into two categories: paralyzable and nonparalyzable. In paralyz-
able systems, each event sets its own dead time, even if it arrives within the dead
time of the previous event and is not counted. Each event prolongs the dead time
induced by the previous event, and thus adds to the total dead time of the system,
whereby a paralyzable system can become totally unresponsive to process events if
the count rate of the source is very high. On the other hand, in nonparalyzable systems, the instrument remains insensitive to successive events for a period of time
equal to the dead time, and these events are lost. But unlike paralyzable systems, the
dead time is not changed or lengthened. When the system recovers after the detection of the rst event, only then is the second event processed and detected. The two
types of dead time losses are illustrated in Fig.8.10.
The paralyzable and nonparalyzable systems can be represented by mathematical relationships among the observed count rate R
τ. For nonparalyzable systems,
, true count rate Rt, and dead time
o
(8.7)
and for paralyzable systems,
R
-
t
RRe
0
t
(8.8)
Different components of a radiation detection system can have either paralyzable
or nonparalyzable dead time. Scalers and pulse-height analyzers are nonparalyzable
systems, whereas radiation detectors themselves are paralyzable systems.
TRUE COUNT RATE
NONPARALYZABLE
Fig. 8.10 Plot of observed
count rates versus true
count rates indicating the
dead time loss in
paralyzable and
nonparalyzable systems
2.0
1.5
1.0
0.5
6
10
×
0.51.5 2.0
1
PARALYZABLE
Scintillation cameras have both paralyzable and nonparalyzable components of
dead time. As can be seen from Eq. (8.8), the radiation detectors become totally
paralyzed at very high count rates giving no reading.
Dead time loss is a serious problem for a counting system at high count rates.
Therefore, either count rates must be lowered or corrections must be made to the
observed count rates. There are several methods to determine or correct for dead
time. An empirical method is to plot the observed count rates as a function of
increasing concentrations of known activity. From the plot and Eqs. (8.7) and (8.8),
the dead time is calculated for the nonparalyzable or paralyzable system. For subsequent measurements of unknown samples, correction is made to compensate for
the dead time loss giving true count rates. Another method uses two radioactive
sources, which are counted in the counter individually and together. From these
three measurements, one can calculate dead time using appropriate equations (see
Cherry etal. 2012). Various techniques, such as use of buffers, in which overlapping
events are held off during the dead time, use of pulse pileup rejection circuits, and
use of high-speed electronics have been employed to improve the dead time
correction.
8.7 Gamma Well Counter
The gamma well counter consists of a NaI(Tl) detector with a hole in the center for
a sample to be placed and associated electronics such as a PM tube, preamplier,
amplier, PHA, and scaler–timer. Placing a radioactive sample in the central hole of
the detector increases the geometric efciency (almost 99%) and hence the counting
efciency of the counter. The NaI(Tl) detectors have dimensions in the range of
5-cm diameter × 5-cm thick to 23-cm diameter × 23-cm thick. Smaller detectors are
used for low-energy γ-rays (less than 200keV), and larger detectors are used for
high-energy γ-rays. Most well counters are shielded with about 8.5-cm thick
Radioactive
Fig. 8.11 A schematic
diagram of a NaI(Tl) well
counter with a PM,
photomultiplier tube
sample
Nal (TI) Crystal
circular lead ring to reduce background from cosmic rays, natural radioactivity such
as 40K, or background activity in the work area. A typical well counter detector is
shown in Fig.8.11.
8.7.1 Calibration ofWell Counter
It is essential that the dial settings of the discriminators on the PHA are calibrated
so that the dial readings correspond directly to the pulse height (i.e., the energy of
the γ-ray photon); that is, the dial readings can be read in units of keV.This calibration is called the high-voltage or energy calibration of the well counter. The energy
calibration is carried out by using the 662-keV photons of
137
Cs source in the well counter, the lower and upper discriminator levels are set at
640 divisions and 684 divisions, respectively, thus assigning the center of the photopeak at 662 divisions corresponding to the 662-keV γ-ray. Starting from low values, the high voltage is increased in small increments for a given amplier gain until
the observed count rate reaches a maximum. The high voltage at the maximum
count rate is kept as the operating voltage for subsequent counting of photons of
different energies. The discriminator dials are then said to be energy calibrated; for
example, each dial unit corresponds to 1keV at an amplier gain of 1. Thus, the
99m
center of the 140-keV photopeak of
Tc can be set at 140 divisions of the discriminator setting, with lower and upper values set as desired. After calibration, well
counters should be checked regularly for any voltage drift using a long-lived source,
such as
137
Cs.
137
Cs. After placing a
8.7.2 Counting inWell Counter
For relative comparison of count rates between samples, the well counter does not
need to be calibrated, provided all samples for comparison have the same volume.
In radioimmunoassays, ferrokinetics, blood volume, red cell mass measurements, a
standard of the same geometry (volume) and with relatively the same activity is
counted along with all samples, and then a comparison is made between each