Quality Control of Gamma Counters I. Experimental Evaluation of Sources of Error

Transcription

1 ANNALS OF CLINICAL AND LABORATORY SCIENCE, Vol. 7, No. 1 Copyright 1977, Institute for Clinical Science Quality Control of Gamma Counters I. Experimental Evaluation of Sources of Error MICHAEL M. LUBRAN, M.D., Ph.D. Department of Pathology, Harbor Campus, University of California, Los Angeles, CA ABSTRACT Errors of counting rate as large as 2 percent may occur through variations in instrumental parameters during the measurement of activity using a gamma counter. Much larger errors result from failure to maintain constant sample geometry; in particular, the slope of calibration curves depends on sample volume. Introduction The measurement of radioactivity, particularly of 1-125, is frequently made in clinical pathology laboratories in tests using radioimmunoassay and competitive protein binding. Manufacturers of counting equipment have responded to the needs of users unskilled in electronics and with little knowledge of the complex nature of the interaction of radiation with matter by producing push-button instruments with preset instrumental parameters. The use of these sophisticated instruments may lead to an uncritical acceptance of their reliability; errors owing to irregular behavior during the counting period are believed not to occur or to be sufficiently trivial to be ignored. In designing a complete quality control program for assays using radioisotopes, it is important to know the contribution to the total amount of errors owing to the counting equipment. This paper presents the results of experiments designed to measure the magnitude of the effects resulting from instrumental changes that might occur during normal operation of a gamma counter. In addition, the consequences of variation in sample geometry (sample volume and size of sample tube), sample temperature and long-term operation of the counter were determined. Although the results reported here were obtained with one instrument, they apply qualitatively to all similar types of gamma counters; only the magnitudes of the effects may differ. To facilitate understanding of the experiments carried out, a brief description of a typical gamma counter is given. Further information can be obtained from the operator s manuals of the various instruments and from the references.1,3,4 Gamma counters Typically, a single channel counter consists of five functional units: a crystal detector, a photomultiplier tube, a linear amplifier and pulse height analyzer, a

2 58 LU BRAN discriminator and a timer-scaler. Multichannel instruments, capable of measuring simultaneously two or more radioisotopes in the same sample, share some of these units. Gamma (and X-ray) photons interact with the crystal to produce flashes of light (scintillations), which are detected and converted into weak electric currents by the photomultiplier tube. These are amplified and converted into voltage pulses, the heights of which are related to the energy of the radiation and their number to the activity of the isotope (i.e., to the number of disintegrations in unit time). The pulse heights appropriate to the isotope to be counted are selected by means of the discriminator and their number counted by means of the timerscaler. The individual units and their mode of operation are described in more detail. C r y s t a l D e t e c t o r Most laboratory instruments utilize a single crystal of sodium iodide containing about 1 percent of thallium iodide as activator. The crystal is cut into a cylinder, usually two or three inches in diameter and height (other sizes are sometimes used) and is drilled with a coaxial cylindrical well to about three-quarters of its depth. The diameter of the well is about 0.6 to 0.8 inches and its volume between 6 and 10 cc, depending on crystal size. As sodium iodide is hygroscopic, the crystal is encapsulated in an hermetically sealed metal can, except for the bottom flat face which is covered with lucite, a transparent plastic. (Some crystals are drilled all the way through; the window is then on part of the curved surface). The well is also lined with metal. The lucite plate is optically coupled with a high refractiveindex oil to the transparent end-window of the photomultiplier tube. The crystal and tube are enclosed in a light proof metal container, the well remaining accessible. The crystal responds mainly to gammaradiation; beta-radiation is mostly removed by the metal case. Gamma photons of the energy usually measured in the laboratory interact with the crystal in two ways to produce the photoelectric effect and the Compton effect (a third effect, pair-production, occurs only with high energy radiation). In the photoelectric -effect, an electron in the K (sometimes the L or higher shell) is ejected from the atom by the gamma photon. The whole of the energy of the photon (minus the binding energy of the electron) is transferred to the ejected electron, now called the photoelectron. The gamma photon vanishes. The photoelectron travels randomly through the crystal interacting with many atoms, ejecting electrons from their valence shells until all of its energy is dissipated. Some of these secondary electrons excite the atoms of the crystal; when they decay to the unexcited state, light is emitted. Thus, one photoelectron produces many light photons, their number being proportional to the energy of the gamma photon. The light photons are all produced as a burst, in a very short period of time. Not all gamma photo.ns entering the crystal interact with its atoms; however, the proportion which does so is constant for a given isotope and fixed geometry. The number of photon bursts is proportional to the number of gamma photons entering the crystal; the number of photons in each burst is proportional to the energy of the gamma photon. Because of the random motion of the photoelectron and secondary electrons, they meet atoms which are not all in the same energy state. As a result, the number of photons per burst is not constant for gamma photons of the same energy. Over a period of time during which large numbers of gamma photons have entered the crystal, the numbers of photons per burst form a Gaussian (normal) distribution

3 Q U A L IT Y C O N T R O L O F G A M M A COUNTERS 59 curve. This is recorded as a photopeak, the central value of which corresponds to the energy of the gamma photon. The Compton effect results from interactions of the gamma photons with free electrons and loosely bound valence electrons in the crystal. Only part of the energy of the gamma photon is imparted to the electron, which then produces secondary electrons (but of low energy) and eventually light photons. However, the number of light photons produced is small; most of the weak energy of the secondary electrons is dissipated as heat. The gamma photon of reduced energy further interacts to produce secondary electrons (or escapes from the crystal), until its energy is used up or it produces a photoelectron. The total result of the Compton effect is the production of a continuous spectrum of energies having a maximum value (called the Compton edge) and lower values mingling with instrumental noise. The Compton effect is not important in the case of low energy radioisotopes such as (which shows two photopeaks, at about 30 and 60 KeV). It is important in the case of radioisotopes producing gamma photons with energies greater than 1 MeV (e.g., Na-24, 1.37 and 2.75 MeV). A small number of light photons is liberated spontaneously within the crystal owing to the random fluctuations of the atoms in the crystal lattice. These photons contribute to crystal noise. Their energies lie mosdy within the Compton spectrum, but occasional energies lie within the photopeak. They then contribute to background. Crystal noise increases with crystal size and with an increase in temperature. P h o t o m u l t i p l i e r T u b e (PM T u b e ) The PM tube, as usually used, is a linear amplifier. It converts photon bursts into electrons, the number of which (i.e., current) is directly proportional to the number of photons in the burst and therefore to the energy of the gamma photon (figure 1). The principles of its operation are given in the legend to the figure. The output of the PM tube and its associated circuitry is a series of discrete pulses, their number in unit time being proportional to the number of gamma photons interacting with the cyrstal in unit time and their pulse height (i.e., the maximum pulse voltage) being proportional to the energy of the gamma photon. The performance of the PM tube is affected by changes in its operational parameters. Below a threshold voltage, the PM tube does not amplify at all; no pulses are produced. As the operating voltage is increased the number of pulses produced by the same amount of radioactivity increases until eventually the pulses become too numerous to be counted. PM tube noise, owing to electrons generated within the tube (thermal electrons), also increases with increasing voltage. There is an optimal voltage which gives the maximum number of pulses with the least amount of noise. The PM tube should always be operated at this optimal voltage, which varies a little with different isotopes. The amplification factor of the PM tube at optimal setting is about 400,000. It varies as the seventh power of the voltage. For best performance, voltage should be stable within 0.1 percent over a 24 hour period of continuous operation. An increase in voltage w ill result in increased background counts; a decrease in voltage will result in decreased counts of the radioisotope. In either case, the counting efficiency (the ratio of counting rate to disintegration rate, i.e., cpm per dpm) falls. PM tubes are sensitive to temperature changes. In the range 15 to 30, amplification decreases by 0.5 percent for each 1 rise in temperature. Noise also increases.

4 60 LU B RAN Refrigeration reduces noise and in creases the efficiency of the PM tube. The tube must be shielded against heat generated by electrical components, such as transformers, and against electrostatic and magnetic interferences (e.g., centrifuge and refrigerator motors). L i n e a r A m p l i f i e r a n d A n a l y z e r The preamplifier further amplifies the output of the PM tube and the pulse height analyzer shapes the pulses for counting, while still retaining the linear relationship between pulse height and gamma photon energy. The pulse that emerges from the photomultiplier tube is asymmetric in shape. It rises sharply to a maximum but falls off slowly. In order that pulses coming in rapid succession may be counted, it is necessary to shorten the tail of the pulse. The circuitry clips the tail and reshapes the pulse to an essentially Gaussian shape, which is the most suitable form for rapid counting. The degree of amplification is regulated by the gain control (in some instruments, the control is called an attenuator; decreasing attenuation in creases gain). The gain control interacts with the voltage setting of the PM tube. Optimal conditions require adjustment of both gain and voltage. D i s c r i m i n a t o r The pulse height analyzer produces pulses of the same shape but differing pulse heights, related to the energy of the gamma-photon or noise producing them. The discriminator is used to select pulses corresponding to the energy of the radioisotope being measured, and to reject higher and lower energies. In practice, the discriminator is adjusted to include all or most of the photopeak; in those cases (e.g., 1-125) where two photopeaks lie close together, both may be included. Essentially, two adjustments must be made: a lower discriminator setting F i g u r e 1. Photomultiplier tube. An electric field is generated inside the PM tube through a high voltage between the photocathode and anode. The voltage difference is broken into steps by means of a series of dynodes, each at a more positive potential than the preceding one. Photoelectrons resulting from light photons reaching the circular photocathode are accelerated by the electric field and strike the first dynode, which emits several secondary electrons per photon. The secondary electrons strike the second dynode, producing even more electrons. The multiplication process is repeated through the series of dynodes (usually 10) until finally the electrons pass into the anode. The dynodes are shaped to maximize the number of electrons passing from dynode to dynode. The magnitude of the current pulse produced is about 1 < coulombs. excludes energies below the photopeak and an upper discriminator setting excludes energies above the photopeak. The energy range defined by these two settings is called the channel width or window. The object is to have the maximum photopeak energy at the center of the window. For ease of use, the discriminator scale may be calibrated, using an isotope of known gamma energy. The upper and lower discriminator readings are selected

5 Q U ALITY CONTROL O F GAMMA COUNTERS 61 according to instructions in the operator s manual. Voltage and gain are then adjusted to optimal conditions. The discriminator settings for other isotopes can then be calculated from their gamma energies. However, once the voltage has been determined for the calibrating isotope, it must not be changed when the discriminator is adjusted for other isotopes. Decreasing the voltage pushes the energy spectrum to the left, i.e., the photopeak maximum is no longer at the center of the window and only a portion of the peak is measured. Decreasing the gain has the same effect. In most push button instruments, the discriminator settings and window width are preset and cannot be altered. The PM tube voltage is also fixed. Changes in this voltage result in lowered counts because the discriminator settings are no longer optimal. Similarly, inaccurate counts may result from aging of the electronic components. T i m e r -Sc a l e r This unit counts the number of pulses in a preset time or measures the time to count a preset number of pulses. Through the use of various logic circuits, many complex tasks can be performed; e.g., subtraction of a constant background, rejection of low counts or counting to a fixed statistical error. Most instruments rely on the constancy of the frequency of the AC power supply to run the timing devices. During periods of high demand, the frequency may change (even electric clocks can run slow!); counting error results. However, it seldom exceeds one percent. This error does not arise in instruments using quartz crystal clocks to control timing. The scaler has the slowest response time of all the units which make up a gamma counter. The response time of the counter can be measured easily.4 From its value, the highest counting rate can be calculated that does not lead to measurable loss of counts; corrections can be made for lost counts.5the resolving power of the counter refers to its ability to separate photopeaks of different energies. The resolving power of the Nal(Tl) crystal detector system is not high. New solid state detectors are available which have a high resolving power. Although used in gamma spectrometers, they have not as yet been incorporated into gamma counters. Experimental Design All experiments were carried out using a Nuclear Chicago Series 1085 gamma counter, which had a well-type Nal(Tl) crystal, 3 in. x 3 in., with a capsule 0.1 in. thick. The dimensions of the well were: internal diameter 16.7 mm, depth 44.4 mm and volume 9.7 cc. The mechanical transport system accommodated 100 tubes. The instrument could be adjusted to count the same sample up to six times before the next sample moved into position. All the samples counted consisted of solutions of sodium iodide containing as iodide. For convenience, the solution will be referred to in this paper as solution. In all cases, counting rates were corrected for background. When the experiments lasted more than one hour, counting rates were also corrected for decay, the half-life of being taken as 60 days. In addition, high counting rates were corrected for lost counts, prior to subtraction of background and correction for decay. Samples were counted in polypropylene, screw-capped tubes 16 x 125 mm (standard) in size. In some experiments, small polypropylene tubes (12 x 75 mm) were used which were placed inside a standard tube for the count. Tubes were always capped when placed in the transport system to reduce errors owing to evaporation. Tubes were centrifuged briefly, after samples had been placed in them, to transfer drops from the plastic wall to the bulk of the sample.

6 62 LU BRAN In all experiments, except where stated, samples were introduced into the counting tubes as accurately as possible by appropriate sized pipets and the amount delivered weighed. In this way, pipeting errors were eliminated. Observed counts were corrected for the slight variations in weight that occurred. It was noted that tubes of one size agreed very closely in weight. It was assumed that the internal diameters of the tubes were essentially constant. The resolving time of the counter was found to be 5.4 x 10~6seconds (s.d. 0.4 x 10-6). This means that if the observed counting rate were 60,000 cpm (i.e., 1000 counts per second), the true counting rate would be 60,326 cpm. E x p e r i m e n t s Experiment 1. The effect o f sample volume on the measurement of a constant activity. A volume of 1.0 ml of solution was weighed into each of 30 standard counting tubes (mean sample weight g; s.d g; c.v percent), which were then divided into six sets of five tubes per set. No water was added to the first set; to the other sets were added 1, 2, 3, 4 and 5 ml of water. Thus each set of tubes contained the same activity of 1-125, but in respective volumes of 1, 2, 3, 4, 5 and 6 ml. The tubes, together with five tubes each containing 5 ml of water for background measurement, were placed at random in the first 35 places of the transport system. Each sample was counted for one minute and the counting rate corrected for lost and background counts. Corrected counting rates were calculated as a fraction of the highest count, which was found to occur with the 1 ml volume. The results, shown in figure 2, demonstrate a non-linear decrease in counting rate with increasing volume. The effect was large, the corrected counting rate falling from 125,469 cpm in the 1 SAMPLE VOLUME (ml) F ig u r e 2. E ffect o f sam ple volum e on co u nting rate (experim ent 2). T he same activity was counted in different sam ple volum es. T he ordinate is the ratio o f the co u n tin g rate for a particular volu m e to the counting rate for 1 m l sam ple volum e. ml volume to 86,654 cpm in the 6 ml volume, a decrease of 31 percent. In the volume range of 1 to 3 ml, the curve was linear with a slope equivalent to a decrease in cpm of 4.31 percent for each increase in volume of 1 ml, for a fixed amount of Experiment 2. The effect o f sample volume on the slope of the calibration curve. Six sets of calibration standards were prepared (each in triplicate) from a stock solution of diluted 5, 10, 20 and 50-fold. Dilutions were made accurately using volumetric pipets and flasks. Each tube contained initially 0.05 ml of calibration standard solution (delivered using an SMI microliter pipet, c.v. less than 1 percent); 1, 2, 3, 4 and 5 ml of water were added to the respective sets, resulting in (in triplicate) six sets of calibration standards, with corresponding tubes having the same activity but in volumes of 0.05, 1.05, 2.05, 3.05, 4.05 and 5.05 ml, respectively. Each set contained activities in the proportions 1, 0.2, 0.1, 0.05 and Ten tubes each containing 5 ml of water were used for background counting. All 100 tubes were placed in random order in the transport system and each was counted for one minute.

7 QUALITY CON TROL O F GAMM A COUNTERS 63 Sample Volume (ml) TABLE I Effect of Size of Counting Tube* Tube Size Mean cpm S.D. Percent Change 3 16 mm 424, mm 382, < mm 292, mm 287, < mm 148, mm 149, <0.025 Samples counted in 16 ram and 12 m m diameter tubes for one minute; five replicates per volume, ft test. The counting rates were corrected for lost counts, background and radioactive decay. Linear calibration curves were calculated using a weighted least squares method2 (the usual least squares method could not be used, because the measurements had unequal variances). All the lines had essentially zero intercepts. The slopes were calculated as fractions of the slope obtained using 1.05 ml volumes. The results are shown in figure 3. The maximum slope was found with the 2.05 ml volume. The slope was almost 10 percent less when a 5.05 ml sample volume SAMPLE VOLUME (ml) FIGURE 3. Effect of sample volume on the slope of the calibration curve (experiment 3). Calibration curves were constructed for the same activity in different volumes. The ordinate is the ratio of the slope for a particular volume to the slope for 1.05 ml. There is a marked dependence of slope on sample volume. Pt was used for the same activity. Therefore, for the gamma counter used in this study, the greatest sensitivity was obtained when the sample volume was about 2 ml. Experiment 3. The effect o f sample tube size. Standard sample tubes (16 mm internal diameter) and small tubes (12 mm internal diameter inserted into the standard tubes) were used. Into each tube was weighed either 1, 2 or 3 ml of the same solution of Five replicates were prepared for each volume; 5 small tubes and 5 standard tubes, each containing 3 ml of water, were used for background counting. The tubes were randomized and counted for one minute. Counting rates were corrected for lost counts and background and adjusted for the slight variation in weight of the sample. The results are shown in table I. The counting rate was significantly lower (P < 0.001, t test) when 2 or 3 ml volumes were counted in the small tubes, the differences being about 2 percent and 11 percent, respectively. For the 1 ml volume, the counting rate in the small tube was about 0.6 percent higher than in the standard tube. The difference was statistically significant (P < 0.025, t test). Experiment 4. The effect o f change in gain from optimal setting. Into two standard tubes were pipeted, respectively, 5 ml of solution containing about 310,000 cpm and 163,000 cpm; 5 ml of water were used in a third tube for the background count. The gain control was adjusted to optimal conditions and set to count the same tube six times before the next tube moved into place. Each tube was counted for one min and the time each count was started was recorded. After the three tubes had been counted, the gain control was systematically decreased and increased by convenient integer changes of the gain control, corresponding to decreases of 6.3, 14.1 and 21.9 percent and increases of 4.7, 9.4, 17.2, 25.0 and 32.8 percent of the initial (optimal) setting. (These numbers reflect

8 64 LU BRA N the relative order of change, but not the true magnitude of the change of amplification at each gain setting). All counting rates were corrected for lost counts, background and decay. The mean counting rate per tube was calculated as a fraction of the mean rate observed at the initial gain setting; the fractions were plotted against the percentage changes in gain. The results, shown in figure 4, show that 5 percent change in gain resulted in about 3 percent decrease in counting rate. Experiment 5. The effect o f change of PM tube voltage from optimal setting. Four sample tubes were used containing, respectively, 5 ml of solution of activities about 60,000 cpm, 40,000 cpm, cpm and water. The instrument was adjusted optimally, using the 60,000 cpm sample. Each tube was then counted six times, after which the voltage was changed in steps of two or four volts and the counts repeated. No other parameters were changed. Counting rates were corrected for lost counts, background and decay. Corrected counts were calculated as a percentage of the counting rate for each tube at the initial voltage setting. The results are shown in figure 5. Counting rate varied with voltage, but the optimal voltage also depended on the counting rate, being less at the lower counting rates. A change of 10 volts resulted in less than 1 percent decrease in counting rate. Experiment 6. Effect o f sample temperature on counting rate. As samples are frequently counted shortly after they have been removed from the refrigerator, the effect of sample temperature on counting rate was studied. Standard tubes containing approximately 20,000, and 60,000 cpm, in 5 ml were prepared and kept overnight at 4 in a cold room together with two tubes each containing 5 ml of water. One of the water tubes was used for background counting, GAIN (% Change) F i g u r e 4. Effect of change in gain on counting rate (experiment 4). The curve relating gain setting to counting rate is symmetrical about the optimal value. The curve was obtained using an activity of 163,000 cpm. An almost identical curve resulted when an activity of 310,000 cpm was used. VOLTAGE (Volts) F i g u r e 5. Effect of change of PM tube voltage on counting rate (experiment 5). Counting rate decreases as PM tube voltage departs from its optimal value, which increases with increasing counting rate.

9 Q U A LITY CON TROL O F GAMMA COUNTERS 65 the other for monitoring the temperature changes during the counting process, every two or three minutes. Tubes were counted for one minute; five counts were made on each tube. The tubes were then warmed to 45 and recounted. Results are given in table II. Counts were corrected for lost counts and background. The temperature of the tubes rose from 8.0 to 26.6 during the counting period of 56 minutes. The results show that change in sample tube temperature was without effect on the counting rate. This experiment did not test the effect of temperature change on the PM tube. Experiments 7. Long term counting. This experiment tested the stability of the gamma counting system over approximately 17 hours of continuous use solution (activity about 60,000 cpm) was carefully pipeted into three sets of standard counting tubes, each set containing ten tubes. The first set of tubes contained the activity in 1 ml of solution, the second in 2 ml and the third in 3 ml. A fourth set of tubes, containing 3 ml of water, was used for background measurement. The tubes were placed in random order in the first 40 places in the transport system. Each was counted for two minutes, the system automatically recycled and the count repeated for a total of ten cycles. Each cycle was completed in 100 minutes. The first run was started at 6:30 P.M. Ambient temperature was 22 at the start of the experiment and 25 at the end. Night-time temperatures were not measured; however, it was estimated that the lowest temperature was 18. All TABLE I I Temperature of Sample and Counting Rate Voi (ml) , , ,232 20,967 43,347 65,950 Temperature ,885 43,362 65,756 21,057 43,475 65,596 20,927 43,267 65,990 20,939 43,186 65,870 counts were corrected for lost counts, background and decay, zero time being taken as the starting time of the experiment. The mean of the ten replicates was calculated for each set for each run, and calculated as a percentage of the count obtained in the first run. The deviation of this count from 100 was plotted against the run number for each volume (figure 6). The counting rate fell about 1 percent during the night to a minimum at about 2:30 A.M.; at the end of the counting period (about 11:30 A.M.) it had increased by about 1 percent. The total fluctuation over the 1000 minute period was just over 2 percent of the initial value for all three volumes. Discussion The counting rates used in the experiments were very much greater than those usually found in assays employing radioisotopes. These high rates were necessary in order to make negligible the errors owing to the statistical nature of radioactive disintegration and the variability of the background. In the usual assay procedures lost counts owing to the finite resolving timeof the counter can be ignored. However, they must be taken into consideration when high counting rates are used for quality control procedures. Corrections for decay are not necessary when is used, unless counting times last many hours. After 16 hours, results should be corrected by addition of 0.77 percent, and after 24 hours by 1.16 percent of the recorded value. Although these errors (and others to be considered later) may, individually, be small and therefore considered to be trivial, it must be appreciated that errors are cumulative in that their variances are additive. While, on occasion, individual errors might cancel out, the precision of the method nevertheless is lessened (i.e., the c.v. becomes greater). The precision of a method is therefore improved by correcting for known errors, such as decay.

10 66 L U B RA N The Effect of Geometry Although it is well-known that geometry should be kept constant, the magnitude of the errors is often not realized. It is essential that standards and unknowns should be counted using the same sample volumes, in the same size tubes. If counting time for the run is greater than an hour, the counting tubes must be capped to prevent errors owing to concentration of the sample by evaporation of water. This is of particular importance when small sample volumes or precipitates are counted because loss by evaporation depends on the ambient temperature, humidity and sample surface, and is independent of the sample volume. The observation that the slope of the calibration curve varies with sample volume is of practical importance. In any assay in which a precipitate and a supernatant are counted, separate calibration curves must be made for each, using appropriate volumes. The Effect of Variation of Operational Parameters Although the consequences of small changes in gain and voltage are small, they nevertheless contribute to the total error of measurement. Most instruments have a highly stabilized voltage for the PM tube; errors owing to fluctuation in mains voltage under normal operational conditions are unimportant. However, in localities where the AC supply is unreliable, large fluctuations may occur which exceed the controlling power of the voltage stabilizer. It is advisable, under these circumstances, to monitor the voltage of the PM tube. More important is alteration in gain. When gain is set optimally, the curve produced by systematic changes of gain should be symmetrical (figure 4). Under these conditions, the small changes in gain owing to small fluctuations in voltage are negligible. How- F ig u r e 6. Variation in counting rate with repeated measurements of the same samples (experiment 7). The same samples were counted on ten successive occasions (runs) over approximately 17 hours. The ordinate is the percentage difference in counting rate for each run, taking the first run as 100 percent. ever, if gain is not optimal, i.e., the setting is not at the peak of the curve but on the sloping side, small changes in gain will produce large changes in counting rate. The gain control must therefore be set with great care and checked every time the instrument is used. Because amplification is linear in all the units of the gamma counter, it might be thought that once the discriminator was calibrated, any radioisotope could be counted optimally by adjustment of the lower discriminator and channel width, without changing voltage or gain. Unfortunately, this is only roughly the case, because linear amplification is not precise. For the best results, once the discriminator settings have been made, small adjustments of gain must be made as described previously. Background counts are very sensitive to variations in operational parameters. Although in terms of cpm the numbers are small, they become important when low activities (less than 1000 cpm) are

11 Q U A LITY CON TROL O F GAMMA COUNTERS 67 counted. As the major part of background is not due to random disintegrations of radioactive atoms, its variance cannot be assumed to be equal to the number of counts, as occurs with a Poisson distribution. The variance will be a minimum when the operational parameters remain constant. The long term experiment (# 7) gives a realistic evaluation of the errors arising in continuous operation owing to voltage fluctuation, changes in ambient temperature, variations in the mechanical transport system and in the timer-scaler. During an overnight run, a difference of about 2 percent could occur between the highest and lowest readings of the same sample. If, for example, calibration standards were put at the beginning of the run, sample readings could be in error by as much as 1 percent. If standards were put at the beginning and end of the run (a common practice) and the average taken, samples read in the middle of the run would be in error by a greater amount, possibly as high as 1.5 percent. Sample temperature is not a source of error. Other properties of the sample, such as self absorption, and the nature of the sample tube, will be discussed in another paper. Quality control procedures that will detect and minimize these errors and procedures to check instrumental performance will also be described in that paper. References 1. B o y d, C. M. and D a l r y m p l e, G. V., e d s.: Basic Principles of Nuclear Medicine. New York, C. V. Mosby Co., chapters 7 and 8, D r a p e r, N. R. and Sm it h, H.: Applied Regression Analysis. New York, J. Wiley and Sons, Inc., pp , KRUGERS, J., ED.: Instrumentation in Applied Nuclear Chemistry. New York, Plenum Press, chapter 8, Q u im b y, E. H., e d.: Radioactive Nuclides in Medicine and Biology. Vol. I, Basic Physics and Instrumentation, 3rd ed. Philadelphia, Lea and Febiger, V e a l l, N. and V e t t e r, H.: Radioisotope Techniques in Clinical Research and Diagnosis, London, Butterworth and Co., Ltd., pp , 1958.