BETA-EMITTING RADIONUCLIDES
Procedure
The disintegration rate (
A)of a beta-particle-emitting specimen is obtained by counting a quantitatively deposited aliquot in a fixed geometry according to the formula:
in which
eis the counting efficiency of the counter;
fris the correction factor for counter dead time;
fbis the correction factor for backscatter;and
fsis the correction factor for self-absorption.The count rate for zero absorber is obtained by extrapolation of the initial linear portion of the absorption curve to zero absorber thickness,taking into consideration the mg/cm
2thicknessof specimen coverings,counter window,and the intervening air space between specimen and the counter window.The counter efficiency,
e,is determined by use of a long-lived secondary standard with similar spectral characteristics.RaD+Ehas frequently been used for efficiency calibration of counters for phosphorus 32.By the use of identical measurement conditions for the specimen and the standard (and extrapolation to zero absorber),the ratio of the values of
fr,
fb,and
fsfor the standard and the specimen approaches unity.
The previous relationship is valid also when the counter has been calibrated with a standard of the radionuclide to be assayed.In this case,however,the extrapolations to zero absorber thicknessfor the specimen and standard are not required,as the two absorption corrections cancel for a given geometry.
Another useful and frequently employed method for the determination of the disintegration rate of beta-emitting radionuclides is liquid-scintillation counting,which also utilizes an extrapolation of the specimen count rate to zero pulse-height discriminator bias.
GAMMA-EMITTING RADIONUCLIDES
For the assay of gamma-emitting radionuclides,three methods are provided.The selection of the preferred method is dictated by the availability of a calibration standard of the radionuclide to be assayed and the radionuclidic purity of the article itself.
Direct comparison with a calibration standard is required if a calibration standard of the radionuclide to be assayed is available and if the upper limit of conceivable error in the activity determination arising from the presence of radionuclidic impurities has been determined to be less than 3%.If the required calibration standard is not routinely available,as would probably be the case for a short-lived radionuclide,but was available at some time prior to the performance of the assay for determination of efficiency of the counting system for the radionuclide to be assayed,use a calibrated counting system,provided the radionuclidic impurity content of the specimen meets the requirements stated for the direct comparison method.If the requirements for either of the first two methods cannot be met,use the method for determination of activity from a calibration curve.
With the exception of the first method,the counting systems used are monitored for stability.This requirement is met by daily checks with a long-lived performance check source and weekly checks with at least three sources covering a broad range of gamma-ray emission energies (e.g.,57Co,137Cs,and 60Co).If a discrepancy for any of the aforementioned measurements is found,either completely recalibrate or repair and recalibrate the system prior to further use.
Assay by Direct Comparison with a Calibration Standard
An energy selective measurement system (e.g.,pulse-height analyzer)is not required for this procedure.Use either an ionization chamber or an integral counting system with a NaI(Tl)detector.Aconsistently reproducible geometrical factor from specimen to specimen is essential for accurate results.With proper precautions,the accuracy of this method approaches the accuracy with which the disintegration rate of the calibration standard is known.
Determine the counting rate of the detector system for a calibration standard of the radionuclide to be assayed (e.g.,active enough to give good measurement statistics in a reasonable time,but not so active as to cause serious dead-time problems),selecting such a standard as to provide optimum accuracy with the particular assembly used.Place an accurately measured aliquot of the unknown assay specimen (diluted,if necessary)in a container identical to that used for the standard,and measure this specimen at approximately the same time and under the same geometrical conditions as for the standard.If the elapsed time between the measurements of the calibration standard and the specimen exceeds 12hours,check the stability of the measurement system within 8hours of the specimen measurement time with a long-lived performance check source.Record the system response with respect to the same check source at the time of calibration,and if subsequent checks exceed the original recorded response by more than ±3%,recalibration is required.Correct both activity determinations for background,and calculate the activity,in µCi per mL,by the formula:
in which Sis the µCi strength of the standard,Dis the dilution factor,and gand bare the measured values of counting rate for the specimen and the standard,respectively.
Assay with a Calibrated Integral Counting System
The procedure and precautions given for the preceding direct-comparison method apply,except that the efficiency of the detector system is determined and recorded for each radionuclide to be assayed,rather than simply recording the counting rate of the standard.Thus,the efficiency for a given radionuclide,
x,is determined by
ex=bx/sx,in which
bxis the counting rate,corrected for background and dead-time,for the calibration standard of the radionuclide,
x,and
sxis the corresponding activity of the certified calibration standard in nuclear transformations per second.For subsequent specimen assays,the activity is given by the formula:
in which
Dis the dilution factor,
gxis the specimen counting rate (corrected for background and dead-time),and
exis the corresponding efficiency for the radionuclide.
Determination of Activity from a Calibration Curve
Versatility in absolute gamma-ray intensity measurements can be achieved by employing multi-channel pulse-height analysis.The photopeak efficiency of a detector system can be determined as a function of gamma-ray energy by means of a series of gamma-ray emission rate standard specimens,and the gamma-ray emission rate of any radionuclide for which no standard is available can be determined by interpolation from this efficiency curve.However,exercise care to ensure that the efficiency curve for the detector system is adequately defined over the entire region of interest by using a sufficient number of calibration points along the photopeak-energy axis.
Selection of a Counting Assembly
Agamma-ray spectrometer is used for the identification of radionuclides that emit X-rays or gamma rays in their decay.Requirements for an assembly suitable for identification and assay of the radionuclides used in radiopharmaceuticals are that (a)the resolution of the detector based on the 662-keVphotopeak of 137Cs-137mBa must be 8.0%or better,(b)the detector must be equipped with a specimen holder designed to facilitate exact duplication of counting geometry,and (c)the pulse-height analyzer must have enough channels to delineate clearly the photopeak being observed.
Procedure
Minimal requirements for the maintenance of instrument calibrations shall consist of weekly performance checks with a suitable reference source and a complete recalibration semi-annually.Should the weekly performance check deviate from the value determined at the time of calibration by more than 4.0%,a complete recalibration of the instrument is required at that time.
This method involves three basic steps,namely photopeak integration,determination of the photopeak efficiency curve,and calculation of the activity of the specimen.
PHOTOPEAK INTEGRATION
The method for the determination of the required photopeak area utilizes a Gaussian approximation for fitting the photopeak.Afixed fraction of the total number of photopeak counts can be obtained by taking the peak width,
a,at some fraction of the maximum,where the shape has been experimentally found to be very close to Gaussian,and multiplying by the counting rate of the peak channel,
P,after correction for any Compton and background contributions to the peak channel count rate.This background usually can be adequately determined by linear interpolation.This is illustrated in
Figure 2.
Fig.2Typical Gamma-ray Spectrum Showing the Selection of the Peak Channel Counting Rate,P,after the Correction for Compton and Background Contributions.
The photopeak-curve shape is closest to a straight line at 0.606P,and the contribution of the fractional channels to acan be accurately estimated by interpolation.Calculate aby the equation:
in which
cand
dand also
c¢and
d¢are the single
channel countingrates on either side of 0.606
P,and
Dand
D¢are the channel
numbers(locations)of
dand
d¢,respectively.The location of the required variables on the photopeak is illustrated in
Figure 3.
From the known values for the counting rate in the peak channel of the photopeak,P,and the width of the peak at 0.606P,a,a calibrated fraction of the photopeak area is then obtained from the product,(aP).
To summarize the procedures involved in obtaining a calibrated fraction of a photopeak area using this method,the necessary steps or calculations are presented below in a stepwise manner:
(1)Subtract any Compton and background contributions from the photopeak to be measured.
(2)Determine the counting rate of the peak channel (maximum channel counting rate after subtracting Compton and background),P.
(3)Multiply Pby 0.606,and locate the horizontal line corresponding to the peak width,a.
(4)Obtain the peak width,a,by inserting the values of variables (obtained as shown in the preceding figure)into the equation defining a.
(5)The desired calibrated fraction of the peak area is then equal to the product of atimes Por F=aP,where Fis a fractional area of the peak proportional to the emission rate of the source.
This method provides a quick and accurate means of determining the gamma-ray emission rate of sources while avoiding,to a large extent,subjective estimates of the detailed shape of the tails of the peaks.The error due to using the maximum channel counting rate,rather than the theoretical maximum or peak channel rate,is of the order of 1.0%if ais 6or greater.
PHOTOPEAK EFFICIENCY CALIBRATION
Radionuclides such as those listed in the accompanying table together with some of their nuclear decay data are available as certified reference standards.
*Asufficient number of radioactive standard reference sources should be selected in order to obtain the calibration curve over the desired range.Where possible,standard sources of those radionuclides that are to be assayed should be included.
Nuclear Properties of Selected Calibration Standards(1,2)
| Principal Photon Emissions |
Energy (ke V) |
Photons per 100 Disintegrations |
| 133Ba (T1/2=10.5years) |
|
|
| Ka1 |
30.97 |
63.4 |
| Ka2 |
30.62 |
34.2 |
| Kb |
35.0 |
22.8 |
| g1 |
53.15 |
2.14 |
| g2 |
79.62 |
2.55 |
| g3 |
80.99 |
33.0 |
| g6 |
276.39 |
6.9 |
| g7 |
302.83 |
17.8 |
| g8 |
356.0 |
60.0 |
| g9 |
383.85 |
8.7 |
| 137Cs-137mBa (T1/2=30.17years) |
|
|
| Ka1 |
32.19 |
3.82 |
| Ka2 |
31.82 |
2.07 |
| Kb |
36.4 |
1.39 |
| Weighted Mean(4) |
(32.9) |
(7.28) |
| g1 |
661.6 |
89.98 |
| 22Na (T1/2=2.60years) |
|
|
| hn |
511 |
179.80(5) |
| g1 |
1274.54 |
99.94 |
| 60Co(T1/2=5.27years) |
|
|
| g1 |
1173.2(6) |
100.0 |
| g2 |
1332.5(6) |
100.0 |
| 57Co(T1/2=270.9days) |
|
|
| SXK |
7.0 |
56.0 |
| g1 |
14.4 |
9.5 |
| g2 |
122.06 |
85.51 |
| g3 |
136.47 |
10.60 |
| Weighted Mean |
(125.0) |
(96.11) |
| (g2+g3)(4) |
|
|
| 54Mn (T1/2=312.7days) |
|
|
| SXK |
6.0 |
25.0 |
| g1 |
834.83 |
99.98 |
| 109Cd-109Ag(T1/2=464days) |
|
|
| Ka1 |
22.16 |
35.3 |
| Ka2 |
21.99 |
18.6 |
| Kb |
24.9 |
11.4 |
| Weighted Mean(4) |
|
63.5 |
| g1 |
88.0 |
3.72 |
| 129I(T1/2=1.57×107years) |
|
|
| Ka1(3) |
29.78 |
37.0 |
| Ka2 |
29.46 |
20.0 |
| Kb |
13.2 |
37.0 |
| g1 |
39.58 |
7.52 |
| Weighted Mean(4) |
(31.3) |
(77.80) |
|
(1)
In measurements for gamma-(or X-)ray assay purposes,fluorescent radiation from lead shielding (specifically,lead K X-rays ~76ke V)may interfere with quantitative results.Allowance must be made for these effects,or the radiation suppressed;a satisfactory means of absorbing this radiation is covering the exposed lead with cadmium sheet 0.06to 0.08inch thick,and then covering the cadmium with copper 0.02to 0.04inch thick.
(2)
Only those photon emissions having an abundance ³1%are normally included.
(3)
The Knotation refers to X-ray emissions.
(4)
The weighted mean energies and total intensities are given for groups of photons that would not be resolved by a NaI(Tl)detector.
(5)
For this photon intensity to be usable,all emitted positrons must be annihilated in the source material.
(6)
Cascade.
|
Calculate the gamma-ray emission rate from the equation:
G=Asb,
in which Asis the activity,in disintegrations per second,of the standard used,and bis the number of gamma rays per disintegration at that energy.Accurately measure quantities of standard solutions of each radionuclide into identical containers,and determine the fractional photopeak area (F)for each of the standards.
Using the equation
ep=F/
G,calculate the photopeak efficiency,
ep,and construct a log-log plot of
ep versus the gamma-ray energy as shown in
Figure 4.
DETERMINATION OF SPECIMEN ACTIVITY
In the same manner as in the preparation of the calibration curve,determine the fractional area (F)of the principal photopeak of the specimen under assay or an accurately measured aliquot adjusted to the same volume in an identical container as used for the standards.From the calibration curve,find the value of epfor this radionuclide.Using the equation G=F/ep,calculate the gamma-ray emission rate (G).Calculate the activity (A),in disintegrations per second,of the specimen using the equation A=(G/b)(D),in which bis the number of gamma rays per disintegration and Dis the dilution factor.To obtain the activity,in µCi or mCi,divide Aby 3.7×104or 3.7×107,respectively.The above relationship is equally valid for obtaining the activity of an undiluted specimen or capsule;in this case,the dilution factor,D,is unity.